anonymous
  • anonymous
A box is to be constructed from a sheet of cardboard that is 10 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.)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
@ganeshie8
anonymous
  • anonymous
@Hero
anonymous
  • anonymous
@dan815

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More answers

anonymous
  • anonymous
@pooja195
anonymous
  • anonymous
@triciaal
anonymous
  • anonymous
i already did it but i got it wrong 2 times please help
phi
  • phi
is this calculus?
anonymous
  • anonymous
yes
phi
  • phi
did you draw a picture of what is going on ?
anonymous
  • anonymous
u want me to show u what i have gotten so far?
anonymous
  • anonymous
yes i did i got the equation (50-2x)(10-2x)(x)
anonymous
  • anonymous
then all together 4x^3-120x^2+500x
phi
  • phi
ok, now the derivative wrt x
anonymous
  • anonymous
what do u mean
anonymous
  • anonymous
then i found the maximum of the graph of 4x^3-120x^2+500x
anonymous
  • anonymous
and i got 3.4978761
phi
  • phi
you have \[ V = 4x^3-120x^2+500x \] and people find the derivative of that \[ \frac{dV}{dt} = 12x^2 -240x + 500 \] and set = to zero \[ 12x^2 -240x + 500=0\\ 3x^2 -60x+125=0 \]
anonymous
  • anonymous
and now do i find the maximum of that?
phi
  • phi
you find what x's make the equation 0 use the quadratic formula
anonymous
  • anonymous
so now i use the quadratic formula or do i put it in the graphing calculator and find the maximum?
phi
  • phi
we don't want the maximum of the derivative, we want to find the x value that makes the derivative 0. so we solve for x in 3x^2-60x+125=0 using the quadratic formula
anonymous
  • anonymous
and then my answer from that is the final answer?
anonymous
  • anonymous
i got this
anonymous
  • anonymous
\[60+-\sqrt{-5100} all divided by 6
phi
  • phi
you should get a real number
anonymous
  • anonymous
i dont know how to simplify sqrt
anonymous
  • anonymous
im really bad at it
phi
  • phi
the number inside the square root should be -60*-60 - 4*3*125 that is not -5100
anonymous
  • anonymous
i got 2100 sorry
phi
  • phi
I would use a calculator and get a decimal answer. they say (Round your answer to two decimal places.)
anonymous
  • anonymous
i am using a caluclator
anonymous
  • anonymous
i did 4(3)125 and got 1500 then -60*-60 is 3600 and those 2 subtracted is 2100 right???
phi
  • phi
yes so \[ x = \frac{60\pm\sqrt{2100}}{6} \]
anonymous
  • anonymous
i got 60+10 sqrt{21} all divided by 6 is that right
anonymous
  • anonymous
@phi
phi
  • phi
that root will give you 10+ (sqrt(21))/6 which is bigger than 10 one of your sides is length 10, so x has to be smaller than 10 I would use the other root.
anonymous
  • anonymous
i got 2.362373842
phi
  • phi
yes, that looks ok. round to 2 decimal places.
anonymous
  • anonymous
so 2.36 is the final answer
phi
  • phi
yes

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