Determining if the boundary line should be solid or dashed? A solid line should be drawn if the original inequality contains a or symbol. A dashed line should be drawn if the original inequality contains a < or > symbol; also the dashed line indicates tha
WORKSHEET (6.2) Part I Solve the linear programming using the Simplex Method: Maximize P = 15 x1 + 10 x 2 Subject to 2 x1 + x 2 10 x1 + 3 x 2 10 x1 , x 2 0
Step1: Convert the LP problem to a system of linear equations adding slack variables.
Step 2: Set u
San Jose State University Finite Mathematics Spring 2010
Instructor: Misako van der Poel Email: misako.vanderpoel@sjsu.edu Course: Office Hours: Prerequisites: Text: Course Outline: Math 70 Monday Wednesday Office: MacQuarrie Hall 439 Office Phone: 408-92
WORKSHEET (6.3) Part I Solve the following minimization problem by maximizing the dual: Minimize C = x1 + 2x 2 Subject to x1 + x 2 6 x1 + 3 x 2 12 x1 , x 2 0
Step1: Form a matrix A, using the coefficients and constants in the problem constraints and
the o
San Jose State University Finite Mathematics Spring 2010
Instructor: Misako van der Poel Email: misako.vanderpoel@sjsu.edu Course: Office Hours: Prerequisites: Text: Course Outline: Math 70 Monday Wednesday Office: MacQuarrie Hall 439 Office Phone: 408-92
WORKSHEET (3.2) Part I 1. An amount of $100 is deposited in a bank paying an annual interest rate of 12% compounded annually. (a) What is the balance after 1year? (b) What is the balance after 2years? (c) What is the balance after 3years? (d) What is the
WORKSHEET (3.1) 1. An amount of $100 is deposited in your bank account paying an annual simple interest rate of 12%. (a) What is the interest that you will earn after 1year?
(b) What is the interest that you will earn after 5years?
2.
Suppose that you bor
San Jose State University Finite Mathematics Spring 2010
Instructor: Misako van der Poel Email: misako.vanderpoel@sjsu.edu Course: Office Hours: Prerequisites: Text: Course Outline: Math 70 Monday Wednesday Office: MacQuarrie Hall 439 Office Phone: 408-92
WORKSHEET (6.1)
A Geometric Introduction to the Simplex Method
Key Terms: Standard Maximization Problem in Standard Form Slack Variables Basic and Nonbasic Variables: Basic Solutions and Basic Feasible Solutions Standard Maximization Problem in Standard F
1/30/2009
Review of the Finite Element Method
Discretization: create a finite element mesh
ME297 Introduction
January 26 2009 26, Apply boundary conditions Element level calculations: [Ke]cfw_de = cfw_fe
(variety of element types: springs, trusses, beams,
ACADEMIC YEAR CALENDAR 2005/06 FALL 2005 August 22 August 22-23 August 24 September 5 September 13 September 20 September 21 November 23 November 24-25 December 8 December 9 December 12-16 December 19 December 20 December 21 December 22January 23 SPRING 2
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June 2004
ADM Administration . B-2 AQX Aquatics Facility . D-3 ART Art Building . C-3 ASH Associated Students House . D-1
ATM Automated Teller Machines . B-4 BBC Boccardo Business Center . C-4 BB BT F CL Building BB
Matrix Operations on the TI-83/84
Written by Jeff OConnell joconnell@ohlone.edu Ohlone Colleg e http:/www2 .ohlone.edu/peop le2/joconnell/ti/ Entering a Mat rix: Press [2nd][MATRX] ( TI-83+/84) or [ MA TRX] (TI-83) to see a screen with a menu that looks a
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MATH 70 SPRING PACKET SPRING 2010 NAME: _ ALL the problems must be attempted. The intention of this packet is to provide insight and practice on the concepts covered so far. It is recommended that you work on this packet piece by piece. Attempt some probl
Math 70 HOMEWORK PROBLEMS SPRING 2010 The Problems on the quiz will be very similar to HW problems. Try to do as many different kinds of examples as you can. CHAPTER 7 Section 7.2: 7-20, 22-44, 45-52, 73-84, 85-94. Section 7.3: 1-20, 21-26, 27-32, 35-42,
1/30/2009
Modeling Example
How would you model this mechanical part?
Shells, Composites & Anisotropy
January 28 2009 28,
4
E. Chan SJSU ME297 Spring 2009
Today's Agenda
Shells
Read Ch. 12 in Logan.
Shell Elements - Motivations
3D Solid
3D Shell
Brief rev
WORKSHEET (3.3) Annuity: An annuity is any sequence of equal periodic payments.
Ordinary Annuity: Payments are generally made at the end of each period. This type of annuity is called an ordinary annuity. Term: The total time period between the beginning
San Jose State University Finite Mathematics Spring 2010
Instructor: Misako van der Poel Email: misako.vanderpoel@sjsu.edu Course: Office Hours: Prerequisites: Text: Course Outline: Math 70 Monday Wednesday Office: MacQuarrie Hall 439 Office Phone: 408-92
Formula sheet (6.3) Transpose of a Matrix Given a mxn matrix A, the transpose of A is the nxm matrix AT obtained by putting the first row of A into the first column of AT , the second row of A into the second column of AT . a b c a d g A = d e f AT = b e
Math 70 Assignment 9-24-09 First, rewrite the system of equations using matrix multiplications. Then use inverse matrices to solve the following. Use row operations to find inverse matrices. 1.
x " y = "9 2x + 6y = 11 2x " 3y = 9 ! 3x " 2y = "1 3x + y = 1
Math 70
Assignment 9-8-09
Use the Venn diagram on page 364 to answer the following: 1. P ( A B) 2. P ( A B B) 3. P ( A' B')
4. P ( B A)
a
5. P ( A A B) 6. P ( A' B B) 7. P ( A B' B) 8. P ( A A' B) 9. P ( A B' A' B) 10. P ( A B' A' B) 11. P ( A B' A' B) 12
Math 70 Assignment 9-10-09 Suppose a coin is not fair. At any moment, suppose the probability of obtaining Head is 0.4, and the probability of obtaining Tail is 0.6. We are going to toss this coin 5 times. 1. What is the probability of obtaining all heads
Math 70 Assignment 9-24-09 Use only eliminations to solve the following. Also, use the notations introduced in the class to indicate what you are doing. 1. x- y =-9 2x + 6y = 11
a
2.
2x - y = 9 2x + 3y = 11
3.
2x - 3y = 9 3x - 2y = - 1
4.
3x + y = 12 x +
Math 70 Assignment 10-8-09 Use augmented matrices to solve the following. Also, use the notations introduced in the class to indicate what you are doing. 1. x- y =-9 2x + 6y = 11
a
2.
2x - y = 9 2x + 3y = 11
3.
2x - 3y = 9 3x - 2y = - 1
4.
3x + y = 12 x +