Chapter 8.5, Problem 82STP

(a)

To determine

To find: The polynomial equation to model the given situation.

Answer to Problem 82STP

The polynomial equation to model the given situation is $\left(3-x\right)\left(4-x\right)\left(5-x\right)=24$

Explanation of Solution

Given; The length of the cube is 3 ft.

The width of the cube is 5 ft.

The height of the cube is 4 ft.

Calculation:

The equation from the given situation is,

  $\left(3-x\right)\left(4-x\right)\left(5-x\right)=24$

Thus, the polynomial equation to model the given situation is $\left(3-x\right)\left(4-x\right)\left(5-x\right)=24$

(b)

To determine

To find: The dimension which is taken from the original ice cube.

Answer to Problem 82STP

1 feet dimension is taken from the original ice cube.

Explanation of Solution

Given; The length of the cube is 3 ft.

The width of the cube is 5 ft.

The height of the cube is 4 ft.

Calculation:

Consider the equation from part (a).

  $\begin{array}{l}\left(3-x\right)\left(4-x\right)\left(5-x\right)=24\\ \left(12-7x+x^2\right)\left(5-x\right)=24\\ -x^3+12x^2-47x+36=0\\ \left(x-1\right)\left(-x^2+11x-36\right)=0\end{array}$

Solve further as,

  $\left(-x^2+11x-36\right)$ is prime expression.

So,

  $\begin{array}{l}\left(x-1\right)=0\\ x=1\text{ feet}\end{array}$

Thus, 1 feet dimension is taken from the original ice cube.