1) Suppose y is directly proportial to the product of x and the square of w and inversely proportional to the sum of r and s. If x=2, w=3, r=1, and s=5, then y=15. Find the value of the constant of proportionality,k.
2) Solve the following system of equations for x. Y=x^2+4x-7 and 2x-y=-1
3) Use the functions f(x)=x^2-5 and g(x)=x+2 to answer the following
Find and simplify (f-g)(-1)
Find and simplify (fog)(x)
4) Given the parabla f(x)=3x^2-6x+1, state and identify the maximum or minimum value.
5) If the point, P(-3,1) is on the graph of y=f(x), find the corresponding point on the graph of y=-f(6x)+4
6) Solve the following inequality. Express the answer in interval notation
7) THe Speed of an airplane in still air is constant. The airplane, flying with the wind, travels 1800 miles in 3 hours. The return trip back to the starting point, against the wind, took 4 hours. Find the rate of the wind.
8) During a baseball game, a batter popped up a pitch into the outfield. The path the ball took was in the shape of a parabla. The ball wasnt caught and landed on the ground after 4 seconds. Let y=the height of the ball in feet and x=time in seconds. If the maxiumum height the ball reached was 120 feet, find a standard equation for the path of the ball. Disregard the height of the batter.
9) AN office cubicle is to have 2 rooms with each room having a 4 foot opening as shown below. The total cubicle will have 750 square feet of space. The walls cost 50 dollars per foot. Express the cost,c, of the walls as a function of x. Diregard the thickness of the walls. Simplify your function.