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Annual profit in thousands of dollars is given by the function, P(x) = 100*sqrt(x - 5) + 3000, where x is the number of items sold
Note the polynomial form P(x) = x2 - a. And, note that the two linear factors ( x + a ) ( x - a ), when multiplied together, yield ( x + a ) ( x - a ) = x2 - a.
A student opens a mathematics book to two facing pages. The product of the page numbers is 1980. Find the page numbers for the first and second page.
Verify that 18^3 - 1^3 = 17 ¢ 7^3 and find a point on the curve x^3 + y^3 = 17 with rational coordinates.
Find the critical points of the following functions and determine whether they are local maximums, minimums or otherwise using the second derivative test
Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverse of each other:
What is the maximum area that the farmer can enclose with 100ft of fence? What should the dimensions of the garden be to give this area?
Describe what this x-coordinate means in practical terms. Choose the correct answer below.
I recently read an obituary of Paul MacCready, the father of human powered aircraft. He invented the Gossamer Albatross.
How long, to the nearest minute, after the end of the race will the runner's pulse rate be 80 beats per minute?
Conjugate class.If H and K are conjugate subgroups, show that N(H) and N(K) are also conjugate.
A golf ball is hit at an angle a with the horizontal and moves under gravity with air resistance ?v per unit mass, where v is the velocity and ?>0 is a constant
Solve without graphing. Find the slope and the y-intercept for the graph of each equation in the given system
Cystal drove 110 miles at y miles per hour. She then increased her speed by 3 miles per hour and drove an additional 150 miles.
Car rental: Find and solve a system of equations. A major city car rental agency has a total of 2200 cars rented out of 3 locations
What is our discriminant for the quadratic equation x2 + x + 1 = 0? Do we have a solution to our quadratic formula for the case of a negative discriminant?
Graph both linear equations in the same rectangular coordinate system. Decide if the lines are parallel, perpendicular or neither parallel nor perpendicular:
How many zeros does this expression have? Exhibit those ordered pairs which constitute these zeros.
After t hours on a particular day, a freight train is s(t) = 20t^2 - (4/3)t^3 miles due east of its starting point
In each of parts (a) and (b), an operation *is defined over the set of natural numbers.For each operation, determine:
All boulders and rocks (large enough not to be buffeted by air current) appear to take the same time to hit bottom.
Give your own example of a function using a set of at least 4 ordered pairs. The domain will be any four integers between 0 and +10.
Systems of Equations.Solve the following systems of equations using the method outlined
Let X be a subset of R, let E be a subset of X, let x_0 be an adherent point of E, and let f: X-->R, g: X-->R, h: X-->R be functions such that f(x) <= g(x)
Jack usually mow his lawn in 6 hours. Marilyn can mow the same yard in 3 hours. How much time would it take for them to mow the lawn together?