Nannie Mack
2020-12-29
Answered

Describe in words the region of ${R}^{3}$ represented by the equation(s) or inequality.

${x}^{2}+{y}^{2}=4$

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tafzijdeq

Answered 2020-12-30
Author has **92** answers

Concept:

The equation

Given:

3) Calculation:

The given equation is

The equation

represents the set of all points in

That is,

Here is no restriction on z-coordinate, so a point in the region must lie on a circle with radius 2 and centre on z-axis but it could be any horizontal plane

Therefore, the region consists of all points on the circle

That is, a circular cylinder with radius 2 whose axis is the z - axis

Therefore, the given equations represents the region in

Conclusion:

The given equations represents the region in

asked 2021-02-22

Describe in words the region of ${R}^{3}$ represented by the equation(s) or inequality.

$x=5$

asked 2021-09-21

The Cartesian coordinates of a point are given.

a)$(2,-2)$

b)$(-1,\sqrt{3})$

Find the polar coordinates$(r,\theta )$ of the point, where r is greater than 0 and 0 is less than or equal to $\theta$ , which is less than $2\pi$

Find the polar coordinates$(r,\theta )$ of the point, where r is less than 0 and 0 is less than or equal to $\theta$ , which is less than $2\pi$

a)

b)

Find the polar coordinates

Find the polar coordinates

asked 2021-09-15

This question has to do with binary star systems, where i is the angle of inclination of the system.

Calculate the mean expectation value of the factor$\mathrm{sin}}^{3$ i, i.e., the mean value it would have among an ensemble of binaries with random inclinations. Find the masses of the two stars, if $\mathrm{sin}}^{3$ i has its mean value.

Hint: In spherical coordinates,$(\theta ,\varphi )$ , integrate over the solid angle of a sphere where the observer is in the direction of the z-axis, with each solid angle element weighted by $\mathrm{sin}\left\{3\right\}\left(\theta \right)$ .

$v}_{1}=100k\frac{m}{s$

$v}_{2}=200k\frac{m}{s$

Orbital period$=2$ days

${M}_{1}=5.74e33g$

${M}_{2}=2.87e33g$

Calculate the mean expectation value of the factor

Hint: In spherical coordinates,

Orbital period

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The vector x is in $H=Span\text{}{v}_{1},{v}_{2}$

and find the beta-coordinate vector$[x{]}_{\beta}$

and find the beta-coordinate vector

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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.

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Convert the point from spherical coordinates to rectangular coordinates.

$(9,\pi ,\frac{\pi}{2})$

$(x,y,z)=?$

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Plot the given point $(-4,0)$ in a rectangular coordinate system.