9.3 notes
•
0 likes•244 views
This document contains notes from a geometry class on reflections. It includes the definitions of a line of reflection and the coordinate rules for reflecting points across the x-axis, y-axis, lines y=x and y=-x. It also states that a reflection is an isometry and provides the reflection matrices used to calculate the reflected image of a point by multiplying the matrix and the coordinates of the pre-image point. The document records the student working through homework problems on reflections.
Report
Share
Report
Share
Download to read offline
![9.3 Reflections
February 13, 2014
Bellwork
Add or subtract
[6.3 –3.1]
1. [2.8 –9.2] + [3.5 6.1]
3. Triangle ABC has vertices A(2, –1 ), B(1, 3), and C
(–2, –2). Write a matrix equation that shows how to
find the image matrix that represents the
translation of ABC 4 units left and 5 units up.
Jan 279:14 AM
HW pg. 593 #422 even
1](https://image.slidesharecdn.com/9-140213131450-phpapp02/85/9-3-notes-1-320.jpg)
Recommended
Area between curves
This document discusses calculating the area between two curves. It provides the following key points:
1) The area between two curves f(x) and g(x) from x=a to x=b is calculated as the integral from a to b of f(x) - g(x) dx.
2) It provides examples of finding the area between various curve pairings by first finding their intersection points, then setting up and evaluating the integral from the top curve minus the bottom curve.
3) The final example shows how to set up and calculate the area between the curves x=3-y^2 and y=x-1 by integrating the top curve minus the bottom curve with respect
Lar calc10 ch07_sec1
This document discusses using integration to find the area between two curves. It defines the area between two functions f and g on an interval [a,b] as the area under f subtracted by the area under g. This is calculated using the integral from a to b of f(x) - g(x) dx. Examples are provided of finding the area between two non-intersecting curves and between two intersecting curves, where the intersection points define the limits of integration a and b. Integration is described as an accumulation process where the integral represents summing the areas of thin rectangles between the curves.
Surface areas and volumes gs
jstse 2015 question paper with solution,
jstse books,
jstse book for class 9 pdf,
jstse 2016-17,
how to prepare for jstse,
jstse 2015 answer key,
jstse exam sample paper for class 9,
jstse official website,
jstse previous year papers,
jstse,
21
The question asks to determine the equation of the tangent line to the curve y = f(x) = 5x^2 - 3x at the point (2,14). The curve is a parabola with the equation y = 5x^2 - 3x. To find the tangent line, we take the derivative of f(x) to find f'(x), then plug in the x-value of the point (2) to determine the slope. The slope and the point (2,14) are then used to find the equation of the tangent line using point-slope form.
Translations (day 2)
The document discusses transformations of plane figures using translations. It provides examples of graphing translations of triangles and quadrilaterals on a coordinate plane by adding or subtracting values from the x- and y-coordinates of each vertex. Students are reminded to submit their formative assessments and that IXL Skill Q.3 on translations was assigned.
2 5 Bzca5e
The document discusses various ways to transform graphs of functions including vertical and horizontal shifts, reflections, stretching and shrinking. It provides examples of transforming graphs by applying these techniques sequentially in a specified order: first horizontal shifting, then stretching or shrinking, then reflecting, and finally vertical shifting. The summary provides examples of transforming an original function f(x) into another function g(x) by applying these transformations.
Areas between curves
This document discusses calculating the area between two curves using integrals. It notes that the integral from a to b of f(x) - g(x) dx gives the area between the graphs of f and g, even if one or both curves dip below the x-axis. It asks what to do if both curves lie partially or entirely below the x-axis, or if one curve dips below while the other remains above. It concludes that you must find the intersection points of the curves, determine which is above and which is below over the interval, and compute the integral, being cautious about cases where the absolute value approach does not work.
K-map method
The document describes the Karnaugh map method for minimizing Boolean functions with various numbers of variables. It includes:
- Introduction to K-maps and their use for simplifying logic functions
- Construction of 2, 3, and 4 variable K-maps and the relationship between variable assignments and map cells
- Examples of simplifying 2-variable and 3-variable logic functions using K-maps
- Rules for grouping cells in K-maps to minimize logic functions
Recommended
Area between curves
This document discusses calculating the area between two curves. It provides the following key points:
1) The area between two curves f(x) and g(x) from x=a to x=b is calculated as the integral from a to b of f(x) - g(x) dx.
2) It provides examples of finding the area between various curve pairings by first finding their intersection points, then setting up and evaluating the integral from the top curve minus the bottom curve.
3) The final example shows how to set up and calculate the area between the curves x=3-y^2 and y=x-1 by integrating the top curve minus the bottom curve with respect
Lar calc10 ch07_sec1
This document discusses using integration to find the area between two curves. It defines the area between two functions f and g on an interval [a,b] as the area under f subtracted by the area under g. This is calculated using the integral from a to b of f(x) - g(x) dx. Examples are provided of finding the area between two non-intersecting curves and between two intersecting curves, where the intersection points define the limits of integration a and b. Integration is described as an accumulation process where the integral represents summing the areas of thin rectangles between the curves.
