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Vitek1552 [10]
3 years ago
12

Convert 3 - 3i to polar form.

Mathematics
1 answer:
Blababa [14]3 years ago
3 0

Answer:

Option d is correct that is z=\sqrt{18} cos(\frac{7\pi}{4})+i sin(\frac{7\pi}{4})

Step-by-step explanation:

We have been given a complex number 3-3i we have to convert it in the polar form:

polar form of a complex number:

z=r(cos{\theta}+i sin{\theta})

Where, r=\sqrt{x^2+y^2}

the general form of complex number is:

x+iy

Here, x=3 and y=-3

Hence, r=\sqrt{3^2+(-3)^2}=\sqrt{18}

And \theta=tan^{-1}\frac{y}{x}

   \theta=tan^{-1}\frac{-3}{3}

\Rightarrow \theta=tan^{-1}(-1)

\Rightarrow \theta=2{\pi}-\frac{\pi}{4}

\Rightarrow \theta=\frac{7\pi}{4}

Hence, substituting all the values in polar form formula we get:

z=\sqrt{18} cos(\frac{7\pi}{4})+i sin(\frac{7\pi}{4})

Therefore, option d is correct.

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Answer:

Null hypothesis:\mu = 52.6  

Alternative hypothesis:\mu \neq 52.6  

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Since the p value is lower than the significance level wedon't have enough evidence to conclude that the true mean is significantly different from 52.6 MPG.

Step-by-step explanation:

Information provided

\bar X=52.8 represent the sample mean  for the MPG of the cars

\sigma=1.6 represent the population standard deviation

n=250 sample size  of cars

\mu_o =52.6 represent the value that we want to test

\alpha=0.05 represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

p_v represent the p value for the test

Hypothesis

We need to conduct a hypothesis in order to check if the true mean of MPG is different from 52.6 MPG, the system of hypothesis would be:  

Null hypothesis:\mu = 52.6  

Alternative hypothesis:\mu \neq 52.6  

Since we know the population deviation the statistic is given by:

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}  (1)  

Calculate the statistic

Replacing we have this:

z=\frac{52.8-52.6}{\frac{1.6}{\sqrt{250}}}=1.976    

Decision

Since is a two tailed test the p value would be:  

p_v =2*P(z>1.976)=0.0482  

Since the p value is lower than the significance level wedon't have enough evidence to conclude that the true mean is significantly different from 52.6 MPG.

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3 years ago
Classify the triangle shown below. Check all that apply.
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Answer:

A and B

Step-by-step explanation:

A. Since 2 angles are congruent you know that there has to be 2 equal sides

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C. Triangle has 2 congruent sides so this is incorrect

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Answer:

The graph can show you how much distilled water for 4 milliliters of ammonia and 5 milliliters of ammonia. You can use the graph to find 4.5 by find the midpoint of two amounts of distilled water. Such as, say that 4 milliliters of ammonia = 200 distilled water and 5 milliliters of ammonia=  250 distilled water. Then the answer to 4.5 milliliters of ammonia is 225 distilled water.

Step-by-step explanation:


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Answer:

The correct answer is wins and rebounds are correlated positively ,but we cannot decided that having more rebounds leads to more wins,on average.

Step-by-step explanation:

From the example given, the most appropriate conclusion is that, because  causation is not the same as correlation, If two variables are compared,this does not mean that one leads to the other.

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