To find the length of the spring when no weights are attached, we can use the rate of change between the length of the spring with weights attached and the weight of those weights.
The rate of change can be calculated by finding the change in length of the spring divided by the change in weight.
For the first spring (no weights attached) to the second spring (2-pound weight attached):
Rate of change = (12 inches - ? inches) / (2 pounds - 0 pounds)
Rate of change = (12 - ?) / 2
For the second spring to the third spring (5-pound weight attached):
Rate of change = (18 inches - 12 inches) / (5 pounds - 2 pounds)
Rate of change = 6 / 3
Rate of change = 2 inches/pound
Now we can set up an equation to find the length of the first spring when no weights are attached:
(12 - ?) / 2 = 2
12 - ? = 4
? = 8
Therefore, the length of the spring when no weights are attached is 8 inches.
Use the image to answer the question.
An illustration shows three coiled wire springs stretched to varying lengths. The first spring does not have any weights pulling it downward, and the length of the spring is marked as a question mark inches. The second spring has a 2-pound weight attached to the bottom, and its length is marked as 12 inches. The third spring has a 5-pound weight attached to the bottom and its length is marked as 18 inches.
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.
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