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:
Your answer is C and D
Step-by-step explanation:
Option C: -3 is the average rate of change between 
and 
Explanation:
The formula to determine the average rate of change is given by
Average rate of change = 
We need to find the average rate of change between and
Thus, from the table, we have,
, 
, 
Thus, substituting these values in the formula, we get,
Average rate of change = 
Thus, the average rate of change between and is -3.
Hence, Option C is the correct answer.
Answer: The answer is “10cm”
Step-by-step explanation: To get to this answer we first need to know the formula for find the hypotenuse which is a^2 + b^2 = c^2. A and B are the two sides in this case a and b are 8 cm and 6 cm. Then you plug in the values into the equation, it looks like this 8^2 + 6^ = c^2 once you solve you get 64 + 36 = c. When you add 64 and 36 you get 100 but their is one more step. You must find the square root of 100 which is 10. So your answer for the hypotenuse is “10cm”
Have a nice day!
