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        riddles >> putnam exam (pure math) >> solving X^3+8x^2
        
(Message started by: lilas224 on Oct 12^th, 2007, 6:57pm)

Title: solving X^3+8x^2
Post by lilas224 on Oct 12^th, 2007, 6:57pm

my question would be how to solve
X^3+8x^2

and my second

The number of bacteria in a refrigerated food product is given by , N(T)=25T^2-120T+57,5<T<35 where is the temperature of the food.
When the food is removed from the refrigerator, the temperature is given by , T(t)=3t+1.7where is the time in hours.
Find the composite function :
\
N(T(t))=?

and
Find the time when the bacteria count reaches 1856
time needed= ?

please help! either one!

Title: Re: solving X^3+8x^2
Post by Michael_Dagg on Oct 12^th, 2007, 7:27pm

We don't know what to do with X^3+8x^2
as you have stated because there is nothing to
solve. If you may mean it is =0 and then that fact
is pretty simple.

I believe you have made some typos in your
subsequent questions.

Title: Re: solving X^3+8x^2
Post by towr on Oct 13^th, 2007, 2:49am

on 10/12/07 at 18:57:36, lilas224 wrote:

my question would be how to solve
X^3+8x^2

If you want to solve for it being 0, it's rather easy, x=0 and x=-8 are solutions. If you want it solved in another way, you'd have to specify.

Quote:

The number of bacteria in a refrigerated food product is given by , N(T)=25T^2-120T+57,5<T<35 where is the temperature of the food.
When the food is removed from the refrigerator, the temperature is given by , T(t)=3t+1.7where is the time in hours.
Find the composite function :
N(T(t))=?

As best as I can tell, you'd just want to replace each T with (3t+1.7), so you'd get N(T(t)) = 25(3t+1.7)^2 - 120(3t+1.7) + 57, for 5 <(3t+1.7)< 35
You can simplify it further of course, but I don't want to have all the fun.

Quote:

Find the time when the bacteria count reaches 1856
time needed= ?

Solve the quadratic N(T(t)) = 1856, you'll get two values for t, pick a positive real one (I suspect they'll both be real, and only one will be positive)

So is this homework?

Title: Re: solving X^3+8x^2
Post by FiBsTeR on Oct 13^th, 2007, 8:13am

on 10/13/07 at 02:49:10, towr wrote:

So is this homework?

Google seems to think so; a user 'lilas224' has posted this question here as well as at Yahoo! Answers (http://answers.yahoo.com/question/index?qid=20071012190045AA7mjiU).

Title: Re: solving X^3+8x^2
Post by temporary on Jan 24^th, 2008, 10:49pm

on 10/13/07 at 02:49:10, towr wrote:

If you want to solve for it being 0, it's rather easy, x=0 and x=-8 are solutions. If you want it solved in another way, you'd have to specify.

As best as I can tell, you'd just want to replace each T with (3t+1.7), so you'd get N(T(t)) = 25(3t+1.7)^2 - 120(3t+1.7) + 57, for 5 <(3t+1.7)< 35
You can simplify it further of course, but I don't want to have all the fun.

Solve the quadratic N(T(t)) = 1856, you'll get two values for t, pick a positive real one (I suspect they'll both be real, and only one will be positive)

So is this homework?

I don't think he means as an equation. Perhaps he means find what it's derivative is or what it is in a single term of x.

Title: Re: solving X^3+8x^2
Post by ima1trkpny on Jan 24^th, 2008, 11:35pm

on 01/24/08 at 22:49:06, temporary wrote:

I don't think he means as an equation. Perhaps he means find what it's derivative is or what it is in a single term of x.

Seriously... just be quiet when you don't know what you are talking about. This is just algebra, no calculus or derivatives required.
But since you apparently need hand-holding to see how it is solved... I'll just finished where Towr left off. (Yes, he was correct.)
First, simplify.
N(T(t))=25(3t+1.7)²-120(3t+1.7)+57
becomes
N(T(t))=225t²-105t-74.75
(assuming you can add, subtract and multiply correctly...)
Which you then set equal to 1856...
1856=225t²-105t-74.75
subtract both sides...
0=225t²-105t-1930.75
using the quadratic formula you get t= (105 +/- 1322.384)/450
which simplifies to t= 3.172, -2.705 (I'm just rounding everything to 3 decimal places because at this math class level that is more than suitable accuracy)
and since time must be positive you can eliminate the second answer.
Therefore, at t=3.172 hours you will have 1856 bacteria.

Title: Re: solving X^3+8x^2
Post by temporary on Jan 25^th, 2008, 6:56am

on 01/24/08 at 23:35:33, ima1trkpny wrote:

What I need isn't hand-holding, what I need is specification to the x^3+8x^2. What am I supposed to do with it?

