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WORD LESSON: EXPONENTIAL DECAY Exponential decay is generally applied to word problems that involve financial applications as well as those that deal with radioactive decay, medicine dosages, and population decline. To decay exponentially means that the topic being studied is decreasing in proportion to the amount that was previously present. The following is an example of an exponential decay problem. BASIC QUADRATIC TERMINOLOGY Regardless of whether the parabola opens up or down, all parabolas will have a vertex.If the parabola opens up, the vertex is the minimum point or the place where the graph bottoms out. If the parabola opens down, the vertex is the maximum point or the place where the graph reaches its peak. Quadratic functions can be written in one of two ways, depending on what you are trying to do with the WORD LESSON: WORKING TOGETHER Word Lesson: Working Together. In order to solve problems involving working together, it is necessary to. analyze and understand the problem so that you can construct an equation for the problem. know how to solve a linear equation in terms of one variable. know how to solve rational equations. The goal of a “working together” problemis
WORD LESSON: PROPORTIONS Word Lesson: Proportions. In order to solve problems involving proportions, you should be able to: work with fractions. set up ratios. set up equivalent fractions. cross multiply. solve one-step equations. A proportion sets two ratios equal to each other. In one ratio, one of the quantities is not known. MULTIPLICATION RULE OF PROBABILITY The addition rule helped us solve problems when we performed one task and wanted to know the probability of two things happening during that task. This lesson deals with the multiplication rule. The multiplication rule also deals with two events, but in these problems the events occur as a result of more than one task (rolling one die then another, drawing two cards, spinning a spinner twice WORD LESSON: EXPONENTIAL GROWTH Exponential growth is generally applied to word problems such as compound interest problems and population growth problems. To grow exponentially means that the topic being studied is increasing in proportion to what was previously there. For example, money deposited in the bank earns interest that is added to the money previously inthe bank.
SOLVING LOGARITHMIC EQUATIONS Solving logarithmic equations usually requires using properties of logarithms.The reason you usually need to apply these properties is so that you will have a single logarithmic expression on one or both sides of the equation. Once you have used properties of logarithms to condense any log expressions in the equation, you can solve the problem by changing the logarithmic equation into an WORD PROBLEM EXERCISES: APPLICATIONS OF 3 EQUATIONS WITH 3 The currents running through an electrical system are given by the following system of equations. The three currents, I1, I2, and I3, are measured in amps. Solve the system to find the currents in this circuit. I 1 + 2I 2 - I 3 = 0.425 3I 1 - I 2 + 2I 3 = 2.225 5I 1 + I 2+ 2I 3 = 3.775
WORD PROBLEM EXERCISES: ARC LENGTHS Assuming that the Earth is a sphere of radius 4000 miles, find the distance between the following two cities whose latitudes are given. You may assume that these cities are on the same basic longitude. Cincinnati, Ohio (39º 8’ 46” N) and Huntsville, Alabama (34º43’ 41” N)
WORD LESSON: LINEAR REGRESSION Linear Regression is a process by which the equation of a line is found that “best fits” a given set of data. The line of best fit approximates the best linear representation for your data. One very important aspect of a regression line is the relationship between the equation and the “science quantity” often represented by the slopeof the line.
WORD LESSON: EXPONENTIAL DECAY Exponential decay is generally applied to word problems that involve financial applications as well as those that deal with radioactive decay, medicine dosages, and population decline. To decay exponentially means that the topic being studied is decreasing in proportion to the amount that was previously present. The following is an example of an exponential decay problem. BASIC QUADRATIC TERMINOLOGY Regardless of whether the parabola opens up or down, all parabolas will have a vertex.If the parabola opens up, the vertex is the minimum point or the place where the graph bottoms out. If the parabola opens down, the vertex is the maximum point or the place where the graph reaches its peak. Quadratic functions can be written in one of two ways, depending on what you are trying to do with the WORD LESSON: WORKING TOGETHER Word Lesson: Working Together. In order to solve problems involving working together, it is necessary to. analyze and understand the problem so that you can construct an equation for the problem. know how to solve a linear equation in terms of one variable. know how to solve rational equations. The goal of a “working together” problemis
WORD LESSON: PROPORTIONS Word Lesson: Proportions. In order to solve problems involving proportions, you should be able to: work with fractions. set up ratios. set up equivalent fractions. cross multiply. solve one-step equations. A proportion sets two ratios equal to each other. In one ratio, one of the quantities is not known. MULTIPLICATION RULE OF PROBABILITY The addition rule helped us solve problems when we performed one task and wanted to know the probability of two things happening during that task. This lesson deals with the multiplication rule. The multiplication rule also deals with two events, but in these problems the events occur as a result of more than one task (rolling one die then another, drawing two cards, spinning a spinner twice WORD LESSON: EXPONENTIAL GROWTH Exponential growth is generally applied to word problems such as compound interest problems and population growth problems. To grow exponentially means that the topic being studied is increasing in proportion to what was previously there. For example, money deposited in the bank earns interest that is added to the money previously inthe bank.
