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
Natali [406]
3 years ago
8

A rectangular page is designed to contain 81 square inches of print. The margins at the top and bottom of the page are each 1 in

ch deep. The margins on each side are 1½ inches wide. What should the dimensions of the page be so that the least amount of paper is used?
Social Studies
1 answer:
Nookie1986 [14]3 years ago
8 0

Answer:

x = 11.02 inch by  y = 7.35 inch

Explanation:

Let the width of the print be = x

Then the width of the page is x + (1.5+1.5) = x + 3

Let the height of the print be = y

Then the height of the page is y + (1+1) = y + 2

Given the area of the print is 81 square inches

That means, xy = 81

Therefore, y = \frac{81}{x}

Therefore, the area of the page is

A = (x + 3)(y + 2)

   = (x + 3)(\frac{81}{x} + 2)

Now for least amount of paper to be used,

\frac{dA}{dx}=(x+3)(\frac{81}{x}+2)

\frac{dA}{dx}= \left (\frac{81}{x}+2  \right )+\left ( x+3 \right )\left ( -\frac{81}{x^{2}} \right )=0

\frac{81+2x}{x}=\frac{(x+3)(81)}{x^{2}}

81x+2x^{2}=81x+81\times 3

2x^{2}=243

x = 11.02 inch

Now y = \frac{81}{x}

          = \frac{81}{11.02}

          = 7.35 inch

Therefore the dimensions of thr page for the least amount of paper is x = 11.02 inch by  y = 7.35 inch

You might be interested in
A political system where wealth is divided equally among citizens.
11Alexandr11 [23.1K]

Answer:

Democracy

Explanation:

I'm pretty positive

8 0
3 years ago
HELP ME PLZZ I NEED HELP!
horsena [70]
The top answer is right
4 0
3 years ago
Read 2 more answers
In observational learning, who are the most effective models?
marissa [1.9K]
The individuals who are steady with their words and activities. Models who "try to do they say others should do" are the well on the way to be powerful at empowering impersonation in others. On the off chance that their words and deeds don't coordinate, they may in any case cause demonstrating, yet just their own particular bad faith will be displayed.
5 0
3 years ago
True or false: it is legal to pass in florida if you believe it is safe
Illusion [34]
False. It is illegal to pass in Florida even if you think it is safe.
6 0
3 years ago
What are the 4 factors used when Geographers name places?
Arisa [49]

Answer:

Places usually have names and boundaries and include continents, islands, countries, regions, state, cities, neighborhoods, villages, and uninhabited areas. Therefore, Standard 4 contains these themes: The Concept of Place and The Characteristics of Places.

4 0
3 years ago
Other questions:
  • What is a passive verb?
    5·2 answers
  • In 1900, _____ of children 10 years old had four living grandparents; in 2000, _____ of children 10 years old had four living gr
    11·1 answer
  • Which is one way Saudi Arabia protects its traditional culture from Westernization?
    11·2 answers
  • Most of the work in considering and editing bills is done
    13·2 answers
  • Parami volunteers at a homeless shelter. It takes a lot of her time, and thus she sometimes takes off time from her job to do th
    11·1 answer
  • All aspects of communication other than the words themselves are known as
    9·2 answers
  • ETHNICITY IS A SHARED HERITAGE OF WHAT TYPE <br> CULTURAL <br> BIOLOGICAL <br> PHYSICAL<br> GENETIC
    13·2 answers
  • Describe two ways that travel improved in the early 1800s
    7·2 answers
  • Identify one unifying characteristic in Russia. How can the country be divided based on this characteristics? Examples include p
    15·1 answer
  • Frances quit her job because she felt that her department’s reward system favored men. This would be diagnosed as a(n) ________
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!