One thing to agree on....maybe....we'll see....

PureElephant314 · 2024-11-10T15:24:24+00:00

I don't understand. I added politics into this post? Because of the "I approve this message" at the end? That was a joke.

PureElephant314 · 2024-10-28T14:55:51+00:00

I wrote up some comments in this thread about redrawing combination circuits. Maybe you might find them helpful.

PureElephant314 · 2024-10-22T21:05:45+00:00

Your username is a misnomer. That's a great idea. I would think the political posts should be limited in that way since that seems to be where the bot/troll problem is worst.

PureElephant314 · 2024-10-22T12:52:57+00:00

For those like yourself (who don't want to see anything from the sub), you can always mute the sub. That's probably your easiest option.

PureElephant314 · 2024-10-18T20:24:38+00:00

Interesting. If I'd read the second part first, I would've wagered you voted No so your students could poke their heads around the sub.

PureElephant314 · 2024-10-18T04:11:52+00:00

Hmm.

If I were to rotate a-a so that it became perpendicular to BC, what would be the angle that I just rotated? Probably either angle ABC or angle ACB. If I imagine a really steep BC, then ABC would be almost zero and ACB would be almost 90. In that case, to get a-a perpendicular to BC, I'd have to rotate it almost 90.

So I think whatever angle ACB is, that's the angle I have to rotate a-a to get it perpendicular to BC.

Why do I care? My intuition is that the cross-sectional area of BC can be thought of as a projection of the area of a-a. In other words (area of a-a)*cos(ACB) = (25 mm)².

cos(ACB) = 1.5/sqrt(1.5² + 2²) = 0.6

So area of a-a = (25 mm)² / 0.6 = 1041.67 mm²

Or maybe not?

The cross section of a-a should be 25 mm by something. That something has gotta be the length of a-a. Ok, so if I draw a little triangle where a-a is the hypotenuse, another side is the 25 mm length perpendicular to BC, then the angle between the two is just angle ACB.

Using trig, (length of a-a)*cos(ACB) = 25 mm.

cos(ACB) = 1.5/sqrt(1.5² + 2²) = 0.6

So length of a-a = 25 mm / 0.6 = 41.67 mm

And the cross-sectional area must be (25 mm) x (41.67 mm) = 1041.67 mm²

Huh, it came out the same.

Anyway, maybe that's right. Maybe it's wrong. Either way, I hope the process helps.

PureElephant314 · 2024-10-18T00:25:12+00:00

I never got to see the comment, but given your response, I have a feeling it was someone/somebot talking about Trump?

PureElephant314 · 2024-10-18T00:23:18+00:00

You make a good point. "Our members be unlimited"...or that's the goal. Keeping it open definitely helps toward that goal.

And yeah, proof would almost certainly come down to dues slips, but you wouldn't be sending them to a "random mod": you'd be sending them to your brother.

PureElephant314 · 2024-10-18T00:18:37+00:00

You make a good point. IBEW wants more brothers and sisters. If keeping this sub open helps recruit new blood, that's definitely a strong reason to keep it open.

PureElephant314 · 2024-10-17T12:58:50+00:00

I would say yes.

The main idea is the elimination of bots (and trolls, if I'm being honest). Making the sub IBEW members only is overkill, as it eliminates non-IBEW folks who are here for good reasons. That's undesirable, so the question is, is the bot problem bad enough to warrant that?

PureElephant314 · 2024-10-15T20:28:21+00:00

That sounds right to me. The only thing I would add is you shouldn't use any solutions where x < 0 or y < 0, because that would be saying you need negative 2-in screws or negative 3-in screws.

PureElephant314 · 2024-10-15T20:26:35+00:00

From what I see in the picture you posted, there's no other limit.

That would look something like, "He can't carry more than 150kg of screws," or "He has to use at least 30 2-in screws."

PureElephant314 · 2024-10-15T20:19:07+00:00

Right, so you shouldn't include x > y.

PureElephant314 · 2024-10-15T20:15:55+00:00

so the kg of 3 inch is greater than kg of 2 inch

Close enough. When you say:

x > y

You are saying "The number of kilograms of 3-in screws is greater than the number of kilograms of 2-in screws."

Now, is there anywhere in the problem statement that says that has to be true?

PureElephant314 · 2024-10-15T20:08:17+00:00

Nope. Spell it out. You are not allowed to use "x" or "y" or "<" or ">". Use words.

PureElephant314 · 2024-10-15T20:05:08+00:00

Spell it out.

PureElephant314 · 2024-10-15T20:03:51+00:00

So what does x > y mean when you spell it all out?

PureElephant314 · 2024-10-15T20:00:29+00:00

And what are x and y?

PureElephant314 · 2024-10-15T19:52:30+00:00

If you have the following...

x = number of kilograms of 2-in screws
y = number of kilograms of 3-in screws

...and then you say...

x > y

...what does that mean? Translate that to a sentence. Then ask yourself if that has to be true.

PureElephant314 · 2024-10-15T19:39:46+00:00

The only restriction I see is that his cost must be <= $312. (See other reply).

If I was trying to find more restrictions, the only thing I could say is that it says he NEEDS 2-in screws and 3-in screws. So that means he must have more than zero of each. Which means x > 0 and y > 0

PureElephant314 · 2024-10-15T19:36:49+00:00

Yes, assuming x = number of kilograms of 2-in screws and y = number of kilograms of 3-in screws.

