Paraphrasing ool X MATH_1241_A02_202315:A5 X 6 MATH1241Assignment4(1).pdf X a PSC|202.FLEX--2023 Winter X + C G File [Users/zawadarwad/Downloads/MATH1241Assignment4%20(1).pdf MATH1241Assignment4 (1).pdf 1 / 2 + E of) \\ . 7. [8 marks] ASSIQ nment 4 (100 marks total) Find an equation of a curve that pass through the point (t, 72) with the Note: Give me] answers where possible (for example, at is exact but 3.142 is approximate). property that the slope of the curve at any point (x. y) is equal to XZ/y. Give your answer in the form y = f(x). 1. {10 marks] . (8 marks] Find the exact length of the curve y : i 712,1 s x s 2. 2 ' Find the solution to the differential equation x2y + dy/dx = y/x for which y(1) : 82. Give your answer in the form y : for). . [10 marks] Find the exact length of the curve x = y? + i, 1 g y g 2. . [12 marks) A tank contains 100 litres of pure water. Brine that contains 0.1 kg of salt per litre enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and - [1" "Wk\" drains from the tank at the same rate. How much salt is in the tank after 6 Find the exact value of the area of the surface obtained by rotating the curve minutes? y=+ Esxslaboutthexaaxis. 10. [12 marks} . [10 marks] a. (6 marks) Find the exact area of the sulfate gmemed by revolving the curve X = yz + 4, Show that, if P is a twice differentiable function of t and satisfies the logistic u g y g 2 around the x axis. differential equation . {10 marks] Given the demand curve D(x) = (x or and the supply curvesor) = r2, find the consumer surplus and the producer surplus. Illustrate by sketching the supply and demand curves and identifying the surpluses as areas. . (6 marks) Suppose a population grows according to the logistic growth model and that . (10 marks] the initial population size is positive but less than half the carrying capacity After an 8-mg injection of dye, the readings of dye concentration at 2-second of the environment. Use the result from part a. of this question to show the intervals are as shown in the table, Use Simpson's Rule to estimate the cardiac growth rate of the papulation is maximal when the papulation size is exactly output, giving the appropriate units. half the carrying capacity. 0 2 4 6 S 10 16 Select resources undated With the following course textbook are used With permixim lrom (engage Learning 0 2.4 5.1 7,8 7.6 5.4 . , 1,5 , Slewan, 1. (2016). single variable calculus: Early transtrndnilals (8th ed). Boston, MA: (engage Learning