Circumference: 2πr C=18 so r= 18/2π= 9π
Arc length = rθ 6=(9π)θ θ=6/9π
Convert to degrees by multiplying by 180/π
6/9π x 180/π = 120 degrees
Answer:
<h2>3(cos 336 + i sin 336)</h2>
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:
n0...
Step-by-step explanation:
Answer:
Train A - 50 miles per hour
train B - 30 miles per hour
Step-by-step explanation:
Let x mph be the speed of the train B, then the speed of the train A is (x+20) mph.
In 3 hours,
- train A travels 3(x+20) miles
- train B travels 3x miles
In total, they covered the distance of 240 miles, so
![3(x+20)+3x=240\ \ \ \text{[Divide by 3]}\\ \\x+20+x=80\\ \\2x=80-20\\ \\2x=60\\ \\x=30\ mph\\ \\x+20=30+20=50\ mph](https://tex.z-dn.net/?f=3%28x%2B20%29%2B3x%3D240%5C%20%5C%20%5C%20%5Ctext%7B%5BDivide%20by%203%5D%7D%5C%5C%20%5C%5Cx%2B20%2Bx%3D80%5C%5C%20%5C%5C2x%3D80-20%5C%5C%20%5C%5C2x%3D60%5C%5C%20%5C%5Cx%3D30%5C%20mph%5C%5C%20%5C%5Cx%2B20%3D30%2B20%3D50%5C%20mph)
Answer:
5
Step-by-step explanation:
The mechanical advantage of a machine is the ratio of the force that you need to input to how much is outputted. 200:1000=1:5, meaning that the mechanical advantage is 5. Hope this helps!
