Rate of change is the change in one variable divided by the change in another variable. In this case, we can find the rate of change by dividing the change in weight by the change in length.
When a 2-pound weight is attached, the length of the spring is 12 inches.
When a 5-pound weight is attached, the length of the spring is 18 inches.
The change in weight is 5 pounds - 2 pounds = 3 pounds
The change in length is 18 inches - 12 inches = 6 inches
Rate of change = change in weight / change in length
Rate of change = 3 pounds / 6 inches
Rate of change = 0.5 pounds per inch
Now we can use this rate of change to find the length of the spring when no weights are attached. Since no weight is attached, the weight is 0 pounds.
Change in weight = 0 pounds
Change in length = rate of change * change in weight
Change in length = 0.5 pounds per inch * 0 pounds
Change in length = 0 inches
Length of the spring when no weights are attached = length of spring with 2-pound weight - Change in length
Length of the spring when no weights are attached = 12 inches - 0 inches
Length of the spring when no weights are attached = 12 inches
Therefore, the length of the spring when no weights are attached is 12 inches.
A spring has a length of 12 inches when a 2-pound weight is attachedand 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
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