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Q and A for the topic: General

Formal proof for Proposition 3.38 Equivalenceofasetofformulasandtheirclausalforms A set of formulas U is equivalent to the set of clauses comprising the union of the clausal forms of the formulas in U . Please use existing theorems to answer the formal logic problem.

253 views

3. Inside a cubic box with edge 35 cm, a ball has been introduced that is tangent to the faces of the cube as shown in the following figure. Calculate the volume included by the free space in the cube-shaped box.

518 views

Find the work done in raising a mass of 50,000 kg from the surface of the Moon to a height of 200 km. CheckinZillintheApplicationsTopicoftheintegral,mechanicalwork,workdoneagainstgravity

342 views

Obtain the derivative of the following function: fx=2e4x/√x

481 views

Let x be a continuous random variable that follows a normal distribution with a mean of 240 and a standard deviation of 51. Find the value of x so that the area under the normal curve to the right of x is approximately 0.3512. Round your answer to two decimal places

725 views

What the formula for critical value?

920 views

A car company estimates that it will sell 5,000 cars in 2023 and over the next 10 years will increase sales by 5% compared to the previous year. Determine how many cars the company intends to sell in that 11-year period.

744 views

3x^2-5x+2=0

526 views

Consider that the fixed costs of a startup are 35,476.00 and that you want to have a profit margin of 20%, and the estimated number of subscribers is only 100 in the first month. The product of this platform is a digital platform, which offers a free plan and a plan with a monthly subscription of R20.00,withpsychologicalcareservicesforR70.00 and professional training for R120.00(intwoservicesareretaineda1015.00, advanced R40.00andcompleteR80.00. The platform hires professionals based on partnerships. How to calculate the number of psychologists and professional training content providers the platform needs to close to obtain the desired profit margin

1432 views

When purchasing a car and 3 documents worth $15,000 will be paid each to be paid in months 2, 4 and 6. If you wish to pay in 2 installments equal, in months 4 and 8. What should be the amount of these payments? Consider that money changes at a rate of 35% compounded semiannually monthly.

1413 views

Exercise 2 For a debt to be settled of $12,000, determine the value equivalent of 3 monthly payments due. The interest rate is 30% annual compounded monthly.

1263 views

What is the exact value of sin 60°? Enter your answer as a fraction in simplest form by filling in the boxes.

1052 views

x +x+y+1=1

1343 views

A 100 ohm resistor is connected to a voltage of 230 V for 2 h. Calculate the heat produced

648 views

2.- Find the equation of the ellipse whose foci are F0,3/2 and F'0,−3/2 and such that the sum of the distances of the points on it to the foci is 5, in Spanish

1285 views

CIF CONTROL SEATS Andean Coffee, whose plant is located in the city of Abrego, Norte de Santander, applies its costs with the following rates: Coffee bean distribution plant Direct labor hours Department Application Rate Department Actual Hours Drying 12,245.00Drying12,008Toasted23,858.00 Toasted 17,380 Packaged 3,357.50Packaged3,476TotalrealCIF 573,547,900.00 Cost management can calculate and account for: CIF applied real CIF CIF closure takeintoaccountunder−andover−applications

974 views

24-2/24

1236 views

What is the equivalent compounded quarterly rate referring to 7.24% per year?

1083 views

What is the mathematical relationship between F and D²?

596 views

Evelyn Aldana deposits a monthly income due for 5 years at a rate of 12% annual compounded monthly and you will not withdraw the money until 2 years later of the last income. If you can withdraw Q 90,000, how much do you deposit monthly?

