the answer..... I got was 18
<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>
Answer:
4:7
Step-by-step explanation:
Okay, so first convert the feet to inches so 3x12=36. So the it's 36:63. Then if you simplify it you get 4:7.
Answer:
y=7x+1
Step-by-step explanation:
From the table, the difference in y is 7 and the difference in x is 1.
Let the linear equation be
Where m is the constant difference in y divided by the constant difference in x.
This means m=7/1=7
Our equation now becomes:
y=7x+b
To find b, we substitute any ordered pair from the table.
From the to table, when x=1, y=8.
This implies that,
8=7(1)+b
b=8-7=1
Therefore the equation is y=7x+1
