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If
p is inversely proportional to the square of
q, and
p is 20 when
q is 5 , determine
p when
q is equal to 2 .
Answer:

If $p$ is inversely proportional to the square of $q$ , and $p$ is $20$ when $q$ is $5$ , determine $p$ when $q$ is equal to $2$ . $\newline$ 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

20

when

q

is

5

, determine

p

when

q

is equal to

2

.

\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 $p = 20$ when $q = 5$ . Substitute these values into the equation $p = \frac{k}{q^2}$ to find $k$ . $20 = \frac{k}{5^2}$ $20 = \frac{k}{25}$ Now, solve for $k$ by multiplying both sides by $25$ . $k$ $0$ $k$ $1$
Write Equation with $k$ : Write the equation with the found constant $k$ . Now that we have found $k$ to be $500$ , we can write the inverse proportionality equation as $p = \frac{500}{q^2}$ .
Find $p$ for $q=2$ : Find $p$ when $q$ is equal to $2$ . $\newline$ Substitute $q = 2$ into the equation $p = \frac{500}{q^2}$ . $\newline$ $p = \frac{500}{2^2}$ $\newline$ $p = \frac{500}{4}$ $\newline$ $p = 125$

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