Apebble is dropped into a calm pond, causing ripples in the form of concentric circles. the radius (in feet) of the outermost ripple is given by r(t) = 0.6t, where t is time (in seconds) after the pebble strikes the water. the area of the circle is given by a(r) = πr2. find (a ∘ r)(t).

Solution-

A pebble is dropped into a calm pond, causing ripples in the form of concentric circles.

The radius of the outer ripple is given by r(t)= 0.6t,

where t is the time in seconds after the pebble strikes the water.

The area of the circle is given by the function

(a ◦ r)(t) = a(r(t))  ( ∵ Using function composition / plugging in the second function into the first function)

⇒

∴ This is the expression for area of circle of outermost ripple, at time t after the pebble strikes the water.

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above