and Py = Price of Good Y $40$\n Calculate the equilibrium elasticity:\n a) 1.6\n b) -6\n c) 6\n d) 0.6","","Primero, vamos a encontrar el precio de equilibrio en el mercado de las pelotas de golf. Para esto, tenemos las funciones de demanda y oferta:\u003Cbr />\u003Cbr />Función de demanda: Q = 120 - 2Px - 2Py + 0,2I\u003Cbr />Función de oferta: Q = 2Px + 40\u003Cbr />\u003Cbr />Para encontrar el precio de equilibrio, igualamos las funciones de demanda y oferta:\u003Cbr />\u003Cbr />120 - 2Px - 2Py + 0,2I = 2Px + 40\u003Cbr />\u003Cbr />Simplificando la ecuación, tenemos:\u003Cbr />\u003Cbr />4Px + 2Py = 80 + 0,2I\u003Cbr />\u003Cbr />Reemplazamos los valores conocidos: I = 200 y Py = 40\u003Cbr />\u003Cbr />4Px + 2$40$ = 80 + 0,2$200$\u003Cbr />4Px + 80 = 80 + 40\u003Cbr />4Px = 40\u003Cbr />\u003Cbr />Dividimos ambos lados de la ecuación por 4:\u003Cbr />\u003Cbr />Px = 10\u003Cbr />\u003Cbr />Ahora que tenemos el precio de equilibrio $Px = 10$, podemos encontrar la cantidad de equilibrio utilizando la función de oferta:\u003Cbr />\u003Cbr />Q = 2Px + 40\u003Cbr />Q = 2$10$ + 40\u003Cbr />Q = 20 + 40\u003Cbr />Q = 60\u003Cbr />\u003Cbr />Por lo tanto, en el equilibrio, el precio es 10 y la cantidad es 60.\u003Cbr />\u003Cbr />Ahora calculemos la elasticidad en el equilibrio. La elasticidad de demanda se calcula utilizando la fórmula:\u003Cbr />\u003Cbr />Elasticidad = $% cambio en cantidad demandada$ / $% cambio en precio$\u003Cbr />\u003Cbr />Dado que estamos en el equilibrio, no hay cambios en el precio ni en la cantidad. Por lo tanto, la elasticidad en el equilibrio es 0.\u003Cbr />\u003Cbr />Respuesta: d) 0,6.",null,1290,258,"suppose-the-golf-ball-market-is-perfectly-competitive-and-the-functions-are-known-q-120-2px-2py-0-2i-q-2px-40-where-i-consumers-income-200-and-py-price-of-good-y-40-calculate-the",{"id":16,"category":7,"text_question":17,"photo_question":9,"text_answer":18,"step_text_answer":11,"step_photo_answer":11,"views":19,"likes":20,"slug":21},534115,"How many anagrams of the word SROMEC there that do not contain STROM, MOST, MOC or CEST as a subword?\r\nBy subword is meant anything that is created by omitting some letters - for example, the word EMROSCT contains both MOC and MOST as subwords.","6!-4!-3!-3!=684",1157,231,"how-many-anagrams-of-the-word-sromec-there-that-do-not-contain-strom-most-moc-or-cest-as-a-subword-by-subword-is-meant-anything-that-is-created-by-omitting-some-letters-for-example-the-word-emr",{"id":23,"category":7,"text_question":24,"photo_question":9,"text_answer":18,"step_text_answer":11,"step_photo_answer":11,"views":25,"likes":26,"slug":27},534114,"How many anagrams of the word STROMEC there that do not contain STROM, MOST, MOC or CEST as a subword?\nBy subword is meant anything that is created by omitting some letters - for example, the word EMROSCT contains both MOC and MOST as subwords.",305,61,"how-many-anagrams-of-the-word-stromec-there-that-do-not-contain-strom-most-moc-or-cest-as-a-subword-by-subword-is-meant-anything-that-is-created-by-omitting-some-letters-for-example-the-word-emr",{"id":29,"category":7,"text_question":30,"photo_question":9,"text_answer":31,"step_text_answer":11,"step_photo_answer":11,"views":32,"likes":33,"slug":34},534113,"There are four times as many roses as tulips in Claire’s garden. Claire picked half of the number of roses and 140 roses were left in the garden. How many roses and tulips were in the Garden the first?","Let's assume the number of tulips in Claire's garden is $x$. \u003Cbr />\u003Cbr />According to the information given, there are four times as many roses as tulips. Therefore, the number of roses in the garden is $4x$.\u003Cbr />\u003Cbr />Claire picked half of the number of roses, so she picked $\\frac{1}{2}(4x) = 2x$ roses.\u003Cbr />\u003Cbr />After Claire picked the roses, 140 roses were left in the garden. This means that $4x - 2x = 140$.\u003Cbr />\u003Cbr />Simplifying the equation, we have $2x = 140$.\u003Cbr />\u003Cbr />To find the value of $x$, we divide both sides of the equation by 2:\u003Cbr />\u003Cbr />$\\frac{2x}{2} = \\frac{140}{2}$\u003Cbr />\u003Cbr />$x = 70$\u003Cbr />\u003Cbr />So, there were 70 tulips in the garden initially.\u003Cbr />\u003Cbr />The number of roses in the garden is $4x = 4(70) = 280$.\u003Cbr />\u003Cbr />Answer: There were 70 tulips and 280 roses in the garden initially.",1320,264,"there-are-four-times-as-many-roses-as-tulips-in-claire-s-garden-claire-picked-half-of-the-number-of-roses-and-140-roses-were-left-in-the-garden-how-many-roses-and-tulips-were-in-the-garden-the-first",{"id":36,"category":7,"text_question":37,"photo_question":9,"text_answer":38,"step_text_answer":11,"step_photo_answer":11,"views":39,"likes":40,"slug":41},534112,"What is the total tolerance for a dimension from 1.996\" to 2.026*?","2.026-1.996=0.03",860,172,"what-is-the-total-tolerance-for-a-dimension-from-1-996-to-2-026",{"id":43,"category":7,"text_question":44,"photo_question":9,"text_answer":45,"step_text_answer":11,"step_photo_answer":11,"views":46,"likes":47,"slug":48},534111,"5.