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Allan Hancock College - INFS - 1200
Today . Quiz Feedback Final Exam Challenging/Practice Questions Consultation Schedule in SWOTVAC week1Quiz I Feedback I N F S1200 / I N F S7900 ntr oduction toI nfor mation Systems S1, 2009 QUI Z (20%) Result s Dist r ibut ion (Aver age: 9.6
Allan Hancock College - INFS - 1200
Today . Quiz Feedback Final Exam Challenging/Practice Questions Consultation Schedule in SWOTVAC week1Quiz FeedbackINFS1200 / INFS7900 Introduction to Information Systems S1, 2009 QUIZ (20%) Results Distribution (Average: 9.6%)45 40 40 35 3
Rutgers - MATH - 251
NameMath 251, Final ExamSAMPLE FINAL EXAMBe sure to show all your work. Unsupported answers will receive no credit. A formula sheet is supplied, for your reference. Use the backs of the exam pages for scratchwork or for continuation of your answ
Rutgers - MATH - 251
SAMPLE FINAL EXAM - Answer Key1. (9 points): Lines and Planes (a) Find parametric equations for the line which passes through (1, 2, 3) and is parallel to the vector 1, 0, 1 . A vector equation for this line is r(t) = 1, 2, 3 + 1, 0, 1 t. x(t) = 1 +
Arizona - MATH - 407044
11 Problem AnalysisThe problem Start out with 99% water. Some of the water evaporates, end up with 98% water. How much of the water evaporates? Guesses 0.01%. Solution: Guesses: Not 1%. 2%. 5%. Not 100%. 3%. 1.01%. 1.5%.First solution We start o
Arizona - MATH - 323044
MATH 323, FALL 2004, FIRST WRITING ASSIGNMENT DUE MONDAY, SEPTEMBER 13, 2004William McCallum September 3, 2004Your assignment is to write a proof of the fact that if a and b are non-negative real numbers, then their arithmetic mean is greater than
Arizona - MATH - 407084
Y 10 9 8 5 5 5 8 9 10 12 15 8 6 9 9 13 6 9 9 9n 55 54 54 55 56 54 55 54 56 56 56 54 55 55 58 57 58 56 57 55phat 0.18 0.17 0.15 0.09 0.09 0.09 0.15 0.17 0.18 0.21 0.27 0.15 0.11 0.16 0.16 0.23 0.1 0.16 0.16 0.16z^2 3.84 3.84 3.84 3.84 3.84 3.84
Arizona - MATH - 407044
Problem AnalysisMath 323, Section 3, Fall 2004 The problem Start out with 99% water. Some of the water evaporates, end up with 98% water. How much of the water evaporates? Guesses 0.01%. Solution: Guesses: Not 1%. 2%. 5%. Not 100%. 3%. 1.01%. 1.5%.
Arizona - MATH - 407044
Analogies between addition and multiplication Both operations have an identity: do the operation with the identity on any number and you get the number back. for addition it's 0: x+0=xfor multiplication it's 1: x1=xAlong with identities, we get i
Arizona - MATH - 407044
Some definitions of function that we came up with. A function is a procedure that takes an input value and gives a single output value. A function is a correspondence between each element in a set A and a single element in a set B. (We call A the
Arizona - MATH - 407044
Is there a function from the empty set to R? Let's consider the definition: A function is a rule that assigns an element of set B to every element in set A. Let A be the empty set and B the real numbers. The rule "assign the number 5 to every x A" d
Arizona - MATH - 407044
Different ways of looking at functions: Graph Table of values Operation Equation1Consider the function from R \ {2} to R \ {0}: 1 f (x) = x-2 Let's look at the question of whether it has an inverse from the operational point of view. In t
Arizona - MATH - 407044
Math 407, Fall 2004, Week 5 assignmentWilliam McCallum September 18, 2004Write an explanation of the rules for logarithms log(AB) log(Ap ) = log A + log B = p log Athat uses the exponent rules and the fact that the logarithm function is the inver
Arizona - MATH - 407044
Math 407, Fall 2004, Week 6 assignmentWilliam McCallum September 27, 2004Explain why the solutions to the equation x2 + x - 2 = 0 are x = -2 and x = 1. (This means you have to both show that those numbers are solutions, and that any solution is one
Arizona - MATH - 407044
How many solutions does the equation 3(x - (5 - 2x) + 42) = 2 - 6x have? The only operations used to build up either side are multiplying by a constant and addition. So both sides have to simplify down to a linear expression, of the form ax + b where
Arizona - MATH - 407044
