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Mathematical Constants
Intriguing, ubiquitous, and at times mysterious, numerical constants set the allowable limits for all universal phenomena. Whether your questions involves π, Avogadro's number, Planck's constant, the atomic mass unit, or any of the other multitudes of immutable numbers used in science, this is the category where they should be asked.
2,332 Questions
no it is not. See Lindemann, 1882, that pi is transcendental.
Is zero real or imaginary number?
Zero is in the set of the whole numbers and also integers, which are subsets of the real numbers. So you could say it's real, but it lies on the imaginary axis (it is the origin). It's kind of like asking: Is zero positive or negative. For most purposes, letting zero be real would be the logical choice, though.
First answer:
It is real. Imaginary numbers only involve square roots of negative numbers.
Is gravitational force constant all over earth?
For the most part, yes; the weight of an object is equal at any point on the Earth as measured by any standard scale. However, using a gravimeter it is possible to detect minute differences in gravitational force. These differences are due to differences in topography or rock density at the site of measurement. For example, a gravimeter will yield a slightly lower gravity measure if read above a granite slab (low density) than it would over a basalt slab (high density), providing that both slabs are at equal altitude and are thick enough to be detected by the gravimeter (often on the order of 10s-100s of meters thick). Measuring gravity is how many features below the ice on Antarctica have been mapped, and is often how oil fields are discovered.
What is the origin of natural number e?
as x goes to infinity, ((1+(1/x))^x), that's all i know
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My improvement to the previous answer is to then try to explain why it is then called "natural". The initial formula shown above, even though it is 100% right, is not the origin of itself and some further explanation of it may then be needed.
e is sometimes called "Euler's Number" Euler was a mathematician who
conceived of this value.
e or epsilon is a constant value of about 2.71828 e is a very important number like PI = 3.14...
This is called a natural number because it occurs in nature alot like the Fibonacci series or numbers. e was chosen since it can then be used to calculate natural growths and decays. For example an object that is cooling down, the temperature can be calculated where the formula for that has e in it. A series for e has been developed which has great power in finding not only powers of e but powers and roots of any value since series for those values have not been developed (such as a series for powers of 10).
The definition of e is based upon (1/1 + 1/n)^n where n is very high. Quickly though it reaches 2.718 even when n is lower. The value of this expression approaches the value of a constant we will just call e. If you have infinitely compounded growth during one period of time, the initial value will grow to about 2.718 times bigger for that entire period, and not some enormous value like some might think initially. The reason is that the compounded growth value to be added in gets very small when the number of intervals (n in the formula) of compounded growth is very high.
Read more: What is the natural base of e
Does pi represent a finite or infinite number?
Pi is an irrational number. As such, it has an infinite number of digits.
Any number from 1 to 10999 can be made using a combination of these numerals...
I = 1
V = 5
X = 10
L = 50
C = 100
D = 500
M = 1000
(IV) = 4000
(V) = 5000
(VI) = 6000
(VII) = 7000
(VIII) = 8000
(IX) = 9000
(X) = 10000
For example... 3 = III, 24 = XXIV, 48 = XLVIII, 296 = CCXCVI, 666 = DCLXVI, 1555 = MDLV, 2009 = MMIX, 4999 = (IV)CMXCIX, 10888 = (X)DCCCLXXXVIII.
How do you find out the atomic mass of an element?
On the periodic table it is the number on the bottom of the element.
If you know the amount of neutrons you can add it to the number of protons to find the atomic mass NUMBER, which is a good approximate of the atomic mass.
Potassium (isotope 39), 19K(39), has 19 protons and 20 neutrons
19 + 20 = 39 atomic mass NUMBER, its atomic mass is 39.10 a.m.u.
What is the definition of 'Atomic Mass'?
the mass of an atom of a chemical element expressed in atomic mass units. It is approximately equivalent to the number of protons and neutrons in the atom (the mass number) or to the average number allowing for the relative abundances of different isotopes.
What are the first 1000 digits of Pi?
3.14159265358979323846264338327950288419716939937510582097494459230781 640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575 959195309218611738193261179310511854807446237996274956735188575272489 122793818301194912983367336244065664308602139494639522473719070217986 094370277053921717629317675238467481846766940513200056812714526356082 778577134275778960917363717872146844090122495343014654958537105079227 968925892354201995611212902196086403441815981362977477130996051870721 134999999837297804995105973173281609631859502445945534690830264252230 825334468503526193118817101000313783875288658753320838142061717766914 730359825349042875546873115956286388235378759375195778185778053217122 68066130019278766111959092164201989 this does not include the "."