- From the probabilities:\n 𝐏$𝐁$ = 𝟑𝟎%\n 𝐏$𝐀 ∩ 𝐁$ = 𝟐𝟎%\n 𝐏$𝐀\n ̅$ = 𝟕𝟎%\n You are asked to calculate: 𝐏$𝐀 ∪ 𝐁$","To calculate the probability of the union of events A and B, you can use the probability addition rule:\n\u003Cmath-field read-only>\\[ P(A \\cup B) = P(A) + P(B) - P(A \\cap B) \\]\u003C/math-field>\nGiven the probabilities:\u003Cmath-field read-only>\\[ P(B) = 30\\% \\]\u003C/math-field>\u003Cmath-field read-only>\\[ P(A \\cap B) = 20\\% \\]\u003C/math-field>\nYou are asked to calculate \u003Cmath-field read-only>\\( P(A \\cup B) \\).\u003C/math-field>\nFirst, let's find P(A) using the complement rule:\u003Cmath-field read-only>\\[ P(\\overline{A}) = 70\\% \\]\u003C/math-field>\nThe complement rule states that \u003Cmath-field read-only>\\( P(\\overline{A}) = 1 - P(A) \\),\\: so\u003C/math-field>\u003Cmath-field read-only>\\[ P(A) = 1 - P(\\overline{A}) \\]\u003C/math-field>\u003Cmath-field read-only>\\[ P(A) = 1 - 0.70 = 0.30 \\]\u003C/math-field>\nNow, substitute these values into the probability addition rule:\u003Cmath-field read-only>\\[ P(A \\cup B) = P(A) + P(B) - P(A \\cap B) \\]\u003C/math-field>\u003Cmath-field read-only>\\[ P(A \\cup B) = 0.30 + 0.30 - 0.20 \\]\u003C/math-field>\u003Cmath-field read-only>\\[ P(A \\cup B) = 0.40 \\]\u003C/math-field>\nSo, the probability of the union of events A and B, \u003Cmath-field read-only>\\( P(A \\cup B) \\),\u003C/math-field> is 40%.",1055,211,"5-from-the-probabilities-p-b-30-p-a-b-20-p-a-70-you-are-asked-to-calculate-p-a-b",{"id":50,"category":7,"text_question":51,"photo_question":9,"text_answer":52,"step_text_answer":11,"step_photo_answer":11,"views":53,"likes":54,"slug":55},534110,"-3(-4x+5)=-6(7x-8)+9-10x","open bracket\n12x-15=-42x+48+9-10x\n12x-15= -52x+57\n52x+12x=57+15\n 64x=72\n x=9/8",1361,272,"3-4x-5-6-7x-8-9-10x",{"id":57,"category":7,"text_question":58,"photo_question":9,"text_answer":59,"step_text_answer":11,"step_photo_answer":11,"views":60,"likes":61,"slug":62},534109,"4x/2+5x-3/6=7/8-1/4-x","\u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;\npadding: 8px;\nborder-radius: 8px;\nborder: 1px solid rgba(0, 0, 0, .3);\nbox-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$\\frac{ 4x }{ 2 }+5x-\\frac{ 3 }{ 6 }=\\frac{ 5 }{ 8 }-x$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;\npadding: 8px;\nborder-radius: 8px;\nborder: 1px solid rgba(0, 0, 0, .3);\nbox-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$48x+120x-12=15-24x$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;\npadding: 8px;\nborder-radius: 8px;\nborder: 1px solid rgba(0, 0, 0, .3);\nbox-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$168x-12=15-24x$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;\npadding: 8px;\nborder-radius: 8px;\nborder: 1px solid rgba(0, 0, 0, .3);\nbox-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$168x-12+24x=15$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;\npadding: 8px;\nborder-radius: 8px;\nborder: 1px solid rgba(0, 0, 0, .3);\nbox-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$168x+24x=15+12$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;\npadding: 8px;\nborder-radius: 8px;\nborder: 1px solid rgba(0, 0, 0, .3);\nbox-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$192x=15+12$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;\npadding: 8px;\nborder-radius: 8px;\nborder: 1px solid rgba(0, 0, 0, .3);\nbox-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$192x=27$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;\npadding: 8px;\nborder-radius: 8px;\nborder: 1px solid rgba(0, 0, 0, .3);\nbox-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$\\begin{align*} & x=\\frac{ 9 }{ 64 } \\\\ & \\end{align*}$\u003C/math-field>\n \u003Cbr>\n \u003C/div>",856,171,"4x-2-5x-3-6-7-8-1-4-x",{"id":64,"category":7,"text_question":65,"photo_question":9,"text_answer":66,"step_text_answer":11,"step_photo_answer":11,"views":67,"likes":68,"slug":69},534108,"prove that if n odd integer then n^2+5 is even","An odd integer can be written in the form 2k + 1, where k is any integer.\n\nSo, if n is odd, we can write n = 2k + 1.\n\nThen, n^2 + 5 = (2k + 1)^2 + 5 = 4k^2 + 4k + 1 + 5 = 4k^2 + 4k + 6.\n\nWe can factor out a 2 from each term to get 2(2k^2 + 2k + 3).\n\nSince 2k^2 + 2k + 3 is an integer (because it’s a sum of integers), let’s denote it as m. So, we have n^2 + 5 = 2m.