team hmwk 5 - Math 115 Section 003 Meghan, Kaydee, Ashley...

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Math 115 Section 003 Team Homework #5 Meghan, Kaydee, Ashley Due 10-16-08 3.1 #56 In this problem, we are given the equation y=x 2 -2x+4. We know that this is a parabola. We know it opens up because the leading coefficient is positive. We also know its vertex is at (1,3). The problem asks us to find the equations of all lines through the origin, and tangent to the parabola. The general equation of a line is y=mx+b. Since the line must pass through (0,0), the y- intercept is at 0, and there will be no b. The derivative of the equation is y’=2x-2. We also know that x 2 -2x+4 = 2x 2 -2x, x 2 = 4, x=+-2 We substitute 2 and -2 in for the derivative: 2(2)-2 = 2 and 2(-2)-2 = -6 Since these are the derivative, 2 and -6 are the values of the slope (m). So, we now have to equations: y = 2x and y = -6 These two lines pass through the origin and are tangent to the parabola y = x 2 -2x+4. 3.2 # 40 The problem tells us that V(t) = 25(0.85) t is the value of a certain automobile purchased in1997. V is the value, in thousands of dollars, and t is the time, in years, from the date
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This note was uploaded on 01/05/2012 for the course MATH 115 taught by Professor Blakelock during the Fall '08 term at University of Michigan.

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team hmwk 5 - Math 115 Section 003 Meghan, Kaydee, Ashley...

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