Difference between revisions of "2016 AMC 12B Problems/Problem 1"
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− | {{ | + | ==Problem== |
+ | |||
+ | What is the value of <math>\frac{2a^{-1}+\frac{a^{-1}}{2}}{a}</math> when <math>a= \frac{1}{2}</math>? | ||
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+ | <math>\textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ \frac{5}{2}\qquad\textbf{(D)}\ 10\qquad\textbf{(E)}\ 20</math> | ||
+ | |||
+ | ==Solution== | ||
+ | By: Dragonfly | ||
+ | |||
+ | We find that <math>a^{-1}</math> is the same as <math>2</math>, since a number to the power of <math>-1</math> is just the reciprocal of that number. We then get the equation to be | ||
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+ | <cmath>\frac{2\times2+\frac{2}{2}}{\frac{1}{2}}</cmath> | ||
+ | |||
+ | We can then simplify the equation to get <math>\boxed{\textbf{(D)}\ 10}</math> | ||
+ | |||
+ | ==See Also== | ||
+ | {{AMC12 box|year=2016|ab=B|before=First Problem|num-a=2}} | ||
+ | {{MAA Notice}} |
Latest revision as of 11:44, 26 July 2022
Problem
What is the value of when
?
Solution
By: Dragonfly
We find that is the same as
, since a number to the power of
is just the reciprocal of that number. We then get the equation to be
We can then simplify the equation to get
See Also
2016 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by First Problem |
Followed by Problem 2 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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