SOLVING LOGARITHMIC EQUATIONS Solving logarithmic equations usually requires using properties of logarithms.The reason you usually need to apply these properties is so that you will have a single logarithmic expression on one or both sides of the equation. Once you have used properties of logarithms to condense any log expressions in the equation, you can solve the problem by changing the logarithmic equation into an WORD PROBLEM EXERCISES: APPLICATIONS OF 3 EQUATIONS WITH 3 The currents running through an electrical system are given by the following system of equations. The three currents, I1, I2, and I3, are measured in amps. Solve the system to find the currents in this circuit. I 1 + 2I 2 - I 3 = 0.425 3I 1 - I 2 + 2I 3 = 2.225 5I 1 + I 2+ 2I 3 = 3.775
WORD PROBLEM EXERCISES: ARC LENGTHS Assuming that the Earth is a sphere of radius 4000 miles, find the distance between the following two cities whose latitudes are given. You may assume that these cities are on the same basic longitude. Cincinnati, Ohio (39º 8’ 46” N) and Huntsville, Alabama (34º43’ 41” N)
MULTIPLICATION RULE OF PROBABILITY The addition rule helped us solve problems when we performed one task and wanted to know the probability of two things happening during that task. This lesson deals with the multiplication rule. The multiplication rule also deals with two events, but in these problems the events occur as a result of more than one task (rolling one die then another, drawing two cards, spinning a spinner twice WORD LESSON: MODELING WITH SINUSOIDS 2 Word Lesson: Modeling with Sinusoids 2. In order to solve problems which require a sinusoidal model, it is necessary to. use basic graphing skills for sine and cosine. know how to find amplitude, period, frequency, displacement, and phase shift. know that use of APPLICATIONS OF EXPONENTIAL FUNCTIONS The best thing about exponential functions is that they are so useful in real world situations. Exponential functions are used to model populations, carbon date artifacts, help coroners determine time of death, compute investments, as well as many other applications. WORD LESSON: WORKING TOGETHER Word Lesson: Working Together. In order to solve problems involving working together, it is necessary to. analyze and understand the problem so that you can construct an equation for the problem. know how to solve a linear equation in terms of one variable. know how to solve rational equations. The goal of a “working together” problemis
WORD LESSON: VECTORS NON-RIGHT TRIANGLES First we make a diagram in standard position. The attempted flight path of the plane is vector OX.Notice that the angle shown is 50° because the 40° bearing is measured clockwise from North. The vector XY represents the wind from the South. The vector OY is the resultant path of the plane, affected by the wind. In the diagram shown below, the known magnitude and angle are labeled. SOLVING LOGARITHMIC EQUATIONS Solving logarithmic equations usually requires using properties of logarithms.The reason you usually need to apply these properties is so that you will have a single logarithmic expression on one or both sides of the equation. Once you have used properties of logarithms to condense any log expressions in the equation, you can solve the problem by changing the logarithmic equation into an WORD LESSON: EXPONENTIAL GROWTH Exponential growth is generally applied to word problems such as compound interest problems and population growth problems. To grow exponentially means that the topic being studied is increasing in proportion to what was previously there. For example, money deposited in the bank earns interest that is added to the money previously inthe bank.
WORD LESSON: PERCENT INCREASE AND DECREASE The solution to this problem begins by finding how much the decrease was. This is done by taking 2000 - 1500 = 500. So the amount of decrease is 500. Now we divide that number by the original amount, or the football attendance in 2003, which was 2000. So the conclusion is that football attendance decreased by 25% from 2003 to 2004. WORD PROBLEM EXERCISES: ARC LENGTHS Assuming that the Earth is a sphere of radius 4000 miles, find the distance between the following two cities whose latitudes are given. You may assume that these cities are on the same basic longitude. Cincinnati, Ohio (39º 8’ 46” N) and Huntsville, Alabama (34º43’ 41” N)
ECONOMICS GRAPHS: PERCENT INCOME VS PERCENT OF POPULATION Economics Graphs: Percent Income vs Percent of Population. Question Group #1. Directions and/or Common Information: This graph is known as the. 1. National Income Curve. Lorenz curve. WORD LESSON: EXPONENTIAL DECAY Exponential decay is generally applied to word problems that involve financial applications as well as those that deal with radioactive decay, medicine dosages, and population decline. To decay exponentially means that the topic being studied is decreasing in proportion to the amount that was previously present. The following is an example of an exponential decay problem. BASIC QUADRATIC TERMINOLOGY Regardless of whether the parabola opens up or down, all parabolas will have a vertex.If the parabola opens up, the vertex is the minimum point or the place where the graph bottoms out. If the parabola opens down, the vertex is the maximum point or the place where the graph reaches its peak. Quadratic functions can be written in one of two ways, depending on what you are trying to do with the MULTIPLICATION RULE OF PROBABILITY The addition rule helped us solve problems when we performed one task and wanted to know the probability of two things happening during that task. This lesson deals with the multiplication rule. The multiplication rule also deals with two events, but in these problems the events occur as a result of more than one task (rolling one die then another, drawing two cards, spinning a spinner twice WORD LESSON: MODELING WITH SINUSOIDS 2 Word Lesson: Modeling with Sinusoids 2. In order to solve problems which require a sinusoidal model, it is necessary to. use basic graphing skills for sine and cosine. know how to find amplitude, period, frequency, displacement, and phase shift. know that use of WORD LESSON: LINEAR REGRESSION Linear Regression is a process by which the equation of a line is found that “best fits” a given set of data. The line of best fit approximates the best linear representation for your data. One very important aspect of a regression line is the relationship between the equation and the “science quantity” often represented by the slopeof the line.
