fin-sum07-m3_sol - 1. (10 points) Give a table that gives...

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Unformatted text preview: 1. (10 points) Give a table that gives the exact values AN D decimal approximations, rounded to the nearest hundredth, for sinoz,cosa and tana for a = 0°,o: = 30°, a = 45°, 0 z:- 60" and 0: 2: 90°. Also give the radian measures of all the angles. 2. (10 points) Use the reference angle principle (and your table above) to give the exact value of the following: 4. (10 points) Show that sin2x — $11143: : (30323: — (20343: for all 2:, 1.63. show that the equation is an identity. / 1 l ) Q 1 gm (" Y a (305' “C05” < :- ’30 ‘ 55"”? .\‘i I \ h.) Smlx ( A—g‘flfl‘rX) .2: my 74 (‘~ (xx "" Wt ‘1 CO; :S‘mly “‘ 1 I (:3 3'“ ‘4 60‘ 2‘ : Carly S‘mlx (c) (8 points) Graph both f (:13) and f’1(:c) in the same coordinate'system. I a w) 6. (20 points) This problem is about modeling population growth With functions: Assume in both parts Mathland has 100 inhabitants now and 110 inhabitants exactly one year later. (a) (10 points) Assuming linear growth, how long will take for Mathland to grow to 5000 inhabitants ? In other words, find a linear function that models the given data and use it to find when the poulation has reached 5000 inhabitants. in} Mt) be Kw ftilmluliofl Mal/bx (Md m t \/€m‘3 2-.) We): too) Hue) silo “CH '3' A'JC +6 =7 [5 3(00 C H10): (3) “Hm _: A + 13 r? A110 We? “0400174. -) HUG): lot + {00 , Now {ital 0‘» the} H63?) :Sooo tr) 5,600 z: 10? H00 ‘) ’V ‘ “‘0 0‘, 1C: “tag .2. do“) , 17L Wm +0166 WququS Hint Find the growth constant It first a Agcuk :1 ) . - K 0m we: too a)“ aw} H <‘I);Ho: \oo 8 M: NO 1-1“119 :\ [vb/ac) c) Q '9 Kgr l0 “A: Now ’1: $0 “Mk 5I000 I ’00 e ‘0 \w“ N - x :1) SO 2 e p .1“) “xi; {3 :2 \IA 50 0‘ t : it? LN Yam/S (0* [2.9.7. +55 Mu *WO ’7. (15 points) Consider the function f (cc) 2 2sin(2$ — 1). Find the following (and don’t forget question (e)): (a) (1 points) The amplitude of f. Amflzg (b) (2 points) The period of f. , \ UT ._.._ r." ‘Ci’iodl: W H (c) (2 points) The phase shift of . \ Q i t I 6%H (e) (4 points) Now graph 9(1):) = 2 csc(233 - 1) into the same coordinate system above. the angles a, fl and 7. Tim lac b- 0qu (:st (m yaw fru’. 10. (20 points) You plan to build a rectangular enclosure with center divider to create two equally large holding areas. You have 240 yards of fencing material available to build the enclosure and you want to maximize the area for your animals. What dimensions should you choose and what is the ranimal area for the enclosure ? Q - Z “01:429. W ’2. Hint: First give the area of the enclosure as a function of length and width. Then use the constraint on the total fencing available to rewrite the area-function as a function of the width alone. Also, don’t forget the center divider requires a fence too. 5. \. Area :2 LO ' 3 . r CZq W .-_-.a w l 1“ l --- ~- W Jr Y2. ml 1. A z .. .19 .. __ 11.9. : uro :7 lsto 1 ex 1‘ S. l V‘ U- in) l} cm CVCw Aim-u 1A. mm {)0 {($30le ’ “J VAC}st \wU~-\ Vulka iS CL)? (,3. {H3 W‘Qum Ls: la: Cw k\. -__-; Q o -) g‘o fire (limit/MU (i an; H t... q. 0. s, a“ to «4 a “‘23. (Extra Credit, 5 points) What shape of the enclosure would give an even bigger area for the animals 7 By how much? P 11. (15 points) Let 6 be an angle such that 7r S 6 S and 0080 = mg. Find the following: g cf: 464— ‘72 2) 3 c: w? \ (c) (1 point) 3e06 = W 0 2V? ((1) (2 points) cot6 = 41? C: ~—-- if 5 - f: (e) (2 pomts) 0809 = «.3 K :54 j) 13’ 53 (h) (2 points) 9 2 your calculator and should use your brain here) . ‘ " " . ’ (a \" - t q 0 9 2 _ a: 9 do the following: 12. (20 points) For the rational function f = $2 _ 4 (a) Find all cc-intercepts. (b) Find the y—intercept. (c) Find all vertical asymptotes. LIL x: r o— (d) Find the horizontal asymptote. s'r.‘ - (z. (e) Sketch the graph (label the axes, asymptotes and all intercepts): 10 13. (Extra Credit, 10 points) Newton’s law of cooling states that the temperature of a body, initially at temperature To, placed. in a surrounding medium at a lower temperature Tm, is given by the formula :— Tm + (To -- Tm)e-—kt Assume a cup of coffee, at temperature 150° at 7am, is brought outside into air at 60°, and cools to 125° by 7:05am, do the following: ...
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This note was uploaded on 08/09/2011 for the course MATH 3 taught by Professor Staff during the Spring '08 term at University of California, Santa Cruz.

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fin-sum07-m3_sol - 1. (10 points) Give a table that gives...

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