Difference between revisions of "1958 AHSME Problems/Problem 38"
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== Problem == | == Problem == | ||
− | Let <math> r</math> be the distance from the origin to a point <math> P</math> with coordinates <math> x</math> and <math> y</math>. Designate the ratio <math> \frac{y}{r}</math> by <math> s</math> and the ratio <math> \frac{x}{r}</math> by <math> c</math>. Then the values of <math> s^2 | + | Let <math> r</math> be the distance from the origin to a point <math> P</math> with coordinates <math> x</math> and <math> y</math>. Designate the ratio <math> \frac{y}{r}</math> by <math> s</math> and the ratio <math> \frac{x}{r}</math> by <math> c</math>. Then the values of <math> s^2 - c^2</math> are limited to the numbers: |
− | <math> \textbf{(A)}\ \text{less than }{ | + | <math> \textbf{(A)}\ \text{less than }{-1}\text{ are greater than }{+1}\text{, both excluded}\qquad\\ |
− | \textbf{(B)}\ \text{less than }{ | + | \textbf{(B)}\ \text{less than }{-1}\text{ are greater than }{+1}\text{, both included}\qquad \\ |
− | \textbf{(C)}\ \text{between }{ | + | \textbf{(C)}\ \text{between }{-1}\text{ and }{+1}\text{, both excluded}\qquad \\ |
− | \textbf{(D)}\ \text{between }{ | + | \textbf{(D)}\ \text{between }{-1}\text{ and }{+1}\text{, both included}\qquad \\ |
− | \textbf{(E)}\ { | + | \textbf{(E)}\ {-1}\text{ and }{+1}\text{ only}</math> |
== Solution == | == Solution == |
Latest revision as of 23:23, 13 March 2015
Problem
Let be the distance from the origin to a point with coordinates and . Designate the ratio by and the ratio by . Then the values of are limited to the numbers:
Solution
See Also
1958 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 37 |
Followed by Problem 39 | |
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All AHSME Problems and Solutions |
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