Nature, in the broadest sense, is the natural, physical, material world or universe. "Nature" can refer to the phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. Although humans are part of nature, human activity is often understood as a separate category from other natural phenomena.The word nature is borrowed from the Old French nature and is derived from the Latin word natura, or "essential qualities, innate disposition", and in ancient times, literally meant "birth". In ancient philosophy, natura is mostly used as the Latin translation of the Greek word physis (φύσις), which originally related to the intrinsic characteristics that plants, animals, and other features of the world develop of their own accord.
The concept of nature as a whole, the physical universe, is one of several expansions of the original notion; it began with certain core applications of the word φύσις by pre-Socratic philosophers (though this word had a dynamic dimension then, especially for Heraclitus), and has steadily gained currency ever since. During the advent of modern scientific method in the last several centuries, nature became the passive reality, organized and moved by divine laws. With the Industrial revolution, nature increasingly became seen as the part of reality deprived from intentional intervention: it was hence considered as sacred by some traditions (Rousseau, American transcendentalism) or a mere decorum for divine providence or human history (Hegel, Marx). However, a vitalist vision of nature, closer to the presocratic one, got reborn at the same time, especially after Charles Darwin.Within the various uses of the word today, "nature" often refers to geology and wildlife. Nature can refer to the general realm of living plants and animals, and in some cases to the processes associated with inanimate objects—the way that particular types of things exist and change of their own accord, such as the weather and geology of the Earth. It is often taken to mean the "natural environment" or wilderness—wild animals, rocks, forest, and in general those things that have not been substantially altered by human intervention, or which persist despite human intervention. For example, manufactured objects and human interaction generally are not considered part of nature, unless qualified as, for example, "human nature" or "the whole of nature". This more traditional concept of natural things that can still be found today implies a distinction between the natural and the artificial, with the artificial being understood as that which has been brought into being by a human consciousness or a human mind. Depending on the particular context, the term "natural" might also be distinguished from the unnatural or the supernatural.
I'm having problems with the work section of my calc book. This is the problem:
If 6 J of work is needed to stretch a spring from 10 cm to 12 cm and another 10 J is needed to stretch from 12 cm to 14 cm, what is the natural length of the spring?
I set up two equations:
6 J= Kx^2/2...
Homework Statement
Let G and G' be groups. Let H and H' be normal subgroups of G and G' respectively. Let
f:G->G' be a group homomorphism.
Show that if f(H) is a subset of H', then there exists a natural homomorphism f*:(G/H)->(G'/H'). (Hint: This fact is used constatntly in...
[SOLVED] Larson 4.1.6
Homework Statement
Prove that there are infinitely many natural numbers a with the following property: The number n^4+a is not prime for any number n.Homework Equations
The Attempt at a Solution
I cannot even think of one such natural number a. :(
I need to find some way...
Homework Statement
\int \frac{1}{1+\sqrt{2x}}dx
Homework Equations
u=1+\sqrt{2x}
\sqrt{2x}=u-1
dx=(u-1)du
The Attempt at a Solution
I was able to get it down to:
\int (1-\frac{1}{u})du
= u-\ln{lul}}+C
= 1+\sqrt{2x}-\ln{l1+\sqrt{2x}l}+C
However, my book says that...
Homework Statement
Find the limit of (tanx)^cosx as x-->infinity
Rearrange the equation so that you can use L'Hopital's rule for the form of (infinity/infinity)
The Attempt at a Solution
I did ln(tanx)^cosx = cosxlntanx
I know the limit of tanx as x-->infinity is pi/2
the limit of cosx as...
I've got a simple question that's been bugging me for a while. I think I know where the problem is, I'd just like a formal mathematical reason why I can't say this:
\ln{(-1)}^2 = \ln(1) = 0
That part is fine...but then:
\ln{(-1)}^2 = 2 \ln(-1) = 2 (i \pi)
when they should...
Homework Statement
The function f is defined for x>2 by f(x)=\ln x+\ln(x-2)-\ln(x^{2}-4)
a. Express f(x) in the form of (\ln\frac{x}{x+a})
b. Find an expression for f^{-1}(x)
Homework Equations
..The Attempt at a Solution
Well, I simplified it to:
f(x)=\ln(\frac{x^{2}-2x}{x^{2}-4})
I can't...
Does hydrogen in its ground state occur naturally, ideally, experimentally? Is it stable? Is this like asking, "Does a center of mass occur naturally, ideally, experimentally? Is it stable?"
Homework Statement
Let f be the function given by f(x) = ln [ x/ (x-1)]
(a) What is the domain of f?
(b) What is the value of the derivative of f at x = -1.
