Math 1050, Week 2 Notes
Math 1050, Week 2 Notes 1050-001
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This 0 page Bundle was uploaded by Andrea Notetaker on Thursday January 14, 2016. The Bundle belongs to 1050-001 at University of Utah taught by Professor Margarita Cummings in Fall 2016. Since its upload, it has received 47 views. For similar materials see College Algebra in Mathematics (M) at University of Utah.
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Date Created: 01/14/16
Counting Questions From lecture on January 19 2016 There are four different types of counting questions quotOptionquot questions quotOrder allquot questions quotOrder somequot questions quotChoosequot questions 1 quotOptionquot Questions To solve this type of question all you need to do is multiply all the different options together AXBXC Example of an quotOptionquot question A local sandwich shop makes sandwiches to order There are 3 kinds of bread 4 kinds of meat and 2 kinds of cheese How many different kinds of sandwiches are available at the shop 1 quotOrder allquot Questions To solve this type of question you take the number of objects factorial N Factorial simply means a multiplication problem The way you multiply factorial is very simple if you have 4 objects you multiply 4x3x2x1 If you have 6 objects you multiply 6x5x4x3x2x1x And so on Example of an quotOrder allquot Question How many ways can you organize the letters RCMBK using all the letters exactly one time Important to Remember If the number of objects is equal to the number of places available it is an order all question 1 quotOrder somequot Questions These types of questions are easy to solve with just logic and by simply thinking through the problem But if you need the formula the formula is N NK N being the number of objects and K being the number of places available Example of an quotOrder somequot Question There are 30 people running a marathon How many ways can lst 2nd and 3rd place be determined 1 quotChoosequot Questions It is important to remember that quotchoosequot questions are not ordering objects so order is unimportant The formula for these questions is N KNK Example of a quotChoosequot Question There are 20 faculty members all hoping to be on a committee of 5 people to select the new chair How many ways can the 5 people be selected Pascal39s Triangle From lecture on January 22 2016 This is Pascal39s Triangle 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 1o 10 5 1 The rows are numbered from top to bottom the topmost row being Row 0 The numbers in the rows are read from right to left as term 0 term 1 term 2 etc There are many patterns that can be found in Pascal39s Triangle but an interesting pattern to recognize is this Row 0 equals 2 aso equals 1 1 Row 1 equals 11 21aso equals 11 Row 2 equals 22aso equals 1331 1331 And so on The notation for Pascal39s Triangle is 4 3 This is read as quot4 choose 3quot This notation is referring to Row 4 term 3 which is 4 This notation is a simpler way of solving 4 343 Writing Polynomials Using Pascal39s Triangle x15 The exponent is refers to a speci c row in the Triangle Since this exponent is 5 you need to use the 5th row Now that you have a row the numbers in that row are your coefficients for writing the polynomial So you can now write 1 5 10 10 5 1 Next you need to separate x1 into two different pieces x1 Place these pieces next to each coef cient 1X1 5X1 10X 10X 5X1 1X 1 1 1 Now add exponents Since this polynomial is in the 5th row or to the 5th exponent the highest exponent will be 5 The lowest exponent will always be 0 for every polynomial you write For both the x piece and the 1 piece the exponents will start at the far right side of the polynomial The x pieces39s exponents will move from 5 to 0 The 1 pieces39s exponents will move from 0 to 5 The result should look as such 1X51 5X41 10X31 10X21 5X11 1X 1 O 1 2 3 4 5 Now simplify The resulting polynomial is X5 5x4 10x3 10x2 5x 1
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