Answered: . The radius r of a circle is…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.6: Variation

Problem 27E

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1. The radius r of a circle is increasing at a rate of 5 inches per minute. Find the rate of change of the area when r = 6 inches and r = 21 inches.

(a)

r = 6 inches_________in²/min

r = 21 inches.___________in²/min

2. A company that manufactures pet toys calculates that its costs and revenue can be modeled by the equations

C = 15,000 + 1.95x and R = 500x −

x²

where x is in the number of toys produced in 1 week. Production during one particular week is 5000 toys and is increasing at a rate of 350 toys per week. Find the rate at which the cost, revenue, and profit are changing.

a) cost

= dollars/week

(b) revenue

= dollars/week

4. The profit P from selling x units of a product is given by

P = 560x − 0.2x².

The sales are increasing at a rate of 6 units per day. Find the rate of change of the profit (in dollars per day) when

x = 500 units

and

x = 800 units.

(a)    500 units
$  per day

(b)    800 units
$  per day

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