Proofs

0 or 1

100 can be expressed as the sum of two primes in 6 different ways (ignoring order):

100 = 3+97 = 11+89 = 17+83 = 29+71 = 41+59 = 47+53

It is 1/4.

Yes, and here's the proof:

Let's start out with the basic inequality 4 < 7 < 9.

Now, we'll take the square root of this inequality:

2 < √7 < 3.

If you subtract all numbers by 2, you get:

0 < √7 - 2 < 1.

If √7 is rational, then it can be expressed as a fraction of two integers, m/n. This next part is the only remotely tricky part of this proof, so pay attention. We're going to assume that m/n is in its most reduced form; i.e., that the value for n is the smallest it can be and still be able to represent √7. Therefore, √7n must be an integer, and n must be the smallest multiple of √7 to make this true. If you don't understand this part, read it again, because this is the heart of the proof.

Now, we're going to multiply √7n by (√7 - 2). This gives 7n - 2√7n. Well, 7n is an integer, and, as we explained above, √7n is also an integer; therefore, 7n - 2√7n is an integer as well. We're going to rearrange this expression to (√7n - 2n)√7, and then set the term (√7n - 2n) equal to p, for simplicity. This gives us the expression √7p, which is equal to 7n - 2√7n, and is an integer.

Remember, from above, that 0 < √7 - 2 < 1.

If we multiply this inequality by n, we get 0 < √7n - 2n < n, or, from what we defined above, 0 < p < n. This means that p < n and thus √7p < √7n. We've already determined that both √7p and √7n are integers, but recall that we said n was the smallest multiple of √7 to yield an integer value. Thus, √7p < √7n is a contradiction; therefore √7 can't be rational, and so must be irrational.

Q.E.D.

It is Equal to 104. :-)

They all relate by adding up the 6+6+3=15 You can not get to the sum of 15 is you don't have the first 3 numbers to add up.

Area of a rectangle = length * width = 72 feet-squared

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It can be rounded to 17,000

To conclude, or deduce, as in, "from the fact that the triangle is equilateral, and the fact that a triangle is isoceles if and only if the base angles are equal, we can infer that it is also equiangular."

I would say so. They are soft enough to eat. Stay away from hard candies and taffy though.

Rectangular bases are congruent to each other. The five other faces connect those bases and are adjacent to each other and the parallel bases to each other. Congruency does not occur on the five equal side shapes. This occurs in odd face prisms. The angle created by the five faces have only partial reflection of each other where as the pentagonal bases are parallel. The reflection on the parallel sides create an optical illusion of bending light.

In a four sided prism however all faces are congruent. A cubed prism would be a perfect congruent prism.

Answer: A regular quadrilateral is one with equal sides and equal angles, so it is a square. To negate this definition, we say an irregular quadrilateral is one where the sides are unequal or the angles are unequal OR BOTH. In simpler terms, we could say it is a quadrilateral which is not a square.

These are exists in d-orbitals only.

"e" refers to doubly degenerate orbitals.It consists of two d-orbitals.

"t" refers to triply degenerate levels orbitals. It consists of three d-orbitals. Degenerate means having same energy. They derive from group theory.

The "g" tells you that the orbitals are gerade (german for even) - they have the same symmetry with respect to the inversion centre.

In a right triangle, the altitude with the hypotenuse as base divides the hypotenuse into two sections p and q. If we denote the length of the altitude by h, we have the relation h2 = p*q (Euklids altitutude theorem).

So, first draw the square root of 2 as the diagonal of a square with side length 1, then construct a right triangle with p=1 and q= sqrt(2) by using the Thales theorem and its altitude will be fourth root of 2 according to Euclids theorem.

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bkt alm mou

BY: H!KAR! AND ke!

A quadrilateral is a parallelogram if one pair of opposite sides are equal and parallel

Let ABCD be a quadrilateral in which ABCD and AB=CD, where means parallel to.

Construct line AC and create triangles ABC and ADC.

Now, in triangles ABC and ADC,

AB=CD (given)

AC = AC (common side)

Angle BAC=Angle ACD

(corresponding parts of corresponding triangles or CPCTC)

Triangle ABC is congruent to triangle CDA by Side Angle Side

Angle BCA =Angle DAC by CPCTC

And since these are alternate angles, ADBC.

Thus in the quadrilateral ABCD, ABCD and ADBC.

We conclude ABCD is a parallelogram. var content_characters_counter = '1032';

Int sqrt(1+x2)/x = sqrt(1+x2) + LN [(sqrt(1+x2) - x -1) / (sqrt(1+x2) - x +1)]

A square. All squares are parallelograms, but not all parallelograms are squares.

The acceleration of an object that falls from a certain height does not depend on its mass, in an ideal condition with no air resistance.

The value of acceleration is the acceleration due to gravity, which is 9.81 m s-2.

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However, in this case, air resistance is going to matter. 12000 feet is high enough for the person to accelerate to what we call terminal velocity. Terminal velocity is the velocity where the force of acceleration due to gravity (9.81 m s-2) is matched by the air resistance. That velocity varies, depending on the outline shape of the person, and is typically around 200 km/h or 125 mph. That will be the velocity of the fall.

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composition

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