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practiceExam2g4solutions

# practiceExam2g4solutions - Exam 2 Practice Exam G4 0 You...

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Unformatted text preview: Exam 2, Practice Exam G4 0. You are offered a series of credit cards in the mail with terms and interest rates listed below. Please select the one on which you would pay the lowest amount of interest in the span of the first year if you transferred a balance of \$1 0,000 to that card at the beginning of the ﬁrst month that you got the card. ( (21+) 3 - ,_. annual yearly interest rate of 24%, compounded annuallyCI +& :2 , /, Zj 3 b. monthly periodic interest rate of 1.9%, compounded monthly 0‘01 7) 52 _ / 2 f5 . '\ weekly periodic interest rate of 0.5%, compounded weekly (l- 005') I r d. 0 daily periodic interest rate of 0.0006%, compounded daily (/ 500006)?6f: M0 Z2: 1. The presence of a double root (eg. ﬁx) = (x-3)2 = 0) in an equation means that which of the following methods would be appropriate to use in ﬁnding that root of the equation? . Bisection Method NO + / “ Ail/HEM/SCE ‘ecant Method [LL/(e, #3591499, uni? 4191'” 5 C. False-Position Method A/u f—/ --— x‘I’V/‘i’ré/‘fébg D. None of the Above a C 2. Which of the following is NOT a bracketing method for optimization of a function? @ewton’s Method B. Golden-Section Search C. None ofthe Above 3. Which of the following represent the gradient of the function f (any) = xy3 . ' . _ evaluated at the point (x,y)=(2,4)? _ Qj 3 LIL 5 6 ‘ “— )3: :. j : .. 7! A. [64 2]” a. B. mgr %§ 327' 3' 5'71 7. D. None ofthe Above 3. (25 pts) You have decided to purchase a Honda Civic, and are trying to decide whether or not the hybrid Option will save you money over the next ﬁve years. The regular Honda Civic costs \$18,000 and the Civic hybrid costs \$22,000. W. W” Assume that you will need to purchase a new battery for the hybrid car after 4 years and that it will cost \$3600 (if you bought the battery today), but that the maintenance costs for the two versions are otherwise the same at \$500 per year. The regular Civic gets 30 miles per gallon, while the hybrid Civic gets 45 miles per gallon. You drive approximately 20,000 miles per year, and gas currently costs \$2.50 per gallon. Assume an annual inﬂation rate of 5% per year for gas and for the battery. Also, assume an annual interest rate of 10%. How much does each option cost you after ﬁve years, in net present value? Which one would you pick for only economic reasons? H in???" : Women/737m ezs/qixwwmga 1/ Ba =27! £0 5 i - . . . - . » 7 , . M lbw“ ‘ZM’ 0 1" WCX—(é‘lﬁrjnm if?) 1. W gym fij+//// ,4? r“ /////77 3 will )1, tin-mg Mg/mﬁ m Inga/(r7 34/027 045/10 5* z 22 MO f/gﬁﬁ‘tlbéﬂr(0(2+»%6-'r—4ZZ+\$¥u—9—2<6/7 gmﬂﬂj, C/WSC 7%: ijWQ/ (W’LJ'M>W 6. (25 pts) Given the function W Use the X; X?— Xr X0 f(x) =—1.5x6 -2x4 +10x Golden-Section method to ﬁnd the maximum of the function over the interval 03x52, and show three iterations and the current estimate of the location of the maximum and the value of the function at that point. 526‘76f/3CL) 007/0 ﬂu) X{ {Z 1569') ((2%) ~46 7mm77 ss 34;“ x0 222 me 0°17 664 4A 97 f0 ’43“ \$4 2 22 M" M m/ 655/ so (3&2?! XL 7. (25 pts) The von Karman equation relates ﬂuid velocity in a pipe to the friction in the ﬂow f. Velocity is described through the Reynolds number Re. 1 F=410gm(Re‘/7)—0.4 (a) (15 pts) Compute f when Re = 10,000, using the secant method. Perform two iterations (Le. compute two new estimates). Use f = 0.001 and 0.01 to get started. (b) (10 pts) Given these initial guesses, does the method work more like false position or Newton-Raphson? Explain how you would implement each of these methods on this problem, and whether or not they would be appropriate. ”>22 4 g: a :7 jzz):7 ~42,0(/0‘*7/F)+ﬂ2 (:kf, ﬂ/ge @2501 (£53? #0073 {M ,ﬂ/{a‘fI/Md/iséw) famyj/ﬁtja/S 4% (Cc, “(k 92 : 9oz, {4:121:22 ”W :22) 2-0—2ch 222222: 20424 75: 00/_//5)/0w/~Jox) 23.09% / W ...
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practiceExam2g4solutions - Exam 2 Practice Exam G4 0 You...

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