Answer:
17. x = y^2 - 2ay +a^2
18. x = y^2 - a
Step-by-step explanation:
17. Since we want to make x the subject of the formula, we first isolate the square root of x and get
= y - a.
squaring both sides,
x = y^2 - 2ay +a^2
18. Since both x and the a are under the square root, we first start by squaring both sides.
So y^2 = x+a.
Isolating the x, we get
x = y^2 - a
$45>(or equal to)$12.99n you can spend less then or equal to forty five dollars without going into debt.
Answer: $56.80
Step-by-step explanation:
71 x .20 = 14.20
71 - 14.20 = 56.80
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
