Coordinate Systems: A point P is described by three coordinates ‚ in cartesian (x‚y‚z)‚ in cylindrical (r‚ ϕ ‚z)‚ and in spherical (r‚θ‚ ϕ )‚ as shown. A point is also defined by the intersection of three orthogonal surfaces‚ as shown. Cartesian Cylindrical Spherical Transformation from Cylinder to Cartesian Coordinates Transformation from Cartesian to Cylindrical: Transformation
Premium Analytic geometry Vector calculus Volume
Solving systems of linear equations 7.1 Introduction Let a system of linear equations of the following form: a11 x1 a21 x1 a12 x2 a22 x2 ai1x1 ai 2 x2 am1 x1 am2 x2 a1n xn a2 n x n ain xn amn xn b1 b2 bi bm (7.1) be considered‚ where x1 ‚ x2 ‚ ... ‚ xn are the unknowns‚ elements aik (i = 1‚ 2‚ ...‚ m; k = 1‚ 2‚ ...‚ n) are the coefficients‚ bi (i = 1‚ 2‚ ...‚ m) are the free terms
Premium
Properties of Chemical Reactions Ms. Whitty‚ Science 10 Fiona Adams‚ November 1st‚ 2012 Introduction Chemical reactions are a part of our daily lives‚ from rusting metal to making bread to leaves changing colour in the fall. A chemical reaction is the process that occurs when two or more substances combine to produce a chemical change. When a chemical reaction takes place‚ the change is indicated by one or more qualitative properties. The colour or odor could change‚ gas could be produced
Premium Chemical reaction Chemistry Sodium
temperature one last time. I repeated the process for the other test foods as well. Results: See table below Discussion: This lab helped me learn how to measure the amount of energy contained within each food item. Questions: A. Peanut B. Considerably well C. Single replacement reaction D. Carbon dioxide and water E. Into the air F. 1. 1400 calories 2. 10.69kJ/gm 3. 158kcal for one serving of fritos Table: Item Description Marshmallow (g) Peanut (g) Potato Chip (g) Mass food
Premium Solubility Sodium hydroxide Sodium chloride
1.1. Equations and Graphs In each of problems 1 - 4‚ find (a) an ordered pair that is a solution of the equation‚ (b) the intercepts of the graph‚ and (c) determine if the graph has symmetry. 1. 2. 3. 4. 5. Once a car is driven off of the dealership lot‚ it loses a significant amount of its resale value. The graph below shows the depreciated value of a BMW versus that of a Chevy after years. Which of the following statements is the best conclusion about the data? a. You should
Premium Function Automobile Elementary algebra
Differential Equations Second Order Differential Equations Introduction In the previous chapter we looked at first order differential equations. In this chapter we will move on to second order differential equations. Just as we did in the last chapter we will look at some special cases of second order differential equations that we can solve. Unlike the previous chapter however‚ we are going to have to be even more restrictive as to the kinds of differential equations that we’ll look at
Premium Derivative
To solve a system of equations by addition or subtraction (or elimination)‚ you must eliminate one of the variables so that you could solve for one of the variables. First‚ in this equation‚ you must look for a way to eliminate a variable (line the equations up vertically and look to see if there are any numbers that are equal to each other). If there is lets say a –2y on the top equation and a –2y on the bottom equation you could subtract them and they would eliminate themselves by equaling zero
Premium Elementary arithmetic Addition Integer
Introduction to Structural Equation Modeling (Path Analysis) SGIM Precourse PA08 May 2005 Jeffrey L. Jackson‚ MD MPH Kent Dezee‚ MD MPH Kevin Douglas‚ MD William Shimeall‚ MD MPH Traditional multivariate modeling (linear regression‚ ANOVA‚ Poisson regression‚ logistic regression‚ proportional hazard modeling) is useful for examining direct relationships between independent and dependent variables. All share a common format: Dependent Variable = Independent variable1 + Independent Variable2 + Independent
Premium Regression analysis
College Department of Chemistry Lab 8 – Ionic Reactions Submitted by Ryan T. Crawford Date Submitted: 7/10/2014 Date Performed: 7/10/2104 Lab Section: Chem-181DL1 Course Instructor: Amal Bassa Purpose: The purpose of the particular is to study the nature of ionic reactions and to learn how to write balanced equations and to learn how to write net ionic equations for precipitation reactions. Procedure: For this particular
Premium Chemistry Chemical reaction Laboratory
CHEM111AC‚ Experiment#9 - Ionic Reactions Discussion/Error Analysis In the first part of this experiment‚ the student was presented with 7 unique and unidentified bottles of solutions labeled A-G and was expected to be able to analyze the 7 solutions through trial and error and mixing them with one another. For solution A: mixing A + B formed a precipitate‚ A + C generated heat‚ A + D gave no reaction‚ A + E gave no reaction‚ A + F gave no reaction‚ A + G formed a precipitate. For solution B: mixing
Premium