Circle S is shown. Line segment R T is a diameter. The length of S T is 4. Sector R S T is shaded. The measure of central angle
RST is radians. What is the area of the shaded sector? 4Pi units squared 8Pi units squared 16Pi units squared 20Pi units squared
2 answers:
Answer:
<h3>Second option is correct.</h3>8\pi units^{2}
Step-by-step explanation:
The shaded sector is half the area, because its divided in two parts by the diameter, which is in the middle. So, one way we could get the answer is finding the total area, then divide it by two, like this:
Then, the shaded sector is half:
<em>Therefore, the correct answer is the second option.</em>
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The rate of change of the angle of elevation when the firework is 40 feet above the ground is 0.12 radians/second.
First we will draw a right angle triangle ΔABC, where ∠B = 90°
Lets, assume the height(AB) = h and base(BC)= x
If the angle of elevation, ∠ACB = α, then
tan(α) =
Taking inverse trigonometric function, α = tan⁻¹ () .............(1)
As we need to find the rate of change of the angle of elevation, so we will differentiate both sides of equation (1) with respect to time (t) :
Here, the firework is launched from point B at the rate of 10 feet/second and when it is 40 feet above the ground it reaches point A,
that means h = 40 feet and = 10 feet/second.
C is the observer's position which is 50 feet away from the point B, so x = 50 feet.
= 0.12 (Rounding up to two decimal places)
So, the rate of change of the angle of elevation is 0.12 radians/second.
