1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alja [10]
3 years ago
5

A rectangular page is to contain 24 square inches of print. The margins at the top and the bottom of page are to be 1.5 inches,

and the margins on the left and right are to be 1 inch. What should the dimensions of the page be so that the least amount of paper is used? Justify your answer.

Mathematics
1 answer:
posledela3 years ago
4 0

Answer:

  9 inches high by 6 inches wide

Step-by-step explanation:

Page area is minimized when the aspect ratio is the same as the ratio of margin widths. Here, that means the ratio of height to width should be ...

  1.5 : 1 = 3 : 2 = 6 : 4

The latter dimensions for the print area make it be 24 square inches. When 3" of vertical margin and 2 inches of horizontal margin are added, the page size should be 9 inches high by 6 inches wide.

_____

If the width of the paper is x inches, the height is ...

  h = 24/(x -2) +3

and the overall area is the product of length and width:

  paper area = x(24/(x -2) +3)

Differentiating area with respect to x, we can find the minimum when the derivative is zero.

  d(area)/dx = 24/(x -2) +3 -24x/(x -2)² = 0

  -3(x² -4x -12)/(x -2)² = 0 . . . . . combine terms

The numerator factors as ...

  (x -6)(x +2) = 0

So, the paper width giving minimum area is 6 inches. The height is ...

  h =  24(6 -2) +3 = 9 . . . . inches

The least paper is used when the page dimensions are 6 inches wide by 9 inches high.

You might be interested in
Simplify the expression. w - .25w
balandron [24]
Combine like terms.

1w - 0.25w = 0.75w

Hope this helps!
3 0
3 years ago
Evaluate the expression if x=4 and y=72x(3y-4x)^2
Pavlova-9 [17]
I believe it would be 160000
7 0
3 years ago
What property justifies this statement
Varvara68 [4.7K]

Answer:

B. SUBTRACTION PROPERTY OF EQUALITY

Step-by-step explanation:


4 0
3 years ago
Help me guyssssss skeks
monitta

Answer:

19

Step-by-step explanation:

|-8 -11|=19

7 0
3 years ago
Read 2 more answers
Look at the photo and put your answer down.
Margarita [4]
No solution, I hope I helped (:
8 0
3 years ago
Read 2 more answers
Other questions:
  • Solve this inequality: 3p – 16 < 20.
    11·1 answer
  • Write 84 as a product of prime factors
    9·1 answer
  • (-8/11) (-3/4) = ?<br> find ? not really answer WILL BE REPORT and you WILL LOSE YOU ACCOUNT
    9·2 answers
  • Can anyone help me with this one
    10·2 answers
  • HELP PLEASE !!!! Will give points (9)
    13·1 answer
  • What is 2,356 divided by 27​
    15·2 answers
  • 23) Find the length of the median of each trapezoid.<br><br> A) 7.4<br> C) 5.6<br> B) 5.8<br> D) 6.1
    8·1 answer
  • if 2 man and 3 boys can do a piece of work in 8 days then how long do 3 man and 4 boys take to do the same work
    15·2 answers
  • The perimeter of a circle=πr², where π=22/7. find the area of r=21cm <br>​
    15·1 answer
  • Joe is painting his wooden fenceposts before putting them in his yard. They are each 8 feet tall and have a diameter of 1 foot.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!