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Math 148 - 001 - 002EXAM 1 Name:Dr. P.D. McCray 27 September20061. (6 points) Circlethe numbers in the list below that are rational.G) a*J ~ (2) 2; 0.14159)Page 1of42. (5 points) Circlethe expressions in the following list that are polynomials.x+2x+31+~3. (5 points) Find a polynomial P(x) of degree 4 with leading coefficient5 for whichP(1)= P(3) = P(5) = OandP(x) ¥-o otherwise. T~ ~:prx)=- 5(~-1)~(?(-"3){'X-5) tfLILP f::t)= 5 (?C- f) (?C- 3) -z...(?C.-I;) ~P (PC)::: S ("'K-() (X- 3) (~-5) ~Math 148 - 001 - 002 EXAM 1 Name:Math 148 - 001 - 002EXAM 1Name:Dr. P.D. McCray 27 September2006 Page 3 of 46. (2pointseach) ConsiderthepointP(9, 5) andlinel withequation3x + 4y - 48 =O.(a) Does the line l pass through the point P?3 ~ -t-4'f -1-(1 ::::.3(<3) +4(5) -48 -::.'2."7-+ ~ -4- ~=-I~~~tAfl!J ~~.R.~~~(b) Whatistheslopeofthelinel? ~..z~ T +~ - f-l( =0 o-? Ct';:: -£ ;Y~/2..//J-fJ~~ -.!I.f 't 'T iT -r ~(c) What is the x -interceptof the linel?~Jt=OaM4~~ ~.'.3~ = 4-3~ l-?(=:;/bU:J~-)(d) What is the y-intercept of l? Ll~ = -~ ~+I 2.. ~ -:X-::=O ~:= /2.. .Tt1 ~ -Ult ~c4 /2..(e)flat is the slope of a line perpendicular to l? , /L _ I? _! _, ~~ A~"~~~~~-r J_ ~(~ ~ -/.4 _ ~ #~.., , _/~ 1-/_~~ - /~ ,AkJ ~ ~FttK:. ~ l-s.../ .37. (10pointseach) ConsiderthreepointsP(9, 5), Q(-4, 9), andR(20, 1)andthe melwith equation 3x + 4y - 48 =O. (See problem 6 above.)(a) Find an equation of the line parallelto the line l that passes through the point Q.Th~"ft:N~M~~ 4r4~~t1{£)~ -f.tt£e~~-~~ tI-/I / = ""., (::y -'X,) -It;f1e:t'- c£fA-~'tr>1 cY - 9 = -~ (?t"- {-i,l)) ~~ -:J= -~~ +~(b) Find an equationof the perpendicular bisector of the line segment QR.TAt. '~~~:14~~¥ 6<(2)M (E-«9-);t'ZC ~j-/J6 'Z- ) z.. 7 1 /_:: M(~.>~)~ M (~,!>J. ~-m0~~6<'~/~-Y-wJ~~~-'-h~. ~ (Ql(.h~ = ((:;)-( I )) -::. 8 __~ {f-5/"= 3 (~-'~)((-f )-(7-{))) - oz-y - 3' .Math 148 - 001 - 002EXAM 1 Name:Dr. P.D. McCray 27 September2006 Page4 of 48. (10 points) Find an equation of the circle with center C(2, 3) that passes through thepoint P(-6, -3). C (~, 3)Ik~ ¥~~MLe M 0r= v((z )-(-b)"2..+((3 )-(_3))7-' ~ .#.tl. dA~ . P(-',~)r:. , (8)2..i-(~)2..' ==- 64- t-3.b ~ v'/~ '==-/~.-rL-r. ~~Q"1 ~ a ~M-ee W7:u:'~ (-rf,~)~ ~ h t..O (?(-~J~7-(fI'-?f.)c..=".'---r~ (~_ 2.) 2..-1-(V-3) '-/0 'Z...9. (10 points) Find the centerand radius of the circlewith the followingequation.x2-4x+y2-6y+21=O AI~'fo~~'~~ ~ ~ (")(~ )Z.~(ff-k)<'::::I-~4- · ~ ~ /17~kt.~ d4, 1£) ~ /h,~ '2 _ t1?( +-+ +-c¥ '2._6~ -1-q == -2.../ r- 7' ~,', {-:;( - "2-J ?...7- (~ -3) ~ =- -2../ "t-(~ =:- 0 ~ 0 ,~~~~~,up~('):_2.,)'2. -I- (V~)'Z ? 0 ~ ~ ~ ¥~~~~,~- - ~ ~)d«~~")1 ~ r-~ E&l/,lf-770NIS" QC>r ~,. &'.I-"~


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IIT MATH 148 - Math 148 EXAM 1

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