<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:
2/2
Step-by-step explanation:
There are only red and green jump ropes so she is for sure going to get a red or green jump rope. If she wants specifically a red or green jump rope her chances are 1/2.
Answer:
32.625
Step-by-step explanation:
a square has all equal side so u divieded the amount of she used by 4
We want to know when we brought it back in to the room. at that time
the temperature difference is 80 - 42 = 38 so we have to solve
<span>
38=9<span>e<span>^−.3344t</span></span></span> for t
this time we get
<span><span>38 / 9</span>=<span>e^<span>−.3344t</span></span></span>
<span>t=<span><span>ln(<span>38 / 9</span>)</span><span> / −.3344</span></span></span>
<span>t=−4.3</span>
so 4.3 minutes before 2:10
Answer:
boiling and melting
Step-by-step explanation: