Test2Key - Test 2 study guide (Show all your work) Math...

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Unformatted text preview: Test 2 study guide (Show all your work) Math 1101 No.: Name: 1. Solve the inequality, giving the solution in interval form. MW ‘E« n) A ., -90 L; gs) »§x%§a>sx»a, .52: , 1) ~9(x-6)>5x—2 {w if, 2) 7<3x~11<25 7 6);. )3 2r; §§ <nnn3n, gang. 2. Bob can be paid in one of two ways for the furniture he sells. Plan A: Salary of $ 550 per month, plus a commission of 10% of sales. Plan B: Salary of $ 750 per month, plus a commission of 15% of sales in excess of $ 5000. For what amount of monthly sales is plan B better than plan A, assuming that ’le 7 one than $5000? 2:: saéses g33a , is fré‘firan t? {Keg'wej > §§€n nan; :2: ; nag}: > §§tn rattx”; 9&5" T? X L} 3. If a student has an average exam score between 70 and 79, he will earn a grade of C in his algebra course. Suppose he has three exam scores of 75, 62, and 81 and that his teacher said the final exam has twice the weight of the other three exams. What range of scores on the final exam . . . . Wu.» J , . » W111resultmhimearmngagradeofC? x w Matti , 7 fins 73?” 2% § ?? f t ' . gmfinz‘x‘ a; 3%”? é —F'"atl.. Exam g 88'g tag 5 an é t3? rMM ’ A 2 as x .t 4; 3: '5: 4. A company is planning to make a new kind of radio. The cost to produce i radios is C = 94,000+17x. Meanwhile, the revenue earned by selling x radios is given by R224x. If R < C, the company losesoney. Aal: 5. Simplify the exponential expresion. ' «tax/“(t {£4 ff *1? l4 1) (—8x3yx—3x7y3) “+me z 6 2) (~2x4zx3x3y2xyz5) ’éxU Z 6. Analyze the following quadratic functions (i.e. determining its concavity, vertex, and whether the vertex of the graph is a maximum or a minimum) sketch its graph. E 1) y=-3x2+6x_5 concave GLOW“, V9.4“: 1‘" Maximum {2‘ 2) y=2x2 +2x+7 2) (Ottawa «NP Vedax : 7-“; 7. Write the following quadratic functions in the form of y = a(x — h)2 + k and find its vertex. 1 z t g .. 1) y=2x2+2x—5 yszmwé) +<~‘£ vertex; 1 * r kt"; . 2) Y=—3x2+6x+8 y :2»? (1M); “‘ ”, VMW= 5" k:n 8. The profit for a product can be described by the function P(x)= 202x — 5000 — x2 dollars, Where x is the number of units produced and sold. To maximize profit, how many units must be , produced and sold? What is the maximum possible profit? Verses : 3a. 2”: 4W ,0, Wm, mus-k be producecL, ’rhe maximum man i: 5801 , 9. If 800 feet of fence are used to enclose a rectangular pen, the resulting area of the pen is A(x) = x(400-x), where x is the width of the pen. Is A(x) a quadratic function? What is the maximum area of the pen? What are the dimensions of the maximum pen? ; ‘ ~ ‘ 0000 1 yer/s, Am s ?uadracJ—vc, “rive mmfgnfm mean u ft _ “a ., ~=— y 3:: 5&2;er x. at? Vfisiggg , 10. You are given 116 feet of flexible material to enclose a rectangular pen. Suppose that a long straight wall is used for one side of the pen, find the maximum area you can enclose . . . \ \ \mmand the dimensmns of the max1mum pen. 2 \ \ WA u. \ Lem,” : :8 H 1'56 m“"‘7’““m, ave“ :5 [682 ft‘ In? 573 '17 Wc'aH'") : 2741 i. Ramada: J3¥€i%:i‘§W:§%§«ZW?W :grawwgwj ymiéxpixé 159%sz fififiggu : 3.1%; Kfiégfg 11. If a baseball is hit with upward velocity 48 feet per second w en t=0, frdiff a height of 4 feet, a) Find the function that models the height of the ball as a function of time, t. H :—:bt‘+ u8f +114 b) Find the maximum height of the ball. The M owlw um hag H U Q o A . (the height function =-16t2 + v0; + SG , where v0 and so are the velocity and height when t=0 "f “ézféxz’ 3)): respectively) 9 “a 35’ e w; a a a, i ,;~, g : .74: M A we? RX“ h M ‘zausas V it i} éfffié’gwéfii’i a ‘13 wééér’éx‘gév 53%;: 12. Between 1989 and 1998, the population of Johnsboro, USA (in thousands) can be modeled by f(x)= 0.84x2 —— 6.72x+ 20.4 , where x=0 represents 1989. Based on this model, in what year ‘ i ror i minimum? r , . ,, , N a. ,4, dld the populat on ofJohnsbo each ts 9; gpgéxsw£¥3v2X ,f, gag i a, saga; at, aim...» at? I 51€3V§s9”¥3643’?