Using <span>De Moivre's formula
</span>
if z = a ( cos x + i sin x ) ⇒⇒⇒ ∴ z^n = a^n ( cos nx + i sin nx)
Part (1)
∴ [ 3 (cos 27° + i sin 27°) ]⁵ = (3⁵) ( cos 5*27° + i sin 5*27°)
= 243 ( cos 135° + i sin 135°) ⇒⇒⇒⇒ Polar form
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Part (2)
The angle 135° in the second quadrant ⇒ sin is (+) and cos is (-)
and its reference angle = 180° - 135° = 45°
sin 45° = cos 45°= 1/√2 = (√2)/2
∴ sin 135° = (√2)/2 and cos 135° = -(√2)/2
∴ 243 ( cos 135° + i sin 135°) = 243 [ -(√2)/2 + i (√2)/2 ]
= - 243(√2)/2 + 243 (√2)/2 i ⇒⇒⇒⇒ standard form
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The correct answers are options (1) and (3)
option (1) ⇒⇒⇒ 243 ( cos 135° + i sin 135°) ⇒⇒⇒⇒ Polar form
option (3) ⇒⇒⇒ - 243(√2)/2 + 243 (√2)/2 i ⇒⇒⇒⇒ standard form
I'm not too sure, but I think it's like this: Emily; 46.50/173.22= 0.2684
Ally: 47.04/ 173.22= 0.272
Rosalia: 39.84/173.22= <span>0.2299</span>
Answer:
1. vertical-line test
2.y=x
3.x
4.domain
Step-by-step explanation:
I just did it on edg and it’s right.
A dot plot is a type of frequency graph just like a histogram. Whereas a histogram uses 2 axes and bars to fill the frequency graph, the dot plot is only a number line with dots. A number line presents a parameter. For this problem, this is the number of books. When you ask a group of people on how many books they've read this summer, they would give a variety of numbers. These numbers are data point as listed above. If you want to see the frequency, you place a dot on top of the number every time a person answers that number. For example, 3 people said they've read 2 books this summer. So, on top of number two, you place 3 dots. Overall, you will be able to see which has the highest frequency by stacking the dots on top of each other.
The dot plot for this data set is shown in the picture.
Answer:
28.6 ft
Step-by-step explanation:
Given an hemisphere of volume 
Volume of a Hemisphere of radius r 
Therefore:
![\frac{2}{3}\pi r^3=49037 \\r^3=49037 X \frac{3}{2 \pi}\\r=\sqrt[3]{49037 X \frac{3}{2 \pi}} \\r=28.6\: foot](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%5Cpi%20r%5E3%3D49037%20%5C%5Cr%5E3%3D49037%20X%20%5Cfrac%7B3%7D%7B2%20%5Cpi%7D%5C%5Cr%3D%5Csqrt%5B3%5D%7B49037%20X%20%5Cfrac%7B3%7D%7B2%20%5Cpi%7D%7D%20%5C%5Cr%3D28.6%5C%3A%20foot)
The radius of the hemisphere is 28.6 foot to the nearest tenth.