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 ratio is multiplying 1.6 so just pick all the proportional relationships where you have to multiply by 1.6.
Step-by-step explanation:
Proportional relationships man you have to multiply, but since I didn't know what you multiplied 5 to get to 8 I divided.
8÷5=1.6
And if you want to check your answer then multiply.
5×1.6=8
<u><em>Could I please have BRAINLIEST?</em></u>
First, add the profit wanted with the costs.
1500 + 200 + 100 = 1800
The total amount wanted is 1800. Each student pays $5, and so you divide by 5
1800/5 = 360
360 students must show up.
The equation used is:
Let student = s
Total cost = 200 + 100
Charge = 5n
Profit = 1500
1500 = 5n - 300 (is equation)
Hope this helps
We are given with
x1 = 20 min
s1 = 2 min
x2 = 30 min
s2 = 4 min
p = 0.9
Condition (x > 25)
We need to get the t-value between the two means and comparing it wit the t-value for the time of 25 minutes given that there is a 90% probability that the weather will be good. Simply use the t-test formula and use the t-test table to get the probability.
Answer:
Step-by-step explanation:
Actually, the complete question includes the expression of each hypothenuse, because the problem is about congruence between right triangle.
So, the hypothenuse for 
is: 
.
The hypothenuse for 
is: 
.
So, the postulate HL (Hypothenuse-Leg) states that both right triangles are equal if their hypothenuses and legs are equal. So, we have to make equal both hypothenuse expression and solve for 
:
Therefore, when these triangles are congruent.
