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3 years ago

Complex numbers simplify square roots of negative numbers

Mathematics

2 answers:

sergey [27]3 years ago

8 0

Step-by-step explanation:

√-100

√-(10)²

√10²√-1

10i

0+10i

Bogdan [553]3 years ago

3 0

Lets do

$\\ \sf\longmapsto \sqrt{-100}$

$\\ \sf\longmapsto \sqrt{-(10)^2}$

$\\ \sf\longmapsto \sqrt{10^2}\sqrt{-1}$

$\\ \sf\longmapsto 10i$

Write in standard form

$\\ \sf\longmapsto 10i$

$\\ \sf\longmapsto \boxed{0}+\boxed{10}i$

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When a number is divided by -3, the result is 12 more than the number. What is the number?

otez555 [7]

Answer:

x = -9

Step-by-step explanation:

let the number = x

So x ÷ -3 = x + 12

Mulitply both sides by -3: x = -3x -36

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2 years ago

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3 years ago

A school replaced 20% of its computers with new ones what is the total number of computers in the school if 55 computers were re

pentagon [3]

Answer:

There were 275 computers

Step-by-step explanation:

Computers replaced = total computers * percent replaced

What do we know?

The percent replaced is 20 = .2

55 computers were replaced.

Substitute this in

55 = total computers * .2

Divide each side by .2

55/.2 = total computers *.2 /.2

275 = total computers

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3 years ago

4. Find the sum of the first eighteen terms of the arithmetic sequence whose nth

vova2212 [387]

Answer:

The sum of first eighteen terms of the arithmetic sequence is $\mathbf{S_{18}=1638}$

Option B is correct option.

Step-by-step explanation:

We need to find the sum of the first eighteen terms of the arithmetic sequence whose nth term is an = 15 + 8n

The formula used to calculate sum of arithmetic sequence is: $S_n=\frac{n}{2}(a_1+a_n)$

Finding a₁ by putting n=1

$a_n=15+8n\\a_{1}=15+8(1)\\a_{1}=15+8\\a_{1}=23$

We have $a_1=23$

Finding 18th term n=18

$a_n=15+8n\\a_{18}=15+8(18)\\a_{18}=15+144\\a_{18}=159$

So, the sum of first eighteen terms of the arithmetic sequence is:

$S_n=\frac{n}{2}(a_1+a_n)\\S_{18}=\frac{n}{2}(a_1+a_{18})\\S_{18}=\frac{18}{2}( 23+159)\\S_{18}=9(182)\\S_{18}=1638$

So, the sum of first eighteen terms of the arithmetic sequence is $\mathbf{S_{18}=1638}$

Option B is correct option.

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3 years ago

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Firdavs [7]

Answer:

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Step-by-step explanation:

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3 years ago