Answer: 957.8
Step-by-step explanation:
When will he have less than 40 wheels left? Well you can make the equation...
85-4x=40
And then solve for x.
85-4x=40
-4x=-45
x=11 1/4 rounded up to 12
answer: He will have less than 40 wheels left after he has built 12 cars.
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:
x > 36 in
Step-by-step explanation:
Let x = the width of the picture frame.
Then x + 6 = the length of the frame.
The formula for the perimeter P of a rectangle is'
P = 2l + 2w.
So, the condition is
2l + 2w > 156
2(x + 6) + 2x > 156 Distribute the 2
2x + 12 + 2x > 156 Combine like terms
4x + 12 > 156 Subtract 12 from each side
4x > 144 Divide each side by 4
x > 36
The perimeter of the picture frame will be greater than 156 in if x > 36 in.