\n\nA number is even if it can be written in the form 2m, where m is an integer. Therefore, n^2 + 5 is even.",825,165,"prove-that-if-n-odd-integer-then-n-2-5-is-even",{"id":71,"category":7,"text_question":72,"photo_question":9,"text_answer":73,"step_text_answer":11,"step_photo_answer":11,"views":74,"likes":75,"slug":76},534107,"A force of 750 pounds compresses a spring 3 inches from its natural length, which is 15 inches. What will be the work done to compress it 3 inches more?","To determine the work done to compress the spring an additional 3 inches, we can utilize the formula for the elastic potential energy of a spring:\n\nU = 1/2 * k * x^2\n\nwhere:\n\nU is the elastic potential energy (in inch-pounds)\nk is the spring constant (in pounds per inch)\nx is the compression or extension of the spring (in inches)\n\nWe know that a force of 750 pounds compresses the spring 3 inches, so we can deduce the spring constant:\n\n750 pounds = k * 3 inches\nk = 250 pounds per inch\n\nNow, let's calculate the work done to compress the spring an additional 3 inches (from 3 inches to 6 inches):\n\nU = 1/2 * 250 pounds per inch * (3 inches)^2\nU = 1125 inch-pounds\nTherefore, the work done to compress the spring an additional 3 inches is 1125 inch-pounds.",1114,223,"a-force-of-750-pounds-compresses-a-spring-3-inches-from-its-natural-length-which-is-15-inches-what-will-be-the-work-done-to-compress-it-3-inches-more",{"id":78,"category":7,"text_question":79,"photo_question":9,"text_answer":80,"step_text_answer":11,"step_photo_answer":11,"views":81,"likes":82,"slug":83},534106,"Find the equation of the line perpendicular to −5𝑥−3𝑦+5=0 passing through the point (0,−2)","Rearranging the equation:\u003Cmath-field read-only> 3y=-5x+5 \u003C/math-field>\u003Cmath-field read-only> y=-\\frac{5}{3}x+\\frac{5}{3} \u003C/math-field>\nSo slope here is \u003Cmath-field read-only> -\\frac{5}{3} \u003C/math-field>\nSince it is perpendicular, slope should be negative reciprocal:\u003Cmath-field read-only> m_{perpendicular}=\\frac{3}{5} \u003C/math-field>\nEquation as it passes through (0,-2):\u003Cmath-field read-only> y-\\left(-2\\right)=\\frac{3}{5}\\left(x-0\\right) \u003C/math-field>\u003Cmath-field read-only> y+2=\\frac{3}{5}x \u003C/math-field>",906,181,"find-the-equation-of-the-line-perpendicular-to-5x-3y-5-0-passing-through-the-point-0-2",{"id":85,"category":7,"text_question":86,"photo_question":9,"text_answer":87,"step_text_answer":11,"step_photo_answer":11,"views":88,"likes":89,"slug":90},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?","(1, 6), (6, 1), (1,5), (5, 1), (2, 6), (6, 2) favorable 6 cases\nTotal 36 cases\nProbability 6/36= 1/6",1158,232,"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":92,"category":7,"text_question":93,"photo_question":9,"text_answer":94,"step_text_answer":11,"step_photo_answer":11,"views":95,"likes":96,"slug":97},534104,"78 percent to a decimal","\u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;\npadding: 8px;\nborder-radius: 8px;\nborder: 1px solid rgba(0, 0, 0, .3);\nbox-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$\\frac{ 78 }{ 100 }$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;\npadding: 8px;\nborder-radius: 8px;\nborder: 1px solid rgba(0, 0, 0, .3);\nbox-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$0.78$\u003C/math-field>\n \u003Cbr>\n \u003C/div>",1042,208,"78-percent-to-a-decimal",{"id":99,"category":7,"text_question":100,"photo_question":9,"text_answer":94,"step_text_answer":11,"step_photo_answer":11,"views":101,"likes":102,"slug":103},534103,"Convert 78 percent to a decimal",997,199,"convert-78-percent-to-a-decimal",{"id":105,"category":7,"text_question":106,"photo_question":9,"text_answer":107,"step_text_answer":11,"step_photo_answer":11,"views":108,"likes":109,"slug":110},534102,"logy/logx + logz/logy + logt/logz = 8x².t \r\nx=?","its take too long for step by step so i can send only answer.\n\u003Cmath-field read-only>\\sqrt{\\frac{z^{8x^{2}t}}{y}}\u003C/math-field>",423,85,"logy-logx-logz-logy-logt-logz-8x-t-x",{"id":112,"category":7,"text_question":113,"photo_question":9,"text_answer":114,"step_text_answer":11,"step_photo_answer":11,"views":115,"likes":116,"slug":117},534101,"find all matrices that commute with the matrix A=[0 1]","To find all matrices that commute with the matrix A, we need to find matrices B such that AB = BA.