To find the length of the spring when no weights are attached, we need to determine the rate of change of the length of the spring with respect to the weight.
First, we can calculate the rate of change using the information given. The length of the spring increases by 6 inches when the weight increases from 2 pounds to 5 pounds.
Rate of change = (change in length)/(change in weight) = (18 - 12)/(5 - 2) = 6/3 = 2 inches per pound.
Since the length of the spring increases by 2 inches for every pound of weight, we can determine the length of the spring when no weights are attached by subtracting 2 inches from the length of the spring when a 2-pound weight is attached.
Length of the spring without weights = 12 inches - 2 inches = 10 inches.
Therefore, the length of the spring when no weights are attached is 10 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.
(1 point)
inches
3 answers
ARE YOU SURE
Yes, I am confident that the length of the spring when no weights are attached is 10 inches, based on the information provided and the calculation of the rate of change.
2 answers