Suppose that in one stunt, two Cirque du Soleil performers seesaws. The first performer are launched toward each other from two is launched, and 1 s later the second performer both perform a flip and give each other a high five in the air. Each performer seesaw versus time for each performer during the stunt is approximated height of the first performer versus time is h time is h a. = -5{t = -5(t - 2)2 + 5. When are the performers lightly offset is launched in the opposi direction. They is in the air for 2 s. The h ight above the by a parabola as shown. The quation for the - 1)2 + 5. The equation for the height of the second erformer versus at the same height so they can give each other a hi five? Write a system that will model this situation: [ -::.- L fr) =- - 5( -f _/)2. ..L 5 '? (+ -l) '2-T 5 b. Solve the system using substitution and factoring/quadratic formula: c. List the ordered pairs: d. Solution Sentence: - (1.5", 3115) '5 (+ -()l.t5:: -5(t-2.)2+5 - S l t -I) 2. (t -I )2.:: ~ - 5 (t -2)'l. f _{)"2 1+ +akes J, 5" Sec.~s ~'f tht m ~ r-.eQch a ~j d'at o~ 3,1 S WIrt(XL -1hUj cu.rt S1oc elA.('t, O~t,(' o: h\~ ~I/t A car manufacturer . does performance tests on its cars. During one test, a car starts from rest and acc erates at a constant rate for 20 s. Another car starts from rest 3 s later and accelerates at a faster constant rate. e equation that models the distance the first car travels is d :: 1.16t2 , and the equation that models the distance the s cond car travels is d = 1.74(t - 3)2 , where t is the time, in seconds, after the first car starts the test, and d is the distance, long will it take for the two cars to have traveled the same distance? . a. -t'l. d ; (0 . d =-1.1 4- (~-3» Write a system that will model this situation; b. Solve the system using substitution and factoring/quadratic formula: c. List the ordered pairs: (I. tos \ \.p ) 3 .llo4 a) d. . Solution (/10 Sentence: 1... /.1 db \.~5\~.Q.(' 2- = 2 (ot "l.::. I fllf-t'-IO.<-f4t+{Z),fIp o = #5 t2..-10. t.ti+I5,b" t z: IO,tt :± [lo.y...l--t.t( !~)(rf,C,{, .3~8"'h3\0.0334') 2-(·58) Iht 1wa (U(S iYaLXJ 1ttS4:VU dl&+l.tnu.. ~ How l. i 'I [f ..3) LI(at~.:1.1tf{ta.-/o +4) I. I ~ l n metres. t: =- 10. '+1.../ ± 172.& f;;zl/ and I~· atitt( ..sfC. i. I V; t::IO·4 j:~.l52¥:;} ./~ A Canadian cargo plane drops a crate of emergency supplies to aid-workers on the ground. The crate before a parachute opens to bring the crate gently to the ground. The crate's height, h, in metres, ab seconds after leaving the aircraft is given by the following two equations. h = -4.9t2 + 700 represents t e height of the crate during free fall. h = -St + 650 represents the height of the crate with the parachute open. a) Ho crate leaves the aircraft does the parachute open? Express your answer to the nearest hundredth {h'h"=-- 4 of height above the ground is the crate when the parachute opens? Express your answer to the nearest· IQ-(L+700 5i: -f-ioSO a. . a system th at will mo de1thiss Situation: si . Wnte b. Solve the system using substitution and factoring/quadratic formula: -. rops freely at first e the ground t long after the second. b) What etre. During a basketball game, Ben completes an impressive "alley-oop." From one side of the hoop, his te mmate Luke lobs a perfect pass toward the basket. Directly across from Luke, Ben jumps up, catches the ball and tips it 2 The path of the ball thrown by Luke can be modelled by the equation d - to the basket. 2d + 3h = 9, where d is the h rizontal distance of the ball from the centre of the hoop, in metres, and h is the height of the ball above the floor, in m ers. The path of 10d + h = 0, where d is his horizontal distance from he centre of the Ben's jump can be modelled by the equation 5d2 - hoop, in metres, and h is the height of his hands above the floor, in metres. a) Solve the system of equ tions h~ -d 2.+ld q algebraically. Give your solution to the nearest hundredth. a. w' rite a system th at will d 1this si . mo e s Situation: -tJn::: q Lf Sdd 2._2 2..._1 Od +h::: 0 b. Solve the system using substitution and factoring/ quadratic formula: c. List the ordered pairs: d. d -= -d ~l.d +c, .3 -I ":)d'+ od e -d Z+2.d q o /4d 1._2~-eL+q Solution Sentence: \h t .3 h:; _ Sd !.