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Find an equation for the parabola that has the vertex at the origin and satisfies the given condition. Focus F(0,2). Focus F(-5,0).
Write an equation of an ellipse with the foci at (0,+/-2) and the lenght of the major axis equal to 8. Write an equation of an ellipse with the vertices at (+/-4,0) and +/-1 as y-intercepts.
Correct to the nearest hundredth of a degree, find the angle of rotation necessary in a change of axes to rotate the xy term from the equation.
If the value has increased at a rate of 4% per year, what will its value be, correct to the nearest hundred dollars, at the end of 2010?
How long until the boys are 100cm apart? What is the area of the triangle formed by their positions after 2 seconds? What is the peremeter?
What is the physical significance of the fact that k is negative? This function has a horizontal asymptote. Where is it and what is its physical significance?
A hyperbola has a vertical transverse axis of length 8 and asymptotes of y=7/2x-3 and y=-7/2x-1. Find the center of the hyperbola, its focal length, and its eccentricity.
State the properties of the cosine function. State the domain and range of f(x) := cos x. Determine all values of x where f(x) is zero (i.e. the x-intercepts).
Let L be the distance between the boat and the top of the lighthouse. Let be the angle of elevation between the boat and the top of the lighthouse. Express b as a function of theta.
On the return trip it flies with the tailwind and has an effective ground speed of 124 mi/h. Find the speed p of the plane in still air, and the speed w of the wind.
Show that this can be done two different ways and find the exact dimensions of the box in each case (note, one of your answers may have dimensions that will require you to approximate).
Determine the equation of both parabolas that pass through the three points. Graphically display the results an axes.
Find the area of the triangle enclosed by the graph of f(x), the x-axis and the y-axis. express your answer in terms of just b.
A rancher has 12 milesof fenching to fence a rectangular pieve of grazinglang along a straight river. Find the dimensions of the rectangle that has the largest possible area.
Find end the domain and range of x and express in interval notation and find all values of x at which the graph of f(x) is discontinuous.
Using a context of quadratic functions and their graphs, explain the concept of optimization to someone without a background in mathematics.
You spent a lot of time during this unit working with linear functions. For which of the following situations would a linear function be a reasonable choice for a mathematical model?
What is the displacement (magnitude and direction) of the 2nd airport from the 1st airport? Roud your final answers to 3 decimal places.
How long will it take the insect population to grow to nine times its initial size? Simplify your answer as much as possible.
How long does it take for an investment to double in value if its invested at 11% compounded monthly and compunded continuously?
If the marginal revenue for the product is given by the equation MR=80x what is the profit generated from the production of 8 units of this product?
Find the equillibrium point, the consumer's surplus, and the producer's surplus if the demand function is p(x)=f(x)=200-.4x^2.
Determine the tax per item that will maximize the total tax revenue and use it to compute the maximum total tax revenue possible.
Use the information developed in the notes for formic acid as a guide to determine the concentration of [H+] and pH of 0.1N and 1N solutions of acetic acid.