<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:
C
Step-by-step explanation:
(6 * 4 ) * 2 = 48
( 4 * 12 ) * 2 = 96
( 6 * 12 ) * 2 = 144
48 + 96 + 144 = 288
Answer:
Answer: B( hope this helps)
Step-by-step explanation:
Answer:
<h2>
6 1/2 lbs</h2>
Step-by-step explanation:
Given the weight of granite to be 74 26/36 lbs,
Weight of quartz is 81 9/40 lbs.
To know how much more quartz weight than the granite, we will take the difference between the weight of quartz and granite as shown.
Weight of quartz - Weight of granite
= 81 9/40 - 74 26/36
= 3,249/40 - 2690/36
= (29, 241 - 26,900)/360
= 2,341/360
= 6 181/360
≈ 6 1/2 lbs
quartz weighs approximately 6 1/2 lbs much more than granite
In order to have the variable by itself you have to add 20 to both sides. So your answer would be a=b+20. I hope this helps love! :)
