FS10_1825_006_Oct6_notes_5pages

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Unformatted text preview: MTH 1825 sec. 006    Wednesday, Oct. 6, 2010  Section 3.4 – Applications of Systems of Linear Equations in Two  Variables    We will just set up a system of two equations for each problem.  Solve these on your own  using the substitution method or the addition method.    Objective 1:  Applications Involving Cost    Ex 1)   Kathleen sells two sizes of a handmade craft at a kiosk in a mall.  The small size costs  \$5 and the large size costs \$12.  If Kathleen sells a total of 105 items during a particular  week and has a total revenue of \$826 for that week, how many of each type did she sell?                        Ex 2)   Ronald bought 3 hamburgers and 2 orders of fries for his family and paid \$8.25.   Leon bought 5 hamburgers and 4 orders of fries for his family and paid \$14.61.  What was  the cost of one hamburger?  What was the cost of one order of fries?                      Ex 3)   Janice has 3 less dimes than nickels.  The total value of her dimes and nickels is  \$4.80.  How many dimes does she have?  How many nickels does she have?                  Page 1 of 5  MTH 1825 sec. 006    Wednesday, Oct. 6, 2010  Objective 2:  Applications Involving Mixtures    Ex 4)   A chemist has two concentrations of solution:  40% and 72%.  How much of each  concentration should be mixed to produce 20 liters of a 52% solution?                        Ex 5)   John needs to make 102 gallons of a 60% bleach solution.  He has pure bleach and a  32% bleach solution.  How much of each should be combined?                          Objective 3:  Applications Involving Principal and Interest    **Read Example 3 on p. 231    Ex 6)   Helen invested \$300 less in an account that pays 4% simple interest than she did in  an account that pays 6.5% interest.  If the total amount she earned after 1 year was \$73.68,  how much did she invest in each account?        Page 2 of 5  MTH 1825 sec. 006    Wednesday, Oct. 6, 2010  Ex 7)   George invested a total of \$4000 in two accounts:  one that pays 1.5% simple  interest and one that pays 2% simple interest.  At the end of 8 years, the total interest  earned was \$550.24.  How much was invested in each account?                            Objective 4:  Applications Involving Uniform Motion    Ex 8)   A plane can travel 800 miles in 4 hours with the wind.  The same plane takes 5 hours  for the return trip against the wind.  Find the speed of the plane in still air and the speed of  the wind.                          Ex 9)   A boat travels upstream (against the current) for 40 miles in 2.5 hours.  The boat  then turns around and travels 60 miles going downstream (with the current) for 2 hours.   What is the speed of the boat in still water?  What is the speed of the current?          Page 3 of 5  MTH 1825 sec. 006    Wednesday, Oct. 6, 2010  Objective 5:  Applications Involving Geometry    Ex 10)  One angle measures 9 degrees less than twice the other.  If the two angles are  supplementary, find the measure of each angle.                          Section 4.1:  Addition and Subtraction of Polynomials    A polynomial in x is defined as a finite sum of terms of the forms  ax n , where a is real and n  is a whole number (0, 1, 2, 3, etc.)    For each term, a is called the __________________________ and n is the _________________ of the term.  €     An example of a polynomial in x is:      If a polynomial has exactly one term, it is called a ____________________________.    If a polynomial has exactly two terms, it is called a _____________________________.    If a polynomial has exactly three terms, it is called a _____________________________.      In a polynomial, the term with the highest degree is called the ______________________________  (because it is the most important) and we usually write it as the first term.  The coefficient  of the leading term is called the ______________________________________________.      The degree of a polynomial is ______________________________________________________________________    ________________________________________________________________________________________________________.      Page 4 of 5  MTH 1825 sec. 006    Wednesday, Oct. 6, 2010  Examples of polynomials in x:  Polynomial  Type  4 x 3 + 7x 5 − 2x   −8 x + 3   Degree          Leading Coefficient                  € € −53  4 3 x5  € €     Polynomials can have more than one variable.  The degree of each term is the sum of the  exponents on the variables within the term.  The degree of the polynomial is the largest of  those degrees.    4 x 6 y 3 z − 9 xyz + 12 xy2 − y2 z 5                     Adding and Subtracting Polynomials    To add polynomials, just add like terms.    To subtract polynomials, distribute the negative sign first then add like terms.    Note:  Polynomials are not equations, so you cannot clear fractions!    2 4 4 2 312 x + 5 x − 7 x + 3 − 2 x − 3 x − x + 5   3 4       €     Page 5 of 5  ...
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