Title: Re: solving X^3+8x^2
Post by ima1trkpny on Jan 25^th, 2008, 7:22am

on 01/25/08 at 06:56:05, temporary wrote:

What I need isn't hand-holding, what I need is specification to the x^3+8x^2. What am I supposed to do with it?

And that was already explained if you care to read... whoever posted that was not at a point where they understood calculus. The only method to solve the equation would be to set it equal to zero. At which point even you should be able to solve it.

But if you'd like to see derivatives...
f(x)=x³+8x²
f'(x)= 3x²+16x
f"(x)=6x+16
f"'(x)=6

Anything else you'd like to see done with the function?

Title: Re: solving X^3+8x^2
Post by ThudanBlunder on Jan 25^th, 2008, 7:40am

on 01/25/08 at 07:22:01, ima1trkpny wrote:

But if you'd like to see derivatives...
f(x)=x³+8x²
f'(x)= 3x²+8

Oops, f'(x) = 3x² + 16x

Title: Re: solving X^3+8x^2
Post by ima1trkpny on Jan 25^th, 2008, 3:38pm

on 01/25/08 at 07:40:16, ThudanBlunder wrote:

Oops, f'(x) = 3x² + 16x

Oops :-[ fixed... that's what I get for being in a hurry. Thanks :)

Title: Re: solving X^3+8x^2
Post by Icarus on Jan 25^th, 2008, 6:35pm

on 01/24/08 at 23:35:33, ima1trkpny wrote:

Seriously... just be quiet when you don't know what you are talking about. This is just algebra, no calculus or derivatives required.

I'm sorry, but I don't think this was called for. Temporary appears to me to have been doing his best to suggest his ideas on what was meant. He was not impolite or impolitic in his reply. Even if you don't agree that it was wise, rudeness is not necessary.

I agree that the nature of the problems and wording are indicative of pre-calculus mathematics. But temporary may not have the experience of teaching/tutoring mathematics at this level to recognize this fact, and assumed that in this forum the level of the question would be at least a little higher.

It seems to me that a lot of bad feelings raised by an apparently different poster have been transferred to temporary because of his expressed support for said poster. I personally don't care for nonsense-trolls either. Some of the longer members may recall one several years ago who went around posting mathematics-related gibberish on every thread, until I finally got so fed up with it that I started deleting the posts. After a day-long fight, he finally tired of the game and moved on.

But it seems to me that temporary does not fall in this category. If he is mistaken or takes things too lightly, well, I can with very little effort find numerous posts from each of us where the same can be said. If he has been rude, we have been rude to him as well. If we disagree about the worth of his questions, I've seen considerably worse posted that have not received the ire that his have.

You don't have to like him. But outright rudeness is not appropriate.

Title: Re: solving X^3+8x^2
Post by ThudanBlunder on Jan 25^th, 2008, 7:57pm

on 01/25/08 at 18:35:26, Icarus wrote:

It seems to me that a lot of bad feelings raised by an apparently different poster have been transferred to temporary because of his expressed support for said poster.

ima1trkpny obviously believes that Temporary is the net pest srn347, and I tend to agree with her. There seem to be too many similarities, eg. multitudinous posts in one session, baldly stating quirky, half-baked ideas as established facts, obsession with infinity, same log on time, brevity of posts, unrequired, unprovoked defence of srn347, etc. If so, her tone is understandable. Although his attitude does seem to have improved, it is a measure of the similarity that even pavlovian towr has sworn not to react to his posts again. ;)

Title: Re: solving X^3+8x^2
Post by ima1trkpny on Jan 26^th, 2008, 6:42am

on 01/25/08 at 18:35:26, Icarus wrote:

I'm sorry, but I don't think this was called for.

Fair enough. I may have been a bit too harsh and for that I apologize.

Quote:

I agree that the nature of the problems and wording are indicative of pre-calculus mathematics. But temporary may not have the experience of teaching/tutoring mathematics at this level to recognize this fact, and assumed that in this forum the level of the question would be at least a little higher.

Again... fair enough. But this is the reason I'm quite convinced srn347/Temporary are indeed the same person. Both problems were of the kind taught in Algebra II/Pre-calc. I've never been a math teacher and only did tutoring in high school, but I remember learning this at about 14 years old... and would have recognized the problem as doable with the math I'd learned up to that point. Temporary can't recognize the problem which sounds to me like either he hasn't yet studied them or hasn't done it for long. In which case his age matches up with Srn347's who was 13.

Quote:

You don't have to like him. But outright rudeness is not appropriate.

I will endeavor to be more polite but I would like to see a little more thought put into temporary's posts... or better yet, ask questions because most of the people here are willing to explain things and help him learn.