A circular oil slick is expanding with radius, r in yards, at time t in hours given by r=2t-0.1t^2, for t in hours, 0<t<10
50 (1 point) The density of oil in a circular oil slick on the surface of the ocean at a distance of r meters from the center of the slick is given by S(r) = 10 kilograms per square meter. Find the exact value of the 1 + p2 mass of the oil slick if the slick extends from r = 0 to r = 4 meters. Mass = Include units in your answer.
(1 point) The density of oil in a circular oil slick on the surface of the ocean at a distance of r meters from the center of the slick is 50 given by S(r) kilograms per square meter. Find the exact value of the mass of the oil slick if the slick extends from r= 1+r2 to r = 11 meters. 0 Mass = Include units in your answer.
An oil well of the Gulf Coast is leaking with the leak spreading oil over the surface as a circle. At any time t (in minutes) after the beginning of the leak, the radius of the circular oil slick on the surface is r(t) VE feet. Let A (r) πγ 2 represent the area of a circle of radius r. a) Find and interpret A[r(t) b) Find and interpret D A[r(t)] when t-100
An oil well of the Gulf Coast...
h(t) be the radius of the circle at time t. (1 point) Let A- f(r) be the area of a circle with radius r and r Which of the following statements correctly provides a practical interpretation of the composite function f(h(t) ? Select all that apply if more than one is appropriate. | ■ A. The area of the circle which at time t has radius h(t) B. At what time t the area will be A-f(r). C. The area...
Be sure to show all work and all problem solving strategies. Give complete explanations for each step. 1. A forest fire leaves behind an area of grass burned in an expanding circular pattern. The radius of the circle of burning grass is increasing at the rate of r(t) = 2t + 1 where t is the time in minutes. (a) Find a function that gives the area burned as a function of time. Remember, A = ar? (b) Find the...
Find the steady-state temperature u(r.0) in a circular plate of radius r = 1 if the temperature on the circumference is as given (show all work!): 0 0 T 1) u(1,0) = 0, T<02T
Find the steady-state temperature u(r.0) in a circular plate of radius r = 1 if the temperature on the circumference is as given (show all work!): 0 0 T 1) u(1,0) = 0, T
(3) For the following velocity fields F on R3, find the flow along the given curve. r(t) = (t, t2, 1) F=(-4xy, 83, 2) with 0 2 t 1l F=(z-z, 0,2) r(t)-(cost, 0, sin t) with 0 t π F = (-y,2, 2) with r(t) = (-2 cost, 2 sin t, 2t) 0 < t < 2π
(3) For the following velocity fields F on R3, find the flow along the given curve. r(t) = (t, t2, 1) F=(-4xy, 83,...
10 sin 2t if 0 <t< 4. (a) Let r(t) if t > T Show that the Laplace transform of r(t) is L(r) 20(1 - e - e-78) 32 + 4 (b) Find the inverse Laplace transform of each of the following functions: s – 3 S2 + 2s + 2 20 ii. (52 + 4)(52 + 25 + 2) 20e-S ini. (s2 + 4)(52 + 25 + 2) (c) Solve the following initial value problem for a damped mass-spring...
2t +1 if 0 <t< 2 Consider f(t) = { | 3t if t > 2. (a) Use the table of Laplace transforms directly to find the Laplace transform of f. (b) Express f in terms of the unit step function, then use Theorem 6.3.1 to find the Laplace transform of f.