Math 107 Quiz 4 Spring 2017 OL4
Professor: Dr. Katiraie Name________________________________ Instructions: The quiz is worth 100 points. There are 10 problems, each worth 10 points. Your score
will be posted in your Portfolio with comments.
This quiz is open book and open notes, and you may take as long as you like on it
provided that you submit the quiz no later than the due date posted in our course schedule
of the syllabus. You may refer to your textbook, notes, and online classroom materials,
but you may not consult anyone.
You should show all of your work to receive full credit. If you do not show work, you
may earn only partial or no credit.
Please type your work in your copy of the quiz, or if you prefer, create a document
containing your work. Scanned work is also acceptable. Be sure to include your name in
the document. Review instructions for submitting your midterm exam in the Quizzes and
Exams Conference.
If you have any questions, please contact me by e-mail
(farajollah.katiraie@faculty.umuc.edu). At the end of your quiz, you must include the following dated statement with your name typed
in lieu of a signature. Without this signed statement you will receive a zero.
I have completed this quiz myself, working independently and not consulting anyone except the
instructor. I have neither given nor received help on this quiz.
Name: Date: Please remember to show ALL of your work on every problem. If there is no
work to show, then include a sentence or two explaining your answer.
Here are the basic rules of showing work:
a) Each step should show the complete expression or equation rather than a piece of it.
b) Each new step should follow logically from the previous step, following rules of algebra.
c) Each new step should be beneath the previous step.
d) The equal sign, =, should only connect equal numbers or expressions.
Our textbook is full of good models of work shown correctly. If you have questions about
showing work, please ask.
Please Show or Explain Your Work on Each Problem. Math 107
Quiz 4 Page 2 1) In the following Exercises, find all real solutions. Check your answers
Round your answers to three decimal places.
(Hint: Please see section 0.7 of the ebook)
a) 4 x 2 +2 x=7 b) 3 t + 42t=13 t 2 2) In the following Exercise, use the given complex numbers Z and W
Z =5+4 i ∧W =4 i
And find and simplify the following. (Hint: Please see section 0.10 of the ebook) a) Z +W b) ZW c) Z d) 1
Z e) Z
W f) W
Z 2 Math 107
Quiz 4 Page 3 3) In the following Exercise, the revenue and cost functions are given.
2
R ( x ) =30 x −0.5 x
C ( x )=5 x+ 10
Where x is the number of staplers, and R(x) and C(x) are in dollars.
(Hint: Please see section 2.3 of the ebook)
a) Find the profit function P(x). b) Find the number of staplers which need to be sold in order to maximize profit. c) Find the maximum profit. 4) The height of an object thrown downward with a velocity of 32 ft/sec from the roof of a 150
feet tall building is modeled by
h ( t ) =−16 t 2−32 t+150
Here, h is the height of the object off the ground (in feet), t seconds after the object is thrown.
(Hint: Please see section 2.3 of the ebook)
How long does it take before the object hits the ground? 5) The height of a rocket thrown upward with a velocity of 32 ft/sec from the roof of a 40 feet
tall building is modeled by Math 107
Quiz 4 Page 4 2 h ( t ) =−16 t +32t +40
Here, h is the height of the object off the ground (in feet), t (seconds) after the object is thrown.
(Hint: Please see section 2.3 of the ebook)
a) When does the rocket reach its maximum height above the ground? b) What is its maximum height? 6) In the following Exercise, solve the inequality. Write your answer using interval notation.
(Hint: Please see section 2.4 of the ebook) |2 x+ 8|−12 ≤ 0 7) In the following Exercise, solve the inequality. Write your answer using interval notation.
(Hint: Please see section 2.4 of the ebook) Math 107
Quiz 4
−11 x +30+x 2 <0 8) Perform the indicated operation and simplify
(Hint: Please see section 0.8 of the ebook)
x +5
x3 −4 x 2
∙
2
2
3 x −12 x x +3 x−10 9) Solve the following equation.
(Hint: Please see section 0.8 of the ebook)
x +3 x−1
−
=11
2
3 Page 5 Math 107
Quiz 4 10) Given the function. Page 6 f ( x )= 20+6 x
10−2 x (Hint: Please see section 4.1 of the ebook)
a) Find the domain of f(x). b) Identify any vertical asymptote of the graph of y = f(x).
c) Identify any holes in the graph.
d) Find the horizontal asymptote, if it exists.
e) Find the slant asymptote, if it exists.
f) Graph the function using a graphing utility and describe the behavior near the
asymptotes. End of Quiz 4: please do not forget to write and sign (or type) the required statement
explained in the box above Part I of the Quiz 4.

 

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