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Problem
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amogus
The ratio <math>\frac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}}</math> is closest to which of the following numbers?
 
 
 
<math>\text{(A)}\ 0.1 \qquad \text{(B)}\ 0.2 \qquad \text{(C)}\ 1 \qquad \text{(D)}\ 5 \qquad \text{(E)}\ 10</math>
 
 
 
Helo,
 
<cmath>
 
\begin{align*}
 
\frac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}} &= \frac{10^{2000}(1+10^2)}{10^{2000}(10+10)}\\
 
&= \frac{101}{20}\\
 
&= 5.05
 
\end{align*}
 
soo obv the sol is <math>\text{(F)} \ 420.69</math> q.e.d.
 

Latest revision as of 20:29, 28 August 2024

amogus