Question

select the correct answer.

the variable (f) varies inversely as the square root of (g). when (f = 4), (g = 4). jordans work finding the value of (f) when (g = 100) is shown:

(fsqrt{g} = k)
(4(4) = k)
(16 = k)

(fsqrt{g} = 16)
(fsqrt{100} = 16)
(10f = 16)
(f = 1.6)

what is the first error, if any, in jordans work?

he used an equation that models direct variation instead of inverse variation.
he incorrectly calculated the constant of variation.
he took the square root of the wrong variable.
he did not make any errors.

Explanation:

Identify the correct variation model

$$ f = \frac{k}{\sqrt{g}} \implies f\sqrt{g} = k $$

Analyze Jordan's first step

$$ f\sqrt{g} = k $$

Evaluate Jordan's substitution and calculation

$$
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$$

Jordan wrote:

$$ 4(4) = k \implies 16 = k $$

Jordan substituted \(g = 16\) or forgot to take the square root of \(g = 4\), which means he incorrectly calculated the constant of variation.

Answer:

• He used an equation that models direct variation instead of inverse variation.
• (B) He incorrectly calculated the constant of variation. (Correct answer)
• He took the square root of the wrong variable.
• He did not make any errors.