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Q.31.

Expert-verified

Precalculus Enhanced with Graphing Utilities

Found in: Page 695

Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

In Problems 27–34, find two different parametric equations for each rectangular equation $y = x^{3}$

Two different parametric equations are $y = t^{3} a n d y = t$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Equation

$y = x^{3}$

Step 2. Solve for getting parametric equations .

let us assume that $x = t$

then putting the value of x in given equation we get $y = t^{3}$ $- \infty \leq t \leq \infty$ ---------(1)

again solving given equation for x

we get $x = y^{\frac{1}{3}}$

Now again let us assume that $x = t^{\frac{1}{3}}$

we get $y = {(t^{\frac{1}{3}})}^{3} = t$ $- \infty \leq t \leq \infty$ ---(2)

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