# PROBLEM 1-9

1. Sailboat stability. To be considered safe for ocean sailing, the capsize screening value C should be less than 2 ( www.sailing.com ). For a boat with a beam (or width) b in feet and displacement d in pounds, C is determined by the function  a) Find the capsize screening value for the Tartan 4100, which has a displacement of 23,245 pounds and a beam of 13.5 feet. b) Solve this formula for d. c) The accompanying graph shows C in terms of d for the Tartan 4100 (b = 13.5). For what displacement is the Tartan 4100 safe for ocean sailing?

Problem 104

1. Sailboat speed. The sail area-displacement ratio S provides a measure of the sail power available to drive a boat. For a boat with a displacement of d pounds and a sail area of A square feet S is determined by the function a) Find S to the nearest tenth for the Tartan 4100, which has a sail area of 810 square feet and a displacement of 23,245 pounds. b) Write d in terms of A and S.
 I picked O On page 636, solve the following problem by factoring Solve the following problem by using the Quadratic Formula O or X 42 52 on p.636

Problem 42: y2 − 3y − 10 = 0

Problem 52: · For the factoring problem, be sure you show all steps to the factoring and solving. Show a check of your solutions back into the original equation.

· For the Quadratic Formula problem, be sure that you use readable notation while you are working the computational steps. Refer to  Inserting Math Symbols  for guidance with formatting.

· Present your final solutions as decimal approximations carried out to the third decimal place. Due to the nature of these solutions, no check is required.

· Incorporate the following four math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.):

· Factoring

· Completing the square

· Discriminant

Math 1: 1 PAGE: DUE IN 24 HRS

Factor the polynomials using whatever strategy seems appropriate. Referring back to the processes covered in Chapter Five of Elementary and Intermediate Algebra, state which factoring methods you will use and then demonstrate the methods on your problems, explaining the process as you go. Discuss any challenges those particular polynomials posed for the factoring. y2 + yt?12t2 and 20w2 + 100w + 40

PROBLEM 2: Real World Quadratic Functions: 1 PAGE

Read the following instructions in order to complete this assignment: 1. Solve problem 56 on pages 666-667 of Elementary and Intermediate Algebra.  2. Write a two to three page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the example and be concise in your reasoning. In the body of your essay, please make sure to include: o An explanation of the basic shape and location of the graph and what it tells us about the Profit function.  o Your solutions (it is a double question) to the above problem, making sure to include all mathematical work for both problems. o Discuss how and why this is important for managers to know, and explain what could happen if the ideal conditions were not met. Problem 56: Maximum profit. A chain store manager has been told by the main office that daily profit, P, is related to the number of clerks working that day, x, according to the function P = ?25x^2 + 300x. What number of clerks will maximize the profit, and what is the maximum possible profit?

PROBLEM 3: Solving Quadratic Equations: 1 PAGE

• For the factoring problem, be sure you show all steps to the factoring and solving. Show a check of your solutions back into the original equation. • For the Quadratic Formula problem, be sure that you use readable notation while you are working the computational steps. Refer to Inserting Math Symbols for guidance with formatting. • Present your final solutions as decimal approximations carried out to the third decimal place. Due to the nature of these solutions, no check is required. • Incorporate the following four math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.): o Quadratic formula o Factoring o Completing the square o Discriminant

PROBLEM 4: 2 PAGES: Real World Radical Formulas

Read the following instructions in order to complete this assignment: Solve parts a and b of problem 103 on page 605 and problem 104 on page 606 of Elementary and Intermediate Algebra.  Write a two to three page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the example and be concise in your reasoning. In the body of your essay, please make sure to include: An explanation of what the parts of the formula mean before using it to get your answers. Study the Instructor Guidance examples to learn how to solve the formula for another variable. Your solution to the above problems, making sure to include all mathematical work. A discussion of how and why these concepts are important in the “real world.” Describe another situation that could be evaluated using these concepts.

PROBLEM 5: Simplifying Radicals

Find the rational exponent problems assigned to you in the table below. If the last letter of your first name is M or Z On pages 576 – 577, do the following problem 38 and 72 • Simplify each expression using the rules of exponents and examine the steps you are taking. • Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing the thought behind your math work.):  o Principal root  o Product rule  o Quotient rule  o Reciprocal  o nth root  Refer to Inserting Math Symbols for guidance with formatting. Be aware that with regards to the square root symbol, you will notice that it only shows the front part of a radical and not the top bar. Thus, it is impossible to tell how much of an expression is included in the radical itself unless you use parenthesis. For example, if we have ?12 + 9 it is not enough for us to know if the 9 is under the radical with the 12 or not. Thus we must specify whether we mean it to say ?(12) + 9 or ?(12 + 9). As there is a big difference between the two, this distinction is important in your notation. Another solution is to type the letters “sqrt” in place of the radical and use parenthesis to indicate how much is included in the radical as described in the second method above. The example above would appear as either “sqrt(12) + 9” or “sqrt(12 + 9)” depending on what we needed it to say.

