<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:
7 feet
Step-by-step explanation:
Pythagorean theorem
sqrt(4.5^2 + 5.3^2) = hypotenuse
sqrt(48.34) = hypotenuse
6.95269732 = hypotenuse
round to nearest tenth
7 feet = the length of the hypotenuse
B.becuase he paid that much in total, and we divide them by 100
Answer:
Convert into same base
Step-by-step explanation:
Convert both sides into same bases and equate the powers to solve for the variable.
Example:
8^x = 32
You can either use logs to bring the power down or convert both sides into the same base
8 = 2³
8^x = (2³)^x = 2^(3x)
32 = 2⁵
2^(3x) = 2⁵
3x = 5
x = 5/3
x = 1⅔
Answer:
20
Step-by-step explanation:
