<span>12.3
Volume function: v(x) = ((18-x)(x-1)^2)/(4pi)
Since the perimeter of the piece of sheet metal is 36, the height of the tube created will be 36/2 - x = 18-x.
The volume of the tube will be the area of the cross section multiplied by the height. The area of the cross section will be pi r^2 and r will be (x-1)/(2pi). So the volume of the tube is
v(x) = (18-x)pi((x-1)/(2pi))^2
v(x) = (18-x)pi((x-1)^2/(4pi^2))
v(x) = ((18-x)(x-1)^2)/(4pi)
The maximum volume will happen when the value of the first derivative is zero. So calculate the first derivative:
v'(x) = (x-1)(3x - 37) / (4pi)
Convert to quadratic equation.
(3x^2 - 40x + 37)/(4pi) = 0
3/(4pi)x^2 - (10/pi)x + 37/(4pi) = 0
Now calculate the roots using the quadratic formula with a = 3/(4pi), b = -10/pi, and c = 37/(4pi)
The roots occur at x = 1 and x = 12 1/3. There are the points where the slope of the volume equation is zero. The root of 1 happens just as the volume of the tube is 0. So the root of 12 1/3 is the value you want where the volume of the tube is maximized. So the answer to the nearest tenth is 12.3</span>
It is the first answer, loss of $701.80
Answer:
Step-by-step explanation:
From table 1,
f(x) = bˣ
For x = -1,
f(-1) = 0.5
0.5 = (b)⁻¹
b = 
b = 2
For x = 1.585,
f(1.585) = 3
3 = 
3 = 
For x = 2.585,
f(2.585) = 
= 
= 4 × 1.5 [Since, ]
= 6
From table 2,
g(x) = 
For x = 0.5,
g(0.5) = -1
-1 = 
b⁻¹ = 0.5
b = 2
For x = 2,
g(2) = 1
1 = 
For x = 6,
g(6) = 2.585
2.585 = 
2.585 = 
2.585 = 
2.858 - 1 = 
For x = 3,
g(3) =
g(3) = 1.585
Answer:
The bottom Right one
Step-by-step explanation:
96/43 = 196/43
the equation is false.
Hope this helps!
