Review L19 through L21

# Review L19 through L21

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Review for MAC 1140 L19 L21 1. (L19) Solve the systems of equations: (a) 8 < : x 2 + y 2 = 17 3 y x = 1 ans:( 4 ; 1) ; ( 19 5 ; 8 5 ) (b) 8 < : 1 2 x 2 3 y = 2 12 y = 9 x + 15 ans: inconsistent, no solution. (c) ( y = p 40 x 2 y = 8 x ans: (2 ; 6) ; (6 ; 2). Find j x + y j ans: 8. 2. (L19) A chemist needs 120 cc of a 36% alcohol solution but has only solution of concentration 24% and 60 % alcohol available. How many cc’s of each should be mixed to get a solution with the desired concentration? Solve using a system of equations. ans: 40cc of 60%, and 80cc of 24%. 3. (L19) A tourist traveled from one town to another along a river by speedboat. The 200km round trip took 2 hours 30 minutes going downstream, but the return trip upsteam took 3 hours. Find both the speed of the boat and the current speed (assume both speeds remained constant) ans: boat:110/3 km/hr; current speed 10/3 km/hr. 4. (L21) solve the logarithmic equations: (a) log 3 p x 6 = 2 : ans: x = 87 (b) log( x 3) = log 4 : ans: x = 7. 5. (L20-21)Solve the equations: (a) 9 x p 3 = 1 81 x 1 ans: x = 3 = 4 (b) 8 2 x +1 = 16(2 x 2 +4 ) : ans: x = 1 ; 5 6. (L21) Evaluate a) log 25 5 b) log 2 1 2 c) ln e 3 d) log 1 3 81 ans: 1 2 ; 1 ; 3 ; 4 7. (L21)Find the domain, range, asymptotoes, intercepts and transformations and sketch the graph of f ( x ) = 2 2 log 2 ( x + 1) ans: D : x > 1; R : ( 1 ; 1 ); V A : x =

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