Complete this assessment to review what you've learned. It will not count toward your grade.%0D%0A2 of 52 of 5 Items%0D%0A%0D%0AQuestion%0D%0AUse the image to answer the question.%0D%0A%0D%0A%0D%0AA 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.%0D%0A%0D%0A(1 point)%0D%0A6 inches
To solve this problem, we can use the concept of rate of change. Rate of change is a measure of how one variable changes in relation to another variable.
In this case, we are given the length of the spring when different weights are attached. We can assume that the relationship between the weight and the length of the spring is linear.
To find the length of the spring when no weights are attached, we can set up a proportion using the given information:
(Length when 2-pound weight is attached) / 2 pounds = (Length when 5-pound weight is attached) / 5 pounds
Let's substitute the given values into the proportion:
12 inches / 2 pounds = 18 inches / 5 pounds
Now, we can cross-multiply and solve for the length of the spring when no weights are attached:
2 * 18 inches = 5 * 12 inches
36 inches = 60 inches
Therefore, the length of the spring when no weights are attached is 6 inches.
During my first Fitness Gram assessment, I felt a mix of excitement and nerves. Testing my strength made me a bit intimidated, but I was pleasantly surprised to find out that I had more strength than I thought. Endurance was challenging, and I struggled with fatigue and weakness during running tests. Coordination was a concern, but with practice, it improved gradually. Energy levels decreased as the tests progressed, and I learned the importance of proper fueling and hydration. Overall, the assessment was a mix of emotions, highlighting areas for improvement and motivating me to set goals for better physical fitness.
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I felt excited and nervous during my first Fitness Gram assessment, and learned how to improve my physical fitness.
To find the length of the spring when no weights are attached, we need to find the rate of change of the spring's length with respect to the weight.
Let's denote the length of the spring when no weights are attached as x (in inches). We can use a proportion to set up an equation:
(rate of change) = (change in length of the spring) / (change in weight)
From the information given, when a 2-pound weight is attached, the spring has a length of 12 inches. When a 5-pound weight is attached, the spring has a length of 18 inches.
Using the equation, we can set up the proportion:
(rate of change) = (18 - 12) / (5 - 2)
(rate of change) = 6 / 3
(rate of change) = 2
Now we can use the rate of change to find the length of the spring when no weights are attached:
x = 12 - (2 * 2)
x = 12 - 4
x = 8 inches
Therefore, the length of the spring when no weights are attached is 8 inches.