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 ______?
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Two variables can relate in such a way that one ______ on the other.
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In the initial situation, we related time with the ______ of the river.
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For each month of the year, a unique ______ corresponds.
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This document discusses the relation of ______ to subjects.
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The function g(z) is defined as g(z) = ______
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The independent variable in the expression is ______
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The dependent variable, g, represents the ______ of the integer z
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In a polygon, the sum of the interior angles can be calculated using the formula y = S(n) = 180º(n - ______)
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For n = 4, the corresponding value of y according to the function is ______
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The image of 5 in the function corresponds to ______
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The point (3; ______º) belongs to the function
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The sum of the interior angles of a hexagon is ______º
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In the polar coordinate system, the distance from point A to the pole O is represented by ______.
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The angle formed between the polar axis and the line segment AO is indicated by the Greek letter ______.
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A point in the polar coordinate system can be represented as A (______; alpha).
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The polar coordinate system is particularly useful in ______ for detecting objects out of sight.
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Radar screens display the presence and movement of objects, which are based on ______ projections.
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In a three-dimensional Cartesian coordinate system, points are represented with three values, such as (3; 4; ______).
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To find the coordinates of the vertices of quadrilateral ABCD, you must use the ______ coordinates.
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The points (3; 45º) and (5; 120º) are located in a system of ______ coordinates.
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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.
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In the table, when x = -2, y = ______.
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The relationship between two real numbers whose product is -30 can be written as f : R -{0} R / f ( x) = y = ______ / x.
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The graph of the function relating to -30 is a ______.
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In the examples, we obtained a line passing through the origin or a ______.
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If xi and yi are corresponding values, we observe that y1, y2, y3 = ______ = ....
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The equation of line a is y = -3x + ______
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In the equation 2x + y = ______, the value of y is determined by the value of x.
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For the sector formed with 50 [m] of rope, if the width is ______ m, its length is determined accordingly.
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The monthly salary for Option A is a fixed amount of ______ dollars.
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In Option B, the seller earns $2000 per month plus a commission of ______ dollars for each computer sold.
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If a seller earns $4750 this month, they sold ______ computers.
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The equation of line d can be rewritten as y = -3(x + ______) + x + 2.
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A linear function is determined if it can be represented in the form y = mx + ______.
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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.
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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.
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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.
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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.
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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.