+\ bcdl o..nd Ben mt~+ , 3~q S'-(Ctl ~ ~+~ t~f3 I i'11( 'f. P.." d- o..'os\tt. 4lt.. {' 100 r, The 20l5-m-tall Mount Asgard in Auyuittuq National Park, Baffin Island, Nunavut, was used in the op ing scene for the James Bond movie The Spy Who Loved Me. A stuntman skis off the edge of the mountain, free-falls fo several seconds, and then opens a parachute. The height, h, in meters, of the stuntman above the ground t seconds a edge of the mountain is given by two functions. opens the parachute. h(t) h(t) = -4.9t2 + 2015 represents the height of the stunt r leaving the an before he = -10.5t + 980 represents the height of the stuntman after he opens the par chute. a} For how many seconds does the stuntman free-fall before he opens his parachute? b) What height above the 1..'2- stuntman when he opened the parachute? ) h(±}~-4t +1016 [ h Lt): .. lO.;i': +ct~ a. Write a system that will model this situation: b. Solve the system using substitution and factoring/ quadratic formula: c. List the ordered pairs: ©http://gabrielmathnorth.weebly (I S ,~lw}~ round was the ) ~ll5 Ilqq~ ') .com/uploads/l/2/6/9/l2696930/pre-calculus_ll_- _chapter _ 8_ w bsite.pdf The revenue for a production production , where t is the ticket price in dolla s. The cost for the is y = 600 - SOt. Determine the ticket price that will allow the production even when revenue = cost.) a. = - 5Ot2 + 300t by a theatre group is y Write a system that will model this situation: r H ::.-SDt 4- 8 == (DCO -6'D to break even. ( company breaks :t30ot ...t.. L b. Solve the system using substitution and factoring/ quadratic formula: c. 3") LJ50) List the ordered pairs: ( (4 )400) d. Solution Sentence: 1hz -H-u..().:+,~Bro P w II t fb b'l'-i-etL e..uer I CL+aT)(lJi-pnl.l.. of is a.PS'O ~ 1) clU.:tiVl·~~f;4 fbr o: Uor Ob A daredevil jumps off the r Q $'+00. eN Tower and falls freely for several seconds before releasing his parachute His height, h, in meters, t seconds after jumping can be modelled by: h -4.9t2 + t + 360 before he released his parach te; and = h = -4t +142 after he released his parachute. How long after jumping did the daredevil release his par chute? a. Write a system that will model this situation: r h::-4 .Glt "2-+-t ~ L h:::. ~(t) 0 -L.%-t + IY " b. Solve the system using substitution and factoring/quadratic formula: c. List the ordered pairs: (- <0. l 1q ) llo (p, 11 -4,Qt t-=- (p 'Z.. t ~-5:- 4~q7,'?'=-S.± b5.Sse - ~Li -q~i' 6~ -.. 2. se <..cnt.i.o. i ~- /1 q ) 1, / 9qa A punter kicks a football. Its height, h, in meters, t seconds after the kick is given by the equation h = -4.9t2 + 18.24t + 0.8. The height of an approaching blocker's hands is modeled by the equation h a. f h =- - L\ ,l1 t '2. + <6-,2.'t 1. 'e h~-'·tf~t Solve the system using substitution and factoring/quadratic formula: c. List the ordered pairs: d. Solution Sentence: . !) Co.,;) ("3 ~"3) - \ , '2.-\ \0 q ) L \%'4) 3/1Q,) t O. t +4.~ b. blocJu,.- -1.43t + 4.26, Can the blocker knock down the punt? If so, at what point will it happen? Write a system that will model this situation: ~t. 5~ +2..\2':::.0 -'1,g l-k Y'f-\eQs~s his ~c.ha:tt using the same time. . -s± j5~Y.(-YfqXll6') ( 1 . 2 ) " 3. L ') d. Solution Sentence: , -t 1'"3(00 = -'+t+lt.frl -t.f,qt - Y-,'lt2.+f8. -4 .qt' -t-Iq.£o1t - •tflo =0 t ':: -~I '0+ ~,q(fl Me he' y.j'- ±J3IQ,fiiZ9 -IGilt lV)oc.J(~-thl p.1l~ O-b1e,r ,g see and Z4-t-r .~::; - '/t-~-t+"I.I" t= The height, h, of a baseball, in meters, at time t seconds after it is tossed out of a window is modelled y h = - st2 + 20t + 15. A boy shoots at the baseball with a paintball gun. The trajectory of the paintball is iven by the equation h = 3t + 3. Will the paintball hit the baseball? If so, when? At what height will the baseball b a. Write a system that will model this situation: f h-:;. - 5 -t £+1.0++ \5 ? "L h~3t+3 b. Solve the system using substitution and factoring/quadratic formula: c. List the ordered pairs: d. Solution Sentence: \+ IN it \ -5t~+llt tZ--\lt- ~ a. b. . The cost for the production lL =-0 0 (t- - ~O X t + .3) +:.~ of 11. o: htts~ The revenue for a company producing electronic components dollars of each component. \'2-=- D StL-llt -hA\c..t . Lf se <.b')ds for-thL pa Ivrtba.U to h\+-thL production -5t2+1..ot f?=3++3 t=..-3 6 "? is given by y =- 20x2 - SOx + 200, wher x is the price in is given by y = 60x -10 .-Determine the price t at will allow the to break even. . .. . . Wnte a system that will model this situation: ~~~-'2..Q>('2...-~x +l,OQ 2J::: <nDf..- t 0 . Solve the system using substitution and factoring/quadratic formula: -LOX. 4 X:t l..UJ.:: Wc»)(-, .:- - 2..ox 2._ \ I ~Ox.t.+\ \ 0 c. List the ordered pairs: d. Solution Sentence: A pv1~ ( - -, ) -y. '30 (I.?) 30) o-r 'tLSO bY-~ t e- © http://www.lcboe.net/userfiles/l025/Classes/3196/ 20systems%200f%20equations.pdf7id=497278 - 2- 0 ::.0 oLX?"'", II X -2..1 hcux. ~ I 'PO w-d- ext-o. <..a+ of s go. u.:)\ \\ x ""\'""LlC=-O X'L+IIX 4-2 l1-tl~)Cl< a ~) )(-::-1 /userfiles/l025/my%20files/107%20Iinear%20a @ X::I ..5 d%20quad ratic% D

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