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>
The linear equation in standard form is
.
<h3>Linear Function</h3>
An equation can be represented by a linear function. The standard form for the linear equation is: ax+b , for example, y=7x+2. Where:
a= the slope. It can be calculated for
.
b= the constant term that represents the y-intercept.
The question gives: X-intercept:3 and y-intercept: 5. Then,
- The x-intercept is the point that y=0, then the x-intercept point is (3,0).
- The y-intercept is the point that x=0, then the x-intercept point is (0,5).
With this information, you can find the slope (a).

The question gives the coefficient b since it gives the y-intercept=5.
Therefore the linear equation is :
.
Read more about the linear equations here:
brainly.com/question/2030026
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The answer is 1/2 the last one
Answer: 
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals, so as the slope of the given line is -5/4, the slope of the perpendicular line is 4/5.
Substituting into point-slope form,
