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.
(1 point)
inches
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To find the length of the spring when no weights are attached, we can set up a ratio using the given information.
The ratio of weight to length is constant for this spring, so we can set up the following proportion:
2 pounds / 12 inches = 5 pounds / 18 inches
To find the length when no weight is attached, we can set up the following ratio:
2 pounds / 12 inches = 0 pounds / x inches
Simplifying the proportion, we get:
2 / 12 = 0 / x
Cross multiplying, we get:
2x = 0
Since anything multiplied by 0 is 0, the length of the spring when no weights are attached is 0 inches.
are you sure?
Apologies for the mistake in my previous response. The length of the spring when no weights are attached can be found using the concept of rate of change.
Let's consider the rate of change for the weight-length relationship. The rate of change is the change in length divided by the change in weight.
The change in length is 18 inches - 12 inches = 6 inches.
The change in weight is 5 pounds - 2 pounds = 3 pounds.
So, the rate of change is 6 inches / 3 pounds = 2 inches/pound.
To find the length of the spring when no weights are attached, we can use the rate of change and the weight difference between 2 pounds and 0 pounds.
The weight difference is 2 pounds - 0 pounds = 2 pounds.
Using the rate of change of 2 inches/pound, we can calculate the length:
2 inches/pound * 2 pounds = 4 inches.
Therefore, the length of the spring when no weights are attached is 4 inches.