Gauss' method for addition relies on the fact that you can 'pair' certain numbers together. Look at the example:
1+2+3+4+5+6+7+8+9+10
We could manually add all these together from left to right but a clever way to think about this is if we add together the ends of the sum (10+1) we get 11. If we then move one in from the ends and add these (2+9) we also get 11. This means that 1+2+...+9+10 is the same as 11+11+...+11+11.
Because each 2 numbers adds to 11 we know the total number of 11's we have to add together is the length of the sum divided by 2. In our case 5 (10 ÷ 2). We need to add 5 lots of 11 to get our answer. This is the same as 11 × 5 which is easily seen to be 55.
(If you add the 10 numbers together on a calculator you'll see 1+2+3+4+5+6+7+8+9+10 = 55) so this method really makes it a lot quicker.
Looking at your sequence, if we pair the ends together we get 401 (400+1) and we multiply this by the length of the sequence divided by 2. In your case, 200 (400 ÷ 2).
So the sum of all the numbers from 1 to 400 must be 401 × 200 = 80,200.
Remember the steps:
1. Pair the ends together and add them
2. Times this number by the length of the sequence halved
Hope this helps.
C = 11*(2*d) Try it and see that it fits every sample you have. Again this can be simplified to
C = 22 * d
Answer:
17
Step-by-step explanation:
Answer:
The answer is 3418.1 ft rounded to the nearest tenth.
Step-by-step explanation:
The total volume of the cylinder can be defined by the Area of circular base * Perpendicular height.
The area of the circular base can be calculated as
where r is the radius of the circular base, which is 8 ft.
The area of the circular base is
We also know the height of the cylinder is 17 ft.
Hence, the volume of the cylinder is
This will be rounded up to 3418.1 with the nearest tenth
Answer:
20
Step-by-step explanation:
