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:
Triangle inequality rule states that the sum of eachpair of sides must be greater than the third sides.
240 + 123 > 207 true
240 + 207 > 123 true
123 + 207 > 240 true
A = √(s(s-a)(s-b)(s-c))
s is the semi-perimeter (a + b + c)/2
s = (240 + 123 + 207)/2
s = 285
A = √(285*(285-249)(285-123)(285-207))
A = 12,730 units^2
Step-by-step explanation:
Answer:
I think your answer is b and c if not right sorry
Step-by-step explanation:
Hopefully this helps
Answer:
See explanation
Step-by-step explanation:
Since about ten percent of users do not close Windows properly, we have
- the probability that a user does not close Windows properly is
- the probability that a user closes the Windows properly is
A. On the average,
- one of 10 users does not close the Windows properly;
- 10 of 100 users do not close Windows properly.
B. The probability that exactly 8 of the next 10 users will close Windows properly is
