Question

Math 2413 Derivative Applications Assignment Due: Tuesday, June 18, 2019 (5:30 pm) Name Show all work. Label your answers with the proper units. (3 points each ) A spherical ball is being inflated at the rate of 12 cubic inches per second. Find the rate at which the radius of the sphere is growing when the radius is 2 inches. long. 2. A 13 foot ladder is leaning against a wall. The base of the ladder is being palled away from the wall at the rate of 4 feet per minute. How fast is the top of the ladder coming down the wall when the base of the ladder is 5 feet from the wall? 3, A weather balloon travels vertically at a speed of 40 f/min. The balloon is tracked by an observer stationed 500 feet from the launching pad. Find the rate at which the angle between the telescope and the ground is increasing 30 minutes after lift- off 4. A stone dropped in a still pond creates a circular ripple whose radius increases at the constant rate of 2 feet per second. At what rate is the area of the circle increasing when the radius is 8 feet? Find the values of x and y that will maximize the function T given that x+y=8. 5. T= 3y A rancher needs to enclose a rectangular plot of land with a fence. She has 600 feet of fencing material. A building will be on one side of the field so she won't need any fencing for that side of the field. Determine the dimensions of the field that will enclose the largest area using the given amount of fencing. 6. A printed page will have 2 inch margins of white space on the sides and 1 inch margins of white space on the top and bottom. The area of the printed portion of the page is 32 square inches. Find the dimensions of the page so that the least amount of paper is used. 7.

Answer 1

(1) Let r be the radius of the spherical ball Recollect the following 4 Volume of the sphere is given by V = dV Given 12 cubic inches per second dt dr when dt 2 inches Require to find Now V _ Differentiating both sides with respect to t, we get dV 4 dr -(3r2) dt 3 dt dV That is dt dr 47T dt dV 12 andr 2 dt Substituting the values we get _ - dr 12 4T(2) dt dr 12 dt 16T dr dt 47T inches per second Therefore, the radius of a spherical ball is growing at the rate of 1