:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> m = \\frac{9300 \\, \\text{g}}{1000} = 9.3 \\, \\text{kg} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Calculate the force due to gravity:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> F = m \\times g = 9.3 \\, \\text{kg} \\times 9.81 \\, \\text{m/s}^2 = 91.233 \\, \\text{N} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Convert the length of the hammer from centimeters to meters:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 18 \\, \\text{cm} = 0.18 \\, \\text{m} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Calculate the torque:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\tau = 0.18 \\, \\text{m} \\times 91.233 \\, \\text{N} = 16.42194 \\, \\text{Nm} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nThus, the torque about the pivot point due to the weight of the screw at the end of the hammer handle is approximately \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 16.42 \\, \\text{Nm} \u003C/math-field>\u003C/math-field>.",484,97,"suppose-you-have-to-use-a-hammer-in-your-hand-on-a-wall-with-a-screw-of-mass-9300-g-the-hammer-is-18-cm-long-calculate-the-torque-of-the-screw",{"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},538046," A cylinder makes six turns in 2 seconds, calculate: a) its angular velocity in rad/s; b) its period and c) its frequency.","a) Angular velocity $\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\omega\u003C/math-field>\u003C/math-field>$ is given by the formula:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\omega = \\frac{\\Delta \\theta}{\\Delta t}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nHere, the cylinder makes 6 turns, and each turn is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2\\pi\u003C/math-field>\u003C/math-field> radians. Therefore, in 6 turns, the angle in radians is:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\Delta \\theta = 6 \\times 2\\pi = 12\\pi \\text{ radians}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nThe time period $\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\Delta t\u003C/math-field>\u003C/math-field>$ is 2 seconds, so the angular velocity is:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\omega = \\frac{12\\pi}{2} = 6\\pi \\text{ rad/s}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nb) The period $\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>T\u003C/math-field>\u003C/math-field>$ is the time it takes to complete one full rotation $1 turn$. Since the cylinder makes 6 turns in 2 seconds:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>T = \\frac{\\Delta t}{\\text{number of turns}} = \\frac{2}{6} = \\frac{1}{3} \\text{ s}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nc) The frequency $\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f\u003C/math-field>\u003C/math-field>$ is the reciprocal of the period:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f = \\frac{1}{T} = \\frac{1}{\\frac{1}{3}} = 3 \\text{ Hz}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nThus, the answers are:\u003Cbr />\n\u003Cbr />\na) \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\omega = 6\\pi \\text{ rad/s}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nb) \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>T = \\frac{1}{3} \\text{ s}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nc) \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f = 3 \\text{ Hz}\u003C/math-field>\u003C/math-field>",250,50,"a-cylinder-makes-six-turns-in-2-seconds-calculate-a-its-angular-velocity-in-rad-s-b-its-period-and-c-its-frequency",{"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},538045," A 73,000 g Ferris wheel accelerates from rest to an angular speed of 6.2 rad/s in 2 minutes. Considering the wheel as a hollow circular disk of radius 200 cm, calculate the net force on it?","1. Convert mass from grams to kilograms: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> m = 73,000 \\, \\text{g} = 73 \\, \\text{kg} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Convert radius from centimeters to meters:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> r = 200 \\, \\text{cm} = 2 \\, \\text{m} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Convert time from minutes to seconds: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> t = 2 \\, \\text{minutes} = 120 \\, \\text{seconds} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Calculate angular acceleration:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\alpha = \\frac{\\omega_f - \\omega_i}{t} = \\frac{6.2 \\, \\text{rad/s} - 0 \\, \\text{rad/s}}{120 \\, \\text{s}} = 0.0517 \\, \\text{rad/s}^2 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. Moment of inertia of a hollow circular disk:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> I = m \\cdot r^2 = 73 \\, \\text{kg} \\cdot $2 \\, \\text{m}$^2 = 292 \\, \\text{kg} \\cdot \\text{m}^2 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>6. Calculate net torque:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\tau = I \\cdot \\alpha = 292 \\, \\text{kg} \\cdot \\text{m}^2 \\times 0.0517 \\, \\text{rad/s}^2 = 15.1044 \\, \\text{N} \\cdot \\text{m} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>7. Calculate net force $since torque = force × radius$:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> F = \\frac{\\tau}{r} = \\frac{15.1044 \\, \\text{N} \\cdot \\text{m}}{2 \\, \\text{m}} = 7.5522 \\, \\text{N} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Rounding to a sensible number of significant figures gives the net force:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>F\\approx7.55\\,\\text{N}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Therefore, the net force on the Ferris wheel is approximately \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>7.55\\,\\text{N}\u003C/math-field>\u003C/math-field> .",655,131,"a-73-000-g-ferris-wheel-accelerates-from-rest-to-an-angular-speed-of-6-2-rad-s-in-2-minutes-considering-the-wheel-as-a-hollow-circular-disk-of-radius-200-cm-calculate-the-net-force-on-it",{"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},538044," A