WORD LESSON: CIRCLES When two secants, or a secant and a tangent, are drawn to a circle from the same external point, one of the following two relationships exists. The first is between the products of the lengths of the external portion of the secant and the lengths of the entire secant. The second is between the square of the length of the tangent segment and the external portion of the secant and the length of APPLICATIONS OF EXPONENTIAL FUNCTIONS The best thing about exponential functions is that they are so useful in real world situations. Exponential functions are used to model populations, carbon date artifacts, help coroners determine time of death, compute investments, as well as many other applications. WORD LESSON: QUADRATIC REGRESSION Quadratic Regression is a process by which the equation of a parabola is found that “best fits” a given set of data. Let's look at an example of a quadratic regression problem. The table below lists the total estimated numbers of AIDS cases, by year of diagnosis from 1999 to 2003 in the United States (Source: US Dept. of Health and Human Services, Centers for Disease Control and Prevention WORD PROBLEM EXERCISES: LAW OF COSINES Word Problem Exercises: Law of Cosines. General Questions. To approximate the length of a lake, a surveyor starts at one end of the lake and walks 245 yards. He then turns 110º and walks 270 yards until he arrives at the other end of the lake. Approximately how longis the lake?
WORD PROBLEM EXERCISES: APPLICATIONS OF 3 EQUATIONS WITH 3 The currents running through an electrical system are given by the following system of equations. The three currents, I1, I2, and I3, are measured in amps. Solve the system to find the currents in this circuit. I 1 + 2I 2 - I 3 = 0.425 3I 1 - I 2 + 2I 3 = 2.225 5I 1 + I 2+ 2I 3 = 3.775
WORD LESSON: EXPONENTIAL DECAY Exponential decay is generally applied to word problems that involve financial applications as well as those that deal with radioactive decay, medicine dosages, and population decline. To decay exponentially means that the topic being studied is decreasing in proportion to the amount that was previously present. The following is an example of an exponential decay problem. BASIC QUADRATIC TERMINOLOGY Regardless of whether the parabola opens up or down, all parabolas will have a vertex.If the parabola opens up, the vertex is the minimum point or the place where the graph bottoms out. If the parabola opens down, the vertex is the maximum point or the place where the graph reaches its peak. Quadratic functions can be written in one of two ways, depending on what you are trying to do with the MULTIPLICATION RULE OF PROBABILITY The addition rule helped us solve problems when we performed one task and wanted to know the probability of two things happening during that task. This lesson deals with the multiplication rule. The multiplication rule also deals with two events, but in these problems the events occur as a result of more than one task (rolling one die then another, drawing two cards, spinning a spinner twice WORD LESSON: MODELING WITH SINUSOIDS 2 Word Lesson: Modeling with Sinusoids 2. In order to solve problems which require a sinusoidal model, it is necessary to. use basic graphing skills for sine and cosine. know how to find amplitude, period, frequency, displacement, and phase shift. know that use of WORD LESSON: LINEAR REGRESSION Linear Regression is a process by which the equation of a line is found that “best fits” a given set of data. The line of best fit approximates the best linear representation for your data. One very important aspect of a regression line is the relationship between the equation and the “science quantity” often represented by the slopeof the line.
WORD LESSON: CIRCLES When two secants, or a secant and a tangent, are drawn to a circle from the same external point, one of the following two relationships exists. The first is between the products of the lengths of the external portion of the secant and the lengths of the entire secant. The second is between the square of the length of the tangent segment and the external portion of the secant and the length of APPLICATIONS OF EXPONENTIAL FUNCTIONS The best thing about exponential functions is that they are so useful in real world situations. Exponential functions are used to model populations, carbon date artifacts, help coroners determine time of death, compute investments, as well as many other applications. WORD LESSON: QUADRATIC REGRESSION Quadratic Regression is a process by which the equation of a parabola is found that “best fits” a given set of data. Let's look at an example of a quadratic regression problem. The table below lists the total estimated numbers of AIDS cases, by year of diagnosis from 1999 to 2003 in the United States (Source: US Dept. of Health and Human Services, Centers for Disease Control and Prevention WORD PROBLEM EXERCISES: LAW OF COSINES Word Problem Exercises: Law of Cosines. General Questions. To approximate the length of a lake, a surveyor starts at one end of the lake and walks 245 yards. He then turns 110º and walks 270 yards until he arrives at the other end of the lake. Approximately how longis the lake?
