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1105_A4_Solutions_F11 - MAC1105 Activity 4 Name 5 oi ML 0...

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Unformatted text preview: MAC1105 Activity 4 Name: 5 oi ML! 0 “5 Fall, 2011 7 Period: (circle yours) TH 11:00 TH 12:30 TH 2:00 Show algebraic details in spaces provided, and confirm answers with the calculator. 1. The table below shows the output for functions f and g for input x-values 0, 1, 2, and 3. a) Complete the table by calculating the average. rate of change over the last two-unit input interval for each function. Which is function is linear, f or g? 5" bacon s e W5 owe not re. A st 5 Comic-mt“ at 2. X20 x=2 x=4 x:6 X:8 average rate of change of f [0,2] ' [2:4] [4,6] [6,8] over input . _ ._ _ .m. 11+ interval... m:_6__m%=2 inf-:10 6:2 7}):14 m; $2 2~0 4—2 6—4 3-4: g(x) 2 6 j 18 I 38 ‘ 66 average rate of change of f [0:2] [2:4] [4:6] [6,8] over input ‘ interval... m=§£322 ,,,=18‘6'=6 m=38""18:10 m: 6.93 6 — 4 _. a!" ‘ b) Fact: The average rate of ‘1 ange o a quadrai - 'm: decreases by a ‘- ' J; Complete this sentence: g is - gem?!” ecause over two~unit input intervals the average rate of change of g in great 5:. by the constant amount ( increases or decreases ? ) 2. As an experiment in motion acted on oniy by the force due to gravity, a stone is thrown upward from a bridge and we time it as it falls to the water below. The height, h, in feet above the water t seconds from the moment it’s released is given by the quadratic function h(r) = —16t2 + 321 + 48 . a) Find 11(0) and write a sentence that interprets the answer. Use appropriate units. . 2w _ Mo)a»!t(o)+32(o)+aa ==1+a . _ At dime i; 210; Malawi" (sheave “tine W’s/Lift" 15 Li“? + (Eel/u] Vchiam'i'ibf) We, \OV’i IS $665+: 6-000»??- MPMQ We. em) 1)) Find the time it takes for the rock to reach its maximum height above the water, and find this maximum height. Record answers below using appropriate units. Um“le "‘ 3:6?) time to max height: 1‘ = { Second F AL: .. em = Wt 20‘ 261°) J max height: 1‘ 2 956+ MI): filthy-+326) 4» Q9 2. Ht 6) Find the time when the rock impacts the water. A‘\‘ ‘rmdaaa‘i‘ W‘IJAA “43 Walter; height is zero, “memmpacti PM o .3 469+ 323;, M18 m *b i W o: »|(o(‘t"‘—~2t:—3> M p _ WM oewlto (vb-«336::th- t: tea-:0 mat t+t==o W... - Melt») ti?) and {trawl Mazuflgzw . i: .... a...” make: no “’32- igfififlg WI fence at; it “git (01+ fl «$32... aAg‘me” “33,2” 35 A d) Sketch the function from launch to h ‘53 2“ impact with the ground, labeling the vertical intercept, horizontal intercept, and the vertex with ordered pairs. (o #8) I ’L 3 e) Over what time interval is height increasing? [DJ J or i 0 g: ’6: fit I} t). State the domain and range for this experiment. Domain: [0,3] 0““ ltlbé'té‘fi} Range. [0,643 of" €140 a in a ...
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