MATH 117 Complete Course DQ
MATH 117 Complete Course DQ
Popular in Course
verified elite notetaker
Popular in Department
This 6 page Study Guide was uploaded by needhelp Notetaker on Monday November 16, 2015. The Study Guide belongs to a course at a university taught by a professor in Fall. Since its upload, it has received 13 views.
Reviews for MATH 117 Complete Course DQ
Report this Material
What is Karma?
Karma is the currency of StudySoup.
You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!
Date Created: 11/16/15
MATH 117 Complete Course DQ’s and Capstone DQ Week 1 DQ 1 Post a response to the following: Explain three rules for exponents listed in the chart on p. 239 (section 4.2). Do not explain the first two definitions listed in the table (Exponent of 1 or 0). Create an expression for your classmates to solve that uses scientific notation and at least one of the rules for exponents you have described. Consider responding to your classmates by assisting them in solving the problem you created, developing their explanations of the rules of exponents, or describing reallife situations where their examples might exist. A negative exponent just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side. An example would be: 5 10 x ÷x = x over x =10 1x over 1x =0 5 10 1x x over 1 = x15 The explanation of product rule is “When multiplying with exponential notation, if the bases are the same keep the base and add the exponents”. An example of this would be as follows: n * m * n * m 3 = 11+ 2 12+3 n * m = n * m 15 The power rule can be simply put as multiplying the exponents to raise a power to a power. An example of this would be as follows: (12 ) = 6*4 12 = 12 24 Here is an expression to solve. 2 9 3.78/4 *4 1253 Week 1 DQ 2 Post a response to the following: How is dividing a polynomial by a binomial similar to or different from the long division you learned in elementary school? Can understanding how to do one kind of division help you with understanding the other kind? What are some examples from real life in which you might use polynomial division? Dividing a polynomial by a binomial is similar to the method of long division that I was taught back in elementary school. However, Instead of simply using numbers as we did back then, there are variables to deal with as well but the process is effectively the same. Divide, multiply, subtract and bring down the term in line and do it all over again until the problem is solved. Just as in long division though there might be a remainder which is expressed with an “R=” and then the variable or number. If one can understand the long division then it is very possible for one to adapt that same technique to dividing a polynomial by a binomial. The multiplication of numbers and subtraction of numbers in the long division is relatively the same when dividing a polynomial by a binomial. One might want to recheck their work several more times that what is required with long division though, it does get a little trickier. Dividing numbers is just systematic and is something that all have done their whole lives where as dividing polynomials is less systematic and requires a more complex thought process. The only example I can think of is for chemists. They would have to use formulas like this all the time to come up with certain types of chemical compounds or even medicine. Other than that I would be lost for the use of these division techniques. Week 3 DQ 1 Post a response to the following: Take any number (except for 1). Square that number and then subtract one. Divide by one less than your original number. Now subtract your original number. Did you reached 1 for an answer? You should have. How does this number game work? (Hint: Redo the number game using a variable instead of an actual number and rewrite the problem as one rational expression). How did the number game use the skill of simplifying rational expressions? Create your own number game using the rules of algebra and post it for your classmates to solve. Be sure to think about values that may not work. State whether your number game uses the skill of simplifying rational expressions. Consider responding to your classmates by solving their number games or expanding on their games to create an even more challenging one. You may want to review responses to your number game in case you need to make changes or help another student. The number that I chose to try this interesting game with is 10, so the first thing to do is to square the number so here it goes. 2 10 = 100 100 1 = 99 99 ÷ 9 = 11 11 – 10 = 1 If we do this with a variable it would look like this with y as our variable: y y2 square your variable y – 1 subtract 1 2 (y 1)÷(y1) divide by one less than your original variable (x+1)x subtract the original variable 1 final answer is 1, yes. The following number game uses the skill of simplifying rational expressions. Choose a number except for 4 and add 2. Multiply by 2 less than the number and add 3 times the original number. Divide by 4 more than the original number. Finally, add 1. Did you end with the same number you started with and why is 4 not allowed. This game works the same if you are to plug in a variable in the place of a number. Week 3 DQ 2 Post a response to the following: How is doing operations (adding, subtracting, multiplying, and dividing) with rational expressions similar to or different from doing operations with fractions? Can understanding how to work with one kind of problem help understand how to work another type? When might you use this skill in real life? In a sense fractions are rational expressions so I would think that yes they are similar. Whatever we can do with a fraction we can do with rational expressions. Fractions have always been the Achilles heel to most everyone but once we learn to properly solve a fraction I feel that most all other forms of operations should come fairly easy. Since fractions deal with parts of a whole number the only way to find the correct answer is by being able to add, subtract, multiply and divide in some way during that process. So I would feel that learning any step in mathematics would most certainly help in learning other areas of operations. A real life skill that would most defiantly call for one to know how to use these operations could be in the production field of a food processing plant. The Sanitation department at these facilities might seem like they are just laborers but they really need to know how to measure chemicals in order to stay within the government regulation limit for PPM (parts per million) of water and chemicals. Any deviation from this could land many workers in hot water. Week 5 DQ 1 Post a response to the following: Why is it important to simplify radical expressions before adding or subtracting? How is adding radical expressions similar to adding polynomial expressions? How is it different? Provide a radical expression for your classmates to simplify. Consider participating in the discussion by simplifying your classmates’ expressions. Detail what would have happened or if the expression was not simplified first. Simplifying radical expressions is a very necessary step in solving the problem right. Without simplification of like radicals the answer produced at the end will be wrong. However, if the radicals are different then there is no way to simplify