Question

Parker and Glenn, the two sons of railroad tycoon Scott Piggy, are having a contest to see who can make a longer set of tracks on the interval ( [-1,1] ). Parker built his track along ( x^{2 / 3}+y^{2 / 3}=1 ) while Glenn followed the route of ( y=-|2 x|+2 ). Which of the two brothers has the longest track and will win his father's pride? (To get full credit, use calculus to find the lengths!)

Name: Parker and Glenn, the two sons of railroad tycoon Scott Piggy, are having a contest to see who can make a longer set of tracks on the interval ( [-1,1] ). Parker built his track along ( x^2 / 3+y^2 / 3=1 ) while Glenn followed the route of ( y=-|2 x|+2 ). Which of the two brothers has the longest track and will win his father's pride? (To get full credit, use calculus to find the lengths!)
Uploaded: 2024-10-23T10:10:28-08:00
Duration: 4 min 34 s
Channel: Shu Naito
Description: Parker and Glenn, the two sons of railroad tycoon Scott Piggy, are having a contest to see who can make a longer set of tracks on the interval ( [-1,1] ). Parker built his track along ( x^2 / 3+y^2 / 3=1 ) while Glenn followed the route of ( y=-|2 x|+2 ). Which of the two brothers has the longest track and will win his father's pride? (To get full credit, use calculus to find the lengths!)

          Parker and Glenn, the two sons of railroad tycoon Scott Piggy, are having a contest to see who can make a longer set of tracks on the interval ( [-1,1] ). Parker built his track along ( x^{2 / 3}+y^{2 / 3}=1 ) while Glenn followed the route of ( y=-|2 x|+2 ). Which of the two brothers has the longest track and will win his father's pride? (To get full credit, use calculus to find the lengths!)

Parker and Glenn, the two sons of railroad tycoon Scott Piggy, are having a contest to see who can make a longer set of tracks on the interval ( [-1,1] ). Parker built his track along ( x^2 / 3+y^2 / 3=1 ) while Glenn followed the route of ( y=-|2 x|+2 ). Which of the two brothers has the longest track and will win his father's pride? (To get full credit, use calculus to find the lengths!)

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Precalculus with Limits

Ron Larson 2nd Edition

Chapter 6

Instant Answer

Solved by Expert Shu Naito

10/23/2024

Step 1

Parker's track is along the curve \( x^{2/3} + y^{2/3} = 1 \). This is the equation of an astroid. We can parameterize this curve using: \[ x = \cos^3 \theta, \quad y = \sin^3 \theta \] where \( \theta \) ranges from \( 0 \) to \( 2\pi \). The derivatives Show more…

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