Question

@Michele_Laino

Answer 1

does it really say "cube"?

Answer 2

i seriously doubt it means cube
i think it means a box

Answer 3

wait a moment please, I have to reply to a physics question, only a few seconds!

Answer 4

it says open box??

Answer 5

volume is the product of all three dimensions, namely
\[V(x)=x(16-2x)(30-2x)\] maximize that one

Answer 6

multiply out, take the derivative, set it equal to zero (it will be a quadratic, if you are lucky if factors) and that will be your answer for \(x\)

Answer 7

if it was me, i would cheat
http://www.wolframalpha.com/input/?i=x%2816-2x%29%2830-2x%29

Answer 8

yeah it does factor! did you get the derivative?

Answer 9

on nvm take the derivative first

Answer 10

\[V(x)=4 x^3-92 x^2+480 x\] find
\[V'(x)\]next

Answer 11

@mondona answer of @satellite73 is the right answer!

Answer 12

k set
\[3x^2-46x+120=0\] and solve
it actually factors

Answer 13

k good so critical points are
\(x=\frac{10}{3}\) and also \(x=12\)
you get to pick one
hint: 12 is not in the domain of your function

Answer 14

wait what? pick one as in thats it to the question?

Answer 15

@satellite73 whats the next step?

Answer 16

please, note thatyou function is V(x)=x(30-2x)(16-2x) as @satellite73 as wrote. Now we have to consider that:
\[x>0\]
\[30-2x>0\]
and
\[16-2x>0\]
in order that V(x) has Mathematical sene.
Solving the systm frmed by the above thee ineualities, we find:
0<x<8
so x=12 can't belong to the domain of V(x)

Answer 17

...sorry has mathmatical sense..

Answer 18

@mondona

Answer 19

that's right!

Answer 20

is that my final answer thoug?..

Answer 21

noo, please you have to substitute x=10/3 into the formula for V(x), in other words, you have to calculate V(10/3)

Answer 22

please you have:
\[V(10/3)=\frac{ 19,600 }{ 27 }\]
@mondona
check my result please!

Answer 23

yup thats what i got! thanks!

Answer 24

Thanks! @mondona