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If
p is inversely proportional to the square of
q, and
p is 3 when
q is 9 , determine
p when
q is equal to 3 .
Answer:

If $p$ is inversely proportional to the square of $q$ , and $p$ is $3$ when $q$ is $9$ , determine $p$ when $q$ is equal to $3$ . $\newline$ 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

3

when

q

is

9

, determine

p

when

q

is equal to

3

.

\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: Use the given values to find the constant $k$ . We know that $p = 3$ when $q = 9$ . Substitute these values into the equation $p = \frac{k}{q^2}$ to find $k$ . $3 = \frac{k}{9^2}$ $3 = \frac{k}{81}$ Now, solve for $k$ by multiplying both sides by $81$ . $3 \times 81 = k$ $p = 3$ $0$
Write Equation: Write the equation with the found constant $k$ . $\newline$ Now that we have found $k$ to be $243$ , we can write the inverse proportionality equation as: $\newline$ $p = \frac{243}{q^2}$
Find $p$ : Find $p$ when $q$ is equal to $3$ . Substitute $q = 3$ into the equation $p = \frac{243}{q^2}$ . $p = \frac{243}{3^2}$ $p = \frac{243}{9}$ Now, divide $243$ by $9$ to find $p$ . $p$ $1$

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