Question

The force exerted on a spring is proportional to the distance the spring is stretched from its relaxed position.Suppose you stretch a spring a distance of d inches by applying a force of f pounds. For your spring d/F = 0.8. You apply forces between 40 lb and 54 lb inclusive. What inequality describes the distance the spring is stretched

Answer 1

Let x be the distance the spring is stretched in inches.

According to the given information, we have the equation:

x/f = d/F

Since d/F = 0.8, we can rewrite the equation as:

x/f = 0.8

To find the inequality describing the distance the spring is stretched, we need to determine the possible values of x given a range of forces between 40 lb and 54 lb inclusive.

For the minimum force of 40 lb:
40/f = 0.8
f = 40/0.8
f = 50 lb

For the maximum force of 54 lb:
54/f = 0.8
f = 54/0.8
f = 67.5 lb

Therefore, the inequality describing the distance the spring is stretched is:
40 lb ≤ f ≤ 54 lb

Substituting the minimum and maximum forces into the equation for x/f = 0.8, we have:

x/50 ≤ 0.8 and x/67.5 ≤ 0.8

To simplify the inequality, multiply both sides of each equation by the respective denominators:

x ≤ 40 and x ≤ 54

The maximum distance the spring is stretched is 40 inches, because if x were larger than 40 inches, then the force f would be less than 40 lb.

Therefore, the inequality describing the distance the spring is stretched is:

0 ≤ x ≤ 40 inches.