If f(x) varies directly with x2, and f(x) = 75 when x = 5, find the value of f(4).

Question

anonymous · Answer

please help me?

parthkohli · Answer

When $a$ varies directly with $b$, then $a = cb$ where $c$ is a constant.  You understand this, right?

anonymous · Answer

yes, but I am in quadratic variation atm, so I don't klnow if it wants direct or quad

parthkohli · Answer

Don't worry about it.  It's simple.  And yes, the earlier points come in fast.

anonymous · Answer

what should I start with?

parthkohli · Answer

f(x) varies directly with x^2.

So,$$f(x) = c \times x^2$$Let's do a job: find the $c$ with the information we're given.  It is given that $f(5) = 75$.  But $f(5)$ is also the number you get when you plug in 5 for x in the expression $c \times x^2$.

anonymous · Answer

mhm...

parthkohli · Answer

So you get $f(5)=c \times (5)^2=25c$.  But $f(5) = 75$ as given.  Therefore,$$25c =75 \Rightarrow c = 3$$

parthkohli · Answer

Since we're doing direct relation, the constant is always the same.  So $c=3$ in this direct relation.  Thus, here's our direct relation:$$f(x)=3\times x^2$$

parthkohli · Answer

You can now find $f(4)$

anonymous · Answer

brb urinating... sorry about that.

parthkohli · Answer

...

anonymous · Answer

back

parthkohli · Answer

I've explained everything to you.  You're left with$$f(x) = 3x^2$$

anonymous · Answer

so...

anonymous · Answer

48?

parthkohli · Answer

You have to find f(4), so plug 4 into that.