MathDB

14

Part of 2008 AMC 12/AHSME

Problems(2)

Inequality Region Area

Source: AMC 12 2008A Problem 14

2/17/2008
What is the area of the region defined by the inequality |3x\minus{}18|\plus{}|2y\plus{}7|\le 3? <spanclass=′latex−bold′>(A)</span> 3<spanclass=′latex−bold′>(B)</span> 72<spanclass=′latex−bold′>(C)</span> 4<spanclass=′latex−bold′>(D)</span> 92<spanclass=′latex−bold′>(E)</span> 5 <span class='latex-bold'>(A)</span>\ 3 \qquad <span class='latex-bold'>(B)</span>\ \frac{7}{2} \qquad <span class='latex-bold'>(C)</span>\ 4 \qquad <span class='latex-bold'>(D)</span>\ \frac{9}{2} \qquad <span class='latex-bold'>(E)</span>\ 5
inequalitiesgeometryinvariantgeometric transformationanalytic geometryAMC
Logarithmic Radius and Circumference

Source: AMC 12 2008B Problem 14

2/29/2008
A circle has a radius of log⁡10(a2) \log_{10}(a^2) and a circumference of log⁡10(b4) \log_{10}(b^4). What is log⁡ab \log_ab? <spanclass=′latex−bold′>(A)</span> 14π<spanclass=′latex−bold′>(B)</span> 1π<spanclass=′latex−bold′>(C)</span> π<spanclass=′latex−bold′>(D)</span> 2π<spanclass=′latex−bold′>(E)</span> 102π <span class='latex-bold'>(A)</span>\ \frac {1}{4\pi} \qquad <span class='latex-bold'>(B)</span>\ \frac {1}{\pi} \qquad <span class='latex-bold'>(C)</span>\ \pi \qquad <span class='latex-bold'>(D)</span>\ 2\pi \qquad <span class='latex-bold'>(E)</span>\ 10^{2\pi}
logarithmsAMC