cylindrical piece of material 12 in in diameter is rotated on a lathe at 1300 rev/min. What is the tangential velocity at the surface of the cylinder? Value 4 points","1. Find angular velocity: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\omega = 1300 \\times 2\\pi \\text{ radians per minute} \u003C/math-field>\u003C/math-field>\u003Cbr />\n2. Calculate the radius: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> r = \\frac{12}{2} = 6 \\text{ inches} \u003C/math-field>\u003C/math-field>\u003Cbr />\n3. Use the formula for tangential velocity:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> v = \\omega \\cdot r = $1300 \\times 2\\pi$ \\cdot 6 = 15600\\pi \\text{ inches per minute} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nAnswer: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> v = 15600\\pi \\text{ inches per minute} \u003C/math-field>\u003C/math-field>",649,130,"a-cylindrical-piece-of-material-12-in-in-diameter-is-rotated-on-a-lathe-at-1300-rev-min-what-is-the-tangential-velocity-at-the-surface-of-the-cylinder-value-4-points",{"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},538043," A pulley in a well with a diameter of 1200 cm initially rotates at 1.3 rev/s and then receives a constant angular acceleration of 3.12 rad/s2 . What is the tangential velocity of a belt mounted on said pulley? After 1 second, what is the tangential acceleration of the belt?","1. Calculate the initial angular velocity in radians per second: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\omega_0 = 1.3 \\, \\text{rev/s} \\times 2\\pi \\, \\text{rad/rev} = 2.6\\pi \\, \\text{rad/s} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Determine the final angular velocity after 1 second using the equation for angular velocity with constant acceleration:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\omega = \\omega_0 + \\alpha t \u003C/math-field>\u003C/math-field>\u003Cbr />\n where \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\alpha = 3.12 \\, \\text{rad/s}^2 \u003C/math-field>\u003C/math-field> and \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> t = 1 \\, \\text{s} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Calculate \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\omega \u003C/math-field>\u003C/math-field>:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\omega = 2.6\\pi + 3.12 \\times 1 = 2.6\\pi + 3.12 \u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\n4. Calculate the radius of the pulley:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> r = \\frac{1200 \\, \\text{cm}}{2} = 600 \\, \\text{cm} = 6 \\, \\text{m} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Find the tangential velocity \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> v \u003C/math-field>\u003C/math-field> at \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> t = 1 \\, \\text{s} \u003C/math-field>\u003C/math-field>:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> v = \\omega \\times r \u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> v = $2.6\\pi + 3.12$ \\times 6 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Simplify to find \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> v \u003C/math-field>\u003C/math-field>:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> v = $8.168 + 3.12$ \\times 6 = 11.288 \\times 6 = 67.728 \\, \\text{m/s} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n7. Calculate the tangential acceleration \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> a_t \u003C/math-field>\u003C/math-field>, which is constant:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> a_t = \\alpha \\times r = 3.12 \\times 6 = 18.72 \\, \\text{m/s}^2 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n8. Final answers: \u003Cbr />\n Tangential velocity after 1 second: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 67.728 \\, \\text{m/s} \u003C/math-field>\u003C/math-field>\u003Cbr />\n Tangential acceleration: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 18.72 \\, \\text{m/s}^2 \u003C/math-field>\u003C/math-field>",955,191,"a-pulley-in-a-well-with-a-diameter-of-1200-cm-initially-rotates-at-1-3-rev-s-and-then-receives-a-constant-angular-acceleration-of-3-12-rad-s2-what-is-the-tangential-velocity-of-a-belt-mounted-on-s",{"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},538041,"Why do we use multiplication when dividing fractions. I know how to do the steps, but why do you keep the first number, changed to multiplication, and then write the reciprocal of the fraction.\n\nI guess I just don’t understand why we switched to multiplication. Thank you.","1. **Keep the First Fraction:** Write the first fraction as it is. \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{a}{b}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. **Change the Operation:** Change the division sign to a multiplication sign. \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\times\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. **Use the Reciprocal:** Use the reciprocal of the second fraction $flip the numerator and denominator$. \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{d}{c}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. **Multiply the Fractions:** Multiply the numerators and denominators. \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{a \\times d}{b \\times c}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. **Answer:** The division of the two given fractions as multiplication results in: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{a \\times d}{b \\times c}\u003C/math-field>\u003C/math-field>",702,140,"why-do-we-use-multiplication-when-dividing-fractions-i-know-how-to-do-the-steps-but-why-do-you-keep-the-first-number-changed-to-multiplication-and-then-write-the-reciprocal-of-the-fraction-i-gu",{"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},538040,"Prove the trig identity:\n\nSec^2x-Sin^2xSec^2x=1","1. Start with the left-hand side of the equation: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\sec^2{x} - \\sin^2{x} \\sec^2{x} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Factor