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It's kind of hard to visualize the picture I have, but possible without seeing. A piece of cardboard measures 10 in. by 15 in. Two equal squares are...
It's kind of hard to visualize the picture I have, but possible without seeing.A piece of cardboard measures 10 in. by 15 in.. Two equal squares are removed from the corners of a 10. in side as shown in the figure. Two equal rectangles are removed from the other corners so that the tabs can be folded to form a rectangular box with a lid. Find the maximum volume of the box.I set the sides of the little cutout squares as x, so got the sides to be 7.5-x and 10-2x .So volume is all the 3 sides multiplied, the height being the same as any of the sides of the little square things, so x. So x(7.5-x)(10-2x)Multiplied out, got 75x - 25x^2 + 2x^3Then derived, so 75 - 50x + 6x^2, or rather 6x^2 - 50x + 75.Can't really factor, I guess you quadratic formula, then plug the number back into the orig.Got 6.37, not sure if it's right for x, if someone could confirm, that'd be great.This problem is a really big part of my grade for Calculus, and just want to make sure I did it right, thanks.
