rational expressions and equations
... LCD = 15x since 3x * 5 = 15x. Multiply both sides of the equation by 15x. Whatever we do to one side of the equation, we must do the same to the other side of the equal sign. We do this to cancel the denominators soon, Distribute 15x over each of the terms on the left so we can cancel the denominato ...
... LCD = 15x since 3x * 5 = 15x. Multiply both sides of the equation by 15x. Whatever we do to one side of the equation, we must do the same to the other side of the equal sign. We do this to cancel the denominators soon, Distribute 15x over each of the terms on the left so we can cancel the denominato ...
Section 11.6
... Solving Polynomial Equations The techniques used to solve polynomial equations of degree 3 or higher are not as straightforward as those used to solve linear equations and quadratic equations. The next example shows how the factor theorem can be used to solve a third-degree polynomial equation. ...
... Solving Polynomial Equations The techniques used to solve polynomial equations of degree 3 or higher are not as straightforward as those used to solve linear equations and quadratic equations. The next example shows how the factor theorem can be used to solve a third-degree polynomial equation. ...
![A) Area Between Curves in [a , b]](http://s1.studyres.com/store/data/010244503_1-8d5ca7e45bea07d60196d1e4f510559f-300x300.png)
![Groebner([f1,...,fm], [x1,...,xn], ord)](http://s1.studyres.com/store/data/011295364_1-f9178b6b2a17852cc3e0f2685417c144-300x300.png)
High School Algebra II Standards and Learning Targets
... N-CN.1. Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi I can describe complex numbers in terms of with a and b real. their real and imaginary parts. N-CN.2. Use the relation i2 = –1 and the commutative, I can apply the commutative, associative, and a ...
... N-CN.1. Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi I can describe complex numbers in terms of with a and b real. their real and imaginary parts. N-CN.2. Use the relation i2 = –1 and the commutative, I can apply the commutative, associative, and a ...
1 - Mu Alpha Theta
... -x + -y = 1, where the lines are cut-off by the coordinate axes. This set of lines forms a diamond. 16. E (35 pi/18). Let y = sin(3x). Then the given equation is a quadratic in y such that y^2- y/2 1/2 = 0. Solving for y gives y = (1, -1/2). Thus sin(3x) = 1 or sin(3x) = -1/2. Consider all possible ...
... -x + -y = 1, where the lines are cut-off by the coordinate axes. This set of lines forms a diamond. 16. E (35 pi/18). Let y = sin(3x). Then the given equation is a quadratic in y such that y^2- y/2 1/2 = 0. Solving for y gives y = (1, -1/2). Thus sin(3x) = 1 or sin(3x) = -1/2. Consider all possible ...
Solving a Linear Inequality
... Finding an Inequality Boundary Boundary Point: A solution(s) that makes the inequality true (equal). It could be the smallest number(s) that make it true. Or it is the largest number(s) that makes it NOT true. EX: Find the boundary point of 2 x 5 3 To find a boundary replace the inequality symb ...
... Finding an Inequality Boundary Boundary Point: A solution(s) that makes the inequality true (equal). It could be the smallest number(s) that make it true. Or it is the largest number(s) that makes it NOT true. EX: Find the boundary point of 2 x 5 3 To find a boundary replace the inequality symb ...
Math 110 Placement Exam Solutions FRACTION ARITHMETIC 1
... 25. Find the equation of the line in the x-y plane that goes through the point (−1, 1) and is parallel to the line whose equation is given by 2x + 3y + 4 = 0. Solution From problem 19 the slope of the line is − 23 . The parallel line has the same slope and passes through (−1, 1). Using the point-slo ...
... 25. Find the equation of the line in the x-y plane that goes through the point (−1, 1) and is parallel to the line whose equation is given by 2x + 3y + 4 = 0. Solution From problem 19 the slope of the line is − 23 . The parallel line has the same slope and passes through (−1, 1). Using the point-slo ...
notes
... du( x ) sinh u( x) cosh u( x ) dx dx Alternatively, we note that we are trying to get their derivatives at x=0. Inspecting the slopes of the plots of Fig. 2 at x=0, one can conclude that: ...
... du( x ) sinh u( x) cosh u( x ) dx dx Alternatively, we note that we are trying to get their derivatives at x=0. Inspecting the slopes of the plots of Fig. 2 at x=0, one can conclude that: ...
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.