Need Math Help?

[Corpsecreate]

Another argument I have with my lecturer and I am coming here to seek extra opinions.

The question is as follows:

There are 5 Patrol Cars available that can be allocated to 3 different Precincts. The more cars allocated, the lower the crime rates are in that area. The crime rates for each precinct are given for the number of patrol cars allocated.

Patrol Cars | 0 1 2 3 4 5
Precinct 1 | 14 10 7 4 1 0
Precinct 2 | 25 19 16 14 12 11
Precinct 3 | 20 14 11 8 6 5

The question is: "Use dynamic programming to determine the optimal allocation of Patrol Cars".

Now, the argument is here. I used dynamic programming and I obtained the optimal allocation. There are in fact 5 different set of allocations that are all equally optimal. My allocations are correct and are exactly the same as what my lecturer gets. The problem lies in the fact that I didnt state what the minimum value is with the optimal allocation. I didnt add this in because the question doesn't ask for it.

Do I deserve full marks for the question or is it reasonable for me to have my mark deducted because I didnt answer a question that wasnt being asked?

 

[Elyssa Xey Hexen]

Depends. Many tests are graded on things you are expected to take into consideration.

If you use substitution in an indefinite integral (single variable) and are expected to evaluate the integral, you are expect to revert that substitution back to its original form. Your answer in the substituted form might be equivalent to the original variable, but you are typically required to be in terms of the original variable even if the questions does not ask for it. In this case, points are most likely going to be taken off.

So, if you were expected to have listed that detail because the instructor emphasized it as an assumption, then you can hardly complain about getting points taken off.

Either way, it sounds like a rather trivial detail that wouldn't be worth many points off even if you did argue for them back. But do you feel slighted and want that full mark? Argue for them back then and at least say you gave the effort?

 

[Corpsecreate]

using substitution is 'changing' the question though so it makes sense you would have to revert it back to its original variable. The integral of a new function in terms of a new variable isnt the really the solution to the original function.

In this case of this question, the question is exactly as I quoted it, so there is no emphasis anywhere that this information is being asked for. Ultimately, losing that mark costs me 0.2% of the whole unit, which is almost nothing, the reason I am angry about it is because I feel that I was cheated off that mark. Its not the first time this has happened to me either.

The only reason I didnt put that optimal value in was because the question didnt ask for it. Its not that I wasnt able to find it or anything so why should I lose marks. In fact, in the process of finding the optimal allocations, you need to find the optimal value anyway. I do have the value on my page, its just not explictly stated as "The minimum number of crimes is - 37".

 

[Faithkeeper]

Do I have to know highly advanced math to understand Large Cardinals? I understand the basics of WHAT they are, but I want to understand WHY they are. I don't know if that makes sense. But I think I will need to know more math to really understand why.

Math is interesting, I'm decent at it, but I haven't taken any advanced classes and don't have room for more than one throughout my next three years of study. I'm a Behavioral Neuroscience major that effectively only has an american public high school math background. :/ Thanks.

Btw, anyone know any good sites to teach yourself math? Thing is, I'm only actually interested in the "why." I'm not so interested in being able to identify situations to use various equations or methods. I want to understand why the equations and methods work. I should be able to understand how to apply them from there. I'm not sure if math is even taught like that, and if it isn't, oh well.

 

[terr13]

It's kind of weird. Advanced math is all proofs, and if you're give any equation it's probably so pivotal that you had better not forget it. However, each branch of mathematics is completely different, and for the most part unrelated. To be honest, everything you need to learn you can learn from wikipedia.

 

[Corpsecreate]

You have 2 paints, paint X and paint Y. Your goal is to combine these paints together to form paint Z. Each paint has 3 coloured tints associated with it, A, B and C. The value of these tints corresponds to the amount there is per litre. So A = 7 would mean that there is 7 units of A for every 1 litre of paint X.

Paint X
A: 3
B: 3
C: 1

Paint Y
A: 4
B: 6
C: 1

Paint Z
A: 12
B: 9
C: 2

One thing to be careful of when adding paints is that the amount of paint increases. For instance X + Y would yield 7A, 9B and 2C in 2 litres, so the real values of their combination is 3.5A, 4.5B and 1C as it must always be standardized down to 1 litre.

