To determine Find the values of x and y and slope of the curve for x 3 + 2 t 2 = 9 , 2 y 3 − 3 t 2 = 4 , t = 2 . Explanation Given data: x 3 + 2 t 2 = 9 (1) 2 y 3 − 3 t 2 = 4 (2) t = 2 Formula used: Consider the Parametric Formulas. d y d x = d y / d t d x / d t (3) Calculation: Rearrange equation (1) as follows. x 3 = 9 − 2 t 2 Substitute 2 for t as follows. x 3 = 9 − 2 ( 2 ) 2 = 9 − 2 ( 4 ) = 9 − 8 = 1 Simplify the equation as follows. x = 1 3 = 1 Rearrange equation (2) as follows. y 3 = 4 + 3 t 2 2 Substitute 2 for t as follows. y 3 = 4 + 3 ( 2 ) 2 2 = 4 + 3 ( 4 ) 2 = 4 + 12 2 = 16 2 Simplify the equation as follows. y = 8 3 = 2 Find d x d t . Differentiate equation (1) with respect to t . d d t ( x 3 + 2 t 2 ) = d d t ( 9 ) d d t ( x 3 ) + 2 d d t ( t 2 ) = d d t ( 9 ) 3 x 2 d x d t + 2 ( 2 t ) = 0 3 x 2 d x d t + 4 t = 0 d x d t = − 4 t 3 x 2 Find d y d t . Differentiate equation (2) with respect to t

Thomas' Calculus: Early Transcendentals plus MyLab Math with Pearson eText -- Title-Specific Access Card Package (14th Edition)

14th Edition

ISBN: 9780134768496

Author: Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher: PEARSON

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Chapter 11.2, Problem 15E

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Find the values of x and y and slope of the curve for x3+2t2=9, 2y3−3t2=4,t=2.

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Chapter 11.2, Problem 14E

Chapter 11.2, Problem 16E

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Thomas' Calculus: Early Transcendentals plus MyLab Math with Pearson eText -- Title-Specific Access Card Package (14th Edition)

Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Finding Cartesian from Parametric...

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