1201 views
\nA set of formulas U is equivalent to the set of clauses comprising the union of the\nclausal forms of the formulas in U . Please use existing theorems to answer the formal logic problem.","","To prove Proposition 3.38, we need to show that a set of formulas U is equivalent to the set of clauses comprising the union of the clausal forms of the formulas in U.\u003Cbr>\u003Cbr>Let's denote the set of formulas U as \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\Phi\u003C/math-field>\u003C/math-field> , and the set of clauses comprising the union of the clausal forms of the formulas in U as \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\Psi\u003C/math-field>\u003C/math-field> . We want to show that \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\Phi \\equiv \\Psi\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>Given a formula \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\phi\u003C/math-field>\u003C/math-field> , its clausal form is denoted as \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>clphi\u003C/math-field>\u003C/math-field> . The clausal form of a set of formulas is the union of the clausal forms of each formula.\u003Cbr>\u003Cbr>We need to show two things:\u003Cbr>1. If a formula \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\phi \\in \\Phi\u003C/math-field>\u003C/math-field> , then \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>clphi \\in \\Psi\u003C/math-field>\u003C/math-field> .\u003Cbr>2. If a clause \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>C \\in \\Psi\u003C/math-field>\u003C/math-field> , then there exists a formula \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\phi \\in \\Phi\u003C/math-field>\u003C/math-field> such that \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>clphi = C\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>Let's prove each part:\u003Cbr>1. Let \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\phi \\in \\Phi\u003C/math-field>\u003C/math-field> , then by definition of clausal form, \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>clphi\u003C/math-field>\u003C/math-field> is in the union of the clausal forms of the formulas in U. Therefore, \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>clphi \\in \\Psi\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>2. Let \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>C \\in \\Psi\u003C/math-field>\u003C/math-field> , then \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>C\u003C/math-field>\u003C/math-field> is a clause in the union of clausal forms of the formulas in U. By the definition of clausal form, there exists a formula \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\phi \\in \\Phi\u003C/math-field>\u003C/math-field> such that \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>clphi = C\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>Therefore, we have shown that if \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\Phi\u003C/math-field>\u003C/math-field> is a set of formulas, and \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\Psi\u003C/math-field>\u003C/math-field> is the set of clauses comprising the union of the clausal forms of the formulas in \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\Phi\u003C/math-field>\u003C/math-field> , then \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\Phi \\equiv \\Psi\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{\\Phi \\equiv \\Psi}\u003C/math-field>\u003C/math-field>",253,51,"formal-proof-for-proposition-3-38-equivalence-of-a-set-of-formulas-and-their-clausal-forms-a-set-of-formulas-u-is-equivalent-to-the-set-of-clauses-comprising-the-union-of-the-clausal-forms-of-the-fo",{"id":44,"category":36,"text_question":45,"photo_question":38,"text_answer":46,"step_text_answer":8,"step_photo_answer":8,"views":47,"likes":48,"slug":49},536044,"3. Inside a cubic box with edge 35 cm, a ball has been introduced that is tangent to the faces of the cube as shown in the following figure. Calculate the volume included by the free space in the cube-shaped box.","Let's start by finding the radius of the ball. Since the ball is tangent to the faces of the cube, the diameter of the ball is equal to the edge length of the cube. Therefore, the radius of the ball is half of this length:\u003Cbr>\u003Cbr>Let \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r\u003C/math-field>\u003C/math-field> be the radius of the ball. We know that the diameter of the ball is equal to the edge length of the cube, which is 35 cm. Therefore, \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2r = 35\u003C/math-field>\u003C/math-field> , and \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r = \\frac{35}{2} = 17.5\u003C/math-field>\u003C/math-field> cm.\u003Cbr>\u003Cbr>Next, we need to calculate the volume of the ball:\u003Cbr>\u003Cbr>The volume of a ball is given by the formula \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V = \\frac{4}{3} \\pi r^3\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>Substitute the radius \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r = 17.5\u003C/math-field>\u003C/math-field> cm into the formula:\u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V=\\frac{4}{3}\\pi17.5^3\\approx\\frac{4}{3}\\times3.1416\\times17.5^3\\approx4.1889\\times17.5^3\\approx22449.85\u003C/math-field>\u003C/math-field> cubic cm.\u003Cbr>\u003Cbr>The volume of the free space in the cube-shaped box is equal to the difference between the volume of the cube and the volume of the ball:\u003Cbr>\u003Cbr>The volume of the cube is given by \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V_{\\text{cube}} = s^3\u003C/math-field>\u003C/math-field> , where \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s\u003C/math-field>\u003C/math-field> is the edge length of the cube.\u003Cbr>\u003Cbr>Substitute the edge length \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s = 35\u003C/math-field>\u003C/math-field> cm into the formula:\u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V_{\\text{cube}} = 35^3 = 42875\u003C/math-field>\u003C/math-field> cubic cm.\u003Cbr>\u003Cbr>Therefore, the volume included by the free space in the cube-shaped box is:\u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V_{\\text{free space}}=V_{\\text{cube}}-V_{\\text{ball}}=42875-22449.35=20425.65\u003C/math-field>\u003C/math-field> cubic cm.\u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{20425.65\\text{ cubic cm}}\u003C/math-field>\u003C/math-field> is the volume included by the free space in the cube-shaped box.",518,104,"3-inside-a-cubic-box-with-edge-35-cm-a-ball-has-been-introduced-that-is-tangent-to-the-faces-of-the-cube-as-shown-in-the-following-figure-calculate-the-volume-included-by-the-free-space-in-the-cube",{"id":51,"category":36,"text_question":52,"photo_question":38,"text_answer":53,"step_text_answer":8,"step_photo_answer":8,"views":54,"likes":55,"slug":56},536043,"Find the work done in raising a mass of 50,000 kg from the surface of the Moon to a height of 200 km. CheckinZillintheApplicationsTopicoftheintegral,mechanicalwork,workdoneagainstgravity","To find the work done in raising a mass of 50,000 kg from the surface of the Moon to a height of 200 km, we can use the formula for work done against gravity:\u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>W = \\int_{r_1}^{r_2} F \\cdot dr\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Where:\u003Cbr>- W is the work done,\u003Cbr>- F is the force weightofthemass exerted vertically upward, which is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>F = mg\u003C/math-field>\u003C/math-field> ,\u003Cbr>- r1 is the initial position at the surface of the Moon,\u003Cbr>- r2 is the final position at a height of 200 km.\u003Cbr>\u003Cbr>The force applied is equal to the weight of the mass:\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>F = mg\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Where:\u003Cbr>- m = 50,000 kg massoftheobject,\u003Cbr>- g = 1.62 m/s^2 accelerationduetogravityontheMoon.\u003Cbr>\u003Cbr>We need to convert the distance to meters:\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>200 \\, km = 200,000 \\, m\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Plugging in the values, we get:\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>W = \\int_{0}^{200000} F \\cdot dr = \\int_{0}^{200000} mg \\cdot dr\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>W = \\int_{0}^{200000} 50000 \\cdot 1.62 \\cdot dr = 50000 \\cdot 1.62 \\cdot \\int_{0}^{200000} dr\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>W = 50000 \\cdot 1.62 \\cdot 200000−0 = 50000 \\cdot 1.62 \\cdot 200000\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>W=50000\\cdot1.62\\cdot200000=1.62\\times10^8\\,J\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Therefore, the work done in raising a mass of 50,000 kg from the surface of the Moon to a height of 200 km is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1.62\\times10^8\\,J\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{1.62\\times10^8\\,J}\u003C/math-field>\u003C/math-field>",342,68,"find-the-work-done-in-raising-a-mass-of-50-000-kg-from-the-surface-of-the-moon-to-a-height-of-200-km-check-in-zill-in-the-applications-topic-of-the-integral-mechanical-work-work-done-against-gravi",{"id":58,"category":36,"text_question":59,"photo_question":38,"text_answer":60,"step_text_answer":8,"step_photo_answer":8,"views":61,"likes":62,"slug":63},536042,"Obtain the derivative of the following function:\n fx=2e4x/√x","\u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0,0,0,.3;box-shadow: 0 0 0 rgba0,0,0,.2\n\" read-only>f′left(xright)=fracmathrmdmathrmdxleft(frac2e4xsqrtxright)\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0,0,0,.3;box-shadow: 0 0 0 rgba0,0,0,.2\n\" read-only>f′left(xright)=fracfracmathrmdmathrmdxleft(2e4xright)timessqrtx−2e4xtimesfracmathrmdmathrmdxleft(sqrtxright)sqrtx2\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0,0,0,.3;box-shadow: 