Yes, the volume of the cylinder will remain constant. As the radius decreases, the height will increase to make sure that the volume is kept the same.
We have been given a value of dr/dt and are required to find dh/dt
Because the volume is constant, we can plug it into the formula for the volume of the cylinder and rearrange it to make h the subject:
128 = πr²h
h = 128/πr²
Now we differentiate both sides:
dh/dr = -256/πr³
Applying the chain rule:
dh/dt = dh/dr x dr/dt
dh/dt = (-256/πr³) x -0.05
dh/dt = 64/5πr³; substituting the value of r
dh/dt = 64/5π(1.5)³
dh/dt = 1.21 in/sec
Answer:
Addition reactions with benzenes lead to the loss of aromaticity.
Benzene and its derivatives undergo a type of substitution reaction in which a hydrogen atom is replaced by a substituent, but the stable aromatic benzene ring is regenerated at the end of the mechanism.
Benzene and its derivatives tend to undergo electrophilic aromatic substitution reactions.
Explanation:
Answer:
Explanation:
Given height of lamp from the ceiling = 2.6m
mass of the lamp = 3.8kg
acceleration due to gravity = 9.81m/s²
As the body falls to the ground, it falls under the influence of gravity.
Gravitational potential energy = mass*acc due to gravity * height
Gravitational potential energy = 3.8*2.6*9.81
Gravitational potential energy = 96.923 Joules
b) Kinetic energy = 1/2 mv²
m = mass of the body (in kg)
v = velocity of the body (in m/s²)
To get the velocity v, we will use the equation of motion 

Since mass = 3.8kg

c) To know how fast the lamp is moving when it hits the ground, we will use the formula. When the body hits the ground, the height covered will be 0m. this means that the body is not moving once it hits the ground. It stays in one position. The energy possessed by the body at this point is potential energy. The correct answer is therefore 0 m/s
[r] =6
Solve for r by simplifying both sides of the equation, then isolating the variable.
<em> </em>I hope this makes sense