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For the following problems, a varies jointly with b and the square of c.

If a is 64 when b=1 and c = 4, find b when a = 32 and c=1.

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HAJRUDINGO

Answer:

The value of b is 8

Step-by-step explanation:

Equation:

[tex]a = kb {c}^{2} [/tex]

Given:

[tex]a = 64 \\ b = 1 \\ c = 4[/tex]

Solve for the constant of variation (k):

[tex]64 = k(1)(4)^{2} \\ 64 = k(1)(16) \\ 64 = 16k \\ k = 4[/tex]

Solve for b:

Given:

[tex]k = 4 \\ a = 32 \\ c = 1[/tex]

Solution:

[tex]32 = (4)(b)(1) ^{2} \\ 32 = 4b \\ b = 8[/tex]

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