Find the circulation done by the velocity field V(x,y)= -y/[(x+1)^2 +4y^2]i + (x+1)/[(x+1)^2 +4y^2]j around the positively oriented square with vertices (2, 0), (0, 2), (−2, 0), and (0, −2).

The circulation of V around the given path (call it C) is simply the line integral of V along C. Since C is a closed curve, we can use Green's theorem.

where int(C) is the interior or region bounded by C.

We have

so the double integral and hence the circulation is zero.

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

The answer is in the image 

The total nom of  code that can be used is equal to 5+3 = 8

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

30% of 420 are first year students

first year students = (30/100 )*420

=126 students

Student who are not in first year = 420-126

=294 students  

The solution is given below

Cost of 6 gallons =$15

Cost of 1 gallon =15/6

                           =$2.5

Cost of 7 gallons=$2.5 * 7

                           =$17.5