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Pre-Calc Homework Solutions 447

Pre-Calc Homework Solutions 447 - Cumulative Review 68 Let...

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68. Let t be the time in minutes where t 5 0 represents right now, and let T ( t ) be the number of degrees above room temperature. Then we may write T ( t ) 5 T 0 e 2 kt where T (0) 5 50 and T ( 2 15) 5 65, giving T 0 5 50 and k 5 } 1 1 5 } ln } 1 1 3 0 } < 0.0175. (a) 50 e 2 k (120) < 6.13°C above room temperature. (b) Solving 5 5 50 e 2 kt gives t 5 } ln 2 0 k .1 } < 131.6 minutes, or about 2 hours and 12 minutes from now. 69. } d d y x } 5 0.08 y 1 1 2 } 50 y 0 } 2 } y (5 5 0 0 0 0 2 dy y ) } 5 0.08 dx } (5 y 0 ( 0 50 2 0 y 2 ) 1 y ) y } dy 5 0.08 dx 1 } 1 y } 1 } 500 1 2 y } 2 dy 5 0.08 dx Integrate both sides. ln ) y ) 2 ln ) 500 2 y ) 5 0.08 x 1 C 1 } 500 y 2 y } 5 C 2 e 0.08 x y ? (1 1 C 2 e 0.08 x ) 5 500 C 2 e 0.08 x y 5 } 1 1 C 50 e 0 2 0.08 x } 70. } d d y x } 5 ( y 2 4)( x 1 3) } y d 2 y 4 } 5 ( x 1 3) dx E } y d 2 y 4 } 5 E ( x 1 3) dx ln ) y 2 4 ) 5 } x 2 2 } 1 3 x 1 C 1 y 2 4 5 e C 1 e ( x 2 /2) 1 3 x 1 4 y 5 Ce ( x 2 /2) 1 3 x 1 4 71. Use EULERT. x y 0 0 0.1 0.1 0.2 0.2095 0.3 0.3285 0.4 0.4568 0.5 0.5946 0.6 0.7418 0.7 0.8986 0.8 1.0649 0.9 1.2411 1.0 1.4273 72. The region has four congruent portions, so Area 5 4 E p /2 0 sin 2 x dx 5 4 3 2 } 1 2 } cos 2 x 4 5 4 73. Solve 5 2 x 2 5 x 2 2 3 to find the integration limits: 2 x 2 5 8 x 5 6 2. Then Area 5 E 2 2 2 [(5 2 x 2 ) 2 ( x 2 2
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