<span>V(o) = 1/3 πr²h - old volume
</span>V(n) = 1/3 π(2r)²(h/2)=1/3 π(2r)²(h/2)=1/3*4/2* πr²h=1/3*2* πr²h
V(n)/V(o)=1/3*2* πr²h/1/3 πr²h=2/1
V(n)/V(o)=2/1 - ratio
the volume will be doubled
Answer:132 combinations
Step-by-step explanation:
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>
B is correct as -4 is smaller than 7
d is correct as -30 is smaller than -18
e is correct as -3 is bigger than -8
No, John is incorrect.
<h3>
Correct work shown:</h3>
The correct answer should be x = 7 or x = -1
