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:
ok so if equilateral triangle has 1 inch and box has 9 inch of height, the lateral area would be 27 square-inch
Step-by-step explanation:
Answer:
150
Step-by-step explanation:
the equation for this is l x w x h
5 x 10 x 3 = 150
Answer: B
Explanation: ONE triangle can be formed.
According to the triangle inequality theorem, the sum of any two sides must be greater or equal than the length of the third side.
Here, the sides are 1 m, 2 m, and 2m. 1m + 2m = 3m > 2m (theorem followed) 2m + 2m = 4m > 1m (theorem followed)
Since, the triangle inequality theorem is followed, Hence, ONE triangle can be formed.