Chapter 9.2, Problem 27E

a.

To determine

To interpret the x -intercept of the graph

Answer to Problem 27E

  $x=0,x=5$ are the intercepts.

Explanation of Solution

Given information:

  $y=-x^2+5x$

Calculation:

The given equation is $y=-x^2+5x$

Rearranging,

  $y=x^2-5x$

To get the x -intercept, solve for x .

  $x^2-5x=0$

Taking out common,

  $x(x-5)=0$

For equation to be 0,

  $x=0,(x-5)=0$

Solving,

  $x=0,x=5$

Hence, $x=0,x=5$ are the intercepts.

b.

To determine

To find how far does golf ball land

Answer to Problem 27E

10 yards is the distance golf ball will cover.

Explanation of Solution

Given information:

  $y=-x^2+5x$

Calculation:

To find the distance, differentiate $y=-x^2+5x$

So,

  $\frac{d}{dx}(y)=\frac{d}{dx}(x^2-5x)$

Differentiating,

  $\frac{d}{dx}(y)=\frac{d}{dx}(x^2)-\frac{d}{dx}(5x)$

So,

  $\frac{d}{dx}(y)=2\frac{d}{dx}(x^{2-1})-5\frac{d}{dx}(x^{1-1})$

And,

  $\frac{d}{dx}(y)=2(x)-5(1)$

Distance is ${\left[2x-5\right]}_0^5$

Solving,

Distance= $\{2(5)-5-\{2(0)-5\}$

So,            Distance= $\{2(5)-5-(-5)\}$

And,

Distance= $\{2(5)-5+5\}$

Hence, 10 yards is the distance golf ball will cover.