1999^2-1998^2+1997^2-...-2^2+1^2​

675 (6913)

1999000

Step-by-step explanation:

1²-2²=(1-2)(1+2)=-1*3=-3

3²-4²=(3-4)(3+4)=-7

5²-6²=(5-6)(5+6)=-11

7²-8²=(7-8)(7+8)=-15

...

1997²-1998²=(1997-1998)(1997+1998)=-3995

1²-2²+3²-4²+....+1997²-1998²+1999²=1999²-(3+7+11+15+...+3995)

Number of terms in the parenthesis: =(3995-3)/(7-3)+1=998+1=999

Parenthesis=

1²-2²+3²-4²+....+1997²-1998²+1999²==1999²-1997001=1999000

answer: 15

step-by-step explanation:

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.