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3 years ago

5

6) Describe the relationship between angles D and F.

1 answer:

Arturiano [62]3 years ago

4 0

Answer:

d

Step-by-step explanation:

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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

Please help me <br>what is the value of x+y

Norma-Jean [14]

The correct answer ic C)12

7 0

3 years ago

Read 2 more answers

A high school track coach wanted to test whether giving the students an energy drink could affect performance during the 100 met

kondaur [170]

The inference that can be made about the results is that; energy drinks enhances performance during 100 meters race.

<h3>How to find inference from a given data?</h3>

From the given table and histogram, we can see that;

Group 1 average race time = 10.8

Group 2 average race time = 11.6

Thus, since group 1 drank energy drink and had faster times than group 2 without energy drinks, the inference that can be made about the results is that energy drinks has enhancing performance during 100 meters race.

Read more about Inference at; brainly.com/question/1611703

#SPJ1

4 0

3 years ago

Bas_tet [7]

Answer:

A

Step-by-step explanation:

using formula

area of triangle=1/2 × AB×AC×sinA

WHERE AB=10 andAC=15 and sinA=37○

7 0

4 years ago

Read 2 more answers

Paha777 [63]

33,155.22 is the correct answer for this

4 0

3 years ago

Read 2 more answers