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If
p is inversely proportional to the square of
q, and
p is 20 when
q is 10 , 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 $10$ , 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

10

, 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 the 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. $\newline$ We know that $p = 20$ when $q = 10$ . Substitute these values into the equation $p = \frac{k}{q^2}$ to find $k$ . $\newline$ $20 = \frac{k}{10^2}$ $\newline$ $20 = \frac{k}{100}$
Solve for k: Solve for k. $\newline$ Multiply both sides of the equation by $100$ to isolate $k$ . $\newline$ $20 \times 100 = k$ $\newline$ $2000 = k$
Write Equation with $k$ : Write the equation with the found constant $k$ . Now that we have found $k$ to be $2000$ , we can write the inverse proportionality equation as $p = \frac{2000}{q^2}$ .
Find $p$ for $q=2$ : Find $p$ when $q$ is $2$ . $\newline$ Substitute $q = 2$ into the equation $p = \frac{2000}{q^2}$ . $\newline$ $p = \frac{2000}{2^2}$ $\newline$ $p = \frac{2000}{4}$
Calculate $p$ : Calculate the value of $p$ . $\newline$ Divide $2000$ by $4$ to find $p$ . $\newline$ $p = 500$

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