Answer:
Flux = 16π
Step-by-step explanation:
The outward flux of F across the solid cylinder and z = 0 is
∫∫F*ds = ∫∫∫ DivF*dv
F = 2xy²i + 2x²yj + 2xyk
DivF = D/dx (2xy²) + D/dy (2x²y )
DivF = 2y² + 2x²
In cylindrical coordinates dV = rdrdθdz and as z = 0 the region is a surface ds = rdrdθ
Parametryzing the surface equation
x = rcosθ y = r sinθ and z = z
Div F = 2r²sin²θ + 2r²cos²θ
∫∫∫ DivF*dv = ∫∫ [2r²sin²θ + 2r²cos²θ]* rdrdθ
∫∫ 2r² [sin²θ + cos²θ]* rdrdθdz ⇒ ∫∫ 2r³ drdθ
Integration limits
0 < r < 2 0 < θ < 2π
2∫₀² r³ ∫dθ
(2/4)(2)⁴ 2π
Flux = 16π
The opposite of -358 is on the opposite side
the opposite of 429 is on the opposite side
Okay. I used to struggle with this one too sweetie. First off, you are using multiplication, when two numbers are close together it means they need to be multiplied. You are also using addition which means you can add the exponents together. In this case, it would equal x to the power of nine. Then add 12 and 35 which equals 47. So the equation is 47 multiplied by x to the power of nine.
Answer:
13:00 or 1:00
Step-by-step explanation:
Good Night
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