(1) show that no combination of paints X and Y can give paint Z.
(2) find the combination of X and Y so that their combination is as close as possible to Z.

 

[terr13]

It's a system of 3 equations, you can just show there is no solution to that system and then try to find the closest possible number.

 

[Corpsecreate]

Yes however the equations are not these:

3x + 4y = 12
3x + 6y = 9
x + y = 2

For the equations I get:

3x^2 + 7xy + 4y^2 = 12
3x^2 + 9xy + 6y^2 = 9
x^2 + 2xy + y^2 = 2

And how do you find the closest number?

 

[1048576]

Wait, you want 12 units of tint A in 1 liter of paint Z? Cause that's obviously never gonna happen. The most you can have is 4. Looking at X and Y, just using 0-X and 1-Y is trivially closest, since all values of Y are equal to or closer than the target than X.

I imagine the intent of the problem is to allow you to make as much paint as you want, and then try to match the total amount of A, B, and C, since then it becomes meaningful. If you make that assumption, then your first batch of equations is correct. Now it's a matter of what do you mean by "closer." Do you want the closest ratio, or do you want the closest total? For example, which is closer to A:1 B:2 C:3? Is it A:10 B:2 C:3, which is off by 10X the amount of A but only 9 units of A? Or is it A:1 B:2 C: 21, which is off by only 7X the amount of C, but 18 units of C.

Going by the former, you have to find min(abs(([3x + 4y] / 12) - 1) + abs(([3x + 6y] / 9) - 1) + abs(([x + y] / 2) - 1))

If it's the latter, you have to find min(abs(3x + 4y - 12) + abs(3x + 6y - 9) + abs(x + y - 2))

 

[Corpsecreate]

The "closest" is the the resulting paint which is most similar in colour to the desired paint. How you quantify what this means numerically is part of the problem im struggling with. I believe you have to find the "point of best fit" of the three lines. I've never encountered this problem before and in my attempt to solve it I have found 4 different solutions depending on what the definition of the point of best fit is.

I have one solution that has the least square differences in the y value, I have another solution that has the least square differences of the distances and another value that has the least difference in distance and another value using a method I found in some of my linear algebra notes.

Basically I want the answer to this:

y = -0.75x + 3
y = -0.5x + 1.5
y = -x + 2

It is clear that these lines do not all intersect at one point. Find the point that is 'closest' to a triple intersection.

 

[Neontiger94]

Dammit

I have a trigonometry regents exam in an hour, and now I stumble on this thread...

anyway can someone quickly describe how to factor trigonometric equations. Like so

2Cos^2x + 3Sinx - 3 = 0

I know it has something to do with those forsaken identities >_>

 

[Druggedfox]

rewrite cos^2(x) as 1- sin^2(x):

2(1-sin^2(x)) + 3sin(x) - 3 = 0; at this point the entire value sin(x) is no different than any other variable. Just use u substitution; sin(x) = u. The equation becomes:

2(1-u^2) + 3u - 3 = 0

-2u^2 + 3u - 1 = 0

-2u^2 + 2u + u - 1 = 0

2u(1-u) - 1(1-u) = 0

(2u-1)(1-u) = 0

u = 1/2;1

sin(x) = 1/2 --> x = pi/6
sin(x) = 1 --> x = pi/2

 

[1048576]

x = 3, y = 0, because it's right. I don't have a proof

 

[Corpsecreate]

Why does linear regression find the least square distances and not the least distances? I got 91% in Linear Algebra and 88% in statistics and I still dont know this.

 

[Corpsecreate]

So right, if I have a summation:

Sum from x = 0 up to x = 10 of f(x) = x
Then I get 0+1+2+3+4+...10= 55

But how do I write a summation that increments x by 2 so that I would get:
0+2+4+6+8+10 = 30

 

[Deleted member]

eh summation from n=0 to n=5 for f(n)=2n I guess?

 

[Corpsecreate]

Of course that works but I mean for any function f(x). How can it be written?

Hmm maybe you could replace f(x) with f(p*x) where p is your increment and replace the upper bound by the integer of the max/p.

So what im saying is to transform f(x) incrementing by 1 to f(x) increasing by p you have to rewrite it like this:

 

[Doraki]

Do I have to know highly advanced math to understand Large Cardinals? I understand the basics of WHAT they are, but I want to understand WHY they are. I don't know if that makes sense. But I think I will need to know more math to really understand why.

I don't understand your question "why they are", especially the "they" and "are" part.

if "they" = "large cardinals", then the sentence "large cardinals exist" makes no sense by itself, and "why they should be" even less so.
if "they" = "large cardinal axioms", then they are because someone wrote them down at some point. Maybe you should detail the "are" part then.

But yes you should read up logics until Godel's 2nd incompleteness theorem if you want to have a chance of understanding the point of large cardinal axioms.
Then you should look at Peano Arithmetic and Gentzen's proof of "PA is consistent", and understand why the proof cannot be carried out in PA. This is possibly the simplest example of why large cardinal axioms are important.

 

[Deleted member]

Of course that works but I mean for any function f(x). How can it be written?

Hmm maybe you could replace f(x) with f(p*x) where p is your increment and replace the upper bound by the integer of the max/p.

So what im saying is to transform f(x) incrementing by 1 to f(x) increasing by p you have to rewrite it like this:

(you probably meant to write f(p*i) in the summation)

roughly speaking, yes that's how you would write it down. technically speaking you would use sequence notation but because of the ridiculous amount of sub-/superscript involved I won't bother going into that here

[COLLAPSE="nothing new here since you're already correct but whatevers"]
if f(n) is a discrete function, in other words a list of numbers,let's say 1,1,2,3,5,8,13,21..., so f(0)=1, f(1)=1 and f(5)=8, and you only wanted the ones with and even index (in other words 1,2,5,13,...) then f(2n) would give you that list (which would then be summed from 0 to k/2 also), and that would also work if you only wanted every p-th entry (so you take the sum of f(p*n) from 0 to k/p, like you wrote already)[/COLLAPSE]

kind of wondering what you needed this for though because I'm guessing it's not related to any school activities.

 

[Corpsecreate]

kind of wondering what you needed this for though because I'm guessing it's not related to any school activities.

Just out of curiosity. To be honest I hadn't even thought about the answer until after I had asked the question.

 

[Dastrn]

I'm new to this thread, so I didn't read all 32 pages. But I was a math kid in high school, and have always been interested in math stuff in general. I got 2nd place in a calculus competition for all the top calc students on the entire east coast of the U.S. back in 1999.

I never went on to study any more math formally. But I've done some computer programming projects on the site projecteuler.net that have been fun. In particular, I'm very interested in prime numbers. I've done some pretty fun programs that analyzes the gap between consecutive primes, and looks for patterns. Fun stuff.

 

[dr.neo]

DSPM 0800* DS Elementary Algebra A 3.000 12.000

Straight off the transcript. I'm a senior in college. If you need help with math you know who the real genius is now.

 

[Corpsecreate]

I've done some pretty fun programs that analyzes the gap between consecutive primes, and looks for patterns. Fun stuff.

Wow cool. I've done a little bit of that myself in java (just for 'fun'). I noticed theres a gap of 6 between a lot of primes. I'm sure you went into it far more than I did, I didn't do anything spectacular.

Im just wondering then, if you were a math wiz at school, what did you end up studying/working as instead of something math related?

 

[Dastrn]

I manage a behavior program for teenage boys who are in trouble.

I'm considering a switch to a web programming career soon, so I just started learning C# to prep myself for an upcoming job interview. I wrote a 15-Puzzle program today in a few hours. It's super simple, but was fun to put together.

I'll post some screenshots of one of my prime gaps programs, and my 15 puzzle in a sec.


Edit:

This first one finds prime numbers between 1 and 1 million, and then looks at the gap between this prime and the last one. If that gap is the highest gap yet, it will print it out.

Spoiler

Here's the first occurrence of every gap between primes between 1 and 10 million.

Spoiler

Here's my 15-Puzzle Program that I wrote today. It's my first time using C#, although I have some experience with C++ and Python.

Spoiler

 

[Riddle]

e^x + e^ -x = 3

 

[UTDZac]

That prime number program is pretty cool. Never thought to do stuff with gaps between primes.

As for your game, what's the purpose or how do you play? Looks pretty good for your first C# project lol.

 

[Dastrn]

That game is a 15 puzzle, which you can look up anywhere. it's a classic sliding pieces puzzle.
I've got 4 projects now that I've spent some time in. The two best are a dope-wars style drug dealing game, and a match the colors fast-paced clicking game called Quick Clicks. I don't really know how to describe it. You have to click on buttons that are a certain color, but they keep changing colors, and the color you are looking for keeps changing too, so you have to stay on your toes. As you get through the levels, it gets faster, and adds new colors and whatnot. It's pretty fun.

Maybe I'll throw up a video on youtube demoing my 4 games I've done in the last two weeks. I think I could make it as a game programmer if i keep this going.

I'm also going to be working on an RPG really soon. It'll be a short adventure, maybe only 3-4 hours total. It will be sort of Mist mixed with Dragon Warrior mixed with old school MUD games, if any of you are old enough to remember those. (text based MMOs, basically.) We've got the game already written as a text-based adventure in C++, but we are going to rewrite it in C# so it's graphical. (by we, I mean my code, with my partner's art design.)

 

[Lore]

I'm taking a one semester (block scheduling) AP calculus class... You guys might see me in here soon. >_<

 

[Corpsecreate]

e^x + e^ -x = 3

is this a question?

 

[Dastrn]

is this a question?

x = ln [ 3 ± √5 ] / 2

 

[Corpsecreate]

x = ln [ 3 ± √5 ] / 2

I wasnt the one asking the question

Your answer does not yield 3 when substituted into the equation.

EDIT: Oh you mean ln [ (3 ± √5)/2 ], yes now it works

x = Cosh^-1(3/2) also.

 

[Dastrn]

I want to post more of my progamming stuff, but I suppose it's off-topic when it's not specifically about maths.

 

[Corpsecreate]

im sure u can post it. I dont think anybody is going to punish you for it...I dont think humanity has degraded that far yet.

 

[Dastrn]

If you write any Mersenne Prime in binary, it will have the form 111111111.....111111. All 1s. That's cool.

http://www.mae.ufl.edu/~uhk/BINARY-OF-PRIME-NUMBERS.pdf

 

[Corpsecreate]

wow that is pretty cool

 

[M.K]

I shouldn't be having trouble with this, but:

As sales manager for Montevideo Productions, you are planning to review the prices you charge clients for television advertisement development. You currently charge each client an hourly development fee of $2500. With the pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 15 contracts. That is down 5 contracts from the figure last year when your company charged only $2000.

A) Construct a linear demand equation giving the number of contracts Q as a function of the hourly fee P Montevideo charges for development.

B) On average, Montevideo bills for 50 hours of production time on each contract. Give a formula for the total revenue obtained by charging $P per hour.

C) The costs to Montevideo productions are estimated as follows:

Fixed Cost: $120,000
Variable Cost: $80,000

Express Montevideo's monthly cost (1) as a function of the number Q of contracts and (2) as a function of the hourly production charge P.

D) Express Montevideo's monthly profit as a function of the hourly development fee P and hence the price it should charge to maximize the profit.

I think I got the answer to A (Q = -.01P + 20), but I just don't understand B/C/D. at all.

Anyone that can help, I'd be greatly appreciative.

 

[Corpsecreate]

I shouldn't be having trouble with this, but:

I think I got the answer to A (Q = -.01P + 20), but I just don't understand B/C/D. at all.

Anyone that can help, I'd be greatly appreciative.

for A) you have 15 = 2500m + c
and you have 20 = 2000m + c

You need to find m and c, I think you were on the right track before but you probably just made a careless error.

B) is easy. R = 50PQ

C) The fixed cost is dependent on the number of contracts (Q) and the variable cost is dependent on the hourly charge. This shouldnt be too hard to find.

D) Once you have A/B/C D should be easy.

 

[Neontiger94]

Got some h.w from my pre calculus class. However for now we are just reviewing a bit of advanced algebra.

anyway how would one simplify this : (I can't use the symbols properly so i'll just type the problem in english) The Cube Root of 16x^5

 

[Corpsecreate]

 

[UTDZac]

cube root of 16 = 16 ^ (1/3) = 2 ^ (4/3)

cube root of x ^ 5 = x ^ (5/3)