Question

Determine the dimensions of a rectangular solid (with a square base) of maximum volume if its surface area is 150 square inches.
base dimension

Answer 1

I NEED HELP I THINK THE ANSWER IS 5*5*5 BUT EVERYTIME I SUBMIT THAT IT DOES NOT WORK!!

Answer 2

I got exactly the same yours. but I think may be the | 5 | will work because when solving for x ( the side of base) we get x^2 =25 . In fact the length of side must be positive and everybody knows that except the computer. try again.

Answer 3

\[V(x,y,z)=xyz\\
S(x,y,z)=2(xy)+2(yz)+2(zy)=150
\]

Answer 4

the problem gives us " square base", does it mean y =x?

Answer 5

yep

Answer 6

\[V(x,y)=x^2y\\S(x,y)=2x^2+2xy+2xy=150\implies x(x+2y)=75\]

Answer 7

now, the cost function becomes,
\[V(x)=x^2{1\over2}\left({75\over x}-x\right)={1\over2}(75x-x^3)\]
maximize this the ususal way

Answer 8

exactly 5,5,5

Answer 9

but he said that it doesn't work when he submited

Answer 10

i am submitting it as 5x5x5 and i tried 5*5*5 and it does not work...

Answer 11

thank you both for your help i really appreciate it, i just dont know why it is marking it wrong? should it be written in a different way?

Answer 12

\[V'(x)={75\over2}-{3\over2}x^2=0\implies x^2-15=0\implies x=\pm\sqrt{15}\]

Answer 13

that does not work either.

Answer 14

:)
length of a side cannot be negative. hope you put in the positive squre-root

Answer 15

i cannot submit it as square root it does not give me that option..

Answer 16

so, should be 3.8 or somethign like that

Answer 17

hi friend, how can you get x =+- sqr 15? i don't know

Answer 18

hehe.
HINT: 15 lies between what two perfect squares? -> 9 and 16

Answer 19

and then close to which one

Answer 20

why don't we go on the simplest way to get x ?

Answer 21

@Hoa I do not see what you mean

Answer 22

\[\frac{ 75 }{ 2 }-\frac{ 3x^2 }{ 2 }=0 --->\frac{ 3x^2 }{ 2 }= \frac{ 75 }{ 2 }---> x^2=25\]

Answer 23

ooohh "25".. I put "15".. duh

Answer 24

hihihi.... magic mathematic ?

Answer 25

@hayatabz1 just to verify, is the solid closed or open?

Answer 26

like there is no suface on the top!!!

Answer 27

yeah... I know what you mean

Answer 28

but i dont' think it is the case.

Answer 29

it is asking for "base dimension". I do not think it includes the height. Those online classes are so crazy sometomes. Esp with physics and numbers

Answer 30

you mean it's vector of base?

Answer 31

so, it's \[\left(\begin{matrix}1 \\ 1\\1\end{matrix}\right)\]

Answer 32

cant say. dont have "O".
but it says base dimensions..

Answer 33

I surrender!!! cannot follow anymore. too complicated.. if it's a vector, I'm ok. if it's open solid, it engages to chemistry. I am hand off, long time ago when I studied it.

Answer 34

no. just subtract one of the surfaces from S(x,y)

Answer 35

:)

Answer 36

ok. let the asker does his work. I think after 3 times submit, he has no more option for re submit the answer. he lost it

Answer 37

Hi there! Welcome to Openstudy :)

If you have any doubts on how the site works ,feel free to ask me or any other Ambassador with purple A near them .Have great time here .

Check out our COC : http://openstudy.com/code-of-conduct

Answer 38

its a solid

Answer 39

hold on, in the question does it say "square base" or is that somethig you came up with?

Answer 40

it says exactly this..

Answer 41

and im looking for the base dimension

Answer 42

Determine the dimensions of a rectangular solid (with a square base) of maximum volume if its surface area is 150 square inches.
base dimension

Answer 43

base dimension =???

Answer 44

the base dimentions are just (5,5)

Answer 45

not
5,5,5 (this includes the third dimension of height)

Answer 46

its not 5,5

Answer 47

i just tried that also...

Answer 48

this is frustrating!

Answer 49

check the units.. "in" for inches..
sometimes they ask for the units

Answer 50

i guess i will just skip that one bc it is not working

Answer 51

On a given day, the flow rate F (in cars per hour) on a congested roadway is given by the equation below, where v is the speed of traffic in miles per hour.
F =
v
22 + 0.07v2
What speed will maximize the flow rate on the road? (Round your answer to one decimal place.)


mi/h

Answer 52

do you know how to figure this out?

Answer 53

Refer to a Mathematica solution attached.

Answer 54

@robtobey thats cheating, lol

Answer 55

and you did ignore the top surface