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1105_T1Bsolutions_F11

# 1105_T1Bsolutions_F11 - emits(0.723“ I2.15 MA(L14 0...

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Unformatted text preview: emits; (0.723“) I2 .15) MA (L14, 0) MACIIUS Test 1 (form B) Name: 50! Uri”)? Um}. I Fall, 2011 Period: (circle yours) TH 11:00 TH 12:30 TH 2:00 Calculator allowed. Follow round—off directions where applicable. Show work in spaces provided to earn partial credit. 1. The table shows the height of a spring—board diver during a dive. Let h be'the height, in feet above the water, of the diver f seconds from the moment she leaves the board. Assume the maximum height of 13.5 feet is reached at 0.4 seconds. (seconds) (feet) “— 0.75 12.25 —m- fer-i406 o": snark when: heist/{\- decimases ('0 . 10) 10 i 5 OPE = _ ' I‘ 3 'f . ganja mg... L); «‘5 “Wren B of 4llS {all ge'r “aha“ 2 . . . time inieWoi WET” mm. height decreases 0.5 “0.25 0.25 0.5 0.75 1 1.25 1.5 1.75 2 . . H2 . ’ . . . . . . . . . - . . . , , .i. a) Height a function of time. Which IS the Independent variable, t 01' h? E” b) Let 11(1) denote height at time t seconds. According to the table, h(1.25) 2 3 fl G” 0) According to the graph, over What time interval is height increasing? _ d) This function makes sense only until the diver hits the water. State the domain and range. 6) Working from information in the table, calculate the average rate of change in height over the time interval 0.75 S f S 1.4 seconds, and write a sentence that interprets the answer in context using appropriate units. aver “ﬁx: “iimc. ‘W‘iicrvmg {gem .tw; C) “75:; .596: “to Hi (QC, heecjix‘i decreaswi ioj an O ”1975“.-. (we “(i-"9' 5i” I“ m 5"“ “"““'””"“”"” 9”” «4%.? Average. 6? l5 {ecii"’ per" Sarawak (I ‘L‘ “a "75 \fh‘rig if? 3% 7%, If 11/11th X '1 Must matte 13:5; 3e 2. State the domain of each functioné) .-<- 2 m9 / “WK a 7% K giwsiwtr j ’7 . z 7 1 I Z :1 ' x we"; ”I“? a x — f K ”Half”? b x =V3Hx ‘ “baa ”Xekfcdueg'x '2’ i“ 77 Domain: (“W ”7) we"? I)U (71“ 00) Domain: éQii‘jf‘Z’J or: ix} £433 5 ”11\$: :: 1:111:11} 13:: {1191: 5:11,. J? F‘ 5 {(2 C 11‘: alibi i '19 F 'T coals 3 f “PM ”Iua‘ekg‘” 3. The graph of parabolic function f (x) 9 x extends y 12 . _ r (5,9) 1:} Graph of {(x) downward forever over domain ( oo ,+co) “E m a) W :1 :1 :1 :1 (N11: """ 611 CE?) b) Complete the sentence below with the app10p11ate x- axis inter,val(s) using either inte1val 01 set- builder notation. f (x) is positive over (1:3, :29) and increasing over (Ed?! 561 . 4. A cold can of soda is removed from the refrigerator and set on the counter. The soda warms up quickly at first, but slower and slower as the temperature of the soda gets closer to room temperature. a) Check the box for the graph that best represents temperature as aﬁmciion offime. Is this graph linear, concave up, 01 concave down? CD‘M" (AV E? KI (21:0 3" n” D ’ Y El Temperature Terrperatu re Temperature b) Clearly, temperature is increasing. Is the average rate of change of temperature increasing or decreasing ovei time? d 9: (”Life 01\$ mg 5. Consider the line shown. ' is Z a)'THesiopeofthisiineism= 2. 2.5 (5)“?33) (2.10) x‘ 7‘ x2. YL _ \ ms 7'2“?! * 0—02.12): 30% weeks...“ ‘2" 3 b) Write an equation for this line: Y”}’. :m(xfxc‘> ywc>=2.5(Xw2) y: 2.5x“? I c) Any line perpendicular to this line must have slope m = 5 . " 516% a“? given [Eng 15 war—225;; %> So a"? ‘preniiﬁcﬂﬁw New: momici have, deiiver Veﬁi'prCO-Q ﬁiéf‘ﬁ‘ ”7%; 0“” ”t4 . 6. Hooke’s Law states that the Me, F , mssarxto stretch a sgﬁmngx units‘beyond its natural "Aux“: a: .