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Write an equation that describes the following relationship:
y varies jointly as
x,z, and
w and when
x=4,z=2,w=4, then
y=128

Write an equation that describes the following relationship: $y$ varies jointly as $x, z$ , and $w$ and when $x=4, z=2, w=4$ , then $y=128$

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Write direct variation equations

Full solution

Q. Write an equation that describes the following relationship:

y

varies jointly as

x, z

, and

w

and when

x=4, z=2, w=4

, then

y=128

Define joint variation relationship: Define the joint variation relationship. $\newline$ Joint variation means that $y$ varies directly with the product of $x$ , $z$ , and $w$ . Therefore, the equation can be written as: $\newline$ $y = k \times x \times z \times w$
Substitute given values: Substitute the given values into the equation to find the constant of variation $k$ . We know that $y=128$ , $x=4$ , $z=2$ , and $w=4$ . Substituting these values into the equation gives us: $128 = k \times 4 \times 2 \times 4$
Solve for k: Solve for k. $\newline$ To find $k$ , we divide both sides of the equation by the product of $x$ , $z$ , and $w$ : $\newline$ $k = \frac{128}{(4 \times 2 \times 4)}$ $\newline$ $k = \frac{128}{32}$ $\newline$ $k = 4$
Write final equation: Write the final joint variation equation. $\newline$ Now that we have found $k$ to be $4$ , we can write the final equation as: $\newline$ $y = 4 \times x \times z \times w$

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