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Let a ∈ R and consider the evaluation homomorphism φ : R[x] → R where φ(f(x)) = f(a). Find the kernel of φ? If cos x = 3/7; x is an angle in the fourth quadrant; what is cos(x/2)? Explain what causes the difference in oxygen concentration between blood leaving the lungs and blood leaving skeletal muscles? What is the economic life span of water cooled medium sized chillers for office use 5 days a week operating hours 8:00 AM to 5:00PM? Calculate the mass of butane needed to produce 88.2 g of carbon dioxide.?