out \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\sec^2{x} \u003C/math-field>\u003C/math-field>: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\sec^2{x} $1 - \\sin^2{x}$ \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Use the Pythagorean identity \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\sin^2{x} + \\cos^2{x} = 1 \u003C/math-field>\u003C/math-field> to replace \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 1 - \\sin^2{x} \u003C/math-field>\u003C/math-field> with \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\cos^2{x} \u003C/math-field>\u003C/math-field>: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\sec^2{x} \\cdot \\cos^2{x} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Substitute \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\sec{x} = \\frac{1}{\\cos{x}} \u003C/math-field>\u003C/math-field>: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\left$\\frac{1}{\\cos^2{x}}\\right$ \\cdot \\cos^2{x} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Simplify: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 1 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nTherefore, the identity is proven: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\sec^2{x} - \\sin^2{x} \\sec^2{x} = 1 \u003C/math-field>\u003C/math-field>",294,59,"prove-the-trig-identity-sec-2x-sin-2xsec-2x-1",{"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},538039,"Prove the trig identity:\n\n1+Sec^2x/Sec^2x = 1 + cos^2x","1. Start with the left-hand side of the equation: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{1+\\sec^2 x}{\\sec^2 x}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Recall that \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\sec x = \\frac{1}{\\cos x}\u003C/math-field>\u003C/math-field> , so \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\sec^2 x = \\frac{1}{\\cos^2 x}\u003C/math-field>\u003C/math-field> . Therefore, substitute:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{1+\\frac{1}{\\cos^2 x}}{\\frac{1}{\\cos^2 x}}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Simplify the fraction:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{\\cos^2x+1}{\\frac{\\cos^2\\left$x\\right$}{\\cos^2x}}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Multiply by the reciprocal of the denominator:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>$\\cos^2x+1$\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>6. Simplify to get:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\cos^2 x + 1\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>7. Compare with the right-hand side, which is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1 + \\cos^2 x\u003C/math-field>\u003C/math-field> . Since \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\cos^2 x + 1\u003C/math-field>\u003C/math-field> is equivalent to \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1 + \\cos^2 x\u003C/math-field>\u003C/math-field> , the trigonometric identity is proved.\u003Cbr>\u003Cbr>Answer: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1 + \\cos^2 x\u003C/math-field>\u003C/math-field>",1031,206,"prove-the-trig-identity-1-sec-2x-sec-2x-1-cos-2x",{"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},538038,"Prove the trig identity:\n\nCos x/1-sinx - Cos x/1+sin x = 2tan x","\u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba$0, 0, 0, .3$;box-shadow: 0 0 0 rgba$0, 0, 0, .2$\n\" read-only>$=\\frac{\\sin(2x)}{(-\\sin(x)+1)(\\sin(x)+1)}$\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 rgba$0, 0, 0, .3$;box-shadow: 0 0 0 rgba$0, 0, 0, .2$\n\" read-only>$=\\frac{\\sin(2x)}{\\cos^{2}(x)}$\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 rgba$0, 0, 0, .3$;box-shadow: 0 0 0 rgba$0, 0, 0, .2$\n\" read-only>$=2\\tan(x)$\u003C/math-field>\n \u003Cbr>\n \u003C/div>",770,154,"prove-the-trig-identity-cos-x-1-sinx-cos-x-1-sin-x-2tan-x",{"id":107,"category":36,"text_question":108,"photo_question":38,"text_answer":109,"step_text_answer":8,"step_photo_answer":8,"views":110,"likes":111,"slug":112},538037,"Prove the trig identity:\n\n1+cos x/sin x = csc x + cot x","1. Start with the right-hand side of the equation: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\csc x + \\cot x \u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cbr />\n2. Express \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\csc x \u003C/math-field>\u003C/math-field> and \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\cot x \u003C/math-field>\u003C/math-field> in terms of sine and cosine:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\csc x = \\frac{1}{\\sin x} \u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\cot x = \\frac{\\cos x}{\\sin x} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Add the fractions:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\csc x + \\cot x = \\frac{1}{\\sin x} + \\frac{\\cos x}{\\sin x} = \\frac{1 + \\cos x}{\\sin x} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. The expression \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{1 + \\cos x}{\\sin x} \u003C/math-field>\u003C/math-field> matches the left-hand side of the identity.\u003Cbr />\n\u003Cbr />\nTherefore, the identity is valid: \u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{1 + \\cos x}{\\sin x} = \\csc x + \\cot x \u003C/math-field>\u003C/math-field>",605,121,"prove-the-trig-identity-1-cos-x-sin-x-csc-x-cot-x",{"id":114,"category":36,"text_question":115,"photo_question":38,"text_answer":116,"step_text_answer":8,"step_photo_answer":8,"views":117,"likes":118,"slug":119},538036,"Prove the trig identity:\n\n $1-cos θ$$1+cos θ$= 1/csc^2 θ","1. Start with the left side of the equation: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>$1 - \\cos \\theta$$1 + \\cos \\theta$\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Apply the difference of squares formula: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>$1 - \\cos \\theta$$1 + \\cos \\theta$ = 1 - \\cos^2 \\theta\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Use the Pythagorean identity: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1 - \\cos^2 \\theta = \\sin^2 \\theta\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Relate to the right side: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\sin^2 \\theta = \\frac{1}{\\csc^2 \\theta}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>",1096,219,"prove-the-trig-identity-1-cos-1-cos-1-csc-2",{"id":121,"category":36,"text_question":122,"photo_question":38,"text_answer":123,"step_text_answer":8,"step_photo_answer":8,"views":124,"likes":125,"slug":126},538035,"Prove the trig identity:\n\n Sec θ - Cos θ/Sec θ = Sin^2 θ","1. Start with the left-hand side $LHS$: \u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{LHS} = \\frac{\\sec \\theta - \\cos \\theta}{\\sec \\theta}\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\n2. Rewrite the terms in terms of sine and cosine:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\sec \\theta = \\frac{1}{\\cos \\theta}\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\n3. Substitute into the LHS:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{LHS} = \\frac{\\frac{1}{\\cos \\theta} - \\cos \\theta}{\\frac{1}{\\cos \\theta}}\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\n4. Simplify the expression inside the fraction:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= \\frac{\\frac{1 - \\cos^2 \\theta}{\\cos \\theta}}{\\frac{1}{\\cos \\theta}}\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\n5. Simplify further by multiplying by the reciprocal:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= $1 - \\cos^2 \\theta$\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Substitute the Pythagorean identity:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= \\sin^2 \\theta\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\nHence, the identity is proven since:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{\\sec \\theta - \\cos \\theta}{\\sec \\theta} = \\sin^2 \\theta\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\nSo, the right-hand side $RHS$ and transformed LHS are equal. \u003Cbr />\n\u003Cbr />\nThis completes the proof of the identity.",1434,287,"prove-the-trig-identity-sec-cos-sec-sin-2",{"id":128,"category":36,"text_question":129,"photo_question":38,"text_answer":130,"step_text_answer":8,"step_photo_answer":8,"views":131,"likes":132,"slug":133},538032,"How much is 18% of a kilometer?","18% of a kilometer can be calculated by multiplying 18% with the length of a kilometer. \u003Cbr />\n\u003Cbr />\n[SOLUTION] \u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 180 \\text{ meters} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n[STEP-BY-STEP]\u003Cbr />\n\u003Cbr />\n1. Convert percentage to a decimal.\u003Cbr />\n - 18% is the same as 0.18.\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 18\\% = \\frac{18}{100} = 0.18 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. A kilometer is 1,000 meters.\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 1 \\text{ kilometer} = 1000 \\text{ meters} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Calculate 18% of a kilometer in meters.\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 0.18 \\times 1000 = 180 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Therefore, 18% of a kilometer is:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 180 \\text{ meters} \u003C/math-field>\u003C/math-field>",520,104,"how-much-is-18-of-a-kilometer",{"id":135,"category":36,"text_question":136,"photo_question":38,"text_answer":137,"step_text_answer":8,"step_photo_answer":8,"views":138,"likes":139,"slug":140},538031,"How much is 10% of a kilogram?","1. A kilogram is equal to 1000 grams. \u003Cbr />\n\u003Cbr />\n2. To find 10% of a kilogram, calculate 10% of 1000 grams: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.1 \\times 1000 = 100\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\n3. Convert the result back to kilograms:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>100 \\, \\text{grams} = 0.1 \\, \\text{kg}\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\nThus, 10% of a kilogram is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.1 \\, \\text{kg}\u003C/math-field>\u003C/math-field>.",763,153,"how-much-is-10-of-a-kilogram",{"id":142,"category":36,"text_question":143,"photo_question":38,"text_answer":144,"step_text_answer":8,"step_photo_answer":8,"views":145,"likes":146,"slug":147},538030,"98/100 \nWrite the fraction as a decimal","1. Begin with the fraction \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{98}{100}\u003C/math-field>\u003C/math-field>. \u003Cbr />\n\u003Cbr />\n2. Convert the fraction to a decimal by dividing the numerator by the denominator: \u003Cbr />\n \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{98}{100} = 98 \\div 100 = 0.98\u003C/math-field>\u003C/math-field> \u003Cbr />\n \u003Cbr />\n3. Thus, the fraction \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{98}{100}\u003C/math-field>\u003C/math-field> is equivalent to the decimal 0.98.\u003Cbr />\n\u003Cbr />\nAnswer: 0.98",383,77,"98-100-write-the-fraction-as-a-decimal",{"id":149,"category":36,"text_question":150,"photo_question":38,"text_answer":151,"step_text_answer":8,"step_photo_answer":8,"views":152,"likes":153,"slug":154},538029,"$-3,-2$ and $-8, -2$\nFind the distance between 2 points","To find the distance between two points \\((-3,-2)\\) and \\((-8, -2)\\) in a 2D coordinate plane, we use the distance formula:\u003Cbr>\u003Cbr>1. The distance formula is: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> d = \\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Substitute the given points \\((-3, -2)\\) and \\((-8, -2)\\) into the formula:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> d = \\sqrt{((-8) - (-3))^2 + ((-2) - (-2))^2} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Simplify the expression inside the square root:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> d = \\sqrt{(-8 + 3)^2 + (0)^2} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> d = \\sqrt{(-5)^2 + 0} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Calculate:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> d = \\sqrt{25} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. Hence, the