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Proofs
Proof means sufficient evidence to establish the truth of something. It is obtained from deductive reasoning, rather than from empirical arguments. Proof must show that a statement is true in all cases, without a single exception.
1,294 Questions
Does a square bisect each other?
The diagonals of any rhombus bisect each other. A square is a special kind of a rhombus.
Does a pause between rings on cellphones mean they were on another call?
No i don't think so i think it just need help connecting/calling to the phone.
g => (g or h) => (s and t) => t => (t or u) => (c and d) => c.
We are given premises:
# (g or h) -> (s and t) # (t or u) -> (c and d) We would like to derive g -> c.
If we assume g (the antecedent in the conclusion) we have the following derivation: # g (assumption) # g or h(weakening) # s and t (premise 1 (modus ponens)) # t(weakening) # t or u (weakening) # c and d (premise 2 (modus ponens)) # c (weakening)
So, assuming g we can derive c, i.e. g -> c
There is no such thing as the number "zillion". It is used only in slang term, as meaning "many". There is no definite number for zillion, because technically there isn't a 'zillion'.
Angle between intanceous and linear velocity?
The answer could depend on what you mean by "intanceous". The word is not recognised and I cannot guess what it was meant to be.
Cayley's theorem:Let (G,$) be a group. For each g Є G, let Jg be a permutation of G such that
Jg(x) = g$x
J, then, is a function from g to Jg, J: g --> Jg and is an isomorphism from (G,$) onto a permutation group on G.
Proof:We already know, from another established theorem that I'm not going to prove here, that an element invertible for an associative composition is cancellable for that composition, therefore Jg is a permutation of G. Given another permutation, Jh = Jg, then h = h$x = Jh(x) = Jg(x) = g$x = g, meaning J is injective.Now for the fun part!
For every x Є G, a composition of two permutations is as follows:
(Jg â—‹ Jh)(x) = Jg(Jh(x)) = Jg(h$x) = g$(h$x) = (g$h)$x = Jg$h(x)
Therefore Jg ○ Jh = Jg$h(x) for all g, h Є G
That means that the set Ђ = {Jg: g Є G} is a stable subset of the permutation subset of G, written as ЖG, and J is an isomorphism from G onto Ђ. Consequently, Ђ is a group and therefore is a permutation group on G.
Q.E.D.
Prove that a chord which is not passing from centre is less than diameter?
Suppose AB is a chord of a circle which does not pass through its centre.From A, draw the diameter AC. Join BC.
Now, by the Circle Theorems (different courses number them differently), angle ABC is a right angle (angle subtended by a semicircular arc).
In other words, ABC is a right angled triangle with its right angle at B.
If |AB| represents the length of the line AB, and so on,
by Pythagoras's theorem, |AC|^2 = |AB|^2 + |BC|^2
then since |BC|^2 > 0, |AC|^2 > |AB|^2
the logical structure of the formulation of the CAP is on the form "p implies q", or "If p, then q". In symbols: p => q
with p being the statement "l and l' are lines cut by a transversal t in such a way that two corresponding angles are congruent"
and q the statement "l is parallel to l'"
It's corollarys are also on this form, obviously with other p and q.
Not sure if this is what you were looking for.
Could you please prove the Pythagreon Theorem?
Consider a square with a smaller square inside of it, where each of the corners of the smaller square touch the midpoints of the sides of the larger square. ( I would suggest drawing a picture of this. I tried to post one, but I can't for WikiAnswers) There are 4 congruent right triangles formed from this picture. There are two legs to these triangles, of length a and b. The hypotenuse of each of these triangles will be called c. Let us add up one side of the big square. This quantity is (a+b). Let us square this, so the area of the big square is (a+b)2. Thus the area of the big square is a2 + 2ab + b2. We can now subtract the area of the smaller circle which is c2. So we now have a2 + 2ab + b2-c2. We now need to subtract the 4 congruent triangles. The area of a triangle is one half the base times height. In this case, one triangle is .5ab. Multiply this by 4, and we have 2ab. Now we have the entire expression a2 + 2ab + b2-c2 - 2ab = 0, since we have taken the full area of the square, and subtracted out all of the individual parts. The 2ab and the -2ab add up to zero, so we now have a2 + b2-c2 = 0. We can add the -c2 to the other side, thus giving us a2 + b2 = c2 This is one of the many ways to prove the Pythagorean Theorem.
The positive number is always greater.
How do you construct a congruent angle?
We know two triangles are congruent if and only if all of their sides are equal.
So that's the best way to do it. Pick a triangle you want to copy, on the side, draw a beam (one end extends infinitely sort), let the centre of your beam be point a.
Then use your compass to measure one of the triangle's side length by moving it from one endpoint to the other, then without changing the width of the compass, set the pointer at the point a and use the pen side draw a small arc. The intersection between the arc and the beam, we will call it point b.
Now measure another side of the triangle using the compass, and draw an arc from a. We will call this arc arc A.
Do the same for the remaining side of the triangle and draw an arc from point b, we will call this arc arc B.
The point if intersection of arc A and B we will call it c.
Triangle abc should be congruent to the original triangle.
Note: If you do it by hand (likely), it will not be perfect due to human and environmental errors.
An axiom is a basic mathematical truth used in proofs, outlined initially by Euclid. Axioms are self-evident and do not need to be proven, they can be combined and used logically to prove more complex mathematical concepts, especially in geometry.
Example: "The shortest distance between two points is a straight line."
Multiplying any number by 1 leaves that number unchanged - 5 x 1 = 5; 29 x 1 = 29; and so on. So. multiplying 1 by 1 will always equal 1, no matter how many times you multiply it..... 1 x 1 x 1 x 1 x 1 x 1 x 1 x ...... x 1 = 1. So, if 1n = 1 then the nth root of 1 is always going to be 1.
How the heat conduction equations for spherical and cylindrical coordinates were derived?
The coordinates for equations dealing with cylindrical and spherical conduction are derived by factoring in the volume of the thickness of the cylindrical control. Coordinates are placed into a Cartesian model containing 3 axis points, x, y, and z.
How do you find perimeter of a circle without pi?
pi = C / r C = pi times r pi = 3.141592654... If you do not like pi, than use the number 3 instead, like little childen do.
When you add 2 negatives numbers is the result a positive number?
Never, it will always be negative, regardless the numbers.
How is the mgf of Hypergeometric distribution driven?
A moment generating function does exist for the hypergeometric distribution.
Prove if a union c equals b union c and a intersect c equals b intersect c then a equals b?
suppose x is in B. there are two cases you have to consider.
1. x is in A.
2. x is not in A
Case 1: x is in A. x is also in B. then x is in A intersection B. Since A intersection B = A intersection C, then this means x is in A intersection C. this implies that x is in C.
Case 2: x is not in A. then x is in B. We know that x is in A union B. Since A union B = A union C, this means that x is in A or x is in C. since x is not in A, it follows that x is in C.
We have shown that B is a subset of C. To show that C is subset of B, we do the same as above.
What are the advantages of binary digit over decimal digits in computer operation?
It is relatively easy to code things in terms of on-and-off or magnetised-and-not (magnetic storage), or pit-or-no-pit (CDs). Coding in terms of 10 levels of magnetisation or ten depths of pits is much more difficiult and prone to error - both in writing and reading.
