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Unformatted text preview: Math 34A Practice Midterm II Solutions Fall 2007 Problem 1 Solve the following equation for x: 5 2+3 x 2 x = 0 Solution: First, add 2 x to both sides of the equation to get 5 2+3 x = 2 x Next, take log of both sides, then simplify: log (5 2+3 x ) = log (2 x ) (2 + 3 x ) log (5) = xlog (2) 2 log (5) + 3 xlog (5) = xlog (2) Now isolate x: 2 log (5) = xlog (2) 3 xlog (5) 2 log (5) = x ( log (2) 3 log (5)) 2 log (5) log (2) 3 log (5) = x Problem 2 Line A goes through (3 , 1) and (5 , 9). Line B goes through the point (2 , 7) and has twice the slope of line A. What is the equation of line B? Solution To find the slope of line A, we compute rise/run using the two points given: rise run = 9 1 5 3 = 8 2 = 4 So, the slope of line B is 8. Using the pointslope formula, the equation for line B is: y 7 = 8( x 2) or y = 8 x 9 Problem 3 Can A is 3 g L of salt water, and can B has 4 L of water which is y g L salt water....
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This note was uploaded on 12/27/2011 for the course MATH 5B taught by Professor Rickrugangye during the Fall '07 term at UCSB.
 Fall '07
 RickRugangYe
 Math

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