The area of an equilateral triangle of side "s" is s^2*sqrt(3)/4. So the volume of the slices in your problem is
(x - x^2)^2 * sqrt(3)/4.
Integrating from x = 0 to x = 1, we have
[(1/3)x^3 - (1/2)x^4 + (1/5)x^5]*sqrt(3)/4
= (1/30)*sqrt(3)/4 = sqrt(3)/120 = about 0.0144.
Since this seems quite small, it makes sense to ask what the base area might be...integral from 0 to 1 of (x - x^2) dx = (1/2) - (1/3) = 1/6. Yes, OK, the max height of the triangles occurs where x - x^2 = 1/4, and most of the triangles are quite a bit shorter...
9514 1404 393
Answer:
2
Step-by-step explanation:
Each image point is twice as far from the origin as its preimage point. Each image segment is twice as long as its preimage segment. (LM=2, L'M'=4, for example)
The scale factor is 2.
Answer:
6 1/2 cubic feet
Step-by-step explanation:
A carton has a length of 2 1/6 feet
The width is 1 1/5 feet
The height is 2 1/2 feet
Therefore the volume of the carton can be calculated as follows
= length × width × height
= 2 1/6 × 1 1/5 × 2 1/2
= 13/6 × 6/5 × 5/2
= 390/60
= 13/2
= 6 1/2 cubic feet
Hence the volume of the carton is 6 1/2 cubic feet
B I think but wait for other people to answer
