Colegio maria de nazaret mindo Denisse Jara GarciaDenisse HK
Este documento describe la ubicación y características naturales de Mindo, Ecuador. Mindo es un pequeño poblado de 2500 habitantes ubicado a 1250 metros sobre el nivel del mar, donde la temperatura oscila entre 15-24°C y las lluvias son comunes. La reserva de Mindo alberga más de 170 especies de orquídeas y abundantes bromelias, heliconias y helechos. La fauna incluye 500 variedades de aves y 40 tipos de mariposas. Los habitantes se dedican principalmente a la agricultura, gan
The document is a resume for Tabitha Barkley. It summarizes her education, including a Bachelor of Arts in Graphic Design from Otterbein University and an Associate of Business in Graphic Communications from Baker College. It lists her graphic design portfolio and proficient skills with Adobe Creative Suite, Microsoft Office, and major web platforms. It also provides details on her graphic design internship experience at Heritage Newspapers and customer service experience at Lowe's Home Improvement. Currently, she is self-employed trying to establish her own graphic design business.
El documento describe diferentes tipos de energías renovables y no renovables, incluyendo la energía geotérmica, eólica, solar, nuclear, cinética, potencial, química, hidráulica, sonora, radiante, fotovoltaica y de reacción. Explica brevemente cada tipo de energía, sus fuentes y usos.
Bacall Development: Build-to-suit construction and its advantagesDawn Hertz
Build-to-suit buildings provide room for future expansions to current tenants. It is often viewed as a long-term investment which can be leased to several tenants according to reviews.
El documento describe la historia y el desarrollo de Internet. Comenzó en la década de 1960 como una red de computadoras del gobierno llamada ARPANET que usaba protocolos de comunicación nuevos. ARPANET evolucionó para usar el protocolo TCP/IP y se expandió a nivel mundial, formando la base de lo que hoy conocemos como Internet.
Colegio maria de nazaret mindo Denisse Jara GarciaDenisse HK
Este documento describe la ubicación y características naturales de Mindo, Ecuador. Mindo es un pequeño poblado de 2500 habitantes ubicado a 1250 metros sobre el nivel del mar, donde la temperatura oscila entre 15-24°C y las lluvias son comunes. La reserva de Mindo alberga más de 170 especies de orquídeas y abundantes bromelias, heliconias y helechos. La fauna incluye 500 variedades de aves y 40 tipos de mariposas. Los habitantes se dedican principalmente a la agricultura, gan
The document is a resume for Tabitha Barkley. It summarizes her education, including a Bachelor of Arts in Graphic Design from Otterbein University and an Associate of Business in Graphic Communications from Baker College. It lists her graphic design portfolio and proficient skills with Adobe Creative Suite, Microsoft Office, and major web platforms. It also provides details on her graphic design internship experience at Heritage Newspapers and customer service experience at Lowe's Home Improvement. Currently, she is self-employed trying to establish her own graphic design business.
El documento describe diferentes tipos de energías renovables y no renovables, incluyendo la energía geotérmica, eólica, solar, nuclear, cinética, potencial, química, hidráulica, sonora, radiante, fotovoltaica y de reacción. Explica brevemente cada tipo de energía, sus fuentes y usos.
Bacall Development: Build-to-suit construction and its advantagesDawn Hertz
Build-to-suit buildings provide room for future expansions to current tenants. It is often viewed as a long-term investment which can be leased to several tenants according to reviews.
El documento describe la historia y el desarrollo de Internet. Comenzó en la década de 1960 como una red de computadoras del gobierno llamada ARPANET que usaba protocolos de comunicación nuevos. ARPANET evolucionó para usar el protocolo TCP/IP y se expandió a nivel mundial, formando la base de lo que hoy conocemos como Internet.
El documento describe la importancia del agua para la vida y los tres estados en que se encuentra el agua en la naturaleza: sólido, líquido y gaseoso. Luego, recomienda varias formas de cuidar el agua en el hogar como cerrar la llave mientras se enjabona, usar regadera en lugar de tina, juntar agua fría de la regadera para otros usos, y reparar tuberías que gotean.
The document contains a schedule for May and June 2011, listing exercises, tests, and exams for different days of the week. It includes Exercise #1-35 on May 11th, a test on May 12th, no school on May 13th for prom, and Victoria Day on May 23rd with no school. The June schedule focuses on provincial exam review from June 6th to 10th, with the provincial exam taking place from 8:45-12:00 on June 16th in the library.
Calculators can evaluate base 10 logarithms. The change of base theorem, logb a = logc a / logc b, allows evaluating logarithms with non-base 10 bases by relating them to base 10 logarithms. Some useful properties of logarithms are that logb b = 1, logb b^y = y, and b^logb a = a. Students are assigned exercises 23 problems 1-13, 15-16, 18, and 20 to practice evaluating logarithms.