Surface areas and volumes gs
jstse 2015 question paper with solution,
jstse books,
jstse book for class 9 pdf,
jstse 2016-17,
how to prepare for jstse,
jstse 2015 answer key,
jstse exam sample paper for class 9,
jstse official website,
jstse previous year papers,
jstse,
21
The question asks to determine the equation of the tangent line to the curve y = f(x) = 5x^2 - 3x at the point (2,14). The curve is a parabola with the equation y = 5x^2 - 3x. To find the tangent line, we take the derivative of f(x) to find f'(x), then plug in the x-value of the point (2) to determine the slope. The slope and the point (2,14) are then used to find the equation of the tangent line using point-slope form.
Translations (day 2)
The document discusses transformations of plane figures using translations. It provides examples of graphing translations of triangles and quadrilaterals on a coordinate plane by adding or subtracting values from the x- and y-coordinates of each vertex. Students are reminded to submit their formative assessments and that IXL Skill Q.3 on translations was assigned.
2 5 Bzca5e
The document discusses various ways to transform graphs of functions including vertical and horizontal shifts, reflections, stretching and shrinking. It provides examples of transforming graphs by applying these techniques sequentially in a specified order: first horizontal shifting, then stretching or shrinking, then reflecting, and finally vertical shifting. The summary provides examples of transforming an original function f(x) into another function g(x) by applying these transformations.
Areas between curves
This document discusses calculating the area between two curves using integrals. It notes that the integral from a to b of f(x) - g(x) dx gives the area between the graphs of f and g, even if one or both curves dip below the x-axis. It asks what to do if both curves lie partially or entirely below the x-axis, or if one curve dips below while the other remains above. It concludes that you must find the intersection points of the curves, determine which is above and which is below over the interval, and compute the integral, being cautious about cases where the absolute value approach does not work.
K-map method
The document describes the Karnaugh map method for minimizing Boolean functions with various numbers of variables. It includes:
- Introduction to K-maps and their use for simplifying logic functions
- Construction of 2, 3, and 4 variable K-maps and the relationship between variable assignments and map cells
- Examples of simplifying 2-variable and 3-variable logic functions using K-maps
- Rules for grouping cells in K-maps to minimize logic functions
Area and Surface Area Volume
jstse 2015 question paper with solution,
jstse books,
jstse book for class 9 pdf,
jstse 2016-17,
how to prepare for jstse,
jstse 2015 answer key,
jstse exam sample paper for class 9,
jstse official website,
jstse previous year papers,
jstse,
Lesson 11 plane areas area by integration
This document discusses calculating the area under a curve using integration. It begins by approximating the area under an irregular shape using squares and rectangles. It then introduces defining the area A as a limit of approximating rectangles as their width approaches 0. This is written as the integral from a to b of f(x) dx, where f(x) is the curve. Examples are given of setting up definite integrals to calculate the areas under curves and between two curves. Steps for determining the area of a plane figure using integration are also provided.
Introduction to graphs and their ability to represent images
This document introduces graphs and their ability to represent images. It defines what a graph is and different types of graphs. It discusses common data structures used to store graphs like adjacency lists, adjacency matrices, and incidence matrices. It then covers how graphs can represent images by having vertices represent pixels and edges represent pixel adjacency. Region adjacency graphs and dual graphs are introduced as ways to represent image regions and relationships. Combinatorial maps are presented as another way to represent graphs and implicitly store dual graphs. Finally, applications of using graphs for image segmentation are mentioned.
Graphing Quadratic Functions
This document discusses how to graph quadratic functions by finding the axis of symmetry, vertex, and y-intercept. The axis of symmetry is located at x = -b/2a. The vertex is found by plugging the x-coordinate from the axis of symmetry into the original function. The y-intercept is simply the constant term c. Graphing involves marking the axis of symmetry, vertex, y-intercept, and sketching the basic quadratic shape.
Karnaugh Graph or K-Map
The document provides an introduction to Karnaugh maps (K-maps), which are a graphical method for simplifying Boolean logic expressions. It outlines the basics of K-maps, including their advantages, different types (2, 3, 4 and 5 variable maps), and how to group cells and derive simplified logic expressions. The document also discusses sum-of-products (SOP) form, product-of-sums (POS) form, don't care conditions, prime implicants, and includes examples of mapping truth tables to K-maps and simplifying expressions.
Presentation on Karnaugh Map
This presentation summarizes Karnaugh maps, which are a graphical technique for simplifying Boolean expressions. Karnaugh maps arrange the terms of a truth table in a two-dimensional grid, making common factors between terms visible. They can be used for functions with up to five variables. Examples show how to identify groupings of terms and simplify expressions using Karnaugh maps for two, three, and four variables. The presentation concludes with an example of a five variable Karnaugh map.
Area Under the Curve
The area under a curve between two x-values is the definite integral of the function. This area can be positive if above the x-axis and negative if below. To find the total area under a curve, the curve is broken into sections where the function is either above or below zero and the integral is evaluated over each section adding or subtracting areas as appropriate. The example problem demonstrates finding the total area under the curve defined by y=x^2-x-2 between -2 and 3 by breaking it into three sections and evaluating the integral over each.
