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The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a+b.
Finding the Equation of a line, Given a Slope and a Point ? Find the equation of a line with slope m = 2, which passes through the point (-1, -3). Solution: Use the po
Three shirts and five ties cost $23. Five shirts and one tie cost $20. What is the price of one shirt? Let x = the cost of one shirt. Let y = the cost of one tie. The ?rst part
The exponential functions are useful for describing compound interest and growth. The exponential function is defined as: y = m. a x where '
what is patterns with fractions mean?
The Distributive Law : If you were asked to mentally multiply 37 with 9, how would you proceed? 1 would do it as follows - 37 is 30 + 7, 30 x 9 = 270, 7 x 9 = 63, so 270 + 63, th
Proof of Alternating Series Test With no loss of generality we can assume that the series begins at n =1. If not we could change the proof below to meet the new starting place
Without solving, find out the Wronskian of two solutions to the subsequent differential equation. t 4 y'' - 2t 3 y' - t 8 y = 0 Solution : First thing that we want to d
Solve sin (3t ) = 2 . Solution This example is designed to remind you of certain properties about sine and cosine. Recall that -1 ≤ sin (θ ) ≤ 1 and -1 ≤ cos(θ ) ≤ 1 . Th
Power Series and Functions We opened the previous section by saying that we were going to start thinking about applications of series and after that promptly spent the section
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