Recent questions in Mathematics

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What is the most beautiful theorem proof, and why?

For instance- the Pigeon hole principle. Simple and elegant :)
16/12/2016

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Parabola given by the function f(x) = x^2

Let (r, r^2) be an arbitrary point on the parabola f(x) = x^2. Show that the equation of the tangent line to the graph of f(x) at (r, r^2) is given by y = 2rx − r^2.
18/02/2016

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Series and sequences

The first ,second and fifth terms of a linear sequence are three consecutive terms o an exponential sequence .if the first term of the linear sequence is 7 find its a)The common difference of ...
31/10/2015

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Gradient for functions in two variables

Find ∇f(1, 1) for the function in two variables f(x, y) = x^2 + y^2.
20/10/2015

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Given nonzero vectors ⃗u, ⃗v, and ⃗w, use dot product and cross product notation, as appropriate, to describe the following

The vector projection of ⃗u onto ⃗vA vector orthogonal to ⃗u and ⃗vA vector orthogonal to ⃗u × ⃗v and ⃗wA vector orthogonal to ⃗u × ⃗v and ⃗u × ⃗wA vector orthogonal to ...
14/10/2015

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What is the probability that the relabeled dices beat the other to have the highest number?

Suppose we have three dice with relabled faces. Die A has sides marked {1,1,6, 6, 8, 8}. Die B has sides marked {2, 2, 4, 4, 9, 9}. Die C has sides marked{3, 3, 5, 5, 7, 7}. If we roll die A and ...
10/10/2015

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You want to accumulate $1,000,000 over the next 10 years? Find the the monthly investment required.

You want to accumulate $1,000,000 over the next 10 years. You intend to do this by making deposits of X into an investment account at the end of each month, for 30 years.The account ...
08/10/2015

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Consider the two univariate polynomials p(x) = x^3 − 12x^2 + 41x − 42; and q(x) = x^2 − 2x − 35

 Consider the two univariate polynomials p(x) = x^3 − 12x^2 + 41x − 42; and q(x) = x^2 − 2x − 35If the two polynomials share a common root, use the ratio method to find that root.
08/10/2015