Quadrilaterals Theorem and Axcioms
jstse 2015 question paper with solution,
jstse books,
jstse book for class 9 pdf,
jstse 2016-17,
how to prepare for jstse,
jstse 2015 answer key,
jstse exam sample paper for class 9,
jstse official website,
jstse previous year papers,
jstse,
Design of slabs using wood
This document discusses the Wood-Armer method for designing reinforced concrete slabs to resist calculated bending moments. It provides recommendations for determining design moments (Mx*, My*) to size the bottom and top reinforcement. The design moments account for twisting moments (Mxy) in addition to bending moments (Mx, My). An example calculation is shown for a simply supported slab where design moments are calculated at various points and change based on location. Reinforcement requirements also change across the slab depending on the design moments.
Day 1 examples u1f13
This document discusses horizontal shifts of functions. It states that a shift of "h" units to the right is represented by (x - h) and a shift of "h" units to the left is represented by (x + h). It provides examples of sketching graphs after a horizontal shift and finding the domain and range of a shifted function. The document also mentions stretching and compressing graphs vertically with "a" and gives examples of writing equations of translated functions in terms of a base function M(x). It concludes by assigning practice problems from page 168.
Assignment 2 unit
This document contains 7 problems involving 2-D transformations of geometric shapes including scaling, rotation, translation, reflection, shearing, and coordinate system changes. The problems involve finding new vertex coordinates after transformations like rotating a triangle 30 degrees about a given point, translating and rotating a triangle in different orders, reflecting a figure across a line and shearing it, and converting between coordinate systems. Original and transformed diagrams are required for each problem.
Applications of integrals
This document provides examples of using integrals to calculate the area of bounded regions. It gives formulas for finding the area under a curve, between two curves, and bounded by curves and lines. It then lists 24 practice problems involving finding areas bounded by geometric shapes, curves, and regions defined with inequalities. The problems cover areas bounded by circles, ellipses, parabolas, lines, and combinations thereof. They require the use of integral calculus to calculate the exact area or to sketch the region and set up the appropriate integral.
Day 1 examples u1f13
This document discusses horizontal shifts of functions. It states that a shift of "h" units to the right is represented by (x - h) and a shift of "h" units to the left is represented by (x + h). It provides examples of sketching graphs after a horizontal shift and finding the domain and range of a shifted function. The document also mentions stretching and compressing graphs vertically with "a" and gives examples of writing equations of translated functions in terms of a base function M(x). It concludes by assigning practice problems from page 168.
Eight Curve[1][1]
The document discusses the lemniscate curve defined by the equation (x^2 + y^2)^2 = 2a^2(x^2 - y^2). It provides steps to graph this curve using a graphing calculator and describes how the parameter a affects the shape of the curve. It also determines the points where the tangent line is horizontal and discusses potential real-world applications of the lemniscate curve, such as racetracks and figure skating.
Karnaugh maps
The document discusses Karnaugh maps, which are used to simplify logic problems with 2, 3, or 4 variables. It provides examples of 2-variable and 3-variable Karnaugh maps, showing how 1s are grouped to minimize logic. It also addresses why the ordering of states in Karnaugh maps is typically 00, 01, 11, 10 rather than 00, 01, 10, 11 to avoid race conditions in asynchronous logic.
Graphs
This document defines and explains key concepts related to graphs. It defines a graph as G=(V,E) where V is a set of vertices and E is a set of edges. It distinguishes between directed and undirected graphs. Key graph terminology explained includes adjacent nodes, paths, cycles, degrees, and connections. Graph searching algorithms depth-first search (DFS) and breadth-first search (BFS) are also summarized, including their ideas and implementations.
chapter22.ppt
The document discusses various graph algorithms and representations including:
- Adjacency lists and matrices for representing graphs
- Breadth-first search (BFS) which explores edges from a source vertex s level-by-level
- Depth-first search (DFS) which explores "deeper" first, producing a depth-first forest
- Classifying edges as tree, back, forward, or cross based on vertex colors in DFS
- Topological sorting of directed acyclic graphs (DAGs)
- Strongly connected components (SCCs) in directed graphs and using the transpose
Karnaugh map
Karnaugh maps (K-maps) are used to simplify Boolean logic expressions. A K-map arranges the minterms from a truth table into an array of cells where adjacent cells differ by only one variable. Groups of adjacent 1s in the K-map correspond to terms in a sum-of-products expression. The process of mapping a logic function onto a K-map and grouping 1s results in a minimum simplified expression. Don't care conditions can be treated as 1s to form larger groups for greater simplification. Both sum-of-products and product-of-sums expressions can be mapped and minimized using K-maps.
Use of integral calculus in engineering
The document discusses several applications of integration in engineering, including:
1) Finding shear force and bending moment by integrating shear force.
2) Finding the volume of solids of revolution by slicing the solid and integrating the area of each slice.
3) Using integration to calculate moments of inertia, which are important for measuring structural resistance to bending and buckling.
4) Finding the centroid or center of mass of irregular shapes by dividing them into simpler shapes and taking integrals of the coordinates weighted by area.
10.3 notes
The document appears to be notes from a math class on February 28th, 2014 about chord properties. It includes instructions for students to complete a bellwork activity individually without sharing answers. The class will later split into groups to learn different theorems - group A will cover theorem 10.3, group B theorem 10.4, and so on. The document provides space for each group to take notes. At the end, it reminds students to complete homework problems #3-19 odds from page 667.
