Answer:
2(cos135° + isin135°)
Step-by-step explanation:
z^6 = 64i
We need to change i to polar form
cos (90) + isin (90) = i
x^6 = 64 cos (90) + isin (90)
Now we need to take the sixth root of each side
(x^6) ^ 1/6 = ((64)( cos (90) + isin (90)) ^ 1/6
(x^6) ^ 1/6 = ((64) ^ 1/6 * cos (90) + isin (90)) ^ 1/6
(x^6) ^ 1/6 = 2( * cos (90) + isin (90)) ^ 1/6
We we take the roots of the trig functions, we have 6 roots
360/n means the roots are 60 degrees are apart
take 90 /6 = 15 degrees
The first root is at 2 (cos (15) + isin (15))
The second root is at 2 (cos (15+60) + isin (15+60))
2 (cos (75) + isin (75))
The third root is at 2 (cos (75+60) + isin (75+60))
2 (cos (135) + isin (135))
and so on
Answer:
13.71 m
Step-by-step explanation:
Draw the tunnel so the width marks the zeroes at (-12,0) and (12,0)
then y = a ( x+12)(x-12) is the equation..
..to calculate 'a' sub in the point 9, 6 (where the width is 18)
6 = a ( (9+12)(9-12) shows a = -2/21
y = -2/21 (x+12)(x-12) Max is when x = 0
-2/21 ( 12)(-12) =<u> 288/21 = 13.71 m </u>
This mean that ashley add 36 litres at a rate of 4 litre/mins
therefore t is equal to 36/4=9 minute
Therefore ashley take 9 mins.
Answer:
the answer is (c)
Step-by-step explanation:
-(-1)-13= 1-13=-12