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.

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0