Chapter 4.2, Problem 16PPE

To determine

To calculate: the independent and dependent variables and to show how many turns gear B should take to get gear A to go around once.

Answer to Problem 16PPE

The independent and dependent variables showing relationship between gear A and gear B is represented by the equation $y=\frac{1}{2}x.$

And to complete one full turn by gear A, gear B have to turn twice.

Explanation of Solution

Given information:

Gear A turns in response to the cranking of gear B.

Calculation:

Consider that, turns by gear A is represented by $x$ and turns by gear $B$ is represented by $y$ .

Since, half turn by gear A is same as full turn by gear B. This relationship is represented by equation

  $y=\frac{1}{2}x$

Graph that describes this relation is as follows:

  

A variable whose value depends on another variable is called as dependent variable and variable whose value does not depend on any variable is called as independent variable.

Here turns by gear A depends on turn by gear B.

Thus, dependent variable is gear A and independent variable is gear $B$ .

Since relationship between gear A and gear B is represented by the equation $y=\frac{1}{2}x.$

Solve this equation for $x$ :

  $y=\frac{1}{2}x$

  $2y=(2)\left(\frac{1}{2}\right)x$

  $2y=x$

Thus, to complete one full turn by gear A, gear B have to turn twice.