I think the answer would be C because variability means average.
It looks like the vector field is
<em>F</em><em>(x, y)</em> = 3<em>x</em> ^(2/3) <em>i</em> + <em>e</em> ^(<em>y</em>/5) <em>j</em>
<em></em>
Find a scalar function <em>f</em> such that grad <em>f</em> = <em>F</em> :
∂<em>f</em>/∂<em>x</em> = 3<em>x</em> ^(2/3) => <em>f(x, y)</em> = 9/5 <em>x</em> ^(5/3) + <em>g(y)</em>
=> ∂<em>f</em>/∂<em>y</em> = <em>e</em> ^(<em>y</em>/5) = d<em>g</em>/d<em>y</em> => <em>g(y)</em> = 5<em>e</em> ^(<em>y</em>/5) + <em>K</em>
=> <em>f(x, y)</em> = 9/5 <em>x</em> ^(5/3) + 5<em>e</em> ^(<em>y</em>/5) + <em>K</em>
(where <em>K</em> is an arbitrary constant)
By the fundamental theorem, the integral of <em>F</em> over the given path is
∫<em>c</em> <em>F</em> • d<em>r</em> = <em>f</em> (0, 1) - <em>f</em> (1, 0) = 5<em>e</em> ^(1/5) - 34/5
Answer:
Step-by-step explanation:
f(x) = a(x-p)(x-9) is the equation of a vertical parabola.
If a>0, the parabola opens upwards.
If a<0, the parabola opens downwards.
Also, the focal length of the parabola is 1/|4a|.
To graph the equation of the line, find the x-intercept and the y-intercept of the function
we have
we know that
The x-intercept is the value of x when the value of y is equal to zero
The y-intercept is the value of y when the value of x is equal to zero
Step 1
<u>Find the x-intercept</u>
For 
the x-intercept is the point 
Step 2
<u>Find the y-intercept</u>
For 
the y-intercept is the point 
Step 3
Graph the points and draw the line
see the attached figure
therefore
the answer in the attached figure
