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anonymous
 one year ago
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.)
anonymous
 one year ago
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.)

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i already did it but i got it wrong 2 times please help

phi
 one year ago
Best ResponseYou've already chosen the best response.0did you draw a picture of what is going on ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0u want me to show u what i have gotten so far?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes i did i got the equation (502x)(102x)(x)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then all together 4x^3120x^2+500x

phi
 one year ago
Best ResponseYou've already chosen the best response.0ok, now the derivative wrt x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then i found the maximum of the graph of 4x^3120x^2+500x

phi
 one year ago
Best ResponseYou've already chosen the best response.0you have \[ V = 4x^3120x^2+500x \] 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
 one year ago
Best ResponseYou've already chosen the best response.0and now do i find the maximum of that?

phi
 one year ago
Best ResponseYou've already chosen the best response.0you find what x's make the equation 0 use the quadratic formula

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so now i use the quadratic formula or do i put it in the graphing calculator and find the maximum?

phi
 one year ago
Best ResponseYou've already chosen the best response.0we 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^260x+125=0 using the quadratic formula

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and then my answer from that is the final answer?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[60+\sqrt{5100} all divided by 6

phi
 one year ago
Best ResponseYou've already chosen the best response.0you should get a real number

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i dont know how to simplify sqrt

phi
 one year ago
Best ResponseYou've already chosen the best response.0the number inside the square root should be 60*60  4*3*125 that is not 5100

phi
 one year ago
Best ResponseYou've already chosen the best response.0I would use a calculator and get a decimal answer. they say (Round your answer to two decimal places.)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i am using a caluclator

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i did 4(3)125 and got 1500 then 60*60 is 3600 and those 2 subtracted is 2100 right???

phi
 one year ago
Best ResponseYou've already chosen the best response.0yes so \[ x = \frac{60\pm\sqrt{2100}}{6} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i got 60+10 sqrt{21} all divided by 6 is that right

phi
 one year ago
Best ResponseYou've already chosen the best response.0that 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.

phi
 one year ago
Best ResponseYou've already chosen the best response.0yes, that looks ok. round to 2 decimal places.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so 2.36 is the final answer
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