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[answered] MATH 115 QUIZ 5 NAME: _______________________________ Decem


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MATH 115 QUIZ 5

 

NAME: _______________________________ December, 2016 Instructor: S. Sands 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, December 11. Show work/explanation where indicated. 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. 1. (6 pts) The note 'A' below the note 'middle C' is a sound wave with ordinary frequency f = 220 Hertz

 

= 220 cycles/second. State a sinusoid which models this note, assuming that the amplitude is 1 and the

 

phase shift is 0. (no explanation required) 2. (10 pts) Solve the equation ( x )+ ? ?3 sin ( x )=0

 

, finding all solutions in the

 

sin(x) tan? interval [0, 360). Show work. HINT: Note that sin(x) is a factor. (You should be able to provide the exact

 

values of the solutions and state them in degrees.) 3. (8 pts) Solve the equation 4 arccos(5 x)=3 ? . Find the exact value(s). HINT: Write an appropriate

 

corresponding equation involving sine. Show work. 4. (10 pts) Solve the equation sin(2 x)+ ? 2 cos(x )=0 , finding all solutions in the interval [0, 2). Show work. HINT: Start by applying an appropriate trig identity. (You should be able to provide the exact

 

values of the solutions and state them in radians.) 5. (12 pts) For the triangle ABC, we are given that B = 80, a = 52.0, and b = 78.0.

 

(Side a is the side opposite angle A, side b is the side opposite angle B, and side c is the side opposite angle C.) Solve the triangle; that is, find the two remaining angles and the remaining side.

 

Report angles to the nearest degree and the length rounded to the nearest tenth. Show work. 6. (8 pts) A kite has the shape of an isosceles triangle, with largest angle 115 and two sides of length

 

24 inches. Find the area of the kite in square inches, to the nearest square inch. Show work. (Sketch not

 

to scale) 24 in. 115o 24 in. 7. (8 pts) For the Pentagon in Washington D.C, the distance from each vertex (corner point) to the

 

center of the Pentagon. is 783.5 feet. (In the diagram below, Side AC is 783.5 feet long.) C

 

783.5 ft.

 

54 A 54 B How long is each of the five exterior sides of the Pentagon? Show work. Round the distance to the

 

nearest foot. 8. (10 pts) Two hikers leave the same tent at a campground and go separate ways. One hiker walks 14

 

miles directly east to Ashville, and the other hiker walks 6 miles directly northwest (i.e., N45W) to

 

Bellville. (Assume that the terrain is flat.) How far apart are Ashville and Bellville (by the most direct

 

route)? Show work. (You may find it very helpful to draw a picture, but you do not need to submit it.) Round your answer to

 

the nearest tenth of a mile. 9. (10 pts) An airplane proceeds at a bearing of N30E, flying at 520 miles per hour.

 

(no explanations required)

 

(a) State the angle in standard position which corresponds to the bearing N30E.

 

(b) Find the easterly and northerly components of the airplane's velocity. That is, find the component

 

form of the vector which has a magnitude of 520 and makes the angle with the positive x-axis. (Use

 

the value of you stated in part (a).) Label your answers, state the exact values, and also give

 

approximations to the nearest mile per hour. 10. (18 pts) Let ?v w

 

= 1, ? 4 and ? = 3, 2. (Work required only for parts e and f, on the next page.)

 

(a) Which of the following graphs shows these two vectors? Choose I, II, III, or IV.

 

(I) (b) Find 2 ?v (II) w

 

+ 6? (III) and state the result in component form. (c) State the exact magnitude (length) of ?v ? .

 

and the exact magnitude of w (IV) (d) State the dot product ?v ? . w (e) Find proj?w ( ?v ) in component form. Give exact values. Show work. (f) Determine the angle between ?v ? . Show work. Write the exact angle as the arccosine

 

and w of an appropriate number. Also, use a calculator to approximate the value of the angle, rounding the

 

result to the nearest degree.

 


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