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Linear Algebra

Heating Water : Modeling with a Linear Equation

Water is the most importnt substance on Earth. One reason for its usefulness is that is exists as a liquid over a wide range of temp. In its liquid range, water absorbs or releases heat directly in proportion to its change in temp. Consider the following data that shows temp of a 1,000 g sampe of water at normal atmospheric pres

Solve the equation by graphing.

These are questions that I got wrong on a test..can someone show me how to do these? ________ Solve the equation by graphing. 2x-3y=12 3y-2x=-12 is this equation independent inconsistent or dependent? __________________________________________ Solve the equation by graphing. 3x-y=4 3x-y=0 is this equation

Systems of Linear Equations Differences

Please assist to understand the difference in these different methods. Please show work so I can follow the solution. Determine if the given ordered pair is a solution to the system: 12. 2x + y = 5 (4, -3) x - y = 1 22. 4x - y = -2 (-1, -2) 3x + y = -5 Solve each system of equations by the graphing method:

Systems of Equations and Inequalities and Absolute Values

How do you solve by the substituation method? x=y+3 3x-2y=4 would it be inconsistent, independent or dependent? ______________ word problem Ziggys famous yogurt blends regular yogurt that is 3% fat with its no-fat yogurt to obtain lowfat yogurt that os 1% fat. How many pounds of regular yogurt and how many pounds o

Linear Equations and Graphs

Please show work so I can understand how to solve. Need assistance with the following word problems: A. Given the following linear equation: 2x - 5y = 5 a. Graph the line for the given equation. b. Derive an equation for a line parallel to the given line passing through the origin (0 ,0). c. Graph the second line.

Linear Equations

Determine if the given ordered pair is a solution to the equation: 4. -3x + y = -2 (0,2) 6. 2x - y = -3 (-2, -1) Find the specified values: 8. 6x - 3y = 12 x-intercept & y-intercept 10. 4x - 2y = 6 slope & y-intercept Re-write the equations in the specified form: 12. y = 2x -3 write in standard form

Inequality and line equation

1.) The price of a personal computer is $2000. The markup is $150. What is the dealer cost? 2.) Solve the inequality 4y - 7 > 9y - 2. Use set-builder notation. 3.) Graph using slope and y-intercept method of y = (3/2)x - 3 4.) Graph using slope and y-intercept method of 5x + 5y = 10 5.) Graph the inequality

Linear Equations and Solving Equations

The function that relates weight in grams of a crystal (w) to the temperature t in degrees Fahrenheit in which it was grown is as follows (fictitious): W(t) = 0.8t + 12 Find w(-6). a. impossible to tell from info given b. less than 8 grams c. at least 8 grams but less than 10 grams d. at least 10 grams but less t

Systems of Equations with Three Variables and Real-Life Applications

Hello again ! trying to solve for x and Y in the following problems. please explain 1. a. X + Y=6 ; 2X + Y =8 b. 7X + 3Y=14 ; 5X + 9Y= 10 c. 4X + Y= 16 ; 2X + 3Y= 24 d. 12X + Y= 25 ; 8X - 2Y= 14 2. Suppose Bob owns 8000 shares of company X and 6000 shares of Company Y. The total value of Bobs holding of these

MATLAB Signals Theory- Linear Time - Inveriant Discrete Time System

A linear time-invariant discrete-time system has transfer function h(z)=((z^2)-z-2)/((z^2) + 1.5z-1) a. Use MATLAB to obtain the poles of the system. Is the system stable? Explain. b. Compute the step response. This should be done analytically, but you can use MATLAB commands like conv and residue. c. Plot the first seve

Differential Equations : Bifurcations in Linear Systems

In Chapter 3, we have studied techniques for solving linear systems. Given the coefficient matrix for the system, we can use these techniques to classify the system, describe the qualitative behavior of solutions, and give a formula for the general solution. In this lab we consider a two-parameter family of linear systems. The g

Solving Systems of Equations

1. Solve each system by graphing. y = - 2/3 x 2x + 3y = 5 2. Solve each system by the substitution method. Determine whether the equations are independent, dependent, or inconsistent. 2x - y = 4 2x - y = 3 3. Write a system of two equations in two unknowns for each problem. Solve each system by substation.