(c) Write an expression for f^(-1) of x, where f^(-1) denotes the inverse function of f.
The Attempt at a Solution
a. x / x-1...
http://www.physorg.com/news115220493.html
In this context, I think it is important to avoid debate about causes [AGW], and focus on the best means to avoid disasters and respond to the emergencies. San Diego did a fabulous job of managing the fires this year, but many homes were lost. Much...
Homework Statement
1. Let f be the function defined by f(x) = -2 + ln(x^2).
a) For what real numbers x is f defined
b) Find the zeros of f
c) Write an equation for the line tangent to the graph of f at x=1
Homework Equations
The Attempt at a Solution
a) all...
How To Fing Angular and Natural Frequencies WITH ANSYS ??
Good Day every body,
I am student in Ruhr Universität Bochum and I would like to ask please about the procedure how to find Natural and angular frequencies for a simple beam to get the idea fro it and to solve my proble.
I will be...
Homework Statement
e^x - e^-x all divided by 2 = -1
express answer in natural logs
Homework Equations
No equations, just properties of logs and natural logs
The Attempt at a Solution
First, I multiplied everything by 2
e^x - e^-x = -2
then i took the natural log of both...
http://www.sciencedaily.com/releases/2005/05/050502190314.htm
ScienceDaily (May 2, 2005) — DURHAM, N.C. -- Duke University engineers have led the most detailed analyses of links between some lightning events and mysterious gamma ray emissions that emanate from Earth's own atmosphere. Their...
Hi,
I've encountered this exercise which I'm having a hard time proving. It goes like this:
Prove that if m and n are natural, then the nth root of m is either integer or irrational.
Any help would be greatly appreciated. Thanks.
natural frequency of a spring(self-weight only)
giving the length,mass, and spring constant of a spring...how do you find the resonance frequency..having been thinking about this question for so long, does anyone know how to approach this question...
So I'm taking an introductory number theory course as an undergraduate, and this particular "genre" of questions really just has me stumped.
Pick a prime p such that p is odd. Now, take various sums up of natural numbers from 1 to p, and show that the results are divisible by p.
For...
Homework Statement
Find y'
y=ln(x^2 + y^2)
Homework Equations
d/dx ln(u)= 1/u du/dx
The Attempt at a Solution
y' = [1/(x^2 + y^2)] (2x + 2y)
y' = (2x+2y)/(x^2 + y^2)
But my book says the answer is 2x/(x^2 + y^2 - 2y)
How can that be?
Homework Statement
I'm supposed to find the voltage v0(t) for t > 0 for the following circuit:
http://img516.imageshack.us/img516/5858/circuitta7.jpg
Homework Equations
The first part of the excercise was to find the current io(t). I did this by using the node-voltage method to find the...
i have this question that i don't totally get what it wants exactly so if anyone can help me understand it correctly, thx
Find the natural domain of the function algebraically,and confirm that your result is consistent with the graph produced by your graphing utility. note: set your graphing...
One question which I was meant to be doing has stumped me. It is "Can the basis of natural law be located other than in social convention?". I have written "Aquinas believed the basis of natural law to be located in God’s will and the fundamental nature of humans not being corrupted." so far but...
Homework Statement
ln(x^2 + 1 ) -3lnx=ln2
Solve for x.
Homework Equations
The Attempt at a Solution
I used laws of logarithms to simplify it down to -x^2(x-1)=1 . I don't think this is the answer I'm under the impression you need x = for the answer. First I brought the 3...
Hello I'm new to the forum. I was wondering if some people can help me in trying to get some answers.
I am involved in alternative fuels and it has come up where an engineer is telling me that there is 185btus/lb inside of a 100 gallon vehiculer tank. He is using a bueauro of standard empathy...
A part of an example on my book goes from the following:
e^(lnlnx) > e^0
to
(e^lnx)^lnx > e^0
and to
ln x > e^0
this last step is what threw me off--shouldn't it be x^lnx instead of ln x on the right side since they are inverse functions. Is anything being done that I have...
Well I came across this when someone asked me this question:
(-2)^n = 16
I can clearly see n=4. However, he did this:
ln((-2)^n) = ln(16)
n*ln(-2) = ln(16)
n*ln(2)+n*i*pi = ln(16)
How can I show that n=4 from this?
Homework Statement
I was given a spring mass system and asked to calculate the natural frequency by theorectical analysis and by using experimental data.
There was a difference between the natural frequency calculated theorectically and experimentally.
I was asked to discuss the...
