![jgpjessi1854](/avatars/21789.jpg)
jgpjessi1854
02.12.2020 •
Mathematics
A rectangular poster is to contain 578 square inches of print. The margins at the top and bottom of the poster are to be 2 inches, 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?
Solved
Show answers
More tips
- C Computers and Internet How to Download Movies from Torrents?...
- S Style and Beauty How to Sew Harem Pants?...
- C Computers and Internet Е-head: How it Simplifies Life for Users?...
- F Family and Home How to Choose the Best Diapers for Your Baby?...
- F Family and Home Parquet or laminate, which is better?...
- L Leisure and Entertainment How to Properly Wind Fishing Line onto a Reel?...
- L Leisure and Entertainment How to Make a Paper Boat in Simple Steps...
- T Travel and tourism Maldives Adventures: What is the Best Season to Visit the Luxurious Beaches?...
- H Health and Medicine Kinesiology: What is it and How Does it Work?...
- O Other How to Choose the Best Answer to Your Question on The Grand Question ?...
Answers on questions: Mathematics
- M Mathematics Renan found the sum (4.2x + 3) + (5.7x – 2) + (5 – 2.6x), as shown. 4.2x + 3 + 5.7x – 2 + 5 – 2.6x 4.2x + 5.7x + 2.6x + 3 – 2 + 5 (4.2 + 5.7 + 2.6)x + 3 – 2 + 5 12.5x...
- M Mathematics The weight of 1000 identical samples of substance is 0.1 pounds. what is the weight of 100 samples...
- M Mathematics Answer please. Correct answer...
Ответ:
19 by 38
Step-by-step explanation:
The area of the poster, A=xy
Margin at both up and bottom is 2inches, at the right and left is 1 inch
Then we can say
(x-4)(y-2)= 578
Let us make y subject of the formula
(y-2)= 578/(x-4)
y=[ 578/(x-4)] + 2
If we substitute into the area A equation we have
A= x { [ 578/(x-4)] + 2}
A= 2x + (578x)/(x - 4)
If we differentiate we have
A'(x)= [2+578(x-4)+578x ]/ (x-4)^2
=[ 2(x-4)^2 + 578(x -4) + 578x ] / (x-4)^2
=[ 2(x^2 - 8x +16) + 578(x-4) + 578x ] /(x-4)^2
If we simplify this we have
=[ 2x^2 -16x +32+578x -578x - 2312]/ (x-4)^2
=( 2x^2 -16x - 2312) / (x-4)^2
At A'(x)= 0
= ( x^2 - 8x - 2312) / (x-4)^ =0
If we divide through by 2 we have
x^2 - 8x - 1156= 0
Solving the quadratic eqn( CHECK THE ATTACHMENT)
X= 38 or -30 then we choose the positive one, then x= 38
Then from area of the poster
A= (x-4)(y-2)= 578
Substitute 38 as value of x
(38-4)(y-2)= 578
34(y-2)=578
34y-68=578
34y=646
y=19
Hence dimensions of the poster is 19 by 38
CHECK THE ATTACHMENT FOR QUADRATIC SOLUTION
Ответ: