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Luden [163]
3 years ago
5

Compute the flux H F of F(x,y) = hxy, x − yi across the boundary of the square given by −1 ≤ x ≤ 1, −1 ≤ y ≤ 1.

Mathematics
1 answer:
Softa [21]3 years ago
7 0

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  

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Answer:

a = 0

Step-by-step explanation:

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The sum of two numbers is twice their difference. the larger number is 2 more than twice the smaller. find the numbers. smaller
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If you add​ natalie's age and​ fred's age, the result is 43. if you add​ fred's age to 44 times​ natalie's age, the result is 88
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Let Natalie be x, and Fred, y.
So based on 1st condition, we get
x + y =43         - Equation 1   
â´ x = 43-y - Equation 2
Now based on 2nd condition, we get
44x+y=88
Using x from Equation 2, we get
44(43-y) + y = 88
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â´ 1892 -44y + y = 88
â´ -44y + y = 88 - 1892
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â´ y = 1804/43
â´ y = 41.95

Using the value of y in Equation 2
x = 43 - 41.95
â´ x = 1.05

So Natalie is 1.05 yrs and Fred is 41.95 yrs old.
8 0
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