Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
Answer:
The amount to remove from each corner is a square, 4/3 ft by 4/3 ft.
Step-by-step explanation:
The piece of cardboard measures 8 ft by 8 ft.
Each corner will be cut to create the sides of the box.
Let the square cut from each corner measure x by x ft.
The base of the box will measure 8 - 2x by 8 - 2x, and the height of the box will be x.
V = (8 - 2x)^2 * x
V = 64x - 32x^2 + 4x^3
Now we differentiate and set the derivative equal to zero to find a maximum value.
64 - 64x + 12x^2 = 0
3x^2 - 16x + 16 = 0
(3x - 4)(x - 4) = 0
3x - 4 = 0 or x - 4 = 0
3x = 4 or x = 4
x = 4/3 or x = 4
The solution x = 4 must be discarded since 8 - 2x = 8 - 8 = 0, and the sides would have 0 length.
The amount to remove from each corner is a square, 4/3 ft by 4/3 ft.
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.