Answer:
The coefficient is "12"
Step-by-step explanation:
Step 1: Encircle the variable along with its power whose coefficient we are finding.
Step 2: Leave that variable and consider all other numbers or variables written with it. That will be the coefficient.
The table in Part A represents y as a function of x. This means that the value of Y is dependent on the value of X. The table can be represented by an equation that describes the relation of X and Y:

or

By substituting any value of X, you get a specific value of Y based from the given relationship, thus Y is a function of X.
For Part B, the value of f(150) is $470 and it represents the total cost for borrowing a rowboat for 150 hours. By substituting the value of x = 150 into the function, you get the total cost:
F=5 dollar bills
t=twent dollar bills
38 total bills
f+t=38
400 in bills
400=5f+20t
we have
f+t=38
5f+20t=400
multipy first equation by -5 and add to second equation
-5f-5t=-190
5f+20t=400 +
0f+15t=210
15t=210
divide both sides by 15
t=14
subsitute
t+f=38
15+f=38
f=23
23 five dolar bills
15 twenty dollar bills
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