AA Section 1-3
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El documento presenta 4 ejercicios de funciones notacionales. Los ejercicios 1 y 2 piden calcular el valor de y cuando x es 0 y 3 respectivamente, dado que y es una función de x. Los ejercicios 3 y 4 piden lo mismo pero cuando x es 5 y 6.
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1) Verifica si la función xy2 - y3 = c es solución de la ecuación diferencial ydx + (2x - 3y)dy = 0.
2) Verifica si la función y = Ae5x + Be-2x - 1/2ex es solución de la ecuación diferencial y'' - 3y' - 10y = 6ex.
3) Para la ecuación diferencial xM(x,y) + yN(x,y) = 0, encuentra la solución de la forma M(x,y)dx + N(x,y)dy = 0.
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El resumen consta de 3 oraciones:
1) Se presentan dos desafíos matemáticos que involucran ecuaciones y sistemas de ecuaciones.
2) En el primer desafío se pide calcular expresiones dadas ciertas condiciones.
3) En el segundo desafío se pide determinar valores dados ciertas igualdades y relaciones entre variables.
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Calculo difer trabajo 2
Este gráfico muestra la función lineal y = 2x para valores de x entre -3 y 3. La tabla asociada lista pares de valores (x, y) que satisfacen la ecuación y = 2x.
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2) Verifica si la función y = Ae5x + Be-2x - 1/2ex es solución de la ecuación diferencial y'' - 3y' - 10y = 6ex.
3) Para la ecuación diferencial xM(x,y) + yN(x,y) = 0, encuentra la solución de la forma M(x,y)dx + N(x,y)dy = 0.
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El resumen consta de 3 oraciones:
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Here are the steps to solve problem #1 on page 74:
1) Simplify the expression: -3(x - 5)
2) Use the property that anything inside the parentheses will be opposite if there is a negative sign outside: -3(x - 5) = -3x + 15
3) Simplify: -3x + 15
The simplified expression is: -3x + 15
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Algebra 2 Section 5-3
The document discusses inverse functions and relations. It defines an inverse relation as one where the coordinates of a relation are switched, and an inverse function as one where the domain and range of a function are switched. It provides examples of finding the inverse of specific relations and functions by switching their coordinates or domain and range. It also discusses how to determine if two functions are inverses using their graphs and the horizontal line test.
Algebra 2 Section 5-2
The document discusses composition of functions. It defines composition of functions as using the output of one function as the input of another. It provides an example of composing two functions f and g, showing the steps of evaluating f(g(x)) and g(f(x)) at different values of x. Another example is given with two functions defined by sets of ordered pairs, finding the compositions f∘g and g∘f by evaluating them at different inputs and stating their domains and ranges.
Algebra 2 Section 5-1
The document discusses operations that can be performed on functions, including addition, subtraction, multiplication, and division. Definitions of each operation are provided, along with examples of applying the operations to specific functions. Addition of functions involves adding the outputs of each function, subtraction involves subtracting the outputs, multiplication involves multiplying the outputs, and division involves dividing the outputs given the denominator function is not equal to 0. Several examples are worked through applying the different operations to functions like f(x)=2x and g(x)=-x+5. The examples also demonstrate evaluating composite functions and restricting domains as needed.
Algebra 2 Section 4-9
The document discusses determining the number and type of roots of polynomial equations. It states that every polynomial with degree greater than zero has at least one root in the set of complex numbers according to the Fundamental Theorem of Algebra. Descartes' Rule of Signs is introduced, which relates the number of changes in sign of a polynomial's terms to its possible positive and negative real roots. An example problem is worked through applying these concepts to determine the possible number of positive, negative, and imaginary roots.
Algebra 2 Section 4-8
This document discusses synthetic division and the remainder and factor theorems. It provides examples of using synthetic division to evaluate functions, determine the number of terms in a sequence, and factor polynomials. The key steps of synthetic division are shown, along with checking the remainder and determining common factors. Three examples are worked through to demonstrate these concepts.
Algebra 2 Section 4-6
This document discusses solving polynomial equations by factoring polynomials. It begins with essential questions and vocabulary about factoring polynomials and solving polynomial equations by factoring. It then provides the number of terms in a polynomial and the corresponding factoring technique that can be used. Examples of factoring various polynomials are also provided. The document aims to teach students how to factor polynomials and solve polynomial equations by factoring.
Geometry Section 6-6
The document defines key terms and theorems related to trapezoids and kites. It provides definitions for trapezoid, bases, legs of a trapezoid, base angles, isosceles trapezoid, midsegment of a trapezoid, and kite. It also lists theorems about properties of isosceles trapezoids and kites. Two examples problems are included, one finding measures of an isosceles trapezoid and another showing a quadrilateral is a trapezoid.