WORD PROBLEM EXERCISES: APPLICATIONS OF 3 EQUATIONS WITH 3 The currents running through an electrical system are given by the following system of equations. The three currents, I1, I2, and I3, are measured in amps. Solve the system to find the currents in this circuit. I 1 + 2I 2 - I 3 = 0.425 3I 1 - I 2 + 2I 3 = 2.225 5I 1 + I 2+ 2I 3 = 3.775
ALGEBRALAB: MAKING MATH AND SCIENCE CONNECTIONS Welcome to AlgebraLAB, an online learning environment that focuses on topics and skills from high school mathematics that students must be able to draw upon in their introductory science courses.Since math is the language of science, science courses are often where students first realize “Oh, so this is why we learned that in algebra ” ALGEBRALAB: HANDS-ON ACTIVITIES Table of Contents. Given below is a comprehensive listing of all topics on which hands-on activities have been written. Clicking on a topic's name will open a list of its current curriculum. Clicking on an title will take you to the chosen activity. If you would like to locate a specific activity on a subject of your choice, use our search BASIC QUADRATIC TERMINOLOGY Regardless of whether the parabola opens up or down, all parabolas will have a vertex.If the parabola opens up, the vertex is the minimum point or the place where the graph bottoms out. If the parabola opens down, the vertex is the maximum point or the place where the graph reaches its peak. Quadratic functions can be written in one of two ways, depending on what you are trying to do with the WORD LESSON: LINEAR REGRESSION Linear Regression is a process by which the equation of a line is found that “best fits” a given set of data. The line of best fit approximates the best linear representation for your data. One very important aspect of a regression line is the relationship between the equation and the “science quantity” often represented by the slopeof the line.
WORD LESSON: CIRCLES When two secants, or a secant and a tangent, are drawn to a circle from the same external point, one of the following two relationships exists. The first is between the products of the lengths of the external portion of the secant and the lengths of the entire secant. The second is between the square of the length of the tangent segment and the external portion of the secant and the length of APPLICATIONS OF EXPONENTIAL FUNCTIONS The best thing about exponential functions is that they are so useful in real world situations. Exponential functions are used to model populations, carbon date artifacts, help coroners determine time of death, compute investments, as well as many other applications. TRIGONOMETRY: OBLIQUE TRIANGLES Derivation of the Law of Sines: To calculate side or angle lengths of right triangles, you can set up a trigonometric ratio using sine, cosine, or tangent. However, if the triangle does not include a right angle, these basic trigonometric ratios do not apply. Triangles that do not have a right angle are called oblique triangles. Although the basic trig ratios do not apply, they can be modified WORD LESSON: BORDER PROBLEMS A typical 60-pound bay of pre-mixed concrete costs between $1.35-$1.80 and yields one-half of a cubic foot. They would need a minimum of 68 bags to complete the project: 68 x $1.80 = $122.40 plus a strong back. One cubic yard equals (1 yd) 3 = (3 ft) 3 = 27 ft 3, so they will need 34 ft 3 /27 ft 3 = 1.26 yd 3. WORD PROBLEMS: RATES, SALARIES, AND COMMISSIONS Rewrite each equation so that they are in the form . Multiply the bottom row by - 1: Add the two rows: Divide both sides by -0. 1: minutes. To find the monthly cost, solve for y using either of the original equations: dollars. Therefore, the cost for using eachcompany’s
WORD PROBLEM EXERCISES: ARC LENGTHS Assuming that the Earth is a sphere of radius 4000 miles, find the distance between the following two cities whose latitudes are given. You may assume that these cities are on the same basic longitude. Cincinnati, Ohio (39º 8’ 46” N) and Huntsville, Alabama (34º43’ 41” N)
BASIC QUADRATIC TERMINOLOGY Regardless of whether the parabola opens up or down, all parabolas will have a vertex.If the parabola opens up, the vertex is the minimum point or the place where the graph bottoms out. If the parabola opens down, the vertex is the maximum point or the place where the graph reaches its peak. Quadratic functions can be written in one of two ways, depending on what you are trying to do with the MULTIPLICATION RULE OF PROBABILITY The addition rule helped us solve problems when we performed one task and wanted to know the probability of two things happening during that task. This lesson deals with the multiplication rule. The multiplication rule also deals with two events, but in these problems the events occur as a result of more than one task (rolling one die then another, drawing two cards, spinning a spinner twice WORD LESSON: EXPONENTIAL DECAY Exponential decay is generally applied to word problems that involve financial applications as well as those that deal with radioactive decay, medicine dosages, and population decline. To decay exponentially means that the topic being studied is decreasing in proportion to the amount that was previously present. The following is an example of an exponential decay problem. WORD LESSON: MODELING WITH SINUSOIDS 2 Word Lesson: Modeling with Sinusoids 2. In order to solve problems which require a sinusoidal model, it is necessary to. use basic graphing skills for sine and cosine. know how to find amplitude, period, frequency, displacement, and phase shift. know that use of WORD LESSON: LINEAR REGRESSION Linear Regression is a process by which the equation of a line is found that “best fits” a given set of data. The line of best fit approximates the best linear representation for your data. One very important aspect of a regression line is the relationship between the equation and the “science quantity” often represented by the slopeof the line.
