Chapter 11.6, Problem 41PPE

a.

To determine

Explain how the variable y changes.

Answer to Problem 41PPE

The value of y doubles.

Explanation of Solution

Given information:

y varies directly with x. The value of x is doubled.

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 variables is constant is called inverse variation.

Calculation:

According to question y varies directly with x.

  $\begin{array}{c}y\propto x\\ y=kx\end{array}$

The value of x is doubled

  $\begin{array}{c}lety=2x\\ ifx=1then\\ y=2\cdot x\\ y=2\cdot 1\\ y=2\\ nowxisdoubledi.ex=2\\ y=2\cdot 2\\ y=4\end{array}$

So the value of y is also doubled.

b.

To determine

Explain how the variable y changes.

Answer to Problem 41PPE

The value of y becomes half.

Explanation of Solution

Given:

y varies inversely with x. The value of x is doubled.

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 variables is constant is called inverse variation.

Calculation:

According to question y varies inversely with x.

  $\begin{array}{c}y\propto \frac{1}{x}\\ yx=k\\ xy=k\end{array}$

The value of x is doubled

  $\begin{array}{c}letxy=2\\ ifx=1then\\ 1\cdot y=2\\ y=2\\ nowxisdoubledi.ex=2\\ 2\cdot y=2\\ y=\frac{2}{2}\\ y=1\end{array}$

So the value of y is halfed.