is conservative if we can find a scalar function
such that
. This is equivalent to solving the system of PDEs,


Integrate both sides of the first PDF with respect to
:

where
is some function independent of
. Then differentiatng with respect to
, we have


and so
is indeed conservative, with

Assignment: 
<><><><><>
Answer: 
<><><><><>
Explanation: 
<><><><><>
[ Step One ] Follow PEMDAS Order Of Operations; Calculate Within Parenthesis
Note: 

[ Step Two ] Rewrite Equation

[ Step Three ] Calculate Within Parenthesis

[ Step Four ] Rewrite Equation

[ Step Five ] Calculate Exponents

[ Step Six ] Rewrite Equation

[ Step Seven ] Multiply

[ Step Eight ] Rewrite Equation

[ Step Nine ] Subtract

[ Step Ten ] Rewrite Equation

<><><><><><><>
Answer:
-3 < x
Step-by-step explanation:
15 > -5x
Divide each side by -5, remembering to flip the inequality since we are dividing by a negative
15/-5 < -5x/-5
-3 < x
Answer:
352 cm/s
Step-by-step explanation:
circ = 44pi
speed = distance * time
distance = circ * 4 = 176pi
speed = 176pi/0.5