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Fall 2005 - Tesler's Class - Exam 1

# Fall 2005 - Tesler's Class - Exam 1 - Math 20C Name Prof...

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Math 20C Prof. Tesler Midterm #1 Answer Key October 17, 2005 Name Answer Key Student ID No. Circle the section in which you are enrolled on Tuesdays: T.A. Vladimir Pesic C01 3–3:50 p.m. WLH 2208 C02 4–4:50 p.m. WLH 2208 C07 5–5:50 p.m. Sequoyah 147 T.A. Michael Ferry C03 5–5:50 p.m. WLH 2208 C04 6–6:50 p.m. WLH 2208 C05 7–7:50 p.m. WLH 2208 C06 8–8:50 p.m. WLH 2208 Do not open this booklet until instructed to do so. Work alone. Use the space provided. If necessary, write “see other side” and continue working on the back of the same sheet. Circle your final answers when relevant. You are allowed to have one double-sided sheet of notes made according to the specifica- tions explained in class. No other resources are permitted. No calculators. You may leave answers in symbolic form, like 42, unless they simplify further, like 9 = 3, e 0 = 1 or cos(3 π/ 4) = - 2 / 2. Time for midterm: 50 minutes. 1 36 / 36 2 40 / 40 3 24 / 24 Total 100 / 100 There are different versions of the test. This answer key contains detailed answers for one version of the test, and just final answers for the other versions. If you want to write down questions for your T.A. or you want to rework problems, please do so on separate paper; do not write on or mark up your graded exam.

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(1) Let ~v = h 7 , 5 i and (yellow/pink) ~w = h 4 , - 3 i (green) ~w = h 6 , - 3 i (blue) ~w = h 8 , - 3 i . Use these values for all questions on this page. (a) Compute 6 ~v - 10 ~w . (yellow/pink) 6 h 7 , 5 i - 10 h 4 , - 3 i = h 42 , 30 i - h 40 , - 30 i = h 42 - 40 , 30 - ( - 30) i = h 2 , 60 i (green) 6 h 7 , 5 i- 10 h 6 , - 3 i = h 42 , 30 i-h 60 , - 30 i = h 42 - 60 , 30 - ( - 30) i = h- 18 , 60 i (blue) 6 h 7 , 5 i- 10 h 8 , - 3 i = h 42 , 30 i-h 80 , - 30 i = h 42 - 80 , 30 - ( - 30) i = h- 38 , 60 i (b) Find all unit vectors perpendicular to ~v . The vectors perpendicular to h a, b i are all the scalar multiples of h b, - a i . In this case, h 5 , - 7 i is perpendicular to h 7 , 5 i : h 5 , - 7 i · h 7 , 5 i = 5(7) - 7(5) = 0. The length is | h 5 , - 7 i | = p 5 2 + ( - 7) 2 = 25 + 49 = 74. One unit vector is h 5 , - 7 i / | h 5 , - 7 i | = D 5 / 74 , - 7 / 74 E The other one is its negative D - 5 / 74 , 7 / 74 E . (c) Compute - 10 proj ı ( ~w ). (yellow/pink) proj ~a ( ~ b ) = ( ~a · ~ b ) ~a | ~a | 2 ; here, ~a = 9ˆ ı , ~ b = ~w proj ~a ( ~ b ) = (9ˆ ı ·h 4 , - 3 i )9ˆ ı 9 2 = (9(4)+0( - 3))9ˆ ı 9 2 = (9 2 )(4)ˆ ı 9 2 = 4ˆ ı .
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Fall 2005 - Tesler's Class - Exam 1 - Math 20C Name Prof...

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