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:
q + 7
Step-by-step explanation:
(q² + 4q − 21) / (q − 3)
Factor the numerator:
(q + 7) (q − 3) / (q − 3)
Divide:
q + 7
Answer: Equation: E= 20H
Earning's after 15 hours: E= 20(15)
E = 300
Step-by-step explanation:
The equation would be E =20H. E means her total earnings. 20 is how much money she earns per hour. H is how many hours she tutors. If you put it all together, you get E = 20H.
To solve how much she would get for 15 hours, plug in 15 for H so E=20(15). 20 x 15 = 300. Therefore, she will get $300 after teaching for 15 hours.
Altho' I can easily guess what you're supposed to do here, I must point out that you haven't included the instructions for this problem.
I'll help you by example. Let's look at the first problem:
"Evaluate 6(z-1) at z-4."
Due to "order of operations" rules, we must do the work inside the parentheses FIRST. Replace the z inside (z-1) with "-4". We obtain
6(-4-1) = 6(-5) = -30 (answer.)
Your turn. Try the next one. If it's unclear, as questions.
Answer:
A=(1/2)BxH
10x6=60m
