1. The power P obtained from a windmill is directly proportional to the cube of the...

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1. The power P obtained from a windmill is directly proportional to the cube of the wind speed s. a) Write an equation that expresses this variation. b) Find the constant of proportionality for a windmill that produces 96 watts of power when the wind is blowing at 20 mi/hr. c) How much power will this windmill produce if the wind speed increases to 30 mi/hr? 2. Find the domain of the following function, and give your answer in interval notation: h(x) = x+8x+15 3. A hotel chain charges $75 each night for the first two nights and $50 for each additional night's stay. The total cost function T is a function of the number of nights x that a guest stays. Write the piecewise function T(x), and then calculate T(2), T(3), and T(5). 4. Determine whether the equation defines y as a function of x. a) x + y = 25 b) x + y = 25 c) x = y 5. Sketch a graph of the piece-wise defined function: -x if x <0 f(x) = 9-x2 if 0 < <3 X - 3 if 3x 1. The power P obtained from a windmill is directly proportional to the cube of the wind speed s. a) Write an equation that expresses this variation. b) Find the constant of proportionality for a windmill that produces 96 watts of power when the wind is blowing at 20 mi/hr. c) How much power will this windmill produce if the wind speed increases to 30 mi/hr? 2. Find the domain of the following function, and give your answer in interval notation: h(x) = x+8x+15 3. A hotel chain charges $75 each night for the first two nights and $50 for each additional night's stay. The total cost function T is a function of the number of nights x that a guest stays. Write the piecewise function T(x), and then calculate T(2), T(3), and T(5). 4. Determine whether the equation defines y as a function of x. a) x + y = 25 b) x + y = 25 c) x = y 5. Sketch a graph of the piece-wise defined function: -x if x <0 f(x) = 9-x2 if 0 < <3 X - 3 if 3x