Surface integral: Parameterize the closed surface by
with
and
, where
defines the paraboloid part and
the planar part of the total surface
.
We have
so we get
The second integral vanishes when computing the dot product, so we're left with the first integral which reduces to
Volume integral (divergence theorem): We have divergence
By the divergence theorem, the flux is equivalent to the volume integral
where
denotes the space enclosed by the surface
. Converting to cylindrical coordinates lets us write the integral as
as desired.
Answer:
Paint one: 99in
Paint Two: 120in
Step-by-step explanation:
11 x 9 = 99
15 x 8 = 120
Answer:
-9
Step-by-step explanation:
Slope is the same so y=-2x+b
Plug in x and y
-3=-2(-3)+b
-3=6+b
b=-9
(Y-intercept is -9)
Two x plus five equals ten
Answer:
150 miles
Step-by-step explanation:
We can split 3 hours into six sections of 30 minutes, then multiply those six sections by the 25 miles. 6 times 25 equals 150