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Basic Algebra

Radicals and Radical Expressions (15 Problems)

All variable in the following exercises represent positive numbers. Simplify the sum and differences. Give exact answers. Please see the attached file for the fully formatted problems.

Important information about Quadratic Inequality

A person's revenue "R" (in dollars) on the sale of "X" fruitcakes is determined by the formula R = 50x - x squared. Her cost "C" in dollars for producing "X" fruitcakes is given by the formula C = 2x + 40. For what value of "X" is the person's profit positive? (Profit = revenue - cost).

Power Series, Partial Sums and Radius of Convergence

Suppose that you have done some mathematical modelling. This has produced a differential equation which you have solved by assuming a power series solution. The power series you have found is the following.... (a) What is the radius of convergence of the power series? (b) Use Mathematica to plot the partial sums....

Convergence of series

Please help with the following problem. This problem is from Advanced Calculus II class. It is also an introduction to real analysis. Consider the series n = 1 to infinity 1/( 1 + n^2 x) (a) For what values of x in R does the series converge absolutely? (b) On what intervals of R does it converge uniformly? (c) On wh

Finite Extension Field and Isomorphism

Argue that every finite extenstion field of R is either R itself or is isomorphic to C. Note: R is set of all real numbers C is set of all complex numbers

Toy Rocket

A toy rocket is launched from the ground so that its distance in feet above the ground after t seconds is s(t) = -16t squared + 208t. I am trying to determine the maximum height it reaches and the number of seconds it takes to reach that height.