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:
y=-1/5x-16/15
Step-by-step explanation:
slope intercept form y=mx+b
3x+15y=-16
15y=-3x-16 divide both sides by 15
y=-3/15x-16/15 simplify -3/15 to -1/5
y=-1/5x-16/15
Answer:
3 cups of water
Step-by-step explanation:
Henry is making a corn grits recipe that calls for 1/4 cup of corn grits for every 1/2 cup of water. How much water will he need if he uses 1 1/2 cups of corn grits?
Expand 1/2 to 2/4, if there is 1 1/2 cups of corn grits, that means that 1/4 cups of corn grits was used 6 times, 1/2x6=3. He will need 3 cups of water
The parameter used in the probability is the average number of students represented by u.
How to calculate the probability?
The confidence interval based on the information will be:
= 3.85 - 2.09(1.348 / ✓20)
= 3.22
Also, 3.85 + 2.09(1.348 / ✓20) = 4.48
The confidence interval simply means that one is 95% confident that the true mean is between 3.22 and 4.48.
They show the decomposition of a multiplication expression into smaller parts
