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Basic Algebra

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.

Quadratic Equation Application Word Problem : 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

Simplify the logarithm.

Use the properties of exponents to condense the expression to the logarithm of a single quantity. ln y - 51n(y+3)

Logarithmic Function

Write as the logarithm of a single quantity: 4log(10) x-5log(10) (x-4). The "10's" represent the mathematical form that is suppose to be on the lower write side of each log.

Logarithmic Functions

Evaluate the expression log(4) 64. The 4 is suppose to be on the lower right side of log.

Solving for a variable

I am trying to solve for P lower squared (lower 2) P lower 1 V lower 1/T lower 1 = P lower 2 V lower 2/T lower 2

Economy's Lorenz curve

Author's explanation of a Lorenz curve: Economists use a cumulative distribution called a Lorenz curve to describe the distribution of income between households in a given country. Typically, a Lorenz curve is defined on [0,1] with endpoints (0,0) and (1,1) and is continuous, increasing, and concave upward. The points on th

Newton-Cotes formula

Derive all the weights for closed Newton-Cotes formula. Please see attached for full question.

Constructing a polynomial

1 (a) Consider the function values... Consider a polynomial P(x) of least degree (the osculating polynomial) through the points xi=x0+i*h, i.e. polynomial that satisfies P(x0)=f0, P(x1)=f1, P'(x1)=f'(x1), P(x2)=f2 (b) Prove that df(x1)/dx = dP(x1)/dx for any smooth function f(x) (c) Construct the polynomial P(x) for the

Discharge over a spillway

The formula Q = 3.32LH^3/2 is used to find the maximum water discharge over a spillway before the water overflows the main part of the dam. Q is the discharge in cubic feet per second, L is the length of the spillway, and H is the depth of the spillway below the level of the dam. Find H when Q is 3000 cu. ft. per second and L =

Quadratic Equation Application Word Problems

A graphic artist is designing a poster that consists of a rectangular print with a uniform border. The print is to be twice as tall as it is wide, and the border is 3 inches wide. If the area of the poster is to be 680 square inches, find the demensions of the print. The foot of an extension ladder is 9 feet from the base