Integral problem: f(x)=∫2x-733 dx = 0 when f(0)=83472 and x∈Z. Find x

[NilsGN]

In my hobby, geocaching, I ran in to this problem:
f(x)=∫2x-733 dx = 0 when f(0)=83472 and x∈Z. Find x

Can I get step by step help?

Or the solution?

I do some calculation on my own and I get to the answer x=2 is that correct?

Thanks in advance

 

[stapel]

In my hobby, geocaching, I ran in to this problem:
f(x)=∫2x-733 dx = 0 when f(0)=83472 and x∈Z. Find x

Can I get step by step help?

Or the solution?

Please re-read the "Read Before Posting" message. Thank you!

I do some calculation on my own and I get to the answer x=2 is that correct?

Please reply showing how you obtained this value. Thank you!

 

[BigBeachBanana]

In my hobby, geocaching, I ran in to this problem:
f(x)=∫2x-733 dx = 0 when f(0)=83472 and x∈Z. Find x

Can I get step by step help?

Or the solution?

I do some calculation on my own and I get to the answer x=2 is that correct?

Thanks in advance

You have 2 contradicting statements.

You said [imath]f(x)=\int 2x-733 \, dx = 0[/imath] this implies [imath]f(x)[/imath] is a constant function and always equal to 0 regardless of x.

However, you also said [imath]f(0)=83472[/imath].

 

[NilsGN]

You have 2 contradicting statements.

You said [imath]f(x)=\int 2x-733 \, dx = 0[/imath] this implies [imath]f(x)[/imath] is a constant function and always equal to 0 regardless of x.

However, you also said [imath]f(0)=83472[/imath].

Yes!, that's my problem!
If x∈Z ((witch means that x= some integer value (or?)).
and
f(0)=83472 >: meaning that the function of x = 0 if f(0)=83472
How do I do to calculate: f(x)=∫2x−733 dx=0
And find out what x is?
With above limits.?
For as an example: what is: f(1) if f(0)=83472 (if f(x)=∫2x−733 dx=0)?

 

[Dr.Peterson]

In my hobby, geocaching, I ran in to this problem:
f(x)=∫2x-733 dx = 0 when f(0)=83472 and x∈Z. Find x

Can I get step by step help?

Or the solution?

I do some calculation on my own and I get to the answer x=2 is that correct?

Thanks in advance

If you didn't quote the problem exactly, please show us an image of the original, so we can judge for ourselves. As you show it, it isn't well-written.

But my guess is that it is meant to say that f(x) is an antiderivative of 2x - 733 such that f(0) = 83472, and you are to solve for x such that f(x) = 0.

There are in fact two integer solutions of that equation.

 

[NilsGN]

OK the image:
The text is in Swedish:
'Beräkna' = Count
'då' = when / then
'Och' = and

 

[BigBeachBanana]

what is: f(1) if f(0)=83472 (if f(x)=∫2x−733 dx=0)?

I'm still having a hard time deciphering what you're trying to ask. Perhaps you can tell us more about the actual problem you're trying to solve. How did you come up with this function?

Otherwise, I'll answer based on how Dr.Peterson interpreted it above.
Given [imath]f(x)=\int 2x−733 \, dx[/imath], and [imath]f(0) = 83472[/imath]. Find [imath]x \in \Z[/imath] such that [imath]f(x) = 0[/imath].

First, can you integrate this? [imath]f(x)=\int 2x−733 \, dx[/imath]

 

[Steven G]

If A=B and B=C, then A=C.

That is if f(x)= ∫(2x−733)dx = 0, then f(x)=0. If f(x)=0, then f(any number)=0. However, you say that f(0) = 83472!! This can't be true, since f(0) must equal 0, not 83472.

This is nothing to be confused about with this problem. There is a contradiction and it can't be solved.

Above is exactly what @BigBeachBanana said!

 

[NilsGN]

OK, thanks! All I have is the image that I posted above.
So, it's an unsolvable problem?

It may mean, for my part, that it is the numbers themselves that is the problem that I should 'look at', in the image.