3.1 notes
The document defines and describes various types of lines and angles. It defines parallel lines as lines that do not intersect and are coplanar. Skew lines do not intersect and are not coplanar. A transversal is a line that intersects two or more lines at different points, and can be used to define corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles. The document also presents the parallel postulate and perpendicular postulate.
12.6 notes
This document contains notes from a math class lesson on the surface area and volume of spheres. It includes the objectives of being able to apply the formulas for surface area and volume of spheres. Examples are provided for students to calculate the surface area and volume of various spheres given measurements like diameters and radii. Students are assigned homework problems applying these concepts.
More Related Content
What's hot
Area and Surface Area Volume
jstse 2015 question paper with solution,
jstse books,
jstse book for class 9 pdf,
jstse 2016-17,
how to prepare for jstse,
jstse 2015 answer key,
jstse exam sample paper for class 9,
jstse official website,
jstse previous year papers,
jstse,
Lesson 11 plane areas area by integration
This document discusses calculating the area under a curve using integration. It begins by approximating the area under an irregular shape using squares and rectangles. It then introduces defining the area A as a limit of approximating rectangles as their width approaches 0. This is written as the integral from a to b of f(x) dx, where f(x) is the curve. Examples are given of setting up definite integrals to calculate the areas under curves and between two curves. Steps for determining the area of a plane figure using integration are also provided.
Introduction to graphs and their ability to represent images
This document introduces graphs and their ability to represent images. It defines what a graph is and different types of graphs. It discusses common data structures used to store graphs like adjacency lists, adjacency matrices, and incidence matrices. It then covers how graphs can represent images by having vertices represent pixels and edges represent pixel adjacency. Region adjacency graphs and dual graphs are introduced as ways to represent image regions and relationships. Combinatorial maps are presented as another way to represent graphs and implicitly store dual graphs. Finally, applications of using graphs for image segmentation are mentioned.
Graphing Quadratic Functions
This document discusses how to graph quadratic functions by finding the axis of symmetry, vertex, and y-intercept. The axis of symmetry is located at x = -b/2a. The vertex is found by plugging the x-coordinate from the axis of symmetry into the original function. The y-intercept is simply the constant term c. Graphing involves marking the axis of symmetry, vertex, y-intercept, and sketching the basic quadratic shape.
Karnaugh Graph or K-Map
The document provides an introduction to Karnaugh maps (K-maps), which are a graphical method for simplifying Boolean logic expressions. It outlines the basics of K-maps, including their advantages, different types (2, 3, 4 and 5 variable maps), and how to group cells and derive simplified logic expressions. The document also discusses sum-of-products (SOP) form, product-of-sums (POS) form, don't care conditions, prime implicants, and includes examples of mapping truth tables to K-maps and simplifying expressions.
Presentation on Karnaugh Map
This presentation summarizes Karnaugh maps, which are a graphical technique for simplifying Boolean expressions. Karnaugh maps arrange the terms of a truth table in a two-dimensional grid, making common factors between terms visible. They can be used for functions with up to five variables. Examples show how to identify groupings of terms and simplify expressions using Karnaugh maps for two, three, and four variables. The presentation concludes with an example of a five variable Karnaugh map.
Area Under the Curve
The area under a curve between two x-values is the definite integral of the function. This area can be positive if above the x-axis and negative if below. To find the total area under a curve, the curve is broken into sections where the function is either above or below zero and the integral is evaluated over each section adding or subtracting areas as appropriate. The example problem demonstrates finding the total area under the curve defined by y=x^2-x-2 between -2 and 3 by breaking it into three sections and evaluating the integral over each.
Quadrilaterals Theorem and Axcioms
jstse 2015 question paper with solution,
jstse books,
jstse book for class 9 pdf,
jstse 2016-17,
how to prepare for jstse,
jstse 2015 answer key,
jstse exam sample paper for class 9,
jstse official website,
jstse previous year papers,
jstse,
Design of slabs using wood
This document discusses the Wood-Armer method for designing reinforced concrete slabs to resist calculated bending moments. It provides recommendations for determining design moments (Mx*, My*) to size the bottom and top reinforcement. The design moments account for twisting moments (Mxy) in addition to bending moments (Mx, My). An example calculation is shown for a simply supported slab where design moments are calculated at various points and change based on location. Reinforcement requirements also change across the slab depending on the design moments.
Day 1 examples u1f13
This document discusses horizontal shifts of functions. It states that a shift of "h" units to the right is represented by (x - h) and a shift of "h" units to the left is represented by (x + h). It provides examples of sketching graphs after a horizontal shift and finding the domain and range of a shifted function. The document also mentions stretching and compressing graphs vertically with "a" and gives examples of writing equations of translated functions in terms of a base function M(x). It concludes by assigning practice problems from page 168.
Assignment 2 unit
This document contains 7 problems involving 2-D transformations of geometric shapes including scaling, rotation, translation, reflection, shearing, and coordinate system changes. The problems involve finding new vertex coordinates after transformations like rotating a triangle 30 degrees about a given point, translating and rotating a triangle in different orders, reflecting a figure across a line and shearing it, and converting between coordinate systems. Original and transformed diagrams are required for each problem.
