4. Alan's go-kart travels 1600 feet per minute, and Barry's go-kart travels 23 miles per hour. Whose

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

3 years ago

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Q Searchmatics Gr 7)I need 4 cups of flours and 2 cups of sugar to make a cake. How many cups of sugar do I need if Ihave 12 cup

Ede4ka [16]

You will need 6 cups of sugar.

Step - by - Step Explanation

What to find? The number of cups of sugar needed to make a cake with 12 cups of flour.

Given:

Cups of flours = 4

Cups of sugar = 2

Cups of flour =12

Let x be the number of cups of sugar needed to make a cake with 12 cups of flour.

Using proportion;

4 cups of flour = 2 cups of sugar

12 cups of flour = x

Cross - multiply

4x = 24

Divide both-side of the equation by 4

$\frac{\cancel{4}x}{\cancel{4}}=\frac{24}{4}$

x =6

Hence, you will need 6 cups of sugar.

6 0

1 year ago

2.8, 3.4, 4.0, 4.6, . . . Write an equation for the nth term of the arithmetic sequence. Then find a50.

vova2212 [387]

Answer:

a_n = 2.2 + 0.6 n

a_50 = 32.2

Step-by-step explanation:

What's the common difference of this series?

$a_1 = 2.8$

$a_2 = 3.4$

Common difference = $a_2 - a_1 = 3.4 - 2.8 = 0.6$ .

Expression for the nth term:

$a_n = a_1 + (n - 1) \cdot\text{Common Difference} \\\phantom{a_n } = 2.8 + 0.6 \; (n-1) \\\phantom{a_n} = 2.8 + 0.6 \; n - 0.6\\\phantom{a_n} = 2.2 + 0.6\; n$

n = 50 for the fiftieth term. Therefore

$a_{50} = 2.2 + 0.6 \times 50 = 32.2$ .

6 0

3 years ago

Pls help me with my beestar

Minchanka [31]

Mmmmm Maybe you should try doing something doing something doing something during

8 0

3 years ago

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What is the value of n in the equation shown below? 2²×2n=(2

pychu [463]

Answer:

Step-by-step explanation:

$2^2 \times 2n= (2)\\\\\mathrm{Simplify\:}2^2\times\:2n:\quad 8n\\\\\mathrm{Simplify\:}\left(2\right):\quad 2\\\\8n=2\\\\\mathrm{Divide\:both\:sides\:by\:}8\\\\\frac{8n}{8}=\frac{2}{8}\\\\Simplify\\\\n=\frac{1}{4}$

4 0

4 years ago