Difference between revisions of "2021 AMC 12B Problems/Problem 13"
Jamess2022 (talk | contribs) (→Solution) |
Jamess2022 (talk | contribs) (→Solution 1) |
||
Line 30: | Line 30: | ||
add(legend(),point(E),20E,UnFill); | add(legend(),point(E),20E,UnFill); | ||
</asy> | </asy> | ||
− | We have <math>\boxed{(A) 6}</math> solutions. | + | We have <math>\boxed{(A) 6}</math> solutions. ~Jamess2022 (burntTacos) |
== Video Solution by OmegaLearn (Using Sine and Cosine Graph) == | == Video Solution by OmegaLearn (Using Sine and Cosine Graph) == |
Revision as of 06:19, 12 February 2021
Contents
[hide]Problem
How many values of in the interval satisfy
Solution
First, move terms to get . After graphing, we find that there are solutions (two in each period of ). -dstanz5
Solution 1
We can graph two functions in this case: and . Using transformation of functions, we know that is just a cos function with amplitude 5 and frequency . Similarly, is just a sin function with amplitude 3 and shifted 1 unit downwards. So: We have solutions. ~Jamess2022 (burntTacos)
Video Solution by OmegaLearn (Using Sine and Cosine Graph)
~ pi_is_3.14
See Also
2021 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 12 |
Followed by Problem 14 |
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 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.