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:
Step-by-step explanation:
For a number to be divisible by 4 you just need to worry about the 10s and 1s place. You also want to know that the 1s cylce every 20, or in other words:
4 8 12 16 20
24 28 32 36 40 and so on. So the only numbers that x can be there are 1, 3, 5, 7, 9. Does that make sense? and can you manage the rest?
Answer:
Step-by-step explanation:
1.Based on the equation the y-intercept is -2(go down 2 places on the y axis)
2.Since here is only x in the equation the rise over run will be 1/-1 (go up 1 and to the left 1 from the point -2 on the y axis) keep doing that all the way down the graph marking your points, also reverse the process going down 1 and to the right 1 to mark the points on the opposite side.
3.Draw the line through the points you marked from step 2
4.In the equation it is x-2 so it is a positive slope and a negative y-intercept
m=1
b= -2
Answer:
57
Step-by-step explanation:
1) According to PEMDAS, <em>multiply </em>first: 27+ 5x6= 27+30
2) Then <em>add</em>: 27+30=57
