Its a progressive degradation, similar to that of a light bulb.
Also, your test was probably in free air. The ratings on the wire are for it to be safe while in a wall packed with insulation. Any self-heating of the wire is going to stay by the wire there.
221 miles. This is the fastest route:Out of the airport, follow signs to I-240. Once you are at I-240, you want to take I-240 EAST to NASHVILLE.Take I-240 EAST to I-40 EAST to NASHVILLE at EXIT 12C.Take I-40 EAST to the INT'L AIRPORT at EXIT 216A. To bypass downtown Nashville, take I-440 (EXIT 206 off I-40).Follow signs to the terminal.
This sequence is puzzling, particularly because the steps initially increase in magnitude; and yet the sequence then takes three steps just to fall from 30 to 24, a surprise which runs counter to our intuitions. Alternative reasons for this odd behaviour could be: * The sequence isn't a straightforward function, but rather involves some recursive relationship between terms. * The series is an elementary function, but it isn't using the counting numbers as its input. It might be based on the prime numbers, for instance. * The individual digits of each term are manipulated to determine the next. * The sequence is based upon a constant, like pi or e. * It involves geometric / trigonometric ideas. * The sequence is not using the decimal system. * The sequence isn't purely mathematical - it makes reference to some independent external data or sequence. I list all these exotic possibilities for one reason: there will be a great many different rules that could produce such a succession of terms. Some of them will be more elegant than others, so it's a good idea to keep an open mind. But here is the more mundane hypothesis that I will work with: * The sequence is confusing because it is produced by a function that is neither linear or quadratic but of a higher degree. If you sketch a graph of the sequence*, it is absolutely clear that it cannot possibly be a quadratic function, because it is neither concave nor convex, but first one and then the other. What this means in mathematical terms is that the rate of change of gradient (the second differential) undergoes a sign change somewhere. For this to happen, d2y/dx2 must be variable, i.e. it is a function of degree 1 or greater. It follows that dy/dx must be at least degree 2, and the actual function must have at least degree 3. In other words, the function could be a cubic of form ax3 + bx2 + cx + d Normally cubic sequences can be identified at once because the third difference (the difference of the difference of the difference) is constant. This method requires 5 consecutive terms however, and we were only given three. To pin down the function that we are dealing with, we would need to solve for the coefficients a, b, c and d: four unknowns to find. It happens that we have been given 4 terms in the sequence, therefore we can form four equations and solve for four unknowns. Actually, that is why this approach is rather disappointing and lacking in elegance. If you are given a number n terms of a sequence, then it is always possible to find a valid rule using a polynomial of degree n-1. For instance, if you gave me the first twenty terms of the Fibonacci series, I could find a rule that worked using powers of x up to x19, but it wouldn't be the best answer. Still, I can't see a better way forward, so let's proceed with our cubic function. We have four simultaneous equations: a + b + c + d = 45 a + b + c + d = 45a + b + c + d = 39 8a + 4b + 2c + d = 39 a + b + c + d = 39 27a + 9b + 3c + d = 30 a + b + c + d = 24 216a + 36b + 6c + d = 24 The way to solve them is to rearrange an equation to get one variable in terms of all the others, and then to substitute for it in the remaining equations. Repeating this tedious process will eventually eliminate all but one variable: the solution for this one variable can then be used to find the value of the others. To cut a long story short, the solution is: a = 13/20 b = -108/20 c = 113/20 d = 882/20 We can write a function giving y in terms of x that applies to the sequence: y = [13x3 - 108x2 + 113x + 882] / 20 As predicted, it is far from pretty, and I suspect there was some simpler rule that you were meant to find. Still, this one is perfectly valid. It gives the missing terms as 21.9 andf 18.6, in that order. *Plotting the given values against their positions in the sequence, y against x.