distance between the points is:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5\u003C/math-field>\u003C/math-field> units",1078,216,"3-2-and-8-2-find-the-distance-between-2-points",{"id":156,"category":36,"text_question":157,"photo_question":38,"text_answer":158,"step_text_answer":8,"step_photo_answer":8,"views":159,"likes":160,"slug":161},538028,"2.01c-6=-0.15c+6.96","Solution:\u003Cbr />\n1. Start with the given equation:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2.01c - 6 = -0.15c + 6.96\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Move all terms involving \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>c\u003C/math-field>\u003C/math-field> to one side by adding \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.15c\u003C/math-field>\u003C/math-field> to both sides:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2.01c + 0.15c = 6.96 + 6\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Simplify the equation:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2.16c = 12.96\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Solve for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>c\u003C/math-field>\u003C/math-field> by dividing both sides by \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2.16\u003C/math-field>\u003C/math-field>:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>c = \\frac{12.96}{2.16}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Calculate the value:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>c = 6\u003C/math-field>\u003C/math-field>",865,173,"2-01c-6-0-15c-6-96",{"id":163,"category":36,"text_question":164,"photo_question":38,"text_answer":165,"step_text_answer":8,"step_photo_answer":8,"views":166,"likes":167,"slug":168},538027,"1/4x+13>0.25(2x-32)","Solution:\u003Cbr />\n1. Given inequality:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{1}{4}x + 13 > 0.25(2x - 32)\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Simplify the right side:\u003Cbr />\n * Convert 0.25 to a fraction: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.25 = \\frac{1}{4}\u003C/math-field>\u003C/math-field>\u003Cbr />\n * Distribute: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{1}{4}(2x - 32) = \\frac{1}{4} \\cdot 2x - \\frac{1}{4} \\cdot 32 = \\frac{1}{2}x - 8\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Rewrite the inequality:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{1}{4}x + 13 > \\frac{1}{2}x - 8\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Eliminate fractions by multiplying all terms by 4:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x + 52 > 2x - 32\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Rearrange terms:\u003Cbr />\n * Subtract \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field> from both sides:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>52 > x - 32\u003C/math-field>\u003C/math-field>\u003Cbr />\n * Add 32 to both sides:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>84 > x\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. The solution to the inequality is:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x \u003C 84\u003C/math-field>\u003C/math-field>",301,60,"1-4x-13-0-25-2x-32",{"id":170,"category":36,"text_question":171,"photo_question":38,"text_answer":172,"step_text_answer":8,"step_photo_answer":8,"views":173,"likes":174,"slug":175},538026,"0.5(4x+24)=22x-2","Solution:\u003Cbr />\n1. Given equation:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.5(4x + 24) = 22x - 2\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Simplify the left side:\u003Cbr />\n- Apply the distributive property: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.5 \\times 4x + 0.5 \\times 24 = 22x - 2\u003C/math-field>\u003C/math-field>\u003Cbr />\n- This gives us: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2x + 12 = 22x - 2\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Rearrange to solve for x:\u003Cbr />\n- Subtract \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2x\u003C/math-field>\u003C/math-field> from both sides: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2x + 12 - 2x = 22x - 2 - 2x\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Simplify: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>12 = 20x - 2\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Add 2 to both sides to isolate terms:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>12 + 2 = 20x - 2 + 2\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Simplify: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>14 = 20x\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Divide by 20 to solve for x:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = \\frac{14}{20}\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Simplify the fraction: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = \\frac{7}{10}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nThe solution to the equation is $x = \\\\frac{7}{10}$.",614,123,"0-5-4x-24-22x-2",{"first":6,"last":177,"prev":8,"next":10},186,{"current_page":6,"from":6,"last_page":177,"links":179,"path":213,"per_page":214,"to":214,"total":215},[180,183,186,188,190,192,194,197,200,203,206,209,211],{"url":6,"label":181,"active":182},"1",true,{"url":10,"label":184,"active":185},"2",false,{"url":13,"label":187,"active":185},"3",{"url":16,"label":189,"active":185},"4",{"url":19,"label":191,"active":185},"5",{"url":22,"label":193,"active":185},"6",{"url":195,"label":196,"active":185},7,"7",{"url":198,"label":199,"active":185},8,"8",{"url":201,"label":202,"active":185},9,"9",{"url":204,"label":205,"active":185},10,"10",{"url":207,"label":208,"active":185},185,"185",{"url":177,"label":210,"active":185},"186",{"url":10,"label":212,"active":185},"Next »","https://api.math-master.org/api/question",20,3704,{"data":217},{"questions":218},[219,223,227,231,235,239,243,247,251,255,259,263,267,271,275,279,283,287,291,295],{"id":220,"category":36,"text_question":221,"slug":222},532052,"-6n+5=-13","6n-5-13",{"id":224,"category":36,"text_question":225,"slug":226},532068,"5/8 x 64","5-8-x-64",{"id":228,"category":36,"text_question":229,"slug":230},532082,"Calculate