Please help me!

[divadreka]

1) I answered 48 math problems but stuck on these 2. can someone please help and explain how u got it? Thanks in advance!

Given the following function f(x)=?3 sinx+cosx on the interval [0,2?].

A. Determine the open interval(s) where f(x) is increasing.
B. Determine the open interval(s) where f(x) is decreasing.
C. Determine the relative maximum(s) or minimum(s).




2) Iraq is pumping crude oil into the Persian Gulf from an oil storage3 tank (a cylinder, V=?r^2h) that is 80 feet in diameter. The pump will deliver a constant flow of crude oil at 9 cubic feet per second.

A. How fast is the oil level in that tank falling?

B. Hollied Forces are planning an air strike to stop the flow of the oil. If the original oil level was 18 feet above the base and it will be 3 hours before the air strike can be conducted, will the air strike be necessary? Why or why not?

 

[galactus]

2) Iraq is pumping crude oil into the Persian Gulf from an oil storage3 tank (a cylinder, V=?r^2h) that is 80 feet in diameter. The pump will deliver a constant flow of crude oil at 9 cubic feet per second.

A. How fast is the oil level in that tank falling?

Assuming it is upright and not on its side. You did not specify. If it is on its side, that is another matter.

Using the volume of a cylinder, we can differentiate implicitly and get \(\displaystyle \frac{dV}{dt}=1600\pi \frac{dh}{dt}\)

We are given dV/dt. Sub it in and solve for dh/dt. dh/dt will be the rate it is falling in feet per second. Remember, since the oil is coming out, dV/dt is negative.

B. Hollied Forces are planning an air strike to stop the flow of the oil. If the original oil level was 18 feet above the base and it will be 3 hours before the air strike can be conducted, will the air strike be necessary? Why or why not?

The result from part A gives how fast the oil level is falling in feet per second. So, how many feet does it fall in 3 hours(10800 seconds)?.

 

[Deleted member 4993]

1) I answered 48 math problems but stuck on these 2. can someone please help and explain how u got it? Thanks in advance!

Given the following function f(x)=?3 sinx+cosx on the interval [0,2?].

A. Determine the open interval(s) where f(x) is increasing. - What is the "sign" of f'(x) [= df/dx], when f(x) is increasing?

B. Determine the open interval(s) where f(x) is decreasing.- What is the "sign" of f'(x) [= df/dx], when f(x) is decreasing?

C. Determine the relative maximum(s) or minimum(s).- What is the "value" of f'(x) [= df/dx], at relative maxima/minima?






2) Iraq is pumping crude oil into the Persian Gulf from an oil storage3 tank (a cylinder, V=?r^2h) that is 80 feet in diameter. The pump will deliver a constant flow of crude oil at 9 cubic feet per second.

A. How fast is the oil level in that tank falling? (The answer will depend on whether the tank is sitting upright or laying along its length or somewhere in between)

B. Hollied Forces are planning an air strike to stop the flow of the oil. If the original oil level was 18 feet above the base and it will be 3 hours before the air strike can be conducted, will the air strike be necessary? Why or why not?

 

[galactus]

Yes, SK. I assume it was upright. Perhaps I shoould not have been so hasty.