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:
Perimeter= 44.2 inches
Area= 70 inches squared
Step-by-step explanation:
Perimeter- Add all your sides together (10+ 17.2+2+3+7+5=44.2)
Area- 1/2bh (b=base, h=height)
Your base is the bottom of the triangle, so 2+7+5=14.
14 is your base
Your height is the 10
1/2 *14*10
1/2 of 14 is 7
7*10= 70
Don't forget to write inches squared or it will be wrong
Hope this helps :)
Answer:
No Mr.Linton will not take 7 days to finish the book
Explanation
Since the book has 900 pages, you will have to divide 900 by 100 which equals 9. 9 is the number of days it will take for Mr.Linton to read the book. Therefore he is wrong.
hope this is helpful
Answer:
Step-by-step explanation:
x²-7x+10=0
(x-2)(x-5)=0
x=2 or x=5
Thats it the correct answer
