Module 5, topic 1 examples
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The document provides examples of solving direct variation problems by setting up proportions and cross-multiplying. It gives three example problems: 1) writing the direct variation equation for a line through (0,0) and (4,2), 2) finding the value of k in an equation, and 3) finding an x value when given a y value. It also provides links to additional direct variation example resources.
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2. Discussion of integral curves and the existence and uniqueness theorem for differential equations.
3. Classification and methods for solving first and higher order linear differential equations, including separable, exact, integrating factors, Bernoulli, homogeneous with constant coefficients, and undetermined coefficients.
4. Brief introduction to additional solution methods like Euler's method, power series, and Laplace transforms.
5. Mention of solving systems of linear differential equations.
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This document contains slides from a lecture on linear regression models given by Dr. Frank Wood. The slides:
- Review properties of multivariate Gaussian distributions and sums of squares that are important for understanding Cochran's theorem.
- Explain that Cochran's theorem describes the distributions of partitioned sums of squares of normally distributed random variables, which is important for traditional linear regression analysis.
- Provide an outline of the lecture, which will prove Cochran's theorem by first establishing some prerequisites around quadratic forms of normal random variables and then proving a supporting lemma.
Algebra graphs and functions 4 4 4-5
The document discusses writing function rules from tables, direct variation, and writing equations to model direct variations. It provides examples of determining if equations represent direct variations and writing direct variation equations given points. Direct variations have the form y=kx, where k is the constant of variation and y and x vary directly with each other. The ratio y/x is constant for direct variations and can be used to identify and write equations for direct variations from tables.
Direct variation
Jovie earns money tutoring at a rate of 125 pesos per hour. Her earnings increase directly with the number of hours tutored. The question asks to determine the equation that relates her earnings (E) to the number of hours tutored (t). The document explains that because E and t are directly proportional, their relationship can be written as an equation with a constant of variation. It provides the example relationship E = 125t, where 125 is the constant of variation. Therefore, the equation that determines Jovie's earnings for tutoring t hours is E = 125t.
Direct variation
Jovie earns 125 pesos per hour for tutoring. She earns 250 pesos for 2 hours and 375 pesos for 3 hours. Her earnings vary directly with the number of hours tutored, according to the equation E=125t, where E is earnings in pesos and t is time in hours.
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Average Value of a Function
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The document discusses the importance of renewable energy sources and outlines several benefits they provide, including being cleaner than fossil fuels and helping reduce the impacts of climate change. It notes that renewable sources like solar, wind, hydroelectric, and geothermal can help meet energy needs in a more sustainable way and promote energy independence. Transitioning to greater use of renewable resources will help ensure access to reliable and affordable energy for future generations.
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Evaluating Limits - A General Checklist
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2. Try algebraic techniques like factoring, rationalizing, or using common denominators to simplify before direct substitution again.
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Module 5, topic 1 examples
- 1. Module 5, Topic 1 Examples Some Help from Mrs. M
- 2. Direct Variation Is an equation of the form y = kx, where k is the slope of the line Is proportional…so we can set up our problems as a proportion and then cross-multiply to solve Here’s an example to go back over how to cross- multiply: Solve:
- 3. Some Direct Variation Examples 1. Write the direct variation equation of 2. Find the value of k in the line through (0,0) the direct variation and (4, 2). equation 4y = 5x. Solve for y: k=
- 4. 3. x varies directly as y. When x = 4, y = 12. Find x when y = 36. Direct variation means proportional change, so let’s write a proportion and substitute our given information:
- 5. Some Other Examples http://quiz.uprm.edu/tutorials/direct_var/direct_var _right.xml http://www.freemathhelp.com/direct-variation.html