Question

1. [10 points] 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 $y = -|2x| + 2$. 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: 1. [10 points] 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 = -|2x| + 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: 2024-10-14T06:10:09-08:00
Duration: 4 min 51 s
Channel: Shu Naito
Description: 1. [10 points] 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 = -|2x| + 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!)

          1. [10 points] 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 $y = -|2x| + 2$. 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!)

1. [10 points] 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 = -|2x| + 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!)

Added by Jeffrey T.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shu Naito

10/14/2024

Step 1

The equation is $x^{2/3} + y^{2/3} = 1$. We can rewrite this as $y = (1 - x^{2/3})^{3/2}$. The derivative is: $\frac{dy}{dx} = \frac{3}{2}(1 - x^{2/3})^{1/2} \cdot (-\frac{2}{3}x^{-1/3}) = -x^{-1/3}(1 - x^{2/3})^{1/2}$ The arc length is given by: $L_P = Show more…

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1. [10 points] 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 $y = -|2x| + 2$. 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!)