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:
2 and 6, 4 and 8, 1 and 5, 3 and 7
Step-by-step explanation:
The angle rule of corresponding angles states that the corresponding angles are equal if a transversal cuts two parallel lines.
In this example, lines m and l are two parallel lines
line n cuts through both, making every other angle corresponding and congruent, etc...
Answer:
B. 5 units
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, dilation, rotation or translation.
If a point X(x,y) is rotated about the origin 180 degrees clockwise the new point is at X'(-x, -y).
If the square with vertices at A(0, 0), B(0, 5), C(5, 5) and D(5, 0) is rotated about the origin 180 degrees clockwise the new points are at A'(0, 0), B'(0, -5), C'(-5, -5), D'(-5, 0)
A square has four equal sides. The distance between two points 
is:
Hence:
Answer:
We want to divide 30 by it's half.
The half of 30 is 30/2 = 15
then we have: 30/15 = 2
Now we want to add the half of 18, that has ben divided by the half of the half of 12 hafter been divided by half.
The half of 12 is 12/2 = 6
the half of the half of 12 is 6/2 = 3
now, we wanto to divide the half of 18 by that number.
The half of 18 is 18/2 = 9
then we have 9/3 = 3
and we wanted to add this to the number previous found:
2 + 3 = 5
Answer:
(4, -2)
Step-by-step explanation:
if you do process of elimination you find that 'a' doesn't work out but 'b' will . . . substitute -2 for 'y' and 4 for 'x' and see if the equation is true
-2 = -3/4(4) + 1
-2 = -3 + 1
-2 = -2
