Solutions to Exam 2, take-home portion, Ma123, F05

Calculus (With Analytic Geometry)(8th edition)

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Unformatted text preview: Math 123 Calculus l Take-Home Portion of Exam II Rules: Work alone {i.e. without the heip of others} but use any reference materials antlfor technologyr you fincl useful. if the problems are unclear to you see your instructor [only] liar clarification I. An outfielder throws a ball at 84 tniiese'hr = ill? fir'sec at an angle :9 above the horizontal: _—-'—'_ _'*-.. "it Me. may 9mg :13. W m isms; Museum '7 (Li I on tttl a. it~ the release point is 6.5 it above growtu, what angle fl maximises the distance the hull travels”? {ignore air resistance} Express your answer in degrees. b. How the does the ball travel in the honacntai direction, assuming the flight is not intpctlctl in any way? {Again i gnorc air resistance} c. The [1i ght ot" the ball (ignoring air resistance} thatr be described by what geometrical - a cune. Fa i (Note: Don’t make this problem harder than it is - use the javelin handout discussed in class and any,r formulas that appear on it to quickly work parts a. and b.} t I; it ‘ m we. 1) J 1 cams-ems) 2: 44.51? l §:?1Lr r"—————_n_—-——‘-I—l-- a .2. a = L?— J {2111+ 1(3'1)(£L§) : '51.. ffo.’??e. H I For the baseball purists, I realise that it‘sbettcr to "hit the cutoff titan" since the real goal is to get the ball itt as cutest}! as possible. 2. Teams A and B play in the World Series. By convention the first team to win 4 games wins the WDI‘ld Series [it’s often referred to as a ‘best ofseven‘ series}. Suppose team A beats team 33 in each individual garrth with probability 3:. Then the probability that team A wins the lit'ort’eT Series in either a‘ or 5 games is given by {trust me} 5.x“ —4_r5 in this problem, your goal is to find the value of the first probability {3:} to make the second probability — the chance A wins the 1v‘r'orld Series in 4 or 5 games - equal to il.?5. That is. you are attempting solve the problem fix} = 5x' — 4s" — tits = e where .r is necessarily between [t and l . a. What is ffll)? What is fill“? it What theorem {give a name} guarantees that there is at least one I between ll and 1 making fix) = it? You will need to use part a. to answer this question. c. 1liltihy is therey'trst one I for which fix} = ll? (Hint: Give an explanation wltieh uses the derivative oi: f and the Fact that x. a probability. is between t] and 1.] d. Use Newton’s method to find {approximately} the value oi" .‘t' making _f'{x]=tl. Continue using Newton‘s method {you get to choose the starting pointjl until subsequent values agree to at least three decimal digits (Le. they agree to llflfll}. Please list the sequence of values I: .1’2 that you generate. @ $9): #555 {i (it’ll): {prod-5‘ @ flfldm '7C [IL-5 {MW as. (0)13) (9 gECfiJfiE first): Slog—213mg: %x3(t-¥)abj (C t5 taco-wag I The baseball fans among you may object to this assumption {because the outcome is affected by a number or" variable factors including the particular pitehcrs playing a given clay1 the location of the game1 etc} but let's keep things simple here and try a fixed chance of winning as a first approsiniation. 3 Since team It is going to win the series in 4 or 2'1 games with chance 035 this might suggest how to choose your starting point. Should you start with an initial guess ofless than ELS or greater than [1.5.- for example? T) fi-DIN "FINE 59% M Nfirm‘e— 5 WE ’1'. NH fig JLJ {PIN @ “1 fix- J $ 0?; .— frxh Eh .— m 49 t 4 .. H in “KPH: 5 .. Wm RXth “ 3 3 052.10??? = ’g $13é3 7ft. '39 K3 7' E3 2? $9236 _F W4 "A f OD rd “131: w I (I?) K fur 'T‘f 6Wfi m hAN 6L QM fflt 3» I5 foé ?C: 3. Verify, using a computation dune by haan ihat J' I 3,,dx=~I-{I+2.x-}“+ I v}: {1+2x] * 2 {His-1" L [Q4— 1nf'“ + U.» 'foh‘] 4- c; 1 59* Ek- ’ '3' .— J. .— l “('11 ' z liculx) l 1 (“I”) is f l 1.. J, (w. fl '2. (pg-Lg!“ (44413) 6. 1 l far-1r H I - 3*,» 1; 2 04-1101 0+1?) *1 .. 7f ((+LT>2’L ,u ...
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This homework help was uploaded on 01/22/2008 for the course MATH 123 taught by Professor Johnson during the Fall '06 term at SDSMT.

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Solutions to Exam - Math 123 Calculus l Take-Home Portion of Exam II Rules Work alone{i.e without the heip of others but use any reference

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