Applications of integrals
This document provides examples of using integrals to calculate the area of bounded regions. It gives formulas for finding the area under a curve, between two curves, and bounded by curves and lines. It then lists 24 practice problems involving finding areas bounded by geometric shapes, curves, and regions defined with inequalities. The problems cover areas bounded by circles, ellipses, parabolas, lines, and combinations thereof. They require the use of integral calculus to calculate the exact area or to sketch the region and set up the appropriate integral.
Day 1 examples u1f13
This document discusses horizontal shifts of functions. It states that a shift of "h" units to the right is represented by (x - h) and a shift of "h" units to the left is represented by (x + h). It provides examples of sketching graphs after a horizontal shift and finding the domain and range of a shifted function. The document also mentions stretching and compressing graphs vertically with "a" and gives examples of writing equations of translated functions in terms of a base function M(x). It concludes by assigning practice problems from page 168.
Eight Curve[1][1]
The document discusses the lemniscate curve defined by the equation (x^2 + y^2)^2 = 2a^2(x^2 - y^2). It provides steps to graph this curve using a graphing calculator and describes how the parameter a affects the shape of the curve. It also determines the points where the tangent line is horizontal and discusses potential real-world applications of the lemniscate curve, such as racetracks and figure skating.
Karnaugh maps
The document discusses Karnaugh maps, which are used to simplify logic problems with 2, 3, or 4 variables. It provides examples of 2-variable and 3-variable Karnaugh maps, showing how 1s are grouped to minimize logic. It also addresses why the ordering of states in Karnaugh maps is typically 00, 01, 11, 10 rather than 00, 01, 10, 11 to avoid race conditions in asynchronous logic.
Graphs
This document defines and explains key concepts related to graphs. It defines a graph as G=(V,E) where V is a set of vertices and E is a set of edges. It distinguishes between directed and undirected graphs. Key graph terminology explained includes adjacent nodes, paths, cycles, degrees, and connections. Graph searching algorithms depth-first search (DFS) and breadth-first search (BFS) are also summarized, including their ideas and implementations.
chapter22.ppt
The document discusses various graph algorithms and representations including:
- Adjacency lists and matrices for representing graphs
- Breadth-first search (BFS) which explores edges from a source vertex s level-by-level
- Depth-first search (DFS) which explores "deeper" first, producing a depth-first forest
- Classifying edges as tree, back, forward, or cross based on vertex colors in DFS
- Topological sorting of directed acyclic graphs (DAGs)
- Strongly connected components (SCCs) in directed graphs and using the transpose
Karnaugh map
Karnaugh maps (K-maps) are used to simplify Boolean logic expressions. A K-map arranges the minterms from a truth table into an array of cells where adjacent cells differ by only one variable. Groups of adjacent 1s in the K-map correspond to terms in a sum-of-products expression. The process of mapping a logic function onto a K-map and grouping 1s results in a minimum simplified expression. Don't care conditions can be treated as 1s to form larger groups for greater simplification. Both sum-of-products and product-of-sums expressions can be mapped and minimized using K-maps.
Use of integral calculus in engineering
The document discusses several applications of integration in engineering, including:
1) Finding shear force and bending moment by integrating shear force.
2) Finding the volume of solids of revolution by slicing the solid and integrating the area of each slice.
3) Using integration to calculate moments of inertia, which are important for measuring structural resistance to bending and buckling.
4) Finding the centroid or center of mass of irregular shapes by dividing them into simpler shapes and taking integrals of the coordinates weighted by area.
What's hot (19)
Introduction to graphs and their ability to represent images
Introduction to graphs and their ability to represent images
Viewers also liked
10.3 notes
The document appears to be notes from a math class on February 28th, 2014 about chord properties. It includes instructions for students to complete a bellwork activity individually without sharing answers. The class will later split into groups to learn different theorems - group A will cover theorem 10.3, group B theorem 10.4, and so on. The document provides space for each group to take notes. At the end, it reminds students to complete homework problems #3-19 odds from page 667.
3.1 notes
The document defines and describes various types of lines and angles. It defines parallel lines as lines that do not intersect and are coplanar. Skew lines do not intersect and are not coplanar. A transversal is a line that intersects two or more lines at different points, and can be used to define corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles. The document also presents the parallel postulate and perpendicular postulate.
12.6 notes
This document contains notes from a math class lesson on the surface area and volume of spheres. It includes the objectives of being able to apply the formulas for surface area and volume of spheres. Examples are provided for students to calculate the surface area and volume of various spheres given measurements like diameters and radii. Students are assigned homework problems applying these concepts.
7.1 & 7.2 notes
The document discusses the Pythagorean theorem and its converse. It provides examples of using the theorem to find the length of a hypotenuse or the area of a triangle. It also lists several Pythagorean triples and explains how to determine if a triangle is a right triangle using the converse of the theorem. The homework assignment is to complete all problems on the worksheet except problems 7-9 dealing with the converse and problem 21 which is extra credit.
