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  • https://math.libretexts.org/Courses/Las_Positas_College/Math_27%3A_Number_Systems_for_Educators/08%3A_Additional_Activities/8.05%3A_5._Egyptian_Pizza
    Explain to students how if that was the case then they would all get at least half a loaf, so you would use 4 of the pizzas to give all 8 of them half a pizza each. Although they had a notation for 1 ...Explain to students how if that was the case then they would all get at least half a loaf, so you would use 4 of the pizzas to give all 8 of them half a pizza each. Although they had a notation for 1 / 2 and 1 / 3 and 1 / 4 and so on (these are called reciprocals or unit fractions since they are 1 / n for some number n), their notation did not allow them to write 2 / 5 or 3 / 4 or 4 / 7 as we would today.
  • https://math.libretexts.org/Courses/Las_Positas_College/Math_27%3A_Number_Systems_for_Educators/08%3A_Additional_Activities/8.02%3A_2._Regular_Tiling
    A polygon is a closed 2-dimensional figure with straight sides A regular n-gon is a polygon with exactly n sides, where all sides are of equal length and all interior angles of the polygon are equal. ...A polygon is a closed 2-dimensional figure with straight sides A regular n-gon is a polygon with exactly n sides, where all sides are of equal length and all interior angles of the polygon are equal. The sum of the interior angles of a regular n-gon is 180°(n - 2). A regular 3-gon is an equilateral triangle. A regular 4-gon is a square. A regular 5-gon is a regular pentagon. A regular 6-gon is a regular hexagon. A regular 7-gon is a regular heptagon. A regular 8-gon is a regular octagon.
  • https://math.libretexts.org/Under_Construction/Purgatory/Remixer_University/Username%3A_Matthew.Lathrop@heartland.edu/test_cb2/1%3A_How_to_process_the_data
    Generally, you do not need a computer to process the data. However, contemporary statistics is “heavy” and almost always requires the technical help from some kind of software.
  • https://math.libretexts.org/Under_Construction/Purgatory/Remixer_University/Username%3A_Matthew.Lathrop@heartland.edu/test_cb/1%3A_How_to_process_the_data/1.6%3A_How_to_start_with_R
    If you know how to work with R, it is a good idea to check the fresh installation typing, for example, plot(1:20) to check if graphics works. If you by chance answered “yes” on the question in the end...If you know how to work with R, it is a good idea to check the fresh installation typing, for example, plot(1:20) to check if graphics works. If you by chance answered “yes” on the question in the end of the previous R session, you might want to remove unwanted files: The more mistakes you do when you learn, the less you do when you start to work with R on your own.
  • https://math.libretexts.org/Courses/Mount_Royal_University/Calculus_for_Scientists_I/3%3A_Derivatives/3.0%3A_Tangent_lines_and_Rates_of_change/3.0E%3A_Exercises
    For the following exercises, use the equation to find the slope of the secant line between the values x1 and x2 for each function y=f(x). For the following exercises, use the limit defin...For the following exercises, use the equation to find the slope of the secant line between the values x1 and x2 for each function y=f(x). For the following exercises, use the limit definition of derivative to show that the derivative does not exist at x=a for each of the given functions. Use the ZOOM feature on the calculator to approximate the two values of x=a for which mtan=f(a)=0.
  • https://math.libretexts.org/Courses/Mount_Royal_University/Calculus_for_Scientists_I/3%3A_Derivatives/3.4%3A_Derivatives_of_Trigonometric_functions/3.4E%3A_Exercises
    For the following exercises, find the equation of the tangent line to each of the given functions at the indicated values of x. The number of hamburgers sold at a fast-food restaurant in Pasadena,...For the following exercises, find the equation of the tangent line to each of the given functions at the indicated values of x. The number of hamburgers sold at a fast-food restaurant in Pasadena, California, is given by y=10+5sinx where y is the number of hamburgers sold and x represents the number of hours after the restaurant opened at 11 a.m.
  • https://math.libretexts.org/Courses/Mount_Royal_University/Calculus_for_Scientists_I/3%3A_Derivatives/3.7%3A_Derivatives_of__Inverse_Trigonometric_Functions
    In this section, we explore the relationship between the derivative of a function and the derivative of its inverse. For functions whose derivatives we already know, we can use this relationship to fi...In this section, we explore the relationship between the derivative of a function and the derivative of its inverse. For functions whose derivatives we already know, we can use this relationship to find derivatives of inverses without having to use the limit definition of the derivative. In particular, we will apply the formula for derivatives of inverse functions to trigonometric functions. This formula may also be used to extend the power rule to rational exponents.
  • https://math.libretexts.org/Courses/Mount_Royal_University/Mathematical_Methods/1%3A_Power_Series/1.1%3A__Power_Series
    if there exists a real number R>0 such that a power series centered at x=a converges for |xa|<R and diverges for |xa|>R, then R is the radius of convergence; if the power series ...if there exists a real number R>0 such that a power series centered at x=a converges for |xa|<R and diverges for |xa|>R, then R is the radius of convergence; if the power series only converges at x=a, the radius of convergence is R=0; if the power series converges for all real numbers x, the radius of convergence is R=
  • https://math.libretexts.org/Courses/Mount_Royal_University/Mathematical_Methods/2%3A_Ordinary_differential_equations/2.3%3A_Linear_Second_Order_Nonhomogeneous_Linear_Equations/2.3E%3A_Exercises
    If ω is a constant, differentiating a linear combination of cosωx and sinωx with respect to x yields another linear combination of cosωx and \(\sin\omega ...If ω is a constant, differentiating a linear combination of cosωx and sinωx with respect to x yields another linear combination of cosωx and sinωx. has a particular solution that's a linear combination of cosωx and sinωx if and only if the left side of (???) is not of the form a(y+ω2y), so that cosωx and sinωx are solutions of the complementary equation.
  • https://math.libretexts.org/Courses/Mount_Royal_University/Mathematical_Methods/5%3A_Vector-Valued_Functions
    He stated that comets that had appeared in 1531, 1607, and 1682 were actually the same comet and that it would reappear in 1758. Halley’s Comet follows an elliptical path through the solar system, wit...He stated that comets that had appeared in 1531, 1607, and 1682 were actually the same comet and that it would reappear in 1758. Halley’s Comet follows an elliptical path through the solar system, with the Sun appearing at one focus of the ellipse. Kepler’s third law of planetary motion can be used with the calculus of vector-valued functions to find the average distance of Halley’s Comet from the Sun.
  • https://math.libretexts.org/Courses/Mount_Royal_University/Mathematical_Methods/9%3A_Vector_Calculus/9.1%3A_Vector_Fields/9.1E%3A_Exercises
    For the following exercises, let \vecsF=xˆi+yˆj,\vecsG=yˆi+xˆj,and\vecsH=xˆi+yˆj. Match ...For the following exercises, let \vecsF=xˆi+yˆj,\vecsG=yˆi+xˆj,and\vecsH=xˆi+yˆj. Match the vector fields with their graphs in (I)−(IV).

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