The document discusses logarithmic functions and their inverses, exponential functions. It provides examples of logarithmic and exponential forms and how to convert between them. It also covers graphing logarithmic functions, their domains and ranges, characteristics like asymptotes. It provides examples of evaluating logarithmic expressions and transformations of logarithmic functions.
This document discusses logarithmic functions and their inverses, exponential functions. It provides examples of logarithmic and exponential forms and how to convert between them. It also covers graphing logarithmic functions, their domains and ranges, characteristics like asymptotes. It provides examples of evaluating logarithmic expressions and transformations of logarithmic functions.
This document outlines three theorems for logarithms:
1) The Product Theorem states that the log of a product is equal to the sum of the logs of the factors.
2) The Quotient Theorem states that the log of a quotient is equal to the difference of the logs of the factors.
3) The Power Theorem states that the log of a factor to a given power is equal to the power times the log of the factor.
These theorems only apply when the logarithms have the same base. Examples are provided to demonstrate applying the theorems to simplify logarithmic expressions and evaluate logarithms.
The document discusses exponential functions of the form f(x) = a^x where a is a constant. It provides examples of exponential functions with a = 2 and a = 1/2. It describes the domain, range, and common point of exponential functions. The document also discusses transformations of exponential functions by adding or subtracting constants, and provides examples of sketching and describing transformed exponential functions. Finally, it lists common exponential expressions.
This document presents sum and difference identities for trigonometric functions sine and cosine. It gives the formulas for sin(α + β), cos(α + β), sin(α - β) and cos(α - β) in terms of sinα, cosα, sinβ and cosβ. It then provides examples of using these formulas to evaluate trigonometric functions at values that are not covered by special triangles.
This document discusses double angle identities for sine, cosine, and tangent. It provides the formulas for sin(2θ), cos(2θ), and tan(2θ) in terms of sin(θ) and cos(θ). The document also includes examples of using the double angle identities to evaluate trigonometric functions and solve equations.
This document contains examples of using sum and difference identities to express trigonometric functions with combined arguments in terms of single variables. It provides the identity cos(A + B) = cos(A)cos(B) - sin(A)sin(B) and uses it to express cos(π/2 + x) in terms of x alone. It also gives examples of using identities to prove relationships between trigonometric functions with combined arguments.
This document provides instructions for graphing trigonometric transformations in 3 steps: 1) Determine the a, b, c, and d values from the function's factored form. 2) Draw the median position and amplitude. 3) Determine the period and mark points to graph the wave-like function. Examples graph y=3sin(2x)-1, f(x)=sin(1/2x+1), and f(x)=2cos(3x)-2.
El documento describe la importancia del agua para la vida y los tres estados en que se encuentra el agua en la naturaleza: sólido, líquido y gaseoso. Luego, recomienda varias formas de cuidar el agua en el hogar como cerrar la llave mientras se enjabona, usar regadera en lugar de tina, juntar agua fría de la regadera para otros usos, y reparar tuberías que gotean.
The document contains a schedule for May and June 2011, listing exercises, tests, and exams for different days of the week. It includes Exercise #1-35 on May 11th, a test on May 12th, no school on May 13th for prom, and Victoria Day on May 23rd with no school. The June schedule focuses on provincial exam review from June 6th to 10th, with the provincial exam taking place from 8:45-12:00 on June 16th in the library.
Calculators can evaluate base 10 logarithms. The change of base theorem, logb a = logc a / logc b, allows evaluating logarithms with non-base 10 bases by relating them to base 10 logarithms. Some useful properties of logarithms are that logb b = 1, logb b^y = y, and b^logb a = a. Students are assigned exercises 23 problems 1-13, 15-16, 18, and 20 to practice evaluating logarithms.
The document discusses logarithmic functions and their inverses, exponential functions. It provides examples of logarithmic and exponential forms and how to convert between them. It also covers graphing logarithmic functions, their domains and ranges, characteristics like asymptotes. It provides examples of evaluating logarithmic expressions and transformations of logarithmic functions.
This document discusses logarithmic functions and their inverses, exponential functions. It provides examples of logarithmic and exponential forms and how to convert between them. It also covers graphing logarithmic functions, their domains and ranges, characteristics like asymptotes. It provides examples of evaluating logarithmic expressions and transformations of logarithmic functions.
This document outlines three theorems for logarithms:
1) The Product Theorem states that the log of a product is equal to the sum of the logs of the factors.
2) The Quotient Theorem states that the log of a quotient is equal to the difference of the logs of the factors.
3) The Power Theorem states that the log of a factor to a given power is equal to the power times the log of the factor.
