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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.
why minimum three coplanar vectors are required to give zero resultant and not two?
The time in seconds that it takes for a sled to slide down a hillside inclined at and angle θ is where d is the length of the slope in metres. Find the time it takes to sli
52/7
If the p th , q th & r th term of an AP is x, y and z respectively, show that x(q-r) + y(r-p) + z(p-q) = 0 Ans: p th term ⇒ x = A + (p-1) D q th term ⇒ y = A + (
Greatest Common Factor The primary method for factoring polynomials will be factoring the greatest common factor. While factoring in general it will also be the first thing
Does this Point Lie on The Line? How do you know if a point lies on a given line? For example, does the point (1, 2) lie on the line 3x + y = 7? If you graph the line and the
Activity This activity will help you recognize the importance of some very famous numbers, as well as learn more about approximations. Directions Using the Internet, provi
Estimation of population mean If the sample size is small (n In this case Population mean µ = x¯ ± tS x¯ x¯ = Sample mean S x¯ = s/√n S = standard deviation
writ the equation that describes the motion of a point on the wheel that has a center of 4m off the ground, has radius of 15 cm, makes a full rotation every 10 seconds and starts a
50387 divided by 21
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