0 0 0 rgba0,0,0,.2\n\" read-only>f′left(xright)=frac2e4xtimes4sqrtx−2e4xtimesfracmathrmdmathrmdxleft(sqrtxright)sqrtx2\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0,0,0,.3;box-shadow: 0 0 0 rgba0,0,0,.2\n\" read-only>f′left(xright)=frac2e4xtimes4sqrtx−2e4xtimesfrac12sqrtxsqrtx2\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0,0,0,.3;box-shadow: 0 0 0 rgba0,0,0,.2\n\" read-only>f′left(xright)=frac8xe4x−e4xsqrtxx\u003C/math-field>\n \u003Cbr>\n \u003C/div>",481,96,"obtain-the-derivative-of-the-following-function-f-x-2e-4x-x",{"id":65,"category":36,"text_question":66,"photo_question":38,"text_answer":67,"step_text_answer":8,"step_photo_answer":8,"views":68,"likes":69,"slug":70},536041,"Let x be a continuous random variable that follows a normal distribution with a mean of 240 and a standard deviation of 51. Find the value of x so that the area under the normal curve to the right of x is approximately 0.3512. Round your answer to two decimal places","To find the value of x such that the area under the normal curve to the right of x is approximately 0.3512, we need to use the z-score formula:\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>z = \\dfrac{x - \\mu}{\\sigma}\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />where:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field> = the value we are looking for,\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\mu = 240\u003C/math-field>\u003C/math-field> mean,\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\sigma = 51\u003C/math-field>\u003C/math-field> standarddeviation.\u003Cbr />\u003Cbr />First, we need to find the z-score corresponding to the given area using the standard normal distribution table:\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>PZ>z = 0.3512 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Since the standard normal table gives the area to the left of z, we need to find the z-score corresponding to the area to the left of our desired area:\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>PZ\u003Cz = 1 - 0.3512 = 0.6488 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Looking up 0.6488 in the z-table gives us a z-score of about 0.37.\u003Cbr />\u003Cbr />Now, we can plug the z-score into the z-score formula and solve for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field>:\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.37 = \\frac{x - 240}{51}\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.37 * 51 = x - 240\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 0.37 * 51 + 240\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 18.87 + 240\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x \\approx 258.87\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Therefore, the value of \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field> such that the area under the normal curve to the right of \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field> is approximately 0.3512 is approximately 258.87. \u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{x \\approx 258.87}\u003C/math-field>\u003C/math-field>",725,145,"let-x-be-a-continuous-random-variable-that-follows-a-normal-distribution-with-a-mean-of-240-and-a-standard-deviation-of-51-find-the-value-of-x-so-that-the-area-under-the-normal-curve-to-the-right-of",{"id":72,"category":36,"text_question":73,"photo_question":38,"text_answer":74,"step_text_answer":8,"step_photo_answer":8,"views":75,"likes":76,"slug":77},536040,"What the formula for critical value?","\u003Cmath-field read-only> z=\\frac{\\leftx−muright}{\\frac{\\sigma}{\\sqrt{n}}} \u003C/math-field>\nZ: critical value\n\u003Cmath-field read-only> \\sigma\\colon \u003C/math-field> : population standard deviation.\nn: sample size\n\u003Cmath-field read-only> \\mu\\colon \u003C/math-field> population mean",920,184,"what-the-formula-for-critical-value",{"id":79,"category":36,"text_question":80,"photo_question":38,"text_answer":81,"step_text_answer":8,"step_photo_answer":8,"views":82,"likes":83,"slug":84},536039,"A car company estimates that it will sell 5,000 cars in 2023 and over the next 10 years will increase sales by 5% compared to the previous year. Determine how many cars the company intends to sell in that 11-year period.","A continuación se explica cómo calcular la cantidad total de automóviles que la empresa pretende vender durante el período de 11 años:\n\n **Año | Ventas | Aumentar**\n\n 2023 | 5000 | -\n 2024 | 5250 | 5% de 5000 = 250\n 2025 | 5512,5 | 5% de 5250 = 262,5\n 2026 | 5788.13 | 5% de 5512,5 = 275,63 redondeado\n 2027 | 6082.53 | ...\n 2028 | 6396.66\n 2029 | 6731.49\n 2030 | 7088.07\n 2031 | 7467.47\n 2032 | 7870.84\n 2033 | 8299.39\n\n Para encontrar las ventas totales durante los 11 años, simplemente sume las ventas de cada año. La suma es aproximadamente **65,540**.\n\n **Nota importante:** Como estamos tratando con autos enteros, podemos redondear la respuesta final al número entero más cercano.\n\n **Por lo tanto, la empresa pretende vender aproximadamente 65.540 automóviles durante el período de 11 años.**",744,149,"a-car-company-estimates-that-it-will-sell-5-000-cars-in-2023-and-over-the-next-10-years-will-increase-sales-by-5-compared-to-the-previous-year-determine-how-many-cars-the-company-intends-to-sell-in",{"id":86,"category":36,"text_question":87,"photo_question":38,"text_answer":88,"step_text_answer":8,"step_photo_answer":8,"views":89,"likes":90,"slug":91},536038,"3x^2-5x+2=0","\u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0,0,0,.3;box-shadow: 0 0 0 rgba0,0,0,.2\n\" read-only>x1,2=frac−(−5)pmsqrt(−5)2−4cdot3cdot22cdot3\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0,0,0,.3;box-shadow: 0 0 0 rgba0,0,0,.2\n\" read-only>x1,2=frac−(−5)pm12cdot3\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0,0,0,.3;box-shadow: 0 0 0 rgba0,0,0,.2\n\" read-only>x1=frac−(−5)+12cdot3,x2=frac−(−5)−12cdot3\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0,0,0,.3;box-shadow: 0 0 0 rgba0,0,0,.2\n\" read-only>=1\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0,0,0,.3;box-shadow: 0 0 0 rgba0,0,0,.2\n\" read-only>=frac23\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0,0,0,.3;box-shadow: 0 0 0 rgba0,0,0,.2\n\" read-only>x=1,x=frac23\u003C/math-field>\n \u003Cbr>\n \u003C/div>",526,105,"3x-2-5x-2-0",{"id":93,"category":36,"text_question":94,"photo_question":38,"text_answer":95,"step_text_answer":8,"step_photo_answer":8,"views":96,"likes":97,"slug":98},536037,"Consider that the fixed costs of a startup are 35,476.00 and that you want to have a profit margin of 20%, and the estimated number of subscribers is only 100 in the first month. The product of this platform is a digital platform, which offers a free plan and a plan with a monthly subscription of R20.00,withpsychologicalcareservicesforR70.00 and professional training for R120.00(intwoservicesareretaineda1015.00, advanced R40.00andcompleteR80.00. The platform hires professionals based on partnerships. How to calculate the number of psychologists and professional training content providers the platform needs to close to obtain the desired profit margin","To calculate how many service providers psychologistsandprofessionaltrainingcontentproviders your platform needs to meet the desired profit margin, follow these steps:\u003Cbr />\u003Cbr />### Step 1: Calculate Required Revenue\u003Cbr />Using the formula for the target revenue \u003Cmath−fieldread−onlydefault−mode=\"inline−math\"class=\"math−expression\">\u003Cmath−fieldread−only>R\u003C/math−field>\u003C/math−field>:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> R = \\frac{\\text{Fixed Costs}}{1 - \\text{Profit Margin}} \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> R = \\frac{35,476.00}{1 - 0.20} = \\frac{35,476.00}{0.80} = 44,345.00 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />### Step 2: Estimate Revenue from Different Sources\u003Cbr />- Revenue from Subscriptions: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>100 \\times 20 = 2,000.00\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Find the remaining revenue needed from services and e-books to meet the target.\u003Cbr />\u003Cbr />### Step 3: Calculate Required Number of Services\u003Cbr />- For psychological care:\u003Cbr /> The number of Psychological Sessions Needed = \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{21,172.50}{7.00} \\approx 3025\u003C/math-field>\u003C/math-field> sessions\u003Cbr />\u003Cbr />- For professional training:\u003Cbr /> The number of Training Sessions Needed = \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{21,172.50}{12.00} \\approx 1764\u003C/math-field>\u003C/math-field> sessions\u003Cbr />\u003Cbr />### Step 4: Assumptions for Revenue Split\u003Cbr />Assume equal revenue split for psychology and training:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Revenue from Psychology} = \\text{Revenue from Training} = \\frac{42,345.00}{2} = 21,172.50 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />### Step 5: Calculate Number of Sessions Required\u003Cbr />- For Psychological care: 3025 sessions\u003Cbr />- For Professional training: 1764 sessions\u003Cbr />\u003Cbr />### Step 6: Determine Number of Providers Needed\u003Cbr />If each provider can handle 40 sessions per month:\u003Cbr />- Number of Psychologists Needed: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{3025}{40} \\approx 76\u003C/math-field>\u003C/math-field> psychologists\u003Cbr />- Number of Trainers Needed: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{1764}{40} \\approx 44\u003C/math-field>\u003C/math-field> trainers\u003Cbr />\u003Cbr />### Answer:\u003Cbr />The platform needs approximately 76 psychologists and 44 professional training providers to meet the desired profit margin.",1432,286,"consider-that-the-fixed-costs-of-a-startup-are-35-476-00-and-that-you-want-to-have-a-profit-margin-of-20-and-the-estimated-number-of-subscribers-is-only-100-in-the-first-month-the-product-of-this-p",{"id":100,"category":36,"text_question":101,"photo_question":38,"text_answer":102,"step_text_answer":8,"step_photo_answer":8,"views":103,"likes":104,"slug":105},536036,"When purchasing a car and 3 documents worth 15,000willbepaid\neachtobepaidinmonths2,4and6.Ifyouwishtopayin2installments\nequal,inmonths4and8.Whatshouldbetheamountofthesepayments?