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
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.
To find the inequality that describes the distance the spring is stretched, we can use the given information that d/F = 0.8.
Let's assume the distance the spring is stretched is represented by the variable "d" and the force applied is represented by the variable "f".
According to the given information, we can write the equation:
d/F = 0.8
To express this equation as an inequality, we need to rearrange the equation:
d = 0.8 * F
Now, we need to consider the range of forces applied, which is between 40 lb and 54 lb inclusive.
Let's start by replacing F with the lower limit of the force range:
d = 0.8 * 40
Simplifying, we get:
d = 32
Next, let's replace F with the upper limit of the force range:
d = 0.8 * 54
Simplifying, we get:
d = 43.2
Therefore, the inequality that describes the distance the spring is stretched is:
32 ≤ d ≤ 43.2
To determine the inequality that describes the distance the spring is stretched, we need to use the given information that d/F = 0.8.
We know that the force exerted on a spring is proportional to the distance it is stretched. In this case, we need to find the range of possible distances the spring can be stretched based on the range of forces applied (40 lb to 54 lb inclusive).
1. Begin by setting up the equation for the proportionality: d/F = k, where k is the constant of proportionality.
2. Substitute the given proportionality constant (0.8) into the equation: d/F = 0.8.
3. Rearrange the equation to solve for F: F = d/0.8.
4. Since F must be between 40 lb and 54 lb, we can write the following inequality: 40 ≤ d/0.8 ≤ 54.
To find the inequality that describes the distance the spring is stretched, we can multiply all parts of the inequality by 0.8 to eliminate the fraction:
40 × 0.8 ≤ d × 0.8 ≤ 54 × 0.8,
32 ≤ d ≤ 43.2.
Therefore, the inequality that describes the distance the spring is stretched is 32 ≤ d ≤ 43.2.