The formula to find the volume of a cylinder is 3.14 • r squared • h
Answer:
193.53 miles
Step-by-step explanation:
Please see the diagram for understanding of how the angles were derived,
Applying Alternate Angles, ABO =77 degrees
The bearing from B to C is 192=180+12 degrees
Subtracting 12 from 77, we obtain the angle at B as 65 degrees.
We want to determine the boat's distance from its starting point.
In the diagram, this is the line AC.
Applying Law of Cosines:

The distance of the boat from its starting point is 193.53 miles (correct to 2 decimal places).
Answer:
See below.
Step-by-step explanation:
Fifth root of 243 = 3,
Suppose r( cos Ф + i sinФ) is the fifth root of 243(cos 240 + i sin 240),
then r^5( cos Ф + i sin Ф )^5 = 243(cos 240 + i sin 240).
Equating equal parts and using de Moivre's theorem:
r^5 =243 and cos 5Ф + i sin 5Ф = cos 240 + i sin 240
r = 3 and 5Ф = 240 +360p so Ф = 48 + 72p
So Ф = 48, 120, 192, 264, 336 for 48 ≤ Ф < 360
So there are 5 distinct solutions given by:
3(cos 48 + i sin 48),
3(cos 120 + i sin 120),
3(cos 192 + i sin 192),
3(cos 264 + i sin 264),
3(cos 336 + i sin 336).. (Answer).
Remember that the volume of a cylinder is

so we have that
![r=\sqrt[]{\frac{V}{\pi\cdot h}}=\sqrt[]{\frac{1909.92384}{3.14\cdot6.6}}=\sqrt[]{92.12}=9.6](https://tex.z-dn.net/?f=r%3D%5Csqrt%5B%5D%7B%5Cfrac%7BV%7D%7B%5Cpi%5Ccdot%20h%7D%7D%3D%5Csqrt%5B%5D%7B%5Cfrac%7B1909.92384%7D%7B3.14%5Ccdot6.6%7D%7D%3D%5Csqrt%5B%5D%7B92.12%7D%3D9.6)
so the radius is 9.6 milimeters
Regular is
$97.99 after sale price is 83.30
97.99- 83.30= 14.69 is the discount
You can do it same way with B C and D