Factorizing Polynomials and Solving Rational Expressions Answer the following questions and show all your calculations. There are different methods for factoring. All methods involve some sort of trial and error. That’s why it is always important to check your answer by foiling. 1.
Would any restrictions apply to the domain and range of those equations? Explain your reasoning using complete sentences. No, because a line is the set of all points. As long as the point
Mat 117 Problem set 6 (System of Equations) Write your name and date 1. Solve the following systems of equations: a) 3x y 8 15 x 2 y 26 a) solution x c) No solution , y Write your answer here: b) Many solutions {( x, y ) | x , y any real number} b) 3x y 8 15 x 5 y 13 a) solution x c) No solution , y Write your answer here: b) Many solutions {( x, y ) | x , y any real number} c) 5x y 8 15 x 3 y 24 a) solution x c) No solution , y Write your answer here: b) Many solutions {( x, y ) | x , y any real number} 2. Use matrix method (Augmented form) and solve the following systems: a) x 3 y 4 z 21 2x y z 7 2 x 3 y 3z 19 a) solution x c) No solution , y
Set up the matrix equation to solve this system. 2. Given the inequality y < x2 + 2x – 3, is the point (0, -3) part of the solution? Name a point that is part of the solution and one that is not. 3.
Two real irrationals solutions Two real rationals solutions f(x) has two real rational solutions and and g(x) has two real irrational solutions. After matching these functions, explain to Professor McMerlock how you know these functions meet each condition. Remember, he is a professor, so use complete sentences. When the function crosses the x axis meaning f(x) = 0 there are two real numbers of x that satisfy the equation. Numbers where you can't write them as a fraction, and thus can't write them as a decimal which repeats are irrational.
Problem 2. Find a recurrence relation for un , the number of bit strings of length n that do not contain two consecutive zeros, by (a): using the recurrence relation zn for the number of bit strings of length n that do contain two consecutive zeros. SOLUTION: We simply observe that all strings of length n either do or don’t have two consecutive zeros; mathematically, this means that zn +un = 2n . Hence, un = 2n −zn = 2n −(zn−1 +zn−2 +2n−2 ). (b): by reasoning from scratch.
The vector function r(t) = t sin t, ___________ , t describes a spiral on the surface of a cone. B. For vector function r(t), unit tangent vector T(t) = b C. 10pts . r (t) dt is the __________________________ of a space curve r(t) from t = a t o t = b. a D. TRUE or FALSE: Curvature is negative when moving out of a curve. D. The normal plane for space curve C at a point is the plane containing unit vectors ______ and _______ E. F. TRUE or FALSE: B(t) does not need to be scaled since it is already a unit vector.
Unit 3 – Algebra Basics Module 3C Sections 10.3 – 10.8 3C Addition of Real Numbers Addition on the Number Line To do the addition a + b on the number line, start at 0, move to a, and then move according to b. a) If b is positive, move from a to the right. b) If b is negative, move from a to the left. c) If b is 0, stay at a. Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. Slide 2 3C Addition of Real Numbers Add real numbers without using the number line. Add: –4 + 9.
This changes the now rational exponent to x^3/3, which simplified leaves x as the final answer. * The product of powers property states that exponents with the same base, when multiplied, add their exponents together. So we add the numerators up and keep the denominator to get x^3/3, which is simply x. * When a negative exponent is in the denominator as it is here, you make it bring it upward to make a positive. One times x^1 leaves x when simplified.
Using the truth table, write the un-simplified logic expression for the output function Decision. Be sure that your answer is in the Sum-of-Products form. 3. Design an AOI logic circuit that implements the un-simplified logic expression Decision. Limit your implementation to only 2-input AND gates (74LS08), 2-input OR gates (74LS32), and inverters (74LS04).