I think the correct answer from the choices listed above is option C. <span>The graph of a system of equations with the same slope and the same y-intercepts will never have no solutions. Rather, it has an infinite number of solutions since all points of the lines intersects.</span>
The paraboloid meets the x-y plane when x²+y²=9. A circle of radius 3, centre origin.
<span>Use cylindrical coordinates (r,θ,z) so paraboloid becomes z = 9−r² and f = 5r²z. </span>
<span>If F is the mean of f over the region R then F ∫ (R)dV = ∫ (R)fdV </span>
<span>∫ (R)dV = ∫∫∫ [θ=0,2π, r=0,3, z=0,9−r²] rdrdθdz </span>
<span>= ∫∫ [θ=0,2π, r=0,3] r(9−r²)drdθ = ∫ [θ=0,2π] { (9/2)3² − (1/4)3⁴} dθ = 81π/2 </span>
<span>∫ (R)fdV = ∫∫∫ [θ=0,2π, r=0,3, z=0,9−r²] 5r²z.rdrdθdz </span>
<span>= 5∫∫ [θ=0,2π, r=0,3] ½r³{ (9−r²)² − 0 } drdθ </span>
<span>= (5/2)∫∫ [θ=0,2π, r=0,3] { 81r³ − 18r⁵ + r⁷} drdθ </span>
<span>= (5/2)∫ [θ=0,2π] { (81/4)3⁴− (3)3⁶+ (1/8)3⁸} dθ = 10935π/8 </span>
<span>∴ F = 10935π/8 ÷ 81π/2 = 135/4</span>
Answer:
15.2
Step-by-step explanation:
PiRsquared
Pi x 2.2²
Answer:
A y = 3x
Step-by-step explanation:
We can check each line to see if the point is on it
A y = 3x 6 = 2*3 6=6 this is true so the point is one the line
B y = 4-x 6 = 2-4 6 = -2 false
C y = -3x 6 = -3(2) 6=-6 false
D y =-x+4 6 = -2+4 6 = 2 false
