Assessment 1 Grade 12 ACTASPIRE Practice Test Questions TOC | Lumos Learning

Assessment 1 Question & Answer Key Resources Lumos StepUp High School Integrated Mathematics 2 - Workbooks and Online Assessments

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Two passengers are located at fixed distances R and 2R from the axis about which an amusement park ride rotates, such that they travel in circular paths. Answer the following questions to determine the ratio of the arc lengths traveled by the riders during the same time interval.

a) During a certain time interval, it is observed that the ride rotates through an angle \(\theta = \frac{\pi }{4}.\) Find the distance traveled along the arc by the rider located R from the ride axis.

Resource: Question

Question Type: Extended Constructed Response

Standard(s):HSG.C.B.5

Standard Description: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

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