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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.

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9) 80 is 20% of what number?
sweet-ann [11.9K]
<h3><u>Answer:</u></h3>
  • 400 is the number.
<h3><u>Step-by-step explanation:</u></h3>

<em>There can be many ways to find the number.</em><em> I have found the number with the help of fractions and multiplication. </em><em>Below is the solution to your problem.</em>

  • 80 = 20/100
  • => 5 x 80 = 20 x 5/100
  • => 400
<h3><u>Conclusion:</u></h3>

<em>Hence, 80 is 20% of 400. </em><em>I hope my method helped you.</em>

BrainiacUser1357

8 0
2 years ago
Read 2 more answers
Chapter one course 2
Marysya12 [62]
What you need help with
8 0
3 years ago
Y = 3/2x + 5/4 −2x + 8y = −25
Andreyy89

Answer:

<h2>x = -347 1/2</h2>

Step-by-step explanation:

When solving algebra, it is important the we follow the steps in correct order and check our answer at the end.

Step 1: Simplify by combining like terms

y = -x/2 + 5/4 + 8y = -25

Step 2: Substitute

y = -25

-25 = -x/2 + 5/4 + 8(-25)

-25 = -x/2 + 5/4 + -200

-25 = -x/2 - 198 3/4

Step 3: Answer

x = -347 1/2

Step 4: Check

y = 3/2x + 5/4 −2x + 8y = −25

-25 = 3/2(-347 1/2) + 5/4 −2(-347 1/2) + 8(-25)

-25 = -25✔️

Step 5: Verified Answer

x = -347 1/2

I'm always happy to help :)

3 0
3 years ago
Which equation is equivalent to 10+2(x−1)+7x=3x+1?
Eva8 [605]

Answer:

Answer is x = -7/6

Step-by-step explanation:

please look at the image

8 0
2 years ago
I would appreciate it if you help me pls asap !!
masha68 [24]

Answer:

BC= 20 units

Step-by-step explanation:

Since ∆ ABC is an equilateral triangle, all the sides are equal in length.

AC= BC

=>-y+23= 6y+2

=>-y-6y= 2-23

=>-7y= -21

=>y= 21/7

=>y= 3

BC = 6y+2 = 6(3)+2 = 18+2 = 20 units

7 0
3 years ago
Read 2 more answers
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