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
0.006
That's you're answer
Answer:
30th day
Step-by-step explanation:
5*6=30
and 6*5=30
basically we have to take Lcm of 5 and 6=30
30th day they both will be together
Answer:
A'(7,-3)
Step-by-step explanation:
We were given the coordinates, A(-7,3) of quadrilateral ABCD and we want to find the image of A after a reflection across the x-axis followed by a reflection in the y-axis.
When we reflect A(-7,3) across the x-axis we negate the y-coordinate to obtain: (-7,-3).
When the image is again reflected in the across the y-axis, we negate the x-coordinate to get (--7,-3).
Therefore the coordinates of A' after the composed transformation is (7,-3).
Answer:
Johnny will be able to reach the safe zone before the gate is closed.
Step-by-step explanation:
Given that:
Distance of Little Johnny from safe zone = 4000 feet
Time = 3 minutes
Speed = 22 mph
To find:
Will Johnny be able to reach the safe zone ?
Solution:
Johnny can only be safe if he can travel 4000 feet in 3 minutes with the given speed.
Let us try to find out, the distance that he can travel in 3 minutes at speed of 22 mph.
Let us have a look at the formula of distance traveled:

Time = 3 minutes =
hrs
Speed = 22 mph

We know that 1 mile = 5280 feet
Therefore 1.1 miles = 5280
1.1 feet = 5808 feet
Distance traveled by Little Johnny is greater than 4000 feet.
Therefore Johnny will be able to reach the safe zone before the gate is closed.