These theorems only apply when the logarithms have the same base. Examples are provided to demonstrate applying the theorems to simplify logarithmic expressions and evaluate logarithms.
The document discusses exponential functions of the form f(x) = a^x where a is a constant. It provides examples of exponential functions with a = 2 and a = 1/2. It describes the domain, range, and common point of exponential functions. The document also discusses transformations of exponential functions by adding or subtracting constants, and provides examples of sketching and describing transformed exponential functions. Finally, it lists common exponential expressions.
This document presents sum and difference identities for trigonometric functions sine and cosine. It gives the formulas for sin(α + β), cos(α + β), sin(α - β) and cos(α - β) in terms of sinα, cosα, sinβ and cosβ. It then provides examples of using these formulas to evaluate trigonometric functions at values that are not covered by special triangles.
This document discusses double angle identities for sine, cosine, and tangent. It provides the formulas for sin(2θ), cos(2θ), and tan(2θ) in terms of sin(θ) and cos(θ). The document also includes examples of using the double angle identities to evaluate trigonometric functions and solve equations.
This document contains examples of using sum and difference identities to express trigonometric functions with combined arguments in terms of single variables. It provides the identity cos(A + B) = cos(A)cos(B) - sin(A)sin(B) and uses it to express cos(π/2 + x) in terms of x alone. It also gives examples of using identities to prove relationships between trigonometric functions with combined arguments.
This document provides instructions for graphing trigonometric transformations in 3 steps: 1) Determine the a, b, c, and d values from the function's factored form. 2) Draw the median position and amplitude. 3) Determine the period and mark points to graph the wave-like function. Examples graph y=3sin(2x)-1, f(x)=sin(1/2x+1), and f(x)=2cos(3x)-2.
This document discusses graphing absolute value functions. It provides examples of graphing various absolute value functions, including f(x)=|x|^2, f(x)=2|x|-1, f(x)=|x|^2-1, f(x)=3|x|^2-4, f(x)=|cos(x)|, f(x)=2|x|-3-1, and shows how to write a piecewise function definition for f(x)=|x|^2. The graphs are V-shaped and symmetric about the y-axis, with vertices at the points where the absolute value terms are equal to zero.
This document provides information on writing trigonometric equations from sinusoidal graphs. It outlines the two basic sinusoidal equations as f(x) = a sin(b(x - c)) + d or f(x) = a cos(b(x - c)) + d. The variables a, b, c, and d represent the amplitude, period, start point, and median, respectively. Formulas are given to identify each variable based on properties of the graph like maximum, minimum, and period.
This document discusses proving trigonometric identities. It lists four common operations for proving identities: 1) adding or subtracting rational expressions, 2) multiplying or dividing rational expressions, 3) factoring, and 4) multiplying by the conjugate. It then provides four examples of identities to prove using these techniques.
The document discusses trigonometric identities, including 8 fundamental identities. It provides examples of using identities to simplify trigonometric functions and proves identities by showing the left and right hand sides are the same. Examples include simplifying tan θ cos θ, expressing tan θ in terms of sin θ, and proving cot θ sin θ = cosθ.
This document discusses how to sketch graphs resulting from transformations of basic parent functions, including horizontal and vertical stretches as well as translations. It provides examples of stretching and translating graphs of f(x) = x^2 and generalizes the effects of stretches and translations on basic parent functions. The document concludes with instructions on combining multiple transformations and an example problem determining the x-intercepts resulting from a composite transformation.
1) Reflections of functions f(x) over the x-axis or y-axis produce new equations by changing the sign of the y-values or x-values respectively.
2) The inverse of a function f(x) is denoted f^-1(x) and is found by switching the x and y values when graphed, effectively reflecting over the line y=x.
3) For example, the inverse of f(x)=2x+5 is found by graphing f^-1(x) which treats x as the output and y as the input.
This document provides examples for graphing reciprocals of functions. It explains that for reciprocals, smaller numbers on the x-axis become larger on the y-axis, and vice versa. An example graphs the reciprocal of f(x)=1/x^2. It notes that reciprocals can be written in the form f(x)=k/x+h, where k and h are determined from the original function. Further examples graph the reciprocals of f(x)=2/x+4 and f(x)=sin(x).
This document discusses transformations of graphs including vertical and horizontal shifts. It provides examples of parent functions being shifted vertically by adding or subtracting a number, and horizontally by adding or subtracting inside or outside the function. Examples are given of shifting the graph of f(x)=sinx by 1 unit vertically and horizontally shifting and vertically shifting the graph of f(x)=x^2-3.
This document provides information for four tax situations including land and building assessments, mill rates, property frontages, improvement taxes, school and education levy taxes, tax credits, and penalties. The questions involve calculating statements and demands for residential properties with varying assessments, mill rates, improvement taxes, and school division taxes.