Answer:
x =53.1
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp side/ adjacent side
tan x = 28 /21
Take the inverse tan of each side
tan ^-1 (tan x) = tan ^-1 (28/21)
x = 53.13010235
Rounding to the nearest tenth
x =53.1
The area of the kite can be found as follows;
Area=[area of XWY]+[areaYWZ]
area XWY=1/2*b*h
=1/2*4*3=6 sq units
area YWZ=1/2*b*h
=1/2*4*4=8 sq units
Hence the area of the kite will be:
Area=6+8=14 sq. units
Hi,
That would be a circle because it has 360 degrees.
Using the intersecting chord theorem:
15 x 2 = 5 x n
Simplify:
30 = 5n
Divide both sides by 5:
n = 30/5
n = 6 m
8 x n+8 = 16 x n+2
Simplify:
8n +64 = 16n +32
Subtract 8n from both sides:
64 = 8n +32
Subtract 32 from both sides:
32 = 8n
Divide both sides by 8:
n = 32 /8
n = 4
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
