Answer:
50π ≈ 157.08 cubic units
Step-by-step explanation:
The volume of revolution of a plane figure is the product of the area of the figure and the length of the path of revolution of the centroid of that area. The centroid of a triangle is 1/3 the distance from each side to the opposite vertex. (It is the intersection of medians.)
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<h3>length of centroid path</h3>
One side of this triangle is the axis of revolution. Then the radius to the centroid is 1/3 the x-dimension of the triangle, so is 5/3. Then the circumference of the circle along which the centroid is revolved is ...
C = 2πr
C = 2π(5/3) = 10π/3 . . . units
<h3>triangle area</h3>
The area of the triangle is found using the formula ...
A = 1/2bh
A = 1/2(5)(6) = 15 . . . square units
<h3>volume</h3>
The volume is the product of the area and the path length:
V = AC
V = (15)(10π/3) = 50π . . . cubic units
The volume of the solid is 50π ≈ 157.08 cubic units.
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<em>Additional comment</em>
In the attached figure, the point labeled D is the centroid of the triangle. The label has no significance other than being the next after A, B, C were used to label the vertices.
The volume of revolution can also be found using integration and "shell" or "disc" differential volumes. The result is the same.
Answer:
X = 5
Step-by-step explanation:
I think there a problem with the question, If there is one less person in the group then the payment by each remaining person is must more than $2 than the previous, because the rent cost unchanged but the number of people in the group decreased.
Before, cost per person :
After cost per person: =
However, the payment by each remaining person is more than $2 than the previous, so
= + 2
<=> - 2x -40 = 0
<=> X = 5
Answer: C)
Step-by-step explanation:
Equation: (420-(10*9))/5.50=x
x=60
2/5 + p = 4/5 + 3/5 pSimplifyp + 2/5 = 3/5 p + 4/5Subtract 3/5p from both sidesp + 2/5 -3/5p = 3/5p + 4/5 -3/5 p2/5 p + 2/5 =4/5Subtract 2/5 from both sides2/5 p +2/5 -2/5 = 4/5 -2/52/5 p = 2/5Divide both sides by 2/52/5 p / 2/5 = 2/5 /2/5p = 1