Answer:
-2007/4018
Step-by-step explanation:
1. Given
(1/3+1/4+...+1/2009)(1+1/2+...1/2008) - (1+1/3+1/4+...+1/2009)(1/2+1/3+...+1/2008)
2. Set new variable
k = 1/3+1/4+...+1/2008
3. Rewrite the equation
(k+1/2009)(1+1/2+k) - (1+k+1/2009)(1/2+k)
4. Simplify
(k+1/2009)(k+3/2) - (k+2010/2009)(k+1/2)
5. Expand
[k^2 + (1/2009 + 3/2)k + (1/2009)(3/2)] - [k^2 - (2010/2009+1/2)k - (2010/2009)(1/2)]
6. Rewrite
(1/2009 + 3/2 - 2010/2009 - 1/2)k + (1/2009)(3/2) - (2010/2009)(1/2)
7. Simplify
(3/2 - 2009/2009 - 1/2)k + 1/2(3/2009-2010/2009)
8. Evaluate
0*k + 1/2(-2007/2009)
= -2007/4018
Answer:
Step-by-step explanation:
Lowest common denominator of 4, 5, and 6:
60
Answer:
200 questions on the final exam.
Step-by-step explanation:
38% = 76 questions, 100% = 2.63157894737 x 76 = 200
(100/38=2.63157894737 hence this is the answer)
Answer:
56x
Step-by-step explanation:
Think of it an a triangle and a rectangle. The area of the rectangle is obviously 13 x 4x, which is 52x
for triangle, the hypotenuse is C, Right hand side is B and the side that is in the shape is B.
Area of triangle = (bh) / 2
B = 13 - 9, so B = 4
A = 6x - 4x, so A = 2x
the area is 2x x 4, which is 8x.
8x / 2 = 4x
The area is 4x + 52x, so the final answer is 56x
