OldChemE

The title question and the discussion seem to be at odds. Parallel lines (the title question) being massless creations of geometry do not converge-- ever. The only exception is in art, where an artificial convergence point is selected for parallel lines in order to create the illusion of perspective. But, in fact the parallel lines do not converge. Beams of light, on the other hand, being subject to gravity, would presumably converge at some point (assuming they started out parallel but close enough for the very small gravitational effect to bring them together). The problem is proving this by experiment-- for all the reasons given above.

I appreciate the responses-- but I don't think the question has been answered. If x = 1 and y = 3 then the GCF of x2y2 becomes 9, which does not satisfy the constraints of the problem. If x = 3, then the GCF of both terms becomes 81, which does not satisfy the constraints of the problem. If x = square root of 3, then the GCF constraint is satisfied, but x then is not a positive integer, which violates the other constraint of the problem. I'm still trying to understand how both constraints of the problem (x and y both positive integers, and the GCF of both terms = 27) can be satisfied with the available answers.

The arrangement of elements in the periodic table was done before we had extensive knowledge of electron orbitals and all that. The original(s) of the periodic table were based on atomic weights and the reactive properties of the elements, not their electron structures. The Halogens all have nearly complete outer electron shells (missing only one electron), and are rather aggressive about stealing an electron to fill that outer shell. Thus, they tend to form ions with a -1 charge. That led to the classification called halogens. Technically, Hydrogen is also just 1 electron away from filling its outer (and only) electron shell, but Hydrogen usually (but not always) gives up one electron forming a +1 ion instead of stealing a second electron-- a behavior more like lithium, sodium and the others in its group.

In my spare time I work as a substitute teacher. In High School math today, students were working on a standardized practice test to prepare for the ACT exam. The following question baffled me. Given x and y are positive integers, such that both x2Y2 and xy3 have a greatest common factor (GCF) of 27, which of the following could be a value of y? The available answers are 81, 27, 18, 9 and 3 I ruled out 81, 27, 18 and 9 as values of y because in all cases y2 would be greater than 27, so the GCF could not be 27. It appears the intended answer is y = 3. However, if y = 3, then x2 y2 becomes 9x2. In order for this to have a GCF of 27, x2 must contain at least one factor of 3. If x2 contains a single (or odd number) factor of 3, then x must contain a factor of square root of 3, and x will not be a positive integer, which violates the problem statement. If x2 contains two (or an even number) factors of 3, then x will contain one or more factors of three, and the GCF will be at least 81, which violates the problem statement. What am I missing?? Any thoughts? Thanks

I too agree that given sufficient time the works would be reproduced-- but there is no guarantee that the works would be produced in any finite time. The catch is that, if the letters are being produced at random, multiple repetitions of previously produced patterns may occur. In other words, this is different from a computer produce methodically working through all the permutations of letters. Thus, we can posit that the works of Shakespeare will eventually be produced but we cannot know that it will occur within any arbitrarily large finite time.

he example of 6 + 6, 4 + 8 and 8 + 4 is different from 6 bolts and 6 nuts, 4 bolts and 8 nuts and 8 bolts and 4 nuts because the first set are pure numbers, the second are things. In other words, let x = bolts, y = nuts. Then your two examples form to : Numerical equivalence: 6 + 6 = 4 + 8 = 8 + 4 But for nuts and bolts 6x + 6y does not necessarily equal 4x + 8y which does not necessarily equal 8x + 4y Said differently, that which holds with pure numbers need not hold when representing numbers of things.

and-- it seems like locating based on IP addresses can be faulty. In Northern Nevada where I am we get our internet via a large cell phone provider. Every time we try to check to see if something we want is available at Walmart the internet links us to a store 500 miles away in California. I'm wondering is this has to do with the way IP addresses get assigned.

RoadPro model RP12SB Not to advertise the product, but my wife bought one several years ago-- just the size to hold a 12 pack and plugs into the 12 volt car outlet-- keeps everything cold just fine.

Seems like it should be easy if you just set up the permutations in a spreadsheet and plug in the formula-- maybe I'll play with it later.

The bottom line is that there is not astronomical significance. But-- if you want to count years, you need to start somewhere. Jan 1 as the beginning of the new year is an artifact of human history that is currently accepted by a large segment of human population. The rest of the universe doesn't care one way or the other.

ok-- I see it

hey-- you asked for viewpoints and you got mine-- no harm. It really is your decision and nobody else's. The important thing is that you don't let it lead to a case of short-term gratification that leads to long-term regret. Only you can decide. Regardless of which way you go, good luck!