\u003Cbr />\u003Cbr />Let B be the matrix:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> B = \\begin{bmatrix} a & b \\ c & d \\end{bmatrix} \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Now, let's multiply AB and BA and set them equal to each other:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> AB = \\begin{bmatrix} 0 & 1 \\ 0 & 0 \\end{bmatrix} \\begin{bmatrix} a & b \\ c & d \\end{bmatrix} = \\begin{bmatrix} c & d \\ 0 & 0 \\end{bmatrix} \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> BA = \\begin{bmatrix} a & b \\ c & d \\end{bmatrix} \\begin{bmatrix} 0 & 1 \\ 0 & 0 \\end{bmatrix} = \\begin{bmatrix} 0 & a \\ 0 & c \\end{bmatrix} \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Setting AB and BA equal to each other:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\begin{bmatrix} c & d \\ 0 & 0 \\end{bmatrix} = \\begin{bmatrix} 0 & a \\ 0 & c \\end{bmatrix} \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Comparing the entries, we get the following equations:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> c = 0 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> d = a \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />This means that any matrix B that commutes with A has the form:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> B = \\begin{bmatrix} a & b \\ 0 & a \\end{bmatrix} \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />So, the matrices that commute with A are of the form:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\begin{bmatrix} a & b \\ 0 & a \\end{bmatrix} \u003C/math-field>\u003C/math-field>\u003Cbr />where a and b can be any real numbers.\u003Cbr />\u003Cbr />Answer: The matrices that commute with A are in the form \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\begin{bmatrix} a & b \\ 0 & a \\end{bmatrix}\u003C/math-field>\u003C/math-field>, where a and b can be any real numbers.",296,59,"find-all-matrices-that-commute-with-the-matrix-a-0-1",{"id":119,"category":7,"text_question":120,"photo_question":9,"text_answer":121,"step_text_answer":11,"step_photo_answer":11,"views":122,"likes":123,"slug":124},534100,"Reparameterize the curve r(t)= cos(t)i without (t)j (t)k by the arc length.","Para reparametrizar a curva \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\mathbf{r}(t) = \\cos(t)\\mathbf{i} + \\sin(t)\\mathbf{j} + t\\mathbf{k}\u003C/math-field>\u003C/math-field> pelo comprimento de arco, primeiro precisamos calcular o comprimento de arco \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s(t)\u003C/math-field>\u003C/math-field> da curva.\u003Cbr />\u003Cbr />O comprimento de arco \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s(t)\u003C/math-field>\u003C/math-field> é dado por:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s(t) = \\int_{a}^{t} |\\mathbf{r}'(\\tau)| \\ d\\tau\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Onde \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\mathbf{r}'(\\tau)\u003C/math-field>\u003C/math-field> é a derivada de \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\mathbf{r}(t)\u003C/math-field>\u003C/math-field> em relação a \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\tau\u003C/math-field>\u003C/math-field>, e \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a\u003C/math-field>\u003C/math-field> é uma constante de integração que podemos escolher. Vamos escolher \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a = 0\u003C/math-field>\u003C/math-field> para simplificar o cálculo.\u003Cbr />\u003Cbr />A derivada de \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\mathbf{r}(t)\u003C/math-field>\u003C/math-field> em relação a \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>t\u003C/math-field>\u003C/math-field> é dada por:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\mathbf{r}'(t) = -\\sin(t)\\mathbf{i} + \\cos(t)\\mathbf{j} + \\mathbf{k}\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Então, podemos calcular \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>|\\mathbf{r}'(t)|\u003C/math-field>\u003C/math-field>:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>|\\mathbf{r}'(t)| = \\sqrt{(-\\sin(t))^2 + (\\cos(t))^2 + 1} = \\sqrt{2}\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Agora, podemos escrever a expressão para \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s(t)\u003C/math-field>\u003C/math-field>:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s(t) = \\int_{0}^{t} \\sqrt{2} \\ d\\tau = \\sqrt{2}t\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Para reparametrizar a curva pelo comprimento de arco, precisamos inverter a fórmula anterior para resolver em termos de \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>t\u003C/math-field>\u003C/math-field>. Temos:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>t = \\frac{s}{\\sqrt{2}}\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Agora, substituímos \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>t\u003C/math-field>\u003C/math-field> novamente na expressão original da curva \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\mathbf{r}(t)\u003C/math-field>\u003C/math-field>:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\mathbf{r}(s) = \\cos\\left(\\frac{s}{\\sqrt{2}}\\right)\\mathbf{i} + \\sin\\left(\\frac{s}{\\sqrt{2}}\\right)\\mathbf{j} + \\frac{s}{\\sqrt{2}}\\mathbf{k}\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Portanto, a curva \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\mathbf{r}(t) = \\cos(t)\\mathbf{i} + \\sin(t)\\mathbf{j} + t\\mathbf{k}\u003C/math-field>\u003C/math-field> reparametrizada pelo comprimento de arco é:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\mathbf{r}(s) = \\cos\\left(\\frac{s}{\\sqrt{2}}\\right)\\mathbf{i} + \\sin\\left(\\frac{s}{\\sqrt{2}}\\right)\\mathbf{j} + \\frac{s}{\\sqrt{2}}\\mathbf{k}\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Resposta: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\mathbf{r}(s) = \\cos\\left(\\frac{s}{\\sqrt{2}}\\right)\\mathbf{i} + \\sin\\left(\\frac{s}{\\sqrt{2}}\\right)\\mathbf{j} + \\frac{s}{\\sqrt{2}}\\mathbf{k}\u003C/math-field>\u003C/math-field>",470,94,"reparameterize-the-curve-r-t-cos-t-i-without-t-j-t-k-by-the-arc-length",{"id":126,"category":7,"text_question":127,"photo_question":9,"text_answer":128,"step_text_answer":11,"step_photo_answer":11,"views":129,"likes":130,"slug":131},534099,"(5y 9)-(y 7)","4y+2",527,105,"5y-9-y-7",{"id":133,"category":7,"text_question":134,"photo_question":9,"text_answer":135,"step_text_answer":11,"step_photo_answer":11,"views":136,"likes":137,"slug":138},534098,"A person borrows rm 1000 from a bank at an interest rate of 10%. After some time, he pays the bank rm 1900 as full and final settlement of the loan. Estimate the duration of his loan.","Given:\nTotal amount=A=1900.\nPrincipal amount=P=1000.\nannual interest rate=r=0.1%.\nCompound interest:\n\u003Cmath-field read-only> A=P\\left(1+\\frac{r}{100}\\right)^n \u003C/math-field>\nSubstitute the given values in above formula, we get\n\u003Cmath-field read-only> 1900=1000\\left(1+0.1\\right)^n \u003C/math-field>\n\u003Cmath-field read-only> 1.1^n=\\frac{1900}{1000} \u003C/math-field>\n\u003Cmath-field read-only> 1.1^n=1.9 \u003C/math-field>\napply natural logarithm on both sides, we get\n\u003Cmath-field read-only> \\ln\\left(1.1^n\\right)=\\ln\\left(1.9\\right) \u003C/math-field>\n\u003Cmath-field read-only> n\\cdot\\ln\\left(1.1\\right)=\\ln\\left(1.9\\right) \u003C/math-field>\n\u003Cmath-field read-only> n=\\frac{\\ln\\left(1.9\\right)}{\\ln\\left(1.1\\right)} \u003C/math-field>\nn=6.734.\nTherefore, The duration of the loan in compounding period is 6.734.",1375,275,"a-person-borrows-rm-1000-from-a-bank-at-an-interest-rate-of-10-after-some-time-he-pays-the-bank-rm-1900-as-full-and-final-settlement-of-the-loan-estimate-the-duration-of-his-loan",{"id":140,"category":7,"text_question":141,"photo_question":9,"text_answer":142,"step_text_answer":11,"step_photo_answer":11,"views":143,"likes":144,"slug":145},534097,"Pedro had 80% of the amount needed to buy a game. Of this amount, you spent 15% on a watch and therefore, you will need to add another R$640.00 to purchase this game. Is the value of the game?","Answer:\n\n2000\n\nStep by step solution:\n\nLet x be the amount of the game.\nAt first you have 80% of the amount. So, it is 0.8x.\n\n15% of that, you used, that is (0.8x)(0.15)\n\nWe subtract that to the initial amount, 0.8x-(0.8x)(0.15)\n\nThe difference is 640 less than the amount of game, x - 640\n\nSo, we have x - 640 = 0.8x - (0.8x)(0.15)\n\nSolve for x.\n\nx = 2000",558,112,"pedro-had-80-of-the-amount-needed-to-buy-a-game-of-this-amount-you-spent-15-on-a-watch-and-therefore-you-will-need-to-add-another-r-640-00-to-purchase-this-game-is-the-value-of-the-game",{"first":147,"last":148,"prev":61,"next":149},1,188,173,{"current_page":40,"from":151,"last_page":148,"links":152,"path":187,"per_page":188,"to":189,"total":190},3421,[153,156,158,161,164,167,169,172,174,177,180,183,185],{"url":61,"label":154,"active":155},"« Previous",false,{"url":147,"label":157,"active":155},"1",{"url":159,"label":160,"active":155},2,"2",{"url":162,"label":163,"active":155},169,"169",{"url":165,"label":166,"active":155},170,"170",{"url":61,"label":168,"active":155},"171",{"url":40,"label":170,"active":171},"172",true,{"url":149,"label":173,"active":155},"173",{"url":175,"label":176,"active":155},174,"174",{"url":178,"label":179,"active":155},175,"175",{"url":181,"label":182,"active":155},187,"187",{"url":148,"label":184,"active":155},"188",{"url":149,"label":186,"active":155},"Next »","https://api.math-master.org/api/question",20,3440,3743,{"data":192},[193,195,197,200,203,206],{"id":147,"title":194,"slug":11},"Algebra",{"id":159,"title":196,"slug":11},"Geometry",{"id":198,"title":199,"slug":11},3,"Coordinate-geometry",{"id":201,"title":202,"slug":11},4,"Statistics",{"id":204,"title":205,"slug":11},5,"Calculus",{"id":207,"title":208,"slug":11},6,"General",{"data":210},[211,212,213,214,215,216],{"id":147,"title":194,"slug":11},{"id":159,"title":196,"slug":11},{"id":198,"title":199,"slug":11},{"id":201,"title":202,"slug":11},{"id":204,"title":205,"slug":11},{"id":207,"title":208,"slug":11},{"data":218},[219,228,236,246,258,267,276,285,297,305,316,323,335,344,350,357,365,376,384,394],{"id":220,"name":221,"photo":222,"certificates":223,"diplomas":225,"biography":226,"rating":227,"total_answer":123},19,"Seamus","https://api.math-master.org/img/experts/19/19.webp",[224],"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,{"id":229,"name":230,"photo":231,"certificates":232,"diplomas":233,"biography":235,"rating":227,"total_answer":109},18,"Nash","https://api.math-master.org/img/experts/18/18.webp",[],[234],"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",{"id":237,"name":238,"photo":239,"certificates":240,"diplomas":242,"biography":244,"rating":227,"total_answer":245},15,"Miles","https://api.math-master.org/img/experts/15/15.webp",[241],"https://api.math-master.org/img/experts/15/certificates/2fd3f3a1-34c4-417d-a85a-1459c7fc0356.webp",[243],"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":198,"name":247,"photo":248,"certificates":249,"diplomas":253,"biography":255,"rating":256,"total_answer":257},"Timmothy","https://api.math-master.org/img/experts/3/3.webp",[250,251,252],"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",[254],"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.",4.8,96,{"id":259,"name":260,"photo":261,"certificates":262,"diplomas":263,"biography":265,"rating":256,"total_answer":266},22,"Hank","https://api.math-master.org/img/experts/22/22.webp",[],[264],"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":268,"name":269,"photo":270,"certificates":271,"diplomas":272,"biography":274,"rating":256,"total_answer":275},35,"Hester","https://api.math-master.org/img/experts/35/35.webp",[],[273],"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":277,"name":278,"photo":279,"certificates":280,"diplomas":282,"biography":284,"rating":256,"total_answer":245},14,"Brice","https://api.math-master.org/img/experts/14/14.webp",[281],"https://api.math-master.org/img/experts/14/certificates/a53728ab-4dc7-40ba-8d75-9938dd4881d9.webp",[283],"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":286,"name":287,"photo":288,"certificates":289,"diplomas":292,"biography":294,"rating":295,"total_answer":296},28,"Esmeralda","https://api.math-master.org/img/experts/28/28.webp",[290,291],"https://api.math-master.org/img/experts/28/certificates/883 C.webp","https://api.math-master.org/img/experts/28/certificates/883 CC.webp",[293],"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":298,"name":299,"photo":300,"certificates":301,"diplomas":302,"biography":303,"rating":295,"total_answer":304},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.",86,{"id":306,"name":307,"photo":308,"certificates":309,"diplomas":313,"biography":314,"rating":295,"total_answer":315},13,"Maude","https://api.math-master.org/img/experts/13/13.webp",[310,311,312],"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.",104,{"id":317,"name":318,"photo":319,"certificates":320,"diplomas":321,"biography":322,"rating":295,"total_answer":144},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.",{"id":324,"name":325,"photo":326,"certificates":327,"diplomas":332,"biography":333,"rating":295,"total_answer":334},16,"\nClarabelle","https://api.math-master.org/img/experts/16/16.webp",[328,329,330,331],"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",91,{"id":207,"name":336,"photo":337,"certificates":338,"diplomas":341,"biography":343,"rating":295,"total_answer":123},"Jett","https://api.math-master.org/img/experts/6/6.webp",[339,340],"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",[342],"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":204,"name":345,"photo":346,"certificates":347,"diplomas":348,"biography":349,"rating":295,"total_answer":130},"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":351,"name":352,"photo":353,"certificates":354,"diplomas":355,"biography":356,"rating":295,"total_answer":245},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":159,"name":358,"photo":359,"certificates":360,"diplomas":361,"biography":363,"rating":364,"total_answer":315},"Corbin","https://api.math-master.org/img/experts/2/2.webp",[],[362],"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":366,"name":367,"photo":368,"certificates":369,"diplomas":370,"biography":374,"rating":364,"total_answer":375},29,"Eliseo","https://api.math-master.org/img/experts/29/29.webp",[],[371,372,373],"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