Chapter 7.1, Problem 53E

a.

To determine

The polynomial for distance between the two balls after $t$ $\sec onds$ is to be represented.

Answer to Problem 53E

  $-46t+92$

Explanation of Solution

Given Information:

Polynomials representing the heights (in feet) of two balls after are $t$

  $\sec onds$ are $-16t^2+98\&-16t^2+46t+6$ .

Calculation:

Subtracting the two given polynomials, the required height is

  $-16t^2+98-(-16t^2+46t+6)=$ $-16t^2+98+16t^2-46t-6$

  $=-46t+92$

b.

To determine

To interpret the coefficients of the polynomial in (a).

Explanation of Solution

Given Information:Polynomials representing the heights (in feet) of two balls after are $t$

  $\mathrm{seconds}$ are $-16t^2+98\&-16t^2+46t+6$ .

Calculation:

When $t=0$ , the distance between the balls is $-46(0)+92=92feet$ .

So, the constant term $92$ represents the distance between the balls when both begin to fall.

As the value of $t$ increases by $1$ , the value of $-46t+92$ decreases by $46$ . This means that the balls become $46feet$ closer to each other each second. So, $-46$ represents the amount that the distance between the balls changes each second.