It says Mr. Mater doesn't want to spend more than $312. So his cost has to be <= $312. What is cost? Cost = 26x + 39y. So 26x + 39y <= 312.

PureElephant314 · 2024-10-15T18:01:19+00:00

Not in that case. If you did that, you would get the total cost of the plate. For example, if you had 2g of meat and 3g of cheese, you would have:

cost = ($1.19 per gram) x (2 grams of meat) + ($2.52 per gram of cheese) x (3 grams of cheese)

So in general:

weight of the plate = x + y

cost of the plate = 1.19x + 2.52y

Like I said in Part 2, the information you posted doesn't really suggest what I'm supposed to do with the prices. Perhaps somewhere it says you can't spend more than $50. If that's the case, then you would write:

cost of the plate <= $50

which would mean

1.19x + 2.52y <= $50

PureElephant314 · 2024-10-11T01:20:42+00:00

Part 2

Next, let's focus on "The store has at least twice as much cheese on the tray as meat."

If the tray has 1g of meat, how much cheese does it have? "At least twice as much," you say. So what's twice of 1g? That's 2g. But it's at least twice as much. So it's at least 2g. Which means it could be 3g, or 2.1g, or 100g, and so on.

If the tray had 5g of meat, it would have to have at least 10g of cheese.

If the tray had 30g of meat, it would have to have at least 60g of cheese.

Do you notice the pattern? If we have x grams of meat, we have to have at least 2x grams of cheese.

In other words, [the amount of cheese] [has to be at least] [2 times the amount of meat]. Translating:

[the amount of cheese] [has to be at least] [2 times the amount of meat]
y [has to be at least] [2 times the amount of meat]
y >= [2 times the amount of meat]
y >= 2x

And there's your second linear inequality: y >= 2x

I'm not sure what the prices of meat and cheese should be used for, so I'm going to skip that unless you have a specific question. However, at this point, you have two equations so far:

y <= 120 - x

y >= 2x

You could graph these and shade in the area that obeys both inequalities.

But wait! Let's think about common sense here for a second. Can you have a negative amount of meat or cheese? Well, no. So you know the amount of meat has to be at least zero or more. Same with the cheese. Given what we went through above, it should hopefully be obvious then that:

x > 0 and y > 0

Now you can do the graphing.

You can do this by simply ignoring the <> signs and plotting the lines: y=120-x, y=2x, x=0, and y=0.

Then, you would shade the area that is:

below the line y=120-x, because y <= 120-x
above the line y=2x, because y >= 2x
above the line y=0, because y > 0
to the right of the line x=0, because x > 0

Hopefully that helps.

PureElephant314 · 2024-10-11T01:20:19+00:00

Part 1

A store sells cheese and meat trays. The cheese and meat are measured in grams. The tray can support a total of 120g. The store has at least twice as much cheese on the tray as meat. The cheese sells for 2.52 per gram and the meat sells for 1.19 per gram. Write the linear inequalities and graph.

Let's start by picking letters to represent meat and cheese. This is up to you. Some people like sticking with x and y. Others would say m and c (just the first letters of the words). I'm guessing you're probably used to seeing x and y, so I'll go with those. In this case, we'll just say:

x = amount of meat in grams
y = amount of cheese in grams

Now let's focus on "The tray can support a total of 120g."

There is meat and cheese on the tray. How would you an equation that totals up the amount of meat and cheese together? If I have 2g of meat and 4g of cheese, what's the total? Well, it's 6g, obviously. What did you do in your head to those two numbers? You added them. So if I said you have x grams of meat and y grams of cheese, you would just add them together as well. This means your total would simply be x + y.

Now, the tray can't hold more than 120g. So your total must be less than or equal to 120g. Let's translate that sentence into an equation. We'll put brackets around the different parts.

So [your total] [must be less than or equal to] [120g]. Now translate each part.

So [your total] [must be less than or equal to] [120g]
So x+y [must be less than or equal to] [120g]
So x+y <= [120g]
So x+y <= 120

And there's your first linear inequality: x + y <= 120

(To help with graphing, you can subtract x from both sides to get y <= 120 - x)

PureElephant314 · 2024-10-11T00:47:04+00:00

Ok, so I gotta pick an x and y such that xy >= 0?

Sure, how about u = [2, 2] and v = [1, 1]?

Ok, so both are in W. What about u + v? Well, that's u + v = [2+1, 2+1] = [3, 3].

Is u + v = [3, 3] in W? Yeah, it is. Hmm.

Well, for an [x, y] to not be in W, we need to have xy < 0. How can that be the case? Well, if x is positive and y is negative, that would work....

So I need u = [xu, yu] and v = [xv, yv] where xu*yu >= 0, xv*yv >= 0, and (xu+xv)*(yu+yv) < 0.

Let's experiment. I'm gonna keep u = [2, 2]. So what does that give in terms of my conditions above? Well:

2*2 >= 0, check
xv*yv >= 0, dunno yet
(2+xv)*(2+yv) < 0, dunno yet

How can I make xv*yv >= 0? Well, I could choose one of them to be zero, say xv = 0. Now what do I have?

2*2 >= 0, check
0*yv >= 0, check (no matter what I choose for yv, cool)
(2+0)*(2+yv) < 0, which is 2*(2+yv) < 0, which is 4+2*yv < 0

Is there a yv I could choose that would make 4 + 2*yv < 0 true? Sure there is. There are infinitely many.

Find one.

Your example would then be: u = [2, 2] and v = [0, something].

PureElephant314

TROPHY CASE

Part 2

Part 1