Simplify this expression: i ^257

Mathematics

1 answer:

Katarina [22]3 years ago

8 0

Okay!
What is i?
i = √(-1)

What is i^2?
i^2 = √(-1) * √(-1)

Note: Whenever you multiply two square roots with the same numbers you get this:

√(a^2)

Or in this case:

√(-1 * -1) = -√(1) = -1

So,
i^2 = -1

What does i^3 equal?
i^3 = √(-1) * √(-1) * √(-1) = 1 * √(-1) = √(-1) which is... -i

What does i^4 equal?
i^4 = √(-1) * √(-1) * √(-1) * √(-1) = √(-1 * -1 * -1 * -1) = 1

After that the cycle does it thing and cycles back.
So, with this information we can figure out what i^157 equals.

Knowing long division here helps a lot!
Take 157 and divide it by 4 using long division. If you don't know it, I'll show you how to do it to the best of my abilities. (Refer to the picture. If you have any questions about it then ask. Even if the question is... what does this say?)

After using long division we see that we get:
39 with a remainder of 1.

What that means is:
(i^4)^39 is what we have. The remainder of 1 means that we have 1 i left. So our answer is i.

The reason we divided by 4 and not some other term is because i^4 = 1, so it is easy to work with. In this case (i^4)^39 still just equals 1. Which leaves our remainder as our answer.

So once again the final answer is:
i

As for i^257. I'll show you the answer, but I won't give the work for this one. I'd recommend you try it out for yourself.

i^257 = (i^4)^64 * i = i.

I hope that I helped, and if you have any further questions then ask away!

Read more about polynomials at:

brainly.com/question/4142886

#SPJ1

8 0

2 years ago

What percentage of babies born in the United States are classified as having a low birthweight (<2500g)? explain how you got

lawyer [7]

Answer:

2.28% of babies born in the United States having a low birth weight.

Step-by-step explanation:

The complete question is: In the United States, birth weights of newborn babies are approximately normally distributed with a mean of μ = 3,500 g and a standard deviation of σ = 500 g. What percent of babies born in the United States are classified as having a low birth weight (< 2,500 g)? Explain how you got your answer.

We are given that in the United States, birth weights of newborn babies are approximately normally distributed with a mean of μ = 3,500 g and a standard deviation of σ = 500 g.

Let X = birth weights of newborn babies

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean = 3,500 g

$\sigma$ = standard deviation = 500 g

So, X ~ N( $\mu=3500, \sigma^{2} = 500$ )

Now, the percent of babies born in the United States having a low birth weight is given by = P(X < 2500 mg)

P(X < 2500 mg) = P( $\frac{X-\mu}{\sigma}$ < $\frac{2500-3500}{500}$ ) = P(Z < -2) = 1 - P(Z $\leq$ 2)

= 1 - 0.97725 = 0.02275 or 2.28%

The above probability is calculated by looking at the value of x = 2 in the z table which has an area of 0.97725.

4 0

3 years ago

Geometry :))), please help me

amm1812

Answer:

x = -5

Step-by-step explanation:

Since these two triangles are similar, the ratio between the corresponding lengths of each triangle will be the same.

This means the ratio between one side of each triangle (e.g. AD and DC) will be the same as the ratio between a different side of each triangle (e.g. BE and BC).

So, to create an equation for the sides which contain the unknown 'x', we must first find the ratio between the two sides by using a different set of sides.

On the right side we are given 9 for AD, and 18 for DC.

9/18 = 0.5

This means that the extra length of the larger triangle from the smaller one (AD) is half the length of the smaller triangle (DC). We can use this to make an equation for x:

If AD/DC = 0.5, then BE/EC will also = 0.5

BE = x+23

EC = x+41

Therefore:

$\frac{x+23}{x+41} = 0.5$