281.9 is the answer, but rounded it would be about 282
hope this helps, im not 100% sure
Using <span>De Moivre's formula
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if z = a ( cos x + i sin x ) ⇒⇒⇒ ∴ z^n = a^n ( cos nx + i sin nx)
Part (1)
∴ [ 3 (cos 27° + i sin 27°) ]⁵ = (3⁵) ( cos 5*27° + i sin 5*27°)
= 243 ( cos 135° + i sin 135°) ⇒⇒⇒⇒ Polar form
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Part (2)
The angle 135° in the second quadrant ⇒ sin is (+) and cos is (-)
and its reference angle = 180° - 135° = 45°
sin 45° = cos 45°= 1/√2 = (√2)/2
∴ sin 135° = (√2)/2 and cos 135° = -(√2)/2
∴ 243 ( cos 135° + i sin 135°) = 243 [ -(√2)/2 + i (√2)/2 ]
= - 243(√2)/2 + 243 (√2)/2 i ⇒⇒⇒⇒ standard form
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The correct answers are options (1) and (3)
option (1) ⇒⇒⇒ 243 ( cos 135° + i sin 135°) ⇒⇒⇒⇒ Polar form
option (3) ⇒⇒⇒ - 243(√2)/2 + 243 (√2)/2 i ⇒⇒⇒⇒ standard form
Answer:
They are 108 8th graders at Jefferson Middle School
Step-by-step explanation:
324 x 5/12 = 135 7th graders
324 x 3/12 = 81 9th graders
324 x 4/12 = 108 8th graders
Answer:
the answer is 21
Step-by-step explanation:
the number she thinks of is 21 add 21 + 19 to get 40.
divide 40 by 5 to get 8.
