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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
What are the Math proof letters?
QED from the Latin "quod erat demonstrandum", meaning "that which was to be demonstrated", normally put at the end of a mathematical proof
What is the meaning of letter you of tau gamma phi?
Tau is a letter of the Greek alphabet and without a "U" it would be Ta, which is meaningless. However, the letter "U" does not, of itself, have a meaning.
Why is the greatest range of a projectile produced when the angle is 45 degrees?
Suppose the projective is launched, over a level surface, with initial velocity u, which makes an angle x with the horizontal. Then 0 <= x <= 90 degrees.Ignore the effects of all forces other than gravity,
Ananlyse the motion in the vertical direction.
The vertical component of u is u*sin(x), and the projectile is in the air until its vertical displacement returns to 0.
That is t is given by
0 = u*sin(x)*t - 1/2*g*t^2 where g is the acceleration due to gravity.
ie 0 = t*{u*sin(x) - 1*2*g*t}
that is t = 0 or u*sin(x) - 1/2*g*t
ignoring t = 0 since that is the initial position,
t = 2*u*sin(x)/g.
Now consider the horizontal motion.
The horizontal component of the initial velocity is u*cos(x) and [since we have chosen to ignore aerodynamic drag], this is a constant.
Therefore, horizontal distance covered in t units of time = u*cos(x)*t units of length.
Substituting for t gives
range = u*cos(x)*2*u*sin(x)/g = (u^2/g)*2*cos(x)*sin(x)
= c*2*cos(x)*sin(x) where c is a constant
= c*sin(2x) [using the double angle formula].
Now d(range)/dx = 2c*cos(2x) must be 0 at the maximum.
[It cannot be the minimum since x = 90 degrees gives a minimum range of 0].
therefore cos(2x) = 0
therefore 2x = 90 degrees and so x = 45 degrees.
State and prove stokes theorem?
You can find an introduction to Stokes' Theorem in the corresponding Wikipedia article - as well as a short explanation that makes it seem reasonable. Perhaps you can find a proof under the links at the bottom of the Wikipedia article ("Further reading").
Can copies of a dodecagon be used to tile a surface?
no it can't If each angle is 150 so 150 times anything does not equal 360
* * * * *
A correct answer but incorrect reasoning. First, there is no requirement in the question that the polygon is regular so the each angle need not be 150 degrees. As a counter-example to your reasoning, each interior angle of a regular pentagon is 108 degrees. 108 times anything does not equal 360. Yet there are 14 different non-regular pentagons which can be used to tile a surface.
What is the formula for the mass of a sphere?
The mass of a sphere is 4/3*pi*r3*d where r is the radius of the sphere and d is the density of the material of the sphere.
The other two sides may be equal, but they do not have to be equal. For example: 3, 4, 5 and sqrt(25/2), sqrt(25/2), 5. Here sqrt is short for square root. Also 15, 20, 25 and 7, 24, 25.
What happends to a egg when it is in water or vinegar?
Vinegar makes the egg wrinkly/takes off the shell and water makes and egg stronger
Why does a hexagon tessellate?
They tessellate because one of their interior angles is exactly 120 degrees provided that it is a regular polygon. Since this is exactly a third of a full circle, three of them will always create a 360 degree angle in the center. When you repeat this pattern, they form multiple 360 degree angles, which forms a tessellation. This is true with any polygon that has an interior angle that is a factor of 360, and this is why pentagons do not tessellate.
What is the axiomatic approach in Euclidean Geometry?
In Euclid's version, all geometric theorems are deduced from just ten assumptions divided among five axioms and five postulates. Euclid's axioms (also called "common notions") are algebraic statements such as " equals added to equals are equal". The postulates are geometrical in nature and thus embody the essence of Euclidean geometry.
Euclid's postulates are:
1. Any two points can be joined by a straight line.
2. Any straight line segment can be extended indefinitely in a straight line.
3. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center.
4. All right angles are congruent.
5. Parallel postulate: If two lines intersect a third line in such a way that the sum of the inner angles on one side of the third line is less than two right angles, then the two lines, extended indefinitely if necessary, will meet on that side of the third line.
