Answer:
4i.
Step-by-step explanation:
To find the flux through the square, we use the divergence theorem for the flux. So Flux of F(x,y) = ∫∫divF(x,y).dA
F(x,y) = hxy,x - yi
div(F(x,y)) = dF(x,y)/dx + dF(x,y)dy = dhxy/dx + d(x - yi)/dy = hy - i
So, ∫∫divF(x,y).dA = ∫∫(hy - i).dA
= ∫∫(hy - i).dxdy
= ∫∫hydxdy - ∫∫idxdy
Since we are integrating along the boundary of the square given by −1 ≤ x ≤ 1, −1 ≤ y ≤ 1, then
∫∫divF(x,y).dA = ∫₋₁¹∫₋₁¹hydxdy - ∫₋₁¹∫₋₁¹idxdy
= h∫₋₁¹{y²/2}¹₋₁dx - i∫₋₁¹[y]₋₁¹dx
= h∫₋₁¹{1²/2 - (-1)/2²}dx - i∫₋₁¹[1 - (-1)]dx
= h∫₋₁¹{1/2 - 1)/2}dx - i∫₋₁¹[1 + 1)]dx
= 0 - i∫₋₁¹2dx
= - 2i[x]₋₁¹
= 2i[1 - (-1)]
= 2i[1 + 1]
= 2i(2)
= 4i
Answer:
Step-by-step explanation:
To complete the square: add 4 to both sides because the product of 4 as 2 as the factor which 2 * 2 so 
Now we can factor the expression
Move the 4 to the other side to isolate y which changes the sign
Answer and Step-by-step explanation:
For 2 dice, we have 36 possibles outcomes:
D₁ = {1,2,3,4,5,6}
D₂ = {1,2,3,4,5,6}
U = ({1,1};{1,2};{1,3};...;{2,1};{2,2};...;{6,6})
This way, it's 6 for D₁ and 6 for D₂, 6.6 = 36
The possible 3 that might appear when rolling a pair of dice would be
{1,2} and {2,1}, so, 2.
The probability of rolling 3 is 2/36 = 1/18
Your simplified answer is indeed 2/3 (or 60%, or 0.6) because the fraction 24/36 can be simplified by dividing both the numerator and denominator by 6, which leaves you with 2/3.
