Question

a spring has a length of 12 inches when a 2-pound weight is attached, and a length of 18 inches when a 5-pound weight is attached. use rate of change to find the length of the spring when no weights are attached

____ inches

Answer 1

Let x be the weight in pounds and y be the length of the spring in inches.

We can set up a system of equations based on the information given:
1. y = kx, where k is the rate of change.
2. When x = 2, y = 12.
3. When x = 5, y = 18.

Substitute the values from equations 2 and 3 into equation 1:

12 = 2k
18 = 5k

Solve for k in the first equation:
k = 12/2 = 6

Now, substitute k back into the second equation:
18 = 5(6)
18 = 30

So, the length of the spring when no weights are attached is:
y = k(0)
y = 6(0)
y = 0 inches

Therefore, the length of the spring when no weights are attached is 0 inches.