Geometry Section 6-5
The document discusses rhombi and squares. It defines a rhombus as a parallelogram with four congruent sides and gives its properties. A square is defined as a parallelogram with four right angles and four congruent sides. The document provides theorems for identifying rhombi and squares. It then gives examples of using the properties and theorems to determine if a shape is a rhombus, rectangle, or square.
Geometry Section 6-4
The document discusses properties of rectangles. A rectangle is defined as a parallelogram with four right angles. The key properties are that opposite sides are parallel and congruent, opposite angles are congruent, and consecutive angles are supplementary. The diagonals of a rectangle bisect each other and are congruent. Theorems are presented regarding the diagonals of rectangles. Examples apply the properties of rectangles to find missing side lengths, angles, and diagonals. One example uses the distance formula and slope to determine if a quadrilateral is a rectangle.
Geometry Section 6-3
The document discusses properties of parallelograms and provides examples of determining if a quadrilateral is a parallelogram. It defines four theorems for identifying parallelograms based on opposite sides, opposite angles, bisecting diagonals, and parallel/congruent sides. Examples solve systems of equations to find values of variables such that the quadrilaterals satisfy parallelogram properties. One example uses slopes of side segments to show a quadrilateral is a parallelogram due to parallel opposite sides.
Geometry Section 6-2
The document discusses properties of parallelograms. It defines a parallelogram as a quadrilateral with two pairs of parallel sides. It then lists several properties of parallelograms: opposite sides are congruent, opposite angles are congruent, consecutive angles are supplementary, and if one angle is a right angle all angles are right angles. It also discusses properties of diagonals in parallelograms, including that diagonals bisect each other and divide the parallelogram into two congruent triangles. Several examples demonstrate using these properties to solve problems about parallelograms.
Geometry Section 6-1
The document summarizes key concepts about polygons, including:
- The sum of the interior angles of a polygon with n sides is (n-2)180 degrees.
- The sum of the exterior angles of a polygon is 360 degrees.
- Examples are provided to demonstrate calculating sums of interior/exterior angles and finding missing angle measures using angle sums.
- Regular polygons are defined by their number of sides.
Algebra 2 Section 4-5
The document discusses analyzing graphs of polynomial functions. It provides examples of locating real zeros of polynomials using the location principle and estimating relative maxima and minima. Example 1 analyzes the polynomial f(x) = x^4 - x^3 - 4x^2 + 1 and locates its real zeros between consecutive integer values. Example 2 graphs the polynomial f(x) = x^3 - 3x^2 + 5 and estimates the x-coordinates of relative maxima and minima.
Algebra 2 Section 4-4
This document discusses polynomial functions. It defines key terms like polynomial in one variable, leading coefficient, and polynomial function. It provides examples of power functions of varying degrees like quadratic, cubic, quartic and quintic functions. The document also includes examples of evaluating polynomial functions, finding degrees and leading coefficients, graphing polynomial functions from tables of values, and describing properties of graphs.
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Aqui vemos conceptos relacionados a las infecciones respiratorias.
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¡Experimenta una Mayor Concentración, Claridad y Energía con RISE! 🌟
¿Te cuesta mantener la concentración, la claridad mental y la energía durante todo el día?
La falta de concentración y claridad puede afectar tu rendimiento mental, creatividad y motivación, haciéndote sentir agotado y sin ánimo. Las soluciones tradicionales pueden ser ineficaces y a menudo vienen con efectos secundarios no deseados. ¿No sería genial tener una solución natural que funcione rápidamente y sin efectos secundarios negativos?
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Beneficios de RISE:
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Claridad mental: Aumenta tu enfoque y claridad.
Energía: Proporciona energía sostenida sin picos y caídas.
Creatividad y motivación: Estimula tu creatividad y te mantiene motivado.
Concentración: Mejora tu capacidad de concentración.
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Ánimo: Mejora tu estado de ánimo y bienestar general.
Respuesta antiinflamatoria: Reduce la inflamación y promueve una salud óptima.
viene en un delicioso sabor a limonada de mango, haciendo de esta bebida no solo un potente estimulante cerebral, sino también un manjar saludable y delicioso para tu cuerpo y mente.
¡Siéntete mejor ya y experimenta por ti mismo! Esta limonada de mango te volará la mente. 🤯
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ASFIXIA Y HEIMLICH.pptx- Dr. Guillermo Contreras Nogales.
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AA Section 1-3
- 1. Section 1-3 Function Notations
- 2. Warm-up x2 1. If y = 3x − 2 , 2. If y = 4x + , 16 find y when x = 0. find y when x = 3. 4−x x −1 3. If y = 2 , 4. If y = 3 , x find y when x = 5. find y when x = 6.
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