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3 years ago

For z = 2cis 60°, find z4 in rectangular form.

2 answers:

5 0

By DeMoivre's theorem,

$z=2\mathrm{cis}60^\circ\implies z^4=2^4\mathrm{cis}(4\times60)^\circ=16\mathrm{cis}\,240^\circ$
$z^4=16(\cos240^\circ+i\sin240^\circ)$
$z^4=16\left(-\dfrac12-i\dfrac{\sqrt3}2\right)$
$z^4=-8-i8\sqrt3$

REY [17]3 years ago

5 0

Answer:

For plato users the answeris -8-8 $\sqrt{3i}$

Step-by-step explanation:

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3 years ago

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andreev551 [17]

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Step-by-step explanation:

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7 0

3 years ago

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An automotive manufacturer wants to know the proportion of new car buyers who prefer foreign cars over domestic. Step 2 of 2 : S

ziro4ka [17]

Answer:

The 85% onfidence interval for the population proportion of new car buyers who prefer foreign cars over domestic cars is (0.151, 0.205).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

Sample of 421 new car buyers, 75 preferred foreign cars. So $n = 421, \pi = \frac{75}{421} = 0.178$

85% confidence level

So $\alpha = 0.15$ , z is the value of Z that has a pvalue of $1 - \frac{0.15}{2} = 0.925$ , so $Z = 1.44$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.178 - 1.44\sqrt{\frac{0.178*0.822}{421}} = 0.151$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.178 + 1.44\sqrt{\frac{0.178*0.822}{421}} = 0.205$

The 85% onfidence interval for the population proportion of new car buyers who prefer foreign cars over domestic cars is (0.151, 0.205).

8 0

2 years ago

Katie has read 32 % of a book. If she has read 80 pages, how many more pages does Katie have left to read?

mestny [16]

Percentage of pages of a book read by Katie = 32%
Total number of pages of the book read by Katie = 80
Let us assume the number of pages that the book has = x
Then
(32/100) * x = 80
32x = 80 * 100
32x = 8000
x = 8000/32
= 250
So the book has a total of 250 pages in it.
Then
The number of pages that Katie still needs to read = 250 - 80
= 170
So Katie needs to read 170 more pages in the book.

7 0

3 years ago

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