math118 sum02 exam

# math118 sum02 exam - NAME(Printed 11341 MATH 118 EXAM 2...

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Unformatted text preview: NAME (Printed) 11341: MATH 118 EXAM 2 August 19, 2002 Professor Borzellino Instructions: Read each question care- fully and answer it in the space provided. Calculators, books and notes are not to be used. Read through the entire exam before he- g‘inning work. There are a total of 6 ques— tions on 6 pages, not counting this page. Question 1 [20 points] Consider the polynomial P(r1:) : 2:4 -— 36. a) Factor the polynomial completely over 1R into linear factors and irreducible quadratic factors. 7 - ax" , Kira} 5x34; 13) List all real roots of P(.'I:). X21” c) Factor the polynomial completely over (C into linear factors. * O )5 ‘“ “i” ') l: (1) List all complex roots of P(:I;). trim? \/ if 19‘ Question 2 [10 points] a) For what value of B will the function f(::r:) : 2.1:2 +3.7; — 5 have a minimum at :1: = 3? 3 Question 3 [20 points] Sarah invests \$1000 in government bonds. Assume the bonds yield 6% annual interest. a) Write a formula for the value of her investment afte‘ at years assuming interest compounded monthly. 1L ‘ 115,".va + b) Write a formula for the value of her investment after t years assuming interest is compounded continuously. ' [issues-.11; «MUM- ‘1 {Rio r m! L cl'How long will it take before the value of her investment reaches \$5000? J .t 5:50“ unsweer ‘ RPM» :— d) SkEtCh the g1" aph 0f y = Tm” 0n the axes below. Label the y—intercept. Question 4 [20 points] 3.) Find a polynomial with real coefﬁcients of degree 4 that has roots :1: = 1, 2 and 1 + 225 KXJ) “-1300- (\Jr2',))(x+(\+aw)) ()(lngwzl Macaw-2" ) xz—si via-“am . Kl ‘35” +Z><LFS¢Z +\\$>t— \O \-. j? b) Give an example of a polynomial with real coefﬁcients of degree 4 that has no real roots. Explain. It might be easier to represent your polynomial in factored form. 2. . 3: 1L 6 s 1 S 0) Use the rational root theorem to factor completely 3:3 — 5:1:2 + 2:1: — 10. \25«12g+Io-l0 i}’ta‘t:3¢ IO ->z?-+Z ig<~6ibé3+23 "3 K‘ S \l 7‘31- 53L2' 1'“c:DL—- 1C) c___..__.__.————-—‘M ‘ 7( +3?- ” Z_ i 7 £241.19. Mm": T"- '“‘\ 5 \$105.. . . 1 + i . . . . . d) Simplify the complex number 2, by writing 1t 1n the form a + bx. "'" 19 MB L3» 2") 3+3'w2x ,_. I +31 ". " 273-23 1 +L|i [L502 lel‘VBﬁZ‘i’ol 01 Question 5 [20 points] Suppose that the function 19 2 —-%rr: + 200 relates the selling price of p of a Calculus book to the number of books .7; that are sold. a) Find a function that represents the total revenue from selling .1: books. Re— member total revenue 2 (price)1(quantity sold) .qu , r __d thbﬁ 31‘ v‘ —‘ f1 + Edi—(3 A 126%) =— ""l/sycl-+2a~x>,< b) How many books should be sold to generate maximum revenue? _ __ —— 20C”) . A E _ _ a; 33; ~—1 i :5 J} - 4:00 . i I, .‘ “~92 Vi) ' :3 c) What price should the books he sold to generate maximum revenue? F) 3 ‘VSC&M)+ZDO - l Go 4 ;> o 0/ F: 10 O 45 me Rosie -.~. ‘15 xﬁ‘zoo; » {.71- l 3) Proﬁt = “wheel +5 4/3 L: 4‘- Question 6 [10 points] Solve the equations: a) 84x9+2m 2 «E “Z 6 __\___ Wk" “2 \L» V3 "‘1 .u. 24-09. \ L..- 3 he ii I “T -235 Jq——c-4(q)(~\zz.\ ﬂ-ziﬁTﬁf ...
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