-)(— "WW—(m tam-ya W". "Fe-L‘czna (equiiibriurn) length is directgympfgfaiiional to the length of the stretch. Let k be the constantwgg Wﬁwwwwprmw 'Jwﬂrw w a ”immiwwdemiwmgqmnma proportionaiitz. Fekx Cf; 21) Suppose a 10—pound weight stretches a spring 6 inches. Find k, and write the equation that gives force F as a function of stretch iength x. Fsz ‘0 ”w”- K' Q 5 : 5,, s; 19:; 5 Answers: k=_/3; and F =::5M:<M_ (a 3 m L '0.) How far will a 12-pound force stretch this spring? 7. Q inches é Fsax r 3 5:; \Z 3 guess 7. The table and scatter plot show the dollar value of a certain truck over time. 30000 Boiler Value effort]: Value - (dollars) 25008 ~5000 The linear regression feature of the calculator gives this output: y = ax + b a= 458714285"? b 3 2371904762 a) Write this linear model with slope and yaintercept rounded to the nearest whole number. y: ”i587x + 237”? Use this equation for'the remaining parts of this question. - b) Find the x-intercept. Then write sentences that interpret the x-intercept and slope in context, suing appropriate units. the vertical intercept, horizontal intercept, and slope in the context of value and age. x—intercept interpretation: “This linear model suggests that... Winch, ﬁﬁ "i'WJrﬁk 3-5 i5 \/ ea #25 g Jr '_. 0: *lSB'TKthSMQ oici HS Value wi“ ice. ﬁﬁa e. 7““ I521: 2:237”? x .2 aims/ism w 15 . - slope interpretation: “This linear model suggests that... Hui {tweak 5 Vagina déCV’aAGES by om aveMJe a“? \$53? per- yam-v a? edge” 0) Use the linear model to predict the age when value reaches \$15,000. Round the answer to the nearest tenth of a year. 15000 a ”lasrxwtﬂlt‘l AgexaiLye-ars I5s7>< ":2 3‘7”? X“? 8'7"? 5’5”” ”if???" N a 8.. A student takes out two loans totaling \$4000, one loan compounded at 4% annual interest and the _ other at 6% annual interest. The total interest for a year is \$254. 'Let x = arnount borrowed at4%. Let y = 31110th bonowed até%. Write a system of two linear equations whose solution gives +‘ne. ampmg borrowed “j- 470 and 070 . ' a. ‘ - ' Do NOT so we Equation 1: X +— Y = 4000 Equationz; .O‘tx .3. _0(0¥: 254v. 9. Choose to answer Question A. or B. but'not both. Check the box for‘the one you want graded. [:1 A. The region shown represents which system? (Circle letter of correct choice) ' ‘ y ‘ \ > L. 50im‘i‘wv‘t region, is A: t Y— La x+2y22 ' 2x+y21_ a) b y<—x+1 y<—x+1 rx+2y>2 - d) 8) none of these yS—x+1 I‘ We \ \ﬁas y—in']: :L g y>.—»i-;<ft-.|1égacé% “‘9‘ “"Pt “ft->71. {lay > “3+2- _ X+37>rz 1 ‘ D B. The region shown represents which system? (Ciicle letter_ of correct choice) Skuhﬁ regiom «Forges X570) >030, invasiviagdfé absoloqLe value (3}: V y<5-§xl \ ySS—lxl ‘ a) x20 1)) x30 y20 ' yéo y>5~hl_ d) x30 e) none of these 3220. , . . 10. Rip’s Cleaners has a leather cieaning service. The ﬁxed cost to setup this service was \$9000, and it costs the \$25 for labor and materials to clean each leather item. Rip’s charges customers \$40 to clean each leather item. Let Cﬁt) : Rip’s total cost to clean at items. Let R(x) = Rip’s revenue on x items. a) Write linear function formulas for Rﬁr) and Cﬁt}. cm: Woof: +~ 2.0x Ra): 3+0 K b) Find both coordinates of .4-rekevenp01'1hen sketch both functions on the axes p10vided,andjabeietﬁﬁ ieak-evenpom w1t both coordinates (“71ch am; when: tevcanuf’ a: tic-5‘7!” aoK:eamm-t2§s \SK 3 ﬁooe X's: (013—30 wmwx 12:)(900 revenue. 2:ch ms“? nee sari/cecal afi (40>(0063 if? “\$20000 (moon) t” ONO) 1200 400 1000 600 \$00 2 C(t)_ c) The region satisfying the system < R(ic ) is called thé‘hfﬁhgion. Shade the region in the y — . WWW ... ﬁgure representing the proﬁt region. gee. nice/we, ...
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