Exam 4: Lines parabolas and Systems

A deep sea diver has spent a week in a submerged research facility at 2000 feet below sea level.He is now ready to move to a deeper facility at 3500 feet below sea level.He descends at the rate of 50 feet per minute.Write an equation that shows this relationship,and determine when the diver will reach 3500 feet below sea level.

Find the Point of Equilibrium for a product with Demand Equation and Supply Equation as follows: Demand: p = 300 - 8q Supply: p = q + 5

Show that the points A(-1,2),B(3,-2),and C(-6,-3),are the vertices of a right triangle.

The demand function for a manufacturer's product is p = f(q)= 6 - q where p is price per unit when q units are demanded by consumers.Find the level of production that will maximize the manufacturer's total revenue and determine this revenue.

Find the slope and y-intercept of a line 2y + 3(x - 1.9)= 0.

State whether f(x)= 10 + 16x - 4 has maximum or minimum value and find that value.

A printer charges a fixed setup cost plus a charge for every copy of single page flyers.If x is the number of copies requested,the total cost of a printing job can be described by the function f(x)= 0.02x + 80.Graph the function on your graphing calculator.

Suppose f(p)is a linear function given by f(p)= .Find the slope and the y-intercept.

Suppose that a manufacturer will place 1000 units of a product on the market when the price is $10 per unit,and 1400 units when the price is $12 per unit.Find the supply equation for the product assuming the price p and quantity q are linearly related.

Two types of chickens,A and B,are raised in a chicken coop.Each day they receive 1.4 kilograms of corn and 2.4 kilograms of millet.Each chicken of type A requires 100 grams of corn and 150 grams of millet.Each chicken of type B requires 60 grams of corn and 120 grams of millet.How many of each type of chicken will the corn and millet support so that all of the food is consumed each day? Use a graphing calculator to solve the system by finding the point of intersection of the two equations.

A mathematical model can approximate the winning distance for the Olympic discus throw by the formula d = 175 + 1.75t,where d is in feet and t = 0 corresponds to the year 1948.We might want to predict in what year a certain distance will be exceeded,so rewrite the equation to solve for t.Use a graphing calculator to graph the resulting equation and find the coordinates of any two points on the line and use them to estimate the slope.Compare this with your answer.

A retired couple has $500,000 invested in two bond funds that earn 5% and 7%.If the total yearly income from the investments is $30,000,how much is invested at each rate?

Solve the following system of equations algebraically.(If the system does not have a solution,then say so or if it has more than one unique solution,then please describe the solutions.)

A line has slope and passes through the point (4,2).The point on the line that has its second coordinate equal to -5 is

Graph the function y = f(x)= - 6x + 5 and indicate the coordinates of the vertex and intercepts.

For the linear function f(x)= 2x + 1,find: (a)the slope and (b)the vertical axis intercept.(c)Sketch the graph of f.

Find the vertex and axis of symmetry of the parabola y = - + 6x + 3.Also find if it opens upward or downward.

A swimming pool owner has two solutions which contain different concentrations of chlorine.One is a 5% solution and the other is a 10% solution.How many liters of each should she mix to obtain 8 liters with a 6% concentration?

The slope of the line passing through the points (-4,5)and (3,-2)is

The function is a Quadratic Function.