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Let the cubic equation ax^3 + bx^2 +cx + d =0 have integral coefficients a, b, c, and d.
Show that if a =1, every rational root of the cubic must be an integer that divides the constant term d.
Convex Sets and Linear Transformations, Prove that the following sets are convex, where E stands for the sum symbol:
Test at the 5% level of significance.
Suppose that f_n(0) converges to some number, denoted f(0), and also suppose that the sequence (f'_n) converges uniformly on (0,1) to some function g: (0,1) -> R. Prove that the sequence (f_n) converges uniformly. What is its limit?
Automorphisms and Conjugation, Show that if H is any group then there is a group G that contains H as a normal subgroup with the property that for every automorphism f of H there is an element g of G such that the conjugation by g
Finding the dimensions of a rectangle using second derivative test - Find length and width should the rectangle have so that its area is a maximum?
Construct appropriate probabilistic models - appropriate probabilistic model and find the probability of getting doubles.
Find the nth term of the given sequences - Write out the nth term for the continuation of the sequences
At noon, ship A is 100 km west of ship B. A is sailing south at 35 km/h and B is sailing north at 25 km/h. How fast is the distance between the ships changing at 16:00 h?
Find an equation for the sphere, in the form of a level surface
Calculate the mean of each sample
A particular test for the presence of steroids is to be used after a professional track meet. If steroids are present, the test will accurately indicate this 95% of the time.
A thin plate occupies the region x^2/4 + y^2/9 is less than or equal to 1. If the temerature of the plate is T(x,y)= x^2 + y^2 - 5y + 5, find the coldest and hottest points on the plate.
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