
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:
h = 15
Step-by-step explanation:
Use Pythagorean Theorem to solve for h.
a² + b² = c²
8² + h² = 17²
64 + h² = 289
h² = 225
h = 15
Answer:
It is 25 units
Step-by-step explanation:
The triangles are equal
Step-by-step explanation:
this is how you solve it :)
Answer:
here!
Step-by-step explanation:
How to write a function rule using the concept of slope. Let us do this for example #3. The goal is use the equation y = mx + b. y = 4x + b. Use (1,6) to find b. 6 = 4 + b.