The correct answer for the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x2, y = 4x is 128/3 * π.
Volume of Solid of Revolution by Shell method is given by
V = 2π * integrate x(height) dx Here, height = 4x-x2
(1)& x-varies from x = 0 to x = 4 then from eqn(1) V = 2π * integrate x(4x - x ^ 2) dx from x = 0 to 4 = 2π * integrate (4x ^ 2 - x ^ 3) dx from x = 0 to 4
Basic Rule(1) ∫ x^n dx =x^ n+1/ n+1
V=2 π [4((x ^ 3)/3) - (x ^ 4)/4] 0 ^ 4 =2 π[ 4/3 x^ 3 - x^ 4/4 ] 0 ^ 4
V = 2π [4/3 * 4 ^ 3 - (4 ^ 4)/4} - 0]
V = 128/3 * π.
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Answer:
A-Light from the Sun reflects off the Moon as it orbits Earth
The angular speed is decreasing and direction of rotation clockwise of the rod immediately after time t.
<h3>
</h3><h3>What is angular speed ?</h3>
The rate of change of angular displacement is defined as angular speed. It is stated as follows:
ω = θ t
Where,
θ is the angle of rotation,
t is the time
ω is the angular velocity
The torque is found as;l

If the force is acting on the rod from the three point is the same, the value of the torque is depends upon the radius or the perpendicular distance.
The perpendicular distance of the right force is grater. Hence, the force acting on the right side is more, and the rod will rotate clockwise.
Both the forces are acting downwards. Thus, the resultant force is the less due to which the speed is increasing.
Hence, the angular speed is decreasing and direction of rotation clockwise of the rod immediately after time t.
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The wave speed to this question is 400 meters