7.times the second num8. The sum of the first number squared and the second number is9. The sum of the first number and twice the second number is10. The sum of the first number cubed and the second number issFindoduct is54 and the product is a maximum.22. Маy-a108 and the product is a maximum.the onetable to500 and the product is a maximum.lenMaximum Area In Exercises 11 and 12, findthe length and width of a rectangle that has thegiven perimeter and a maximum area.a m1000512. Perimeter: P units180011. Perimeter: 80 meters4Minimum Perimeter In Exercises 13 and 14find the length and width of a rectangle that hasthe given area and a minimum perimeter.2ction in(b) and14. Area: A square centimeters13. Area: 49 square feet-11FiguMinimum Distance In Exercises 15 and 16,find the points on the graph of the function that areclosest to the given point.is Ansquare23. Мquarestri15. y 2, (0, 3)16. y x2- 2, (0, -1)a17. Minimum Area A rectangular poster is to contain648 square inches of print. The margins at the top and bottomof the poster are to be 2 inches, and the margins on the letand right are to be 1 inch. What should the dimensions of theposter be so that the least amount of poster is used?18. Minimum Area A rectangular page is to conta36 square inches of print. The margins on each side are to be1inches. Find the dimensions of the page such that the least(a24.tamount of paper is used.s the one19. Minimum Length A farmer plans to fence a rectangularpasture adjacent to a river (see figure). The pasture mustcontain 405,000 square meters in order to provide enoughgrass for the herd. No fencing is needed along the river. Whattable toVdimensions will require the least amount of fencing?= 484800

Question
Asked Nov 7, 2019

17

7.
times the second num
8. The sum of the first number squared and the second number is
9. The sum of the first number and twice the second number is
10. The sum of the first number cubed and the second number is
sFind
oduct is
54 and the product is a maximum.
22. Ма
y-a
108 and the product is a maximum.
the one
table to
500 and the product is a maximum.
len
Maximum Area In Exercises 11 and 12, find
the length and width of a rectangle that has the
given perimeter and a maximum area.
a m
1000
5
12. Perimeter: P units
1800
11. Perimeter: 80 meters
4
Minimum Perimeter In Exercises 13 and 14
find the length and width of a rectangle that has
the given area and a minimum perimeter.
2
ction in
(b) and
14. Area: A square centimeters
13. Area: 49 square feet
-11
Figu
Minimum Distance In Exercises 15 and 16,
find the points on the graph of the function that are
closest to the given point.
is An
square
23. М
quares
tri
15. y 2, (0, 3)
16. y x2- 2, (0, -1)
a
17. Minimum Area A rectangular poster is to contain
648 square inches of print. The margins at the top and bottom
of the poster are to be 2 inches, and the margins on the let
and right are to be 1 inch. What should the dimensions of the
poster be so that the least amount of poster is used?
18. Minimum Area A rectangular page is to conta
36 square inches of print. The margins on each side are to be
1inches. Find the dimensions of the page such that the least
(a
24.
t
amount of paper is used.
s the one
19. Minimum Length A farmer plans to fence a rectangular
pasture adjacent to a river (see figure). The pasture must
contain 405,000 square meters in order to provide enough
grass for the herd. No fencing is needed along the river. What
table to
V
dimensions will require the least amount of fencing?
= 484
800
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7. times the second num 8. The sum of the first number squared and the second number is 9. The sum of the first number and twice the second number is 10. The sum of the first number cubed and the second number is sFind oduct is 54 and the product is a maximum. 22. Ма y-a 108 and the product is a maximum. the one table to 500 and the product is a maximum. len Maximum Area In Exercises 11 and 12, find the length and width of a rectangle that has the given perimeter and a maximum area. a m 1000 5 12. Perimeter: P units 1800 11. Perimeter: 80 meters 4 Minimum Perimeter In Exercises 13 and 14 find the length and width of a rectangle that has the given area and a minimum perimeter. 2 ction in (b) and 14. Area: A square centimeters 13. Area: 49 square feet -11 Figu Minimum Distance In Exercises 15 and 16, find the points on the graph of the function that are closest to the given point. is An square 23. М quares tri 15. y 2, (0, 3) 16. y x2- 2, (0, -1) a 17. Minimum Area A rectangular poster is to contain 648 square inches of print. The margins at the top and bottom of the poster are to be 2 inches, and the margins on the let and right are to be 1 inch. What should the dimensions of the poster be so that the least amount of poster is used? 18. Minimum Area A rectangular page is to conta 36 square inches of print. The margins on each side are to be 1inches. Find the dimensions of the page such that the least (a 24. t amount of paper is used. s the one 19. Minimum Length A farmer plans to fence a rectangular pasture adjacent to a river (see figure). The pasture must contain 405,000 square meters in order to provide enough grass for the herd. No fencing is needed along the river. What table to V dimensions will require the least amount of fencing? = 484 800

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check_circleExpert Solution
Step 1

Consider the given information about the rectangular poster:

Rectangular poster has print-area ( A)= 648in2
Margin at top and bottom (y) 2in
Margin at left and right(x)lin
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Rectangular poster has print-area ( A)= 648in2 Margin at top and bottom (y) 2in Margin at left and right(x)lin

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Step 2

Now draw the figure to represent the area:

Prnt
Area
A
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Prnt Area A

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Step 3

Now do the calculation for the mi...

Let PO b
OR
Print-area(A) 648
lb 648
AB b+2
BC 1+4
Poster-area(A)AB BC
A=(b+2) (1+4)
Alb+2+4b+8
648
Putb.
648
+8
A648+24.
A648+21+28
2592
di
For minimum area
2592
2592
2
1=1296
1-36
648
b
18
36
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Let PO b OR Print-area(A) 648 lb 648 AB b+2 BC 1+4 Poster-area(A)AB BC A=(b+2) (1+4) Alb+2+4b+8 648 Putb. 648 +8 A648+24. A648+21+28 2592 di For minimum area 2592 2592 2 1=1296 1-36 648 b 18 36

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