Examples of Coordinate Systems and Equations

College
Algebra
Linear algebra
Alternate coordinate systems

Recent questions in Alternate coordinate systems

allhvasstH 2020-12-24

The equivalent polar equation for the given rectangular-coordinate equation:
$x^{2} + y^{2} + 8 x = 0$

defazajx 2020-12-21

To solve:
the system of equation $2 x + 3 y = 5 and 6 x + 9 y = 15$ .

nagasenaz 2020-12-17

The coordinate vector of $[p (t) = 6 + 3 t - t^{2}]$ relative to the basis ${B} = {1 + t, 1 + t^{2}, t + t^{2}}$

Tabansi 2020-12-16

To determine.To fill:
a) The blank in the statement "Del operator: $\nabla = ?$ "
b) The blank in the statement "Gradient: $\nabla f = ?$ "
c) The blank in the "Laplacian: $\nabla^{2} f = ?$ "

amanf 2020-12-13

Find the value of x or y so that the line passing through the given points has the given slope. (-9,y),(0,-3), $m = \frac{- 7}{9}$

lwfrgin 2020-12-09

The equivalent polar coordinates for the given rectangular coordinates: $[\begin{array}{cc} 5 & 180^{\circ} \end{array}]$

necessaryh 2020-12-02

As you can see the solution to the system is the coordinates of the point where the two lines intersect. So, when solving linear systems with two variables we are really asking where the two lineas will intersect.

cistG 2020-12-02

The equivalent rectangular coordinates for the given polar coordinates:
$[\begin{array}{cc} 6 & - 135^{\circ} \end{array}]$

Jerold 2020-11-22

To find: The equivalent polar equation for the given rectangular-coordinate equation.
Given:
$x = r \cos θ$
$y = r \sin θ$
b. From rectangular to polar:
$r = \pm \sqrt{x^{2} + y^{2}}$
$\cos θ = \frac{x}{r}, \sin θ = \frac{y}{r}, \tan θ = \frac{x}{y}$
Calculation:
Given: equation in rectangular-coordinate is $y = x$ .
Converting into equivalent polar equation -
$y = x$
Put $x = r \cos θ, y = r \sin θ,$
$\Rightarrow r \sin θ = r \cos θ$
$\Rightarrow \frac{\sin θ}{\cos θ} = 1$
$\Rightarrow \tan θ = 1$
Thus, desired equivalent polar equation would be $θ = 1$

geduiwelh 2020-11-22

True or False? In Exercises 99 and 100, determine whether the statement is true or false. Justify your answer, : 99. The line through (−8,2) and (−1,4) and the line through (0,−4) and (−7,7) are parallel.

waigaK 2020-11-17

The coordinates of the point in the $x^{'} y^{'}$ - coordinate system with the given angle of rotation and the xy-coordinates.

Phoebe 2020-11-16

Thealternate sets of representations for the points A-F from the Figure.

aortiH 2020-11-14

Consider the bases $B = (\begin{matrix} [\begin{matrix} 2 \\ 3 \end{matrix}], [\begin{matrix} 3 \\ 5 \end{matrix}] \end{matrix}) o f R^{2} a n d C = (\begin{matrix} [\begin{matrix} 1 \\ 1 \\ 0 \end{matrix}], [\begin{matrix} 1 \\ 0 \\ 1 \end{matrix}] \end{matrix}, [\begin{matrix} 0 \\ 1 \\ 1 \end{matrix}]) o f R^{3}$ .
and the linear maps $S \in L (R^{2}, R^{3}) a n d T \in L (R^{3}, R^{2})$ given given (with respect to the standard bases) by $[S]_{E, E} = [\begin{matrix} 2 & - 1 \\ 5 & - 3 \\ - 3 & 2 \end{matrix}] a n d [T]_{E, E} = [\begin{matrix} 1 & - 1 & 1 \\ 1 & 1 & - 1 \end{matrix}]$ Find each of the following coordinate representations. $(b) {[S]}_{E, C}$
$(c) {[S]}_{B, C}$

alesterp 2020-11-12

The given system of inequality:
${\begin{matrix} y < 9 - x^{2} \\ y \geq x + 3 \end{matrix}$
Also find the coordinates of all vertices, and check whether the solution set is bounded.

vazelinahS 2020-11-10

Consider the following linear transformation $T : P_{2} \to P_{3}$ , given by $T (f) = 3 x^{2} f$ '.

That is, take the first derivative and then multiply by $3 x^{2}$

(a) Find the matrix for T with respect to the standard bases of $P_{n}$ : that is, find $[T]_{ϵ}^{ϵ}$ , where- $ϵ = 1, x, x^{2}, x^{n}$

(b) Find N(T) and R(T). You can either work with polynomials or with their coordinate vectors with respect to the standard basis. Write the answers as spans of polynomials.

(c) Find the the matrix for T with respect to the alternate bases: $[T]_{A}^{B}$ where $A = x - 1, x, x^{2} + 1, B = x^{3}, x, x^{2}, 1 .$

jernplate8 2020-11-09

Prove that by setting these two expressions equal to another, the result is an identity:
$d = \cos^{- 1} (\sin (L T_{1}) \sin (L T_{2}) + \cos (L T_{1}) \cos (L T_{2}) \cos (\ln_{1} - \ln_{2}))$
$d = 2 \sin^{- 1} (\sqrt{\sin^{2} (\frac{L T_{1} - L T_{2}}{2}) + \cos (L T_{1}) \cos (L T_{2}) \sin^{2} (\frac{\ln_{1} - \ln_{2}}{2})})$

Braxton Pugh 2020-11-08

Whether the statement "I need to be able to graph systems of linear inequalities in order to solve linear programming problems" makes sense or not.

Trent Carpenter 2020-11-06

(i)Prove that if $v_{1}, v_{2}$ is linearly dependent, then are multiple of each other, that is, there exists a constant c such that $v_{1} = c v_{2} o r v_{2} = c v_{1}$ .
(ii)Prove that the converse of(i) is also true.That is to say, if there exists a constant c such that $v_{1} = c v_{2} o r v_{2} = c v_{1}$ , 1. then $v_{1}, v_{2}$ is linearly dependent.

Amari Flowers 2020-11-06

The line $2 x + 3 y = 8$ meets the curve $2 x^{2} + 3 y^{2} = 110$ at the points A and B.
Find the coordinates of A and B.

Kaycee Roche 2020-11-05

To determine:
Find the sets of points in space whose coordinates satisfy the given combinations of equation and inequalities:
a) $y \geq x^{2}, z \geq 0,$
b) $x \leq y^{2}, 0 \leq z \leq 2 .$

Coordinate system examples can be met in college geometry among architects and 3D designers as they are dealing with the Euclidean space and other objectives. The solutions and answers that have been presented below will also include linear algebra for various calculations. Do not forget to look through the list of questions as these will have great coordinate system equations that will help you determine how to solve your unique problem. Start with given coordinates, provide a position of existing points, and just change your task's problem accordingly by learning from the answers provided.

Linear algebra

Understanding Coordinate Systems and Equations