Answer:
32
Step-by-step explanation:
I am assuming you meant y=sin(x) from 0 to 2pi? Remember that the maximum and minimum points on the sine graph will occur 1/4 and 3/4 through the cycle, or period and the zeros occur at the beginning, middle and end. So you want to find the distance 1/4 of the way to 2pi and 3/4 of the way to 2pi.
With this information, you can easily calculate your answer:)
Answer:
The way a proportion is set is as follows;
The Distance from Rio de Janeiro and San Jose Costa Rica is then found as 800 miles
Step-by-step explanation:
The dimension of the distance between Rio de Janeiro and San Jose Costa Rica = 4 inches
The map scale = 1 inch to 200 miles
To figure out how many miles it is or the actual distance from Rio de Janeiro and San Jose Costa Rica, we have;
Therefore, we have;
(4 inches × 200 miles)/(1 inche) = Distance from Rio de Janeiro and San Jose Costa Rica
Which gives;
Distance from Rio de Janeiro and San Jose Costa Rica = 800 miles.
Surface Area of the square = 8 x 8 = 64 cm²
Surface Area of the 4 triangle = 4 x [ 1/2 x 8 x 14]
Surface Area of the 4 triangle = 4 x [ 56]
Surface Area of the 4 triangle = 224 cm²
Total Surface Area = 64 + 224 = 288 cm²
Answer: 288 cm²
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
