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:
The inequality equation is 12 ≤ 2x + 3y
Step-by-step explanation:
Protein in a cheese square = 2 grams
Protein in a turkey square = 3 grams
And She can eat 12 or more grams of proteins
Let x be the number of cheese squares and y be the number of turkey squares that she eats.
So, we can write an inequality equation, that describes the given situation in the problem.
i.e. 2x + 3y ≥ 12 or 12 ≤ 2x + 3y
So the inequality equation is 12 ≤ 2x + 3y
3a =18
3a/3 = 18/3
a = 18/3
a = 6
Hope this helps
It's hard to type and hard to read the "inverse tangent" function, as you've seen (above).
So, use "arctan x" instead.
Then the problem becomes: "differentiate cos (arctan x)."
You must apply first the rule for differentiating the cosine function, and next apply the rule for differentiating the arctan function:
(d/dx) cos (arctan x) = - sin (arctan x) * [1/(1+x^2)]
