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Grace [21]
2 years ago
12

What does the imaginary number i represent

Mathematics
2 answers:
VikaD [51]2 years ago
8 0
I represent the imaginary part like a+bi where a is the real part 

but in the other words i = sqrt(-1) 

hope helped 
soldier1979 [14.2K]2 years ago
8 0

Imaginary numbers always confused me. Like understanding e, most explanations fell into one of two categories:

∴<span>It’s a mathematical abstraction, and the equations work out. Deal with it.
</span>∵<span>It’s used in advanced physics, trust us. Just wait until college.</span>

Gee, what a great way to encourage math in kids! 

                                               x²= 9

The answers are 3 and -3. But suppose some wiseguy puts in a teensy, tiny minus sign:

                                                      i²= -1

Uh oh. This question makes most people cringe the first time they see it. You want the square root of a number less than zero? That’s absurd! (Historically, there were real questions to answer, but I like to imagine a wiseguy.)

It seems crazy, just like negatives, zero, and irrationals (non-repeating numbers) must have seemed crazy at first. There’s no “real” meaning to this question, right?

Wrong. So-called “imaginary numbers” are as normal as every other number (or just as fake): they’re a tool to describe the world. In the same spirit of assuming -1, .3, and 0 “exist”, let’s assume some number i exists where:

That is, you multiply i by itself to get -1. What happens now?

Well, first we get a headache. But playing the “Let’s pretend i exists” game actually makes math easier and more elegant. New relationships emerge that we can describe with ease.

You may not believe in i, just like those fuddy old mathematicians didn’t believe in -1. New, brain-twisting concepts are hard and they don’t make sense immediately, even for Euler. But as the negatives showed us, strange concepts can still be useful.

I dislike the term “imaginary number” — it was considered an insult, a slur, designed to hurt i‘s feelings. The number i is just as normal as other numbers, but the name “imaginary” stuck so we’ll use it.

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Three people invest in a treasure dive, each investing the amount listed below. The dive results in 40 gold coins. Apportion tho
garri49 [273]

Answer:

Alice: 20 coins, Ben: 16 coins, and Carlos: 4 coins.

Step-by-step explanation:

We know that the dive results in 40 gold coins.

We know that:

Alice: $7,600 Ben: $5,900 Carlos: $1,400.

So they have $ 14900 in total.

Now we will divide that money by 40.

x=\frac{14900}{40}\\\\x=372.5

So 1 gold coin costs $ 372.5. Now we will calculate how much they can get for the money they have.

A=\frac{7600}{372.5}=20.4\\\\B=\frac{5900}{372.5}=15.8\\\\C=\frac{1400}{372.5}=3.75\\

We conclude that:

Alice: 20 coins, Ben: 16 coins, and Carlos: 4 coins.

6 0
3 years ago
For a certain model of car the distance d required to stop the vehicle if it is traveling at v mi/h is given by the formula d =
enyata [817]
Given that <span>For a certain model of car the distance d required to stop the vehicle if it is traveling at v mi/h is given by the formula d=v+\frac{v^2}{20}, where [tex]d is measured in feet.

If Kerry wants her stopping distance not to exceed 75 ft, then the range of speeds (in mi/h) can she travel is obtained as follows:

v+ \frac{v^2}{20} \leq75 \\  \\ 20v+v^2\leq1,500 \\  \\ v^2+20v+100\leq1,500+100 \\  \\ (v+10)^2\leq1,600 \\  \\ |v+10|\leq\sqrt{1,600} \\  \\ -40\leq v+10\leq40 \\  \\ -40-10\leqv\leq v\leq40-10 \\  \\ -50\leq v\leq30

Therefore, the range of speed she can travel is v\leq30\ mi/hr
</span>
8 0
3 years ago
The first T-shirt you buy costs $7, and every additional shirt costs only $5. Let f(n) be the total cost of n shirts. F is a seq
Zina [86]

Answer:

f(n) = 2 + 5n. This is an arithmetic sequence.

Step-by-step explanation:

f(1) = 7

f(2) = 7 + 5

f(3) = 7 + 5 + 5 = 7 +10

f(4) = 7 + 5 + 5 + 5 = 7 + 15

In general,

f(n) = 7 + 5(n -1 )

        = 7 + 5n - 5

        = 2 + 5n

We have the sequence 7, 12, 17, 22, 27 …

This is an arithmetic sequence, because it is a sequence of numbers in which the <em>common difference</em> between consecutive terms is 5.

6 0
3 years ago
3(x^2+4x)+4(y^2-2y)=32
nekit [7.7K]

Answer:

3x^2 + 12x + 4y^2 - 8y = 32

Step-by-step explanation:

3(x^2+4x)+4(y^2-2y)=32

At first we have to break the parenthesis to get the variables in normal position. To break those, we have to multiply each with the help of algebraic expression:

or, (3*x^2) + (3 × 4x) + (4 × y^2) - (4 × 2y) = 32

or, 3x^2 + 12x + 4y^2 - 8y = 32

Since the equation does not have anything to add or deduct, therefore, it is the answer.

5 0
3 years ago
What's the slope of -4,6 and 3,-8
notsponge [240]

Answer:

The slope is -2

Step-by-step explanation:

(-4,6) (3,-8)

(y₂ - y₁) / (x₂ - x₁)

((-8) - (6)) / ((3) - (-4))

(-8 - 6) / (3 + 4)

-14/7 = -2

4 0
3 years ago
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