Chapter 6.7, Problem 72STP

(a)

To determine

To find:The relationship for $-8.1r^2+46.9r-38.2=0$

Answer to Problem 72STP

The owner will break charges $0.98 and $4.81 per square feet.

Explanation of Solution

Given:

The polynomial is given as,

  $P\left(r\right)=-8.1r^2+46.9r-38.2$

Calculation:

Calculate the roots of the equation using Quadratic formula.

  $\begin{array}{c}r=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ =\frac{-46.9\pm \sqrt{{46.9}^2-4\left(-8.1\right)\left(-38.2\right)}}{2\left(-8.1\right)}\\ =\frac{-46.9\pm 31.01}{-16.2}\\ =0.98,4.81\end{array}$

Thus, the owner will break charges $0.98 and $4.81 per square feet.

(b)

To determine

To find:The relationship for $-8.1r^2+46.9r-38.2>0$

Answer to Problem 72STP

The owner will break charges $1or $5 per square feet.

Explanation of Solution

Given:

The polynomial is given as,

  $P\left(r\right)=-8.1r^2+46.9r-38.2$

Calculation:

The factors are already calculates in part (a).

The regions are divided as,

  $\left\{r|0.98<r<4.81\right\}$

Thus, the owner will break charges $1 or $5 per square feet.

(c)

To determine

To find:The relationship for $-8.1r^2+46.9r-38.2>10$

Answer to Problem 72STP

The owner will break charges $1 or $5 per square feet.

Explanation of Solution

Given:

The polynomial is given as,

  $P\left(r\right)=-8.1r^2+46.9r-38.2$

Calculation:

The factors are already calculates in part (a).

The regions are divided as,

  $\left\{r|0.98<r<4.81\right\}$

Thus, the owner will break charges $1 or $5 per square feet.

(d)

To determine

To find:The relationship for $-8.1r^2+46.9r-38.2<10$

Answer to Problem 72STP

The owner will break charges $\left\{r<0.98\text{ and }r>4.81\right\}$ per square feet.

Explanation of Solution

Given:

The polynomial is given as,

  $P\left(r\right)=-8.1r^2+46.9r-38.2$

Calculation:

The factors are already calculates in part (a).

The regions are divided as,

  $\left\{r<0.98\text{ and }r>4.81\right\}$

Thus, the owner will break charges $\left\{r<0.98\text{ and }r>4.81\right\}$ per square feet.