I didn't know where to put this since it pertains to both chemistry and biology so i put it here. One time i accedently spilt 31.45% concentrated HCl on my skin and didn't notice it right away but then i saw this fuming drop on my skin and i immediately washed it off, it never tingled, burned...
Natural selection needs the feeling??
Human(at least) has their feelings, such as anger, happiness, and depression, etc. But, is there an advantage for the survival of human being?? why natural selection choose the human being who has feelings??
I thought about this theme at last night...
Problem: If 2^{x}=3, what does 3^x equal?
I solved this by taking the log_{2} of both sides. However, the book's solution involves taking the natural log of both sides. Can someone show me why that would work? I don't get what the x power changes to a x term. The natural log is base 10 right?
Homework Statement
f(x) = (x+1)/x^2
a)prove that f is bounded in N (N is the set of natural numbers so we have to prove that f(N) is a bounded set)
b)find supf(N) and inff(N).
c) does f have a maximum or minimum in N?
Homework Equations
The Attempt at a Solution
First I...
I am trying to prove that the set of natural numbers is well-ordered using induction. I am assuming of course that the natural numbers are defined as as the smallest inductive set (of the type specified by the Axiom of Infinity) and that the usual order is defined by n<m iff n\in m. I have an...
I'm having real problems integrating a natural log. The problem I have been set is (where S = integration sign)
S (x - 2) Ln(3x)
I'm trying to use the integration by parts rule but keep getting the wrong answer and I think it might be to do with the natural log. I have used
f(x) =...
If we have a function of the form
Ln(ax)
Is it the case that the derivative is simply 1/x no matter what the initial value of 'a' might be? Or do we take into account 'a' in some way
The thing i need clarifying is this... If we have Ln(3x), the derivative is 1/x, but the integral of...
Homework Statement
the indefinite integral of (1+lnx)^(1/2)/(xlnx) dx
Homework Equations
n/a
The Attempt at a Solution
There aren't any x^2 in the root sign, so I don't think it can be a trig substitution. The only logical u sub I see is to let u=lnx. In that case, du=dx/x so the...
I'm tired of hearing people like the skeptic Michael Shermer or James Randi talk about natural explanations for supernatural events. I believe that supernatural events are natural events that we are not advanced enough to explain. These events are true and we can deduce there truthfulness...
Hi, just can't get my head around how to draw these three graphs. Any help appreciated. Thanks
In each case below, draw the graph of a function f that satisfies the given property.
Give an example of a function f : N -> Z that is bijective/that is injective but not surjective/that is...
This is a new book from Cambridge University Press, scheduled to go on sale 30 June 2007, available now for pre-order
https://www.amazon.com/dp/0521848415/?tag=pfamazon01-20
The Cambridge.org webpage for the book is here
http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521848411...
Homework Statement
Using a highly sensitive parabolic sound collector, Sara records the frequency of a tuning fork as it drops into the Grand Canyon. She drops the vibrating tuning fork form rest at t=0. She records a frequency of 1783.0Hz at t=8.590s. What is the natural frequency of the...
I was working on an experiment for the vapor pressure of water and I have the following formula
ln (p) = -L/(RT) + ln (p_o)
L=heat of vaporization of water
R=Molar gas constant
T=temperature in Kelvins
I have some data points for the pressure p in units of mm Hg, when I take the...
Hello all,
Another quick question for the number theory gurus here:
Let P(n) predicate, n Natural number. Suppose that P(n) satisfies that P(1) is true, and if k in N, P(k) is true, then P(k+2) is true. Is P(n) true for ALL n in N? Why?
Thanks in advace guys!
-William
Homework Statement
xln(2x+1)-x+\frac{1}{2}ln(2x+1) = \frac{1}{2}(2x+1)ln(2x+1)-xHomework Equations
ln(x^a) = aln(x), ln(xy) = ln(x) + ln(y), ln(\frac{x}{y}) = ln(x) - ln(y)The Attempt at a Solution
I have no idea how you can go from xln(2x+1)-x+\frac{1}{2}ln(2x+1) to...
Can someone explain to me when to use natural log or common log? I understand that natural log gives creates a base e and the common base 10 but i don't understand why there are 2 different ones.
Creativity...learned or natural (born-with)
I had this conversation with some friends / coworkers today at lunch and both sides made good points. I'd like to get a view from everyone on these forums on the subject. I guess it all comes back to the big question you hear throughout management...
Homework Statement
Reading about the raditation dominated era I saw that the radiation energy density today was given by:
\rho_r = \frac{\pi^2}{30} g_* T^4 = 8.09 * 10^{-34} g/cm^3
where g_*=3.36 is the degree of freedom of the radiation (equivalent) and T=2.75 K is the CBR...