TECHNOLOGY AND SCIENCE‚ PILANI - K.K. BIRLA GOA CAMPUS Mathematics-2 Tutorial–1 1. Use the Gaussian elimination method to solve each of the following systems of linear equations: (a) −5x1 − 2x2 + 2x3 = 14 3x1 + x2 − x3 = −8 2x1 + 2x2 − x3 = −3 (b) 3x1 − 2x2 + 4x3 = −54 −x1 + x2 − 2x3 = 20 5x1 − 4x2 + 8x3 = −83 2. Find the quadratic equation y = ax2 + bx + c that goes through the points (3‚ 18)‚ (2‚ 9) and (−2‚ 13). 3. Use the Gauss Jordan method to determine the complete solution set for the given
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like this one: If we want to get an equation that helps us identify the relationship between the Speed and the breaking distance. We can see that the line makes a form of a parabola so we drive it through out calculator to get the following results: We believe that the data is Quadratic because it goes in a parabola: Thus; When: y=ax2 +bx+c a=0.004 b=0.203 c=-6.428 Thus we come up with this equation: Y= (0.004x X2) + 0.203xX -6.428 To make the equation more realistic we can change the X
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The relationship between an object’s position and time if it travels in a straight line at a constant speed‚ as well as the relationship between the same object’s speed and time‚ will both result in a linear model. This hypothesis will be tested by using a model car‚ a spark timer‚ and timer tape. Procedure 1.Obtain a model car‚ spark timer‚ half a meter of timer tape. 2.Tape the length of timer tape to the back of the model car. 3.Feed the timer tape through the spark timer‚ setting the
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BASIC NUMERACY SKILLS – A REVISION BODMAS B Brackets first O Orders (ie Powers and Square Roots‚ etc.) DM Division and Multiplication (left-to-right) AS Addition and Subtraction (left-to-right) Do things in Brackets First. [pic] | |6 × (5 + 3) |= |6 × 8 |= |48 | | |[pic] | |6 × (5 + 3) |= |30 + 3 |= |33 |(wrong) | |Example: (Powers‚ Roots) before Multiply‚ Divide‚ Add or Subtract. [pic] | |5 × 22 |= |5 × 4 |= |20 | | |[pic] | |5 × 22 |= |102 |= |100 |(wrong) | | | |
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Quadratic Equation A quadratic equation can be solved by using: 1. Factorization i) Arrange the unknowns in general form (ax2+bx+c=0) and factorize it 2. Completing the square i) x2-6x+4=0 ii) x2-6x=-4 iii) x2-6x+-622=-4+-622 iv) x2-6x+-32=-4+-32 v) x-32=5 vi) x-3=±5 vii) x=3±5 viii) x=3+5 OR 3-5 ix) x=5.236/0.7369 3. Quadratic formula x=-b±b2-4ac2a * Forming quadratic equation from
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Linear Function :(Module): Sharmaine N. Sayao Mathematics IV-A Mrs. Imelda Sayao 1.1 Definition of a Linear Function A linear function is a function whose graph is a straight line. The equation of a linear function of x can be written in the form f(x) = mx + b or a linear equation y = mx + b where m is the slope and b is the y-intercept. The equation in the form Ax + By = C where A‚ B and C are real numbers is referred to as the general form of a linear equation. We
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WEST AFRICAN SENIOR SCHOOL CERTIFICATE EXAMINATION FURTHER MATHEMATICS/MATHEMATICS (ELECTIVE) AIMS OF THE SYLLABUS The aims of the syllabus are to test candidates on: (i) (ii) (iii) further conceptual and manipulative skills in Mathematics; an intermediate course of study which bridges the gap between Elementary Mathematics and Higher Mathematics; aspects of mathematics that can meet the needs of potential Mathematicians‚ Engineers‚ Scientists and other professionals. EXAMINATION FORMAT There will
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Chapter 13 Linear Regression and Correlation True/False 1. If a scatter diagram shows very little scatter about a straight line drawn through the plots‚ it indicates a rather weak correlation. Answer: False Difficulty: Easy Goal: 1 2. A scatter diagram is a chart that portrays the correlation between a dependent variable and an independent variable. Answer: True Difficulty: Easy Goal: 1 AACSB: AS 3. An economist is interested in predicting
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Accounting is founded on the basic equation that states a company’s Assets equal their total Liabilities plus their total Owner’s Equity . This equation is summarized as ALOE . This isthe basis of the Balance Sheet.Assets are the company’s furniture‚ fixtures and equipment‚ physical property‚ intellectual property and other resources. These properties include the physical land as well as the equipmentand building improvements on the property.A company’s liabilities
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TOPIC – LINEAR PROGRAMMING Linear Programming is a mathematical procedure for determining optimal allocation of scarce resources. Requirements of Linear Programming • all problems seek to maximize or minimize some quantity • The presence of restrictions or constraints • There must be alternative courses of action • The objective and constraints in linear programming must be expressed in terms of linear equations or inequalities Objective
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