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U is inversely proportional to the cube of V and U = 81 when V = 2. Find U when ...


Question

U is inversely proportional to the cube of V and U = 81 when V = 2. Find U when V = 3

Options

A) 24

B) 27

C) 32

D) 36

The correct answer is A.

Explanation:

U \(\alpha \frac{1}{V^3}\)
U = \(\frac{k}{V^3}\)
k = UV3
k = 81 x 23 = 81 x 8
When V = 3,
U = \(\frac{k}{V^3}\)
U = \(\frac{81 \times 8}{3^3}\)
U = \(\frac{81 \times 8}{27}\) = 24

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Dicussion (1)

  • U \(\alpha \frac{1}{V^3}\)
    U = \(\frac{k}{V^3}\)
    k = UV3
    k = 81 x 23 = 81 x 8
    When V = 3,
    U = \(\frac{k}{V^3}\)
    U = \(\frac{81 \times 8}{3^3}\)
    U = \(\frac{81 \times 8}{27}\) = 24

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