500 I guess it’s not right
Disagree. Even though it has no b it is still a line but a horizontal line. It will be at 7 on the y- intercept but horizontal.
<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>
Equation 1) x + 6y = 2
Equation 2) 5x + 4y = 36
Multiply all of equation 1 by 5.
1) 5(x + 6y = 2)
Simplify.
1) 5x + 30y = 10
2) 5x + 4y = 36
Subtract equations from one another.
26y = -26
Divide both sides by 26.
y = -1
Plug in -1 for y in the first equation.
x + 6y = 2
x + 6(-1) = 2
Simplify.
x - 6 = 2
Add 6 to both sides.
x = 8
D : (8, -1)
~Hope I helped!~
