Answer:
a.



b.

Step-by-step explanation:
Given that:
C: counterclockwise around the triangle with vertices (0, 0), (1, 0), and (0, 1), starting at (0, 0)
a. Find a piecewise smooth parametrization of the path C.
r(t) = { 0
If C: counterclockwise around the triangle with vertices (0, 0), (1, 0), and (0, 1),
Then:

Also:






b Evaluate
:
Integral of (x+2y^1/2)ds














![\mathtt{\int \limits _{c3} (x+ 2 \sqrt{y}) ds = -\dfrac{4}{3} [(0)-(1)]}](https://tex.z-dn.net/?f=%5Cmathtt%7B%5Cint%20%20%5Climits%20_%7Bc3%7D%20%28x%2B%202%20%5Csqrt%7By%7D%29%20ds%20%3D%20-%5Cdfrac%7B4%7D%7B3%7D%20%5B%280%29-%281%29%5D%7D)
![\mathtt{\int \limits _{c3} (x+ 2 \sqrt{y}) ds = -\dfrac{4}{3} [-(1)]}](https://tex.z-dn.net/?f=%5Cmathtt%7B%5Cint%20%20%5Climits%20_%7Bc3%7D%20%28x%2B%202%20%5Csqrt%7By%7D%29%20ds%20%3D%20-%5Cdfrac%7B4%7D%7B3%7D%20%5B-%281%29%5D%7D)




can’t see the whole question
Answer: $122.50
<u>Step-by-step explanation:</u>
In Out
8:00 12:00 = 4 hours
12:45 17:30 =<u> 4.75 hours </u>
Total 8.75 hours
8.75 hours x $14/hr = $122.50
Note: to subtract 12:45 from 17:30, borrow 1 hour from 17 and add 60 minutes to 30:
17:30 → 16:90
- 12:45 -<u> 12:45 </u>
4: 45
4 hours 45 minutes =
= 4.75 hours
Answer:
9
Step-by-step explanation:
the line hits the y-axis at the point (0, 9) where x=0 meaning this point is the y-intercept being 9