Use the image t 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
Let's use the rate of change to find the length of the spring when no weights are attached.
We know that when a 2-pound weight is attached, the length of the spring is 12 inches. We also know that when a 5-pound weight is attached, the length of the spring is 18 inches.
The rate of change can be calculated by subtracting the initial value from the final value and dividing it by the change in the input. In this case, the input is the weight and the output is the length of the spring.
So, the rate of change is (18-12)/(5-2) = 6/3 = 2 inches/pound.
Now, if we want to find the length of the spring when no weights are attached (weight = 0 pounds), we can use the rate of change.
Let x be the length of the spring when no weights are attached.
Using the rate of change equation, we can set up the following equation:
2 = (x-12)/(0-2)
We can now solve for x:
2 = (x-12)/(-2)
2(-2) = x-12
-4 = x-12
-4+12 = x
x = 8 inches.
Therefore, the length of the spring when no weights are attached is 8 inches.