MATH 107 QUIZ 4 April 17, 2017 Instructor: E.Avram NAME: _______________________________ I have completed this assignment myself, working independently and not consulting anyone except the instructor. INSTRUCTIONS The quiz is worth 100 points. There are 10 problems. This quiz is open book and open notes. This means that you may refer to your textbook, notes, and online classroom materials, but you must work independently and may not consult anyone (and confirm this with your submission). You may take as much time as you wish, provided you turn in your quiz no later than Sunday, April 23. Show work/explanation. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is acceptable also. In your document, be sure to include your name and the assertion of independence of work. General quiz tips and instructions for submitting work are posted in the Quizzes module. If you have any questions, please contact me by e-mail. 2 1. Suppose C(x) = x 10x + 27 represents the costs, in hundreds, to produce x thousand pens. How many pens should be produced to minimize the cost? What is this minimum cost? 2. What is the largest rectangular area one can enclose with 14 inches of string? 3. Find all the points on the line y = 1 x which are 2 units from (1, 1). 4. Solve the inequality: 2 2 a. |3x 5| 4 b. x + 4 4x c. x > x 5. Find all real numbers x so that x is within 4 units of 2. 6. Find the domain of the following rational functions: 2 a. (2 x 1) (3 x2) 2 x1 f ( x )= b . r (x)= 2 x+1 (x 1) ( x 21) 2 7. Perform the indicated operations and simplify: 8. Find all real solutions 2 x +17 x +1 x 1 2 x 3x x x6 2 =x+5 9. Carl and Mike start a 3 - mile race at the same time. If Mike ran the race at 6 miles per hour and finishes the race 10 minutes before Carl, how fast does Carl run? 10. Translate the following into mathematical equations: a. The density d of a material is directly proportional to the mass of the object m and inversely proportional to its volume V . b. The drag of an object traveling through a fluid D varies jointly with the density of the fluid and the square of the velocity of the object