Find two numbers differing by 48 whose product is as small as possible. Enter your two numbers as a comma separated list, e.g. 2, 3. The two numbers are 6. Practice similar ITEMS INFO < Previous Ne If 1200 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box. Volume = (include units) 7. Practice similar ITEMS INFO < Previous Next A Norman window has the shape of a rectangle surmounted by a semicircle. Suppose the outer perimeter of such a window must be 600 cm. In this problem you will find the base length x which will maximize the area of such a window. Use calculus to find an exact answer. occurs? When the base length is zero, the area of the window will be zero. There is also a limit on how large x can be: when x is large enough, the rectangular portion of the window shrinks down to zero height. What is the exact largest value of x when this largest x: - cm. Determine a function A(x) which gives the area of the window in terms of the parameter x (this is the function plotted above): A(x) = cm. Now find the exact base length x which maximizes this area: x = A cm. 8. Practice similar < Previous (1 point) A point P needs to be located somewhere on the line AD so that the total length L of cables linking P to the points A, B, and C is minimized (see the figure). Estimate the minimum value of L to two decimals. A P 5 m B 2 m D 3 m C First, give the function to be minimized, using the variable x. L(x) = = Then use your calculator or other software to estimate the minimum value of L to two decimal places. Do not attempt to solve the derivative=0 by hand. 1 m