January 1st, 2010 | 
Author:
Calculus Optimization Problem help?
I had 100 problems Calculation and there are 4 that I can do! Can anyone help?!? 1. A strip of copper wire is 8 inches wide and should be done in a canal in the rain turning the sides to form a channel with a rectangular cross section. Find the dimensions of the cross section, if the carrying capacity should be maximized. 2. Find the coordinates of the point on the curve y = x ^ 2 +3 which is closest to the point (0,3). 3. Find the dimensions of the rectangle of maximum area that can be embedded in a right triangle with sides of 12, 16 and 20. 4. A cone-shaped paper cup of drink is to celebrate 20 cm cubic liquid. Find the height of the cup that require less paper. Thank you! I solved # 2! You just need the rest, thanks!
Hello here is the answet to number 1. Draw the copper wire, is only a straight line 8 inches long. ______________ Now take two equal peices length from the end, and mark them off. Each piece called "x". _x_._________._x_ The cable is still a total of 8 inches wide, so we can call the 8-2x midsection. Now if we are doubling each section X to enable it to hold water that receives a recangle thing. I___________I, with each piece to length x, y Part 8-2x long. The area or cross section (call it A) is based on the height, or: A = x (8-2x) = 8x-2x ^ 2 derive A '= 8-4x to find a maximum, set the derivatives equal to zero. 8-4x = 0 x = 2, so the sides of the channel are 2inches high. Now put x in the equation for the background, 8-2 (2) = 4 dimensions are 2 inches by four inches
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Tags: bleed, construction, detail, downspouts, gutter, gutter dimensions, margin