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tmagloire1
 one year ago
A box is to be constructed from a sheet of cardboard that is 20 cm by 50 cm by cutting out squares of length x by x from each corner and bending up the sides.
What is the maximum volume this box could have? (Round your answer to two decimal places. Do not include units, for example, 10.22 cm would be 10.22.)
tmagloire1
 one year ago
A box is to be constructed from a sheet of cardboard that is 20 cm by 50 cm by cutting out squares of length x by x from each corner and bending up the sides. What is the maximum volume this box could have? (Round your answer to two decimal places. Do not include units, for example, 10.22 cm would be 10.22.)

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SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1calc I prob optimization, correct?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437076558138:dw

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0I got 2029.95 but that isn't correct

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437076685341:dw

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0Yep that's how i set it up

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1do you know why I subtracted 2xfrom 20 and 50?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So you do know why we subtract 2x from 20 and 50, right/

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So, now, we will create the function for volume. Find critical numbers Find the maximum of it (with limits we will later provide/make)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1The volume would be height•lenght•width

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1and in this case v(x)=2x•(202x)•(502x)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1where V stands for volume

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0Why would it be 2x instead of just x

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Why would it be 2x instead of just x, because you bend a cutout of length x from both sides, don't you?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437076945620:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1so the side 20 and side 50 is decreased by 2x. Got that, good:)

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0So now take the derivative of the function we got?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1now we will do a regular process once we got the function V(x)=2x•(202x)•(502x)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1I would perhaps simplify it a little instead of doing a product twice, but you can find the derivative as you wish:)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1V(x)=x•(202x)•(502x) ^ ^ just x, not 2x.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1but 202x and 502x are correct measures

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0Okay so take the derivative of that then?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1V(x)=x•(202x)•(502x) V(x)=x•(100040x100x+4x²) V(x)=x•(1000140x+4x²) I would do derivative, product now

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1V\(\rm ~'\)(x) = 1•(1000140x+4x²)+x•(0140+8x)

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0So it will be 12x^2280x1000?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1I would use wolfram, actually, because I am the laziest person on this planet.

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0Hahaha i just used Wolfram for it because i didn't feel like taking the derivative myself xD

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1V'(x)=4(3x²70x+250) by wolfram.... I did it like this because wolfram can give a handy version faster

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1set V'(x)=0 to find your critical number

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1remember tho, that 0>x>10 or else your volume is going to be =0 or negative.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1that wouldn't make sense, because you get a negative volume if you plug it in our volume function.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1find the roots of 4(3x²70x+250)=0

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.026.48 and 3.146 which still doesn't make sense right?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1And I will tell you will get the ±, and only take the minu one, because the one with the + is greater than 10

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1what crtical number(s) did you get?

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0I am getting 60 now :// sos

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437077863587:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1take the , because + will get x>10

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0Oh I must have been doing some crazy math error when taking the crit #

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0so take 4.4 and use it in the equation at the beginning?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1you did something wrong again:(

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Yup, that is right

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0Oh okay! Thank you so much of all the help. I think I understand it now!!

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Yes.... overview. 1. We created a function V(x)=x • (202x) • (502x) 2. Constraint x>0, because otherwise volume is negative or 0 (based on the first, x, component of V(x)). x<10, because otherwise (based on the 202x part), the volume would be 0 or negative. 3. We differentiated the function to get 2 critical numbers (that is two solutions of V'(x)=0) NOTE: Critical numbers (usually) are also values for which v'(x) is undefined, if defined for initial function v(x)  (but no such values in this case). Also, critical numbers usually can be closed interval boundaries, but our interval is open (we didn't include 0 or 10), so that is not our case. So in our case only solutions to v`(x)=0 are critical numbers. 4. We excluded the (35+5√19)/3 solution based on our constraint (because it is greater than 10), and rather used the only solution remaining, i.e. (355√19)/3. 5. We got the answr
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