4.3 notes
This document discusses the Side-Side-Side (SSS) theorem for proving triangle congruence. It states that if three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent. The document provides an example of two triangles, ΔABC and ΔDEF, where the sides are labeled as equal. It also discusses using Angle-Angle-Angle (AAA) to show similarity, not congruence, of triangles. The homework assignment is problems #5-19 odd, 24, 26 on page 236.
12.2 notes
This document discusses the surface area formulas for prisms and cylinders. For prisms, the surface area is calculated as the perimeter of the base multiplied by the height plus two times the area of the base. For cylinders, the surface area is calculated as two times pi times the radius times the height plus two times pi times the radius squared. The document provides examples of applying these formulas and assigns homework problems calculating surface areas of various prisms and cylinders.
12.1 notes
Students were instructed to make two solids by naming and coloring a base, folding faces, gluing edges, and displaying the solids. They were then asked to classify solids as prisms or pyramids based on the shape of the base. Finally, homework was assigned to complete problems 3 through 27 of odd numbers on page 798.
7.6 notes
This document contains instructions for solving various mathematical formulas by transforming them to solve for different variables. It provides examples of transforming formulas for area, perimeter, rate, distance, and temperature by solving for variables like length, rate, time, and Celsius. The goal is to practice transforming formulas to solve for the desired unknown variable.
10.1 notes
This document discusses tangent properties of circles. It defines various circle terms like radius, diameter, chord, secant, and tangent. It presents theorems for tangents including that a tangent is perpendicular to the radius and tangent segments from outside the circle are congruent. It provides examples applying these theorems to find missing side lengths. The document instructs the reader to draw and label examples of circle terms on a worksheet.
Slugging % & era notes
This document contains notes from a student on baseball statistics including batting average, slugging percentage, earned run average (ERA), and winning percentage. It provides the formulas for calculating batting average, slugging percentage as hits or home runs plus bases per at bat, ERA as earned runs times 9 over innings pitched, and winning percentage as games won over total games played. The student took these notes on April 8th while working on baseball statistics homework.
4.5 notes
The document discusses different postulates and theorems that can be used to prove triangles are congruent, including:
1) Angle-Side-Angle (ASA) - If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.
2) Angle-Angle-Side (AAS or SAA) - If two angles and the non-included side of one triangle are equal to two angles and the non-included side of another triangle, then the triangles are congruent.
3) Angle-Angle-Angle (AAA) only proves triangles are similar, not congruent. Side-Side-Angle (SSA
8.4 notes
The document discusses different types of quadrilaterals:
- Parallelograms have both pairs of opposite sides parallel.
- Rhombuses have four equal sides.
- Rectangles have four right angles.
- Squares are both rhombuses and rectangles, with four equal sides and four right angles.
Theorems state that a quadrilateral is a rhombus if its diagonals are perpendicular, or if each diagonal bisects a pair of opposite sides. A quadrilateral is a rectangle if its diagonals are parallel.
7.4 notes
The document outlines an agenda for a math class that includes writing equations. It provides three word problems asking students to write equations to determine: 1) the original price of a puppy that was $21 less than original price and bought for $48, 2) the number of miles driven for a two-day van rental that cost $79.46 with a $29.95 per day fee plus $0.12 per mile, and 3) the original price of a sweater that was on sale for $48 at 20% less than the original price. Students are assigned homework problems from page 360, numbers 1 through 11.
Prescribing Medicine
This document provides examples and instructions for calculating medication dosages when converting between different units of measurement. It gives five examples of dosage problems where the amount ordered is in a different unit than what is available. For each problem, the student is directed to set up a proportion, convert units to be the same, substitute the converted unit into the proportion, cross multiply, and solve to determine the amount that should be given based on what is available. The document also provides an additional practice problem for students to work through.
7.5 notes
This document contains notes from a math class on solving two-step inequalities. It includes the date, objective of the lesson which is solving two-step inequalities, examples of inequalities to solve, and a word problem involving an inequality about the maximum number of hikers an expedition can support given weight limits of food and equipment. The document appears to be a teacher's notes and worksheets for students covering solving two-step inequalities.
Conversions notes
This document provides information and examples about converting between different units of measurement for length, weight, liquid, time, and dry measurements. It includes questions asking students to convert between inches and feet, miles and feet, fractions of an inch, and measurements in inches. Tables are provided defining relationships between units for weight, liquid, time, and dry measurements.
12.5 notes
The document discusses finding the volume of pyramids and cones. It provides the formulas for calculating volume of a cone as 1/3πr^2h and volume of a pyramid as 1/3Bh, where B is the area of the base and h is the height. Examples are given to practice applying these formulas, such as finding the volume of ice cream in a cone or the area of the base of a trapezoidal pyramid given its volume and height.
Trig 1 notes
This document discusses trigonometric ratios and their use in right triangles. It defines the three basic trig functions - sine, cosine, and tangent - which relate angles to sides of a right triangle. Sine is defined as the ratio of the opposite side to the hypotenuse. Cosine is the ratio of the adjacent side to the hypotenuse. Tangent is the ratio of the opposite side to the adjacent side. Several examples are given of calculating trig ratios and solving for unknown sides or angles in right triangles. Angles of elevation and depression are also defined.
