Question

Hi! I was absent today and did not understand this lesson please I will be really grateful if you help me ! I appreciate it this is classwork assignment does not count as a tes

Answer 1

Inverse proportion is when one quantity increases and the other decreases. The two quantities are said to be inversely proportional. The inverse proportion formula is

$\begin{gathered} y=\frac{k}{x} \\ \text{ for a constant k} \end{gathered}$

So, in this case, we can write the following equation:

$p=\frac{k}{q^2}$

Since we know that the value of p is 18 when q is 2, we can find the value of k:

$\begin{gathered} p=18 \\ q=2 \\ p=\frac{k}{q^2} \\ 18=\frac{k}{(2)^2} \\ 18=\frac{k}{(2)(2)} \\ 18=\frac{k}{4} \\ \text{ Multiply by 4 from both sides of the equation} \\ 18\cdot4=\frac{k}{4}\cdot4 \\ 18\cdot4=k \\ 72=k \end{gathered}$

Now, we can determine the value of p when q is equal to 3:

$\begin{gathered} p=\text{ ?} \\ q=3 \\ p=\frac{k}{q^2} \\ p=\frac{72}{(3)^2} \\ p=\frac{72}{(3)(3)} \\ p=\frac{72}{9} \\ p=8 \end{gathered}$

Therefore,