Both of these numbers have 2 and 5 as their factors
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)
Since each table had 7 women and 3 men at each table, that would mean each table has 10 people. Since there are 9 tables he was waiting on, and 10 people at each table, multiply 9 x 10, and you will find that he served 90 people in total.
Answer:
-ab/1
Step-by-step explanation:
The multiplicative inverse of x/y is y/x, because when multiplied it equals 1.
x/y time y/x = xy/xy, which equals one.
In this case, -1/ab times -ab/1 = -1ab/-1ab, which equals one.
