To find the rate of change of the spring length with respect to the weight, we can set up a proportional relationship between the weight and the spring length.
Let L represent the length of the spring and W represent the weight attached to the spring.
When a 2 lb weight is attached, the length of the spring is 12 in.
L = k * W
12 = k * 2
k = 6
When a 5 lb weight is attached, the length of the spring is 18 in.
L = k * W
18 = 6 * 5
18 = 30
Now, we can find the length of the spring when no weights are attached (W = 0):
L = k * W
L = 6 * 0
L = 0
Therefore, the length of the spring when no weights are attached is 0 in.
A spring has a length of 12 in when a 2 lb weight is attached and a length of 18 in is what a 5 lb weight is attached use rate of change to find the length of the spring when no weights are attached
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