Thanks a lot for Your (all of You) help and time.

 

[Dr.Peterson]

I'm still having a hard time deciphering what you're trying to ask. Perhaps you can tell us more about the actual problem you're trying to solve. How did you come up with this function?

We've been told everything there is to know! This is a puzzle from a geocache (which happens to be located in the region my Peterson ancestors came from); I've visited the website, and the image is all that is provided. Its poorly written nature is not the OP's fault.

The cache description doesn't even clearly say what to do with the solution; presumably when you find the cache there is a way to use two three-digit numbers to open a container. Here is the relevant part, translated by Google:

Open me 4 – Gemini pi

There are three ways to get the codes to get into the twins.

1. solve the equation shown in the spoiler image.
2. visit the cache "before open me 4" (GCA6FH6) and read the codes on its container.
3. figure out the codes yourself through information in the cache's title.

The spoiler image is what we were given.

And the two numbers are indeed related to pi, as suggested by the title.

This is nothing to be confused about with this problem. There is a contradiction and it can't be solved.

No, it is possible to figure out what someone meant even when they don't know how to say it correctly. As a teacher, you should surely know that!

It most definitely can be solved, using what has been suggested about its intended meaning.

 

[JeffM]

We keep forgetting that the person who submitted this is a HOBBYIST, NOT a student. For those who are not math students, help must take a different form.

It is true that the problem as presented does not formally make any mathematical sense. [imath]f(x) = \int 2x - 733 \ dx[/imath] defines a family of functions rather than a function. And a family of functions that all equal zero is only formally a family at all. Moreover, if f(x) = 0, then it is impossible that f(0) = 83472. Dr. Peterson, however, figured out what was almost certainly intended. Indeed, compared to the way most practical problems susceptible to mathematical analysis have been presented to me, this is a model of clarity.

[math]\text {Find } x \text { given}\\ f'(x) = 2x - 733, \text { and}\\ f(0) = 83472, \text { and}\\ f(x) = 0.\\ \text {HINT: } x \text { is an integer.}[/math]
If this were a student, I would proceed as BBB has done, but the poor guy just wants some numbers so he can enjoy his weekend.

[math] f'(x) = 2x - 733 \implies f(x) = x^2 -733x + C.\\ f(0) = 83472 \implies C = 83472\\ f(x) = 0 \implies x^2 - 733x + 83472 = 0 \implies\\ x = \dfrac{-(-733) \pm \sqrt{(-733)^2 - 4 * 1 * 83472}}{2 * 1} \implies \\ x = \dfrac{733 \pm \sqrt{537289 - 333888}}{2} = \dfrac{733 \pm \sqrt{203401}}{2} = \dfrac{733 \pm 451}{2} \implies \\ x = 141 \text { or } 592 [/math]
Then he needs to figure out what 4 - gemini pi is all about, which I doubt is fundamentally mathematical.

 

[Dr.Peterson]

We keep forgetting that the person who submitted this is a HOBBYIST, NOT a student. For those who are not math students, help must take a different form.

Yes, I was just waiting to see if the OP is interested in/capable of trying, and then give more direct help. I feels a little like cheating to give the full solution to a puzzle, even when it's not for a class. But cachers do help one another all the time (even though I've never asked for help).

Now that you see the answer, @NilsGN, do you notice how the two values relate to pi (3.14159...), and thus might (conceivably) have been guessed from the title? The instructions say you don't have to solve the problem in order to find these "codes", since you can find them in two other ways; and I imagine that something you'd find at the cache would give additional reason to pull out two three-digit numbers from pi.

 

[NilsGN]

So many tanks, people!

I went to a geocache that was supposed to contain more information for "Open me 4 gemeni - pi" and there found a couple of additional clues:
X₁=141, X₂=592.
Corresponding to pi (3,141592...) I now see which probable number groups I should use; 141 & 592.
And it matches perfectly well with the generous calculation that JeffM made. And the reasoning that Dr. Peterson led.

Thanks again!