MATLAB Signals - Conv and Transfer Function of System

1. A discrete-time system has the following unit-pulse response: h[n] = 0.5^n - 0.25^n for n >= 0 Correspondingly, the following difference equation describes the behavior of the system: y[n + 2] - 0.75y[n +1] + 0.125y[n] = 0.25x[n +1] a. Use the MATLAB command conv to calculate the response of the system to a unit ste

Systems of Linear Equations and Inequalities

I am at a total loss on these. Any assistance you could give me would be greatly appreciated. I have a total of 9 problems. Thanks a lot!! The start-up cost for producing widgets is $449, and each widget costs $91 to produce. What is the equation for this situation? Use X for # widgets produced and Y for cost. a. none of

Acute, Obtuse, Right or Straight Angles.

1. Along a straight shoreline, two lighthouses, A and B, are located 2000 feet apart. A buoy lies in view of both lighthouses, with angles 1, 2, and 3 as indicated. (Angle 1 is denoted by , angle 2 is denoted by , and angle 3 is denoted by .) A. By looking at the picture, do you think is an acute, obtuse, right, or a st

Discussing Eigenvectors and Eigenvalues

Assume that ST = TS. Prove that the operators S and T have a common eigenvector. Let V be a complex (i.e. F = R) finite dimensional vector space. Let S, T be elements of L(V ) (set of operators on V). Assume that ST = TS. Prove that the operators S and T have a common eigenvector. these are the steps: a) Explain why T

Applications of Linear Equations

The director of a summer day camp estimates that 120 children will join if the camp fee is $250, but for each $25 decrease in the fee, five more children will enroll. Determine the linear equation that will represent the number of children who will enroll at a given fee. Hint: To write the slope, you need two points on the lin

system of linear equation and compound inequality

Please see attached file for full problem description. Solve system by the substitution method. 1. y = 2x - 6 y = x - 5 2. 7x - 4y = 26 y = x - 5 ------------------------------------------------------------------------------------ Solve each system by the addition method. If there is no solution or an

Algebra : Area and Writing Equations from Word Problems

Please see the attached file for all of the problems. 12. Rose's garden is in the shape of a trapezoid. If the height of the trapezoid is 16m, one base is 20m and the area is 224m2, find the length of the other base. 13. The sum of two consecutive integers is 145. Find the two integers. 14. Yuri has a board that is 98

Systems of Equations Word Problems

Please see attached file for full problem description. 1. Two cars leave a restaurant at the same time and travel in opposite directions. One averages 50 miles per hour and the other averages 40 miles per hour. After how long will they be 216 miles apart? 2. How many gallons of a 4% acid solution should be mixed with 2

Mathematics - Linear Operators explained in this solution

1. solve the following equations and show work. 2. You are given the following system of linear equations: x - y + 2z = 13 2x + xy - z = -6 -x + 3y + z = -7 a. Provide a coefficient matrix corresponding to the system of linear equations. b. What is the inverse of this matrix? c. What is the transpose of this mat

Linear Programming Problems: Tax Returns

Matrix methods can be used to solve linear programming problems. A linear programming problem is used to find an optimal solution, subject to stated restraints. For example, consider an accountant who prepares tax returns. Suppose a form 1040EZ requires $12 in computer resources to process and 22 minutes of the accountant's t

Stability of systems

1. A single-loop negative feedback system has a loop transfer function. GH(s) = K(s+2)^2 / s(s^2+1)(s+8) Determine the range of the gain K for which the system is stable. Choose either a. 23 < K < 367 b. K > 14 c. 0 < K < 5 2. A system has a characteristic equation q(s) = s^4 +9s^3 +45s^2 +87s +50 +0. De

Linear Algebra Problems in MTH 212 Unit 1 Individual Project - B

See attached file for full problem description. 1. Solve -3[5+2(-7+x)+x]=-3x-(x+3). 2. Solve -(4x+4)/5 = (5x -1)/2 - x/3. 3. A real estate broker's base annual salary is $18,000. She earns 3% commission on total sales. How much must she sell in real estate value during the year to earn $65,000? Set up an equation and

Linear Programming and Matrix Reducing to Row Echelon Form

1. The Copperfield Mining Company owns two mines, each of which produces three grades of ore-high, medium, and low. The company has s contract to supply a smelting company with at least 12 tons of high-grade ore, 8 tons of medium-grade ore, and 24 tons of low-grade ore. Each mine produces a certain amount of each type of ore d

Systems of Equations

1. Write an equation of the line that passes through (0, -4) and is parallel y = (3/4)x + 2. Write the answer in slope-intercept form. 2. Solve the system of equations by substitution: x + 2y = 9 3x - y = 13 3. Solve the system of equations by substitution: 4x - 3y = 1 12x - 9y = 3