Euclid's axioms are:
1. Things which are equal to the same thing are also equal to one other.
2. If equals are added to equals, the sums are also equal.
3. If equals are subtracted from equals, the remainders are also equal.
4.Things that coincide with one another are equal to one another.
5. The whole is greater than the part.
However, Euclid's axioms turned out not to be enough. For example, the first proof in Euclid (Book I, Proposition 1) shows how to construct an equilateral triangle on a given base, by drawing two circular arcs and locating their point of intersection. But Euclid doesn't have any axiom allowing him to conclude that there is a point of intersection.
This isn't to knock Euclid. He did an extraordinary job, and it took well over two thousand years before substantially better treatments were given.
As far as I know, the definitive modern treatment was given by David Hilbert. The first edition of his book (published in German in 1899) is available for download in English translation from Project Gutenberg at
http://www.gutenberg.org/files/17384/17384-pdf.pdf
It has twenty axioms. However, this version intentionally doesn't cover everything that can be done by ruler and compass. Hilbert revised his work, and his version of 1930 does cover everything that can be done by ruler and compass. The axiom that Euclid needed for his first Proposition is that called by Hilbert the Axiom of Linear Completeness.
To be really complete, one would need to add another layer underneath the geometrical axioms, a layer of axioms for symbolic logic. Hilbert undoubtedly knew this, since he worked in logic, but it would have made the book much harder to read.
My information for Hilbert's 1930 work comes from Morris Kline Mathematical Thought from Ancient to Modern Times, Oxford University Press New York 1972, Chapter 42 "The Foundations of Geometry".
An integer is a number, positive or negative. So 15 is an integer.
the first one is:
(0!+0!+0!)!=6
Because 0!=1
0!+0!+0!=3
and 3!=6
Just use factorial
(1+1+1)! = 6
3 Factorial = 6
2+2+2 = 6
So Simple
(3*3)-3 = 6
Also Simple
Sqrt(4) + Sqrt(4)+ Sqrt(4) = 6
Sqrt(4) = 2
So 2+2+2 =6
5+(5/5) = 6
So Simple
6+6-6 = 6
Its quite simple
7-(7/7) = 6
Cuberoot(8) + Cuberoot(8) + Cuberoot(8) = 6
Cuberoot(8) = 2
Using the phrase "Cuberoot" is not allowed. This written as a mathematical sign viz. ³√x . This involves the number 3 which is not permissible. Since you have correctly solved for 0 and 1 it should be relatively easy to solve for 8. All your other answers are spot on although my cousin's answer for 8 was (cos((d/dx)(8))+cos((d/dx)(8))+cos((d/dx)(8))) = 6 which is correct but way far more complicated than the simpler answer that you should be looking for.
(Sqrt(9) * Sqrt(9)) - Sqrt(9) = 6
Sqrt(9) = 3
(3*3)-3 = 6
Eighteen liters of water, or an eighteen kilogram dumbbell.
In geometry, a circle is a two-dimensional shape formed by all points that are one consistent distance or "radius" from a single central point. For example, if the radius is 5 inches, then the shape formed from the preceding rule would be a perfectly round circle measuring 10 inches in "diameter" (the distance of any one point on a circle to the farthest point on the same circle).
more mass.
How many times does sixteen go into two hundred twenty four?
You seem to be unaware of the fact that you could have obtained the answer much more easily and quickly by using the calculator that comes as part of your computer.
224/16 = 14 times.
How do you convert cm into dm?
10 cm in 1 dm.. then just convert it.. for example:
70 cm = 1dm/10cm = 7 dm...
what i did there was 70 x 1 / 10 = 7 dm
Which metric unit is best for measuring the width of a desk?
It depends on the width of the desk. You could use centimeters or meters.
What is the name that has for 100 zeros?
The number 1 followed by 100 zeros (10^100) is called a "Googol". Often misspelt as google thanks to the search engine that adopted the misspelling as a play on the word.
What does an O with a line through it mean?
It's the greek letter, Theta. It's used to symbolize an angle.
Given a conditional statement of the form:
- If "hypothesis" then "conclusion",
the inverse is:
- If "not hypothesis" then "not conclusion".
