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About 8481 results
  • https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/12%3A_Introduction_to_Calculus/12.05%3A_Derivatives
    Change divided by time is one example of a rate. The rates of change in the previous examples are each different. In other words, some changed faster than others. If we were to graph the functions, we...Change divided by time is one example of a rate. The rates of change in the previous examples are each different. In other words, some changed faster than others. If we were to graph the functions, we could compare the rates by determining the slopes of the graphs.
  • https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/12%3A_Introduction_to_Calculus
    Calculus is the broad area of mathematics dealing with such topics as instantaneous rates of change, areas under curves, and sequences and series. Underlying all of these topics is the concept of a li...Calculus is the broad area of mathematics dealing with such topics as instantaneous rates of change, areas under curves, and sequences and series. Underlying all of these topics is the concept of a limit, which consists of analyzing the behavior of a function at points ever closer to a particular point, but without ever actually reaching that point. Calculus has two basic applications: differential calculus and integral calculus.
  • https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/01%3A_Functions/1.03%3A_Domain_and_Range
    In creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the domain and range. In this se...In creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the domain and range. In this section, we will investigate methods for determining the domain and range of functions.
  • https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/09%3A_Systems_of_Equations_and_Inequalities/9.05%3A_Partial_Fractions
    Decompose a ratio of polynomials by writing the partial fractions. Solve by clearing the fractions, expanding the right side, collecting like terms, and setting corresponding coefficients equal to eac...Decompose a ratio of polynomials by writing the partial fractions. Solve by clearing the fractions, expanding the right side, collecting like terms, and setting corresponding coefficients equal to each other, then setting up and solving a system of equations. The decomposition with repeated linear factors must account for the factors of the denominator in increasing powers. The decomposition with a nonrepeated irreducible quadratic factor needs a linear numerator over the quadratic factor.
  • https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/08%3A_Further_Applications_of_Trigonometry/8.E%3A_Further_Applications_of_Trigonometry_(Exercises)
    If the angle of elevation from the man to the balloon is \(27^{\circ}\), and the angle of elevation from the woman to the balloon is \(41^{\circ}\), find the altitude of the balloon to the nearest foo...If the angle of elevation from the man to the balloon is \(27^{\circ}\), and the angle of elevation from the woman to the balloon is \(41^{\circ}\), find the altitude of the balloon to the nearest foot. For polar coordinates, the point in the plane depends on the angle from the positive \(x\)-axis and distance from the origin, while in Cartesian coordinates, the point represents the horizontal and vertical distances from the origin.
  • https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra_1e_(OpenStax)/07%3A_Factoring
  • https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra_1e_(OpenStax)/09%3A_Roots_and_Radicals/9.08%3A_Rational_Exponents/9.8E%3A_Exercises
    \(\frac{r^{\frac{5}{2}}·r^{−\frac{1}{2}}}{r^{−\frac{3}{2}}}\) \(\frac{a^{\frac{3}{4}}·a^{−\frac{1}{4}}}{a^{−\frac{10}{4}}}\) Simplify \(242^{\frac{1}{2}}\) to find the length of each side of his patio...\(\frac{r^{\frac{5}{2}}·r^{−\frac{1}{2}}}{r^{−\frac{3}{2}}}\) \(\frac{a^{\frac{3}{4}}·a^{−\frac{1}{4}}}{a^{−\frac{10}{4}}}\) Simplify \(242^{\frac{1}{2}}\) to find the length of each side of his patio.Round to the nearest tenth of a foot. Simplify \(\frac{12^{\frac{1}{2}}}{16^{\frac{1}{2}}}\) to find how many seconds it took for the decoration to reach the ground. Simplify \(\frac{1024^{\frac{1}{2}}}{16^{\frac{1}{2}}}\) to find how many seconds it took for the flare to reach the water.
  • https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra_1e_(OpenStax)/08%3A_Rational_Expressions_and_Equations
  • https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/09%3A_Systems_of_Equations_and_Inequalities/9.01%3A_Prelude_to_Systems_of_Equations_and_Inequalities
    In this chapter, we will investigate matrices and their inverses, and various ways to use matrices to solve systems of equations. First, however, we will study systems of equations on their own: linea...In this chapter, we will investigate matrices and their inverses, and various ways to use matrices to solve systems of equations. First, however, we will study systems of equations on their own: linear and nonlinear, and then partial fractions. We will not be breaking any secret codes here, but we will lay the foundation for future courses.
  • https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/08%3A_Further_Applications_of_Trigonometry/8.07%3A_Parametric_Equations
    We begin this section with a look at the basic components of parametric equations and what it means to parameterize a curve. Then we will learn how to eliminate the parameter, translate the equations ...We begin this section with a look at the basic components of parametric equations and what it means to parameterize a curve. Then we will learn how to eliminate the parameter, translate the equations of a curve defined parametrically into rectangular equations, and find the parametric equations for curves defined by rectangular equations.
  • https://math.libretexts.org/Courses/Western_Connecticut_State_University/Draft_Custom_Version_MAT_131_College_Algebra/03%3A_Functions/3.06%3A_Absolute_Value_Functions
    Distances in the universe can be measured in all directions. As such, it is useful to consider distance as an absolute value function. In this section, we will investigate absolute value functions. Th...Distances in the universe can be measured in all directions. As such, it is useful to consider distance as an absolute value function. In this section, we will investigate absolute value functions. The absolute value function is commonly thought of as providing the distance the number is from zero on a number line. Algebraically, for whatever the input value is, the output is the value without regard to sign.

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