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.
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
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