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.

Answer 1

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.

Answer 2

r u sure

Answer 3

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.