\nConsiderthatmoneychangesatarateof3515,000 each, due in months 2, 4, and 6, and then determine the size of two equal payments in months 4 and 8.\u003Cbr />\u003Cbr />### Step 1: Calculate the monthly interest rate\u003Cbr />Given a 35% annual interest rate compounded semiannually:\u003Cbr />- Semiannual rate = 35% / 2 = 17.5% per half year.\u003Cbr />\u003Cbr />To convert a semiannual rate to a monthly rate when compounded semiannually:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\left1+textSemiannualrateright^{\\leftfrac16right} - 1 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Calculating it:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\left1+0.175right^{\\leftfrac16right} - 1 = \\left1.175right^{\\leftfrac16right} - 1 \\approx 0.0273 \\text{ or } 2.73\\% \\text{ per month} \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />### Step 2: Calculate the present value of payments at month 4\u003Cbr />- **Month 2**: 15,000duein2monthsdiscountedtomonth4:\u003Cbr/>\u003Cmath−fieldread−onlydefault−mode=\"inline−math\"class=\"math−expression\">\u003Cmath−fieldread−only>PVtextmonth2to4=frac15000(1.02732)=frac150001.0559approx14212.48\u003C/math−field>\u003C/math−field>\u003Cbr/>−∗∗Month4∗∗:15,000 due in 0 months\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> PV_{\\text{month 4}} = 15000 \u003C/math-field>\u003C/math-field>\u003Cbr />- **Month 6**: 15,000 due in 2 months forward from month 4:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> PV_{\\text{month 6 to 4}} = \\frac{15000}{(1.0273^2)} = \\frac{15000}{1.0559} \\approx 14212.48 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Total present value at month 4:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> PV_{\\text{total}} = 14212.48 + 15000 + 14212.48 \\approx 43424.96 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />### Step 3: Calculate the amount of each of the two equal payments in months 4 and 8\u003Cbr />Let \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x \u003C/math-field>\u003C/math-field> be the payment amount in months 4 and 8.\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x + \\frac{x}{(1.0273^4)} = 43424.96 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x + \\frac{x}{1.1145} = 43424.96 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x (1 + \\frac{1}{1.1145}) = 43424.96 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x (1.7933) = 43424.96 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = \\frac{43424.96}{1.7933} \\approx 24223.72 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />### Answer:\u003Cbr />Each of the two equal payments to be made in months 4 and 8 should be approximately24,223.72 to cover the equivalent value of the three payments worth 15,000eachdueinmonths2,4,and6,consideringthegiveninterestrate.",1413,283,"when−purchasing−a−car−and−3−documents−worth−15−000−will−be−paid−each−to−be−paid−in−months−2−4−and−6−if−you−wish−to−pay−in−2−installments−equal−in−months−4−and−8−what−should−be−the−amount−of−the","id":107,"category":36,"textquestion":108,"photoquestion":38,"textanswer":109,"steptextanswer":8,"stepphotoanswer":8,"views":110,"likes":40,"slug":111,536035,"Exercise2\nForadebttobesettledof12,000, determine the value\n equivalent of 3 monthly payments due. The interest rate is 30%\n annual compounded monthly.","**Step 1:** Convert the interest rate from percentage to decimal.\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> r = 0.025 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />**Step 2:** Use the formula to calculate \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> M \u003C/math-field>\u003C/math-field>.\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> M = 12000 \\times \\frac{0.0251+0.025^3}{1+0.025^3 - 1} \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> M = 12000 \\times \\frac{0.0251.025^3}{1.025^3 - 1} \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> M = 12000 \\times \\frac{0.025 \\times 1.07576}{1.07576 - 1} \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> M = 12000 \\times \\frac{0.026894}{0.07576} \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\boxed{M \\approx 4201.65} \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />**Answer:** The monthly payment required to settle the debt of 12,000withanannualinterestrateof304,201.65.",1263,"exercise-2-for-a-debt-to-be-settled-of-12-000-determine-the-value-equivalent-of-3-monthly-payments-due-the-interest-rate-is-30-annual-compounded-monthly",{"id":113,"category":36,"text_question":114,"photo_question":38,"text_answer":115,"step_text_answer":8,"step_photo_answer":8,"views":116,"likes":117,"slug":118},536034,"What is the exact value of sin 60°?\n\nEnter your answer as a fraction in simplest form by filling in the boxes.","To find the exact value of sin 60°, we can use the special right triangle with angles 30°-60°-90°.\u003Cbr />\u003Cbr />In a 30°-60°-90° triangle, the side lengths are in the ratio \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1 : \\sqrt{3} : 2\u003C/math-field>\u003C/math-field>.\u003Cbr />\u003Cbr />Therefore, in a triangle with a 60° angle, the side opposite the 60° angle is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\sqrt{3}\u003C/math-field>\u003C/math-field> times the side opposite the 30° angle.\u003Cbr />\u003Cbr />Since sin is opposite over hypotenuse, we have:\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\sin 60° = \\frac{\\text{opposite}}{\\text{hypotenuse}} = \\frac{\\sqrt{3}}{2}\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Therefore, the exact value of sin 60° is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{\\frac{\\sqrt{3}}{2}}\u003C/math-field>\u003C/math-field>.",1052,210,"what-is-the-exact-value-of-sin-60-enter-your-answer-as-a-fraction-in-simplest-form-by-filling-in-the-boxes",{"id":120,"category":36,"text_question":121,"photo_question":38,"text_answer":122,"step_text_answer":8,"step_photo_answer":8,"views":123,"likes":124,"slug":125},536033,"x +x+y+1=1","\u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0,0,0,.3;box-shadow: 0 0 0 rgba0,0,0,.2\n\" read-only>x+x+y+1−1=1−1\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0,0,0,.3;box-shadow: 0 0 0 rgba0,0,0,.2\n\" read-only>x+x+y=0\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0,0,0,.3;box-shadow: 0 0 0 rgba0,0,0,.2\n\" read-only>2x+y=0\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0,0,0,.3;box-shadow: 0 0 0 rgba0,0,0,.2\n\" read-only>y=−2x\u003C/math-field>\n \u003Cbr>\n \u003C/div>",1343,269,"x-x-y-1-1",{"id":127,"category":36,"text_question":128,"photo_question":38,"text_answer":129,"step_text_answer":8,"step_photo_answer":8,"views":130,"likes":131,"slug":132},536031,"A 100 ohm resistor is connected to a voltage of 230 V for 2 h. Calculate the heat produced","To calculate the heat produced by the resistor, we can use the formula:\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Heat Joules} = \\text{Power Watts} \\times \\text{Time seconds} \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />First, let's calculate the power using the formula:\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> P = \\frac{V^2}{R} \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />where:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = 230 \\, \\text{V} \u003C/math-field>\u003C/math-field> voltage\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> R = 100 \\, \\Omega \u003C/math-field>\u003C/math-field> resistance\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> P = \\frac{230,textV^2}{100 \\, \\Omega} \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> P = \\frac{52900}{100} = 529 \\, \\text{W} \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Next, we convert the time from hours to seconds:\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Time} = 2 \\, \\text{hours} \\times 3600 \\, \\text{seconds/hour} = 7200 \\, \\text{seconds} \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Finally, we can calculate the heat produced:\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Heat} = 529 \\, \\text{W} \\times 7200 \\, \\text{s} = 3808800 \\, \\text{Joules} \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Therefore, the heat produced by the resistor is 3808800 Joules.\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{3808800 \\, \\text{J}}\u003C/math-field>\u003C/math-field>",648,130,"a-100-ohm-resistor-is-connected-to-a-voltage-of-230-v-for-2-h-calculate-the-heat-produced",{"id":134,"category":36,"text_question":135,"photo_question":38,"text_answer":136,"step_text_answer":8,"step_photo_answer":8,"views":137,"likes":138,"slug":139},536030,"2.- Find the equation of the ellipse whose foci are F0,3/2 and F'0,−3/2 and such that the sum of the distances of the points on it to the foci is 5, in Spanish","Step 1: \u003Cbr />Let the coordinates of the center of the ellipse be h,k.\u003Cbr />The distances from the center to the foci are c and -c, respectively, where c is the distance between the center and one of the foci.\u003Cbr />Since the sum of the distances from any point on the ellipse to the foci is given as 5, we have: \u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2a = 5 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Step 2:\u003Cbr />The distance between the foci is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2c = 3\u003C/math-field>\u003C/math-field>. \u003Cbr />So, we have:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> a = \\frac{5}{2} \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> c = \\frac{3}{2} \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Step 3:\u003Cbr />The equation of an ellipse centered at h,k with major axis along y-axis is: \u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{y−k^2}{b^2} + \\frac{x−h^2}{a^2} = 1 \u003C/math-field>\u003C/math-field>\u003Cbr />where a and b are the semi-major and semi-minor axes lengths, respectively.