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3 years ago

6 Σ (12 – 4 i) i = 3

Mathematics

1 answer:

AnnyKZ [126]3 years ago

3 0

Answer:

- 24

Step-by-step explanation:

We have to get the value of the following sum as given.

$\sum_{3}^{6} (12-4i)$

This can be written in language as the summation of (12 -4i) where value of i ranges from 3 to 6.

$\sum_{3}^{6} (12-4i)$

= [12 - 4(3)] + [12 - 4(4)] + [12 - 4(5)] + [12 - 4(6)]

= 0 + [- 4] + [- 8] + [- 12]

= - 24 (Answer)

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x = 163.84 - 28.09 

x = √135.75 

x = 11.65 ≈ 11.7

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2 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

A chimp is taking a multiple - choice test of course the chip can't read and his guessing for every question. If there are 4 cho

tia_tia [17]

Answer:

Step-by-step explanation:

He will guess correctly 25% of the time.

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3 years ago

HELP 1x3 divided by 56 then multiply that by 9

Sloan [31]

Answer:

0.48

Step-by-step explanation:

1x3/56 then multiply it by 9

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3 years ago

Use complete sentences to describe why √-1 ≠ -√1

tekilochka [14]

Well let's say that to compare these two numbers, we have to start with the definition first.

Definition

$\displaystyle \large{ {y}^{2} = x} \\ \displaystyle \large{ y = \pm \sqrt{x} }$

Looks like we can use any x-values right? Nope.

The value of x only applies to any positive real numbers for one reason.

As we know, any numbers time itself will result in positive. No matter the negative or positive.

Definition II

$\displaystyle \large{ {a}^{2} = a \times a = |b| }$

Where b is the result from a×a. Let's see an example.

Examples

$\displaystyle \large{ {2}^{2} = 2 \times 2 = 4} \\ \displaystyle \large{ {( - 2)}^{2} = ( - 2) \times ( - 2) = | - 4| = 4}$

So basically, their counterpart or opposite still gives same value.

Then you may have a question, where does √-1 come from?

It comes from this equation:

$\displaystyle \large{ {y}^{2} = - 1}$

When we solve the quadratic equation in this like form, we square both sides to get rid of the square.

$\displaystyle \large{ \sqrt{ {y}^{2} } = \sqrt{ - 1} }$

Then where does plus-minus come from? It comes from one of Absolute Value propety.

Absolute Value Property I

$\displaystyle \large{ \sqrt{ {x}^{2} } = |x| }$

Solving absolute value always gives the plus-minus. Therefore...

$\displaystyle \large{ y = \pm \sqrt{ - 1} }$

Then we have the square root of -1 in negative and positive. But something is not right.

As I said, any numbers time itself of numbers squared will only result in positive. So how does the equation of y^2 = -1 make sense? Simple, it doesn't.

Because why would any numbers squared result in negative? Therefore, √-1 does not exist in a real number system.

Then we have another number which is -√1. This one is simple.

It is one of the solution from the equation y^2 = 1.

$\displaystyle \large{ {y}^{2} = 1} \\ \displaystyle \large{ \sqrt{ {y}^{2} } = \sqrt{1} } \\ \displaystyle \large{ y = \pm \sqrt{1} }$

We ignore the +√1 but focus on -√1 instead. Of course, we know that numbers squared itself will result in positive. Since 1 is positive then we can say that these solutions exist in real number.

Conclusion

So what is the different? The different between two numbers is that √-1 does not exist in a real number system since any squared numbers only result in positive while -√1 is one of the solution from y^2 = 1 and exists in a real number system.

5 0

2 years ago

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