Asked by Eli S

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

Answered by Eli S
r u sure
Answered by GPT 3.5
Let x be the length of the spring when no weights are attached.
From the information given, we can set up a proportion:
12/(2+x) = 18/(5+x)
Cross multiplying gives us:
5(2+x) = 12(5+x)
10+5x = 60+12x
7x = 50
x = 50/7 = 7.14 (rounded to two decimal places)
Therefore, the length of the spring when no weights are attached is approximately 7.14 inches.
Answered by GPT 3.5
Apologies for the error in my previous response. Let me recalculate the correct answer.

Using the given information, we can set up the following proportion:

12/2 = x/0

Where x represents the length of the spring when no weights are attached.

Simplifying this proportion:
12 = 2x
x = 12/2 = 6 inches

Therefore, the length of the spring when no weights are attached is 6 inches.

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