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Basic Algebra

Equation - for how many seconds is this arrow more than 86 feet high ...

1) If an arrow is shot straight upward with a velocity of 96 feet per second (ft/sec) from an altitude of 6 feet, for how many seconds is this arrow more than 86 feet high? Note If an object is given an initial velocity straight upward of "v lower case 0" feet per second from a height of "s lower case 0" feet, then its altit

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).

Log Derivatives : Chain Rule

Find the first derivative of the function. 1.) y= ln x^2 2.) y= ln sq rt x^4- 4x 3.) f(x)= x^2 ln x 4.) y=ln x/x+1

Expression as a Sum Difference or Multiplication of Logarithms

Use the properties of logarithms to write the expression as a sum difference or multiplication of logarithms 1.) ln 2/3 2.) ln xyz 3.) ln sq rt x^2 +1 4.) ln 2x/ sq rt x^2 - 1 write the expression as the logarithm of a single quantity. 5.) ln(x - 2) - ln(x+2) 6.) 3 ln x +2 ln y- 4 ln z 7.) 3[ln x+ ln(x+3

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 Maximum Heights

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.

Maximizing and Minimizing Area

A rectangular play yard is to be constructed along the side of a house by erecting a fence on three sides, using house wall as the fourth wall. Find the demensions that produce the play yard of maximum area if 20 meters of fence is available for the project. What are the dimensions of an aluminum can that can hold 28 ounces