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# Class Note for MATH 2303 at UH

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This 11 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 22 views.

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Date Created: 02/06/15

Math 2303 Section 61 Order of Operations Calculators ready This section begins a unit on algebra as you usually think of it Algebra is a generalized form of arithmetic The name comes from the title of a book written by a Muslim mathematician 1200 years ago The title AlJabr means reunion of broken parts Algebra allows us to generalize solutions to problems You can solve one problem and have a model for a lot of other problems Algebra uses variables usually letters of the alphabet to stand in for numbers The typical letter is x but it can be any letter We ll start by looking at expressions collections of variables numbers parentheses and other grouping symbols and operation symbols One thing that is not found in an expression is an equal sign Examples of expressions 2 2 x 7 x 5 x2 8x4 2xl Our first objective is to be able to evaluate expressions We need a tool to do this Example 1 Evaluate 23532 2364l6 2 solution deferred You may recall the order of operations rule First perform all operations inside PARENTHESES or other grouping sympols Next perform all operations involving EXPONENTS Then MULTIPLY and DIVIDE in the order in which those operations appear from left to right Finally ADD and SUBTRACT in the order in which those operations appear from left to right PEMDAS Now let s get back to example 1 Example 1 Evaluate 23532 2364l6 2 Example 2 Evaluate l62gt563 33 43 5 Example 3 Evaluate 2 8 22 An equation is a statement that indicates that two quantities are exactly the same or equivalent For example x 2 states that x and 2 are equivalent We ll use the order of operations rule to help evaluate expressions when we are given equations that state values for the exponents Example 4 Evaluate x2 6x7 ifx 4 Example 5 Evaluate x2y 8x4y9 ifx 2 andy 3 2x2 Sab Example 6 Evaluate 3x 2a ifx ly3a5andb 2 You have probably used formulas in previous math classes or other classes Formulas are equations that have real life applications We want to be able to evaluate formulas of all types Perimeter Area and Volume Exponential Growth and Decay We ll look at the Math of Finance formulas in a fewdays Miscellaneous Formulas There s a formula sheet on my website which you can print out and use in class and on Test 3 We can use the order of operation to help evaluate formulas Example 7 Find the perimeter and area ofa rectangle ifl 16 cm and w 12 cm Example 8 Find the surface area and the volume of a cylinder with radius 4 inches and height 12 inches Example 9 Find the surface area and volume of a box whose sides measure 8 inches 4 inches and 12 inches Example 10 Find the surface area and volume of a sphere with diameter 18 cm Example 11 A rectangular piece of packing material measuring 6 meters by 4 meters by 3 meters has space cut out for a cylinder with a 2 meter diameter to be placed inside Find the volume of the packing material Example 12 Tennis balls are sold in cylindrical cans with diameter 7 centimeters and height 208 centimeters Each tennis ball has diameter 69 centimeters and there are three of them in each can Find the volume of air inside the can of tennis balls Example 13 Find the Fahrenheit temperature if the temperature is 90 Celsius Example 14 Population grows exponentially If the initial population in a bacteria sample was 23000 and population is growing at the rate of 42 per hour what will be the population of the sample after 4 hours Example 15 Some substances decay exponentially Suppose you are studying a substance that decays at the rate of 12 per year You started with a sample of 20 grams at the beginning of your study How much of the substance is left after 6 years

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