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# Study Guide for MATH 104 at KU

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This 8 page Study Guide was uploaded by an elite notetaker on Friday February 6, 2015. The Study Guide belongs to a course at Kansas taught by a professor in Fall. Since its upload, it has received 20 views.

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Date Created: 02/06/15

Math 104 Exam 1 Review Spring 2009 1 Given the points A 72 75 and B 31 a Find the distance between A and B b Find the midpoint of the line segment joining A and B c Find the equation of the circle with center at A and passing through B d Find the equation of the line through both A and B e Find the equation of the line through A with undened slope f Find the equation of the line through B with zero slope 2 Find all intercepts of the graph of the equation 2 y2 7 z 4y l2 3 Find the equation of the line through 71 3 which is perpendicular to the line 72z3y 9 4 Complete the following given the system of equations 73y17 4z3y7 a Write the augmented matrix for this system b Solve the system using your choice of method substitution elimination or matrices and show all work c Are these two lines parallel perpendicular or neither 5 Solve 7 8 a 7 9 774 2l 27l b 2z73l 77 c 2x2 19 33 d z2 8x 14 0 by completing the square then verify by quadratic formula e x45x27360 f f 7 m 71 g 3 4 7524 s 9 z 12 h z 2 i 3 7 2zl gt 7 1 2 7 2x 2 3 gt3 k m 71oh 7 m m m e Iwa m ys cm of equine 72 7 y 7 z 7 7n 2172147 1 322y a Sam um 33mm mg Cmsxun dummhun m mnmmnm 7 smmwz a g g Wmmmmm X For 11Szrzzddcmnnc 1 1H 1 132 fltz h 7 12 1 g m Mina qnahcm Assam h 7 o 9 113mm TN 7 a a mam dumm Indxmguf l7 ma 1 mp1 of m glph of y a nd Hz a thy 1h mm yml mm m 6m 1m pm 3 1h mm of y c ma 1h dumm 1nd mg of 141 9 skmmgwm 11 mdfquotzmuhcsmcg1d 10 m glph of 91 mm mm m glph of j by Shmmg 1 mm m m 1m manna vexhn yby mng 3 1nd sin mgnp 2 mm Wm 9mm of j 11 ms mm 1 Wm glph 3 Shawn bcluw m m glph bdrm 3 an mm wmdaw 71010 mm Indy l7 12 Demmm n am when glphed bdw 3 mm add a name a Any mm mmulmm 1nd mmm l7 mng we wmh am when 3 manning g mng we wmh am when 3 damning 1 Doc am when invc my symmcnj n m Wm mm c mm 1r m 1 Ind 11 mumps of m glph of my 9 x m when gummy 5 11 1 mmzz1mayzzhzm cmc I f 39quot l7 9 fz 4 19 d 19 c 9001 0 1001 15 16 17 18 19 20 21 22 A Leisure Time Cruises riverboat travels 46 kilometers downstream in 2 hours It travels 51 kilometers upstream in 3 hours Find the speed of the boat and the speed of the stream The air mail rate for letters to Europe is 45 cents per half ounce and to Africa as 65 cents per half ounce If Amy paid 1855 to send 35 half ounce letters abroad how many did she send to Europe Find a function Vz to represent the volume of an open box to be made from a piece of cardboard 14 by 11 inches by cutting x by z squares out of each corner and folding up the edges Determine the domain of your function As blood moves through a vein or an artery its velocity 1 is greatest along the central axis and decreases as the distance r from the central axis increases The formula that gives 1 as a function of r us called the law of laminar ow For an artery of 05 cm we have vr18500025 7 r2 0 g r g 05 a Find 101 and v04 b What do your answers in part a tell you about the ow of blood in this artery Find the domain of the functions ofvm7z2 3x 7 1 b 996 x2 7 z 7 6 Determine whether each statement is true or false Justify your answers a There exists no function such that f f 1 b A function with domain 700 0 can be an even function c If f is a one to one function with y intercept b then f 1 has z intercept b d A function with a square root cannot have the domain 700 00 fz z 7 4 and gz 2 7 16 then gf4 a 716 b 4 C 0 d 4 Which of the following is not a function 1 l 3011 by5 C 12y29 oy772 23 The solution set of 3 7 xi gt 7 is a 4710 b 1074 c foo 74 U 1000 d foo 710 U 400 d f 1z does not exist 1 3 is 25 The domain of f a 96 7 3 b 3700 6 700773 CD 3700 26 Which equation represents a transformation of one of our common functions that shifts two units to the right three units up and re ects over the z axis a 95 396 2 b fx m 3 c we ix 23 i 3 d 95 95 i 22 3 27 What is the center and radius of the circle with the equation x 7 22 y 42 9 a C 724 R 9 b C 274 R 9 c C 724 R 3 d C 2 74 R 3 Math 104 Exam 1 Review Key 1 a xa b 12772 c z 2 y 5 61 d y 2x 7 e z 72 f y 1 2 4073007602 3yz 4 a 71 3 17 4 3 7 b9c27y5 c neither 5 az116 b x 725 c z 73211 d z74f747 e Real solutions z 72 2 f z 9 g h 273 1 700772 U 5700 1 700771 U300 k z 7856 1 y 447 6 7y72 77 734 7 D 700700 7300 8 a 714 b 152 i 922 c 5 7 2x 7 h 1 O 11 12 13 14 15 16 17 18 19 a D 74mR 73700 b 071gtlt5ogt c r1ltzgt7ltz 3 7 4x 2 73 d Answers may vary Show f 1 o f o f 1z z e D 73mR 74700 f Answers may vary gz 3fz 1 2 a f96 m b f96 196 i 21 1 even a relative minimum f 2 1 relative maximum f 0 5 b 70070 U 2700 C 07 2 d none e y int 5 z int about 72 f no g f0 4 a fgz z2z4 b 97f96 232 c fgz 2x3 7 x2 5x 3 d f996 7 963 33 e 9 MW 74962 2z3 f fof 4953 Boat 20 kmh Stream 3 kmh 21 letters to Europe Vz 14 7 2x117 2xz with 0 lt z lt 55 or 0 S x S 55 a v01 4440v04 1665 b Flow is faster near central axis a D 08 b D 700772 U 7273 U 3700 20 21 22 23 24 25 26 27 O O U a False b False c True d False

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