Answer:
The volume of the pyramid is not equal to the volume of the cylinder.
Step-by-step explanation:
A right cylinder has the circular cross-sectional area and if the cross-sectional areas of a right pyramid and a right cylinder are the same then the pyramid must be a right circular cone.
Now, the volume of a right cylinder is πr²h and that of a right circular cone is 1/3 πr²h.
Therefore, the radius of the base of the cone and that of the cylinder is the same and their heights are equal to be 5 units, then the volume of the pyramid is not equal to the volume of the cylinder. (Answer)
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>
Greater than 90° but less than 180°.
Answer:the median is 20 and the lower quartile is 16.5
Step-by-step explanation:
Answer:
c. Cos 52 = 17/c
Step-by-step explanation:
sin(x) = cos(90-x)