the 6th term of PA whose 1st term is 6.5 and the ratio 5","calculate-the-6th-term-of-pa-whose-1st-term-is-6-5-and-the-ratio-5",{"id":232,"category":36,"text_question":233,"slug":234},533893,"3(4x-1)-2(x+3)=7(x-1)+2","3-4x-1-2-x-3-7-x-1-2",{"id":236,"category":36,"text_question":237,"slug":238},533907,"X^2 = 25","x-2-25",{"id":240,"category":36,"text_question":241,"slug":242},533918,"5 people can complete a task in 72 hours. How many people are needed to complete the task in 60 hours.","5-people-can-complete-a-task-in-72-hours-how-many-people-are-needed-to-complete-the-task-in-60-hours",{"id":244,"category":36,"text_question":245,"slug":246},533993,"Two events E and F are​ ________ if the occurrence of event E in a probability experiment does not affect the probability of event F.","two-events-e-and-f-are-if-the-occurrence-of-event-e-in-a-probability-experiment-does-not-affect-the-probability-of-event-f",{"id":248,"category":36,"text_question":249,"slug":250},534002,"Equivalent expression of the sequence (3n-4)-(n-2)","equivalent-expression-of-the-sequence-3n-4-n-2",{"id":252,"category":36,"text_question":253,"slug":254},534084,"Determine the minimum degree that an algebraic equation can assume knowing that it admits 2 as a double root and -i as a triple root","determine-the-minimum-degree-that-an-algebraic-equation-can-assume-knowing-that-it-admits-2-as-a-double-root-and-i-as-a-triple-root",{"id":256,"category":36,"text_question":257,"slug":258},534105,"A pair of die is thrown and the absolute difference of the two scores is recorded. What is the probability of the absolute difference being 4 or more?","a-pair-of-die-is-thrown-and-the-absolute-difference-of-the-two-scores-is-recorded-what-is-the-probability-of-the-absolute-difference-being-4-or-more",{"id":260,"category":36,"text_question":261,"slug":262},534251,"A recurring sequence is one where\n elements repeat after completing one\n standard. If the sequence AB8C14D96AB8C1... is\n recurring its twentieth term is equal to:\n (A) B.\n (B) 8.\n (C) A.\n (D) 6.\n (E) D.","a-recurring-sequence-is-one-where-elements-repeat-after-completing-one-standard-if-the-sequence-ab8c14d96ab8c1-is-recurring-its-twentieth-term-is-equal-to-a-b-b-8-c-a-d-6-e",{"id":264,"category":36,"text_question":265,"slug":266},534273,"John he’s going to the carnival with his friends. He spends $25 on an admission ticket. He buys 10 games at X dollars each and two boxes of popcorn at Y dollars each. Write an expression to show the total cost of admission game, tickets and popcorn.","john-he-s-going-to-the-carnival-with-his-friends-he-spends-25-on-an-admission-ticket-he-buys-10-games-at-x-dollars-each-and-two-boxes-of-popcorn-at-y-dollars-each-write-an-expression-to-show-the-t",{"id":268,"category":36,"text_question":269,"slug":270},534421,"Kaya deposits 25,000 into an account that earns 3% interest compounded monthly. How much does Kaya have in the account after 6 years 8 months? Round to the nearest cent.\n\n32,912.50\n30,000\n29,923.71\n30,527.45","kaya-deposits-25-000-into-an-account-that-earns-3-interest-compounded-monthly-how-much-does-kaya-have-in-the-account-after-6-years-8-months-round-to-the-nearest-cent-32-912-50-30-000-29-923-71-30",{"id":272,"category":36,"text_question":273,"slug":274},534433,"A natural gas company has a fixed rate of 1,320 pesos plus 1,590 pesos per cubic meter of gas consumed monthly per customer.\n Indicate the cost function to determine the value in pesos of the cubic meters of gas consumed in a month per customer.\n How much did a customer who consumed 18 cubic meters of gas pay?\n If a customer paid 34,710 pesos, how many cubic meters of gas did he consume?","a-natural-gas-company-has-a-fixed-rate-of-1-320-pesos-plus-1-590-pesos-per-cubic-meter-of-gas-consumed-monthly-per-customer-indicate-the-cost-function-to-determine-the-value-in-pesos-of-the-cubic-me",{"id":276,"category":36,"text_question":277,"slug":278},534437,"nI Exercises 65-68, the latitudes of a pair of cities are given. Assume that one city si directly south of the other and that the earth is a perfect sphere of radius 4000 miles. Use the arc length formula in terms of degrees to find the distance between the two cities.\n65. The North Pole: latitude 90° north Springfield, Illinois: latitude 40° north","ni-exercises-65-68-the-latitudes-of-a-pair-of-cities-are-given-assume-that-one-city-si-directly-south-of-the-other-and-that-the-earth-is-a-perfect-sphere-of-radius-4000-miles-use-the-arc-length-for",{"id":280,"category":36,"text_question":281,"slug":282},534466,"A psychologist is investigating the levels of test anxiety in various university courses. Anxiety is measured on a scale ranging from 0 to 100, where 0 indicates the complete absence of anxiety and 100 represents an extreme level of anxiety.\n From the data obtained, it has been discovered that the psychology score is triple that of nursing, and in turn, the latter has a score 10 points lower than the nutrition major. Furthermore, the score in the veterinary degree is 15 points higher than that of nutrition. Finally, if we add the scores of all the races, we will obtain a total of 173 points.\n Pose the equation that represents the situation described in the previous problem and determine: What is the score that psychology obtained regarding its anxiety level before the exams?","a-psychologist-is-investigating-the-levels-of-test-anxiety-in-various-university-courses-anxiety-is-measured-on-a-scale-ranging-from-0-to-100-where-0-indicates-the-complete-absence-of-anxiety-and-10",{"id":284,"category":36,"text_question":285,"slug":286},534537,"2 - 6x = -16x + 28","2-6x-16x-28",{"id":288,"category":36,"text_question":289,"slug":290},534561,"A membership to the gym cost $25 per person in 1995. The membership cost has increased by an average $6 per person for each year since 1995. Write a linear equation for the cost of a gym membership for one person since 1995. What is the cost of a gym membership in 2009?","a-membership-to-the-gym-cost-25-per-person-in-1995-the-membership-cost-has-increased-by-an-average-6-per-person-for-each-year-since-1995-write-a-linear-equation-for-the-cost-of-a-gym-membership-fo",{"id":292,"category":36,"text_question":293,"slug":294},534580,"4m - 3t + 7 = 16","4m-3t-7-16",{"id":296,"category":36,"text_question":297,"slug":298},534684,"The domain of the function f(x)=x+7x2−144 \nis (−∞,), ( ,), and ( , ∞).","the-domain-of-the-function-f-x-x-7x2-144-is-and",{"data":300},{"id":301,"category":36,"slug":302,"text_question":303,"photo_question":8,"text_answer":304,"step_text_answer":8,"step_photo_answer":8,"views":305,"likes":306,"expert":307},532091,"the-value-of-sin-178-58-39","the value of sin 178°58'","0.0180",1125,225,{"id":308,"name":309,"photo":310,"biography":311,"created_at":8,"updated_at":8,"rating":312,"total_answer":313},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.",4.7,84,{"data":315},{"questions":316},[317,321,325,329,333,337,340,344,348,352,356,360,361,365,369,373,377,381,385,389],{"id":318,"category":36,"text_question":319,"slug":320},532002,"A particular employee arrives at work sometime between 8:00 a.m. and 8:50 a.m. Based on past experience the company has determined that the employee is equally likely to arrive at any time between 8:00 a.m. and 8:50 a.m. Find the probability that the employee will arrive between 8:05 a.m. and 8:40 a.m. Round your answer to four decimal places, if necessary.","a-particular-employee-arrives-at-work-sometime-between-8-00-a-m-and-8-50-a-m-based-on-past-experience-the-company-has-determined-that-the-employee-is-equally-likely-to-arrive-at-any-time-between-8-0",{"id":322,"category":36,"text_question":323,"slug":324},532033,"𝑦 = ( 𝑥2 − 3) (𝑥3 + 2 𝑥 + 1)","y-x2-3-x3-2-x-1",{"id":326,"category":36,"text_question":327,"slug":328},532058,"11(4x-9)= -319","11-4x-9-319",{"id":330,"category":36,"text_question":331,"slug":332},533889,"Suppose that a device has been created that launches objects at ground level and that its operation is modeled by the function h(x) = -4ײ + 256x, with h being the height (in meters) and x being the distance (in meters)\nWhat is the maximum height that the object reaches?","suppose-that-a-device-has-been-created-that-launches-objects-at-ground-level-and-that-its-operation-is-modeled-by-the-function-h-x-4-256x-with-h-being-the-height-in-meters-and-x-being-the-d",{"id":334,"category":36,"text_question":335,"slug":336},533961,"2.5 / 21.85","2-5-21-85",{"id":338,"category":36,"text_question":339,"slug":339},533975,"4x567",{"id":341,"category":36,"text_question":342,"slug":343},533983,"An electrical company manufactures batteries that have a duration that is distributed approximately normally, with a mean of 700 hours and a standard deviation of 40 hours. Find the probability that a randomly selected battery has an average life of less than 810 hours.","an-electrical-company-manufactures-batteries-that-have-a-duration-that-is-distributed-approximately-normally-with-a-mean-of-700-hours-and-a-standard-deviation-of-40-hours-find-the-probability-that-a",{"id":345,"category":36,"text_question":346,"slug":347},534015,"(5u + 6)-(3u+2)=","5u-6-3u-2",{"id":349,"category":36,"text_question":350,"slug":351},534214,"Nice's central library building is considered one of the most original in the world, as it is a mix between a sculpture and a work of habitable architecture. It was called La Tête Carrée and is made up of part of a bust that supports a cube divided into five floors.\n It is known that the building has a total height of approximately 30 meters. It admits that the cubic part of the sculpture is parallel to the floor and has a volume of 2744 meters3\n Calculate, in meters, the height of the bust that supports the cube.\n Displays all the calculations you made.","nice-s-central-library-building-is-considered-one-of-the-most-original-in-the-world-as-it-is-a-mix-between-a-sculpture-and-a-work-of-habitable-architecture-it-was-called-la-tete-carree-and-is-made-u",{"id":353,"category":36,"text_question":354,"slug":355},534266,"0.1x8.2","0-1x8-2",{"id":357,"category":36,"text_question":358,"slug":359},534312,"The sick-leave time of employees in a firm in a month is normally with a mean of 100 hours and a standard deviation of 20 hours. Find the probability that the sick-leave time of an employee in a month exceeds 130 hours.","the-sick-leave-time-of-employees-in-a-firm-in-a-month-is-normally-with-a-mean-of-100-hours-and-a-standard-deviation-of-20-hours-find-the-probability-that-the-sick-leave-time-of-an-employee-in-a-month",{"id":272,"category":36,"text_question":273,"slug":274},{"id":362,"category":36,"text_question":363,"slug":364},534438,"1. A jeweler has two gold bars, with 80% purity and the other with 95% purity. How much of each must be melted to obtain a 5 kilo ingot with 86% purity?","1-a-jeweler-has-two-gold-bars-with-80-purity-and-the-other-with-95-purity-how-much-of-each-must-be-melted-to-obtain-a-5-kilo-ingot-with-86-purity",{"id":366,"category":36,"text_question":367,"slug":368},534460,"(6²-14)÷11•(-3)","6-14-11-3",{"id":370,"category":36,"text_question":371,"slug":372},534465,"Calculate the pH of a solution obtained by mixing 100ml of 0.2M HCl with 100ml of 0.1M NaOH","calculate-the-ph-of-a-solution-obtained-by-mixing-100ml-of-0-2m-hcl-with-100ml-of-0-1m-naoh",{"id":374,"category":36,"text_question":375,"slug":376},534546,"The mean of 4 numbers is 5 and the mean of 3 different numbers is 12. What is the mean of the 7 numbers together? Produce an algebraic solution. Guess and check is acceptable.","the-mean-of-4-numbers-is-5-and-the-mean-of-3-different-numbers-is-12-what-is-the-mean-of-the-7-numbers-together-produce-an-algebraic-solution-guess-and-check-is-acceptable",{"id":378,"category":36,"text_question":379,"slug":380},534570,"The inner radius of a spherical ball is 13 cm. How many liters of air are in it?