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3 years ago

12

The equation, and explanation.

1 answer:

Levart [38]3 years ago

6 0

Answer:

Dunno thanks for the points!

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Which method is better to solve the following equation?

kari74 [83]

Square rooting because you have to find the inverse of the equation to solve

7 0

2 years ago

Teri incorrectly solved the system of equations below. Correctly identify the error Teri made. 2x - 10 y = -30 x - 5y = 20 Step

umka21 [38]

Answer:

See explanations below

Step-by-step explanation:

Given the system of equation

2x - 10 y = -30 ... 1

x - 5y = 20 ... 2

Step: From 2;

x = 20 + 5y ...3

Step 2: Substitute equation 3 into 1

2x - 10y = -30

2(5y+20) - 10y = -30

Open the bracket

10y + 40 - 10y = -30

10y - 10y + 40 = -30

0+40 = -30

40 = -30

The steps taken by Teri are correct all through. He didn't make any error whatsoever

3 0

3 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

3 years ago

What is the exact value of cos 45° as found on the unit circle?

Ber [7]

The exact value of cos 45 as per the special triangle would be

Cos 45 = 1/✔️2

Rationalizing the denominator gives

✔️2/2 = 0.707.

4 0

3 years ago

Find the angle whose measure is 5 times its complement

Ivenika [448]

Answer:

answer is 75 degree

Step-by-step explanation:

you will better understand by this

4 0

3 years ago

Read 2 more answers