Answer:
Please see attached picture for full solution.
Answer:

Step-by-step explanation:
Consider the revenue function given by
. We want to find the values of each of the variables such that the gradient( i.e the first partial derivatives of the function) is 0. Then, we have the following (the explicit calculations of both derivatives are omitted).


From the first equation, we get,
.If we replace that in the second equation, we get

From where we get that
. If we replace that in the first equation, we get

So, the critical point is
. We must check that it is a maximum. To do so, we will use the Hessian criteria. To do so, we must calculate the second derivatives and the crossed derivatives and check if the criteria is fulfilled in order for it to be a maximum. We get that


We have the following matrix,
.
Recall that the Hessian criteria says that, for the point to be a maximum, the determinant of the whole matrix should be positive and the element of the matrix that is in the upper left corner should be negative. Note that the determinant of the matrix is
and that -10<0. Hence, the criteria is fulfilled and the critical point is a maximum
Sin∠R = ST/RS ⇒ ST = RS * sin40° = 9 * 0.6428 ≈ 5.8
Find the volume of the cylinder and divide by 2:
V = pi * r^2 * h
V = 3.14 * 11^2 * 17
V = 6458.98
Divide by 2 since it's half full:
6458.98 / 2 = 3229.49
Now divide it by 46.2 to see how long it will take to drain out:
3229.49 / 46.2 = 69.902
So it will take approximately 70 seconds to drain out.
Answer:
use pythagorean theorem
Step-by-step explanation:
a^2+b^2=c^2