Tthe area of a circle increases at a rate of 5 cm^2/s. Required:
a. How fast is the radius changing when the radius is 4 cm?
b. How fast is the radius changing when the circumference is 5 cm?

(a) 0.198 cm/s (b) 1 cm/s

Step-by-step explanation:

It is given that,

The rate of change of area of a cicle,

(a) The area of a circle is given by :

Differentiate both sides,

(b) Circumference, = 5 cm

Hence,

(a) 0.198 cm/s (b) 1 cm/s

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step-by-step explanation:

ewd

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: