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Misha Larkins [42]
3 years ago
10

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

Mathematics
2 answers:
a_sh-v [17]3 years ago
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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the diagram shows a rectangle four of these rectangles are put to together as shown calculate the shaded area
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42cm squared

Step-by-step explanation:

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andreev551 [17]

Answer:

{10}^{ - 14}

Step-by-step explanation:

\huge\frac{ {10}^{ - 9} }{ {10}^{5} }  \\  \\  \huge =  {10}^{ - 9}  \times  {10}^{ - 5}  \\  \\  \huge =  {10}^{ - 9  + ( - 5)}  \\  \\ \huge =  {10}^{ - 9 - 5}  \\  \\  \huge \orange {=  {10}^{ - 14}}

7 0
3 years ago
Read 2 more answers
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
Read 2 more answers
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