Suggested languages for you:

Americas

Europe

Q10E

Expert-verified
Found in: Page 734

### Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280

# Write the equations in cylindrical coordinates.a. $${\rm{3x + 2y + z = 6}}$$b. $${\rm{ - }}{{\rm{x}}^{\rm{2}}}{\rm{ - }}{{\rm{y}}^{\rm{2}}}{\rm{ + }}{{\rm{z}}^{^{\rm{2}}}}{\rm{ = 1}}$$

1. The equations in cylindrical coordinates $${\rm{z = 6 - 3rcos\theta - 2rsin\theta }}$$
2. The equations in cylindrical coordinates $${\rm{ - }}{{\rm{r}}^{\rm{2}}}{\rm{ + }}{{\rm{z}}^{\rm{2}}}{\rm{ = 1}}$$
See the step by step solution

## Step 1: Concept Introduction

A multiple integral is a definite integral of a function of many real variables in mathematics (particularly multivariable calculus), such as f(x, y) or f(x, y) (x, y, z). Integrals of a two-variable function over a region

## Step 2:Explanation of the solution

a.

To determine the cylindrical coordinates, apply the formulas below:

Remember that $${\rm{x = rcos}}\theta$$ and $${\rm{y = rsin\theta }}$$ in cylindrical coordinates. Because $${\rm{z = z}}$$, we may substitute for x and$$\;y$$ to get the following equation:

$${\rm{z = 6 - 3rcos\theta - 2rsin\theta }}$$

## Step 3: Explanation of the solution

b.

Consider the given integral and simplify

In cylindrical coordinates, we employ the knowledge that $${\rm{x = rcos\theta }}$$ and $${\rm{y = rsin\theta }}$$ once more.

When we plug these into the equation, we get:

The equations in cylindrical coordinates $${\rm{ - }}{{\rm{r}}^{\rm{2}}}{\rm{ + }}{{\rm{z}}^{\rm{2}}}{\rm{ = 1}}$$

## Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.