Answer:
The correct answer option is 192.
Step-by-step explanation:
We know that f(x) varies directly with [tex]x^{2}[/tex] so we can write it as:
[tex]f(x)[/tex] ∝ [tex]x^{2}[/tex]
Changing it to an equality by the addition of a constant [tex]k[/tex]:
[tex]f(x) = k.x^{2}[/tex]
If f(x) = 75 when x = 5, then we can find the value of k:
[tex]75=k(5)^2[/tex]
[tex]k=\frac{75}{25} =3[/tex]
If k = 3, we can find the value of f(8):
[tex]f(8)=3(8)^2[/tex]
[tex]f(8)=3*64[/tex]
[tex]f(8)=[/tex]192
