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timofeeve [1]
3 years ago
7

Select the equivalent expression

Mathematics
1 answer:
Makovka662 [10]3 years ago
4 0
5x-7 first one answer
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Solve the following equation:
Rama09 [41]

Complete the square.

z^4 + z^2 - i\sqrt 3 = \left(z^2 + \dfrac12\right)^2 - \dfrac14 - i\sqrt3 = 0

\left(z^2 + \dfrac12\right)^2 = \dfrac{1 + 4\sqrt3\,i}4

Use de Moivre's theorem to compute the square roots of the right side.

w = \dfrac{1 + 4\sqrt3\,i}4 = \dfrac74 \exp\left(i \tan^{-1}(4\sqrt3)\right)

\implies w^{1/2} = \pm \dfrac{\sqrt7}2 \exp\left(\dfrac i2 \tan^{-1}(4\sqrt3)\right) = \pm \dfrac{2+\sqrt3\,i}2

Now, taking square roots on both sides, we have

z^2 + \dfrac12 = \pm w^{1/2}

z^2 = \dfrac{1+\sqrt3\,i}2 \text{ or } z^2 = -\dfrac{3+\sqrt3\,i}2

Use de Moivre's theorem again to take square roots on both sides.

w_1 = \dfrac{1+\sqrt3\,i}2 = \exp\left(i\dfrac\pi3\right)

\implies z = {w_1}^{1/2} = \pm \exp\left(i\dfrac\pi6\right) = \boxed{\pm \dfrac{\sqrt3 + i}2}

w_2 = -\dfrac{3+\sqrt3\,i}2 = \sqrt3 \, \exp\left(-i \dfrac{5\pi}6\right)

\implies z = {w_2}^{1/2} = \boxed{\pm \sqrt[4]{3} \, \exp\left(-i\dfrac{5\pi}{12}\right)}

3 0
1 year ago
Ya'll please help me!!!!. The water was pumped out of a backyard pond, What is the domain of this graph????
saw5 [17]
Stuck on the same question and it looks like nobody cares to answer on this website
6 0
3 years ago
Read 2 more answers
Writing equivalent ratios and ordered pairs Gallons 1 2 3 Quarts 4 8 12 which ordered pairs represents the equivalent ratios in
Sphinxa [80]

Step-by-step explanation:

gallons to quarts have the ratio 1:4.

there are 4 quarts in a gallon (hence the name of quarts by the way).

so, the question is really, which order pair have also a 1:4 ratio between x and y ?

(1, 4)

(2, 8)

(3, 12)

the (4, 1) would represent a 4:1 ratio.

and as you know, 4/1 is different to 1/4.

a ratio is nothing else than a fraction. just the "whole" is different.

the pure fraction 1/4 means that the whole is 4/4, has 4 times 1/4.

a ratio 1:4 (you can also write as 1/4) means that the whole has 5 (1+4) parts.

other than that they are compared and calculated with the same way as normal fractions.

4 0
2 years ago
A fuel pump at a gasoline station doesn't always dispense the exact amount displayed on the meter. When the meter reads 1.000 L,
pogonyaev

Answer:

P(X > 1.05) = 1 - 0.8413 = 0.1587 = 15.87%.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 1, \sigma = 0.05

Find P(X > 1.05).

This is 1 subtracted by the pvalue of Z when X = 1. So:

Z = \frac{X - \mu}{\sigma}

Z = \frac{1.05 - 1}{0.05}

Z = 1

Z = 1 has a pvalue of 0.8413

So P(X > 1.05) = 1 - 0.8413 = 0.1587 = 15.87%.

8 0
3 years ago
Read 2 more answers
Which expression is equvilanent to 10q + 5<br> A.5q+5q+5<br> B.10q+5+5<br> C.5q+10<br> D.5q+5
Nana76 [90]
I think is alternative a
5 0
3 years ago
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