Answer:
[tex]h = 5\, c^{3}[/tex].
When [tex]c = 5[/tex], [tex]h = 625[/tex].
Step-by-step explanation:
Since [tex]h[/tex] is proportional to the cube of [tex]c[/tex], it would be possible to find some constant [tex]k[/tex] such that for all [tex]c\![/tex]:
[tex]h = k\, c^{3}[/tex].
The next step is to find [tex]k[/tex]. Given that [tex]h = 40[/tex] when [tex]c = 2[/tex]:
[tex]40 = k\, (2)^{3}[/tex].
Solve for [tex]k[/tex] to obtain:
[tex]\displaystyle k = \frac{40}{2^{3}} = 5[/tex].
In other words:
[tex]h = 5\, c^{3}[/tex].
To find the value of [tex]h[/tex] when [tex]c = 5[/tex], substitute the value of [tex]c[/tex] into the expression and evaluate:
[tex]h = 5\, (5)^{3} = 625[/tex].
In other words, [tex]h = 625[/tex] when [tex]c = 5[/tex].
