Answer:
90 minutes
Step-by-step explanation:
Let m represent the number of minutes Juliene practiced on Monday. Then her total for the two days is ...
m + x/2 = 135 . . . . minutes
3/2m = 135 . . . . . . collect terms
m = (2/3)(135) = 90 . . . . minutes
Juliene practiced for 90 minutes on Monday.
In quadrant ll
Hope that helps
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:$9
Step-by-step explanation:Here's what we know:
2 * 24 + 3s = 75 (the pants ($24 each) and shirts all together is $75)
What we need to do is isolate s
Simplify:
48 + 3s = 75
subtract 48 from both sides:
48 + 3s - 48 = 75 - 48
3s = 27
Divide by 3:
3s / 3 = 27 / 3
s = 9
Shirts are $9 each.
