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3 years ago

13

Please help!!! ASAP With all these questions

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

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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