Chapter 3.6, Problem 48PPE

To determine

To write the inequality that describes the distances the spring is stretched.

Answer to Problem 48PPE

The inequality that describes the distances the spring is stretched is given by $20\le d\le 32$

Explanation of Solution

Given Information:

, $\frac{d}{F}=0.8$ where $d$ is the stretch distance of the spring and $F$ is the force applied in pounds.

Force between $25\text{}\text{lb}$ and $40\text{lb}$ is applied.

Solution:

Given the formula $\frac{d}{F}=0.8$

Cross multiply to get $d=0.8F$

Force that is applies is between $25\text{}\text{lb}$ and $40\text{lb}$

To get the minimum value, substitute $25\text{}\text{lb}$ for Force.

  $\begin{array}{c}d=0.8\left(25\right)\\ =20\end{array}$

Therefore, lower constraint for the inequality is $20\le d$ .

Similarly, to get the maximum value, substitute $40\text{lb}$ for Force

  $\begin{array}{c}d=0.8\left(40\right)\\ =32\end{array}$

Therefore, higher constraint for the inequality is $d\le 32$ .

Result:

The inequality that describes the distances the spring is stretched is given by $20\le d\le 32$