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)
This should be the equation:
n + 4/3n + 5/3n = 90
Answer:
x=5
Step-by-step explanation:
-5(-x - 1) + 4x – 1= 49
Distribute
5x +5 +4x -1 = 49
Combine like terms
9x +4 = 49
Subtract 4 from each side
9x+4-4 = 49-4
9x = 45
Divide by 9
9x/9 =45/9
x = 5
7^4 or seven to the fourth power because 7 is being multiplied by 7 when you raise it to a power.
