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1022 quiz 4 B Term 2007 answers

1022 quiz 4 B Term 2007 answers - Name MA 1022 2007 B Term...

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Unformatted text preview: Name: MA 1022 - 2007 B Term Section A02 November 20, 2007 Quiz — Sections 6.3, 6.5, 6.6 1. Using the method of cylindrical shells, calculate the volume of the solid generated by rotating around the y-axis the region bounded by: y = x2 , y = 8 — x2 and the y - axis. (12p0ints) b S Z‘nrhdx 6‘- 2- '2. V: l 1Trx(8—2x‘)olx= 7m (CBX-ifiplx 0 K52 \I a“: 2'“ [dual-:53] 7- X150 vz—m (IL- 2)— (0-03] -.—. 2. Using the method of cylindrical shells, calculate the volume of the solid generated by rotating around the line it = —2 the region bounded by y=~~x2 —l , x=1, x23 andthe x—axis. (I2p0ints) 3 ‘3 V: {0.1T (x+9.)(x‘+|) clx -.= ’1'“ SOP-'- 74‘4—1-1-1) alx \ l 3. Calculate how much work is done by the force F (y) = 53/2 pounds in moving a particle along the y — axis from y = 1 foot to y = 3 feet. Units matter! (10 points) Work =— ¥arce x dts'l'znce 4. A spring has a natural length of 2 meters. A force of 10 newtons is required to hold it stretched out to 4 meters. How much work is done is compressing this Spring from its natural length to a length of 1.5 meters? Units matter! (12 points) AT REST "The what [enSik a? the spring ‘us 2 meters l l i i 5 a F—‘V Noh'ce I Movasl “flu Spmaj 'I’b make it easier “h; se+ E l 7- U? My Integral fin“ 042; 0.5' l Wake:— anl o-$ i 0.; w = gm)“ : SCXAX D 0-K ' ‘ 1 l W” 8X 5 E! 2— El 0 i; ii il l 5. A cylindrical insulated tank of icy cold water is to be placed on top of the Great Pyramid of Giza, so that thirsty visitors can have a refreshing break after climbing to the top. ' The interior diameter of the tank will be 12 ' _ feet, and it will be 15 feet tall. The pyramid itself is 480 feet tall. The empty tank weighs 500 pounds, and the ice water has a density of 62 pounds per cubic foot. Give an expression for the total work involved in moving the tank plus water to the top of the pyramid. You do not have to evaluate your answer — OK to leave it as an expression. You may wish to have two parts to your expression — one for the work moving the empty tank, and another for the work of moving the water itself. (12 points) Work '2 ‘Pbrce X oils “have W‘; Work WOVij ewpiy {Zak WI: 500%: x $80 FF W‘ ":— (§00)('-l-8‘0) "Pbol‘ PCB-incl; 6. Find the centroid of the region bounded by: y = 2 + 3x, y = x , 3C =1, and x = 3.(12p0ints) 7. Set up but do not evaluate an expression to find the centroid of the region bounded by y = 9 — x2 and y = 3 —~ x. (10 points) BONUS QUESTION I Visited a store at the mall last week that only sells socks for men. The store’s sign is shown below. I determined the centroid of every letter on the Sign, and found that the centroid of one of the letters has a unique property. Which letter is it, and what is the unique property? 2 s @x— Th2 cewhm'ial oi enck lei-ler occurs at Hae "Middle ” horizenblly Mal VeffiCOLHS (give—A “HAG syMMC‘I‘Yl‘QS lnvuLJ‘EQ'}; 43w ‘HLQ letter "O", Hue (Zambia! does no} lie on five let-fir ElseIC ...
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