What is the highest named number?
The largest number named by the English conventions (billion,etc) is the number centillion (10303 short scale). The numbers googol and googolplex denote numbers mostly usable only theoretically (10100 and 10googol). Mathematicians have created very large numbers for analysis purposes, which cannot be written out except as increasing series of powers of powers (power towers). A notable examples is Graham's Number (many times too large to be written in the observable universe).
What is the mathematical proof of Faraday's law of electromagnetism?
You need to have some knowledge in Calculus II, but the arguments are very simple. See the link above:
What is the atomic mass of americium?
243.0614
The isotope with the longest half life is 243Am (half life = 7 370 years) with the atomic weight (Audi et alii, 2003) of 243,061 138 11 +/- 0,000 000 25.
How do you calculate the atomic mass of an element?
If you know the mass of one mole of those atoms (the mass number listed on the periodic table), then you divide that number by Avogadro's constant: 6.022x10^23 which gives you the mass of one single atom
What does the atomic mass tell you?
It tells you the average amount of protons and neutrons within the nucleus of an atom. In other words, atomic mass - atomic number (protons)= the number of neutrons within the nucleus.
How do you calculate a dissociation constant?
Determination of the Dissociation Constant and Molar Mass for a Weak Acid
Abstract: We will determine Ka and the molar mass for an unknown weak acid by using a pH meter to record the pH at intervals during the titration with sodium hydroxide. The titration curve and its first derivative will be plotted to establish the equivalence point. Introduction The strength of an acid is defined by its ability to donate a proton to a base. For many common acids, we can quantify acid strength by expressing it as the equilibrium constant for the reaction in which the acid donates a proton to the standard base, water, as shown in the equations below: HA + H2O Û H3O+ + A-, for H3CCOOH: H3CCOOH + H2O Û H3O+ + H3CCOO - The equilibrium constant for a reaction of this type is called the Acid Dissociation Constant, "Ka", for the acid HA Determination of the Dissociation Constant and Molar Mass for a Weak Acid
Abstract: We will determine Ka and the molar mass for an unknown weak acid by using a pH meter to record the pH at intervals during the titration with sodium hydroxide. The titration curve and its first derivative will be plotted to establish the equivalence point. Introduction The strength of an acid is defined by its ability to donate a proton to a base. For many common acids, we can quantify acid strength by expressing it as the equilibrium constant for the reaction in which the acid donates a proton to the standard base, water, as shown in the equations below: HA + H2O Û H3O+ + A-, for H3CCOOH: H3CCOOH + H2O Û H3O+ + H3CCOO - The equilibrium constant for a reaction of this type is called the Acid Dissociation Constant, "Ka", for the acid HA Determination of the Dissociation Constant and Molar Mass for a Weak Acid
Abstract: We will determine Ka and the molar mass for an unknown weak acid by using a pH meter to record the pH at intervals during the titration with sodium hydroxide. The titration curve and its first derivative will be plotted to establish the equivalence point. Introduction The strength of an acid is defined by its ability to donate a proton to a base. For many common acids, we can quantify acid strength by expressing it as the equilibrium constant for the reaction in which the acid donates a proton to the standard base, water, as shown in the equations below: HA + H2O Û H3O+ + A-, for H3CCOOH: H3CCOOH + H2O Û H3O+ + H3CCOO - The equilibrium constant for a reaction of this type is called the Acid Dissociation Constant, "Ka", for the acid HA
What is appraisal ratio exceeds median level of apraisal?
the median level of appraisal is the median appraisal
ratio of a reasonable and representative sample of properties in an
appraisal district. An appraisal ratio is the ratio of a property's
appraised value as determined by the appraisal office or appraisal
review board, as applicable, to:
(1) the appraised value of the property according to
law if the property qualifies for appraisal for tax purposes
according to a standard other than market value; or
(2) the market value of the property if Subdivision
(1) of this subsection does not apply.
(c) The median appraisal ratio for a sample of properties
is, in a numerically ordered list of the appraisal ratios for the
properties:
(1) if the sample contains an odd number of
properties, the appraisal ratio above and below which there is an
equal number of appraisal ratios in the list; or
(2) if the sample contains an even number of
properties, the average of the two consecutive appraisal ratios
above and below which there is an equal number of appraisal ratios
