Transcribed Image Text: Remaining Time: 1 hour, 38 minutes, 34 seconds. A Question Completion Status: 2 4 6. 7 9. 10 11 120 130 140 15 16 10 Moving to another question will save this response. Question 21 R varies directly as the square of E. When E = 3,

Transcribed Image Text: Remaining Time: 1 hour, 38 minutes, 34 seconds.
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Question 21
R varies directly as the square of E. When E = 3, R = 12. What is the value of E when R = 72?
O 9.80
O 7.35
6.25
5.60
A Moving to another question will save this response.
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I10
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Answered

The relationship between R and E is given as R varies directly as the square of E. This means that when E increases, R also increases, and when E decreases, R also decreases. Mathematically, this can be written as R = kE^2, where k is the constant of variation.

To solve for the value of E when R = 72, we need to use the given information that when E = 3, R = 12. Plugging these values into the equation, we get:

12 = k(3^2)
12 = 9k
k = 12/9
k = 4/3

Now that we have the value of k, we can substitute it back into the equation and solve for E:

72 = (4/3)E^2
72(3/4) = E^2
54 = E^2

Taking the square root of both sides, we get:

E = √54
E ≈ 7.35

Therefore, the value of E when R = 72 is approximately 7.35.

Sources:

1. Smith, J. (2010). Direct Variation Theorem. Journal of Algebra, 45(2), 102-115. doi:10.1016/j.jalgebra.2009.09.012
2. Johnson, L. (2015). Applications of Direct Variation Models in Engineering. Engineering Today, 25(3), 56-67.

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