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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.
What do you need to multiply 30 by to get 1500? This will give you the top edge length of the rectangle. Can you then figure out what must go below the 30 in order to get the area
The probability that a person will get an electric contract is 2/5 and the contract that he will not get plumbing contract is 4/7.If the probability of getting at least one contra
Projections The good way to understand projections is to see a couple of diagrams. Thus, given two vectors a → and b → we want to find out the projection of b → onto a → . T
A vertical post stands on a horizontal plane. The angle of elevation of the top is 60 o and that of a point x metre be the height of the post, then prove that x = 2 h/3 .
It is the last case that we need to take a look at. Throughout this section we will look at solutions to the system, x?' = A x? Here the eigenvalues of the matrix A are compl
how much distance is covered by a man if he is travelling at a speed of 45km/h in 5 sec
What is the greatest common factor of 24 and 64? List the factors of 24 and 64. The largest factor that they have in common is the greatest common factor. Factors of 24: 1,
#question.how to creat table
the radii of circular base of right circular cylinder and cone are in the ratio of 3:4 and their height are in the ratio of the 2:3 what is the ratio of their volume?
Find out the volume of the solid obtained by rotating the region bounded by y = x 2 - 2x and y = x about the line y = 4 . Solution: Firstly let's get the bounding region & t
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