1.3 million stocks was there in beginning of the day
Step-by-step explanation:
The required sum
=(1+2+3+...+199)−(3+6+9+...+198)−(5+10+15+...+195)+(15+30+45+...+195)
=2199(1+199)−266(3+198)−239(5+195)+213(15+195)
=199×100−33×201−39×100+13×105=10732
We can use the ratios for special triangles (see the attachment below). We'll be using the 45-45-90 triangle. We notice that side BC is equal to
, and side AC (x using the special right triangle) is equal to 16. We can therefore say that side BC is equal to
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:)
Answer:
12, 13, 14
Step-by-step explanation:
Denote the integers as:
x
x+1
x+2
The sum of their squares, so that would be;
(x^(2)) + (( x + 1 )^(2)) + (( x + 2 )^(2)) = 509
write out the squares
x^2 + x^2 + 2x + 1 + x^2 + 4x + 4 = 509
combine like terms
3x^2 + 6x + 5 = 509
inverse operations
3x^2 + 6x + 5 = 509
-5 -5
3x^2 + 6x = 504
factor
3x^2 + 6x = 504
3 ( x^2 + 2x ) =504
Inverse operations
3 ( x^2 + 2x ) = 504
/3 /3
x^2 + 2x = 168
Factor again
x ( x + 2 ) = 168
At this point, it should be obvious that x is 12 (because 12 * 14 = 168)
So now substitute back into the consecutive numbers
x = 12
x + 1 = 13
x + 2 = 14
