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> | ||
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==Solution== | ==Solution== | ||
− | + | Divide both the numerator and denominator by <math>n</math>, to get <math>C=\frac{e}{\frac{R}{n}+r}</math>. If <math>n</math> increases then the denominator decreases; so that <math>C</math> <math>\boxed{\mathrm{(A)}\text{ }\mathrm{ Increases}.}</math> | |
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==See Also== | ==See Also== |
Latest revision as of 20:28, 18 November 2024
Problem
If in the formula , where , , and are all positive, is increased while , and are kept constant, then :
Solution
Divide both the numerator and denominator by , to get . If increases then the denominator decreases; so that
See Also
1950 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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