APPLICATIONS OF EXPONENTIAL FUNCTIONS The best thing about exponential functions is that they are so useful in real world situations. Exponential functions are used to model populations, carbon date artifacts, help coroners determine time of death, compute investments, as well as many other applications. MAXIMUM AND MINIMUM VALUES OF POLYNOMIALS These four points can occur because P (x) is a polynomial of degree 5. The maximum points are located at x = 0. 77 and -0. 80. The maximum values at these points are 0. 69 and 1. 57 respectively. The minimum points are located at x = -0. 05 and 1. 68. The minimum values are -2. 02 and -6. 00 respectively. WORD PROBLEM EXERCISES: LAW OF SINES 4. Two people are walking toward each other on a path through the park. The path runs east and west. A hot air balloon is directly above the path between them. One of the walkers, a female, sees the balloon when looking east at an angle of elevation of 46°. The other walker, a male, sees the balloon looking west at an angle of elevation of72°.
WORD PROBLEM EXERCISES: SCIENCE 2. A cup of gold colored metal beads was measured to have a mass 425 grams. By water displacement, the volume of the beads was calculated to be 48.0 cm 3 . Given the following densities, identify the metal. 3. I threw a plastic ball in the pool for my dog to fetch. The mass of the ball was 125 grams. BIOLOGY GRAPHS: ISLAND BIOGEOGRAPHY Biology Graphs: Island Biogeography. The theory of island biogeography, developed by Robert MacArthur and Edward O. Wilson, looks to explain the differences in species diversity with island size (for example, why large islands tend to have a greater number of species of a certain category than small islands). BASIC QUADRATIC TERMINOLOGY Regardless of whether the parabola opens up or down, all parabolas will have a vertex.If the parabola opens up, the vertex is the minimum point or the place where the graph bottoms out. If the parabola opens down, the vertex is the maximum point or the place where the graph reaches its peak. Quadratic functions can be written in one of two ways, depending on what you are trying to do with the MULTIPLICATION RULE OF PROBABILITY The addition rule helped us solve problems when we performed one task and wanted to know the probability of two things happening during that task. This lesson deals with the multiplication rule. The multiplication rule also deals with two events, but in these problems the events occur as a result of more than one task (rolling one die then another, drawing two cards, spinning a spinner twice WORD LESSON: EXPONENTIAL DECAY Exponential decay is generally applied to word problems that involve financial applications as well as those that deal with radioactive decay, medicine dosages, and population decline. To decay exponentially means that the topic being studied is decreasing in proportion to the amount that was previously present. The following is an example of an exponential decay problem. WORD LESSON: MODELING WITH SINUSOIDS 2 Word Lesson: Modeling with Sinusoids 2. In order to solve problems which require a sinusoidal model, it is necessary to. use basic graphing skills for sine and cosine. know how to find amplitude, period, frequency, displacement, and phase shift. know that use of WORD LESSON: LINEAR REGRESSION Linear Regression is a process by which the equation of a line is found that “best fits” a given set of data. The line of best fit approximates the best linear representation for your data. One very important aspect of a regression line is the relationship between the equation and the “science quantity” often represented by the slopeof the line.
APPLICATIONS OF EXPONENTIAL FUNCTIONS The best thing about exponential functions is that they are so useful in real world situations. Exponential functions are used to model populations, carbon date artifacts, help coroners determine time of death, compute investments, as well as many other applications. MAXIMUM AND MINIMUM VALUES OF POLYNOMIALS These four points can occur because P (x) is a polynomial of degree 5. The maximum points are located at x = 0. 77 and -0. 80. The maximum values at these points are 0. 69 and 1. 57 respectively. The minimum points are located at x = -0. 05 and 1. 68. The minimum values are -2. 02 and -6. 00 respectively. WORD PROBLEM EXERCISES: LAW OF SINES 4. Two people are walking toward each other on a path through the park. The path runs east and west. A hot air balloon is directly above the path between them. One of the walkers, a female, sees the balloon when looking east at an angle of elevation of 46°. The other walker, a male, sees the balloon looking west at an angle of elevation of72°.
WORD PROBLEM EXERCISES: SCIENCE 2. A cup of gold colored metal beads was measured to have a mass 425 grams. By water displacement, the volume of the beads was calculated to be 48.0 cm 3 . Given the following densities, identify the metal. 3. I threw a plastic ball in the pool for my dog to fetch. The mass of the ball was 125 grams. BIOLOGY GRAPHS: ISLAND BIOGEOGRAPHY Biology Graphs: Island Biogeography. The theory of island biogeography, developed by Robert MacArthur and Edward O. Wilson, looks to explain the differences in species diversity with island size (for example, why large islands tend to have a greater number of species of a certain category than small islands). BASIC QUADRATIC TERMINOLOGY Regardless of whether the parabola opens up or down, all parabolas will have a vertex.If the parabola opens up, the vertex is the minimum point or the place where the graph bottoms out. If the parabola opens down, the vertex is the maximum point or the place where the graph reaches its peak. Quadratic functions can be written in one of two ways, depending on what you are trying to do with the WORD LESSON: MODELING WITH SINUSOIDS 2 Word Lesson: Modeling with Sinusoids 2. In order to solve problems which require a sinusoidal model, it is necessary to. use basic graphing skills for sine and cosine. know how to find amplitude, period, frequency, displacement, and phase shift. know that use of MAXIMUM AND MINIMUM VALUES OF POLYNOMIALS These four points can occur because P (x) is a polynomial of degree 5. The maximum points are located at x = 0. 77 and -0. 80. The maximum values at these points are 0. 69 and 1. 57 respectively. The minimum points are located at x = -0. 05 and 1. 68. The minimum values are -2. 02 and -6. 00 respectively. WORD LESSON: LINEAR REGRESSION Linear Regression is a process by which the equation of a line is found that “best fits” a given set of data. The line of best fit approximates the best linear representation for your data. One very important aspect of a regression line is the relationship between the equation and the “science quantity” often represented by the slopeof the line.
APPLICATIONS OF EXPONENTIAL FUNCTIONS The best thing about exponential functions is that they are so useful in real world situations. Exponential functions are used to model populations, carbon date artifacts, help coroners determine time of death, compute investments, as well as many other applications. WORD LESSON: VECTORS NON-RIGHT TRIANGLES First we make a diagram in standard position. The attempted flight path of the plane is vector OX.Notice that the angle shown is 50° because the 40° bearing is measured clockwise from North. The vector XY represents the wind from the South. The vector OY is the resultant path of the plane, affected by the wind. In the diagram shown below, the known magnitude and angle are labeled. WORD LESSON: CIRCLES When two secants, or a secant and a tangent, are drawn to a circle from the same external point, one of the following two relationships exists. The first is between the products of the lengths of the external portion of the secant and the lengths of the entire secant. The second is between the square of the length of the tangent segment and the external portion of the secant and the length of PROPERTIES OF LOGARITHMS So written is logarithmic form is. Change into exponential form. Since the base is the same whether we are dealing with an exponential or a logarithm, the base for this problem will be 5. We will exchange the 4 and the 625. The 625 was attached to the 5 and the 4 was by itself. In the logarithmic form, the 625 will be by itself and the 4 will WORD LESSON: BORDER PROBLEMS A typical 60-pound bay of pre-mixed concrete costs between $1.35-$1.80 and yields one-half of a cubic foot. They would need a minimum of 68 bags to complete the project: 68 x $1.80 = $122.40 plus a strong back. One cubic yard equals (1 yd) 3 = (3 ft) 3 = 27 ft 3, so they will need 34 ft 3 /27 ft 3 = 1.26 yd 3. WORD PROBLEM EXERCISES: ARC LENGTHS Assuming that the Earth is a sphere of radius 4000 miles, find the distance between the following two cities whose latitudes are given. You may assume that these cities are on the same basic longitude. Cincinnati, Ohio (39º 8’ 46” N) and Huntsville, Alabama (34º43’ 41” N)
BASIC QUADRATIC TERMINOLOGY Regardless of whether the parabola opens up or down, all parabolas will have a vertex.If the parabola opens up, the vertex is the minimum point or the place where the graph bottoms out. If the parabola opens down, the vertex is the maximum point or the place where the graph reaches its peak. Quadratic functions can be written in one of two ways, depending on what you are trying to do with the WORD LESSON: LINEAR REGRESSION Linear Regression is a process by which the equation of a line is found that “best fits” a given set of data. The line of best fit approximates the best linear representation for your data. One very important aspect of a regression line is the relationship between the equation and the “science quantity” often represented by the slopeof the line.
