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Assume that $y$ varies inversely with $x$ . If $y = 2$ when $x = 16$ , find $y$ when $x = 4$ . $\newline$ Write and solve an inverse variation equation to find the answer. $\newline$ $y =$ _____

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Write and solve inverse variation equations

Full solution

Q. Assume that

y

varies inversely with

x

. If

y = 2

when

x = 16

, find

y

when

x = 4

.

\newline

Write and solve an inverse variation equation to find the answer.

\newline

y =

_____

Understand Relationship: Understand the relationship between $y$ and $x$ . Inverse variation means that as one variable increases, the other decreases proportionally. The formula for inverse variation is $y = \frac{k}{x}$ , where $k$ is the constant of variation.
Find Constant of Variation: Use the given values to find the constant of variation $k$ . We are given that $y = 2$ when $x = 16$ . Substitute these values into the inverse variation formula to find $k$ . $2 = \frac{k}{16}$ Now, solve for $k$ by multiplying both sides by $16$ . $2 \times 16 = k$ $32 = k$
Write Inverse Variation Equation: Write the inverse variation equation with the found constant $k$ . Now that we know $k = 32$ , we can write the equation as $y = \frac{32}{x}$ .
Find $y$ for $x=4$ : Find $y$ when $x = 4$ using the inverse variation equation. $\newline$ Substitute $x = 4$ into the equation $y = \frac{32}{x}$ . $\newline$ $y = \frac{32}{4}$ $\newline$ $y = 8$

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