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>
Solution
To find Which two numbers on the number line has an
absolute value of 3
Absolute value means " how far a number is from
zero " .
"3" is 3 away from zero .
and " -3 " is also 3 away from zero .
i.e
| 0 - 3 | = 3
| 3 - 0 | = 3
So , the absolute value of "3 " is 3
similarly , absolute value of "3 " is 3 .
Hence , the two numbers are -3 and 3
The next one is 16 probably
Let P be the number of kids,
we know P>57
take 1-(1/2)-(1/5)=3/10
therefore 57 is 3/10P
3/7P=57
P=57*7/3=133 is the answer
it would be incorrect if we didnt get a positive integer.