WORD LESSON: EXPONENTIAL DECAY Exponential decay is generally applied to word problems that involve financial applications as well as those that deal with radioactive decay, medicine dosages, and population decline. To decay exponentially means that the topic being studied is decreasing in proportion to the amount that was previously present. The following is an example of an exponential decay problem. WORD LESSON: PROPORTIONS Word Lesson: Proportions. In order to solve problems involving proportions, you should be able to: work with fractions. set up ratios. set up equivalent fractions. cross multiply. solve one-step equations. A proportion sets two ratios equal to each other. In one ratio, one of the quantities is not known. SOLVING LINEAR INEQUALITIES If you let x = -5 or -6 or any other value that is less than -5, then the inequality will be true. So you would write your solution as . In the process of solving this inequality using algebraic methods, you would have something that looks like the following. Begin by gettingthe variable on
WORD LESSON: VECTORS NON-RIGHT TRIANGLES First we make a diagram in standard position. The attempted flight path of the plane is vector OX.Notice that the angle shown is 50° because the 40° bearing is measured clockwise from North. The vector XY represents the wind from the South. The vector OY is the resultant path of the plane, affected by the wind. In the diagram shown below, the known magnitude and angle are labeled. ORIGINS OF THE NAMES OF TRIGONOMETRIC FUNCTIONS Introduction: Originally, all six trigonometric values were defined by the lengths of the sides of the triangles, the chord, and the secant as shown in the following unit circle diagram. It wasn’t until the 16th century that Georg Joachim Rhaeticus, a Teutonic astronomer, defined the trigonometric functions as the ratios of the sides of a right triangle as we use them today. WORD LESSON: AREA AND PERIMETER OF TRAPEZOIDS The area is (½ h) (B + b) where B and b are the lengths of the two parallel bases and h is the height (perpendicular distance between parallel bases). The perimeter is found by adding the lengths of the four sides. Use the Pythagorean Theorem in finding the side (s) of a right triangle. In a typical problem involving area and perimeter of a WORD PROBLEMS: RATES, SALARIES, AND COMMISSIONS Rewrite each equation so that they are in the form . Multiply the bottom row by - 1: Add the two rows: Divide both sides by -0. 1: minutes. To find the monthly cost, solve for y using either of the original equations: dollars. Therefore, the cost for using eachcompany’s
WORD LESSON: EXPONENTIAL GROWTH Exponential growth is generally applied to word problems such as compound interest problems and population growth problems. To grow exponentially means that the topic being studied is increasing in proportion to what was previously there. For example, money deposited in the bank earns interest that is added to the money previously inthe bank.
BASIC QUADRATIC TERMINOLOGY Regardless of whether the parabola opens up or down, all parabolas will have a vertex.If the parabola opens up, the vertex is the minimum point or the place where the graph bottoms out. If the parabola opens down, the vertex is the maximum point or the place where the graph reaches its peak. Quadratic functions can be written in one of two ways, depending on what you are trying to do with the WORD LESSON: LINEAR REGRESSION Linear Regression is a process by which the equation of a line is found that “best fits” a given set of data. The line of best fit approximates the best linear representation for your data. One very important aspect of a regression line is the relationship between the equation and the “science quantity” often represented by the slopeof the line.
WORD LESSON: EXPONENTIAL DECAY Exponential decay is generally applied to word problems that involve financial applications as well as those that deal with radioactive decay, medicine dosages, and population decline. To decay exponentially means that the topic being studied is decreasing in proportion to the amount that was previously present. The following is an example of an exponential decay problem. WORD LESSON: PROPORTIONS Word Lesson: Proportions. In order to solve problems involving proportions, you should be able to: work with fractions. set up ratios. set up equivalent fractions. cross multiply. solve one-step equations. A proportion sets two ratios equal to each other. In one ratio, one of the quantities is not known. SOLVING LINEAR INEQUALITIES If you let x = -5 or -6 or any other value that is less than -5, then the inequality will be true. So you would write your solution as . In the process of solving this inequality using algebraic methods, you would have something that looks like the following. Begin by gettingthe variable on
WORD LESSON: VECTORS NON-RIGHT TRIANGLES First we make a diagram in standard position. The attempted flight path of the plane is vector OX.Notice that the angle shown is 50° because the 40° bearing is measured clockwise from North. The vector XY represents the wind from the South. The vector OY is the resultant path of the plane, affected by the wind. In the diagram shown below, the known magnitude and angle are labeled. ORIGINS OF THE NAMES OF TRIGONOMETRIC FUNCTIONS Introduction: Originally, all six trigonometric values were defined by the lengths of the sides of the triangles, the chord, and the secant as shown in the following unit circle diagram. It wasn’t until the 16th century that Georg Joachim Rhaeticus, a Teutonic astronomer, defined the trigonometric functions as the ratios of the sides of a right triangle as we use them today. WORD LESSON: AREA AND PERIMETER OF TRAPEZOIDS The area is (½ h) (B + b) where B and b are the lengths of the two parallel bases and h is the height (perpendicular distance between parallel bases). The perimeter is found by adding the lengths of the four sides. Use the Pythagorean Theorem in finding the side (s) of a right triangle. In a typical problem involving area and perimeter of a WORD PROBLEMS: RATES, SALARIES, AND COMMISSIONS Rewrite each equation so that they are in the form . Multiply the bottom row by - 1: Add the two rows: Divide both sides by -0. 1: minutes. To find the monthly cost, solve for y using either of the original equations: dollars. Therefore, the cost for using eachcompany’s
WORD LESSON: EXPONENTIAL GROWTH Exponential growth is generally applied to word problems such as compound interest problems and population growth problems. To grow exponentially means that the topic being studied is increasing in proportion to what was previously there. For example, money deposited in the bank earns interest that is added to the money previously inthe bank.
