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Write an equation that describes the following relationship:
y varies jointly as
x and the square root of
z, and when
x=1 and
z=9, then
y=15.

Write an equation that describes the following relationship: $y$ varies jointly as $x$ and the square root of $z$ , and when $x=1$ and $z=9$ , then $y=15$ .

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Write a linear equation from a slope and y-intercept

Full solution

Q. Write an equation that describes the following relationship:

y

varies jointly as

x

and the square root of

z

, and when

x=1

and

z=9

, then

y=15

.

Identify Equation Form: Identify the form of the equation for joint variation. $\newline$ Joint variation is described by the equation $y = k(x)(\sqrt{z})$ , where $k$ is the constant of variation.
Determine Constant of Variation: Determine the constant of variation $k$ using the given values. $\newline$ We know that when $x=1$ and $z=9$ , then $y=15$ . Substitute these values into the equation to find $k$ : $15 = k(1)(\sqrt{9})$ .
Calculate Value of k: Calculate the value of $k$ . Since $\sqrt{9} = 3$ , the equation becomes $15 = k(1)(3)$ , which simplifies to $15 = 3k$ . Divide both sides by $3$ to solve for $k$ : $k = \frac{15}{3} = 5$ .
Write Final Equation: Write the final equation using the calculated value of $k$ . Substitute $k = 5$ into the joint variation equation: $y = 5(x)(\sqrt{z})$ . This is the equation that describes the relationship.

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