Difference between revisions of "1957 AHSME Problems/Problem 43"
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== Solution == | == Solution == | ||
| + | |||
| + | <asy> | ||
| + | |||
| + | path p = (0,0){right}..(1,1)..(2,4)..(3,9)..(4,16); | ||
| + | |||
| + | // Shaded Region | ||
| + | fill(p--(4,0)--cycle,lightred); | ||
| + | |||
| + | // x-Axis | ||
| + | draw((-4,0)--(16,0), arrow=Arrows); | ||
| + | label("$x$",(18,0)); | ||
| + | |||
| + | // y-Axis | ||
| + | draw((0,-4)--(0,16), arrow=Arrows); | ||
| + | label("$y$",(0,18)); | ||
| + | |||
| + | // y=x^2 | ||
| + | draw(p); | ||
| + | |||
| + | // x=4 | ||
| + | draw((4,-5)--(4,20), arrow=Arrows(TeXHead)); | ||
| + | |||
| + | </asy> | ||
| + | |||
<math>\boxed{\textbf{(B) }35}</math>. | <math>\boxed{\textbf{(B) }35}</math>. | ||
Revision as of 09:38, 27 July 2024
Problem
We define a lattice point as a point whose coordinates are integers, zero admitted.
Then the number of lattice points on the boundary and inside the region bounded by the 
-axis,
the line 
, and the parabola 
is:
Solution
![[asy] path p = (0,0){right}..(1,1)..(2,4)..(3,9)..(4,16); // Shaded Region fill(p--(4,0)--cycle,lightred); // x-Axis draw((-4,0)--(16,0), arrow=Arrows); label("$x$",(18,0)); // y-Axis draw((0,-4)--(0,16), arrow=Arrows); label("$y$",(0,18)); // y=x^2 draw(p); // x=4 draw((4,-5)--(4,20), arrow=Arrows(TeXHead)); [/asy]](http://latex.artofproblemsolving.com/e/7/7/e77b09ad66588e1406964d354a62c403a76706d9.png)
.
See Also
| 1957 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 42 |
Followed by Problem 44 | |
| 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 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
