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Basic Algebra

Parallel RC Circuit Problem (Transfer Function)

See attached file for full problem description. a. Derive the expression for the transfer function of the circuit above. Simplify the expression as far as possible but do not attempt to rationalize it. Refer to the two reactances as Xc1 & Xc2. b. Using the transfer function obtained in part (a) above, derive an expression

Solving systems of equations by substitution and addition

-3/x+2 * 5x+10/9 ax+am+3x+3m/a^2-9 / 2x+2m/a-3 solve and write the answer in the lowest term: 5a^2b/12a * 2a^3b/15ab^6 solve the equation x/x-1-3/x=1/2 solve for y: 2(b+y)=b solve by substitution y=3x+11 2x+3y=0 x+2y=1 8x+6y=4 solve by addition -3x+y=3 2x-3y=5 solve by addition:

Factoring Equations Root Properties

A^2- 6a +9=0 Use the even -root property to solve each question x^2= 9/4 (x-3)^2=16 (w-3/2)^2=7/4 (w+2/3)^2=5/9 Find the perfect square trinomial whose first two terms are given. w^2-5w p^2+6/5p factor each perfect square trinomial. y^2-5y+25/4 t^2+3/5t+9/100 solve by complteing the square

Simplifying Expressions : Rules of Exponents

(3^-6)^1/3 simplify each expression assume the variables represent any real #s and use absolute value as necessary (y^3)^1/3 Simplify assume all variables represent positive #s write answer with positive exponents only w^1/3 / w^3 Simplify each expression right your answer with positive exponents assume that all

Nilpotents, Ideals and Nilradicals

Prove that if R is commutative ring and N=(a1,a2,..am) where each ai is a nilpotent element, then N is a nilpotent ideal, i.e N^n=0 for some positive integer n. Deduce that if the nilradical of R is finitely generated then it is a nilpotent ideal. P.S. the set of nilpotent elements form an ideal which is called nilradical of

Coefficients of Quadratic Equations

Quadratic Equations Write three quadratic equations, with a, b, and c (coefficients of x2, x, and the constant) as: 1. Integers 2. Rational numbers 3. Irrational numbers See attached file for full problem description.

Tangent Lines and Logarithmic / Exponential Functions

Tangent Line and Logarithmic/Exponential Functions This project is going to consider the relationship between a point (a, b) on the natural logarithmic and exponential functions and its relationship to the intercept of the tangent line to the respective functions at the point (a, b). Hint: Recall the distance between two

Equations for time and rate problems and their solutions

52. How can a graph be used to determine how many solutions an equation has? 8. Bobbi picks 1 qt in 20 minutes. Blanche picks 1 qt in 25 minutes. How long would it take them to pick one quart if they work together? 14. The speed of a freight train is 15 mph slower than the speed of a passenger train. The freight train tr

Solve: Simplifying Expressions

Simplify the following. Make sure to show all the steps involved. Expression: (3t^2 - 8t +3) + (-5t^2 + 4) - (t^2 + 5t - 3)

Algebra Word Problems

The payment sugar beet growers receive is based on the sucrose content of their delivered beets. A sample is taken from each load of beets and the sugar content in the beets is determined by polarimetry of the beet extract. In a typical situation 50 grams of pulverized beet tissue is homogenized with 360 mL of dilute aluminum

Matrix Algebra with Regression Estimation

Consider the linear regression model Yi = BXi+ Ui where B= Beta i = 1,2 .....5 Xi = 2i Yi = [1 2 3 3 4 ] ' (i.e a 5x1 vector) and Sigma ^2 = 1 Compute the OLS Estimate of B . Can you work it out slowly, step by step, as I am having a hard time doing the problems in the book, and need a sample to look back at.

Solving Inequalities Word Problems

How do you solve the inequality (x + 1)(x - 6) < 0, and express the solution using interval notation. If an object is shot upward with an initial velocity of 240 feet per second so that its height s (in feet) above the ground after t seconds is given by s = -16t2 + 240t. For what values of t will the object be at least 416 f

Simplifying Expressions

Three problems: 3/2w + 7/2w a+7 9-5a ______ + _______ a-4 a-4 4h-3 h-6 ______ - ______ h(h+1) H(h+1)

Quadratic Equations

1) Using the quadratic equation x2 - 6x + 8 = 0, perform the following tasks: a) Solve by factoring. b) Solve by using the quadratic formula. 2) For the function y = x2 - 6x + 8, perform the following tasks: a) Put the function in the form y = a(x - h)2 + k. b) What is the equation for the

Rational Expressions & Equations Series

See attached file for full problem description. Solve by factoring and using the principle of zero products. Remember to check. 2 30. - 9x + 14 = 0 2 34. x + 16x = 0 2 46. 3x - 7x = 20 2. The length of a rectangle garden is 4m greater than the width. The a

Vertical motion of a baseball under quadratic drag friction

Problem 1: Consider a two-dimensional problem in the xy-plane. There are two points in space, labeled as P and Q, as shown in the figure to the right a) Using polar coordinates, sketch on the figure at points P and Q the radial and azimuthal unit vectors. b) Write down a general expression for the radial and azimuthal unit

Algebra Word Problems

Jenny purchased a prepaid phone card for $20. The long distance calls cost 10 cents a minute using this card. Jenny used her card only once to make a long distance phone call. If her remaining credit on the card is $18.90. How many minutes did her call last?

Algebra Help

Solve by graphing. Indicate whether each system is independent, dependent or inconsistent. 1. y= 2x-1 x+y= 2 2. 2x-3y=12 3y-2x= -12 3. 3x-y=4 3x-y=0 Solve each system by the substitution method. Indicate whether each system is independent, dependent or inconsistent 4. x-y=3 3x-2y=3 5. 3y=x+5 3x-9y= -10 6

Algebra Questions

See attached file for full problem description. 1. Solve. 6x - 0.37 = 5(x - 0.28) 2. Identify the base in the statment "50% of 300 is 150." 3. Identify the rate in the statment " 260 is 52% of 500." 4. The length of one of the equal legs of an isosceles triangle is 8 cm less than 4 times the length of the base.