/§§s 13. Solve the following equations. if“??? £1 X 7" if > *éeé : 3 5“ if? 3 5 safaris 1) x2=2x+15 x.: I,” X‘s—3 gzsgx»:§:e2 {sfiamggo gag“; gala; 2 a H“ v s a, E‘ :3 »:»§} 2) 2x =1~X X.:% ,YL:-' Exiéxwétfij, waM??? Xi} 2,X: 3) x2-3x=10 14. The profit for a product is given by P(x)= —16 x2 +1440x—22400, where x is the number of units produced and sold. How many units give break even (that is, give zero profit) for this . .22., ,,,,.,7;§ product? , , “5;; agaaaxuzmm om + I JUN {K’ezeéifieigs} 111$; *5}le fiztg§ 15. The total revenue function for a product is given by R=420x dollars, and the total cost function for this same product is given by C=12,000+80x+ x2 , where C is measured in dollars. 3 For both functions, the input x is the number of units produced and sold. P f: ,1; 2 , {g 4% j; 3. Find the profit function for this product from the two given functions. "P :: - X 1+3 4 o x .- 11990 aézféfiawéiLMQw b. What is the profit when 32 units are produced and sold? .- 2. ,4 L4 4:“ ' z” i ” r» c. How many units must be produced and sold to break even on this product? «’4 0 i& 3 0" é“ ‘flxigwx $2 d. How many units must be produced and sold to maximize the profit? I 7 o . . . A M a, 3 a _ 5) gkmizggé} {5; 33132! 53;:6’;av€,r‘{§szg§”§ e. What IS the max1mum Profit? [6900 3“ ‘0’ 36%? j: Jeri} a: + . eesiex :» a: a» “vii? «await 5'! Mex a: - ,5. 33}1+%£§i}2f€?9 35%;}? 16. The function W(x) = -0.01x2+0.29x+8.50 can be used to estimate the number of workers in a certain industry in the United States, in millions, x years after 1980. For wt yars r here (r il here be) 9.7 million workers in this industry? 0 $100 , We“ 7, . I q 8 M a if}, 2% fggexé‘fi‘ “wages; ,ge; g£%3.2€§3€ egafiiig’gE 3 $23.9; 362‘ +§~uf3€e5¢33§i 5‘5”, WWWWMWWWMWWW _ < . fig“... ... , A... 2+x’x>1 as: a. f(-2)= 6 g b. f(0)= 2" 3 c.f(1)=_g____ \ I (1.112): (4 1X *9“: / e. f(3)= 5 1 f. Graph the piecewise linear function. i JWMV i w: 1 Si 5 {a ~x+$x$l 18. f(x)= 2x+ l,x > 1 a. f(—2)= 6 i i b. no): u I g / c. f(1)=_3___. \ i r d. f(2)= S e. K3): '1’ f. Graph the piecewise linear function LWWNW W".W_.‘,ww~..__.wtmw 19. Solve the following equations. 3 1) [2x—5}=7 xcé, v! we??? 535‘ i; “$35” X”: , 95 M :3; 2)l—3x—4l=8 5% #4 wgswazitxrea a???“ é'”%*1”*"§*"§“fi I , ,2» ‘w 3) lx2+2xl=3 :) -3 ‘Xfitix '33 3Q xfzgw'f ’ gigmxsgxe XFWZX*3:§W»MW ,4“ (Fig? {xaxxka i:»% i 36:: 52 ‘f‘gggggqgii 3 gate iéfai-iéa ; 20. Suppose that S varies directly as the -2—— power of T, and that S=7 when T=4. Find S when a; ._ r, E; a w / T:16, $5K§Y§ii §:§<££é}m :2er kg“; I“; 21. Find the equation of the quadratic function whose graph is a parabola containing the points (0,3), (-l,9), and (1,1). 5* Wm; "MW 4:; : git“??? gave?) , 5:: {2.43 5y; ’gsaxzwwwé 2‘)":- megfiuw Waggflamas 3 mamas 3 "’ a”; "ipg’jg‘gflé “‘{e’ is; 7: 51%; +33}: éaivg {3:99 i 53 3"““g 22. Find the equation of the quadratic function whose graph is a parabola containing the point (094), (-19-1)9 and y:-2x"+3x+24 3251a): saggietp ; Lire-iifgfiiégwii Ti” amzaéseiz A? i: “it” 3 it“ Wit“; ’43 '1: {1 W i? 5‘; w I x 1‘3 ’ \- _ a; M} :: Qaéé {2‘} _ m w » 44 x 9w w a. ; Mfiiséffis‘g “W W iééi’ "F f1 ”‘“ kW > 5% tag/33$ §§i:m;i§ "Kiwigia Eéiéiwi‘fii” Q i ...
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Test2Key - Test 2 study guide (Show all your work) Math...

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