Yes because it is correct
Answer:
<u>Volume = 1.535</u>
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Step-by-step explanation:
The region R is bounded by the equations:
y = √sin⁻¹x
y = √(π/2)
y = √(π/3)
x = 0
R is revolved around the x-axis so we will need f(y) for finding out the volume. We need to make x the subject of the equation and then replace it with f(y).
f(x) = √sin⁻¹x
y = √sin⁻¹x
Squaring both sides we get:
y² = sin⁻¹x
x = sin (y²)
f(y) = sin (y²)
Using the Shell Method to find the volume of the solid when R is revolved around the x-axis:
![V = 2\pi \int\limits^a_b {f(y)} \, dy](https://tex.z-dn.net/?f=V%20%3D%202%5Cpi%20%5Cint%5Climits%5Ea_b%20%7Bf%28y%29%7D%20%5C%2C%20dy)
The limits a and b are the equations y = √(π/2) and y = √(π/3) which bound the region R. So, a = √(π/2) and b = √(π/3).
V = 2π ![\int\limits^\sqrt{\frac{\pi }{2}}](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%5Csqrt%7B%5Cfrac%7B%5Cpi%20%7D%7B2%7D%7D)
sin (y²) dy
Integrating sin (y²) dy, we get:
-cos(y²)/2y
So,
V = 2π [-cos(y²)/2y] with limits √(π/2) and √(π/3)
V = 2π [(-cos(√(π/2) ²)/2*√(π/2)] - [(-cos(√(π/3) ²)/2*√(π/3)]
V = 2π [(-cos(π/2)/ 2√(π/2)) - ((-cos(π/3)/ 2√(π/3))]
V = 2π [ 0 - (-0.5/2.0466)]
V = 2π (0.2443)
V = 1.53499 ≅ 1.535
Answer:
50 + 25 + (8*5) - (7 + 4)
Step-by-step explanation:
50 + 25 + (8*5) - 7 + 4 = 50 + 25 + 40 - 7 + 4
= 115 - 7 + 4
= 108 + 4
= 112
Answer:
Should be 5.43
Step-by-step explanation:
x=5.43
Answer:
Sin is the function of an angle
it is the ratio of the length of the side that is opposite of that angle to the length of the longest side of the triangle