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Math 115 Chapter 1 Textbook Notes

by: Stacy Downing

18

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4

Math 115 Chapter 1 Textbook Notes MATH 115

Marketplace > Towson University > Mathmatics > MATH 115 > Math 115 Chapter 1 Textbook Notes
Stacy Downing
Towson
GPA 3.94

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COURSE
Basic Math for The Sciences
PROF.
Ellen M. Johnson
TYPE
Class Notes
PAGES
4
WORDS
CONCEPTS
Math
KARMA
25 ?

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This 4 page Class Notes was uploaded by Stacy Downing on Sunday January 31, 2016. The Class Notes belongs to MATH 115 at Towson University taught by Ellen M. Johnson in Fall 2015. Since its upload, it has received 18 views. For similar materials see Basic Math for The Sciences in Mathmatics at Towson University.

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Date Created: 01/31/16
Math 115 Chapter 1 Textbook Notes  Linear Equation in One Variable ax + b = 0, where a and b are real numbers and a ≠ 0  Solving a Linear Equation: o Simplify the algebraic expression on each side by removing grouping symbols and combining like terms. o Collect all the variables terms on one side and all the numbers on the other side. o Isolate the variables and solve o Check the proposed solution in the original equation  Solving a Linear Equation Involving Fractions o Multiplying the fractional term’s denominators and use it to multiply both fractions. 1+ 3 1 1 3 5 2 x 10 x 10x 30x −5 o = +  )  = +  10=2x+15  =x x 5 2x 10x 1 =10x¿ x 5 2x 2 ()x  Strategy for Solving Word Problems o Let x represent one of the unknown quantities o Represent other unknown quantities in terms of x o Write an equations in x that models the conditions o Solve the equation and answer the question o Check the proposed solution in the original wording of the problem  Common Areas n g  S  Equa l h tions e a  T  A= p r ½ h e a (a+b  S  A = 2 p ) q s e u  P = z a 4s o r i e d  R  A =  Common Volumes e lw c  P = t 2l + a 2w n g l e  C  A = ir πr2 c l  C = e 2πr  T  A= ri ½ bh a  Sh  Eq ap uat e ion s  Cu  V be = s3  Re  V cta = ng lw ula h r  Sol id  Cir  V cul = 2 ar πr  Cy h lin de r  Sp  V he = re 4/3 πr3  Co  V ne = 1/3 πr2 h  2  The imaginary Unit I  I = √−1,wherei =−1  Conjugate of a Complex Number  (a + bi)(a-bi) = a + b2 2  Quadratic Equation ax + bx +c =0  Square Root Property u = d  u ±√d  Completing the Square  x + bx + (b/2) = (x + b/2) 2 2 x= −b± b√−4ac  Quadratic Formula 2a  The Pythagorean Theorem  a + b = c 2 2  Solving a Polynomial Equation by Factoring o Move all nonzero terms to one side and obtain 0 on the other side o Factor o Set each factor equal to zero and solve the resulting equations o Check the solutions in the original equation  Solving a Radical Equation o Isolate a radical on one side o Raise both sides to the nth power o Solve the resulting equation o Check the proposed solutions in the original equation  Solving Radical Equations of the From x m/n= k o Assume that m and n are positive integers, m/n is in the lowest terms, and k is a real number o 1. Isolate the expression with the radical exponent o 2. Raise both sides of the equation to the n/m power  If m is even  If m is odd m m n n m m n n  n ( ) m m  n ( ) m m x =k → x =±k x =k → x =k  o 3. Check all proposed solutions in the original equation to find out if they are actual solutions or extraneous solutions  Solving involving Absolute Value o │ ax – b│ = c  ax – b =c and ax – b = -c and then solve for x  Interval Notations o Open Interval (a,b): the set of real numbers between, but not including a and b  (a,b) = { x│ a < x < b} o Closed Interval [a,b]: the set of real numbers between, and including, a and b  [a,b] = {x│ a ≤ x ≤ b} o Infinite Interval (a,∞): the set of real numbers that are greater than a  (a,∞) = {x│ x > a} o Infinite Interval (-∞, b]: the set of real numbers that are less than or equal to b  (-∞,b] = {x│ x ≤ b}  Properties of Inequalities o The Addition Property: If a < b, then a + c < b + c o The Positive Multiplication Property of Inequality: If a < b and c is positive, then ac < bc o The Negative Multiplication Property of Inequality: if a < b and c is negative then ac > bc  Solving a Linear Inequality Containing Fractions o Simplify each side o Collect variable terms on one side and constant terms on the other side o Isolate the variable and solve o Express the solution set in set-builder or interval notation and graph the set on a number line  Solving an Absolute Value Inequality o If u is an algebraic expression and c is a positive number. o 1. The solutions of │u│ < c are the numbers that satisfy –c < u < c o 2. The solutions of │u│ > c are the numbers that satisfy u < -c or u > c

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