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:
The interval is for those that want to get out earlier is between 43 student to 47 students
The interval is for those that want to get out later is between 48 student to 50 students
Step-by-step explanation:
Given that:
sample size n=128
Probability of those that want to get out earlier = 0.35.
The mean = n × probability = 0.35 × 128 = 44.8 ≈ 45
Margin of error = 4% = 0.04 × 44.8 = 1.79 ≈ 2
Therefore the interval = mean ± Margin of error = 45 ± 2 = (43, 47)
The interval is for those that want to get out earlier is between 43 student to 47 students
Probability of those that want to get out later = 0.39.
The mean = n × probability = 0.39 × 128 = 49.92 ≈ 50
Margin of error = 4% = 0.04 × 50 = 2
Therefore the interval = mean ± Margin of error = 50 ± 2 = (48, 52)
The interval is for those that want to get out later is between 48 student to 50 students
the group that wants to get out of school earlier to win after all the votes are counted if those that have no opinion decide that they want to go earlier
Answer:
C Side ZX
Because ZX is a reflection of CD
Answer:
20.7 miles
Step-by-step explanation:
1 + 2 = 3
1.6 + 2.3 = 3.9
3.9 + 3 = 6.9
6.9 x 3 = 20.7
Answer:
B
Step-by-step explanation:
The answer would be B, because the y-intercept is positive. To double check I used an online graphing calculator and it is correct.
Hope This Helps! Have A Nice Day!!
