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.
Answer:The answer is A, 15 I believe if i did the math right.
Step-by-step explanation: First you take the equation: f(x)= 0.86x-0.09
Then you plug in x witch in this case is 18 so f(18)=0.86(18)-0.09= 15.39 So round to the nearest whole number and you get 15.
Answer:
answer is in the sbs explanation
Step-by-step explanation:
1.5625
Answer:
y = - 2x + (1/2 38) + 2 = y = -2x + 19x + 2 at any second and y = -2x^2 / 2 + 19/2 + 2/2 = <u>- x^2 + 19/2 + 2 </u>= - x (4) + 19/2(4) + 1 = -4+ 38 + 1 = 35 seconds
Step-by-step explanation: We see that 38-2ft = 36ft and y intercept = 2 and then -2x allows us to represent the starting point 2 as -2 (1) to allow a descend to our back to 0 for y one we find y intercept we know - x^2 is our simplified equation and an input into this to find the static and slowed descend back to 0 if you keep inputting at 5 and 6 you see the equation speed up Anyway at (4) substitute = 4 seconds we divide our simplified equation a = -x2 into a b c and divide each by 2 before working out the<u> </u><u>decline</u> of the equation<u> (as equation still represents all ascending and descending) </u>for the 4th second as the height was <u>already said to be at its max at 38 feet see equation in answer to find 4 as substitute for x </u>
