Difference between revisions of "1950 AHSME Problems/Problem 11"
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== Problem== | == Problem== | ||
− | If in the formula <math> C =\frac{en}{R+nr} </math>, <math>n</math> is increased while <math>e</math>, <math>R</math> and <math>r</math> are kept constant, then <math>C</math>: | + | If in the formula <math> C =\frac{en}{R+nr} </math>, where <math>e</math>, <math>n</math>, <math>R</math> and <math>r</math> are all positive, <math>n</math> is increased while <math>e</math>, <math>R</math> and <math>r</math> are kept constant, then <math>C</math>: |
<math> \textbf{(A)}\ \text{Increases}\qquad\textbf{(B)}\ \text{Decreases}\qquad\textbf{(C)}\ \text{Remains constant}\qquad\textbf{(D)}\ \text{Increases and then decreases}\qquad\ \textbf{(E)}\ \text{Decreases and then increases} </math> | <math> \textbf{(A)}\ \text{Increases}\qquad\textbf{(B)}\ \text{Decreases}\qquad\textbf{(C)}\ \text{Remains constant}\qquad\textbf{(D)}\ \text{Increases and then decreases}\qquad\ \textbf{(E)}\ \text{Decreases and then increases} </math> |
Revision as of 10:55, 27 May 2014
Problem
If in the formula , where , , and are all positive, is increased while , and are kept constant, then :
Solution
Assume that the constants are positive, as well as
WLOG let and all equal Then We can see that as increases from it slowly approaches Therefore,
If and were positive and was negative, then would decrease, for example.
See Also
1950 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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All AHSME Problems and Solutions |
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