Question

In: Advanced Math

A page is to have a total area of 96 square inches. The top and bottom...

A page is to have a total area of 96 square inches. The top and bottom margins will be 1 inch each, and the left and right margins will be 11⁄2 inches each as shown in the figure below.

Required:

  1. a) What should be the overall dimensions “x” and “y” that will maximize the area of the space

    inside the margins (the printed area)?

  2. b) Also give the proof that these values of “x” and “y” will maximize this area.

Solutions

Expert Solution

Answer question


Related Solutions

What is the minimum surface area of a box whose top and bottom is a square...
What is the minimum surface area of a box whose top and bottom is a square if the volume is 40 cubic inches. (Surface area is the area of all the sides of the box).
I have a solid square aluminum beam. It is 12 inches long with cross sectional area...
I have a solid square aluminum beam. It is 12 inches long with cross sectional area .25" x .25". A force is applied to the center of the rod and supported at the ends. I need to know the maximum force before the aluminum fails. Equations and work done would be great so I can change the length and cross section if needed bigger or smaller max load.
Suppose you have a trapezoid a vertical height of H with bottom and top widths of...
Suppose you have a trapezoid a vertical height of H with bottom and top widths of B and T. Suppose we draw a line of height h that is parallel to the base of the trapezoid. What are the dimensions of the new trapezoid? (i.e. top widths and height)
The following table gives the total area in square miles​ (land and​ water) of seven states....
The following table gives the total area in square miles​ (land and​ water) of seven states. Complete parts​ (a) through​ (c). State Area 1 52,300 2 615,400 3 115,000 4 53,200 5 159,300 6 104,500 7 6,400 b. Which state is an outlier on the high​ end? If you eliminate this​ state, what are the new mean and median areas for this data​ set? State 2 is an outlier on the high end. The new mean is 81783 square miles....
The following table gives the total area in square miles​ (land and​ water) of seven states....
The following table gives the total area in square miles​ (land and​ water) of seven states. Complete parts​ (a) through​ (c). State   Area 1   52,300 2   615,400 3   115,000 4   53,600 5   159,500 6   104,800 7   6,100 a. Find the mean area and median area for these states. The mean is __ square miles. ​(Round to the nearest integer as​ needed.) The median is ___ square miles. b. Which state is an outlier on the high​ end? If you eliminate...
If the area of a square is 25 square feet, calculate the perimeter of the
If the area of a square is 25 square feet, calculate the perimeter of the square. Enter the value for the perimeter in the first blank and enter the units in the second. Enter units as ft. or square ft. Round your final answer to tenths if rounding is necessary ? 
A box with a square base and open top must have a volume of 32000 cm3....
A box with a square base and open top must have a volume of 32000 cm3. We wish to find the dimensions of the box that minimize the amount of material used. Find the following: 1. First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x.] Simplify your formula...
A rectangular box with no top is to have a surface area of 64 m2.  Find the...
A rectangular box with no top is to have a surface area of 64 m2.  Find the dimensions (in m) that maximize its volume. I got width as X= 8sqrt3/3, length y=8sqrt3/3, and height as z=4sqr3/3 but it is wrong and I don't know why
4)“Bottom-up” vs. “Top-down” Perceptual Processing a). Bottom-up processing – define/ explain what it is. b)Top-down processing...
4)“Bottom-up” vs. “Top-down” Perceptual Processing a). Bottom-up processing – define/ explain what it is. b)Top-down processing - define/ explain what it is. You can use this example: Ca_yo_re_dt_is_en_en_e? C). In perception, bottom-up and top-down processing are believed to occur simultaneously. Explain what that means.
A box with a square base and open top must have a volume of 32000 cm^3....
A box with a square base and open top must have a volume of 32000 cm^3. Find the dimension of the box that minimize the amount of material used. (show all work)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT