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
(x-2)^2(x+1)(x-5)<0

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.

2. Originally Posted by vc15ao4
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.
$\frac{y}{xw^2} = k_1$ and $w(r+s) = k_2$ now substitute.

2) Solve the following system of equations for x. Y=x^2+4x-7 and 2x-y=-1
$2x-y = - 1\implies y = 2x+1$ substitute into first to get $2x+1 = x^2+4x-7$ now solve.
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)
(f-g)(-1) = f(-1) - g(-1)
(fog)(x) = f(g(x)) = f(x+2) = (x+2)^2 - 5
4) Given the parabla f(x)=3x^2-6x+1, state and identify the maximum or minimum value.
Since a=3>0 it means it has a minimum which occurs at x=-b/2a.