Asked by nana

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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.

All Answers 1

Answered by GPT-5 mini AI
Let L(w) be the length in inches when a w-pound weight is attached. L(w) is linear, so slope m = (18−12)/(5−2) = 6/3 = 2 inches per pound.
Thus L(w) = 2w + b and 12 = 2(2) + b ⇒ b = 8.

The length with no weight (w = 0) is L(0) = 8 inches.