PROBLEM 6: Two-Variable Inequalities: 2 PAGES

Read the following instructions in order to complete this assignment:  1. Solve problem 68 on page 539 of Elementary and Intermediate Algebra, and make sure to study the given graph. For the purposes of the assignment, it would be helpful to copy the graph onto your own scratch paper.  2. Write a two to three page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the example and be concise in your reasoning. In the body of your essay, please make sure to include: o An answer to the three questions asked about given real-world situation. o An application of the given situation to the following two scenarios: ? The Burbank Buy More store is going to make an order which will include at most 60 refrigerators. What is the maximum number of TVs which could also be delivered on the same 18-wheeler? Describe the restrictions this would add to the existing graph.  ? The next day, the Burbank Buy More decides they will have a television sale so they change their order to include at least 200 TVs. What is the maximum number of refrigerators which could also be delivered in the same truck? Describe the restrictions this would add to the original graph. 3. An incorporation of the following math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.): o Solid line  o Dashed line  o Parallel  o Linear inequality  o Test point  4. Shipping restrictions. The accompanying graph shows all of the possibilities for the number of refrigerators and the number of TVs that will fit into an 18-wheeler.  a) Write an inequality to describe this region. b) Will the truck hold 71 refrigerators and 118 TVs? c) Will the truck hold 51 refrigerators and 176 TVs?

PROBLEM 7: One-Variable Compound Inequalities, 1 PAGE

Your “and” compound inequality is 0?4+2x?22  Your “or” compound inequality is 3x+6<-3 or 5-x?1 • Solve the compound inequalities as demonstrated in Elementary and Intermediate Algebra and the Instructor Guidance in the left navigation toolbar, being careful of how a negative x-term is handled in the solving process. Show all math work arriving at the solutions. • Show the solution sets written algebraically and as a union or intersection of intervals. Describe in words what the solution sets mean, and then display a simple line graph for each solution set as demonstrated in the Instructor Guidance in the left navigation toolbar. • Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.):  o Compound inequalities  o And  o Or  o Intersection  o Union

PROBLEM 8

 Topic: Solving Proportions Number of Pages: 2 (Double Spaced) Writing Style: APA Read the following instructions in order to complete this assignment: 1. Solve problem 56 on page 437 of Elementary and Intermediate Algebra. Set up the two ratios and write your equation choosing an appropriate variable for the bear population.  2. Complete problem 10 on page 444 of Elementary and Intermediate Algebra. Show all steps in solving the problem and explain what you are doing as you go along. 3. Write a two to three page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the example and be concise in your reasoning. In the body of your essay, please make sure to include: o Your solution to the above problems, making sure to include all mathematical work, and an explanation for each step o A discussion of the following: What form of an equation do you end up with in problem 10? What do you notice about the coefficient of x compared to the original problem? Do you think there might be another way to solve this equation for y than with the proportion method? How would you do it? o An incorporation of the following four math vocabulary words into your paper. Use bold font to emphasize the words in your writing. (Do not write definitions for the words; use them appropriately in sentences describing your math work.):  ? Extraneous  ? Proportion  ? Cross multiply  ? Extreme-means  Problem 56 on page 437: Bear population. To estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist’s estimate of the size of the bear population? Problem 10 on page 444: y-1/x+3= -3/4

PROBLEM 9: DUE IN 30 HRS

 Topic: Can’t Cancel Terms Number of Pages: 1 (Double Spaced) In this discussion, you are assigned two rational expressions with which you will then do a variety of math work. Remember that each polynomial must be fully factored and that you can only cancel factors; you cannot cancel terms. • Find your two rational expressions in the list below based on your first initial. If your first initial is A-L Your first rational expression 7-3b/b to the 2power-12b+20  Your Second rational expression is.  3b-7/b to the 2power-20b+100 • Find the domain of each of the rational expressions. (Identify which values of x will make the denominator zero and thus are not allowed in the domain.)  • Divide your first rational expression by the second one. Write the answer in lowest terms.  • Find and state the common denominator between the two expressions. Build up each expression so that it has the common denominator. (Remember not to do any canceling at this point since you need those extra factors for the common denominator.)  • Add the two rational expressions together. Factor again if possible, and present the answer in lowest terms.  • Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.): o Domain  o Lowest terms  o Opposites  o LCD  o Build up
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