Suppose we have a quadratic equation ax2 + bx + c = 0, where a, b, and c are real numbers, a = 0. What if the expression on the left does not factor? We can complete the square or use the quadratic formula b2 - 4ac x= 2a Hopefully, a, b, and c are re
Arizona - MATH - 407044
Last time we saw that completing the square transforms a quadratic equation into an equation of the form x2 = s. Then we take square roots of both sides and get x= s What is really going on when we solve this equation. What "operation" did we perfor
Arizona - MATH - 407044
You drive to Phoenix at 30 mph and return at 60 mph. Suppose the distance is d miles. Then the total time going is d/30 hours and the total time coming back is d/60 hours. The average speed is Total distance 2d 2 = 40 = = 1 1 Total time d/30 + d/60 3
Arizona - MATH - 407044
To show the solutions to x2 + x - 2 = 0 are 1 and -2, show: (1) If x2 + x - 2 = 0, then x = 1 or x = -2. (2) If x = 1 or x = -2, then x2 + x - 2 = 0. Proof of (1). Suppose that there is a real number x such that x2 + x - 2 = 0. We know using the dist
Arizona - MATH - 407044
Math 407, Fall 2004, Week 6 assignmentWilliam McCallum A transformation M : R2 R2 is said to be linear if M (v + w) M (v) = T (v) + T (w) for all v, w R2 = T (v) for all v R21. Draw figures illustrating what it means for a rotation about the or
Arizona - MATH - 407044
Math 407, Third Midterm, Fall 2004 Due Wednesday November 24, 2004William G. McCallum November 11, 2004You can discuss the problem with each other and with me (not with anybody else). The final write-up should be entirely in your own words. Let =
Arizona - MATH - 355054
t 0 0.03 0.05 0.08 0.1 0.13 0.15 0.18 0.2 0.23 0.25 0.28 0.3 0.33 0.35 0.38 0.4 0.43 0.45 0.48 0.5 0.53 0.55 0.58 0.6 0.63 0.65 0.68 0.7 0.73 0.75 0.78 0.8 0.83 0.85 0.88 0.9 0.93 0.95 0.98 1 1.03 1.05 1.08 1.1 1.13 1.15 1.18 1.2 1.23 1.25 1.28 1.3 1
Arizona - MATH - 355054
Review Sheet for Make-up ExamSeptember 23, 2005For each of the following situations (a) Write an initial value problem, giving the meaning of any parameters. (b) Solve the initial value problem. 1. A population of sh in a pond initially at 1000 gro
Arizona - MATH - 355054
More examples of separable dierential equations Consider the dierential equation v = 9.8 k0 v 2 . Rewriting it in the form 9.8 ) = k0 (v 2 2 ), k0 we see that it is similar in form to the equation v = k0 (v 2 x = x2 1 whose solution we have alrea
Arizona - MATH - 355054
System of dierential equations x y For example, consider x y =y =x = f (x, y, t) = g(x, y, t)x(0) = 1, y(0) = 0 We can learn a lot about the graphs of x and y just from reasoning about this dierential equation. Notice that x starts out at t = 0 wit
Arizona - MATH - 355054
Existence Theorem Just as in the case of ordinary rst-order dierential equations, we have an existence theorem for systems of rst-order dierential equations. It tells that the initial value problem x y = f (x, y, t), = g(x, y, t), x(t0 ) = x0 y(t0 )
Arizona - MATH - 323044
Why is the product of two negative numbers a positive number?Math 323, Section 3 Here's the formulation we settled on for what we wanted to prove. Theorem 0.1 Let n and m be integers. 1. If n > 0 and m < 0, then nm < 0 2. If n < 0 and m < 0, then nm
Arizona - MATH - 323044
Math 323, Assignment 1, due Friday 27 AugustWilliam McCallum Write a proof of the fact that the solutions to the equation x2 + x - 2 = 0 are x = -2 and x = 1. Your proof should show the reasoning behind all of the steps you take, and should be writt
Arizona - MATH - 323044
If, and, or, not These logical connectives are used to make compound sentences, such as Either I'm crazy, or there's a fly in my soup. We will fight them on land, and we will fight them at sea If you do try, you will succeed.1True or false?
Arizona - MATH - 323044
Math 323, Answer to Assignment 1William McCallum We want to prove that the solutions to the equation x2 + x - 2 = 0 are x = -2 and x = 1. This means we have to prove two statements: A. If x = -2 or x = 1, then x2 + x - 2 = 0. B. If x is a real numbe
Arizona - MATH - 323044
Different ways of saying if: implies, only if, sufficient condition, necessary condition. If it's an apple, it's red. Being an apple is a sufficient condition for it to be red. Being red is a necessary condition for it to be an apple.1What