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1. Nena bought a piece of charcoal from Fairbanks, Alaska as a souvenir. She found out that the charcoal has only 11% of carbon 14 of its original amount. When was the tree cut from which the charcoal came? The half-life of C14 is 2300 years. (15 pts) 2. Find the orthogonal trajectories of the following equations: (10 pts each) a. extev=c b. x2 - y2 = kx 3. Use the method of Bernoulli's Equation to solve the equation. (30 pts) xy dx + (y4 - 3x ) dy = 0when x = v2 ,y =2 4. Solve the equation by determination of integrating factor preceding the Exact D.E method. 3(x2 + y?)dx + x(x2 + 3y2 + 6y)dy =0 (15 pts) 5. Solve the equation by inspection y(x2 + y2 - 1)dx + (x3 + xy2 +x)dy =0 (20pts)