Difference between revisions of "2003 AMC 12B Problems/Problem 23"
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Revision as of 17:17, 9 February 2023
Contents
Problem
The number of -intercepts on the graph of
in the interval
is closest to
Solution
The function has roots in the form of
for all integers
. Therefore, we want
on
, so
. There are
solutions for
on this interval.
Solution
We know that belongs to the interval
for
. We see that when we plug in
into
, the argument
is always from the range
. Therefore, the problem simply asks for all the zeros of
with
values between
. We know that the
values of any sine graph is
so, we see that values of
are any integer value from
to
and therefore gives us an answer of approximately
which is answer
~Jske25
See also
2003 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 22 |
Followed by Problem 24 |
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 |
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