DanielaJohana
  • DanielaJohana
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
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
campbell_st
  • campbell_st
let x he the height of the box... length = 18 - 2x width = 11 - 2x |dw:1433120436164:dw| the volume is \[V = x (18-2x)(11-2x)\] multiply it out
campbell_st
  • campbell_st
when you get an equation, then find the 1st derivative. let it equal zero and solve for x
DanielaJohana
  • DanielaJohana
\[V=x(18-2x)(11-2x) \] \[V=(18x-2x^2)(11x-2x^2)\] \[V=198x^2-36x^3-22x^3+4x^4\] \[V=198x^2-58x^3+4x^4\]

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

campbell_st
  • campbell_st
well 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
  • DanielaJohana
yes, it is cubic- and would it be 198-116x+12x^2?
campbell_st
  • campbell_st
now solve for x
DanielaJohana
  • DanielaJohana
x= 2.214 and 7.453 Now what do I do?
campbell_st
  • campbell_st
well you can't use 7.453... as the width is 11-2x 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
  • campbell_st
hope 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
  • DanielaJohana
Yeah, once I plug it in it gives me 197.48 as the answer.. and that's the maximum volume right?
campbell_st
  • campbell_st
I haven't done the caclulations... you can check by graphing thecubic equation
DanielaJohana
  • DanielaJohana
Okay, I see how this worked out, thank you
campbell_st
  • campbell_st
I just graphed it and the smaller value gives the max volume
campbell_st
  • campbell_st
the max is (2.2, 197.5) hope it helped
DanielaJohana
  • DanielaJohana
yes, it did thanks

Looking for something else?

Not the answer you are looking for? Search for more explanations.