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Test2Solutions

# Test2Solutions - 1(10 points A 6-inch thick layer of mulch...

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Unformatted text preview: 1) (10 points) A 6-inch thick layer of mulch is to be spread on a garden bed. The width of the bed is measured every 2 feet as shown. All measurements are in feet. Use Simpson’s rule to estimate the volume of mulch that is required. A: %(I(0)v+ Web 2(s)+9(‘7)+2(3)+~/(z)+ HM) A~ Z (ZW+3W + 8) - .— 3 2) (20 points) Show whether each of the following integrals is convergent or divergent. If convergent, evaluate the integral. ‘ I ml 1w =«&”‘ 1"” l-x hr 1 l‘X b)2hk ; jam 2 Zdﬂ "Hﬂi Ia-w i x1*¥ 3)(20 points) A tank is ﬁlled with water to a depth of2 m as shown. The vertical ends of the tank are trapezoids with width6 m at the top and 3 n] at the bottom. The height of the tank is 4 m, and the length is 7 m as shown. Hip/AH 393 n—l a) Set up, BUT DO NOT EVAL’UATE, an integral to ﬁnd the hydrostatic force on one vertical end of the tank. You must draw a sketch that illustrates your solution, and identify the values of any constants used, including the units. {HOW 9/478 film/wt OPHM 2 v 0/0190” 3 Sgt @275 010+: o .q l . v W .7'vv 03 33 9'67 . - -‘gy W13T7‘7 W‘C’?7 b) Set up, BUT DO NOT EVALUATE, an integral to ﬁnd the work required to pump the water out of an outlet that is 1m above the top of the tank. You must draw a sketch that illustrates your solution, and identify the values of any constants used, including the Qeuxse w Prom pcvl- q units, 4) (20 points) Consider the curve, x =1 +e' , y = t2. 3) Find an equation for the line tangent to the curve at t = 2. Sic/W ; M J _ 2 Cdﬂcayc U w e” C) Set up. BUT DO NOT EVALUATE, an integral to ﬁnd the length of the curve for d) Set up. BUT DO NOT EVALUATE. an integra} to ﬁnd the surface area generated by rotating the curve for 0 S t S 3 around the y—axis. g, I ‘ 5) (l 5 points) Find the area of the region within both of the curves with polar equations, r = l , and r = 25in 6. Your solution must include a well—labeled sketch of the region. poi/’7‘ (Fl3 I’nte/‘sedfon 26148:! t .1. 51/18: 2 _1T ‘9‘e A:(A’+A1)(Z) l a A A5 ff: (2me if L; gum S l WWW ,— j; My 0 ‘6 2a :Jn’io-cdzz(9)d49 rig; 0 17 Z Z I I a ‘ 2 7%(qf7: ‘ W"- ) '17 Z Z : 6) (15 points) Find the coordinates of the centroid of the region bounded by the curves, )7: 4—x2 and yr]. y: b S ‘.M.’YI€I+/‘ . O 7 i 7 with loo/41‘ A JJSM?7§?ga OR “””””“ r {: . ~ _ :t rw ‘ rslﬂa 1 x 23"”‘9 f 59;: M 20428059 F 41 / e, 2 MON/19 1%. 2 frwﬂ A 2 jwﬂzitsc 0M9 T? 64339549 a . ) I )aﬂﬁ Jig “543260439 1r ZSCF LC“ ‘9 T ,g} P 7/3 . - L 209 ~+ ‘ZLSi/t269)l-%T "269+ 3‘ ‘ ‘ J 2 2(%Ie§ ligrﬁ #131545 45. . -, S €(rmz—Dﬂ* (I '5“—)- A (x/V‘ (0’ LFM/E — _ X 4 w w ~ A3 45 J = 4/5 34/?” 3 1 24/3 _,_.—”/’/— " (h I,‘ A 139+ 3 ig’m ...
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