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3 years ago

6

Change The Subject Of The Formula Help!

1 answer:

Leviafan [203]3 years ago

8 0

It would be d-16=t. hope this helps... i might've done my math wrong though...

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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

You score a 95% or your mouth quiz the quiz was out of 60 points how many points did you get

Genrish500 [490]

Answer:

It will be 57 points.

Step-by-step explanation:

7 0

3 years ago

Help me... I did it again! I skipped the practice and study guides

Katyanochek1 [597]

Answer:

X = 1 3/4

Step-by-step explanation:

Hope this helps!

4 0

3 years ago

A tenant rented a store to use as a real estate school at a base rent of $1,500 a month. Additionally, the tenant agreed to pay

allsm [11]

Answer:

3. $600,000

Step-by-step explanation:

We have been given that a tenant rented a store to use as a real estate school at a base rent of $1,500 a month. Additionally, the tenant agreed to pay 3% of gross annual sales over $200,000.

Let us find base annual rent.

$\text{Base annual rent}=\$1500\times 12\\\\ \text{Base annual rent}=\$18,000$

Let us find the amount of rent paid as 3% of gross annual sales.

$\$30,000-\$18,000=\$12,000$

Let us find amount of sales over $200,000 by dividing $12000 by 3% or 0.03.

$\frac{\$12,000}{0.03}=\$400,000$

Total sales would be $400,000 plus $200,000.

$\text{Total sales}=\$400,000+\$200,000\\\\ \text{Total sales}=\$600,000$

Therefore, the total sales for that year was $600,000 and 3rd option is the correct choice.

7 0

3 years ago

Henry has 3 black shirts and 7 blue shirts in his wardrobe two shirts are drawn with out replacement from the wardrobe what is t

laiz [17]

3/10 * 2/9 = 1/15
There is a 1/15 chance that both of the shirts he grabbed are black....

:)

7 0

3 years ago