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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 2.6, Problem 61E

(a)

To determine

**To find:** The function *g* that models the radius as a function of time.

Expert Solution

The value of the function *g* is

**Given:**

The circular ripple travels outward at a speed of

The function *g* models the radius as a function of time.

**Calculation:**

The radius of the ripple is the distance travelled by the ripple.

So, the distance travelled is evaluated as follows,

The radius is given by the function

The required function is

Thus, the value of the function *g* is

(b)

To determine

**To find:** The function *f* that models the area of the circle as a function of the radius.

Expert Solution

The value of the function *f* is

**Given:**

The function *f* is the function that models the area of the circle as a function of the radius.

**Calculation:**

The area of a circular ripple with radius *r* is given by,

Since the *f* is the function that models the area of the circle as a function of the radius, therefore the function *f* is equal to the area of the circle whose radius is *r*.

The function *f* is written as,

Thus, the value of the function *f* is

(c)

To determine

**To find:** The value of the function

Expert Solution

The value of

**Given:**

From part (a), the value of function *g* is ,

From part (b), the value of function *f* is ,

**Calculation:**

The composite function

From equation (1), substitute

Substitute

Substitute

The function

Thus, the value of