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
I think the answer is repulsive.... Sorry if I get this wrong? :)
<u>We call changes between solid liquid and gaseous forms of a substance as phase change or change of state.</u>
<u>Explanation:</u>
To change a substance from one state to another, extreme temperatures or pressures are required. Sometimes when a substance doesn't change states we should use all the ideas when that happens. To create a solid, we should decrease the temperature by a huge amount and then add pressure. For example, oxygen will solidify at -361.8 degrees Fahrenheit at standard pressure. However, it will freeze at warmer temperatures when the pressure is increased.
Phase changes happen when a substance reach some special points. Sometimes when a liquid becomes a solid a freezing point or melting point is used to measure the temperature at which a liquid changes into a solid. Some of the phase changes are: Condensation, Freezing, Melting.
Answer:
the angle is given by
Tan theta = 35/59 = 0.59
so theta = Tan ^-1 ( 0.59 )
theta = 30.54 deg.