There are many reasons to stay in High School-- that far outweigh the value of a GED. Admittedly, education in High school is sort of a 'shotgun' approach-- exposing you to many topics when some will have no importance in your future life. The catch to this is that the brain structure continues to evolve during the teen years, and many, many of us don't know what we will most want to do in our later life until we get there. Something which bores you today can likely end up being the foundation for something that, 5 years from now, will be important (this will be the point when you admit to yourself "Damn-- I should have finished High School"). Additionally, those who hire the really highly skilled people would like to see evidence that you are mentally strong enough to finish what you start-- even when it takes a long time (as many real-world problems do). Finishing High School is just one more proof that you can stick it out. If you cannot stick it out in High School, what makes you think you can stick it out in College? College degrees also require you to take courses outside your specialty-- and they can be equally boring. The GED is just a test of basic knowledge. It does not cover the wealth of added information and exposure to different fields of work that High School can provide you. That's why a High School diploma is valued higher than the GED.

I found the "Pulling off a Nixon" comment interesting-- in how our minds rewrite history based on our conceived notions. Nixon did not extend the war-- see below (from history). Nixon was sworn in as President in January 1969 for his first term-- He immediately started reducing US involvement in the war. I was in the military at the time and was very happy to know I was unlikely to be sent to Vietnam. During Nixon's term as Vice President he spent time on missions to China. He understood that the Vietnam war was a bad idea. He lost his office for good reasons-- the the war was not one of them. The withdrawal was almost complete by the time of the 1972 election. History Channel-- timeline of the Vietnam war: • 1969-1972: The Nixon administration gradually reduces the number of U.S. forces in South Vietnam, placing more burden on the ground forces of South Vietnam’s ARVN as part of a strategy known as Vietnamization. U.S. troops in Vietnam were reduced from a peak of 549,000 in 1969 to 69,000 in 1972.

You have two different metals in an acid bath--look that up in a chemistry book

It can be done-- but it seems sufficiently rare as to be insignificant. I say it can be done because in one recent election I simply showed the poll worker that I had my sample ballot in my hand and they handed me a voter card-- never checked my name or had me sign anything. I suspect this was a moment of carelessness, not a normal practice.

Air is roughly 80% Nitrogen already-- so even if you filled one tire entirely with air, the difference is only 100% vs 80%. Also, Nitrogen and Oxygen have similar properties. I haven't done the math but suspect the difference between 80% nitrogen and 100% nitrogen is trivial from a pressure standpoint. Maybe someone who has the numbers will weigh in on this (and correct me if I'm wrong).

Explaining something in simple terms takes more than knowledge-- it is an art. I've known some brilliant people who knew their subject so completely that the many qualifications and exceptions made it impossible for them to explain things in a simple fashion. Being able to simplify without leaving out key concepts is difficult.

Essentially, what you are proposing is a huge boat that you would allow to fill with rain water. Once it fills beyond a certain point, (determined by buoyancy) it will sink-- unless it is supported from below. The feasibility of that support will depend on the depth and/or technology used to support it (pontoons or equivalent). I don't really know-- but I suspect the cost would far outweigh the cost of simpler solutions such as desalinization.

Regardless of the politics and debates, there is at least one practical reason why a civil war is unlikely in the US: territorial boundaries. For a civil war to be practical you need large areas under the control of one idealogy that have a boundary with those of another. Here we have cities that trend toward liberal views surrounded by urban area with more conservative views. That's not a very practical situation for civil war.

Depends on how small you mean by miniature. The reactor in the research submarine NR-1 is about 6 ft in diameter and not a lot taller. But then you need the control rod drives, recirc pumps and, of course, some way to use the power (traditionally a heat exchanger and steam turbine).

Yes Ghideon-- I didn't think of that.

I'm somewhat sympathetic to the OP. When I taught high school physics it always bothered me that the SI units-- while inherently easy to use, were clouded by the naming-- which made it more difficult for the students to grasp their significance. We confuse the students with Newtons when we mean kg-m/second squared, Joules when we mean kg meters squared per second squared. This makes the learning process more difficult when we are faced with a problem where the inputs are in basic units like kg, m , s. Yes, it can be learned, but it makes in inherently clean system of units cloudy.

You can get much more of an appreciation (good or bad) of the taste by drinking beer at room temperature. Chilling tends to hide some of the flavor. As for Guinness-- definitely a good one. slightly off topic: In 1977 or so I was at a outdoor party in Switzerland with a lot of British, American and other mostly English speakers celebrating the Queen's Jubilee. The beer booth consisted of a stand in the soccer filed with all the beer sitting in cases on the grass (not chilled). The man selling the beer was English. So, when he asked me what I wanted I said "any good English beer." At that point an Irish voice came from over my shoulder: "There isn't any! Have a Guinness." I later learned there are many excellent English Brews-- but that day it was Guinness.

13, not 2-- the sums of odd numbers are along the lines, so the center number should be the sums of the diagonally opposite odd numbers. In both diagonal directions the odd numbers are 9, 3 and 1 which add to 13. That is the odd numbers in 613 add to the odds in 492, and the odds in 389 add to the odds in 841.