\u003Cbr />\u003Cbr />Step 4:\u003Cbr />Substitute the values of a, c, h, and k into the equation:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{y−k^2}{\\leftfracb2right^2} + \\frac{x−h^2}{\\leftfrac52right^2} = 1 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{y−k^2}{\\leftfracb2right^2} + \\frac{x^2}{\\leftfrac52right^2} = 1 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{y−k^2}{\\leftfracb2right^2} + \\frac{x^2}{\\frac{25}{4}} = 1 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Step 5:\u003Cbr />Comparing the equation of the ellipse with the standard form, we get:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> b = 2 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> k = 0 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />So, the equation of the ellipse is:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{y^2}{4} + \\frac{4x^2}{25} = 1 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{\\frac{y^2}{4} + \\frac{4x^2}{25} = 1}\u003C/math-field>\u003C/math-field>",1285,257,"2-find-the-equation-of-the-ellipse-whose-foci-are-f-0-3-2-and-f-0-3-2-and-such-that-the-sum-of-the-distances-of-the-points-on-it-to-the-foci-is-5-in-spanish",{"id":141,"category":36,"text_question":142,"photo_question":38,"text_answer":143,"step_text_answer":8,"step_photo_answer":8,"views":144,"likes":145,"slug":146},536029,"CIF CONTROL SEATS\n\n Andean Coffee, whose plant is located in the city of Abrego, Norte de Santander, applies its costs with the following rates:\n Coffee bean distribution plant\n\n Direct labor hours\n Department Application Rate Department Actual Hours\n Drying 12,245.00Drying12,008\nToasted23,858.00 Toasted 17,380\n Packaged 3,357.50Packaged3,476\n\nTotalrealCIF 573,547,900.00\n\n Cost management can calculate and account for:\n CIF applied\n real CIF\n CIF closure takeintoaccountunder−andover−applications","\"To manage the cost accounting for Andean Coffee's coffee bean distribution plant, we need to calculate the CIF Cost,Insurance,Freight applied, the real CIF, and then determine any under- or over-applications for CIF closure. Here's how these calculations are done based on the data provided: \u003Cbr />\u003Cbr />### Data Given\u003Cbr />- **Drying Department**:\u003Cbr /> - Application Rate: 12,245.00perlaborhour\u003Cbr/>−ActualHours:12,008hours\u003Cbr/>−∗∗ToastedDepartment∗∗:\u003Cbr/>−ApplicationRate:23,858.00 per labor hour\u003Cbr /> - Actual Hours: 17,380 hours\u003Cbr />- **Packaged Department**:\u003Cbr /> - Application Rate: 3,357.50perlaborhour\u003Cbr/>−ActualHours:3,476hours\u003Cbr/>−∗∗TotalRealCIF∗∗:573,547,900.00\u003Cbr />\u003Cbr />### Calculations\u003Cbr />\u003Cbr />#### 1. CIF Applied\u003Cbr />This is the estimated CIF based on the application rates and the actual hours worked in each department. \u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{CIF Applied} = textApplicationRatetextDryingtimestextActualHourstextDrying + textApplicationRatetextToastedtimestextActualHourstextToasted + textApplicationRatetextPackagedtimestextActualHourstextPackaged \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{CIF Applied} = 12,245.00times12,008 + 23,858.00times17,380 + 3,357.50times3,476 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Calculating the CIF applied for each department and summing them up, we get:\u003Cbr />\u003Cbr />- **Drying Department**: 147,037,960.00\u003Cbr/>−∗∗ToastedDepartment∗∗:414,652,040.00\u003Cbr />- **Packaged Department**: 11,670,670.00\u003Cbr/>\u003Cbr/>Therefore,∗∗TotalCIFApplied∗∗:573,360,670.00\u003Cbr />\u003Cbr />#### 2. Real CIF\u003Cbr />The total real CIF, as provided, is 573,547,900.00.\u003Cbr />\u003Cbr />#### 3. CIF Closure (Under- or Over-application)\u003Cbr />To determine the CIF closure, we subtract the total CIF applied from the real CIF:\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{CIF Closure} = \\text{Real CIF} - \\text{Total CIF Applied} \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{CIF Closure} = 573,547,900.00 - 573,360,670.00 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Calculating the CIF closure, we find:187,230.00\u003Cbr />\u003Cbr />So, the CIF closure indicates an under-application of 187,230.00.\u003Cbr />\u003Cbr />## Answer\u003Cbr />The under-applied amount that should be adjusted in the accounting records is187,230.\"",974,195,"cif-control-seats-andean-coffee-whose-plant-is-located-in-the-city-of-abrego-norte-de-santander-applies-its-costs-with-the-following-rates-coffee-bean-distribution-plant-direct-labor-hours-d",{"id":148,"category":36,"text_question":149,"photo_question":38,"text_answer":150,"step_text_answer":8,"step_photo_answer":8,"views":151,"likes":152,"slug":153},536028,"24-2/24","\u003Cmath-field read-only> 24-\\frac{2}{24}=24-\\frac{1}{12}=21.916 \u003C/math-field>",1236,247,"24-2-24",{"id":155,"category":36,"text_question":156,"photo_question":38,"text_answer":157,"step_text_answer":8,"step_photo_answer":8,"views":158,"likes":159,"slug":160},536027,"What is the equivalent compounded quarterly rate referring to 7.24% per year?","7,05%",1083,217,"what-is-the-equivalent-compounded-quarterly-rate-referring-to-7-24-per-year",{"id":162,"category":36,"text_question":163,"photo_question":38,"text_answer":164,"step_text_answer":8,"step_photo_answer":8,"views":165,"likes":166,"slug":167},536026,"What is the mathematical relationship between F and D²?","A relação matemática entre a força F e a distância D ao quadrado D² é normalmente descrita pela lei do inverso do quadrado. Esta lei afirma que a força F é inversamente proporcional ao quadrado da distância D.\n\n Matematicamente, isso pode ser expresso como:\n\n F ∝ 1/D²\n\n ou\n\n F=k/D²\n\n Onde k é uma constante que depende do sistema físico específico e das unidades utilizadas.\n\n Esta relação inversa do quadrado é observada em vários fenômenos físicos, tais como:\n\n Força gravitacional: A força gravitacional entre duas massas é inversamente proporcional ao quadrado da distância entre elas.\n Força eletrostática: A força eletrostática entre duas partículas carregadas é inversamente proporcional ao quadrado da distância entre elas.\n Intensidade da radiação: A intensidade da radiação por exemplo, luz, ondas de rádio diminui com o quadrado da distância da fonte.\n A lei do inverso do quadrado é uma relação fundamental em muitas áreas da física e da engenharia, e compreendê-la é crucial para analisar e prever o comportamento de vários sistemas físicos.",596,119,"what-is-the-mathematical-relationship-between-f-and-d",{"id":169,"category":36,"text_question":170,"photo_question":38,"text_answer":171,"step_text_answer":8,"step_photo_answer":8,"views":172,"likes":173,"slug":174},536025,"Evelyn Aldana deposits a monthly income due for 5 years at a rate of\n 12% annual compounded monthly and you will not withdraw the money until 2 years later\n of the last income. If you can withdraw Q 90,000, how much do you deposit monthly?","\u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0, 0, 0, .3;box-shadow: 0 0 0 rgba0, 0, 0, .2\n\" read-only>90000=\\frac{ x \\times \\left( {\\left( 1+0.01 \\right)}^{2 \\times 12}-1 \\right) }{ \\frac{ 0.12 }{ 12 } }\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0, 0, 0, .3;box-shadow: 0 0 0 rgba0, 0, 0, .2\n\" read-only>90000=\\frac{ x \\times \\left( {\\left( 1+0.01 \\right)}^{24}-1 \\right) }{ \\frac{ 0.12 }{ 12 } }\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0, 0, 0, .3;box-shadow: 0 0 0 rgba0, 0, 0, .2\n\" read-only>90000=\\frac{ x \\times \\left( {\\left( 1+0.01 \\right)}^{24}-1 \\right) }{ 0.01 }\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0, 0, 0, .3;box-shadow: 0 0 0 rgba0, 0, 0, .2\n\" read-only>90000=\\frac{ x \\times \\left( {1.01}^{24}-1 \\right) }{ 0.01 }\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0, 0, 0, .3;box-shadow: 0 0 0 rgba0, 0, 0, .2\n\" read-only>90000=\\frac{ x \\times \\left( {1.01}^{24}-1 \\right) }{ \\frac{ 1 }{ 100 } }\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0, 0, 0, .3;box-shadow: 0 0 0 rgba0, 0, 0, .2\n\" read-only>90000=\\frac{ x \\times \\left( {\\left( \\frac{ 101 }{ 100 } \\right)}^{24}-1 \\right) }{ \\frac{ 1 }{ 100 } }\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0, 0, 0, .3;box-shadow: 0 0 0 rgba0, 0, 0, .2\n\" read-only>90000=\\frac{ x \\times \\left( \\frac{ {101}^{24} }{ {100}^{24} }-1 \\right) }{ \\frac{ 1 }{ 100 } }\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0, 0, 0, .3;box-shadow: 0 0 0 rgba0, 0, 0, .2\n\" read-only>90000=\\frac{ \\frac{ {101}^{24}x }{ {100}^{24} }-x }{ \\frac{ 1 }{ 100 } }\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0, 0, 0, .3;box-shadow: 0 0 0 rgba0, 0, 0, .2\n\" read-only>90000=\\frac{ \\frac{ {101}^{24}x-{100}^{24}x }{ {100}^{24} } }{ \\frac{ 1 }{ 100 } }\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0, 0, 0, .3;box-shadow: 0 0 0 rgba0, 0, 0, .2\n\" read-only>90000=\\frac{ {101}^{24}x-{100}^{24}x }{ {100}^{23} }\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0, 0, 0, .3;box-shadow: 0 0 0 rgba0, 0, 0, .2\n\" read-only>90000 \\times {100}^{23}={101}^{24}x-{100}^{24}x\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0, 0, 0, .3;box-shadow: 0 0 0 rgba0, 0, 0, .2\n\" read-only>{101}^{24}x-{100}^{24}x=90000 \\times {100}^{23}\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0, 0, 0, .3;box-shadow: 0 0 0 rgba0, 0, 0, .2\n\" read-only>\\left( {101}^{24}-{100}^{24} \\right)x=90000 \\times {100}^{23}\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba0, 0, 0, .3;box-shadow: 0 0 0 rgba0, 0, 0, .2\n\" read-only>\\begin{align*} & x=\\frac{ 90000 \\times{100}^{23} }{ {101}^{24}-{100}^{24} } \\\\ & x\\approx3336.61\\end{align*}\u003C/math-field>\n \u003Cbr>\n \u003C/div>",1201,240,"evelyn-aldana-deposits-a-monthly-income-due-for-5-years-at-a-rate-of-12-annual-compounded-monthly-and-you-will-not-withdraw-the-money-until-2-years-later-of-the-last-income-if-you-can-withdraw-q-9",{"first":6,"last":176,"prev":177,"next":178},188,88,90,{"current_page":180,"from":181,"last_page":176,"links":182,"path":216,"per_page":217,"to":218,"total":219},89,1761,[183,186,188,190,193,196,198,201,203,206,209,212,214],{"url":177,"label":184,"active":185},"« Previous",false,{"url":6,"label":187,"active":185},"1",{"url":10,"label":189,"active":185},"2",{"url":191,"label":192,"active":185},86,"86",{"url":194,"label":195,"active":185},87,"87",{"url":177,"label":197,"active":185},"88",{"url":180,"label":199,"active":200},"89",true,{"url":178,"label":202,"active":185},"90",{"url":204,"label":205,"active":185},91,"91",{"url":207,"label":208,"active":185},92,"92",{"url":210,"label":211,"active":185},187,"187",{"url":176,"label":213,"active":185},"188",{"url":178,"label":215,"active":185},"Next »","https://api.math-master.org/api/question",20,1780,3742,{"data":221},{"questions":222},[223,227,231,235,239,243,247,251,255,259,263,267,271,275,279,283,287,291,295,299],{"id":224,"category":36,"text_question":225,"slug":226},532007,"calculate the derivative by the limit definition: fx = 6x^3 + 2","calculate-the-derivative-by-the-limit-definition-f-x-6x-3-2",{"id":228,"category":36,"text_question":229,"slug":230},532021,"Solution of the equation y'' - y' -6y = 0","solution-of-the-equation-y-39-39-y-39-6y-0",{"id":232,"category":36,"text_question":233,"slug":234},532023,"find the value of the tangent if it is known that the cos@= 1 2 and the sine is negative. must perform procedures.","find-the-value-of-the-tangent-if-it-is-known-that-the-cos-1-2-and-the-sine-is-negative-must-perform-procedures",{"id":236,"category":36,"text_question":237,"slug":238},532086,"-8+3/5","8-3-5",{"id":240,"category":36,"text_question":241,"slug":242},532310,"The random variable Y is defined as the sum between two different integers selected at random between -4 and 2 both included. What are the possible values of the random variable Y? What is the value of PY=-3? And whether it is less than or equal to -5?","the-random-variable-y-is-defined-as-the-sum-between-two-different-integers-selected-at-random-between-4-and-2-both-included-what-are-the-possible-values-of-the-random-variable-y-what-is-the-value",{"id":244,"category":36,"text_question":245,"slug":246},533897,"A drawer contains three pairs of white socks, five pairs of black socks and two pairs of red socks. Caden randomly\nselects two pairs of socks on his way to the gym. What is the probability that both pairs of socks are black?","a-drawer-contains-three-pairs-of-white-socks-five-pairs-of-black-socks-and-two-pairs-of-red-socks-caden-randomly-selects-two-pairs-of-socks-on-his-way-to-the-gym-what-is-the-probability-that-both-p",{"id":248,"category":36,"text_question":249,"slug":250},533966,"A juice shop prepares assorted juices, for their juices they have 5 different types of\n fruit. How many types of assortments can be prepared in total, if it is considered an assortment\n to a juice made with two or more fruits?","a-juice-shop-prepares-assorted-juices-for-their-juices-they-have-5-different-types-of-fruit-how-many-types-of-assortments-can-be-prepared-in-total-if-it-is-considered-an-assortment-to-a-juice-mad",{"id":252,"category":36,"text_question":253,"slug":254},533980,"Find the root of x^4-10x^ 5=0 using Newton's method, with a precision of the smallest positive root.","find-the-root-of-x-4-10x-5-0-using-newton-s-method-with-a-precision-of-the-smallest-positive-root",{"id":256,"category":36,"text_question":257,"slug":258},534013,"The function g:Q→Q is a ring homomorphism such that g3=3 and g5=5. What are the values of g8 and g9?","the-function-g-q-q-is-a-ring-homomorphism-such-that-g-3-3-and-g-5-5-what-are-the-values-of-g-8-and-g-9",{"id":260,"category":36,"text_question":261,"slug":262},534106,"Find the equation of the line perpendicular to −5𝑥−3𝑦+5=0 passing through the point 0,−2","find-the-equation-of-the-line-perpendicular-to-5x-3y-5-0-passing-through-the-point-0-2",{"id":264,"category":36,"text_question":265,"slug":266},534124,"Substitute a=2 and b=-3 and c=-4 to evaluate 2ac/-2b^2-a","substitute-a-2-and-b-3-and-c-4-to-evaluate-2ac-2b-2-a",{"id":268,"category":36,"text_question":269,"slug":270},534194,"form a key for your lock containing the numbers 2 2 5 8 How many different keys can you form?","form-a-key-for-your-lock-containing-the-numbers-2-2-5-8-how-many-different-keys-can-you-form",{"id":272,"category":36,"text_question":273,"slug":274},534198,"Calculate the boiling temperature and freezing temperature at 1 atmosphere pressure of a solution formed by dissolving 123 grams of ferrous oxide in 1.890 grams of HCl.","calculate-the-boiling-temperature-and-freezing-temperature-at-1-atmosphere-pressure-of-a-solution-formed-by-dissolving-123-grams-of-ferrous-oxide-in-1-890-grams-of-hcl",{"id":276,"category":36,"text_question":277,"slug":278},534221,"How many square feet of floor area are there in three two-storey apartment houses, each of which is 38 feet wide and 76 feet long?","how-many-square-feet-of-floor-area-are-there-in-three-two-storey-apartment-houses-each-of-which-is-38-feet-wide-and-76-feet-long",{"id":280,"category":36,"text_question":281,"slug":282},534246,"How to do 15 x 3304","how-to-do-15-x-3304",{"id":284,"category":36,"text_question":285,"slug":286},534329,"At the dance there are 150 boys the rest are girls. If 65% are girls what is the total amount in the room","at-the-dance-there-are-150-boys-the-rest-are-girls-if-65-are-girls-what-is-the-total-amount-in-the-room",{"id":288,"category":36,"text_question":289,"slug":290},534371,"Determine a general formula​ or formulas for the solution to the following equation.​ Then, determine the specific solutions​ if any on the interval [0,2π).\ncos30=0","determine-a-general-formula-or-formulas-for-the-solution-to-the-following-equation-then-determine-the-specific-solutions-if-any-on-the-interval-0-2-cos30-0",{"id":292,"category":36,"text_question":293,"slug":294},534450,"In poker, a full house consists of five cards, where two of the cards have the\nsame number or letter and the remaining three also have the same number or\nletter as each other but not as the previous two cards. Use a search engine or\nWikipedia to understand the concept better if necessary.\nIn how many different ways can one obtain a full house?","in-poker-a-full-house-consists-of-five-cards-where-two-of-the-cards-have-the-same-number-or-letter-and-the-remaining-three-also-have-the-same-number-or-letter-as-each-other-but-not-as-the-previ",{"id":296,"category":36,"text_question":297,"slug":298},534623,"7-1=6\r\n6x2=12\r\n\r\nExplain that","7-1-6-6x2-12-explain-that",{"id":300,"category":36,"text_question":301,"slug":302},534656,"A grain silo has a height of 8.8m with a 11.4m diameter.\n\nIf it is filled 0.5% of it's volume, how much grain m^3 is stored in the silo? 0 decimal places","a-grain-silo-has-a-height-of-8-8m-with-a-11-4m-diameter-if-it-is-filled-0-5-of-it-s-volume-how-much-grain-m-3-is-stored-in-the-silo-0-decimal-places",{"data":304},[305,315,324,334,345,354,363,372,384,391,401,409,420,429,435,442,450,461,469,479],{"id":306,"name":307,"photo":308,"certificates":309,"diplomas":311,"biography":312,"rating":313,"total_answer":314},19,"Seamus","https://api.math-master.org/img/experts/19/19.webp",[310],"https://api.math-master.org/img/experts/19/certificates/certif.webp",[],"I had very much interest from the Starting with simple addition and multiplication, my math journey led me to tackle more challenging problems. What I love most about math is how it's like a puzzle-solving adventure. It helps us understand things around us by finding patterns and connections. It's like a secret code that unveils the mysteries of the world, and I enjoy how each solution feels like a small victory. Math is like a playground for our imagination, where we can come up with creative ways to solve problems and learn new things. It's all about exploring, discovering, and having fun along the way.",4.9,94,{"id":316,"name":317,"photo":318,"certificates":319,"diplomas":320,"biography":322,"rating":313,"total_answer":323},18,"Nash","https://api.math-master.org/img/experts/18/18.webp",[],[321],"https://api.math-master.org/img/experts/18/diplomas/diploma.webp","My interest in mathematics boomed in my school days which led me to choose mathematics as my core subject in college and later pursue Engineering in University. I have been working at MathMaster for 10 months now and the fact that I like solving math tasks makes me interested in this field. I can work part-time at any available shift for the day and not get exhausted. Moreover solving math tasks keep my brain sharp and focused.\n\n",85,{"id":325,"name":326,"photo":327,"certificates":328,"diplomas":330,"biography":332,"rating":313,"total_answer":333},15,"Miles","https://api.math-master.org/img/experts/15/15.webp",[329],"https://api.math-master.org/img/experts/15/certificates/2fd3f3a1-34c4-417d-a85a-1459c7fc0356.webp",[331],"https://api.math-master.org/img/experts/15/diplomas/diploma.webp","My name is Ali Haider and I hold a bachelor’s degree in Electrical Engineering and I am also certified Math Expert. I have been teaching Mathematics and Physics for the past 6 years at both the high school and college level. My pass rate for Mathematics is 100%.\nIn addition to teaching, I love playing badminton and video games.\n",108,{"id":13,"name":335,"photo":336,"certificates":337,"diplomas":341,"biography":343,"rating":344,"total_answer":62},"Timmothy","https://api.math-master.org/img/experts/3/3.webp",[338,339,340],"https://api.math-master.org/img/experts/3/certificates/14d1b957-4891-43e9-b5bc-07fdd4d9af21.webp","https://api.math-master.org/img/experts/3/certificates/27b13919-712a-4712-b27a-e09fc16c774f.webp","https://api.math-master.org/img/experts/3/certificates/b70a3a4e-33de-47d7-b0a5-9fbefe397734.webp",[342],"https://api.math-master.org/img/experts/3/diplomas/19c9addf-312a-4437-af41-e89bc3843209 1.webp","Hello, I'm Jamil Omar, and I want to take you on a journey through my experience with math, from school to university.