F(x) = x² -3x +(3/2)² -10 -(3/2)²
= (x -3/2)² -10 -9/4
f(x) = (x -1.5)² -12.25
The value of the integral 3ydx+2xdy using Green's theorem be - xy
The value of
be -xy
<h3>What is Green's theorem?</h3>
Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D bounded by C.
If M and N are functions of (x, y) defined on an open region containing D and having continuous partial derivatives there, then
= ![\int\int\〖(N_{x}-M_{y}) \;dxdy](https://tex.z-dn.net/?f=%5Cint%5Cint%5C%E3%80%96%28N_%7Bx%7D-M_%7By%7D%29%20%5C%3Bdxdy)
Using green's theorem, we have
=
............................... (1)
Here
= differentiation of function N w.r.t. x
= differentiation of function M w.r.t. y
Given function is: 3ydx + 2xdy
On comparing with equation (1), we get
M = 3y, N = 2x
Now,
= ![\Luge\frac{dN}{dx}](https://tex.z-dn.net/?f=%5CLuge%5Cfrac%7BdN%7D%7Bdx%7D)
= ![\frac{d}{dx} (2x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%282x%29)
= 2
and,
= ![\Huge\frac{dM}{dy}](https://tex.z-dn.net/?f=%5CHuge%5Cfrac%7BdM%7D%7Bdy%7D)
= ![\frac{d}{dy} (3y)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdy%7D%20%283y%29)
= 3
Now using Green's theorem
= ![\int\int\〖(2 -3) dx dy](https://tex.z-dn.net/?f=%5Cint%5Cint%5C%E3%80%96%282%20-3%29%20dx%20dy)
= ![\int\int\ -dxdy](https://tex.z-dn.net/?f=%5Cint%5Cint%5C%20-dxdy)
= ![-\int\ x dy](https://tex.z-dn.net/?f=-%5Cint%5C%20x%20dy)
=![-xy](https://tex.z-dn.net/?f=-xy)
The value of
be -xy.
Learn more about Green's theorem here:
brainly.com/question/14125421
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Answer:
8
Step-by-step explanation:
i'm very smart and x=0 is the y intecept so
Answer:
Yeah that's easy -3
Step-by-step explanation:
+3=3 which the opposite of a positive is a negative. So -3. Hope this help.
We are given the statement:
She gets a base pay of $80 a day plus 5 percent of the
value of any merchandise she sells that exceeds a total of $400
Then we are given the equation:
Earnings = 400 + 0.05 (t – 80)
Now if we read the statement carefully, we can understand
that the base pay is $80 and NOT $400. Therefore it should be the constant
value in the equation. Now the statement also tells that what will be added to
her pay is anything beyond 400, therefore it should be the one inside the
parenthesis. That is:
<span>Earnings = 80 + 0.05 (t – 400) ---> correct equation</span>
Now we use the corrected equation to solve for the earnings
when t = 475
Earnings = 80 + 0.05 (475 – 400)
<span>Earnings = 83.75 dollars</span>