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(1) Gas Mileage. The number of miles M that a certain compact car can travel on 1 gallon of gasoline is related to its speed 𝑣 (𝑖𝑛 𝑚𝑖 ℎ𝑟) by 𝑀 = − 1 60 𝑣 2 + 5 3 𝑣 for 0 < 𝑣 < 70 For what speeds will 𝑴 be at least 40 ? [Set up an inequality with the values stated in the problem then through a series of logical steps solve that inequality. DO NOT arrive at the solution by trial and error.] (2) Solve the following equations. Put solutions in exact form (i.e. no decimal answers) √2𝑝 − 5 − 2 = √𝑝 − 2 (3) Solve by any method that applies and find all simplified exact real solutions. (i.e. no decimal answers) (4) Solve by any method that applies and find all simplified exact real and exact complex solutions . (i.e. no decimal answers) 64𝑥 3 − 27 = 0 (5) Solve by using the sign charts provided below and express the solutions in interval form. 𝑥 3 +𝑥 2 𝑥 2 + 2𝑥 − 35 < 0

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