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DanielaJohana
 one year ago
What is the maximum volume of a box that can be made from an 11 inch by 18 inch piece of paper? Show your work
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DanielaJohana
 one year ago
What is the maximum volume of a box that can be made from an 11 inch by 18 inch piece of paper? Show your work Will fan and medal

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campbell_st
 one year ago
Best ResponseYou've already chosen the best response.3let x he the height of the box... length = 18  2x width = 11  2x dw:1433120436164:dw the volume is \[V = x (182x)(112x)\] multiply it out

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.3when you get an equation, then find the 1st derivative. let it equal zero and solve for x

DanielaJohana
 one year ago
Best ResponseYou've already chosen the best response.0\[V=x(182x)(112x) \] \[V=(18x2x^2)(11x2x^2)\] \[V=198x^236x^322x^3+4x^4\] \[V=198x^258x^3+4x^4\]

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.3well you may want to check, as I think the equation is a cubic... V = x(198  58x + 4x^2) then distribute this V = 198x  58x^2 + 4x^3 now find the 1st derivative

DanielaJohana
 one year ago
Best ResponseYou've already chosen the best response.0yes, it is cubic and would it be 198116x+12x^2?

DanielaJohana
 one year ago
Best ResponseYou've already chosen the best response.0x= 2.214 and 7.453 Now what do I do?

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.3well you can't use 7.453... as the width is 112x is x is 7.453 the width is 4....which is impossible... so it must be the smaller choice...is probabbly the solution... just check by substituting

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.3hope that makes sense... the alternative is to find the 2nd derivative... and test the solutions in the 2nd derivative to determine the max value

DanielaJohana
 one year ago
Best ResponseYou've already chosen the best response.0Yeah, once I plug it in it gives me 197.48 as the answer.. and that's the maximum volume right?

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.3I haven't done the caclulations... you can check by graphing thecubic equation

DanielaJohana
 one year ago
Best ResponseYou've already chosen the best response.0Okay, I see how this worked out, thank you

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.3I just graphed it and the smaller value gives the max volume

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.3the max is (2.2, 197.5) hope it helped

DanielaJohana
 one year ago
Best ResponseYou've already chosen the best response.0yes, it did thanks
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