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
The answer for this problem would be x equal to 430 cm and y is equal to 325. This is computed by establishing the equations. This first equation based on first statement would be x = 15 + y and the second would be 5x = 3y + 525. Then it is solve as follows:
5x = 3y + 525
Let's look at an example:
2.24 x 21.6

Do normal multiplication and get
48384 This is not correct, until we put the decimals in. To know how to do this, count the number of decimal spaces from the factors. In 2.24, there are 2, because .24. In 21.6 there are 1 because of .6. This mean three places, so 48384 becomes
48.384
~theLocoCoco
Answer:
y = -1/8 x² + 5
Step-by-step explanation:
Parabola opens vertically and vertex (h,k) = (0,5), pass point (4,3)
basic formula: y = a(x - h)² + k
y = a (x-0)² + 5
y = ax² + 5 pass (4,3)
3 = 16a + 5
a = (3-5)/16 = -1/8
equation: y = -1/8 x² + 5
check: pass another point (-4,3)
-1/8 * (-4)² + 5 = -2 + 5 = 3