MathDB

11

Part of 2021 AMC 10 Fall

Problems(2)

Exercising Emily

Source: 2022 AMC 10A P11

11/11/2021
Emily sees a ship traveling at a constant speed along a straight section of a river. She walks parallel to the riverbank at a uniform rate faster tha the ship. She counts 210210 equal steps walking from the back of the ship to the front. Walking in the opposite direction, she counts 4242 steps of the same size from the front of the ship to the back. In terms of Emily's equal steps, what is the length of the ship? <spanclass=′latex−bold′>(A)</span>70<spanclass=′latex−bold′>(B)</span>84<spanclass=′latex−bold′>(C)</span>98<spanclass=′latex−bold′>(D)</span>105<spanclass=′latex−bold′>(E)</span>126<span class='latex-bold'>(A) </span>70\qquad<span class='latex-bold'>(B) </span>84\qquad<span class='latex-bold'>(C) </span>98\qquad<span class='latex-bold'>(D) </span>105\qquad<span class='latex-bold'>(E) </span>126
AMCAMC 10AMC 10 Aemily
AMC 10B #11

Source:

11/17/2021
A regular hexagon of side length 11{ } is inscribed in a circle. Each minor arc of the circle determined by a side of the hexagon is reflected over that side. What is the area of the region bounded by these 66 reflected arcs?
(<spanclass=′latex−bold′>A</span>) 532−π(<spanclass=′latex−bold′>B</span>) 33−π(<spanclass=′latex−bold′>C</span>) 43−3π2(<spanclass=′latex−bold′>D</span>) π−32(<spanclass=′latex−bold′>E</span>) π+32(<span class='latex-bold'>A</span>)\: \frac{5\sqrt{3}}{2} - \pi\qquad(<span class='latex-bold'>B</span>) \: 3\sqrt{3}-\pi\qquad(<span class='latex-bold'>C</span>) \: 4\sqrt{3}-\frac{3\pi}{2}\qquad(<span class='latex-bold'>D</span>) \: \pi - \frac{\sqrt{3}}{2}\qquad(<span class='latex-bold'>E</span>) \: \frac{\pi + \sqrt{3}}{2}
AMCAMC 10AMC 10 B