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=(k)/(x) \\ \text{ for a constant k} \end{gathered}`

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

`p=(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=(k)/(q^2) \\ 18=(k)/((2)^2) \\ 18=(k)/((2)(2)) \\ 18=(k)/(4) \\ \text{ Multiply by 4 from both sides of the equation} \\ 18\cdot4=(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=(k)/(q^2) \\ p=(72)/((3)^2) \\ p=(72)/((3)(3)) \\ p=(72)/(9) \\ p=8 \end{gathered}`

Therefore,