File - North Meck Math III
... Factor the new quadratic by finding two numbers that multiply to be the new c, and add to be b. ...
... Factor the new quadratic by finding two numbers that multiply to be the new c, and add to be b. ...
Section 4.3-4.6 Section 4.4 Section 4.5 Section 4.6
... 14. A curve that passes through the point (0, 25) has the property that the slope at every point (x, y) is eight times the y coordinate. Find the equation of the curve. 15. A pie is taken from an oven, where the temperature is 450◦ , to a 75◦ room. After 15 minutes, the temperature of the pie reads ...
... 14. A curve that passes through the point (0, 25) has the property that the slope at every point (x, y) is eight times the y coordinate. Find the equation of the curve. 15. A pie is taken from an oven, where the temperature is 450◦ , to a 75◦ room. After 15 minutes, the temperature of the pie reads ...
Regular differential forms
... 2 . It follows that there are no regular differential forms on P . Example Take the projective curve Y 2 Z = X 3 + XZ 2 . The projective plane P2 is covered by three affine pieces: A1 is the part with Z 6= 0 and coordinates (X, Y, 1), A2 is the part with Y 6= 0 and coordinates (U, 1, V ), A3 is the ...
... 2 . It follows that there are no regular differential forms on P . Example Take the projective curve Y 2 Z = X 3 + XZ 2 . The projective plane P2 is covered by three affine pieces: A1 is the part with Z 6= 0 and coordinates (X, Y, 1), A2 is the part with Y 6= 0 and coordinates (U, 1, V ), A3 is the ...
Intermediate Math Circles March 7, 2012 Problem Set
... coin is a quarter, a dime or a nickel. Solution: Let q represent the number of quarters, d represent the number of dimes and n represent the number of nickels. The information given in the problem tells us that q + d + n = 1000 (1) 25q + 10d + 5n = 20000, dividing by 5, 5q + 2d + n = 4000 (2) Subtra ...
... coin is a quarter, a dime or a nickel. Solution: Let q represent the number of quarters, d represent the number of dimes and n represent the number of nickels. The information given in the problem tells us that q + d + n = 1000 (1) 25q + 10d + 5n = 20000, dividing by 5, 5q + 2d + n = 4000 (2) Subtra ...
Chapter 1 Notes
... (We are allowed to use these operations on a matrix when trying to solve a system of linear equations.) Elementary Row Operation: 1. Interchange two rows 2. Multiply (or divide) a row by a nonzero constant. 3. Add (or subtract) a multiple of one row to another. ...
... (We are allowed to use these operations on a matrix when trying to solve a system of linear equations.) Elementary Row Operation: 1. Interchange two rows 2. Multiply (or divide) a row by a nonzero constant. 3. Add (or subtract) a multiple of one row to another. ...
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.