12. Please answer the blanks ty. (a) Solve for v(t) if the raindrop falls from rest.9p4rv(t) =(b) This model assumes that the rate at which the raindrop evaporates-that is, the rate at which it loses mass-is proportional to its surface area, with constant of proportionality k < 0. This assumption implies that the rate at which the radius r of the raindropdecreases is a constant. Show that the radius of the raindrop at time t is r(t) = (k/p)t + ro.Letting A denote the surface area of the raindrop and m the mass, the model assumes thatdmdtSince mass equals density times volumem =A == k. A.43Plugging these formulas into the differential equation gives:[dtr(t) =drdt= k. 4tr²= k. 4πr²= k (assuming r = 0)=Integrating the above differential equation givesr(t) =+ C.Plugging in r(0) = ro gives C = roand a sphere of radius r has volumeXso thatand surface area, we obtain the following formulas for m and A in terms of p and r.(c) If ro = 0.04 ft and r = 0.006 ft 10 seconds after the raindrop falls from a cloud, determine the time at which the raindrop has evaporated completely. (Round your answer to one decimal place.)11.8sec

Basic information: ddxaxn=anxn-1∫axndx=axn+1n+1 + Cρ is a density of the rain drop.…

(a) Solve for v(t) if the raindrop falls from rest. (2) v(t) = (b) This model assumes that the rate at which the raindrop evaporates-that is, the rate at which it loses mass-is proportional to its surface area, with constant of proportionality k < 0. This assumption implies that the rate at which the radius r of the raindrop decreases is a constant. Show that the radius of the raindrop at time t is r(t) = (k/p)t + ro Letting A denote the surface area of the raindrop and m the mass, the model assumes that dmk-A. Since mass equals density times volume m= A = Plugging these formulas into the differential equation gives: =k-4mr²2 dk. 4m² Integrating the above differential equation gives Plugging in r(0)= re gives C= 70 r(t) and a sphere of radius r has volume (assuming r= 0) so that and surface area we obtain the following formulas for m and A in terms of p and r. (c) If ro= 0.04 ft and r= 0.006 ft 10 seconds after the raindrop falls from a cloud, determine the time at which the raindrop has evaporated completely. (Round your answer 11.8 ✔sec one decimal place.)

(a) Solve for v(t) if the raindrop falls from rest. (2) v(t) = (b) This model assumes that the rate at which the raindrop evaporates-that is, the rate at which it loses mass-is proportional to its surface area, with constant of proportionality k < 0. This assumption implies that the rate at which the radius r of the raindrop decreases is a constant. Show that the radius of the raindrop at time t is r(t) = (k/p)t + ro Letting A denote the surface area of the raindrop and m the mass, the model assumes that dmk-A. Since mass equals density times volume m= A = Plugging these formulas into the differential equation gives: =k-4mr²2 dk. 4m² Integrating the above differential equation gives Plugging in r(0)= re gives C= 70 r(t) and a sphere of radius r has volume (assuming r= 0) so that and surface area we obtain the following formulas for m and A in terms of p and r. (c) If ro= 0.04 ft and r= 0.006 ft 10 seconds after the raindrop falls from a cloud, determine the time at which the raindrop has evaporated completely. (Round your answer 11.8 ✔sec one decimal place.)

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section3.5: Mathematical Modeling And Variation

Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...

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