Answer:
a) 
b) 
Step-by-step explanation:
Recall that given a function f(x,y,z) then
. To find f, we will assume it exists and then we will find its form by integration.
First assume that F =
. This implies that
if we integrate with respect to x we get that
for some function g(y,z). If we take the derivative of this equation with respect to y, we get
This must be equal to the second component of F. Then

This implies that
, which means that g depends on z only. So 
Taking the derivative with respect to z and making it equal to the third component of F, we get
which implies that
which means that g(z) = K, where K is a constant. So

b) To evaluate
we can evaluate it by using f. We can calculate the value of f at the initial and final point of C and the subtract them as follows.

Recall that
so
Also
so
So 
Keeping in mind that an hour is 60 minutes.
The correct answer is: [A]: " <span>x(y – 5) = 2 " .
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Consider:
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Choice: [A]: " x(y–5) = 2 " ;
Divide each side by "x" ;
" [x(y – 5)] / x = 2/x " ;
→ y – 5 = 2/x ;
Add "5" to each side of the equation:
y – 5 + 5 = 2/x + 5 ;
→ y = 2/x + 5 ; not a line; since one cannot divide by "zero" ; there would be no "point" on the graph at "x = 0". So, this answer choice: [A] is correct.
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Choice [B]:
y -2x -18 = 0
y - 2x = 18
y = 18 + 2x ; y = 2x + 18 ; is a line.
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Choice C) 3y + 12 - 6x = 5 ;
3y = 5 - 12 + 6x ;
3y = -7 + 6x ; 3y = 6x - 7 ; y = 6x/3 - 7/3 ; y = 2x - 7/3 ; is a line.
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Choice: [D]:
2(y+x) = 0 ;
[2*(y+x)] / 2 = 0/2 ; y + x = 0 ; y = -x ; is a line.
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Answer:
Step-by-step explanation: