math118 f00 exam3 - /MM 88> so Exam#3 U(AK/OO Read...

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Unformatted text preview: /MM 88> so; Exam#3 U/(AK/OO Read through each question carefully — make sure you have answered each part. To receive full credit on each problem, you must show all of your work. GOOD LUCK! V > (10 points) Find the equation of the circle with center (- -4, 2) and tangent to the line y- — —3x + 5 lmxo+b—yo} m: «3 X0 ‘_Li V1+m2 102% 7 =& (3 You will want to use the formula: 0' = d"\ 5( Li} + ‘3 r 6L (9‘ [9 + ‘5 ’ ' [\Sl Jen—.— Wfi/F’ ,. ”MM .- ‘5 ’/ ”VAN/t 0 2. (15 points) Put the parabola y2 + 2y + 4x +13: 0 in standard form. Please graph it on the axis provided and fill in all of the desired information. 2 AxisofSymmetry: ¥: ’i P: ”l 3. (10 points) Put the ellipse 361:2 + 4y — -l44 into standard form Please graph it on the was provided and fill in all of the desired information. @214» 4533 M if H4 - ~ ‘ +95; 1 - 4/3124 V??? L Center. (O a“ '/ Vertices: 0+ — c: 3 3 7;“ / Foci: SO ('51) (( lf‘V J1 1/ Length of the major axis: __L___ Length of the minor axis: :1 / 2 2 4. (15 points) Graph the hyperbola 0/521) — (x 223) = 1 on the axis provided. Please fill in all of the desired information. 29 5. (10 points) A factory owner buys a new machine for $29,000. Afier nine years, the maChine has a salvage value of $2,000. Find a formula for the value of the machine after t years, where 0 s t s 9. lo? Qrol‘OOO Cik‘é' OK \; 7 2x900 _ _ QOMOOO ‘QOOC‘ 327(000 m : «3000 We) «saw reel ‘00 ‘5 i/ ./ .. . . «1‘ 4; 6. (10 points) Suppose that the cost C (x) of producing x units of chairs is given by C (x) = 600 + 45x. a. Find the marginal cost (include units in your answer). Marginal}; cost ‘1'1 $46 Pu“ canoe/tr / / l ("r b. Find the cost of producing 30 chairs (include units in your answer). p L l C" ... ‘3; 2 can ,, taco 1 4$C€O§r “2‘ ‘ ~rt+~ I :3 4:3 :3 V5 5 O J Leafs, r __ 6% 4 / —— "’ 6 [QC/7Q 1 <$900.0 / _ 2 _ “awn“..ww... ___._._. __J, 7. (10 pomts) Graph y = 2x + 6x + 3Mprov1ded (you must first put it mm a standard form). Please fill in the desired information below. Y 1’ ox(>< «Qt “a \/ 1:- l, ;X 2 «C0 1 f “l 8// Vertex: (’3 L-gng“) ’P (/ Direction it opens: Circle One: Wldfiw ‘1;::\ The graph has (Circ e 0 e) 3 Maximum a Minimum/x '/ 8. (10 points) The volume of a right circular cylinder is 10 cubic inches. Express the total surface area , S, of the cylinder as a function of the radius, r. V = 7rr2h \,.. h S = 27rr2 +27rrh ‘ W 4. 90“” r ‘ __fl. , _ ” N) /O I 71% ‘h (r72 L ,/ H” ——-——-'—~"”/ \ H» 1/) w» rl (HM ’\ S t 9 Li; + gm» M WW) ll“ l>\ WEN» a" , IIIIIIIIII ”/JW 505 or g; 9 o * <9qu % "‘ MWMWM r. 9. (10 points) Among all rectangles with a of perimeter 20m, find the dimensions of the one with the largest area. P=2x+2L p, ;.y 4» gal. 1< x ‘ ( w L» J A = xL 20 9% i 0“ f3 4 a L?" 100‘ / ’7‘?” . / A1, >4 (m x} ./ / f‘\ —\,(2‘4 lOX no], 0 Extra Credit: (3 points) What is the maximum area among all rectangles having a perimeter of 20m? 4' 5 {f / fiwmwmwwmwri 5; ”wwwwwwwmmmwmww<r { ...
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