BASIC QUADRATIC TERMINOLOGY Regardless of whether the parabola opens up or down, all parabolas will have a vertex.If the parabola opens up, the vertex is the minimum point or the place where the graph bottoms out. If the parabola opens down, the vertex is the maximum point or the place where the graph reaches its peak. Quadratic functions can be written in one of two ways, depending on what you are trying to do with the MULTIPLICATION RULE OF PROBABILITY The addition rule helped us solve problems when we performed one task and wanted to know the probability of two things happening during that task. This lesson deals with the multiplication rule. The multiplication rule also deals with two events, but in these problems the events occur as a result of more than one task (rolling one die then another, drawing two cards, spinning a spinner twice APPLICATIONS OF EXPONENTIAL FUNCTIONS The best thing about exponential functions is that they are so useful in real world situations. Exponential functions are used to model populations, carbon date artifacts, help coroners determine time of death, compute investments, as well as many other applications. WORD LESSON: VECTORS NON-RIGHT TRIANGLES First we make a diagram in standard position. The attempted flight path of the plane is vector OX.Notice that the angle shown is 50° because the 40° bearing is measured clockwise from North. The vector XY represents the wind from the South. The vector OY is the resultant path of the plane, affected by the wind. In the diagram shown below, the known magnitude and angle are labeled. WORD LESSON: MODELING WITH SINUSOIDS 2 Word Lesson: Modeling with Sinusoids 2. In order to solve problems which require a sinusoidal model, it is necessary to. use basic graphing skills for sine and cosine. know how to find amplitude, period, frequency, displacement, and phase shift. know that use of SOLVING LOGARITHMIC EQUATIONS Solving logarithmic equations usually requires using properties of logarithms.The reason you usually need to apply these properties is so that you will have a single logarithmic expression on one or both sides of the equation. Once you have used properties of logarithms to condense any log expressions in the equation, you can solve the problem by changing the logarithmic equation into an WORD LESSON: AREA AND PERIMETER OF TRAPEZOIDS Know how to use basic formulas for area and perimeter of a trapezoid.The area is (½ h)(B + b) where B and b are the lengths of the two parallel bases and h is the height (perpendicular distance between parallel bases). The perimeter is found by adding the lengths of the four sides.; Use the Pythagorean Theorem in finding the side(s) of a right triangle. MAXIMUM AND MINIMUM VALUES OF POLYNOMIALS These four points can occur because P (x) is a polynomial of degree 5. The maximum points are located at x = 0. 77 and -0. 80. The maximum values at these points are 0. 69 and 1. 57 respectively. The minimum points are located at x = -0. 05 and 1. 68. The minimum values are -2. 02 and -6. 00 respectively. WORD LESSON: EXPONENTIAL GROWTH Exponential growth is generally applied to word problems such as compound interest problems and population growth problems. To grow exponentially means that the topic being studied is increasing in proportion to what was previously there. For example, money deposited in the bank earns interest that is added to the money previously inthe bank.
ECONOMICS GRAPHS: PERCENT INCOME VS PERCENT OF POPULATION Economics Graphs: Percent Income vs Percent of Population. Question Group #1. Directions and/or Common Information: This graph is known as the. 1. National Income Curve. Lorenz curve.Site Navigation
Welcome to ALGEBRALAB, an online learning environment that focuses on topics and skills from high school mathematics that students must be able to draw upon in their introductory science courses. Since math is the language of science, science courses are often where students first realize “Oh, so this is why we learned that in algebra …” In many cases students often discover that it is one or more math skills that initially block their ability to understand and internalize new science concepts. In science classes students must learn how to recognize when particular mathematics procedures are applicable so that they can select from their "mathematics toolboxes" the correct methods needed to solve new problems. And to make matters worse, these new problems are often "word problems" that require not only an ultimate solution but an understanding of how to interpret givens, relate cause-and-effect, and set up any initial conditionalequations.
After 17 years of being online, AlgebraLAB has become an integral component in the curriculum of innumerable instructors at the elementary, secondary, and collegiate levels as well as parents, and students. In the state of Florida , AlgebraLAB's curriculum has been been reviewed and approved with links to specific pages (seeexample
)
meeting required mathematics standards and benchmarks. Moreover, AlgebraLAB has received recommendations from Educational Freeware, Drexel
University's Math Forum , and The Physics Front.
Research-based design models have driven the project’s design and implementation. AlgebraLAB focuses on building the connections between science and the basic mathematics required for its understanding bymeans of:
* Lessons on each topic/skill combination * Practice pages on your choice of of topic/skill combination * Lessons on solving classic word problem situations * StudyAids or “Recipes for Success” * Practice on interpreting science and economics graphs which integrate reasoning as well as reading and math skills * Practice on reading technical scientific passages * Hands-on science activities to support the use of mathematics inscience
* Interactive glossary of math and science terms with pronunciation guides, definitions, and examples * Career profiles, resourced in 2003, illustrating the connections between math and science in a myriad of occupations. During the summer of 2019 the document types called "Passages" and "Word Problems" were reformated to show answers with audio files. The links to reach the new presentations of these pages are provided on the sidebar. If you had previously linked to the older formats, pleaseupdate your sites.
The following page provides more information about the project's history . Our copyright information and usage agreement are available as well as recommendations on how to use thiswebsite .
AlgebraLAB
Project Manager
Catharine H. Colwell Application ProgrammersJeremy R. Blawn
Mark Acton
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