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
jamiebookeater
  • jamiebookeater
See more answers at brainly.com
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.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

anonymous
  • anonymous
anonymous
  • anonymous
anonymous
  • anonymous

Looking for something else?

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

More answers

anonymous
  • anonymous
anonymous
  • anonymous
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
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

Looking for something else?

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