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Fundamental groups of the Moebius strip and the cylinder.Show that the Mobius strip and the cylinder both have fundamental group Z.
An investment offers 4.5% interest compounded continuously. How long until the investment triples in value? Round to the nearest 0.1 year.
The percentage of carbon-14 present in the remains of organic matter can be used to determine the age of the organic matter.
Given A=Pe^rt, with A = 455, P = 5, and r = 0.61, solve for t. Round to the nearest 0.01.
Every rational x can be written in the form x = m/n, where n > 0, and m and n are integers without any common divisors. When x = 0, we take n = 1
A ball is hit into the air. Its height, s, at time t, is given by the equation s(t)=-16t^2+74t+4. Determine the maximum height of the ball.
Find the slope of the line that passes through the given pair of points:
Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $30 one time activation fee.
Explain the difference between intersecting and perpendicular lines. Can two lines exist that are not intersecting or parallel? Explain your answer.
Use the data from problem 3 to randomly pick 10 days of sales. As you would in a simulation.
A student was given the function f(x) = x2 and asked to write the result of translating this function 1 unit to the left. The student wrote the following:
Equivalence of two definitions of a contractible space.We have defined space X to be contractible in two ways:
Wieferich m-squares.It is a fact that for any odd prime p, there is a number b so that b has order p(p-1) modulo p^2.
A company's balance sheet for 1999 showed a balance of retained earnings of 510 million.
Determine the number of Sylow 2-subgroups and Sylow 3-subgroups that G can have. Justify your answer.
Prove the following generalization of the last Sylow's theorem: If |G| is divisible by p^b, and H <= G has order p^a with a <= b
General solution of a system of differential equations.
If f: R^n --> R is continuous on R^n and alpha
Determine whether the system is consistent, inconsistent, or dependent.
Find delta.Let f: D -> R and g: D->R where D is an open interval that contains the point c and let f and g be functions
Orthogonal basis and matrix, Gram-Schmidt process.Find the matrix for the transformation T given in problem 1 with respect to the standard basis
One of the most famous unsolved problems in mathematics is a conjecture made by Christian Goldbach in a letter to Leonhard Euler in 1742.
Find b ^2 – 4 ac and the number of real solutions to each equation. Find all real solutions to each equation.
A stone is thrown upward from the top of a 180 meter building at a speed of 10 meters per second. Its altitude in meters above the ground is modeled