Answer:
Slope = -1/5
Step-by-step explanation:
(-5, -2)(5, -4)
Slope: 
Consider the closed region

bounded simultaneously by the paraboloid and plane, jointly denoted

. By the divergence theorem,

And since we have

the volume integral will be much easier to compute. Converting to cylindrical coordinates, we have




Then the integral over the paraboloid would be the difference of the integral over the total surface and the integral over the disk. Denoting the disk by

, we have

Parameterize

by


which would give a unit normal vector of

. However, the divergence theorem requires that the closed surface

be oriented with outward-pointing normal vectors, which means we should instead use

.
Now,



So, the flux over the paraboloid alone is
Answer:
A nothing
Step-by-step explanation:
Answer:
12π ft², B
Step-by-step explanation:
Area of circle: radius²π
The area of the entire circle would thus be 6²π, or 36π
Note that a circle has a total degree measure of 360°, and the shaded area is 120°. Thus, the area of the shaded region would be 120/360 of the circle's area, or 1/3.
1/3 * total area of the circle = area of the shaded region
1/3 * 36π = 12π
Thus, the answer is 12π ft², or B.
t = 
isolate t by dividing both sides by Pr
= t ⇒ t = 