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3 years ago

Last question, if its wrong expect a pc flying through your window

Mathematics

1 answer:

slavikrds [6]3 years ago

6 0

Answer:

D. 73°

Step-by-step explanation:

The inside angles of a triangle always equal 180° so if we know that a right angle is already 90° we only need one more angle to know all of them:

1. 90° + 17° + ?° = 180

2. 90° + 17° = 107°

3. 180° - 107° = 73°

4. 90° + 17° + 73° = 180

5. XD

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Find the total number of outcomes if you roll two number cubes.

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2. Circumference is around 43.96, area is around 153.94

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A couple decided to have 4 children.

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See below the theee of possibilities:

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3 years ago

Find the coordinates of the midpoint M and the distance between J(4,3) and K(2,-3)

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Answer:

(3,0)

Step-by-step explanation:

Co-ordinates of J =(4,3)

Co-ordinates of K = (2,-3)

Midpoint formula :

= $\frac{x_{1}+x_{2} }{2} , \frac{y_{1} +y_{2} }{2} \\ \frac{4+2}{2} ,\frac{3+(-3)}{2}\\\frac{6}{2},\frac{3-3}{2}\\3, 0$

Coordinates of the midpoint M (3,0)

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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

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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.

Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

3 0

3 years ago