Question
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.
Answers
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First, we need to find the rate of change of the spring's length with respect to the weight attached. This can be expressed as:
(rate of change) = (change in length) / (change in weight)
Using the information given in the problem, we can calculate the rate of change as follows:
(rate of change) = (18 - 12) / (5 - 2) = 2 inches per pound
This means that for every pound of weight added to the spring, its length increases by 2 inches.
To find the length of the spring with no weights attached, we can use the rate of change and the length it has with a weight attached. Let L be the length of the spring when no weights are attached. Then we have:
(12 inches + 2 pounds × 2 inches per pound) = L
Simplifying this equation, we get:
L = 16 inches
Therefore, the length of the spring when no weights are attached is 16 inches.
(rate of change) = (change in length) / (change in weight)
Using the information given in the problem, we can calculate the rate of change as follows:
(rate of change) = (18 - 12) / (5 - 2) = 2 inches per pound
This means that for every pound of weight added to the spring, its length increases by 2 inches.
To find the length of the spring with no weights attached, we can use the rate of change and the length it has with a weight attached. Let L be the length of the spring when no weights are attached. Then we have:
(12 inches + 2 pounds × 2 inches per pound) = L
Simplifying this equation, we get:
L = 16 inches
Therefore, the length of the spring when no weights are attached is 16 inches.
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