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elena55 [62]
3 years ago
13

Please help!!! ASAP With all these questions

Mathematics
1 answer:
andrey2020 [161]3 years ago
7 0
#1. 4:7 8:14 12:21
#2. 5:7 10:14 15:21
#3. 9:7 18:14 27:21
#4. 11:2 22:4 33:6
#5. 7:21 14:42 21:63
#6. 7:5 14:10 21:15
#7. Equals
#8. Equals
#9. Equals
#10 not equal
#11 not equal
# 12. Equals
#13. y=20
#14. y=14
#15. y=15
#16. y=40
#17. y=40
#18. y=36
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A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si
Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

Area = 128

Let the dimension of the paper be x and y;

Such that:

Length = x

Width = y

So:

Area = x * y

Substitute 128 for Area

128 = x * y

Make x the subject

x = \frac{128}{y}

When 1 inch margin is at top and bottom

The length becomes:

Length = x + 1 + 1

Length = x + 2

When 2 inch margin is at both sides

The width becomes:

Width = y + 2 + 2

Width = y + 4

The New Area (A) is then calculated as:

A = (x + 2) * (y + 4)

Substitute \frac{128}{y} for x

A = (\frac{128}{y} + 2) * (y + 4)

Open Brackets

A = 128 + \frac{512}{y} + 2y + 8

Collect Like Terms

A = \frac{512}{y} + 2y + 8+128

A = \frac{512}{y} + 2y + 136

A= 512y^{-1} + 2y + 136

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

A' = -512y^{-2} + 2

Set

A' = 0

This gives:

0 = -512y^{-2} + 2

Collect Like Terms

512y^{-2} = 2

Multiply through by y^2

y^2 * 512y^{-2} = 2 * y^2

512 = 2y^2

Divide through by 2

256=y^2

Take square roots of both sides

\sqrt{256=y^2

16=y

y = 16

Recall that:

x = \frac{128}{y}

x = \frac{128}{16}

x = 8

Recall that the new dimensions are:

Length = x + 2

Width = y + 4

So:

Length = 8 + 2

Length = 10

Width = 16 + 4

Width = 20

To double-check;

Differentiate A'

A' = -512y^{-2} + 2

A" = -2 * -512y^{-3}

A" = 1024y^{-3}

A" = \frac{1024}{y^3}

The above value is:

A" = \frac{1024}{y^3} > 0

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

3 0
2 years ago
What is the value of x, when 5+x+(−2)=−8?
nasty-shy [4]
<span>5+x+(−2)=−8
5 + x - 2 = -8
x + 3 = -8
x = -11</span>
3 0
3 years ago
Read 2 more answers
Darin has 3 pairs of tennis shoes, 4 pairs of pants, 6 shirts, 2 belts, and 3
pshichka [43]
I would say A) or B) but I would say B) because you can take different clothing pieces to Match with many others
5 0
2 years ago
An item is regularly priced at$90. Henry bought it on sale for 70% off the regular price. How much did Henry pay?
Neko [114]
70 times .9 is 63 so 90 minus 63 is27 so it was $27
3 0
2 years ago
Read 2 more answers
18. What is the area of a piece of garden plot 5 yards 2 feet long by 6 yards 1 foot wide? Give your answer in square feet.
34kurt

Answer:

<h2>C. 323 ft²</h2>

Step-by-step explanation:

1 yard = 3 feet

5yd 2ft = (5)(3)ft + 2ft = 17ft

6yd 1ft = (6)(3)ft + 1ft = 19ft

The formula of an area of a rectangle:

A = wl

w - width

l - length

Substitute w = 19ft and l = 17ft:

A = (19)(17) = 323 ft²

5 0
2 years ago
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