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3 years ago

9

Greatest to least 1/4, 0.08, 3/7, 82%

1 answer:

JulijaS [17]3 years ago

6 0

Answer:

.08, .25, .42, .82

Step-by-step explanation:

1/4, 0.08, 3/7, 82%

.25, 0.08, .42, .82

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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

3 years ago

A company donates money to a charity every time the baseball team hits a home run. They donate $450 for every home run. Write a

Svet_ta [14]

Answer:

y= 450x

Step-by-step explanation:

Given data

Let y represent the total amount of money

Let x represent the number of home runs

For each run they donate $450

We can model this situation as

y= 450x

5 0

3 years ago

1 and 2 form a linear pair. If the

natka813 [3]

$Angles$ $that$ $form$ $a$ $linear$ $pair$ $add$ $up$ $to$ $180 degrees$ .

If the measure of angle 1 is 113, then all we must do is subtract:

180-113=67 $degrees$

And we're done!

Good luck! :)

Hope it helps you!

$GraceRosalia$ ✺ ✺ ✺ ✺ ✺ ✺ ✺

8 0

3 years ago

What is 20% of $2,500 how much money has it rased

Reptile [31]

2500 * 0.20 = 500 dollars

6 0

3 years ago

7.21 repeating as a fraction

GalinKa [24]

Answer: 721/100 is 7.21 as a simplified fraction.

3 0

3 years ago

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