allhvasstH
2021-01-28
Answered

Find the Equivalent Polar Equation for a given Equation with Rectangular Coordinates:

$r\mathrm{cos}\theta =\text{}-1$

You can still ask an expert for help

Liyana Mansell

Answered 2021-01-29
Author has **97** answers

The transformation formula for coordinate systems is:

a)$x=r\mathrm{cos}\theta$

$y=r\mathrm{sin}\theta$

b)$r}^{2}={x}^{2}\text{}+\text{}{y}^{2}\text{}\Rightarrow \text{}r=\pm \sqrt{{x}^{2}\text{}+\text{}{y}^{2}$

$\mathrm{cos}\theta =\frac{x}{r},\text{}\mathrm{sin}\theta =\frac{y}{r},\text{}\mathrm{tan}\theta =\frac{x}{y}$

Calculation:

Convert formula to equivalent polar coordinates:

$r\mathrm{cos}\theta =\text{}-1$

Put$x=r\mathrm{cos}\theta ,\text{}y=r\mathrm{sin}\theta ,$

$\Rightarrow \text{}x=\text{}-1$

Hence the desired equivalent polar coordinates would be$x=\text{}-1$

a)

b)

Calculation:

Convert formula to equivalent polar coordinates:

Put

Hence the desired equivalent polar coordinates would be

asked 2021-09-21

Consider the linear system

a) Find the eigenvalues and eigenvectors for the coefficient matrix

b) For each eigenpair in the previos part, form a solution of

c) Does the set of solutions you found form a fundamental set (i.e., linearly independent set) of solution? No, it is not a fundamental set.

asked 2022-05-18

Find linear transformation matrix from a linear transformation matrix of its composition

Let's say that $V$ is a vector space over the field $K$ and suppose we have a linear transformation $f\in \text{End}V$ thats matrix is know on some basis.

How to find a matrix of a linear transformation $g\in \text{End}V$ on the same basis, so that $g\circ g=f$.

For example if $V$ is vector space over the field ${\mathbb{Z}}_{11}$ and matrix of linear transformation $f\in \text{End}V$ on some basis is

$\left(\begin{array}{cccc}\overline{7}& \overline{3}& \overline{4}& \overline{0}\\ \overline{0}& \overline{6}& \overline{9}& \overline{6}\\ \overline{1}& \overline{9}& \overline{3}& \overline{1}\\ \overline{0}& \overline{2}& \overline{8}& \overline{5}\end{array}\right)$

Find matrix of a linear transformation $g\in \text{End}V$ on the same basis, so that $g\circ g=f$

Let's say that $V$ is a vector space over the field $K$ and suppose we have a linear transformation $f\in \text{End}V$ thats matrix is know on some basis.

How to find a matrix of a linear transformation $g\in \text{End}V$ on the same basis, so that $g\circ g=f$.

For example if $V$ is vector space over the field ${\mathbb{Z}}_{11}$ and matrix of linear transformation $f\in \text{End}V$ on some basis is

$\left(\begin{array}{cccc}\overline{7}& \overline{3}& \overline{4}& \overline{0}\\ \overline{0}& \overline{6}& \overline{9}& \overline{6}\\ \overline{1}& \overline{9}& \overline{3}& \overline{1}\\ \overline{0}& \overline{2}& \overline{8}& \overline{5}\end{array}\right)$

Find matrix of a linear transformation $g\in \text{End}V$ on the same basis, so that $g\circ g=f$

asked 2022-06-06

What is the transformation matrix?

In ${\mathbb{R}}^{\mathbb{2}}$ a basis is given $a=({a}_{1},{a}_{2})$ where:

${a}_{1}=(1,-1)$

${a}_{2}=(0,1)$

For $f:{\mathbb{R}}^{\mathbb{2}}\to {\mathbb{R}}^{\mathbb{2}}$ it is known:

$f({a}_{1})=-6\cdot {a}_{1}$

$f({a}_{2})=1\cdot {a}_{2}$

Determine the matrix of transformation with regards to the standard e-basis.

In ${\mathbb{R}}^{\mathbb{2}}$ a basis is given $a=({a}_{1},{a}_{2})$ where:

${a}_{1}=(1,-1)$

${a}_{2}=(0,1)$

For $f:{\mathbb{R}}^{\mathbb{2}}\to {\mathbb{R}}^{\mathbb{2}}$ it is known:

$f({a}_{1})=-6\cdot {a}_{1}$

$f({a}_{2})=1\cdot {a}_{2}$

Determine the matrix of transformation with regards to the standard e-basis.

asked 2021-01-05

Find a set of vectors that spans the plane $P1:2x+3y-z=0$

asked 2022-01-10

Since

ite = 8

int r = 1;

int s = 1;

int R = 0;

for (int i=0,i<ite,1){

R = 3*r+4*s;

s=2*r+3*s;

r=R

}

int result = r/s;

System.out.println(result);

But it's not exactly the code one would get using picard's iteration method, so my answer does not fit the criteria. What am-I doing wrong?

If one does not know the answer but knows how to visualise picard's method for calculating sqrt(2) on a graph that would already help me a lot.

Thanks in advance

asked 2022-07-12

Let $A$ be the set of all $n\times n$ symmetric real matirix and $f\in C(\mathbb{R},A)$. Then whether there is a $g\in C(\mathbb{R},O(n))$ such that for all $t\in \mathbb{R}$, $g(t{)}^{-1}f(t)g(t)$ is a diagonal matrix?

asked 2020-11-12

The given system of inequality:

Also find the coordinates of all vertices, and check whether the solution set is bounded.