Step-by-step explanation:
For the first term

(b)

(c)

(d)

(e)

(f)

Denote the cylindrical surface by
, and its interior by
. By the divergence theorem, the integral of
across
(the outward flow of the fluid) is equal to the integral of the divergence of
over the space it contains,
:

The given velocity vector has divergence

Then the total outward flow is

Converting to cylindrical coordinates gives the integral

Would it be 270? if you take 90 3 times. due to that there are 3 different durations.
Answer:
a) Q(-2,1) is false
b) Q(-5,2) is false
c)Q(3,8) is true
d)Q(9,10) is true
Step-by-step explanation:
Given data is
is predicate that
then
. where
are rational numbers.
a)
when 
Here
that is
satisfied. Then

this is wrong. since 
That is 
Thus
is false.
b)
Assume
.
That is 
Here
that is
this condition is satisfied.
Then

this is not true. since
.
This is similar to the truth value of part (a).
Since in both
satisfied and
for both the points.
c)
if
that is
and
Here
this satisfies the condition
.
Then 
This also satisfies the condition
.
Hence
exists and it is true.
d)
Assume 
Here
satisfies the condition 
Then 
satisfies the condition
.
Thus,
point exists and it is true. This satisfies the same values as in part (c)