Question

When f = 2 and g = 8, n = 4. If n varies jointly with f and g, what is the constant of variation?

Answer 1

`\blue{\huge {\mathrm{CONSTANT \; VARIATION}}}`

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`{\underline{\huge \mathbb{Q} {\large \mathrm {UESTION : }}}}`

• When f = 2 and g = 8, n = 4. If n varies jointly with f and g, what is the constant of variation?

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`{\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}}`

• The constant of variation is 1/4.

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`{\underline{\huge \mathbb{S} {\large \mathrm {OLUTION : }}}}`

If n varies jointly with f and g, the relationship between them can be written as:

• 
  `\sf n = k * f * g`

where:

• k is the constant of variation.

Using the given information, we can solve for k as follows:

• 
  `\begin{aligned}\sf n&=\sf k* f* g \\\sf 4& =\sf k* 2* 8 \\\sf 4& =\sf 16k \\\sf k& =\sf (4)/(16) \\\sf k& =\sf (1)/(4)\end{aligned}`

Therefore, the constant of variation is 1/4.

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Answer 2

The constant of variation is ¹/₄.

Explanation:

When n varies jointly with f and g, we can write the following equation:

`\boxed{n \propto fg \implies n = kfg}`

where k is the constant of variation.

We are given that f = 2, g = 8, and n = 4.

Substitute these values into the equation:

`\implies 4 = k \cdot 2 \cdot 8`

Solve for k:

`\implies 4 = 16k`

`\implies (4)/(16) = (16k)/(16)`

`\implies (1)/(4)=k`

Therefore, the constant of variation is ¹/₄.