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If the rate of change of Q is directly proportional to Q, and if Q(0) = 100 and Q(4) = 440, find k, the proportionality constant. O K = 0.370 O k= 1.482 12.01 Semester Test: Calculus O k = 4.605 lus O k = 6.087 *: "val voBlogs-yofb-419c-a486-ace0599ac widths.myschoolapp. E 12.01 Semester Test: Calculus Find the equation of the curve that pass rough the point (0, It) and has a slope of - sin y at any point (x, y). CUILAILVI. O y = cos (x2 - 1) lculus o y = cos-1(x2 + #) o y = cos(x2) O y = Cos-1(x2 - 7) 1 80 81 82 83 84 85 89 87 80 89 If the rate of change of T is proportional to (20 + T), where T > -20, and if T(0) = 2 and T(4) = 10, find T(20). Calculus 86.643 O 84.31 O 83.652 O 81.745 Given the initial condition y(0) = 1. find the particular solution of the equation yy' - 6x = 0 deeuby9ad9a3.sequence. Oy = V3x2 + 0.5 warilyschoolapp.. o y = 2v3x2 + 0.5 12.01 Semester Test: Calculus o y = V6x2 - 1 o y = Vox2 + 1 culus alculus If the acceleration A(t) of an object is inversely proportional to the square of its speed S(t); write the differential equation for the acceleration of the object. Find the general solution to the equation: y' = 6132 Do not solve oy = - 3x+CI O A(1) = = - o y= -+ + CI A(1) = = 4 O Y = - THE O A(1) = 15 = k$2 oy = 372 + CI O A(1) = ds = VS 4 83 84 85 86 87 88 89 90 91 92 Next Calculus 12.01 Semester Test: Calculus VILBILVI. culus Rewrite the following equation with the variables separated: 2y' = te' 0 2 = adx dy The rate of change in the number of cows, W. in a population is proportional to 150 - W(t), where t is measured in years. 207 Write the differential equation to solve for W(t). Do not solve. 4 77 78 79 80 81 8: aw = (150 - 1)k o aw = (150 + W)k FILVILASILVI. ow = (150 - W)k alculus ow = 150-W 1 82 83 84 85 86 87 88 89 96 wuniceusequenceviewer/2969417?url=https342F%2F/59af8a9-9 419c-a486-ace0599ad9a3.sequence... dths.myschoolapp.. Rewrite the following equation with the variables separated: 3y' = 5*+y. 12.01 Semester Test: Calculus O ay ILVI. us dy _ dx 7 . 5) 0 = 5 dx If the rate of change in the number of children that attend a carnival was found to be proportional to the square of the number 0 * = 2dx write the differential equation that describes the rate of change in the number of children at the carnival at a given time, t. Do not solve. 1 76 77 7 O "C = kVC dr VF o de = kr2 o de 1 81 82 83 84 85 86 87 88 89 90 NON 90