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q varies directly with
p^(2).
When
q=36,p=12
Find a formula connecting
q and
p.

q=theta
Submit Answer

$q$ varies directly with $p^{2}$ . $\newline$ When $q=36, p=12$ $\newline$ Find a formula connecting $q$ and $p$ . $\newline$ $q=\theta$ $\newline$ Submit Answer

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Write and solve direct variation equations

Full solution

Q.

q

varies directly with

p^{2}

.

\newline

When

q=36, p=12

\newline

Find a formula connecting

q

and

p

.

\newline

q=\theta

\newline

Submit Answer

Establish direct variation relationship: Establish the direct variation relationship. $\newline$ Since $q$ varies directly with $p^{2}$ , the relationship can be expressed as $q = kp^{2}$ , where $k$ is the constant of variation.
Find $k$ using given values: Use the given values to find $k$ . We know $q = 36$ when $p = 12$ . Substitute these values into the equation $q = kp^2$ . $36 = k(12)^2$
Solve for $k$ : Solve for $k$ . $\newline$ Calculate $12^2 = 144$ . $\newline$ Then, $36 = k \times 144$ . $\newline$ Divide both sides by $144$ to isolate $k$ . $\newline$ k = $\frac{36}{144}$ $\newline$ k = $0.25$
Write formula connecting $q$ and $p$ : Write the formula connecting $q$ and $p$ . Substitute $k = 0.25$ back into the direct variation equation. $q = 0.25p^2$

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