Solutions
... A common mistake was to find the value of the other constant to be c ln 2 which is correct, but to leave the ± in the answer. Since you are being asked for a specific solution, you have to say whether it is plus or minus. It cannot be both. In this case, the correct sign is minus. ...
... A common mistake was to find the value of the other constant to be c ln 2 which is correct, but to leave the ± in the answer. Since you are being asked for a specific solution, you have to say whether it is plus or minus. It cannot be both. In this case, the correct sign is minus. ...
Exam 3
... (b) If λ = 2 is a repeated eigenvalue of multiplicity 2 for a matrix A, then the eigenspace associated with λ has dimension 2. (c) If an n × n matrix has n distinct eigenvalues, then each eigenvalue has a corresponding one-dimensional eigenspace. ...
... (b) If λ = 2 is a repeated eigenvalue of multiplicity 2 for a matrix A, then the eigenspace associated with λ has dimension 2. (c) If an n × n matrix has n distinct eigenvalues, then each eigenvalue has a corresponding one-dimensional eigenspace. ...
How to Solve a System of Equations by Graphing or Table
... BUSINESS Laura’s Copies has two options for buying photocopies. With Option 1, you can buy a card for $40 each year and then pay $0.03 per copy. With Option 2, you can just pay $0.05 per copy. For how many copies would the cost of Options 1 and 2 be the same? What is the cost? Let x = the number of ...
... BUSINESS Laura’s Copies has two options for buying photocopies. With Option 1, you can buy a card for $40 each year and then pay $0.03 per copy. With Option 2, you can just pay $0.05 per copy. For how many copies would the cost of Options 1 and 2 be the same? What is the cost? Let x = the number of ...
Review Exercise Set 22
... Determine the solution of the following system of equations by using the addition method. x - 4y = 12 2x + 5y = -2 Multiply the first equation by -2 -2(x - 4y = 12) -2x + 8y = -24 Add the new equation to the second equation to eliminate x and solve for y 2x + 5y = -2 -2x + 8y = -24 13y = -26 y = -2 ...
... Determine the solution of the following system of equations by using the addition method. x - 4y = 12 2x + 5y = -2 Multiply the first equation by -2 -2(x - 4y = 12) -2x + 8y = -24 Add the new equation to the second equation to eliminate x and solve for y 2x + 5y = -2 -2x + 8y = -24 13y = -26 y = -2 ...
3.1 Solving Linear Systems Graphically
... $50.00 per month for the first phone line and charges $20.00 per additional phone line. Text Away Wireless charges $80.00 per month for the first phone line and $5.00 per additional phone line. Use your graphing calculator to create the graph of a system of equations to determine the number of addit ...
... $50.00 per month for the first phone line and charges $20.00 per additional phone line. Text Away Wireless charges $80.00 per month for the first phone line and $5.00 per additional phone line. Use your graphing calculator to create the graph of a system of equations to determine the number of addit ...
Solutions 1.5-Page 51
... (a) Her retirement increases by 6% per year of what is in the account, plus 12% of her yearly salary. In equation form, this becomes ∆A = 0.06 A∆t + 0.12 S∆t . Dividing by ∆t and taking the limit as time goes to infinite gives the differential equation. ...
... (a) Her retirement increases by 6% per year of what is in the account, plus 12% of her yearly salary. In equation form, this becomes ∆A = 0.06 A∆t + 0.12 S∆t . Dividing by ∆t and taking the limit as time goes to infinite gives the differential equation. ...
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.