The value of the x is 120
Answer:
y ≤ 2x + 4 and x + y ≥ -6
Step-by-step explanation:
Graphing a system of inequalities is similar to graphing linear functions. It is best to have equations in the form of y = mx + b where m = slope and b = y-intercept. Looking at the graph, you can see that there is one line going uphill (positive slope) and one going downhill (negative slope). There are two y-intercepts, one from each line at (0,4) and (0, -6) So, only the top two equations have a y-intercept equal to 4 and -6. Then, you can find the slope of each line by choosing two points on the same line and using rise/run to find the change in 'y' over the change in 'x'.
Line #1 (uphill): (-2, 0) and (0, 4) = 4-0/0- -2 = 4/2 = 2
The only answer with a positve 2 slope and y-intercepts of 4 and -6 is the second one, so that is your answer.
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
30
dividing the length and width by 2
10 ÷ 2 = 5 and 12 ÷ 2 = 6
he can plant 5 × 6 = 30 pumpkin plants
303.56 x 31%=94.10
303.56-94.10= 209.46
209.46-94.10 =115.36
Connor makes 115.36 more than Maria
