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).
Answer:
First option
h = 4 and k = - 2
Step-by-step explanation:
f(x) = x^3 translated to g(x) = (x – h)^3 + k.
f(x) transformed to g(x) with 4 units to the right and 2 units down
g(x) = (x - 4)^3 - 2
h = 4 and k = - 2
Answer:
The GFC is 1
Step-by-step explanation:
<span>$2,022.92 would be the answer
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A-10, D-11, F-8, I-2, G-1, K-9, B-7, C-3
That's what I got so far, but I'm still working