.",107,{"id":377,"name":378,"photo":379,"certificates":380,"diplomas":381,"biography":382,"rating":364,"total_answer":383},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":385,"name":386,"photo":387,"certificates":388,"diplomas":389,"biography":392,"rating":364,"total_answer":393},31,"Frederik","https://api.math-master.org/img/experts/31/31.webp",[],[390,391],"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":395,"name":396,"photo":397,"certificates":398,"diplomas":400,"biography":402,"rating":364,"total_answer":245},21,"Jon","https://api.math-master.org/img/experts/21/21.webp",[399],"https://api.math-master.org/img/experts/21/certificates/41e2a05c-d94f-4bcc-9258-f2a7fe4c3c02.webp",[401],"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.",{"data":404},{"questions":405},[406,410,414,418,422,426,430,434,438,442,446,450,454,458,462,466,470,474,478,482],{"id":407,"category":7,"text_question":408,"slug":409},532006,"a to the power of 2 minus 16 over a plus 4, what is the result?","a-to-the-power-of-2-minus-16-over-a-plus-4-what-is-the-result",{"id":411,"category":7,"text_question":412,"slug":413},532013,"Using a remarkable product you must factor the expression: f(x) =36x^2-324 and you are entitled to 5 steps","using-a-remarkable-product-you-must-factor-the-expression-f-x-36x-2-324-and-you-are-entitled-to-5-steps",{"id":415,"category":7,"text_question":416,"slug":417},532035,"I want to divide R$ 2200.00 between Antônio, Beto and Cássia, so that Beto receives half from Antônio and Cássia receives a third of Beto. Under these conditions, how much more will Beto receive than Cássia?","i-want-to-divide-r-2200-00-between-antonio-beto-and-cassia-so-that-beto-receives-half-from-antonio-and-cassia-receives-a-third-of-beto-under-these-conditions-how-much-more-will-beto-receive-than",{"id":419,"category":7,"text_question":420,"slug":421},532063,"The sum of an infinite geometric series is 13,5 \r\n The sum of the same series, calculated from the third term is 1,5.\r\n Q. Calculate r if r>0.","the-sum-of-an-infinite-geometric-series-is-13-5-the-sum-of-the-same-series-calculated-from-the-third-term-is-1-5-q-calculate-r-if-r-0",{"id":423,"category":7,"text_question":424,"slug":425},532075,"QUESTION l. An investigation has been carried out in a region to know the perception of "citizen insecurity" of its inhabitants. 1,270 people in the region were interviewed, of which 27.1% responded that it was a "serious" problem. Knowing that this opinion was previously held by 25.3% of the population of that region, we want to know if said opinion has changed significantly for a confidence level of 97.2%. Taking this statement into account, the following is requested: a) Critical value of the contrast statistic. b) Solve the hypothesis test and indicate what conclusion we can reach. c) P-value of contrast.","question-l-an-investigation-has-been-carried-out-in-a-region-to-know-the-perception-of-quot-citizen-insecurity-quot-of-its-inhabitants-1-270-people-in-the-region-were-interviewed-of-which-27-1-r",{"id":427,"category":7,"text_question":428,"slug":429},533895,"what is 456456446+24566457","what-is-456456446-24566457",{"id":431,"category":7,"text_question":432,"slug":433},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":435,"category":7,"text_question":436,"slug":437},534064,"We have spent 1/4 of the inheritance on taxes and 3/5 of the rest on buying a house. If the inheritance was a total of €150,000\n How much money do we have left?","we-have-spent-1-4-of-the-inheritance-on-taxes-and-3-5-of-the-rest-on-buying-a-house-if-the-inheritance-was-a-total-of-150-000-how-much-money-do-we-have-left",{"id":439,"category":7,"text_question":440,"slug":441},534072,"Find the sum of the first 41 terms of the progression that\r\nbegins: 32, 24, 16, …","find-the-sum-of-the-first-41-terms-of-the-progression-that-begins-32-24-16",{"id":443,"category":7,"text_question":444,"slug":445},534130,"solve for x\n50x+ 120 (176-x)= 17340","solve-for-x-50x-120-176-x-17340",{"id":447,"category":7,"text_question":448,"slug":449},534136,"Prove that it is not possible to arrange the integers 1 to 240 in a table with 15 rows and 16 columns in such a way that the sum of the numbers in each of the columns is the same.","prove-that-it-is-not-possible-to-arrange-the-integers-1-to-240-in-a-table-with-15-rows-and-16-columns-in-such-a-way-that-the-sum-of-the-numbers-in-each-of-the-columns-is-the-same",{"id":451,"category":7,"text_question":452,"slug":453},534279,"Which of the methods below can be used to workout 95% of an amount?