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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 /
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