Answer:
[tex]q = 34[/tex] when [tex]p = 2[/tex].
Step-by-step explanation:
Variables [tex]p[/tex] and [tex]q[/tex] ([tex]p \ne 0[/tex], [tex]q \ne 0[/tex]) are inversely proportional to one another if one variable- for example, [tex]p[/tex]- is proportional to the reciprocoal of the other variable- [tex](1/q)[/tex].
In other words, if [tex]p[/tex] and [tex]q[/tex] ([tex]p \ne 0[/tex], [tex]q \ne 0[/tex]) are inversely proportional to one another, there would exist a constant [tex]k[/tex] ([tex]k \ne 0[/tex]) such that:
[tex]\displaystyle p = k\times \left(\frac{1}{q}\right)[/tex].
The value of [tex]k[/tex] is constant and is independent of [tex]p[/tex] and [tex]q[/tex]. Given that [tex]p = 17[/tex] when [tex]q = 4[/tex], rearrange the equation above to find the value of [tex]k\![/tex]:
[tex]k = p\, q = 68[/tex].
Rewrite the equation again to find [tex]q[/tex] in terms of [tex]k[/tex] (which doesn't change) and [tex]p[/tex] (which might change):
[tex]\begin{aligned}q &= \frac{k}{p}\end{aligned}[/tex].
Since [tex]k = 68[/tex], given that [tex]p = 2[/tex], the value of [tex]q[/tex] would be:
[tex]\begin{aligned}q &= \frac{k}{p} \\ &= \frac{68}{2} = 34\end{aligned}[/tex].
