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1. Show that there do not exist integers x and y for which 110x + 315y = 12.
2. If a and b are odd integers, prove that a2 +b2 is divisible by 2 but is NOT divisible by 4. Hint:
Any odd number can be written 2k + 1 for some integer k.
3. Prove that for any prime number p, √ p is irrational. Hint: Follow the same method that was used to prove √ 2 is irrational, by first supposing √ p can be expressed as a=b.
Find the area of PARALLELOGRAM ? A parallelogram is a four-sided shape, of which the opposite sides are parallel. (Because they are parallel, opposite sides also have the same
I would like to calculate the high point of a mathematical formula with two unknown variables. At the same time I made the 1st derivation of the function. How can I best program th
Before searching at series solutions to a differential equation we will initially require to do a cursory review of power series. So, a power series is a series in the form, .
Consider the Van der Pol oscillator x′′- µ(1 - x 2 )x′ + x = 0 (a) Write this equation as a system of first order equations (b) Taking µ = 2, use MatLab's routine ode45 to
Infinite limits : Let's now move onto the definition of infinite limits. Here are the two definitions which we have to cover both possibilities, limits which are positive infinity
a data set has a mean of 3, a median of 4, and a mode of 5.which number must be in the data set-3,4,5?
the ratio of dogs to cats is 2 to 9.if there are 10 dogs how many cats are there?
In the earlier section we modeled a population depends on the assumption that the growth rate would be a constant. Though, in reality it doesn't make much sense. Obviously a popula
72 is 75% what number
what is the perimeter of a rhombus
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