Coordenadas Polares y Cartesianas
38 Questions
4 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

Each student is considered an element of set ______

A

Subjects are considered elements of another set ______

B

Are all elements of set A related to some element of set ______?

B

Is the relationship unique for the elements of set A related to any in set ______?

<p>B</p> Signup and view all the answers

Two variables can relate in such a way that one ______ on the other.

<p>depends</p> Signup and view all the answers

In the initial situation, we related time with the ______ of the river.

<p>height</p> Signup and view all the answers

For each month of the year, a unique ______ corresponds.

<p>height</p> Signup and view all the answers

This document discusses the relation of ______ to subjects.

<p>students</p> Signup and view all the answers

The function g(z) is defined as g(z) = ______

<p>z</p> Signup and view all the answers

The independent variable in the expression is ______

<p>z</p> Signup and view all the answers

The dependent variable, g, represents the ______ of the integer z

<p>magnitude</p> Signup and view all the answers

In a polygon, the sum of the interior angles can be calculated using the formula y = S(n) = 180º(n - ______)

<p>2</p> Signup and view all the answers

For n = 4, the corresponding value of y according to the function is ______

<p>360º</p> Signup and view all the answers

The image of 5 in the function corresponds to ______

<p>540º</p> Signup and view all the answers

The point (3; ______º) belongs to the function

<p>180</p> Signup and view all the answers

The sum of the interior angles of a hexagon is ______º

<p>720</p> Signup and view all the answers

In the polar coordinate system, the distance from point A to the pole O is represented by ______.

<p>r</p> Signup and view all the answers

The angle formed between the polar axis and the line segment AO is indicated by the Greek letter ______.

<p>alpha</p> Signup and view all the answers

A point in the polar coordinate system can be represented as A (______; alpha).

<p>r</p> Signup and view all the answers

The polar coordinate system is particularly useful in ______ for detecting objects out of sight.

<p>navigation</p> Signup and view all the answers

Radar screens display the presence and movement of objects, which are based on ______ projections.

<p>radio</p> Signup and view all the answers

In a three-dimensional Cartesian coordinate system, points are represented with three values, such as (3; 4; ______).

<p>5</p> Signup and view all the answers

To find the coordinates of the vertices of quadrilateral ABCD, you must use the ______ coordinates.

<p>Cartesian</p> Signup and view all the answers

The points (3; 45º) and (5; 120º) are located in a system of ______ coordinates.

<p>polar</p> Signup and view all the answers

The function f can be symbolically written as f : R R / f ( x) = y = 4x, and its graph is a ______ that passes through the origin.

<p>line</p> Signup and view all the answers

In the table, when x = -2, y = ______.

<p>-8</p> Signup and view all the answers

The relationship between two real numbers whose product is -30 can be written as f : R -{0} R / f ( x) = y = ______ / x.

<p>-30</p> Signup and view all the answers

The graph of the function relating to -30 is a ______.

<p>hyperbola</p> Signup and view all the answers

In the examples, we obtained a line passing through the origin or a ______.

<p>hyperbola</p> Signup and view all the answers

If xi and yi are corresponding values, we observe that y1, y2, y3 = ______ = ....

<p>x1.y1 = x2.y2 = x3.y3</p> Signup and view all the answers

The equation of line a is y = -3x + ______

<p>8</p> Signup and view all the answers

In the equation 2x + y = ______, the value of y is determined by the value of x.

<p>5</p> Signup and view all the answers

For the sector formed with 50 [m] of rope, if the width is ______ m, its length is determined accordingly.

<p>15</p> Signup and view all the answers

The monthly salary for Option A is a fixed amount of ______ dollars.

<p>3500</p> Signup and view all the answers

In Option B, the seller earns $2000 per month plus a commission of ______ dollars for each computer sold.

<p>250</p> Signup and view all the answers

If a seller earns $4750 this month, they sold ______ computers.

<p>8</p> Signup and view all the answers

The equation of line d can be rewritten as y = -3(x + ______) + x + 2.

<p>1</p> Signup and view all the answers

A linear function is determined if it can be represented in the form y = mx + ______.

<p>b</p> Signup and view all the answers

Study Notes

Coordinate Systems

  • Polar Coordinates: A method to locate a point in a plane using a distance (r) from a fixed point (polo) and an angle (α) from a reference line (polar axis).
  • Point Representation: Point A can be represented as A(r; α), where r is the radial distance and α is the angle measured counterclockwise.

Applications of Polar Coordinates

  • Radar Technology: Polar coordinates help in displaying the position and movement of objects beyond visibility, beneficial in navigation systems.
  • Electronic Equipment: Records the behavior of radio waves, revealing information about objects in the scanning field.

Geometry and Polygons

  • Sum of Interior Angles: The function calculating the sum of interior angles of a convex polygon is defined as S(n) = 180º(n - 2), where n is the number of sides.
  • Example Values: For a polygon with:
    • 3 sides: 180º (triangle)
    • 4 sides: 360º (quadrilateral)
    • 5 sides: 540º (pentagon)

Functions and Relationships

  • Independent and Dependent Variables:
    • Variable z defined as integers, g(z) is the modulus of z.
    • Independent: z, Dependent: g.
  • Relational Functions:
    • Functions can represent direct relationships like y = 4x, creating linear graphs through the origin.
    • Different functions may have different types of graphs such as straight lines or hyperbolas.

Real-World Scenarios

  • Camping with Ropes: When forming a rectangular area with a fixed length of rope on three sides, varying the width (a) affects the length (e), showing a dependency based on defined constraints.
  • Sales Strategies:
    • Two salary options for computer salespeople exemplify linear and conditional relationships based on sales performance.

Sample Calculation and Graphing

  • Salary Analysis:
    • Option A: Fixed salary of $3500/month.
    • Option B: $2000/month plus $250 per computer sold.
    • A formula can be derived for total salary based on the number sold, allowing for comparisons of which option is more beneficial.

Observations

  • Graphs and tables produced from these functions and scenarios illustrate variable relationships, demonstrating how changes in one aspect can influence others within defined parameters.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Related Documents

Matemática II 2do Año PDF

Description

Explora el sistema de coordenadas polares y su relación con las coordenadas cartesianas. Aprende a ubicar puntos en este sistema utilizando la distancia desde un punto de referencia. Ideal para estudiantes que desean profundizar en la geometría y sus aplicaciones.

More Like This

Spherical Polar Coordinates Quiz
5 questions
Coordinate Geometry Quiz
10 questions

Coordinate Geometry Quiz

RealizableDiction avatar
RealizableDiction
Use Quizgecko on...
Browser
Browser