10.5 notes
The document discusses surface area formulas for prisms and cylinders. It defines surface area as the sum of the areas of all surfaces that enclose the solid. For prisms, surface area is calculated as the perimeter of the base multiplied by the height, plus twice the area of the base. For cylinders, surface area is the circumference of the circular base multiplied by the height, plus twice the area of the circular base. Examples are given to demonstrate how to apply these formulas.
Viewers also liked (19)
More from Mrs. Hedrick's Class
Strafford Volleyball Apparel
This document appears to be an order form for Strafford Indian Volleyball apparel and merchandise. It lists various items available for purchase including short sleeve t-shirts, long sleeve t-shirts, hoodies, wind shirts, shorts, track jackets, hats, and more. The items are available in a range of sizes from youth to adult sizes. Each item lists a price and there are options for different embroidery designs on some of the jackets and hats.
Ch 12 unit schedule
This document outlines the Geometry 2016 Chapter 12 unit on 3D shapes that will be covered from April 11th to April 29th. It includes the chapter sections and topics to be covered each day, such as different types of prisms and pyramids, as well as the homework assignments and assessments including quizzes, tests, and a study guide.
Ch 10 unit schedule
This document provides a schedule for Geometry Chapter 10 on Circles over a two week period from February 29th to March 11th and March 21st to March 25th. Each day covers a different section of the chapter, with assigned problems and quizzes listed. The schedule culminates with a paper plate review, studying for the chapter test, taking the test, and then correcting any errors on the test.
Ch 7 unit schedule
This document outlines the Geometry unit 7 schedule for January 2016. It includes lessons on sections 7.1 through 7.4 focusing on trigonometry, with worksheets and quizzes planned for most days. A practice quiz, study guide, and trigonometry test are scheduled for the third week. Snow days are noted on January 15th and 18th, with tutoring available by arrangement.
Stockton Tournament Schedule 2015
The document summarizes a volleyball tournament taking place on October 3, 2015 in Stockton. It outlines the tournament structure, including three pools (A, B, C) divided by age/skill level with 4 teams each. A schedule is provided for round robin pool play matches between the teams, with the top two teams from each pool and the next two best records advancing to bracket playoff rounds. Bracket play will begin at 1:30 PM and be a best-of-three format to determine 1st, 2nd, and 3rd place trophies.
Lake Volley Fest
The JV Lake Volley Fest 2015 volleyball tournament will take place on September 26th. Seven teams will be split into the Purple Pool and Gold Pool, with the top two teams from each pool advancing to the Championship Bracket and the bottom two advancing to the Consolation Bracket. The tournament schedule lists the matchups for each of the six time slots between 8:30am and 12:15pm across the two courts. Plaques will be awarded to the first and second place finishers.
Lake Volley Fest
Camdenton High School will host the 2015 Lake Volley Fest Tournament on September 26th. There will be two courts located on campus for pool play and bracket play. Teams will be responsible for providing their own line judge. The top four teams will advance to the championship bracket, while the bottom four teams will play in the consolation bracket. Plaques will be awarded to the first and second place finishers.
Volleyfest Schedule 2015
This document contains the schedule for the 19th Annual Strafford Volleyfest volleyball tournament held on September 19, 2015. It lists the three courts where matches will take place and provides the schedule of games for each court, with start times ranging from 8:30 AM to 6:15 PM. It identifies the 12 participating schools that are divided into three pools based on color. It explains that after pool play, the top six teams will advance to the Championship Bracket and the bottom six to the Consolation Bracket for playoff matches.
2015 Branson Tournament Schedule
The document provides information about the 2015 Branson Invitational volleyball tournament including pool and bracket structures. Sixteen teams will be divided into four pools of four teams each to play a round robin. Pool play will consist of best-of-three sets and teams will be ranked 1-16 based on win-loss record, point differential, and head-to-head results. The top eight teams will advance to the gold bracket and bottom eight to the silver bracket for single elimination bracket play consisting of best-of-three sets.
12.7 notes
This document contains notes from a math class on similar solids. It defines similar solids as two solids of the same type that have equal ratios, known as a scale factor. It then states the Similar Solids Theorem: if two similar solids have a scale factor of a:b, their corresponding areas have a ratio of a2:b2 and their corresponding volumes have a ratio of a3:b3. Examples of homework problems involving similar solids are listed.
12.6 notes
The document discusses surface area and volume formulas for spheres. It provides examples of calculating the surface area of spheres with given diameters, as well as the volume of spheres and other objects like snow cones that can be modeled as spheres. Students are assigned homework problems applying these formulas to calculate surface areas and volumes.
12.5 notes
The document is notes from a math class lesson on finding the volumes of cones and pyramids. It includes the objectives of learning the formulas for these volumes. The formulas given are that the volume of a cone is 1/3πr^2h and the volume of a pyramid is 1/3Bh, where B is the area of the base and h is the height. There are examples provided of applying these formulas to find volumes.
12.4 notes
This document contains notes from a math lesson on finding the volumes of prisms and cylinders. It defines volume as the amount of space inside an object. It explains that to find the volume of a prism or cylinder, you calculate the area of the base and multiply it by the height. For a prism, the base can be any shape and its area formula is used. For a cylinder, the base is a circle so the volume formula is πr^2h, with r as the radius and h as the height. Examples of volume problems are shown and homework problems are assigned from the textbook.