\nEarly School Years:\nHigh school marked the beginning of my mathematical journey, a journey that started with skepticism but transformed into something wonderful. At first, I wasn't a fan of math, until a special teacher changed everything. This teacher showed me the beauty of math, and suddenly, everything clicked.\nBecause of this teacher, I started enjoying math and even joined math competitions during my high school days. Surprisingly, I excelled and became a champion at both the provincial and regional levels. These wins boosted my confidence and made me realize that I could excel in math.\nThese victories also gave me the confidence to pursue an engineering degree in college. Thanks to that teacher and my successes in math, I knew I could conquer new challenges and make the most of my education journey.\nUniversity Journey:\nMy strong grasp of mathematics inspired me to pursue a bachelor's degree in Petroleum Engineering at Palawan State University. Confident in my mathematical foundation, I embarked on this academic journey.\nThroughout the course, I discovered that my solid background in mathematics was a true asset. It enabled me to better comprehend the intricate topics within Petroleum Engineering and successfully complete the program.\nMy enthusiasm for engineering led me to actively engage in quiz bee contests, where sharp mathematical skills are crucial for success. Our team's victory in these contests opened doors to a national quiz bee in our country. This experience not only honed my mathematical abilities but also granted us the privilege to participate in seminars related to our field of study.\nOne of my achievements was securing the top rank in our departmental exam for algebra. During my first year in college, I outperformed all other first-year students across the university. This accomplishment underscores the significant impact of mathematics on my academic journey.\nStudying math has proven to be invaluable, not just in terms of academic achievements but also in enhancing my analytical skills and enabling me to earn a degree in Petroleum Engineering.",4.8,{"id":346,"name":347,"photo":348,"certificates":349,"diplomas":350,"biography":352,"rating":344,"total_answer":353},22,"Hank","https://api.math-master.org/img/experts/22/22.webp",[],[351],"https://api.math-master.org/img/experts/22/diplomas/12.webp","When I was in elementary and middle school, I did not feel the importance and beauty of mathematics, but when I joined the secondary stage, I began to feel the beauty and importance of mathematics, and I excelled in mathematics. I joined the College of Education, Department of Mathematics, and now I am a mathematics teacher.\nThen after that, I got a master's degree and a doctorate in curricula and methods of teaching mathematics.",100,{"id":355,"name":356,"photo":357,"certificates":358,"diplomas":359,"biography":361,"rating":344,"total_answer":362},35,"Hester","https://api.math-master.org/img/experts/35/35.webp",[],[360],"https://api.math-master.org/img/experts/35/diplomas/03849782-84d8-46fb-b7ed-7e3204335b13.webp","Mathematics has been my favourite subject since childhood. I studied mathematics in secondary education and secured full marks in this subject which gave me great joy and boost as i was attached to this subject. Then I opted Pre-Engineering in my higher secondary education which was mainly about the mathematics. Then I got admission in Engineering University which is ranked as Number 1 Engineering University of my country and studied different subjects of mathematics there on graduate level. I really enjoy while solving the maths questions and get too much involved in the basics and different branches of maths as it is referred as mother of sciences and I am emotionally attached to this subject.\r\n\r",115,{"id":364,"name":365,"photo":366,"certificates":367,"diplomas":369,"biography":371,"rating":344,"total_answer":333},14,"Brice","https://api.math-master.org/img/experts/14/14.webp",[368],"https://api.math-master.org/img/experts/14/certificates/a53728ab-4dc7-40ba-8d75-9938dd4881d9.webp",[370],"https://api.math-master.org/img/experts/14/diplomas/240b3c4c-3403-49ef-aab8-6caa8f694f93.webp","Muhammad Farooq here. I have done Bachelor's in Electrical Engineering and in my institute mode of studying was in English. Though I don not posses and certificate of diploma in English as it costs much here in Pakistan and I was not required to submit this certificate anywhere, though my courses in English as well mathematics are mentioned in my School as well collage certificate so you can check my record in these certificates",{"id":373,"name":374,"photo":375,"certificates":376,"diplomas":379,"biography":381,"rating":382,"total_answer":383},28,"Esmeralda","https://api.math-master.org/img/experts/28/28.webp",[377,378],"https://api.math-master.org/img/experts/28/certificates/883 C.webp","https://api.math-master.org/img/experts/28/certificates/883 CC.webp",[380],"https://api.math-master.org/img/experts/28/diplomas/883 D.webp","From an early age, I've been captivated by the enchanting world of mathematics. It all began during my childhood when the mere sight of numbers and equations ignited a spark within me. This fascination evolved into a lifelong passion, shaping my journey into becoming a dedicated math enthusiast.\r\n\r\nThroughout my formative years in both primary and secondary school, I eagerly participated in various math contests, emerging victorious and accumulating a treasure trove of accolades that celebrated my mathematical prowess. As I embarked on my college journey, I chose a bachelor's degree program that seamlessly intertwined mathematics with computational problem-solving.\r\n\r\nStepping into the realm of teaching was a natural progression for me. Armed with a deep reservoir of mathematical knowledge and an innate ability to explain complex concepts in simple terms, I found myself guiding college entrance exam reviewees through the intricacies of algebra, geometry, trigonometry, and pre-calculus. In the interstices of my journey, I also dabbled in the realm of freelance mathematics. With the luxury of time, I engaged in tackling a diverse array of mathematical problems and coursework. This not only honed my skills further but also cemented my belief that mathematics, while a field of study, is also a boundless realm of exploration and creativity.",4.7,98,{"id":385,"name":386,"photo":387,"certificates":388,"diplomas":389,"biography":390,"rating":382,"total_answer":191},12,"Madelyn","https://api.math-master.org/img/experts/12/12.webp",[],[],"i am kishan kushavaha from india. i am completed my primary education from jawahar Navodaya vidhyalaya Rath hamirpur utter pradesh India. Currently I am pursuing Btech degree in computer science and engineering. Math my favorite subject i am feel very happyness solving the math problems.",{"id":392,"name":393,"photo":394,"certificates":395,"diplomas":399,"biography":400,"rating":382,"total_answer":48},13,"Maude","https://api.math-master.org/img/experts/13/13.webp",[396,397,398],"https://api.math-master.org/img/experts/13/certificates/664eea5b-1c59-4243-bed8-3a2ffba05ef7.webp","https://api.math-master.org/img/experts/13/certificates/bccb93ad-6ae1-4c1f-bc57-5c2fc5c479b5.webp","https://api.math-master.org/img/experts/13/certificates/cd4c4772-1927-4836-ad8e-340300efad86.webp",[],"i always fond of math ,TILL my matriculation to graduation math is my fvrt subject\nwhen i was in 9th class i had a teacher named as Sir Saleem this is now died but he was bestest teacher ever\nHe teach us each and every question of every exercise of my book of mathematics and what i do is write all those questions in my register as it is and practiced a lot this build my basics and keep them strong i am highly obliged to my sir May God give him high place in jannah ..\nso come to story i have digested too much math in my mind that when i gave math final exams of board i was too much confident and just revise definitions included in course and did not do any question by hand because every question is remembered by heart , i just go through by my register and believe me i got 74/75 marks . this was my initiation in math field that go wide and wide in other fields of math.\nMy interest in mathematics grew as it related to algorithms and data. I moved up into the complexity of algebra and geometry from arithmetic's simplicity because I was fascinated by their complexities. Calculus revealed the language of transformation, while number theory and abstract algebra drove me farther into abstraction. My ability to do rigorous and challenging analysis was put to the test, building a link to the very core of patterns and structures.\n\nThe applications of theory were made possible by probability, statistics, and discrete mathematics, demonstrating the usefulness of mathematical techniques. I incorporated mathematical ideas into my digital self as the digital era developed, optimizing, forecasting, and innovating.\n\n\n\nMy story is a never-ending quest that is inextricably linked to the beauty and logic of mathematics.",{"id":402,"name":403,"photo":404,"certificates":405,"diplomas":406,"biography":407,"rating":382,"total_answer":408},7,"Cristian","https://api.math-master.org/img/experts/7/7.webp",[],[],"I embarked on my academic journey as a sports enthusiast, prior to enrolling in my undergraduate studies. My enthusiasm for mathematics had always been muted, largely owing to the seemingly endless and purposeless calculations it often involved. However, a transformative experience awaited me during my time in college. It was there that I encountered a teacher who, in our very first class, presented a simple yet profound exercise: to complete the sentence \"Mathematics is _______\" with a single word that encapsulated our immediate perception of the subject.\nI hesitated briefly before filling the blank space with the word \"boring.\" To my surprise, my teacher chose the word \"beautiful.