Please help..... thanks
2 answers:
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Answer:
0
Step-by-step explanation:
We want to compute the curve integral (or line integral)
where the force field F is defined by
F(x,y) = (y, -x)
and C is the path consisting of the line segment from (1, 5) to (0, 0) followed by the line segment from (0, 0) to (0, 9).
We can write
C =
where
= line segment from (1, 5) to (0, 0)
= line segment from (0, 0) to (0, 9)
so,
Given 2 points P, Q in the plane, we can parameterize the line segment joining P and Q with
<em>r(t) = tQ + (1-t)P for 0 ≤ t ≤ 1 </em>
Hence can be parameterized as
for 0 ≤ t ≤ 1
and can be parameterized as
for 0 ≤ t ≤ 1
The derivatives are
and
In consequence,
Answer: 0.8 radians
Step-by-step explanation:
To solve this exercise you must apply the formula shown below:
Where S is the arc lenght, r is the radius of the circle and is the central angle in radians.
Solve for the central angle:
Now, when you susbtitute the value of the arc length and the radius, you obtain that the central angle is: