MathDB

23

Part of 2003 AMC 12-AHSME

Problems(2)

Squares in Factorial Product

Source:

2/20/2008
How many perfect squares are divisors of the product 1!⋅2!⋅3!⋯9! 1!\cdot 2!\cdot 3!\cdots 9!? <spanclass=′latex−bold′>(A)</span> 504<spanclass=′latex−bold′>(B)</span> 672<spanclass=′latex−bold′>(C)</span> 864<spanclass=′latex−bold′>(D)</span> 936<spanclass=′latex−bold′>(E)</span> 1008 <span class='latex-bold'>(A)</span>\ 504 \qquad <span class='latex-bold'>(B)</span>\ 672 \qquad <span class='latex-bold'>(C)</span>\ 864 \qquad <span class='latex-bold'>(D)</span>\ 936 \qquad <span class='latex-bold'>(E)</span>\ 1008
factorial
Counting x-intercepts

Source:

1/5/2009
The number of x x-intercepts on the graph of y \equal{} \sin(1/x) in the interval (0.0001,0.001) (0.0001,0.001) is closest to <spanclass=′latex−bold′>(A)</span> 2900<spanclass=′latex−bold′>(B)</span> 3000<spanclass=′latex−bold′>(C)</span> 3100<spanclass=′latex−bold′>(D)</span> 3200<spanclass=′latex−bold′>(E)</span> 3300 <span class='latex-bold'>(A)</span>\ 2900 \qquad <span class='latex-bold'>(B)</span>\ 3000 \qquad <span class='latex-bold'>(C)</span>\ 3100 \qquad <span class='latex-bold'>(D)</span>\ 3200 \qquad <span class='latex-bold'>(E)</span>\ 3300
trigonometry