VOCABULARY Relation: Domain: Range: Function:
... Step 1 Write the equation in standard form. Step 2 Identify the x-intercept by letting ___ = 0 and solving for ____. Use the x-intercept to plot the point where the line crosses the______. Step 3 Identify the y-intercept by letting ____ = 0 and solving for ____. Use the y-intercept to plot the point ...
... Step 1 Write the equation in standard form. Step 2 Identify the x-intercept by letting ___ = 0 and solving for ____. Use the x-intercept to plot the point where the line crosses the______. Step 3 Identify the y-intercept by letting ____ = 0 and solving for ____. Use the y-intercept to plot the point ...
math 1314 noes 3.3 and 3.4
... We can use a process called synthetic division to divide polynomials if the divisor is of the form x – c. This method can be done more rapidly than using long division. Compare the two methods using the problem ...
... We can use a process called synthetic division to divide polynomials if the divisor is of the form x – c. This method can be done more rapidly than using long division. Compare the two methods using the problem ...
First Midterm Exam Solutions
... • Alternatively, find the line L which passes through P and is parallel to n. This line intersects the plane at R. Since the line passes through P (7, −2, −1) and is parallel to n = h2, −3, −1i, it can be described parametrically as h7, −2, −1i + th2, −3, −1i = h7 + 2t, −2 − 3t, −1 − ti. To find whe ...
... • Alternatively, find the line L which passes through P and is parallel to n. This line intersects the plane at R. Since the line passes through P (7, −2, −1) and is parallel to n = h2, −3, −1i, it can be described parametrically as h7, −2, −1i + th2, −3, −1i = h7 + 2t, −2 − 3t, −1 − ti. To find whe ...
允許學生個人、非營利性的圖書館或公立學校合理使用 本
... When the product of two factors is equal to 0, then at least one of the factor is equal to 0. Conversely, if one of the two factors is equal to 0, then their product is equal to 0. e.g. To make ( x − 2)( x + 2) =0, it is necessary and sufficient to have x − 2 = 0 or x + 2 = 0 . Hence solving the equ ...
... When the product of two factors is equal to 0, then at least one of the factor is equal to 0. Conversely, if one of the two factors is equal to 0, then their product is equal to 0. e.g. To make ( x − 2)( x + 2) =0, it is necessary and sufficient to have x − 2 = 0 or x + 2 = 0 . Hence solving the equ ...
SOLUTIONS TO EXERCISES FOR
... In Part (d) of the preceding problem, one cannot find a choice function without assuming something like the Axiom of Choice. The following explanation goes beyond the content of this course but is hopefully illuminating. The first step involves the results from Section I.3 which show that the set of ...
... In Part (d) of the preceding problem, one cannot find a choice function without assuming something like the Axiom of Choice. The following explanation goes beyond the content of this course but is hopefully illuminating. The first step involves the results from Section I.3 which show that the set of ...
Equation
In mathematics, an equation is an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. In this situation, variables are also known as unknowns and the values which satisfy the equality are known as solutions. An equation differs from an identity in that an equation is not necessarily true for all possible values of the variable.There are many types of equations, and they are found in all areas of mathematics; the techniques used to examine them differ according to their type.Algebra studies two main families of equations: polynomial equations and, among them, linear equations. Polynomial equations have the form P(X) = 0, where P is a polynomial. Linear equations have the form a(x) + b = 0, where a is a linear function and b is a vector. To solve them, one uses algorithmic or geometric techniques, coming from linear algebra or mathematical analysis. Changing the domain of a function can change the problem considerably. Algebra also studies Diophantine equations where the coefficients and solutions are integers. The techniques used are different and come from number theory. These equations are difficult in general; one often searches just to find the existence or absence of a solution, and, if they exist, to count the number of solutions.Geometry uses equations to describe geometric figures. The objective is now different, as equations are used to describe geometric properties. In this context, there are two large families of equations, Cartesian equations and parametric equations.Differential equations are equations involving one or more functions and their derivatives. They are solved by finding an expression for the function that does not involve derivatives. Differential equations are used to model real-life processes in areas such as physics, chemistry, biology, and economics.The ""="" symbol was invented by Robert Recorde (1510–1558), who considered that nothing could be more equal than parallel straight lines with the same length.