Steps:1) Draw a picture3) Determine knowns and unknowns5) Differentiate to relate the rates2) Assign variables4) Find an equation that relates the variables6) Use the known rate(s) to find theunknown rateAnswer the following, being sure to include units and show all work.1. A spherical balloon is being filled with helium such that its radius is changing at a constantrate of 2 cm/sec. Answer the following, where the volume of a sphere is V =T r3 and thesurface area of a sphere is S = 4T1² .(a) How fast is the volume changing when the radius of the balloon is 10 cm?(b) How fast is the material of the balloon stretching when its diameter is 30 cm?

Given, A spherical balloon is filled with helium gas and radius is increasing with rate…

Answered: 1. A spherical balloon is being filled…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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5. A dock sits above the water. A rope is attached to a pulley on the edge of the dock. The pulley is located 5ft vertically above the water on the dock. The other end of the rope is attached to a float floating on the water. The rope is pulled in at a constant rate of 3 ft/s. How fast is the float traveling on the surface of the water (towards the dock) at the moment when the boat is 12ft from the dock? Hint: The edge of the dock, down to the water, then over to the float, makes a triangle. d山T06 NOV 10 PACES 18 MacBook Air DII
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A spherical balloon is being inflated at a constant rate of 20 cubic inches per second. How fast is the radius of the balloon changing at the instant the balloon's diameter is 12 inches? Is the radius changing more rapidly when d = 12 or when d = 16? Why? Draw several spheres with different radii, and observe that as volume changes, the radius, diameter, and surface area of the balloon also change. Recall that the volume of a sphere of radius r is V = ar³. Note that in the setting of this problem, both V and r are changing as time t changes, and thus both V and r may be viewed as implicit functions of t, with respective derivatives dV and dr Differentiate both sides of the equation V = ar³ with respect to t (using the chain rule on the right) to find a formula for depends on both r and dr that dV dt At this point in the problem, by differentiating we have "related the rates" of change of V and r. Recall that we are given in the problem that the balloon is being inflated at a constant…

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