\na. Dividing the amount 100 and multiply by 95\nb. Working out 5% of the amount and taking it away from the full amount\nc. Dividing 95 by 100 and multiplying the answer by the amount\nd. Dividing the amount by 95 and then multiply by 100","which-of-the-methods-below-can-be-used-to-workout-95-of-an-amount-a-dividing-the-amount-100-and-multiply-by-95-b-working-out-5-of-the-amount-and-taking-it-away-from-the-full-amount-c-dividing-95",{"id":455,"category":7,"text_question":456,"slug":457},534303,"Using the bank and exact method, calculate the interest on capital 10000 at 12% annual nominal interest rate for the period from 15.3. 2016 until 10/10/2016","using-the-bank-and-exact-method-calculate-the-interest-on-capital-10000-at-12-annual-nominal-interest-rate-for-the-period-from-15-3-2016-until-10-10-2016",{"id":459,"category":7,"text_question":460,"slug":461},534317,"In a company dedicated to packaging beer in 750 mL containers, a normal distribution is handled in its packaging process, which registers an average of 745 mL and a standard deviation of 8 mL.\n Determine:\n a) The probability that a randomly selected container exceeds 765 mL of beer\n b) The probability that the beer content of a randomly selected container is between 735 and 755 mL.","in-a-company-dedicated-to-packaging-beer-in-750-ml-containers-a-normal-distribution-is-handled-in-its-packaging-process-which-registers-an-average-of-745-ml-and-a-standard-deviation-of-8-ml-determ",{"id":463,"category":7,"text_question":464,"slug":465},534354,"Jasminder has made 55% of the recipes in a particular cookbook. If there are 9 recipes that he has never\nmade, how many recipes does the cookbook contain?","jasminder-has-made-55-of-the-recipes-in-a-particular-cookbook-if-there-are-9-recipes-that-he-has-never-made-how-many-recipes-does-the-cookbook-contain",{"id":467,"category":7,"text_question":468,"slug":469},534377,"The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion is greater than 35%, then the lab will modify a proposed enlargement of its facilities. Suppose a hypothesis test is conducted and the test statistic is z= 2.6. Find the P-value for this test.","the-business-college-computing-center-wants-to-determine-the-proportion-of-business-students-who-have-personal-computers-pc-s-at-home-if-the-proportion-is-greater-than-35-then-the-lab-will-modify",{"id":471,"category":7,"text_question":472,"slug":473},534389,"We have received our p&l statement back from accounts. The board has asked for an innovation hub. What items should we prioritise reviewing to decide if we can afford an innovation hub?","we-have-received-our-p-l-statement-back-from-accounts-the-board-has-asked-for-an-innovation-hub-what-items-should-we-prioritise-reviewing-to-decide-if-we-can-afford-an-innovation-hub",{"id":475,"category":7,"text_question":476,"slug":477},534451,"Pablo has a balance of $440,000 and 2/5 of the money is used to pay bills. How much money do you have left after paying the bills?","pablo-has-a-balance-of-440-000-and-2-5-of-the-money-is-used-to-pay-bills-how-much-money-do-you-have-left-after-paying-the-bills",{"id":479,"category":7,"text_question":480,"slug":481},534628,"Triangle ABC has AB=AC and angle BAC =X, with X being less than 60 degrees. \n\nPoint D lies on AB such that CB = CD\n\nPoint E lies on AC such that CE= DE\n\nDetermine angle DEC in terms of X","triangle-abc-has-ab-ac-and-angle-bac-x-with-x-being-less-than-60-degrees-point-d-lies-on-ab-such-that-cb-cd-point-e-lies-on-ac-such-that-ce-de-determine-angle-dec-in-terms-of-x",{"id":483,"category":7,"text_question":484,"slug":485},534673,"Exercise\n The temperature T in degrees Celsius of a chemical reaction is\n given as a function of time t, expressed in minutes, by the function\n defined on ¿ by: T (t )=(20 t +10)e−0.5t.\n 1) What is the initial temperature?\n 2) Show that T' (t )=(−10 t +15)e−0 .5t.\n 3) Study the sign of T' (t ), then draw up the table of variations of T\n . We do not ask for the limit of T in +∞.\n 4) What is the maximum temperature reached by the reaction\n chemical. We will give an approximate value to within 10−2.\n 5) After how long does the temperature T go back down\n to its initial value? We will give an approximate value of this\n time in minutes and seconds.\n DM 2: study of a function\n Exercise\n The temperature T in degrees Celsius of a chemical reaction is\n given as a function of time t, expressed in minutes, by the function\n defined on ¿ by: T (t )=(20 t +10)e−0.5t.\n 1) What is the initial temperature?\n 2) Show that T' (t )=(−10 t +15)e−0.5 t.\n 3) Study the sign of T' (t ), then draw up the table of variations of T\n . We do not ask for the limit of T in +∞.\n 4) What is the maximum temperature reached by the reaction\n chemical. We will give an approximate value to within 10−2.\n 5) After how long does the temperature T go back down\n to its initial value? 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