Ernstfalld
2021-01-28
Answered

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

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hajavaF

Answered 2021-01-29
Author has **90** answers

Step 1

The rectangular coordinate system consists of two real number lines that intersect at a right angle.

The horizontal number line is called the x-axis, and the vertical number line is called the y-axis.

These two number lines define a flat surface called a plane, and each point on this plane is associated with an ordered pair of real numbers (x, y). The first number is called the x-coordinate, and the second number is called the y-coordinate.

The intersection of the two axes is known as the origin, which corresponds to the point (0, 0)

Step 2

An ordered pair (x, y) represents the position of a point relative to the origin.

The x-coordinate represents a position to the right of the origin if it is positive and to the left of the origin if it is negative. The y-coordinate represents a position above the origin if it is positive and below the origin if it is negative.

Using this system, every position (point) in the plane is uniquely identified. For example, the we have pair (-4, 0) denotes the position relative to the origin as shown:

Thus, point A is shown in the above graph.

asked 2020-10-26

Plotting points and finding distance in three dimensions. Two points P and $\underset{\u2015}{O}$ are given.

(a) Plot P and$\underset{\u2015}{O}$ .

(b) Find the distance between P and$\underset{\u2015}{O}.$

$P(3,1,0),\underset{\u2015}{O}(-1,2,-5)$

(a) Plot P and

(b) Find the distance between P and

asked 2020-11-23

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

$z\ge -1$

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

asked 2021-03-11

Convert the point from spherical coordinates to rectangular coordinates.

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

$(x,y,z)=?$

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 2020-11-08

Use a graphing calculator to graph the solution of the system of inequalities. Find the coordinates of all vertices, rounded to one decimal place.

$\{\begin{array}{l}y\ge x-3\\ y\ge -2x+6\\ y\le 8\end{array}$

asked 2020-12-25

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