1-5
... Solving Equations with 1-5 Variables on Both Sides Example 4: Application Jon and Sara are planting tulip bulbs. Jon has planted 60 bulbs and is planting at a rate of 44 bulbs per hour. Sara has planted 96 bulbs and is planting at a rate of 32 bulbs per hour. In how many hours will Jon and Sara hav ...
... Solving Equations with 1-5 Variables on Both Sides Example 4: Application Jon and Sara are planting tulip bulbs. Jon has planted 60 bulbs and is planting at a rate of 44 bulbs per hour. Sara has planted 96 bulbs and is planting at a rate of 32 bulbs per hour. In how many hours will Jon and Sara hav ...
AMS 10/10A, Homework 1
... to counterclockwise rotation by an angle of π/4 and stretching by a factor of 2. Problem 12. Consider a polynomial of odd degree with real coefficients. Show that the polynomial always has at least one real root. Hint: use Proposition 4.5 in the lecture notes; look at what happens to the degree of t ...
... to counterclockwise rotation by an angle of π/4 and stretching by a factor of 2. Problem 12. Consider a polynomial of odd degree with real coefficients. Show that the polynomial always has at least one real root. Hint: use Proposition 4.5 in the lecture notes; look at what happens to the degree of t ...
9.1 Identifying Quadratic Functions Day 1
... 9.1 a - I can graph a quadratic function using a table of values. 9.1 b - I can tell whether a quadratic function opens up or down given an equation. ...
... 9.1 a - I can graph a quadratic function using a table of values. 9.1 b - I can tell whether a quadratic function opens up or down given an equation. ...
Differential equation
A differential equation is a mathematical equation that relates some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two. Because such relations are extremely common, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.In pure mathematics, differential equations are studied from several different perspectives, mostly concerned with their solutions—the set of functions that satisfy the equation. Only the simplest differential equations are solvable by explicit formulas; however, some properties of solutions of a given differential equation may be determined without finding their exact form.If a self-contained formula for the solution is not available, the solution may be numerically approximated using computers. The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy.