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:A) At this same rate (speed) how far can she ride in two hours?
B) how long would it take for her to ride 4 miles?
C) what is her unit rate in miles per hour?
Step-by-step explanation:pls mark me as brainest pls
Answer:(
7
,
6
)
Explanation:
We can find the coordinates of the midpoint of a line segment, by finding the mean of the sum of the
x
coordinates and the mean of the sum of the
y
coordinates.
x
=
8
+
6
2
=
7
y
=
2
+
10
2
=
6
Coordinate of midpoint:
(
7
,
6
)
Answer:
The answer is the first option because 2÷2=1 and 10÷2=5
Answer:
180°
cuz when a line (I forgot the name) and radius meet at the circumference they from an angle of 90°
