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:
Explanation:
We have given initial length of the steel guitar l = 1 m
Cross sectional area 
Young's modulus 
Force F = 1500 N
So stress 
We know that young's modulus 
So 
Now strain 
Kinetic energy =1/2 mv^2
<span>m=2ke/v^2 </span>
<span>m=2(34)/3.6^2 </span>
<span>m=5.24 </span>
<span>force normal = mg </span>
<span>=5.24 x 9.8 </span>
<span>force normal = 51.4N
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Answer:
The minimum coefficient of friction required is 0.35.
Explanation:
The minimum coefficient of friction required to keep the crate from sliding can be found as follows:
Where:
μ: is the coefficient of friction
m: is the mass of the crate
g: is the gravity
a: is the acceleration of the truck
The acceleration of the truck can be found by using the following equation:
Where:
d: is the distance traveled = 46.1 m
: is the final speed of the truck = 0 (it stops)
: is the initial speed of the truck = 17.9 m/s
If we take the reference system on the crate, the force will be positive since the crate will feel the movement in the positive direction.
Therefore, the minimum coefficient of friction required is 0.35.
I hope it helps you!
Answer:
The brightness of bulb 1 dies because it is switched off.
