Quiz1-Solutions

Quiz1-Solutions - Name Math 115 — F2011 Quiz 1 September...

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Unformatted text preview: Name: Math 115 — F2011: Quiz 1 - September 6th 2011 Read the instructions to each question carefully. Provide all required reasoning, and show calculations. The Honor Code is in effect. Calculator use is NOT allowed. fry} 2 0.5 - C 4'} (1) Find the sinusoidal function 9(m) Whose graph is shown below: #2 I W WW W , W‘ max = if? . r sL—nru‘ . w H -, ’ mammal ‘ (1.: m .1_‘ = F == 03“ Q___ .L- V.__—__,___,.___ _,. WE Slim} 3 03902; [x] “l” 1‘ Li} ”x, 15(2) Give the formula for a sinusoidal function h(t) which has these propertieS: h(%) = _1 is the N/ minimum value, h(—%) = 3 is the maximum value. ‘ - i %~(-0 "5+1 1 '\ ampwtudgd; w z ...._.__n =__n _ IL. _ mama 9/ 4* 4' ; -~:c‘ ' W manna ;' mnwrmm : gut : i Q, 11,. l o The period of h(t) is: / ”a \L} P:9.~~o:='ur > lost 0 The amplitude of h(t) is: CL 2: EL {12 o The midline of Mt) is: ' lt, s,— 1 fl ti} r (/6) SU’UJL Mammy. it, fit; first: 0 =9 put) :7 (1, gm U213) Jr‘s: qr 3)th H l L/ (5) A mow Lows moves Wlm velocnzy ME) 2 4 — o -.-- IILBBel‘S/ILOUI', w1m v 111 Hours. 0 Find 11(0), v(10), v(20). ; HOMO avio):4.-3 : 4:133 ( «0.140 “l .7 . wuojzar—a L rpz : drag ‘1‘ 113,17 . a 3 a -0110 ,2, . 5 3 3 a 3 A? 0 At What time does the Slow Loris reach a velocity of 1%? " u—DAW m "01H? mamarfi \Jtflvmfidgé) 4”?) L. ‘ MHz-é 4— -931: "L 108 40% ”-01 l“ ; ratt— -—3 work mm mm Ln 1 % “fr *= 6% J; " 6’ 9% 3 a 3 El?» ‘ l_guv0.‘flc % wv$-$~i~ %% htzvoxigfl} o For very large values of If what is the approximate value of v t ? fl . mm #of mug Langammg 5% ‘% anthem; +haf ‘3 ii: “901%. email- {“1303 L; X We (ac mph algevemw: O m: X gloat “to 00. W—v—“flfl _ . -—O\‘\‘b .‘ > (2:) “thus. i 3m 73 Lax/0% {mag/t0 0 liar % ULYCeS/QJ/ fa}?! W71?) L3 angxLWifi + \w/ WM 3 Math 115 — F2011: Quiz 1 - September 7th 2011 Name: _ V1 [5% ' if; 7Q * Read the instructions to each question carefully. Provide all required reasoning, and show calculations. The Honor Code is in effect. Calculator use is NOT allowed. W (1) Find the sinusoidal function 9(33) whose graph is Shown below: For the sinusoidal function 9(0) is not the max, so g(a:) : asin(bm) + k. The max is O and the min is -4, so the amplitude is a = (0 — (—4))/2 : 2L1) The average value is the k: = (0 + (—4))/2 = —2. C1) midline, The period is p = 277 so I) : 15% a, {WM/‘4 Therefore, 9(33) 2 2 sin(m) — 2. C49 ,g/‘\_ (2) Give the formula for a sinusoidal function h(t) which has these properties: Mg) = 1 is the mini— :’ “a, E «ESE , mum value, 71(0) 2 3 is the maximum value. “‘ng 2 It is simplest to take the period p = T” The amplitude a is half the difference between the max and the min, so a. = (3 — 1) / 2 = 1. The midline is the average of the max and the min, so k = (1 + 3) / 2 = 2. Finally, h(t) is a cosine function since its max is at t = 0. [remember — we don’t use phase shifts!]. a” 1 Thus, h(t) = cos(2t) + 2. (LE) 0 The period of h(t) is: [email protected]} a”) o The amplitude of h(t) is: 1. 1,) o The midline of h(t) is: 2. CV (3) A raccoon moves With velocity v(t) = 5 (5 — 2—0“) meters/ hour, with t in hours. {2“ c Find 12(0), v(10)@£ 1/ 11(0) 2 5(5 — 2—0”) = 5(5 — 1) = 20. 11110) = 5(5 — 2-01-10) = 5(5 — 1/2) = 45/2. fig 0 At What time does the raccoon reach a velocity of %? / Solve 11(231—5 for t 11 (1)—97fk<=”15(5 20-1t)=%1§<=>5— 20:“ 13:15—13:20” :> 2_E'i)=2—O.lt :> 211-22—0'1t fl 2—222—0.1t; Taking log2 on each side —2 : —% 4:» t f 20. g1 Li 0 For very large values of t What is the approximate value of 1205)? f? _‘ e/ For 75 very large 2 0 11__2__01H is very small close to 0; So, v(t ) is approximately 5 - 5 : 25. 1.1 l“ \l 1111! 11111 a 1111 it? 1111111“ M 1” 1211 llama/1:11 1% “111 ”111i 2: 53%» C7 111111111112 (:5 1% ‘15, 1111111113 ...
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