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
When It begins to drop because that when gravity will have its strongest pull on the object.
The annual production of carbon dioxide is 124121.49×10^{6}[/tex] kg.
First we calculate the fuel consumed by each car in a year
Fuel consumed=6990/21.4=326.63 gallon
Now we calculate the amount of fuel consumed by 40 million cars in a year
Fuel consumed=326.63*40*10^6=13065.42 million gallon,
Now we can calculate the annual production of carbon dioxide in the USA
CO2 production rate=9.50*13065.42=124121.49*10^6 kg
Therefore the annual production of carbon dioxide in USA is 124121.49×10^{6}[/tex] kg
Answer:
Explanation:
ignore air resistance
Let t be the time of fall for the dropped stone.
½(9.8)t² = 43.12(t - 2.2) + ½(9.8)(t - 2.2)²
4.9t² = 43.12t - 94.864 + 4.9(t² - 4.4t + 4.84)
4.9t² = 43.12t - 94.864 + 4.9t² - 21.56t + 23.716
0 = 21.56t - 71.148
t = 71.148/21.56 = 3.3 s
h = ½(9.8)3.3² = 53.361 = 53 m
or
h = 43.12(3.3 - 2.2) + ½(9.8)(3.3 - 2.2)² = 53.361 = 53 m