\" This striking contrast sparked my curiosity and set the stage for a remarkable journey of discovery. Guided by her teaching and insights, it took me a span of two to three months to truly grasp the hidden allure of mathematics. What I once considered mere calculations revealed themselves to be the building blocks of exquisite mathematical and geometric forms.\nThis revelation marked the turning point in my relationship with mathematics. I came to realize that nothing in the realm of mathematics is devoid of purpose or significance. Behind every calculation lies a tapestry of captivating patterns and shapes. As I delved deeper into the core concepts, my appreciation for the elegance and depth of mathematics grew exponentially.\nThis newfound passion became the bedrock of my academic pursuits. It paved the way for my entrance into the world of mathematical exploration, ultimately leading me to pursue a PhD in mathematics. The journey has brought me under the mentorship of an esteemed 80-year-old supervisor, a venerable professor renowned for his wisdom, at Jacobs University in Germany.\nLooking back, I can trace the evolution of my perspective from skepticism to fascination, all catalyzed by a single teacher's belief in the beauty that mathematics holds. With each step I take in my academic journey, I am reminded that the seeds of interest and passion can be sown in the most unexpected of places, transforming the trajectory of one's life in ways that are both profound and deeply fulfilling.",112,{"id":410,"name":411,"photo":412,"certificates":413,"diplomas":418,"biography":419,"rating":382,"total_answer":204},16,"\nClarabelle","https://api.math-master.org/img/experts/16/16.webp",[414,415,416,417],"https://api.math-master.org/img/experts/16/certificates/00f2469c-54a4-4a86-a1bd-058b62670da1.webp","https://api.math-master.org/img/experts/16/certificates/82090cc4-0853-4d1d-88d0-3c33cd9dd4e4 1.webp","https://api.math-master.org/img/experts/16/certificates/82090cc4-0853-4d1d-88d0-3c33cd9dd4e4.webp","https://api.math-master.org/img/experts/16/certificates/f073e340-308d-4d20-ab38-8b2c9598137b.webp",[],"Hi,\nI've loved Mathematics and critical thinking for as long as I can remember. I started tutoring my fellow students in grade 6. I've studied Maths in the Faculty of Science. I started tutoring online 10 years ago. I've taken a lot of courses to help me teach the STEM curriculum better ever since.\nRegards\nRania",{"id":22,"name":421,"photo":422,"certificates":423,"diplomas":426,"biography":428,"rating":382,"total_answer":314},"Jett","https://api.math-master.org/img/experts/6/6.webp",[424,425],"https://api.math-master.org/img/experts/6/certificates/a05d6f13-1579-47ba-9f4d-1379fd868a32.webp","https://api.math-master.org/img/experts/6/certificates/fcc9c87f-66d3-4474-adfd-13fee92c6090.webp",[427],"https://api.math-master.org/img/experts/6/diplomas/ff175d15-b3af-4041-89fc-d9ac937be8d4.webp","Hello,\nI am pleased to introduce myself as a Mathmaster Expert 😊\nI am Engr. Paul Eejay Dy, a Registered Civil Engineer in the Philippines and Mathematics has always been my favorite subject.\nStudying Mathematics is a really difficult but fun experience for me and with the help of really great teachers and professors that helped me on this journey, I overcame all the obstacles that came my way until I achieved my dream profession.\nSo for all Mathmaster users, it is a great pleasure to be part of your journey into this rough but fulfilling journey of studying Mathematics. Study hard, and keep fighting for your dreams 😇🙏",{"id":19,"name":430,"photo":431,"certificates":432,"diplomas":433,"biography":434,"rating":382,"total_answer":90},"Rasheed","https://api.math-master.org/img/experts/5/5.webp",[],[],"Born with an insatiable curiosity, I began my journey with mathematics during my school years. From solving basic arithmetic problems to unraveling complex algebraic equations, I developed a deep passion for the subject. Upon entering university, my learnings diving into advanced topics like abstract algebra, numerical analysis and differential equations.\nIn retrospect, my journey through the realm of mathematics has been an exhilarating adventure of discovery, learning, and growth.\n",{"id":436,"name":437,"photo":438,"certificates":439,"diplomas":440,"biography":441,"rating":382,"total_answer":333},34,"Dexter","https://api.math-master.org/img/experts/34/34.webp",[],[],"I had done my schooling in SPHS, one of premier academic institutions in the city which covered all courses upto K-12. Mathematics had always been my forte, love & passion which earned me a good amount of reputation and accreditation at various phases of my career. My penchant in Maths was observed by my professors in school who did not hesitate to shower me the honour of one of the best mathematics students taught by them. I had a straight A in Mathematics and related sciences right from school to university level. After crossing the barrier of high school with elan, I did not hesitate to continue my graduation in Mathematics major from JU which enlists within the top 5 universities in the country. I stood first in my faculty in the final year of graduation with 85% score amounting to GPA 4.0. During the 3 year graduation, I silently earned the recognition of the top Mathematics student of the class in the eyes of my professors and my fellow students who used to crowd around me when they got stuck in any topic of maths. Overall my journey as a student of Mathematics was challenging, rewarding, enriching and a superbly enjoyable phase of my career. ",{"id":10,"name":443,"photo":444,"certificates":445,"diplomas":446,"biography":448,"rating":449,"total_answer":48},"Corbin","https://api.math-master.org/img/experts/2/2.webp",[],[447],"https://api.math-master.org/img/experts/2/diplomas/1ea09f59-7559-4ce7-8bad-50bcc43ea9ed.webp","My names is James Agustin Molina, I am from Philippines. Back when I in high school, I was not the best in Math in my class; but, If I were to compare my math skills to my other subjects, I think Math is my best subject. I always find solving and learning math techniques fun. Because I think my Math is the my best subject and I always fascinated in how things work, I took engineering in my college. In college, I really enjoyed math and thinking of pursuing a teaching career. I also took and passed my licensure exam right after graduation. Currently, I am taking my Masters Degree in Mathematics.",4.6,{"id":451,"name":452,"photo":453,"certificates":454,"diplomas":455,"biography":459,"rating":449,"total_answer":460},29,"Eliseo","https://api.math-master.org/img/experts/29/29.webp",[],[456,457,458],"https://api.math-master.org/img/experts/29/diplomas/458 2.webp","https://api.math-master.org/img/experts/29/diplomas/458 d.webp","https://api.math-master.org/img/experts/29/diplomas/458 dd.webp","In my school days I was not good in Mathematics but there was something which always attracted me towards Mathematics as playing with numbers and doing round of questions of different exercises of workbook was fun for me and as a hobby I inclined to Math's. I never thought of teaching mathematics and making a career out of it but somethings bound to happen.",106,{"id":462,"name":463,"photo":464,"certificates":465,"diplomas":466,"biography":467,"rating":449,"total_answer":468},30,"Bud","https://api.math-master.org/img/experts/30/30.webp",[],[],"I started my mathematics journey when i was in school and i went for a lot of competitions in mathematics back then and after worth, i proceeded into the university to study Electronics and Electrical Engineering and the course of studying it, i came across a lot of mathematics course which grounded me alot in mathematics.",95,{"id":470,"name":471,"photo":472,"certificates":473,"diplomas":474,"biography":477,"rating":449,"total_answer":478},31,"Frederik","https://api.math-master.org/img/experts/31/31.webp",[],[475,476],"https://api.math-master.org/img/experts/31/diplomas/344.webp","https://api.math-master.org/img/experts/31/diplomas/344D.webp","Hi, my name is Nitin,\r\nI started taking an interest in maths, because of my grandfather, who was a maths professor at HNBGU University, initially, I was not that good at maths, but with practice, I improved a lot, and I became pretty good at it when I got excellent marks in class 10th maths, I chose maths as my primary subject I completed my college and graduation, currently I am pursuing my master, I loved teaching maths, I also teach maths in a local school, and I want to become a professor in maths just like my grandfather.",97,{"id":480,"name":481,"photo":482,"certificates":483,"diplomas":485,"biography":487,"rating":449,"total_answer":333},21,"Jon","https://api.math-master.org/img/experts/21/21.webp",[484],"https://api.math-master.org/img/experts/21/certificates/41e2a05c-d94f-4bcc-9258-f2a7fe4c3c02.webp",[486],"https://api.math-master.org/img/experts/21/diplomas/9258cda6-9255-4b34-8806-23628b0a8153.webp","I passed my matric from Govt.City Muslim school Faisalabad and got first division in school by getting 981/1000 marks.\nAfter matric i got admission in Shiblee Colege Faisalabad and got 883/1100 marks in degree of inter with Math.\nNow currently i'm student of BS Math and running my last semester.",{"$sicons":489},{"bxl:facebook-circle":490,"bxl:instagram":494,"mdi:web":496,"la:apple":498,"ph:google-logo-bold":501,"ph:google-logo":504},{"left":491,"top":491,"width":492,"height":492,"rotate":491,"vFlip":185,"hFlip":185,"body":493},0,24,"\u003Cpath fill=\"currentColor\" d=\"M12.001 2.002c-5.522 0-9.999 4.477-9.999 9.999c0 4.99 3.656 9.126 8.437 9.879v-6.988h-2.54v-2.891h2.54V9.798c0-2.508 1.493-3.891 3.776-3.891c1.094 0 2.24.195 2.24.195v2.459h-1.264c-1.24 0-1.628.772-1.628 1.563v1.875h2.771l-.443 2.891h-2.328v6.988C18.344 21.129 22 16.992 22 12.001c0-5.522-4.477-9.999-9.999-9.999\"/>",{"left":491,"top":491,"width":492,"height":492,"rotate":491,"vFlip":185,"hFlip":185,"body":495},"\u003Cpath fill=\"currentColor\" d=\"M11.999 7.377a4.623 4.623 0 1 0 0 9.248a4.623 4.623 0 0 0 0-9.248m0 7.627a3.004 3.004 0 1 1 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