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Unformatted text preview: Ebw‘ﬂo/US m MATH 122 SECTION 021 TEST 33 Show all work for full credit. All decimals should be correct to three (3) digits past the
decimal. Good luck! 1. The graph of ﬂat) is shown. Evaluate each integral by interpreting it in terms of areas.
(3 points each) 05m) dx = gram  2(a)) — m dm = / go rzxso» 2% “2(3sz 71°f(w) dw= ﬂ 1+3) (.5653
: 2. Find the area included between y = 73: + 16 and y = 28 + 3x — 3:2. (6 points) " lVllﬂ’sECi‘ld/l PDWI‘l'b‘ (‘lprer and (2,303 ~ 678 2! (7mg) {286x «alch ’
L V 3. A company’s marginal cost function is
C’(q) = 3(q — 15)2 dollars/item , Where q is the number of items. If the ﬁxed costs are $2000, ﬁnd the additional cost of
increasing production from 10 items to 35 items. Give units. (8 points) C(35)—C(lo): [OS 3/245)de r all r
=$8l25 d “5 2 4. The velocity of a car (in mph) is graphed below. Use sum approximations with n=5 rectangles to estimate the distance traveled by the car in the ﬁrst 10 hours. Give units. (8 points) ‘
velocity
(mph) L\\%=Z(O+5<>+80*(oo+Zo)= mm,
m: z(so+go+zoo +20%) Hwy/melee t (hours) 5 l0 5. Attendance at a local fair can be modeled by
A(t) = "—154 + 121i3 + 30t2 + 6075 people, where t represents hours since gates opened at 9AM. Determine the average attendance
between 4PM and 9PM. Give units. (8 points) [2
4m —9 H S («£q+')2£3+30t2*(00i1>cn3
’1' 9,044 '9 ﬁll
: 5i(25300> = ﬁg, ' “W 'W‘i = We 6. It is estimated that t days from now, consumers Will be buying girl scout cookies at a rate of
r(t) = 15v 5t + 1 boxes per day.
If the girl scouts charge $3.50 per box, how much revenue will they generate in the next week? Give units. (8 points) kbx ANS
1 es .
l wee! r 7Jax1$ 5 [Smdk = 430 boxes 7‘7
o = bows 430 W5. gash? ... 7. In 20117 a tree is 5ft tall and growing at a rate of 1"(t) = \/ 3t + 9 inches / year,
where t is years since 2011. How tall do you expect the tree to be in 2020? Give units.
(8 points) Sam ; makes Lff ‘Mch‘vg
0 HZMCWS, if}. ,1: Neva HEW Lil”: Skis
IZM 3 : oi 8. A particle is moving so that its velocity is v(t) = 6 + 575 — t2 meters/min,
where t is time in minutes. Find the total distance traveled by the particle in the ﬁrst nine
minutes. Give units. (6 points) Sv/msi/ﬁ/Ji: O 9. The math club is selling T—shirts to raise money. They currenty charge $14/shirt
and sell 300 shirts. A survey determines that they would sell 6 fewer shirts for every $0.50
increase in price. What should they charge to maximize revenue? How many T—shirts would they sell? Give units and prove your answer. (8 points) Mame E: (w warm—lo»
F: tax/alive W= [mesxﬂrﬂ 4* (500 "(00(05)
= —8‘1'3X +150 ’3x MSG/614ml"
Cam 0: éKobx {goo—Mu) , It‘
gmls 69x =[pla CWC F2“ 234 shirts x: n 5,—9 ,2”: Mo’lox
@ u 9
Wlax / 4 10. Evaluate the inte als. Reduce coefﬁcients. (3 points each)
a. f 7 dac ; = 5W 5 J
I afﬁda: : d.f3$d:1: ,. f 11. 12. 3/;
X I..— 3/2 +C : Evaluate the integIal. Reduce coefﬁcients. (8 points) 10x+5
x/x2+$—2 da: :) JO(><Z+X ’25,; *Cl Evaluate the integral. Reduce coefﬁcients. (8 points) 3303 + 33: ...
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 Spring '08
 KUSTIN

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