Chapter 11.6, Problem 48PPE

a.

To determine

Write an equation to model each situation.

Answer to Problem 48PPE

  $y=\frac{k}{x^4}$

Explanation of Solution

Given information:

y varies inversely with the fourth power of x.

Concept Used:

• Mathematically relationship between two variables that can be expressed by an equation in which one variable is equal to constant times the other variable is called direct variation.
• Mathematically relationship between two variables that can be expressed by an equation in which the product of two variable is constant is called inverse variation.

Calculation:

According to question y varies inversely with the fourth power of x.

If y varies inversely with x the product of y and x is constant

  $\begin{array}{c}y{x}^4=k\\ y=\frac{k}{x^4}\end{array}$

where k is constant and $k\ne 0$

b.

To determine

The explanation for the solution process.

Answer to Problem 48PPE

  $y=\frac{z\cdot k}{x^4}$

Explanation of Solution

Given information:

y varies inversely with the fourth power of x and directly with z.

Concept Used:

• Mathematically relationship between two variables that can be expressed by an equation in which one variable is equal to constant times the other variable is called direct variation.
• Mathematically relationship between two variables that can be expressed by an equation in which the product of two variable is constant is called inverse variation.

Calculation:

According to question y varies inversely with the fourth power of x and directly with z.

If y varies inversely with x the product of y and x is constant

  $\begin{array}{c}y{x}^4=zk\\ \frac{y{x}^4}{z}=k\\ y=\frac{z\cdot k}{x^4}\end{array}$

where k is constant and $k\ne 0$