Indian volleyball tournament
A volleyball tournament will be held on May 2nd at 9am at the Max Evans Gym to benefit the Strafford Indian Volleyball Program. The tournament will feature fun rules, games and prizes and cost $10 per person to register, either as part of a team of 6-8 players or individually. People can register their teams on Facebook or by contacting the coaches Ashley Bough or Angelina Hedrick by May 1st.
12.3 notes
This document contains notes and examples for calculating the surface area of pyramids and cones. It provides the formulas for finding the surface area of regular pyramids and cones. For pyramids, the surface area equals one-half the perimeter of the base times the sum of the slant height and apothem. For cones, the surface area equals pi times the radius squared plus pi times the radius times the slant height. The document includes practice problems applying these formulas to find the surface area of various pyramids and cones.
12.2 notes
The document discusses surface area formulas for prisms and cylinders. It defines surface area as the sum of the areas of all surfaces that enclose a solid. For prisms, surface area is calculated as the perimeter of the base multiplied by the height, plus twice the area of the base. For cylinders, surface area is the circumference of the base multiplied by the height, plus twice the area of the circular base. The document provides examples of applying these formulas to prisms and cylinders.
12.5 notes
This document contains information about the law of cosines from a geometry homework assignment on page 678 problems 14 through 20, dated April 09, 2015. The document title and date are repeated multiple times.
12.4 notes
This document contains information about the law of sines for a math homework assignment. It lists the topic as the law of sines and directs the student to problems 15-17 and 29-31 on page 672 of their homework, which was assigned on April 08, 2015. The document repeats this information four times.
12.1 notes
This document contains notes from a math class where students were working on homework problems involving trigonometry (SOHCAHTOA) and multiples of 3. The notes are dated April 08, 2015 and reference homework page 648 problems 12 through 36 dealing with multiples of 3.
11.7 notes
This document contains notes from an 11th grade math class on the topic of geometric probability. It includes examples of calculating the probability of events based on ratios of lengths and areas, such as the probability of a driver speeding in front of a school based on the length of road in front of the school over the total road length. The homework problems assigned were problems 4-10 of the even numbers, 20-23, and 30-33 on page 774 of the textbook.
More from Mrs. Hedrick's Class (20)
Recently uploaded
BBR 2024 Summer Sessions Interview Training
Qualitative research interview training by Professor Katrina Pritchard and Dr Helen Williams
Walmart Business+ and Spark Good for Nonprofits.pdf
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
Advanced Java[Extra Concepts, Not Difficult].docx
This is part 2 of my Java Learning Journey. This contains Hashing, ArrayList, LinkedList, Date and Time Classes, Calendar Class and more.
How to Fix the Import Error in the Odoo 17
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
Azure Interview Questions and Answers PDF By ScholarHat
Azure Interview Questions and Answers PDF By ScholarHat
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptxMohd Adib Abd Muin, Senior Lecturer at Universiti Utara Malaysia
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective UpskillingExcellence Foundation for South Sudan
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama UniversityAkanksha trivedi rama nursing college kanpur.
Natural birth techniques are various type such as/ water birth , alexender method, hypnosis, bradley method, lamaze method etcThe Diamonds of 2023-2024 in the IGRA collection
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
Community pharmacy- Social and preventive pharmacy UNIT 5
Covered community pharmacy topic of the subject Social and preventive pharmacy for Diploma and Bachelor of pharmacy
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Aberdeen
Recently uploaded (20)
Walmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdf
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
Azure Interview Questions and Answers PDF By ScholarHat
Azure Interview Questions and Answers PDF By ScholarHat
Liberal Approach to the Study of Indian Politics.pdf
Liberal Approach to the Study of Indian Politics.pdf
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Pride Month Slides 2024 David Douglas School District
Pride Month Slides 2024 David Douglas School District
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Community pharmacy- Social and preventive pharmacy UNIT 5
Community pharmacy- Social and preventive pharmacy UNIT 5
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
9.3 notes
- 2. 9.3 Reflections February 13, 2014 9.3 Reflections snoitcelfeR 3.9 Line of reflection: mirror line Jan 2710:41 AM HW pg. 593 #422 even 2
- 4. 9.3 Reflections February 13, 2014 Coordinate Rules for Reflections x-axis: (x,-y) y-axis: (-x,y) y = x: (y, x) y = -x: (-y,-x) snoitcelfeR Jan 2712:31 PM HW pg. 593 #422 even 4
- 5. 9.3 Reflections February 13, 2014 Reflection Theorem: A reflection is an isometry. Jan 2711:46 AM HW pg. 593 #422 even 5
- 6. 9.3 Reflections February 13, 2014 Reflection Matrix To find the reflected image, write the reflection matrix to the left of the pre-image matrix, then multiply. [ ] x-axis: 1 0 0 -1 [ y-axis: -1 0 ] 0 1 Jan 271:34 PM HW pg. 593 #422 even 6
- 7. 9.3 Reflections February 13, 2014 HW pg. 593 #4-22 evens Jan 271:33 PM HW pg. 593 #422 even 7