Amari Flowers
2020-12-25
Answered

What coordinate system is suggested if the integrand of a triple
integral involves ${x}^{2}+{y}^{2}?$

You can still ask an expert for help

doplovif

Answered 2020-12-26
Author has **71** answers

Step 1

Given: The integrand of a triple integral involves${x}^{2}+{y}^{2}$

Step 2

Explanation:

A cylindrical coordinate system is used in triple integrals only.

Therefore, it is cylindrical coordinate system

Because$x=r\mathrm{cos}(\theta ),y=r\mathrm{sin}(\theta )\text{}and\text{}z=z$

So,${x}^{2}+{y}^{2}={r}^{2}$

z axis is same in both systems.

So, The integrand of a triple integral involves${x}^{2}+{y}^{2}$ then its suggested to use cylindrical coordinate system

Given: The integrand of a triple integral involves

Step 2

Explanation:

A cylindrical coordinate system is used in triple integrals only.

Therefore, it is cylindrical coordinate system

Because

So,

z axis is same in both systems.

So, The integrand of a triple integral involves

asked 2021-03-05

Consider the solid that is bounded below by the cone $z=\sqrt{3{x}^{2}+3{y}^{2}}$

and above by the sphere${x}^{2}+{y}^{2}+{z}^{2}=16.$ .Set up only the appropriate triple integrals in cylindrical and spherical coordinates needed to find the volume of the solid.

and above by the sphere

asked 2021-10-08

Systems of Inequalities Graph the solution set of the system if inequalities. Find the coordinates of all vertices, and determine whether the solution set is bounded.

asked 2021-09-22

Below are various vectors in cartesian, cylindrical and spherical coordinates. Express the given vectors in two other coordinate systems outside the coordinate system in which they are expressed

asked 2021-09-19

Find Maximum Volume of a rectangular box that is inscribed in a sphere of radius r.

The part i do not get the solutions manual got$2x,\text{}2y$ , and $2z$ as the volume. Can you explain how the volume of the cube for this problem is $v=8xyz?$

The part i do not get the solutions manual got

asked 2022-09-12

How do you find a cubic function $y=a{x}^{3}+b{x}^{2}+cx+d$

whose graph has horizontal tangents at the points(-2,6) and (2,0)?

whose graph has horizontal tangents at the points(-2,6) and (2,0)?

asked 2021-03-02

Descibe in words the region of

asked 2021-01-02

Solve the given Alternate Coordinate Systems and give a correct answer 10) Convert the equation from Cartesian to polar coordinates solving for