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If
p is inversely proportional to the square of
q, and
p is 27 when
q is 11 , determine
p when
q is equal to 3 .
Answer:

If $p$ is inversely proportional to the square of $q$ , and $p$ is $27$ when $q$ is $11$ , 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

27

when

q

is

11

, 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 $k$ : Use the given values to find the constant $k$ . We know that $p = 27$ when $q = 11$ . Substitute these values into the equation $p = \frac{k}{q^2}$ to find $k$ . $27 = \frac{k}{11^2}$
Calculate Value of k: Calculate the value of $k$ . Solve the equation for $k$ by multiplying both sides by $11^2$ . $27 \times 11^2 = k$ $k = 27 \times 121$ $k = 3267$
Write Equation with $k$ : Write the inverse proportionality equation with the found value of $k$ . Now that we have $k$ , we can write the equation as $p = \frac{3267}{q^2}$ .
Find $p$ for $q=3$ : Find $p$ when $q = 3$ . $\newline$ Substitute $q = 3$ into the equation $p = \frac{3267}{q^2}$ . $\newline$ $p = \frac{3267}{3^2}$ $\newline$ $p = \frac{3267}{9}$ $\newline$ $p = 363$

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