Pre-Calc Homework Solutions 180

Pre-Calc Homework Solutions 180 - 180 Section 4.6 Step 6:...

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Unformatted text preview: 180 Section 4.6 Step 6: 45 m r 6m h 17. Step 1: 6 6 dy dt [26 (8) 144 1 24 25 6 dy dt (82)] dy dt 0.01326 m/min 1.326 cm/min (13 (13 y)2 y)2 132, 26y y 2. or r h V radius of top surface of water depth of water in reservoir volume of water in reservoir (b) Since r 2 r 169 Step 2: At the instant in question, Step 3: We want to find Step 4: Note that Then V h 6 by similar cones, so r 7.5h. r 45 1 2 1 r h (7.5h)2h 18.75 h3 3 3 dV dt dh . dt dh dr and . dt dt dV dt 50 m3/min and h 5 m. (c) Step 1: y depth of water r radius of water surface V volume of water in bowl Step 2: At the instant in question, dV dt dy dt 6 m3/min, y 1 m/min. 24 8 m, and therefore (from part (a)) Step 3: We want to find the value of Step 5 and 6: (a) Since V Thus 50 18.75 h 3, 56.25 h 2 dr . dt Step 4: From part (b), r Step 5: dr dt 1 2 26y 13 5 288 125 72 26(8) 8 82 y2 dh , and so dt dh 8 32 m/min cm/min. dt 225 9 32 The water level is falling by 1.13 cm/min. 9 dh (Since 0, the rate at which the water level is dt 56.25 (52) 26y y 2. (26 2y) dy dt 13 26y 1 24 y dy y 2 dt Step 6: dr dt 1 24 5 12 falling is positive.) (b) Since r 7.5h, dr dt 7.5 dh dt 80 cm/min. The rate 3 0.00553 m/min 0.553 cm/min of change of the radius of the water's surface is 80 3 or 8.49 cm/min. 18. (a) Step 1: y depth of water in bowl V volume of water in bowl Step 2: At the instant in question, y 8 m. dV dt 19. Step 1: r radius of spherical droplet S surface area of spherical droplet V volume of spherical droplet Step 2: No numerical information is given. 6 m3/min and Step 3: We want to show that Step 4: S 4 r 2, V 4 3 dV r , 3 dt dr is constant. dt Step 3: dy We want to find the value of . dt kS for some constant k Step 4: V 3 Steps 5 and 6: y) or V 13 y 2 3 y 2(39 y3 Step 5: dV dt (26 y y 2) dy dt 4 3 dV dr r , we have 4 r2 . 3 dt dt dV Substituting kS for and S for 4 r 2, we have kS dt dr or k. dt Differentiating V S , dr dt ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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