We want to find 
such that 
. This means
Integrating both sides of the latter equation with respect to 
tells us
and differentiating with respect to 
gives
Integrating both sides with respect to gives
Then
and differentiating both sides with respect to 
gives
So the scalar potential function is
By the fundamental theorem of calculus, the work done by 
along any path depends only on the endpoints of that path. In particular, the work done over the line segment (call it 
) in part (a) is
and does the same amount of work over both of the other paths.
In part (b), I don't know what is meant by "df/dt for F"...
In part (c), you're asked to find the work over the 2 parts (call them 
and 
) of the given path. Using the fundamental theorem makes this trivial:
Answer:
Direct variation
Step-by-step explanation:
It's not iverse because the line is curved so it's direct variation
Answer:
12 customers are waiting each hour to enter the diner
Step-by-step explanation:
20 customers arrive each hour to the diner. 8 customers ocuppy the seats each hour, and 12 are left waiting outside.
(x + 5)(x + 2) = x^2 + 2x + 5x + 10 = x^2 + 7x + 10
middle term is 7x
To find the slope use the Rise over Run rule
It rises 2 units and runs 1 unit, so your slope is
2 or 2/1
To find the y-intercept just find where the line crosses the y-axis
it crosses at the -4 mark
Your slope is 2 and y-intercept is -4
