Maths help PLEASE

Prodigy38

Hi i need to get these questions 100% right to pass my module, i was wondering if someone knows how to do them perfectly. and can show me, so i can make necessary corrections thanks. These are the questions,

Formulas: FV=PV (1+R)-t
PV-FV (1+R)-t
P= R(PV)/1=(1+R)-t

Section A
Q1)
(A) €750,000 is invested for 3 years at 6,5% interest. The interest is compounded MONTHLY. What is the future value of the investment.

(B) An Investment of €16,000 yields €4,000 total interest at the end of 5 years. What is the total % interest?

(C) Which is better €5,000 Now or €10,000 in 7.5 years time when the interest rate is 10% per year.

TheBody

Prodigy38 wrote: »

Hi i need to get these questions 100% right to pass my module, i was wondering if someone knows how to do them perfectly. and can show me, so i can make necessary corrections thanks. These are the questions,

Formulas: FV=PV (1+R)-t
PV-FV (1+R)-t
P= R(PV)/1=(1+R)-t

Section A
Q1)
(A) €750,000 is invested for 3 years at 6,5% interest. The interest is compounded MONTHLY. What is the future value of the investment.

(B) An Investment of €16,000 yields €4,000 total interest at the end of 5 years. What is the total % interest?

(C) Which is better €5,000 Now or €10,000 in 7.5 years time when the interest rate is 10% per year.

It against the charter to simply do them out for you. Post up your attempts so we can have a look at it.

MathsManiac

TheBody wrote: »

It against the charter to simply do them out for you. Post up your attempts so we can have a look at it.

Also, OP, the formulae don't look right - you should check them before you get stuck into attempting the questions.

TheBody

MathsManiac wrote: »

Also, OP, the formulae don't look right - you should check them before you get stuck into attempting the questions.

The op closed their account. Seems we didn't offer what they were looking for!!

MathsManiac

A rather extreme response!

TheBody

MathsManiac wrote: »

A rather extreme response!

I think I need to work on my people skills :pac:

Ompala

Rather than start a new thread just gonna post this here.

Trying to go through Fourier Series atm and am stuck by this question. Don't want anyone to do it out for me just need clarity on a few bits.

The function g : R -> R is an odd function of period 2pi with Fourier
series
Σ bn sin(nx). The function h : R -> R is defined by
h(x) = g(x) + K
where K is a constant. Find the Fourier series of h.

Bits thats confusing me, does g : R -> R (which I assume means g(x) ) represent just a constant, and if it doesn't how can I find bn without knowing what I am integrating?

The K term, would I be correct in saying that since its a constant it has no Fourier Series, so I just add K on to my answer for g(x)?

Any help would be greatly appreciated

Michael Collins

Ompala wrote: »

Rather than start a new thread just gonna post this here.

Trying to go through Fourier Series atm and am stuck by this question. Don't want anyone to do it out for me just need clarity on a few bits.

The function g : R -> R is an odd function of period 2pi with Fourier
series
Σ bn sin(nx). The function h : R -> R is defined by
h(x) = g(x) + K
where K is a constant. Find the Fourier series of h.

Bits thats confusing me, does g : R -> R (which I assume means g(x) ) represent just a constant, and if it doesn't how can I find bn without knowing what I am integrating?

Yep, g: R -> R means g is a function which maps real numbers to real numbers (technically it means the domain and codomain are the set of all real numbers), but there's nothing to suggest it's constant. All you know is that it is odd, and therefore its Fourier series is made up of only [latex]b_{n} \sin(nx)[/latex] terms - there are no [latex]a_{n} \cos(nx)[/latex] terms.

The idea of this question is that you can use the fact that a Fourier series obeys linearity. So, since you know the Fourier series of g(x) (at least in symbolic form), the question comes down to what is the Fourier series of a constant function? Once you have this, you can add the two Fourier series and obtain the final Fourier series for h(x).

The K term, would I be correct in saying that since its a constant it has no Fourier Series, so I just add K on to my answer for g(x)?

Any help would be greatly appreciated

It's not that it has no Fourier series, it would be rare to come across a function that doesn't have a Fourier series (at least in an undergradute course!), but more the fact that the Fourier series is rather straight forward to obtain.

So what is the Fourier series of a constant fucntion [latex] f(x) = K [/latex]? Hint: this is a really really simple question!

Ompala

Michael Collins wrote: »

Yep, g: R -> R means g is a function which maps real numbers to real numbers (technically it means the domain and codomain are the set of all real numbers), but there's nothing to suggest it's constant. All you know is that it is odd, and therefore its Fourier series is made up of only [latex]b_{n} \sin(nx)[/latex] terms - there are no [latex]a_{n} \cos(nx)[/latex] terms.

The idea of this question is that you can use the fact that a Fourier series obeys linearity. So, since you know the Fourier series of g(x) (at least in symbolic form), the question comes down to what is the Fourier series of a constant function? Once you have this, you can add the two Fourier series and obtain the final Fourier series for h(x).



It's not that it has no Fourier series, it would be rare to come across a function that doesn't have a Fourier series (at least in an undergradute course!), but more the fact that the Fourier series is rather straight forward to obtain.

So what is the Fourier series of a constant fucntion [latex] f(x) = K [/latex]? Hint: this is a really really simple question!

I apologise in advance if this sounds really stupid

For g(x) then all I can basically say is that g(x) = Σ bn sin(nx), theres no way to find bn so that all I can do with that, done and dusted?

The concept of a fourier series for a constant function is annoying me though, if I was just to hazard a guess I would say it is K, but I don't see how a constant function can have a fourier series.

Its a constant function, so constant = doesn't change so no movement so no period. If we don't know the period we can't find ao, an, bn. Am I reading into this too much and making the problem harder than it actually is?

Ciaran

Ompala wrote: »

For g(x) then all I can basically say is that g(x) = Σ bn sin(nx), theres no way to find bn so that all I can do with that, done and dusted?

Yes. That's just the general form for an odd function. It's like talking about a quadratic function of y = ax^2 + bx + c

Its a constant function, so constant = doesn't change so no movement so no period. If we don't know the period we can't find ao, an, bn. Am I reading into this too much and making the problem harder than it actually is?

You are, yeah! Just look at the ao term, it has no period.

Ompala

Well its all part of the learning curve!
Think I have it now, but just to be sure (I don't have the answer for this btw) fourier series of h(x) = Σ bn sin(nx) + K?
And if thats wrong I feel I have failed ye both miserably
Thanks guys really appreciate the help

Ciaran

Ompala wrote: »

Well its all part of the learning curve!
Think I have it now, but just to be sure (I don't have the answer for this btw) fourier series of h(x) = Σ bn sin(nx) + K?

That's it. Sometimes the answer is easy.

Ompala

Yes!!!! Definitely one that looks harder than it is!
And that was worth 6% of the exam..