07-06_task (1)

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University of Alabama *

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CALCULUS

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Mathematics

Date

Jan 9, 2024

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docx

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Uploaded by ProfessorWren5558

7.06 Parametric Equations This task requires you to create a graph. You have several options: • Use the Word tools; • Draw the graph by hand, then photograph or scan your graph; or • Use the GeoGebra linked on the Task page of the lesson to create the graph; then, insert a screenshot of the graph into this task. 1. Change these parametric equations to slope-intercept form. Graph the parametric equations. x = -1 - 2t y = 4 - 1t -2 ≤ t ≤ 2

2. Change the parametric equations to rectangular form. (x-3)^2=(y+1)^2=49 3. . Graph the parametric equations. y = -t² and x = 4t -2 ≤ t ≤ 2

4. Use parametric equations to answer each question of the following 250 mile motorcycle race. The first cycle is averaging 135 mph. The second cycle averages 150 mph but has mechanical problems in the first half of the race which causes him to lose 4 minutes during the race. a. Write equations to express the speed of each bike. X1+135t X2=150(t-0.067) b. Which one is ahead after 1 hour if that is past the halfway mark? X1=135(1) =135 X2=150(1-0.067) =140 X2 c. Does the second motorcycle manage to regain the lead? Yes 250+135t T=1.85 250=150t-10.05 260.05=150t T=1.73

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07-06_task (1)

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