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3 years ago

11

Rewrite the expression as an equivalent power with a negative exponent. a. 1/49 b. 27/125

1 answer:

Hunter-Best [27]3 years ago

3 0

$\dfrac{1}{49}=\left(\dfrac{1}{7}\right)^2=7^{-2}\\
\dfrac{27}{125}=\left(\dfrac{3}{5}\right)^3=\left(\dfrac{5}{3}\right)^{-3}$

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5 x5 x 5 divided by 3 times 290

Sveta_85 [38]

Answer:

12083.3314

Step-by-step explanation:

5*5*5= 125

125/3=41.66666

41.66666*290= 12083.3314

3 0

2 years ago

A sapling grew 8 1/2 inches one year 10 3/4 inches the second year and 9 3/4 inches the third year how much did it grow during t

victus00 [196]

8 1/2 = 8.5
10 3/4 = 10.75
9 3/4 = 9.75

8.5 + 10.75 + 9.75 = 29 inches in total <==

6 0

2 years ago

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

Answer this question please and I will give brainliest

erik [133]

Answer:

Jordan

Step-by-step explanation:

Because each person is in debt the one with the least amount of dept will pay less. Think of it like this:

You owe the bank 85 dollars so your account balance is -85 since you owe money

if you were to owe 100 dollars then you owe more money.

Therefore owing 85 dollars is the least amount of money owed in this case

8 0

2 years ago

1.morgan is 15 years old younger than Mrs.santtos their combined age is 442. jenny won the ping-pong championship eight more tim

swat32

If Morgan is 15 years younger then Mrs.Santos and there combined age is 442 that means that Mrs.Santos is 221, and Morgan is 206.

8 0

3 years ago