Test 2A - ‘Test.#2 Math, 241' *—" Form A...

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Unformatted text preview: ‘Test.#2 Math, 241' *—" Form A —‘ 100 points? total *No calculators, No cellphonesmb PDAs. *Nb, questions dufing‘thextc‘st ume'ssflucre isra typing error ‘ *fi’lease'fbegin eachqfiObIem at the topr‘of a new page in the blue book *Writei‘you'r flamesson the offift'side of the? blue book. *ShoW‘ 611' work Mark out'any work ghatryou do; not want‘gradcd,‘ 1; 'A functiOnvflx). satisfies the"f0116Wi11g'-difie‘lte.ntial equation : dy _ 2, dxu— 3; 4y + 3 a?) (~6ptSQ)Whatare‘theeiwilibliium Splutions? b.) (8 fits-Lifer what values airy-fathafimction y(x) decreasing? c) (8_pts.)Given:an initial. cohdi’tfiiflof y(0,)‘=1 ’and‘a'Step size, of Ax=lf2 , use 'Eulef’sxmethodltorapproximate;y(1). 2; (28 pts)"Solve.the‘-follow_ing differexitial equations a)’ 3%: 2M + 3W2 w(Q)=1 (explicit solution) b) 'x‘ + 16%:— = y(4) =_ 1. (itnplicit‘ solutiOn) y 3; 12 pts) A tank initially C'onta'insvl'ZOiggallons of brine, holding ,75 potmds‘of disSOJVed 'salti'n solution. ‘S'aIt water containing ,1 pound of salt per gallon is entering the at the rate-of? I’gallons'perrminuteand. brine flows out at the merge, If the nfixngre is lgeptimifonn: by constant stirring, find the amount of salt :in'the tank'sfl) ‘at time t. ‘ ‘ 4.7 .For. the following ptoblem‘s’, W3fl be sure to QQmpletCly set the problem where 21114th is 1§fiillofidQJiSF=wotk out the integral. Draw afifiiémre‘that clearly shows ’y’ourisetriip; label youfiiai‘iables? label the d'ireCtion‘df yourix Or y- axis, I‘abelf‘where For y'=‘0’ is, etc. a.) '(1'0‘ pts)‘H.owmuch wpfkiisedbnefto bring arl'oad ofore to the Surface=if a ' miner cable weighng 21b5/ft.-to haul a 100 1b bucket of ore up ‘a ‘ mine shaft thatrlis..8_00‘ fl; deep. ‘ h b), (10 pts) Anxgate‘ifi an ifr'if'gationncanalsisein the farm of aftrapezo‘id. 3 11 wide Jat‘th’c Bofiom,_5 f‘tagiwisieat the hp; With heightqu to 2 feet. It is placed V§1Tti9a11Y mime: canalswith the water extending .10 feet above the top of the; gate“ Thesdensjty'of watep'is 6247!) Ifta. Find the hydrostatic force on the-ég‘a'tcr e)- (10 pts)nAfihemispherical tankof 10-fth filled to a point 1 fl. below the. top. Thealiq‘uid’svidensiitytis“ 621bs/fi3. Find the work required to. pump all of the- liquid:o.11t_: through thetop of the 5-. Pts'lPriove/vexify that); = sifn(2t) "is not a solution of 1:"— 4x = 0 . W: ‘ , y.» a... 1' .3. v V _7 j: 7. ._ ' I ,u 11” _"‘- 3 . .. " -‘1"II‘I...‘..nmi’lH'dAr‘v 1 :1- :4 I: ;‘ bdlyfii‘fl 4H.» _". ' ~ mam": ' 4 < —, ‘/_“.'2"7 . —--I--II\"- . 7: .-. ...'.‘.,::, 1‘" 1 In.» , .7 ‘ 1'. " . ‘ I ‘1 ‘ M “ i < 1;“— a! <7; v'v": .~ — III | I" !\!llll-Hl ‘ ‘ ‘ x.» “pp . .m I p .«w 75,! ‘ J: ‘53-”?! ,7 .- ...
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Test 2A - ‘Test.#2 Math, 241' *—&amp;quot; Form A...

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