## 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.)

1. anonymous

@ganeshie8

2. anonymous

@Hero

3. anonymous

@dan815

4. anonymous

@pooja195

5. anonymous

@triciaal

6. anonymous

7. phi

is this calculus?

8. anonymous

yes

9. phi

did you draw a picture of what is going on ?

10. anonymous

u want me to show u what i have gotten so far?

11. anonymous

yes i did i got the equation (50-2x)(10-2x)(x)

12. anonymous

then all together 4x^3-120x^2+500x

13. phi

ok, now the derivative wrt x

14. anonymous

what do u mean

15. anonymous

then i found the maximum of the graph of 4x^3-120x^2+500x

16. anonymous

and i got 3.4978761

17. 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 $12x^2 -240x + 500=0\\ 3x^2 -60x+125=0$

18. anonymous

and now do i find the maximum of that?

19. phi

you find what x's make the equation 0 use the quadratic formula

20. anonymous

so now i use the quadratic formula or do i put it in the graphing calculator and find the maximum?

21. 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

22. anonymous

and then my answer from that is the final answer?

23. anonymous

i got this

24. anonymous

$60+-\sqrt{-5100} all divided by 6 25. phi you should get a real number 26. anonymous i dont know how to simplify sqrt 27. anonymous im really bad at it 28. phi the number inside the square root should be -60*-60 - 4*3*125 that is not -5100 29. anonymous i got 2100 sorry 30. phi I would use a calculator and get a decimal answer. they say (Round your answer to two decimal places.) 31. anonymous i am using a caluclator 32. anonymous i did 4(3)125 and got 1500 then -60*-60 is 3600 and those 2 subtracted is 2100 right??? 33. phi yes so \[ x = \frac{60\pm\sqrt{2100}}{6}$

34. anonymous

i got 60+10 sqrt{21} all divided by 6 is that right

35. anonymous

@phi

36. 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.

37. anonymous

i got 2.362373842

38. phi

yes, that looks ok. round to 2 decimal places.

39. anonymous

so 2.36 is the final answer

40. phi

yes