them. Simplification of radicals can only work with those radicals that are alike, just as with polynomial powers and variables. The similarities between radical expressions and polynomial expressions are that both add or subtract the like terms and radicals, depending on which one is being worked with. The differences between them are radicals deal with the value inside the root and polynomials deal with variables and their powers. Add: √12 + √27 Week 5 DQ 2 Post a response to the following: Review section 10.2 (p. 692) of your text. Describe two laws of exponents and provide an example illustrating each law. Explain how to simplify your expression. How do the laws work with rational exponents? Provide the class with a third expression to simplify that includes rational (fractional) exponents. Consider responding to classmates who have chosen laws different from the ones you selected. Ask clarifying questions of your classmates to make sure you understand the laws. Practice simplifying your classmates’ expressions. When you multiply two exponential terms with the same base, you add the exponent. The formula is m * m = m (a +.b) 3 6 5 *5 = 5 =6 5 = 5*5*5*5*5*5*5= 1953125 a b When you divide two exponential terms with like bases, you subtract the exponents: m ÷ m = m (a –.b) 6 3 5 ÷ 5 = 5 =3 3 5 = 5*5*5= 125 The following is my example to solve. (1/6) (11/6) 16 * 16 = Week 7 DQ 1 Post a response to the following: How do you know if a quadratic equation will have one, two, or no solutions? How do you find a quadratic equation if you are only given the solution? Is it possible to have different quadratic equations with the same solution? Explain. Provide your classmate’s with one or two solutions with which they must create a quadratic equation. Consider responding to your classmates by creating an equation from their solutions. Show that your equation should yield the appropriate number of solutions. If other equations exist with the same solution, provide the alternate equation and provide an explanation. You may want to view responses to the solutions you posted and guide your classmate’s if necessary. The quadratic equation is a special polynomial. It has three terms and is in the form ax² + bx + c. The first term will always be squared, the middle term will always have the same variable, and the last term will contain only an integer. With the equation given above insert the values for a, b, and c and solve for the value of b^2-4ac. this value is called the discriminate of the quadratic equation. If the discriminate is equal to 0, then the quadratic equation has one solution, if it is >0, then it has 2 solutions, and if it is <0, it has no real solution. In order to find a quadratic equation with only one solution, x = a, the corresponding quadratic equation would be y = (x - a)^2. Now if there are two solutions, x = a, and x = b, then the corresponding equation would be y = (x - a) (x - b). It is possible to have different quadratic equations with the same solution, if we have the roots x = a, and x = -b, then we can have C(x-a) (x + b) = 0, where C is a constant. So multiplying with a constant does not change the roots. Here are some solutions in which one must create a quadratic equation: Find a quadratic equation that has roots x = 2 and x = 3: Find a quadratic equation that has two roots at x = 1: Week 7 DQ 2 Post a response to the following: Quadratic equations can be solved by graphing, using the quadratic formula, completing the square, and factoring. What are the pros and cons of each of these methods? When might each method be most appropriate? Which method do you prefer? Why? In my opinion the best way to solve quadratic equations is using the quadratic formula. With just a few steps involved and a little arithmetic involved this method if far more reliable. The only con I can think of is that some quadratic equations can be solved faster by just factoring it out. Factoring on the other hand is great and quick with little actual arithmetic involved. The con of factoring is that there are very few actual real life situations that one can use factoring. The next one down on the list would be graphing, not the best choice but almost as simple as the others or at least in my opinion. Graphing is a great way to visually see what the answer is but unless one is quite the artist their answer could be off. That is one of the cons of graphing the other is that the answers are not always real or whole numbers making it very hard to accurately graph the point. The last method in my opinion is the hardest and requires more mental work, or arithmetic. Completing the square involves more steps and takes longer to complete, the only real pro about it has could be that if done correctly it is quite accurate. The con is that it takes a lot longer to solve and one needs to be very efficient in mathematics or the answers could be wrong. The method I prefer if factoring or just using the quadratic formula to solve the equations. If factoring is possible than that is how I solve the equation if not I solve it by using the quadratic formula. I chose these types because of the accuracy and easiness of solving. Week 9 Capstone DQ Post a response to the following: Has the content in this course allowed you to think of math as a useful tool? If so, how? What concepts investigated in this course can apply to your personal and professional life? In what ways did you use MyMathLab® or the Center for Mathematic Excellence for extra support? I have always envisioned math as something that we all need. Whether it is constructing a new tree house for your kids or planning a garden in your back yard. Math gives you the ability to find the best way in doing either. For instance, when it comes to a tree house, one needs to know exactly how long to cut the boards and how many of them need to be cut at 90 degree angles. Without math one would be doing this one board at a time, measuring and remeasuring to make sure that board one fits with board two. Or even cutting and recutting to make that 90 degree angle corner fit into place. With math these calculations can be done on a broader spectrum allowing for more work to get done faster. I know when I did my garden last year I planned ahead for it. I pulled up some layouts from Better Homes and Gardens and used one of their designs. This required for a lot of measuring and taping off of certain areas and the math I have learned here would have helped this project go a lot faster. However, just as with anything that we might study it depends on our jobs if the information will really be used. As for the job I currently have I feel that most of this math will not be used although some of it might be used when I create graphs for our safety meetings. Linear equations will probably make up the most of what I use, but who knows only the future will hold these answers. As for using the MyMathLab® during own nine week trek across the world of math I would say that the most I used this application was for help with the checkpoint questions. I found that by pressing the ‘show me an example’ button I could figure out the problem a little easier. Other than that I really did not try anything else during this class.
Are you sure you want to buy this material for
You're already Subscribed!
Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'