1. x
2. x + 2
3. x + 4
x + 4 + 2x = 25. Second option is the answer.
Combine like terms
3x + 4 = 25
Subtract 4 from both sides
3x = 21
Divide both sides by 3
x = 7
Answer:
B y = -1/2x + 7/2
Step-by-step explanation:
We know that it has a negative slope since the points go from the top left to the bottom right
We can eliminate A and D
The y intercept is where it crosses the y axis
It should cross somewhere between 2 and 4
C has a y intercept of 9 which is too big
Lets verify with a point
x = -4
y = -4(-4)+9 = 16+9 = 25 (-4,25) not even close to being near the points on the graph
checking B
y = -1/2 (-4) +7/2
= 2 + 7/2 = 11/2 = 5.5 it seems reasonable
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:
The answer will be C. Theme basically means the message of a story.
