Answer:
The volume of a cylindrical conduit,
where
is the inner radius,
is the outer radius, h is the length.
First of all, we would covert each parameter into centimeters.
length of the conduit, 
outer radius, 
inner radius, 
Insert the values in the volume formula,

Hence, the volume of metal in the conduit is 510. 12 cubic centimeters.
<span>Answer:
F(x) = ax^2 - bx
or
F(x) = ax² - bx
F(x) = 30x² - 6x
â«F(x)dx = â«(30x² - 6x)dx
as this is evaluated from zero to x
W = 10x³ - 3x² <===ANS
W = 10(0.42³) - 3(0.42²) - [10(0³) - 3(0²)]
W = 0.212 J <===ANS
W = 10(0.72³) - 3(0.72²) - [10(0.42³) - 3(0.42²)]
W = 1.966 J <===ANS</span>
<h3><u>Answer;</u></h3>
Velocity and wavelength are directly proportional when frequency is kept constant.
<h3><u>Explanation;</u></h3>
- <em><u>Frequency of a wave is the number of complete oscillations made by a given wave in one second. </u></em>
- <em><u>Wavelength on the other hand, is the distance between two successful crests or troughs in a transverse wave or two successful rarefactions or compressions in a longitudinal waves.</u></em>
- <em><u>The speed of a wave is given by the product of the frequency of a wave and the wavelength.</u></em>
- <em><u>Speed = Frequency × wavelength, </u></em>
- <em><u>Therefore, if frequency is kept constant, then the speed of a wave is directly proportional to the wavelength, such that an increase in wavelength increases the speed of the wave and vice versa.</u></em>
According to Newton's second law, the force applied to an object is equal to the product between the mass of the object and its acceleration:

where F is the magnitude of the force, m is the mass of the object and a its acceleration.
In this problem, the object is the insect, with mass

. The acceleration of the insect is

, therefore we can calculate the force exerted by the car on the insect:

How do we find the force exerted by the insect on the car?
According to Newton's third law (known as action-reaction law), when an object A exerts a force on an object B, object B also exerts a force equal and opposite on object A. Therefore, the force exerted by the insect on the car is equal to the force exerted by the car on the object, so it is 0.01 N.
Answer:
The tangential speed of the tack is 8.19 m/s.
Explanation:
The wheel rotates 3.37 times a second that means wheel complete 3.37 revolutions in a second. Therefore, the angular speed ω of the wheel is given as follows:

Use the relation of angular speed with tangential speed to find the tangential speed of the tack.
The tangential speed v of the tack is given by following expression
v = ω r
Here, r is the distance to the tack from axis of rotation.
Substitute 21.174 rad/s for ω, and 0.387 m for r in the above equation to solve for v.
v = 21.174 × 0.387
v = 8.19m/s
Thus, The tangential speed of the tack is 8.19 m/s.