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3 years ago

6

2/3 of the product of 3/8 and 16

1 answer:

Sindrei [870]3 years ago

8 0

2/3(3/8x16). 2/3(6). 4. The answer is 4 :)

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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

Write an equation of the direct variation that includes the point (–10, –17).

Ganezh [65]

Answer: i think the answer is 17 x-10y=0

7 0

3 years ago

What property is shown 4/5 + (-4/5) =0

mina [271]

Answer:

Inverse property of addition

Step-by-step explanation:

When you add two opposite numbers (4/5 is the opposite of [-4/5]) the answer is always zero.

3 0

3 years ago

A line with a slope of 1/3 passes through the point (-8,9). What is its equation in point-slope form?

BARSIC [14]

Answer:

y - 9 = 1/3 (x+8)

Step-by-step explanation:

point slope form is y - y1 = m (x - x1)

8 0

3 years ago

Solve for a side in right triangles

elena55 [62]

Answer:

4.50 = ?

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opposite / hypotenuse

sin 40 = ? / 7

Multiply each side by 7

7 sin 40 = ?

4.499513268 = ?

To the nearest hundredth

4.50 = ?

5 0

3 years ago