What is the output value for the following function if the input value is 3.2?

1 answer:

3 0

For functions, there is only many input values, but there can be only one output value, and there can be no identical x values. For this, x=3.2. If y= 2*3.2 - 1, then y=5.4.

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Prove the following statement.

gayaneshka [121]

Answer:

You can prove this statement as follows:

Step-by-step explanation:

An odd integer is a number of the form $2k+1$ where $k\in \mathbb{Z}$ . Consider the following cases.

Case 1. If $k$ is even we have: $(2k+1)^{2}=(2(2s)+1)^{2}=(4s+1)^{2}=16s^2+8s+1=8(2s^2+s)+1$ .

If we denote by $m=2s^2+2$ we have that $(2k+1)^{2}=8m+1$ .

Case 2. if $k$ is odd we have: $(2k+1)^{2}=(2(2s+1)+1)^{2}=(4s+3)^{2}=16s^2+24s+9=16s^{2}+24s+8+1=8(2s^{2}+3s+1)+1$ .

If we denote by $m=2s^{2}+24s+1$ we have that $(2k+1)^{2}=8m+1$

This result says that the remainder when we divide the square of any odd integer by 8 is 1.

6 0

3 years ago

Find the distance between the two given points. (-6, -5) and (2, 0)

Ipatiy [6.2K]

Answer:

The answer is

<h2> $\sqrt{41} \: \: or \: \: \: 6.403 \: \: \: units$ </h2>

Step-by-step explanation:

The distance between two points can be found by using the formula

$d = \sqrt{( {x1 - x2})^{2} + ({y1 - y2})^{2} } \\$

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-6, -5) and (2, 0)

The distance is

$d = \sqrt{ ({ - 6 - 2})^{2} + ({ - 5 - 0})^{2} } \\ = \sqrt{ ({ - 4})^{2} + ({ - 5})^{2} } \\ = \sqrt{16 + 25} \: \: \: \: \: \: \: \: \: \: \: \: \: \:$