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:
Blue cars, B = 63 cars
Step-by-step explanation:
Let the blue cars be B.
Let the red cars be R.
Given the following data;
Ratio of B:R = 9:7 = 9 + 7 = 16
Red cars, R = 49
To find the number of blue cars;
First of all, we would determine the total number of cars using the expression;
R = 7/16 * x = 49
7x = 49 * 16
7x = 784
x = 112 cars
Now, we can find the number of blue cars;
B = 9/16 * 112
B = 1008/16
Blue cars, B = 63 cars
Answer:
Temperature is the measure of hotness or coldness expressed in terms of any of several scales. An example would be "The cup of beans are boiling hot and has a temperature of 100 °C, whereas the water in the tub is just comfortably warm, with a temperature of about 38 °C. Although the water in the tub has a much lower temperature, it has greater thermal energy".
Step-by-step explanation: