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Write an equation that describes the following relationship:
y varies inversely as the fourth power of
x and when
x=1,y=3.

Write an equation that describes the following relationship: $y$ varies inversely as the fourth power of $x$ and when $x=1, y=3$ .

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Write inverse variation equations

Full solution

Q. Write an equation that describes the following relationship:

y

varies inversely as the fourth power of

x

and when

x=1, y=3

.

Determine Form of Equation: Determine the form of the inverse variation equation. $\newline$ In an inverse variation where $y$ varies inversely as the fourth power of $x$ , the equation takes the form: $y = \frac{k}{x^4}$ , 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 when $x=1$ , $y=3$ . Substitute these values into the equation to find $k$ : $3 = \frac{k}{1^4}$ .
Solve for Constant $k$ : Solve for the constant of variation $k$ . $\newline$ Since $1^4 = 1$ , the equation simplifies to $3 = k$ . Therefore, $k = 3$ .
Write Final Equation: Write the final inverse variation equation using the value of $k$ . Substitute $k = 3$ into the inverse variation equation: $y = \frac{3}{x^4}$ .

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