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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 all the local maximum and minimum values and saddle points of the function f(x, y) = x 2 - xy + y 2 + 9x - 6y + 10
what is the changen intemperature bewtween the highest and the lowest temperture high-40c low-0c
#pqrs is a parallelogram its adjacent side is 2:1.state tHE angles
Rejection and Acceptance regions All possible values which a test statistic may either suppose consistency along with the null hypothesis as acceptance region or lead to the re
Bill traveled 117 miles in 2.25 hours. What was his average speed? Use the formula d = rt (distance = rate × time). Substitute 117 miles for d. Substitute 2.25 hours for t and
what is the diameter of a circle
How many ways can six men and three women form a line if no two women may stand behind each other?
The line 4x-3y=-12 is tangent at the point (-3,0) and the line 3x+4y=16 is tangent at the point (4,1). find the equation of the circle. solution) well you could first find the ra
Evaluate following limits. Solution Here the first two parts are actually just the basic limits including inverse tangents and can easily be found by verifying the fol
Consider the clique graph below. a) How many subgraphs of G with 3 nodes are there? b) How many of the subgraphs defined in part(a) are induced subgraphs?
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