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Find the quotient,q(x) , and the remainder,r(x) , when 5x^3-20x^2+23x-5 is divided by x^2-3x+3.
Trains A And B Are Traveling In The Same Direction On Parallel Tracks. Train A Is Traveling 60 Mph And Train B Is Traveling 64mph
Solve the equations for the different dish designs to be ordered with the desired technique: graphing, substitution, elimination, matrix.
where is the vector space of real-valued functions defined on the interval [0, 2]. Show that is a subspace of this vector space.
Construct a scatter plot using excel for the given data. Determine whether there is a positive linear correlation, negative linear correlation
Find the equation of the line passing through the point (2,-4) and having a slope of -3. Give your answer in slope-intercept form, y=mx+b
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