Solution :
Along the edge 
The parametric equation for is given :
Along edge 
The curve here is a quarter circle with the radius 9. Therefore, the parametric equation with the domain 
is then given by :
Along edge 
The parametric equation for is :
Now,
x = 9t, ⇒ dx = 9 dt
y = 0, ⇒ dy = 0
And
Then :
![$=\int_0^1 \left[\left( 9 \sin \frac{\pi}{2}t\right)^2\left(9 \cos \frac{\pi}{2}t\right)\left(-\frac{7 \pi}{2} \sin \frac{\pi}{2}t dt\right) + \left( 9 \cos \frac{\pi}{2}t\right)^2\left(9 \sin \frac{\pi}{2}t\right)\left(\frac{7 \pi}{2} \cos \frac{\pi}{2}t dt\right) \right]$](https://tex.z-dn.net/?f=%24%3D%5Cint_0%5E1%20%5Cleft%5B%5Cleft%28%209%20%5Csin%20%5Cfrac%7B%5Cpi%7D%7B2%7Dt%5Cright%29%5E2%5Cleft%289%20%5Ccos%20%5Cfrac%7B%5Cpi%7D%7B2%7Dt%5Cright%29%5Cleft%28-%5Cfrac%7B7%20%5Cpi%7D%7B2%7D%20%5Csin%20%5Cfrac%7B%5Cpi%7D%7B2%7Dt%20dt%5Cright%29%20%2B%20%5Cleft%28%209%20%5Ccos%20%5Cfrac%7B%5Cpi%7D%7B2%7Dt%5Cright%29%5E2%5Cleft%289%20%5Csin%20%5Cfrac%7B%5Cpi%7D%7B2%7Dt%5Cright%29%5Cleft%28%5Cfrac%7B7%20%5Cpi%7D%7B2%7D%20%5Ccos%20%5Cfrac%7B%5Cpi%7D%7B2%7Dt%20dt%5Cright%29%20%5Cright%5D%24)
![$=\left[-9^4\ \frac{\cos^4\left(\frac{\pi}{2}t\right)}{\frac{\pi}{2}} -9^4\ \frac{\sin^4\left(\frac{\pi}{2}t\right)}{\frac{\pi}{2}} \right]_0^1$](https://tex.z-dn.net/?f=%24%3D%5Cleft%5B-9%5E4%5C%20%5Cfrac%7B%5Ccos%5E4%5Cleft%28%5Cfrac%7B%5Cpi%7D%7B2%7Dt%5Cright%29%7D%7B%5Cfrac%7B%5Cpi%7D%7B2%7D%7D%20-9%5E4%5C%20%5Cfrac%7B%5Csin%5E4%5Cleft%28%5Cfrac%7B%5Cpi%7D%7B2%7Dt%5Cright%29%7D%7B%5Cfrac%7B%5Cpi%7D%7B2%7D%7D%20%5Cright%5D_0%5E1%24)
= 0
And
x = 0, ⇒ dx = 0
y = 9 t, ⇒ dy = 9 dt
Therefore,
= 0 + 0 + 0
Applying the Green's theorem
Here,
Therefore,
The vector field F is = 
is conservative.
Answer:
C is correct
Step-by-step explanation:
hope this helps u
Answer:
258
Step-by-step explanation:
Check the tenth place. It is 4 which is < 5. So, ignore and write the whole number as it is
So, 258.42 = 258
K = Kate's age nowJ = Joey's age nowK+5 = Kate's age in 5 yearsJ+5 = Joey's age in 5 years From the first sentenceK+5 = 2(J+5) From the second sentenceK=J+11 So our system of equations isK+5 = 2(J+5)K=J+11 The first equation is equivalent toK+5 = 2J+10or by rearranging termsK-2J=5 The second equation is equivalent toK-J=11 This gives us K-2J=5K-J=11 Using the elimination method, we need to multiply one of the equations by a factor such that we can eliminate one of the variables. This means we want one of the variables to have coefficients which are the same magnitude but opposite signs. We can do this by multiplying the 1st equation by -1. This give us -K+2J=-5 K - J = 11 Now add these two equations together, term by term. This gives usJ=6 So Joey is 6 years old now.
Answer:
6382 :VVV
Step-by-step explanation:
