# Homework FAQ

#### Minuend

##### pat pat
Or something like that.

So here we ask all questions regarding homework. I shall give you an example by asking the first question:

Why do we need a medium like agar when growing bacteria? Why can't it just lie down on the nakid petri dish? I mean, if bacteria are unable to break down agar, then nutrition can't be the answer. Unless they are able to absorb some nutrition without the gel becoming liquidfied? Perhaps that's what they mean?

Edit: Okay I went over my notes and forgot that we used a mix of agar with nutritions, so I assume my previous assumption was correct? I read something about using a solid because liquid could make the petri dish foggy. But is that the only reason for using solids?

#### Minuend

##### pat pat
Well, apparently micro organisms have the ability to absorb nutrition outside themselves. So there goes. They take nutrition from the agar without breaking it down. Solved.

#### Minuend

##### pat pat
Hello my good people.

Anyone have any experience with Casio calculators? I can't for the life of my figure out how to write that inequality symbol ≤.

There is a button for <

I can't find > either. Which is ridiculous.

#### Lostwitheal

##### Mr. LoveRobot
What model is it? I'm sure we could abuse Google into yielding the product manual.

Hopefully not in French

#### Jah

##### Mu.
I can't find either of those on my Casio.

#### Lostwitheal

##### Mr. LoveRobot
[ne] is the "not equal" operator found in the PRGM | REL menu.
[le] is the "less than or equal" operator found in the PRGM | REL menu.

#### Cognisant

##### Prolific Member
Hello my good people.

Anyone have any experience with Casio calculators? I can't for the life of my figure out how to write that inequality symbol ≤.

There is a button for <

I can't find > either. Which is ridiculous.
There should be a function button like func, shift, alpha or mode that enables the same keys to have several different uses.

It should have come with a manual, if you bought it recently and it didn't come with one try returning to the store you bought it from and asking (politely) if you can check if it was supposed to come with one, and if it was if you can photocopy the one you found. Better still if you have you're receipt and the box your calculator came in they'll usually just swap it for a new one (that's not a guarantee mind you, don't walk in there expecting it), manners and a smile really help with this sort of thing.

Sales assistants are a grumpy lot.

Edit:
[ne] is the "not equal" operator found in the PRGM | REL menu.
[le] is the "less than or equal" operator found in the PRGM | REL menu.
Or you can ask someone who evidently knows what they're talking about.

#### Minuend

##### pat pat
I don't understand tat losty :~(

And it didn't come with a user manual.

I'll try google one in the morning as I need to figure out how to use lim.

Thanksy

#### Lostwitheal

##### Mr. LoveRobot
That may not pertain to your specific calculator.

You could always take a photo of your calculator and nose - that might help us figure it out

#### Minuend

##### pat pat
NO NUDES FOR YOU

I do think I can use [ and (. Oh, it's been such a long time since I've been doing mathematics, I've forgotten simple things.

I think I'll need more chocolate if I'm going to do this.

*Off to store*

#### Cognisant

##### Prolific Member
Don't focus too hard or you'll warp reality and the maths won't work anymore.

#### Minuend

##### pat pat
Does that mean I get to take a break now? Yayyyyy for coggie.

#### GYX_Kid

##### randomly floating abyss built of bricks
We should offer exchange deals for doing each others' homework assignments here, or something.

#### Reverse Transcriptase

##### "you're a poet whether you like it or not"
GYX: yes! Except I'm out of school now. At best, I might be doing a masters program in the next few years.

But I do have a degree in biochemistry, sooooo

Yes, Agar is made from seaweed extract and forms a "scaffolding" for bacteria & fungi to live in. We could use straight water, but then it would slosh (and you're right-- it would also get foggy on the surface). Agar is still mostly water, and the bacteria treat it as such. The nutrients in the agar are absorbed by the bacteria (yup) and that's how they live/grow.

Sometimes cells accept nutrients by having large cell membrane pores that absorb anything that's out there, and sometimes they have transport proteins that selectively choose which molecules to bring in. In certain scenarios, there are large pores that have "chaperones" transporting material back and forth. (The pores of the nuclear membrane act this way.)

#### Minuend

##### pat pat
I see

Bah, I'm kinda behind on calculus and I have an assignment due tomorrow. I'm trying to get through what I need to to finish the assignment,, but if anybody has any take on this, I'd appreciate it:

Mold grows in petri dish. Part of dish covered after t hours:

A(t) for 0 < t < 20

Okay, I'm not getting this. 0 < t < 20 indicate that the graph is decreasing, right? But according to the text, that formula shows the part (percentage) that is covered after t hours. I would think that more of the petri dish gets covered after time and thus I would have something that is increasing.

Question one is "calculate how many hours that passes before 99% of the dish is covered by mold".

#### Jah

##### Mu.
well... it's easy to see that at t=10, A(t) = 1/2..

E^0 = 1

so I'm guessing you're looking for when A(t) = 0.99
That means you probably should just solve it for e^x where (x) = (10 - t)

so, you say: ( 1/0.99 ) = 1 + e^x, or e^x = 1/0.99 - 1

x = ln (1/99)

x = - 4,59

and then you get that 10 - t = -4.59 or t = 14,59

the 0 < t < 20 means that the time (t) should lie between 0 and 20.

* I think it can also be written as ( | t - 10 | < 10 )

#### Minuend

##### pat pat
THANK YOU NOW I CAN GO TO SLEEP

At least for 5 hours or so.

Now it's been a while since I had math, so did you flip the numerator from
1/ 1 + e^x to the other side making 1/0.99?

I have been wondering if you are allowed to have the numerator just flip sides like that.

Or is 1/0.99 some form of expression for percentage?

I have been dragging along ^10-t all the time, trying to divide it, multiply it, derive and what not. Now it makes sense.

#### Puffy

##### Aquila
How about humanities homework?

I have to write an 800 word commentary on a source depicting Queen Elizabeth I's entrance into Worcester...

Yeah, you're right, I'm sorry.

#### Jah

##### Mu.
THANK YOU NOW I CAN GO TO SLEEP

At least for 5 hours or so.

Now it's been a while since I had math, so did you flip the numerator from
1/ 1 + e^x to the other side making 1/0.99?
Hmm.. I switched the places of the two, yes. (actually it's done by first multiplying each side with (1+e^x) and then dividing both sides with 0.99)

Starting with:
0.99 = 1 / ( 1 + e^x)

You multiply the whole thing with ( 1 + e^x) getting:
0.99 ( 1 + e^x) = 1

Then divide with 0.99 so you get:
(1 + e^x ) = ( 1 / 0.99 )

Then you subtract the 1 :
e^x = ( 1 / 0.99) - 1

and you get:
e^x = 0.01010101...

which you can simplify to 01/99 or 1/99 (when you have recurring numbers after 0 they can be simplified by dividing the recurring number e.g. (01) by an equal number of 9's (so in this case 99) Another example: 0.343434... = 34/99 and so on.. handy for this stuff )

and of course: (ln (e^x)) = x
so:

ln e^x = ln 1/99 = -4.595 = x

then you just put that into the original variable (unknown) ( 10 - t )

10 - t = x <--- (x = -4.595)

- t = -4.595 - 10

- t = -14.595

multiply by -1 (or switch places.)

t = 14.595 ( ≈ 14.6 )

It helps to simplify the expression first, I think.

#### Minuend

##### pat pat
Thanksies ^^

I got up at 6 today, but I didn't really manage to solve much else. I hope it is enough to pass though. I don't know how strict they are or whether they allow second chances...

#### Melllvar

##### Banned
I have a really random question someone somewhere might know the answer to:

Neural networks - approximate non-linear functions by adjusting weights between connections in the network
Evolutionary search techniques - semi-randomly adjusts parameters until finding a possible optimal solution to the problem.

Isn't the latter group, like genetic algorithms and stuff, just doing the same thing as the former, but via a different method with different limitations? So basically they're just being used for non-linear function approximation? Are all AI techniques just searches for an optimal function out of a solution space of all possible functions, and the only real difference is how they search for that optimal function?

Been thinking about this a few days and I'm not entirely sure, but I'm expecting the answers are "yes, yes and yes."

#### Reverse Transcriptase

##### "you're a poet whether you like it or not"
I have a really random question someone somewhere might know the answer to:

Neural networks - approximate non-linear functions by adjusting weights between connections in the network
Evolutionary search techniques - semi-randomly adjusts parameters until finding a possible optimal solution to the problem.

Isn't the latter group, like genetic algorithms and stuff, just doing the same thing as the former, but via a different method with different limitations? So basically they're just being used for non-linear function approximation? Are all AI techniques just searches for an optimal function out of a solution space of all possible functions, and the only real difference is how they search for that optimal function?

Been thinking about this a few days and I'm not entirely sure, but I'm expecting the answers are "yes, yes and yes."
My answer is: "almost yes!"

There's a few key differences. Neural networks are artificially hosted, so the selection constraints and mutation rates are whatever we want them to be. Whereas, anything living doesn't have the luxury of being hosted in memory. Extinction is a real possibility, so every mutation/step between point A and point B has to be a viable organism. Neural networks allow a lot of "failed" steps, because you need that many steps to find a good solution.

So, that's why our genomes encourage duplication of genes. And not just duplication by having two sets of chromosomes, but duplication within the genome. There's a cell membrane signaling protein complex called G-protein. You have a lot of different kinds of G-proteins, that each register a different molecule/hormone/protein/whatever. Although there are also some duplicates. The whole design of G-proteins was so successful that they make a significant % of your total signalling proteins. If I had to guess I'd say 30%... but I'm just going with my gut feeling there.

http://en.wikipedia.org/wiki/G_protein-coupled_receptor

There are elements within our genome that encourage movement & duplication within our genome, because having extra proteins to "play" with gives us better chances of finding a new protein that will be really really useful!

~ramble

#### Cogwulf

##### Is actually an INTJ
I don't suppose anyone here happens to know the composition of the gamma prime phase in the alloy IN939?

#### Melllvar

##### Banned
My answer is: "almost yes!"

There's a few key differences. Neural networks are artificially hosted, so the selection constraints and mutation rates are whatever we want them to be. Whereas, anything living doesn't have the luxury of being hosted in memory. Extinction is a real possibility, so every mutation/step between point A and point B has to be a viable organism. Neural networks allow a lot of "failed" steps, because you need that many steps to find a good solution.
Well, I was thinking of the ones from computer science, in both cases. In either case though, recombination and mutation is what helps keep the search algorithm from getting stuck at any non-optimal point. Recombination allows the algorithm to 'jump' around in the solution space, where as small scale mutations only allow short movements. In either case though the new solution has to survive whatever selection pressures exist, whether it's in comp sci or biology. Neural network weights can be trained by either method too, gradient based ones or random or evolutionary ones, and some aren't necessarily any better at not getting stuck at local optima, I think.

I was more wondering to what extent all solutions to all problems could be viewed as 'non-linear function approximation'. I'm guessing this is mostly true, although 'function' might not be the most correct word, as the basic idea behind any kind of problem solving is f(input) -> output. It's really in the broadness of the concept.

Reverse Transcriptase said:
So, that's why our genomes encourage duplication of genes. And not just duplication by having two sets of chromosomes, but duplication within the genome. There's a cell membrane signaling protein complex called G-protein. You have a lot of different kinds of G-proteins, that each register a different molecule/hormone/protein/whatever. Although there are also some duplicates. The whole design of G-proteins was so successful that they make a significant % of your total signalling proteins. If I had to guess I'd say 30%... but I'm just going with my gut feeling there.

http://en.wikipedia.org/wiki/G_protein-coupled_receptor

There are elements within our genome that encourage movement & duplication within our genome, because having extra proteins to "play" with gives us better chances of finding a new protein that will be really really useful!

~ramble
That was interesting too though.

#### Minuend

##### pat pat
Yo. Noob question, an easy one.

My textbook:

(G = mg)

81kg * 9,81 N/kg = 0,79 kN

So, if you multiply 81 and 9,81 we get 794

So how and why do they move the comma left?

It's probably obvious, but the obvious is usually what I don't understand..

I assume they are converting units, but I don't know how and why

#### Awaken

##### Gone for good
Yo. Noob question, an easy one.

My textbook:

(G = mg)

81kg * 9,81 N/kg = 0,79 kN

So, if you multiply 81 and 9,81 we get 794

So how and why do they move the comma left?

It's probably obvious, but the obvious is usually what I don't understand..

I assume they are converting units, but I don't know how and why
kg x N/kg gives an answer in N. 1000N=1 kN, so to get the answer in kN you divide by 1000. So, it would be 794 N or .794 kN

Side note: That is interesting. I am used to periods instead of commas. I was so confused at first.

Not a homework question, but it popped in my head while doing this. What is the name of the chart/method of converting units as seen below. I remember learning it in school but cannot remember the name of it and it will bother me all day.

xkN= 794 N/blank x 1kN/ 1000 N=.794 kN.......except in a sort of column/row format so you can easily cancel out units that are in the numerator and denominator.

#### Minuend

##### pat pat
Ahhhh, of course XD

Though, why would one go through the trouble of converting N to kN? Is it just because we (by "we" I mean the human race, apparently) like smaller numbers? Because I think N is better-looking single.

Yeah, I forgot Americans and stuff use .

#### Cogwulf

##### Is actually an INTJ
Ahhhh, of course XD

Though, why would one go through the trouble of converting N to kN? Is it just because we (by "we" I mean the human race, apparently) like smaller numbers? Because I think N is better-looking single.

Yeah, I forgot Americans and stuff use .

Something like 0.123kN is harder to use than 123N, it doesn't really make sense in this case. It does make sense if you're writing 123MN instead of 123000000N

#### Awaken

##### Gone for good
No idea on that one as the gravitational constant is usually given in Newtons. Perhaps it is just in your textbook like that to remind students how to convert units?

#### Minuend

##### pat pat
Textbooks are weird.

Thanks a bunch ^^

#### Jah

##### Mu.
hmm.. well that's not gravitational constant, but gravitational acceleration at the face of the earth.
(or : g * (Mass of Earth)/(radius of Earth)^2 where the g is the gravitational constant of approx 6.67 * 10^(-11) )

http://www.wolframalpha.com/input/?i=gravitational+acceleration

Btw. if you want to simplify it, for future calculations; Use the approximation of 10 N/kg.
Especially if what you're doing is just theoretical.

If you get any hassle over that, just point out that the other number hidden in the equation (the Mass of the earth) is astronomical, and bound to carry imprecision anyway.

Same trick for electric fields; use 9*10^9 (which approximates Coloumbs constant) rather than the whole 8.98..somethingsomething

#### Minuend

##### pat pat
I think our professor said that we would use 10 as that was the one used in the book. But our book doesn't use 10. I figured it be easier knowing whether my answer is right.

Btw, anyone know how p1/T1 = p2/ T2
=
P2 = T2/ T1 * p1

I thought it would be p1/T1 * T2 = p2

#### Otherside

##### Active Member
Hello my good people.

Anyone have any experience with Casio calculators? I can't for the life of my figure out how to write that inequality symbol ≤.

There is a button for <

I can't find > either. Which is ridiculous.
Not sure of your major, but a HP48 is an awesome calculator.

#### Melllvar

##### Banned
Btw, anyone know how p1/T1 = p2/ T2
=
P2 = T2/ T1 * p1

I thought it would be p1/T1 * T2 = p2
Assuming those don't signify anything special, should be the same. The bottom just makes more sense because you're multiplying by T2 on both sides.

a/b = c/d --> (a/b) * d = c = (ad)/b = (d/b) * a

For real or complex valued variables, at least.

#### Otherside

##### Active Member
Assuming those don't signify anything special, should be the same. The bottom just makes more sense because you're multiplying by T2 on both sides.

a/b = c/d --> (a/b) * d = c = (ad)/b = (d/b) * a

For real or complex valued variables, at least.
P2 = T2/ T1 * p1

I thought it would be p1/T1 * T2 = p2

They are the same thing and would more typically be written

P2=(T2*p1)/T1

#### Awaken

##### Gone for good
P2 = T2/ T1 * p1

I thought it would be p1/T1 * T2 = p2

They are the same thing and would more typically be written

P2=(T2*p1)/T1

What otherside said. I think you are confusing the properties of fraction multiplication.

The books answer is P2=(T2/T1)(P1/1)

You are saying the answer is P2=(P1/T1)(T2/1)

When you simplify the multiplication of both fractions in the two examples, you are saying the same thing. P2=(T2)(P1)/T1

#### Otherside

##### Active Member
Something like 0.123kN is harder to use than 123N, it doesn't really make sense in this case. It does make sense if you're writing 123MN instead of 123000000N
At the collegiate level, you would almost always write it as 1.23x10^8 N

#### Melllvar

##### Banned
Well, if I have to defend my answer, technically they're applying the associative property after multiplying both sides by T2:

(p1 * (1/T1)) * T2 = p1 * ((1/T1) * T2)

.. which lets them rearrange it to p1 * (T2/T1) = p2. Presumably because they wanted to represent the solution as a ratio of the two T variables, which would make more sense if the T2/T1 ratio had some associated meaning (ratio of two masses, velocities, or something).

Point being Minuend's answer technically skips an extra use of the associative property, which is why I said it "made more sense" that way.

#### Otherside

##### Active Member
Well, if I have to defend my answer, technically they're applying the associative property after multiplying both sides by T2:

(p1 * (1/T1)) * T2 = p1 * ((1/T1) * T2)

.. which lets them rearrange it to (T2/T1) * p1 = p2. Presumably because they wanted to represent the solution as a ratio of the two T variables, which would make more sense if the T2/T1 ratio had some associated meaning (ratio of two masses, velocities, or something).

Point being Minuend's answer technically skips an extra use of the associative property, which is why I said it "made more sense" that way.
Sounds like an ideal gas problem:

PV=nRT In a closed system where n (moles) is constant (R is always constant).

P2=(T2*p1)/T1

is telling you that final the pressure (P2) is proportional to the final temperature (T2) and the initial pressure (P1), and inversely proportional to the initial temperature (T1).

#### Minuend

##### pat pat
Yes, I'm working with ideal gases. I understand what it means, but I still don't unders how you knock p1 off T1 mathematically.

#### Awaken

##### Gone for good
What do you mean by "knock P1 off T1"? Do you mean, how do you rearrange an equation so that one specific variable is on one side of the equation by itself?

#### Melllvar

##### Banned
Yes, I'm working with ideal gases. I understand what it means, but I still don't unders how you knock p1 off T1 mathematically.
If you mean how p1/T1 = p1 * (1/T1), it's because division is equivalent to multiplication of the numerator by the multiplicative inverse of the denominator.

E.g. 7/36 = 7 * (1/36) = 7 * 36^-1

Really you don't even need division as a separate thing, it can be defined completely in terms of multiplication.

#### Minuend

##### pat pat
Oh, so you just separate p1/T1 to 1/p1 and 1/T1 and then clash together T2/1 and 1/T1 (for convenience).

I kinda suspected that.

Thanksies ^^

#### Awaken

##### Gone for good
I think you are over complicating it.MellIvar was saying that the process of dividing something is the same as multiplying that something by the inverse of what you are dividing by. Which means you can "separate out" the left side of the equation by restating it in terms of multiplication.

For example, P1 divided by T1 is the same thing as P1 times 1/T1.

*I hope I am actually answering what you are asking. I am not familiar with your usage of "knock off" or "separate" so I am assuming it means what I think it means.

#### Minuend

##### pat pat
Aha, I see.

"Knock off" is something I said instead of "taking the top part off the bottom part". Like "clash together" instead of "putting together".

#### Otherside

##### Active Member
one is one, any way you look at it.