Let F(x,y)= << 5 cos(y), 8 sin(y)>>.Compute the flux oint F * nds of F across the boundary of the rectangle 0<=x<=5,0<=y<=pi/2 using the vector form of Green's Theorem. (Use symbolic notation and fractions where needed.) oint F * nds = ?

Let ${\displaystyle F(x,y)=⟨4\cos \left(y\right),2\sin \left(y\right)⟩}$. Compute the flux ${\displaystyle \oint F\cdot nds}$ of F across the boundary of the rectangle ${\displaystyle 0\le x\le 5,0\le y\le \frac{\pi }{2}}$ using the vector form of Greens

Set up the integral for the divergence theorem both ways. Then find the flux.
${\displaystyle F(x,y,z)=3x\hat{i}+xy\hat{j}+2xz\hat{k}}$
E is the cube bounded by the planes $x=0,x=3,y=0,y=3,andz=0,z=3$.

Suppose that the plane region D, its boundary curve C, and the functions P and Q satisfy the hypothesis of Greens

Use the Divergence Theorem to calculate the surface integral F · dS, that is, calculate the flux of F across S.
${\displaystyle F(x,y,z)=3x{y}^{2}i+x{e}^{z}j+z^{3}k}$,
S is the surface of the solid bounded by the cylinder ${\displaystyle y^2+z^2=9}$ and the planes x = −3 and x = 1.

Use Green's Theorem to evaluate ${\displaystyle {\int }_C\overrightarrow{F}\cdot d\overrightarrow{r}}$ where ${\displaystyle \overrightarrow{F}(x,y)=x{y}^{2}i+(1-x{y}^3)j}$ and C is the parallelogram with vertices (-1,2), (-1,-1),(1,1)and(1,4).
The orientation of C is counterclockwise.

Use Greens

A camera shop stocks eight different types of batteries, one of which is type A7b.Assume there are at least 30 batteries.
of each type.a. How many ways can a total inventory of 30 batteries be distributed among the eight different types? b.
How many way can a total inventory of 30 batteries be distributed among the eight different types of the inventory must
include at least four A76 batteries?c. How many ways can a total inventory of 30 batteries be distributed among the eight
different types of the inventory includes at most three A7b batteries