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:
27477
Step-by-step explanation:
Subtract 38700 from 29% = 27477.
Answer:
3rd
Step-by-step explanation:
Answer: The correct option is, The coefficient of the first term.
Step-by-step explanation:
The given function is,
End behavior of the polynomial function : It is defined as the graph of f(x) as x approaches 
and 
.
The end behavior of the graph depends on the leading coefficient and degree of the polynomial.
As, the degree of the polynomial is '3'. So, the leading coefficient will determine the structure of the graph.
Therefore, the coefficient of the first term will indicate that the left end starts at the top of the graph.
The graph is also shown below.
Answer:
$600 in commission for the week paying 15% on up to $1000 daily
Step-by-step explanation:
To find the sales commission, multiply the percentage 15% as 0.15 against each sales up to $1000.
Monday - 0.15 (800) = $120
Tuesday - 0.15 (600) = $90
Wednesday - 0.15 (1000) = $150
Thursday - 0.15 (800) = $120
Friday - 0.15 (800) = $120
In total that's, $600 in commission.
