<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:
<em>Choice B. 16 feet.</em>
<em>The height of the tree is 16 ft</em>
Step-by-step explanation:
<u>Similar Triangles</u>
Similar triangles have their corresponding side lengths proportional by a fixed scale factor.
We are given the drawings of a tree and a wall and it's assumed both triangles are similar. We need to find the scale factor and find the height of the tree.
Comparing the corresponding distances from the viewer to the base of the tree and the base of the wall, we can calculate the scale factor as 24/6=4.
Applying the same factor to the height of the model, we get the height of the tree is 4*4 = 16 ft.
Choice B. 16 feet
The height of the tree is 16 ft
Answer:
the answer is B
Step-by-step explanation:
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