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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.
three prices are to be distributed in a quiz contest.The value of the second prize is five sixths the value of the first prize and the value of the third prize is fourfifth that of
If OA = OB = 14cm, ∠AOB=90 o , find the area of shaded region. (Ans:21cm 2 ) Ans: Area of the shaded region = Area of ? AOB - Area of Semi Circle = 1/2 x 14 x
What is Partially Ordered Set? Let S = {a,b,c} and A = P(S). Draw the Hasse diagram of the poset A with the partial order ⊆ (set inclusion). Ans: Let R be a relation define
to plot (5,-4), start at (0,0) and move 5 units left and 4 units down
what is the quotient of 3 and n?
Using the expample provided below, if m∠ABE = 4x + 5 and m∠CBD = 7x - 10, Determine the measure of ∠ABE. a. 155° b. 73° c. 107° d. 25° d. ∠CBD and ∠ABE are vert
Algebraic Word Problems: Equations: 1. The total electrical output of one nuclear facility is 200 megawatts more than that of another nuclear facility. Let L be the
2/3 - 7/12
Calculate the area and perimeter of a square: Calculate the area and perimeter of a square with w = 5´ and l = 6´. Be sure to involved units in your answer. Solution:
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