\n Justify your answer!","the-inner-radius-of-a-spherical-ball-is-13-cm-how-many-liters-of-air-are-in-it-justify-your-answer",{"id":382,"category":36,"text_question":383,"slug":384},534623,"7-1=6\r\n6x2=12\r\n\r\nExplain that","7-1-6-6x2-12-explain-that",{"id":386,"category":36,"text_question":387,"slug":388},534644,"12[4 + (8 + 7) + 5]","12-4-8-7-5",{"id":390,"category":36,"text_question":391,"slug":392},534697,"Write a linear equation in the slope-intercept form. Slope of the line is -1 and goes through (8,4)","write-a-linear-equation-in-the-slope-intercept-form-slope-of-the-line-is-1-and-goes-through-8-4",{"data":394},[395,399,403],{"id":396,"question":397,"answer":398},144086,"Math Question: How many different ways can a committee of 5 members be selected from a pool of 10 candidates?","Answer: Using the combination formula, the number of ways to select the committee is given by C(10, 5) = 10! / (5! * (10 - 5)!) = 252.",{"id":400,"question":401,"answer":402},120062,"Math Question: What is the formula to find the volume of a cone, given its radius \"r\" and height \"h\"?","Answer: The formula to find the volume of a cone is V = (1/3)πr^2h, where V represents the volume, π is a constant (approximately equal to 3.14159), \"r\" is the radius, and \"h\" is the height of the cone.",{"id":404,"question":405,"answer":406},118264,"What is the measure of an angle bisector if one angle is 70 degrees and the other is 110 degrees?","The measure of the angle bisector is 90 degrees because it divides the angle into two congruent angles.",{"$sicons":408},{"bxl:facebook-circle":409,"bxl:instagram":413,"mdi:web":415,"la:apple":417,"ph:google-logo-bold":420,"ph:google-logo":423},{"left":410,"top":410,"width":411,"height":411,"rotate":410,"vFlip":185,"hFlip":185,"body":412},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":410,"top":410,"width":411,"height":411,"rotate":410,"vFlip":185,"hFlip":185,"body":414},"\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 0-6.008a3.004 3.004 0 0 1 0 6.008\"/>\u003Ccircle cx=\"16.806\" cy=\"7.207\" r=\"1.078\" fill=\"currentColor\"/>\u003Cpath fill=\"currentColor\" d=\"M20.533 6.111A4.6 4.6 0 0 0 17.9 3.479a6.6 6.6 0 0 0-2.186-.42c-.963-.042-1.268-.054-3.71-.054s-2.755 0-3.71.054a6.6 6.6 0 0 0-2.184.42a4.6 4.6 0 0 0-2.633 2.632a6.6 6.6 0 0 0-.419 2.186c-.043.962-.056 1.267-.056 3.71s0 2.753.056 3.71c.015.748.156 1.486.419 2.187a4.6 4.6 0 0 0 2.634 2.632a6.6 6.6 0 0 0 2.185.45c.963.042 1.268.055 3.71.055s2.755 0 3.71-.055a6.6 6.6 0 0 0 2.186-.419a4.6 4.6 0 0 0 2.633-2.633c.263-.7.404-1.438.419-2.186c.043-.962.056-1.267.056-3.71s0-2.753-.056-3.71a6.6 6.6 0 0 0-.421-2.217m-1.218 9.532a5 5 0 0 1-.311 1.688a3 3 0 0 1-1.712 1.711a5 5 0 0 1-1.67.311c-.95.044-1.218.055-3.654.055c-2.438 0-2.687 0-3.655-.055a5 5 0 0 1-1.669-.311a3 3 0 0 1-1.719-1.711a5.1 5.1 0 0 1-.311-1.669c-.043-.95-.053-1.218-.053-3.654s0-2.686.053-3.655a5 5 0 0 1 .311-1.687c.305-.789.93-1.41 1.719-1.712a5 5 0 0 1 1.669-.311c.951-.043 1.218-.055 3.655-.055s2.687 0 3.654.055a5 5 0 0 1 1.67.311a3 3 0 0 1 1.712 1.712a5.1 5.1 0 0 1 .311 1.669c.043.951.054 1.218.054 3.655s0 2.698-.043 3.654z\"/>",{"left":410,"top":410,"width":411,"height":411,"rotate":410,"vFlip":185,"hFlip":185,"body":416},"\u003Cpath fill=\"currentColor\" d=\"M16.36 14c.08-.66.14-1.32.14-2s-.06-1.34-.14-2h3.38c.16.64.26 1.31.26 2s-.1 1.36-.26 2m-5.15 5.56c.6-1.11 1.06-2.31 1.38-3.56h2.95a8.03 8.03 0 0 1-4.33 3.56M14.34 14H9.66c-.1-.66-.16-1.32-.16-2s.06-1.35.16-2h4.68c.09.65.16 1.32.16 2s-.07 1.34-.16 2M12 19.96c-.83-1.2-1.5-2.53-1.91-3.96h3.82c-.41 1.43-1.08 2.76-1.91 3.96M8 8H5.08A7.92 7.92 0 0 1 9.4 4.44C8.8 5.55 8.35 6.75 8 8m-2.92 8H8c.35 1.25.8 2.45 1.4 3.56A8 8 0 0 1 5.08 16m-.82-2C4.1 13.36 4 12.69 4 12s.1-1.36.26-2h3.38c-.08.66-.14 1.32-.14 2s.06 1.34.14 2M12 4.03c.83 1.2 1.5 2.54 1.91 3.97h-3.82c.41-1.43 1.08-2.77 1.91-3.97M18.92 8h-2.95a15.7 15.7 0 0 0-1.38-3.56c1.84.63 3.37 1.9 4.33 3.56M12 2C6.47 2 2 6.5 2 12a10 10 0 0 0 10 10a10 10 0 0 0 10-10A10 10 0 0 0 12 2\"/>",{"left":410,"top":410,"width":418,"height":418,"rotate":410,"vFlip":185,"hFlip":185,"body":419},32,"\u003Cpath fill=\"currentColor\" d=\"M20.844 2c-1.64 0-3.297.852-4.407 2.156v.032c-.789.98-1.644 2.527-1.375 4.312c-.128-.05-.136-.035-.28-.094c-.692-.281-1.548-.594-2.563-.594c-3.98 0-7 3.606-7 8.344c0 3.067 1.031 5.942 2.406 8.094c.688 1.078 1.469 1.965 2.281 2.625S11.57 28 12.531 28s1.68-.324 2.219-.563c.54-.238.957-.437 1.75-.437c.715 0 1.078.195 1.625.438c.547.242 1.293.562 2.281.562c1.07 0 1.98-.523 2.719-1.188s1.36-1.519 1.875-2.343c.516-.824.922-1.633 1.219-2.282c.148-.324.258-.593.343-.812s.13-.281.188-.531l.188-.813l-.75-.343a5.3 5.3 0 0 1-1.5-1.063c-.625-.637-1.157-1.508-1.157-2.844A4.08 4.08 0 0 1 24.563 13c.265-.309.542-.563.75-.719c.105-.078.187-.117.25-.156c.062-.04.05-.027.156-.094l.843-.531l-.562-.844c-1.633-2.511-4.246-2.844-5.281-2.844c-.48 0-.82.168-1.25.25c.242-.226.554-.367.75-.624c.004-.004-.004-.028 0-.032q.018-.016.031-.031h.031a6.16 6.16 0 0 0 1.563-4.438L21.78 2zm-1.188 2.313c-.172.66-.453 1.289-.906 1.78l-.063.063c-.382.516-.972.899-1.562 1.125c.164-.652.45-1.312.844-1.812c.008-.012.023-.02.031-.032c.438-.5 1.043-.875 1.656-1.125zm-7.437 5.5c.558 0 1.172.21 1.812.468s1.239.594 2.094.594c.852 0 1.496-.336 2.25-.594s1.559-.469 2.344-.469c.523 0 1.816.333 2.906 1.344c-.191.172-.36.297-.563.531a6.2 6.2 0 0 0-1.53 4.094c0 1.906.831 3.34 1.718 4.25c.55.563.89.696 1.313.938c-.055.125-.086.222-.157.375a19 19 0 0 1-1.093 2.062c-.454.727-1.004 1.434-1.532 1.907c-.527.472-1 .687-1.375.687c-.566 0-.898-.156-1.468-.406S17.581 25 16.5 25c-1.137 0-1.977.336-2.563.594c-.585.258-.89.406-1.406.406c-.246 0-.777-.2-1.375-.688c-.597-.488-1.254-1.23-1.844-2.156c-1.183-1.851-2.093-4.394-2.093-7c0-3.941 2.199-6.343 5-6.343\"/>",{"left":410,"top":410,"width":421,"height":421,"rotate":410,"vFlip":185,"hFlip":185,"body":422},256,"\u003Cpath fill=\"currentColor\" d=\"M228 128a100 100 0 1 1-22.86-63.64a12 12 0 0 1-18.51 15.28A76 76 0 1 0 203.05 140H128a12 12 0 0 1 0-24h88a12 12 0 0 1 12 12\"/>",{"left":410,"top":410,"width":421,"height":421,"rotate":410,"vFlip":185,"hFlip":185,"body":424},"\u003Cpath fill=\"currentColor\" d=\"M224 128a96 96 0 1 1-21.95-61.09a8 8 0 1 1-12.33 10.18A80 80 0 1 0 207.6 136H128a8 8 0 0 1 0-16h88a8 8 0 0 1 8 8\"/>",{"oVhJaef6Ht":8,"t96FybqVTi":8,"5lK7LS5al0":8,"5oSQ2a90xd":8,"nAw1Pszp0k":8,"2QISyIzlyM":8,"HGsO2Ckakl":8},"/general/the-value-of-sin-178-58-39"] AppleWebKit/537.36 $KHTML, like Gecko$ Chrome/64.0.3282.39 Safari/537.36",refreshOnResize:false}},app:{baseURL:"/",buildAssetsDir:"/_nuxt/",cdnURL:"https://gcdn.fx2.io/math-master.org/"}}