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Write an equation that describes the following relationship:
y varies directly as the square of
x and when
x=4,y=80.

Write an equation that describes the following relationship: $y$ varies directly as the square of $x$ and when $x=4, y=80$ .

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Write and solve direct variation equations

Full solution

Q. Write an equation that describes the following relationship:

y

varies directly as the square of

x

and when

x=4, y=80

.

Identify general form: Identify the general form of direct variation when $y$ varies directly as the square of $x$ . The general form of direct variation in this case is $y = k \times x^2$ , where $k$ is the constant of variation.
Substitute values into equation: Substitute $y = 80$ and $x = 4$ into the equation $y = k \times x^2$ . $\newline$ $y = k \times x^2$ $\newline$ $80 = k \times 4^2$
Solve for constant: Solve the equation for the constant of variation, $k$ . $\newline$ $80 = k \times 16$ $\newline$ $\frac{80}{16} = k$ $\newline$ $k = 5$
Substitute value of $k$ : Substitute the value of $k$ into the direct variation formula. $\newline$ Now that we have $k = 5$ , we can write the direct variation equation as: $\newline$ $y = 5 \times x^2$

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\newline

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