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If
p is inversely proportional to the square of
q, and
p is 25 when
q is 12 , determine
p when
q is equal to 5 .
Answer:

If $p$ is inversely proportional to the square of $q$ , and $p$ is $25$ when $q$ is $12$ , determine $p$ when $q$ is equal to $5$ . $\newline$ Answer:

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Write and solve inverse variation equations

Full solution

Q. If

p

is inversely proportional to the square of

q

, and

p

is

25

when

q

is

12

, determine

p

when

q

is equal to

5

.

\newline

Answer:

Understand relationship: Understand the relationship between $p$ and $q$ . Since $p$ is inversely proportional to the square of $q$ , we can write this relationship as $p = \frac{k}{q^2}$ , where $k$ is the constant of proportionality.
Find constant $k$ : Use the given values to find the constant $k$ . We know that $p = 25$ when $q = 12$ . Substitute these values into the equation $p = \frac{k}{q^2}$ to find $k$ . $25 = \frac{k}{12^2}$
Calculate k value: Calculate the value of k. $\newline$ $25 = \frac{k}{144}$ $\newline$ Multiply both sides by $144$ to solve for k. $\newline$ $25 \times 144 = k$ $\newline$ k = $3600$
Write equation with $k$ : Write the inverse proportionality equation with the found value of $k$ . Now that we have $k$ , we can express the relationship as $p = \frac{3600}{q^2}$ .
Find $p$ for $q=5$ : Find $p$ when $q = 5$ . $\newline$ Substitute $q = 5$ into the equation $p = \frac{3600}{q^2}$ . $\newline$ $p = \frac{3600}{5^2}$ $\newline$ $p = \frac{3600}{25}$
Calculate final p: Calculate the final value of p. $\newline$ $p = \frac{3600}{25}$ $\newline$ $p = 144$

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