Do you remember your unit circle? If sin ω = was -1/2, then it would be 7<span>π/6. If you're unfamiliar with the unit circle, we can derive it.
So, you know that sin is OPPOSITE/HYPOTENUSE, and it's in the third quadrant, where x and y would be negative. If sin </span>ω = -1/2, that means that ω = 1/sin*(-1/2), or sin^(-1)*(-1/2). Let's ignore the negative for now and plug sin^(-1)*(-1/2) into your calculator in radians. You get (1/6)π. But that's in Quadrant 1. We want it in Quadrant 3.
In one complete revolution, or 360°, there are 2π radians. That means, if you want to rotate it 180°, you need to add π to what you originally got.
π+(1/6)π=(7/6)π.
I highly recommend you memorize the unit circle if you haven't already, because you'll need it from Precalculus on.
Answer:
∡x = 20°
∡y = 160°
∠z = 160°
Step-by-step explanation:
Angles on a straight line sum to 180°
⇒ ∠z + 20° = 180°
⇒ ∠z = 180° - 20°
⇒ ∠z = 160°
The central angle measure equals the corresponding arc measure.
⇒ ∡x = 20°
⇒ ∡y = ∠z = 160°
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Answer:
5. x = 160; y = 20
6. h = 125°; g = i = 55°
Step-by-step explanation:
Vertical angles are found on opposite sides of a point where lines cross. Each angle is formed from rays opposite those of the other angle. Vertical angles are congruent.
5. x° and 160° are vertical angles: x° = 160°
y° and 20° are vertical angles: y° = 20°
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6. h° and 125° are vertical angles: h° = 125°
The angles g° and 125° form a "linear pair" so total 180°.
g° = 180° -125° = 55°
g° and i° are vertical angles: g° = i° = 55°
Answer:
0.2397
Step-by-step explanation:
Given data:
fX(x) = Cxe^(−x/2) if x >0 0 otherwise, where C > 0 is some constant.
The probability that the system functions for at least 5 months
= 0.2397
attached below is a detailed solution
