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
Elanso [62]
4 years ago
15

A rectangular poster is to contain 882 square inches of print. The margins at the top and bottom of the poster are to be 2 inche

s, and the margins on the left and right are to be 1 inch. What should the dimensions of the poster be so that the least amount of poster is used
Mathematics
1 answer:
Zinaida [17]4 years ago
4 0

Answer:

L  =  23 in

h  = 46  in

Step-by-step explanation:

Let call  " x "  and  " y "  dimensions of the print area of the poster then:

882 = x*y  and   y = 882/x

We also know that dimensions of the poster is:

L  =  x + 2   in  and     h  =  y + 4 in

Therefore area of the poster is:

A(p)  = ( x + 2 ) * ( y + 4 )  And area as function of x is:

A(x)  =   ( x + 2 ) * ( 882/x + 4 )

A(x)  =  882 + 4*x + 1764 /x  + 8

Taking derivatives on both sides of the equation we have:

A´(x)  =  4  - 1764/x²

A´(x)  = 0      ⇒      4  - 1764/x² = 0      ⇒ 4*x² - 1764  =  0

x²  =  1764 / 4

x²  = 441

x  = 21 in      and    y  =  882/x         y  = 42

The second derivative  A´´(x)  is > 0  ( the second term changes its sign to +) there is a minimum for the function at the point      x = 21

As x   and  y are dimensions of the printing area of the poster, dimensions of the poster  are

L  = x  +  2   =   21  + 2  =  23 in   and

h = y  +  4   =   42  + 4  =  46  in

You might be interested in
Is the following relation a function?<br><br> A. Yes<br> B. No
SVETLANKA909090 [29]

Answer:

  B.  No

Step-by-step explanation:

In order for the relation to be a function, each X value must source exactly one arrow. The value -1 maps to two different values (2, -1), so the relation is NOT A FUNCTION.

3 0
2 years ago
The volume of a book is 60 cubic inches.If a large box holds about 12 books,estimate the volume of a large box
Katyanochek1 [597]
The answer is:  720 in³  .
_____________________________________
Explanation:
_____________________________________
  60 in³ * (12) = 720 in³ .
_____________________________________
6 0
3 years ago
The sum of a number and 8 is larger than the difference of the number and 10. (Use x to represent the number)
LiRa [457]

Answer:

2

Step-by-step explanation:

it is talkin about 2

8 + 2 = 10

10 - 2 = 8

8 0
3 years ago
How much is 2 3/4 cup plus 2 3/4 cup
Viefleur [7K]

Answer:

5.5 US cups

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
I don't know if it's correct​
Bond [772]

Hello, This is correct.

first one is whole numbers

the third one natural numbers

the fourth are complex numbers

The last one is irrational numbers

8 0
3 years ago
Other questions:
  • 1/10 times 10 eqauls
    8·1 answer
  • Simplify. <br>√3/10 <br><br><br>A. √15/5 <br><br>B. √30/10 <br><br>C. √3/10 <br><br>D. √3/5
    6·1 answer
  • Is 786 closer to 700 or 800?how do you know
    7·1 answer
  • Which is another way to write 42+63?
    14·1 answer
  • A man whose salary is Ghs1624.5 per month received a Christmas bonus of 4/5 of his monthly salary in the month of December. Find
    15·1 answer
  • The lengths of the sides of a triangle are in the ratios 2:6:7
    8·1 answer
  • According to a 2016 survey, 6 percent of workers arrive to work between 6:45 A.M. and 7:00 A.M. Suppose 300 workers will be sele
    8·1 answer
  • Factor -4a^2b^4+5b^2-4 ​
    9·1 answer
  • GUYSSSSS important question<br><br> whats 9 plus 10 (whoever gets this gets brainliest)
    9·1 answer
  • Plz help answer the following questions
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!