This is a very worthwhile question and the answer is relatively straightforward, although some Christians would describe it differently. To use a simple analogy, if you have a rich Uncle who has left you a vast inheritance, deposited in a bank, your act of going to the bank and collecting it, has enabled you to get access to it, but it has not earned you the inheritance which was simply given to you. The act of collecting it from the bank is simply your means of receiving what is yours, else if you leave it there, it does you no good and remains in the account in which it was deposited.In a similar manner, the blood of Jesus Christ, the lamb slain for the sins of the whole world, will do you no good unless you receive it. The act of receiving it is the means of it becoming yours and does not itself constitute a saving work, as this has already been done, and enough 'light' has been given to every person by the 'light which lights every man' (John 1:9) to enable them to believe. This is a necessity otherwise we would all be robots, being forced to believe against our will, which would amount to nothing. Or, if there was no light, we would remain in 'darkness' and could not justly be held accountable for unbelief.This concept, although seemingly simple to understand intellectually, may be a difficult thing to put into practice as the 18 inches (metaphorically speaking) from the head to the heart can be an infinite distance for some. Yet, as thousands can testify, it is a simple journey well worth making and continuing in.AnswerThe early fathers taught that "Salvation is not by faith alone." Work is required; Psalm 6212For you render to each one according to his works.Proverbs 1016The labour of the righteous tendeth to life: the fruit of the wicked to sin.Jeremiah 1710I the Lord ... give every man according to his ways, and according to the fruit of his doings.Ezekiel 1827When the wicked man turneth away from his wickedness ... and doeth that which is lawful and right, he shall save his soul.Matthew 520Except your righteousness shall exceed the righteousness of the scribes and Pharisees, ye shall in no case enter into the kingdom of heaven.Matthew 1237For by thy words thou shalt be justified, and by thy words thou shalt be condemned.Matthew 1627For the Son of Man will come in the glory of His Father with His angels, and then He will reward each according to his works.Matthew 1917If you want to enter into life, keep the commandments.Matthew 2541-46Then shall he say also unto them on the left hand, Depart from me, ye cursed, into everlasting fire, prepared for the devil and his angels: For I was an hungred, and ye gave me no meat: I was thirsty, and ye gave me no drink: I was a stranger, and ye took me not in: naked, and ye clothed me not: sick, and in prison, and ye visited me not. Then shall they also answer him, saying, Lord, when saw we thee an hungred, or athirst, or a stranger, or naked, or sick, or in prison, and did not minister unto thee? Then shall he answer them, saying, Verily I say unto you, Inasmuch as ye did it not to one of the least of these, ye did it not to me. And these shall go away into everlasting punishment: but the righteous into life eternal.Luke 1026-28He said unto him, What is written in the law? how readest thou? And he answering said, Thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy strength, and with all thy mind; and thy neighbour as thyself. And he said unto him, Thou hast answered right: this do, and thou shalt live.John 529And shall come forth; they that have done good, unto the resurrection of life; and they that have done evil, unto the resurrection of damnation.Romans 26, 13Who will render to each one according to his deeds. ... For not the hearers of the law are just in the sight of God, but the doers of the law will be justified.2 Corinthians 510For we must all appear before the jugment seat of Christ, that each one may receive the things done in the body, according to what he has done, whether good or bad.2 Corinthians 1115Therefore it is no great thing if his ministers also transform themselves into ministers of righteousness, whose end will be according to their works.Philippians 212"Work out your own salvation with fear and trembling."James 214What does it profit, my brethren, if someone says he has faith but does not have works? Can faith save him?James 217Thus also faith by itself, if it does not have works, is dead.James 221-25Was not Abraham our father justified by works? You see then that a man is justified by works, and not by faith only. Likewise, was not Rabab the harlot also justified by works? For as the body without the spirit is dead, so faith without works is dead also.1 Peter 117The Father, who without partiality judges according to each one's work.Revelation 223I will give unto every one of you according to your works.Revelation 2012-13And I saw the dead, small and great, stand before God; and the books were opened: and another book was opened, which is the book of life: and the dead were judged out of those things which were written in the books, according to their works. And the sea gave up the dead which were in it; and death and hell delivered up the dead which were in them: and they were judged every man according to their works.Revelation 2214Blessed are they that do his commandments, that they may have right to the tree of life.Martin Luther, the father of Protestantism argued that "Salvation is by Faith alone." (Justification by faith).Mark 1616He that believeth and is baptized shall be saved; but he that believeth not shall be damned.John 318, 36He that believeth on him is not condemned: but he that believeth not is condemned already .... He that believeth on the Son hath everlasting life: and he that believeth not the Son shall not see life; but the wrath of God abideth on him.Acts 1630-31Sirs, what must I do to be saved? And they said, Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house.Romans 116-17For I am not ashamed of the gospel of Christ: for it is the power of God salvation to every one that believeth.... As it is written, The just shall live by faith.Romans 320By the deeds of the law there shall no flesh be justified in his sight.Romans 328A man is justified by faith without the deeds of the law.Romans 42For if Abraham were justified by works he hath whereof to glory?Romans 413For the promise ... was not to Abraham, or to his seed, through the law, but through the righteousness of faith.Romans 51Therefore, being justified by faith, we have peace with God through our Lord Jesus Christ.Romans 109If thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved.Galatians 216A man is not justified by the works of the law, but by the faith of Jesus Christ.Galatians 311-12The just shall live by faith. And the law is not of faith.Ephesians 28-9For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: not of works, lest any man should boast.Titus 35Not by works of righteousness which we have done, but according to his mercy he saved us, by the washing of regeneration, and renewing of the Holy Ghost. ProtestantismFrom Wikipedia, the free encyclopediaProtestantism encompasses the forms of Christian faith and practice that originated with the doctrines of the Reformation. The word Protestant is derived from the Latin protestatiomeaning declaration which refers to the letter of protestation by Lutheran princes against the decision of the Diet of Speyer in 1529, which reaffirmed the edict of the Diet of Worms against the Reformation. Since that time, the term Protestantism has been used in many different senses, often as a general term to refer to "Western Christianity that is not subject to papal authority." The doctrines of the Reformation can be summarized as a) the rejection of papal authority, b) rejection of some fundamental Roman Catholic doctrines, c) the priesthood of all believers, d) the primacy of the Bible as the only source of revealed truth, and e) the belief in justification by faith alone.Martin Luther, German leader of the Protestant Revolution, founder of Lutheranism, Protestant theologian, was behind much of Protestant Theology."God does not work salvation for fictitious sinners. Be a sinner and sin vigorously.... Do not for a moment imagine that this life is the abiding place of justice; sin must be committed.""Sin cannot tear you away from him [Christ], even though you commit adultery a hundred times a day and commit as many murders."Excerpted from; http://www.positiveatheism.org/hist/quotes/Luther.htm
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