1) Compute
2) One day, I decide to run to the park. On the way there, I run at a rate of miles per hour for hours. On the way back, I take the same path and jog at a slower rate of miles per hour so that it takes me hours to get home. Given that , what is ? Express your answer as a common fraction.
3)
4)
Find a non-zero value for a such that ax^2+8x+4=0 has only one solution.
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3)
Simplify the following:
2 + i - 4 - i + 2 + 4 i
Group like terms in 2 + i - 4 - i + 2 + 4 i.
2 + i - 4 - i + 2 + 4 i = (2 - 4 + 2) + (i - i + 4 i):
(2 - 4 + 2) + (i - i + 4 i)
Evaluate 2 - 4 + 2.
2 - 4 + 2 = 0:
i - i + 4 i
Add like terms in i - i + 4 i.
i - i + 4 i = 4 i:
4 i
1) Just evaluate by any calculator:
(2011^2 - 2006^2) / (2010^2 - 2007^2)
=5 / 3