Mathematics Question Thread

[RuiAce]

Yooo so with superannuation questions: On 31st January 1990 Hayden joined a superannuation fund by investing $5000 at 6%p.a. compound interest. He added $5000 to the fund on 31st January each year and intends to continue to do so until, but not including, the day he intends to retire 31/1/2010. Find the total accumulated value of his investment, to the nearest dollar, on that day.
- I'm confused about the "but not including" part? Would that mean that the final formula used for the final year would be 5000(1.06)^0 ?

"Final formula" is ambiguous and it depends on whether you used the recursive approach, or the accumulation method.

What the question is saying is that in the last year, he does not deposit another $5000. (i.e. There is no cash flow that year.)

[pacione]

Hey,
Could anyone please help me with the attached question, it would be greatly appreciated.

[RuiAce]

Hey,
Could anyone please help me with the attached question, it would be greatly appreciated.

Which parts are you having trouble with?

(Hints in the meantime for all three)
a) That ray OR is drawn so that you have more than one triangle to consider. Use it.
b) A bit easier than part a), but follows the same idea of working around the diagram
c) Your typical maxima/minima problem. The derivative is annoying as it needs the product and chain rule, but then all you have to do is substitute theta=pi/12 in.

[Youssk]

Hey could someone help me with this question please!
Thank you

[RuiAce]

Hey could someone help me with this question please!
Thank you

[cxmplete]

Hi,
How would I do question 8

[jakesilove]

Hi,
How would I do question 8

Hey! Make sure you've drawn this out; the minor segment will have perimeter AB plus the arc length of AB.  We know that the arc length is

We can calculate the chord length of AB by the cosine rule.




Now, we add these two lengths together to get the total perimeter.


However, we know that this is equal to half the circumference, so




Now, from here it seems like you need to use a 3U trick; it this a 2U question? Recall that




As required.

[RuiAce]

[bananna]

Hi, I'm having a lot of trouble with this q
pls help!!!

thank you so much

Ashley has just retired with $1 000 000 in her bank account. This account attracts  interest at a rate of 5% per annum compounded annually.    She intends to withdraw money in equal amounts at the end of each year, and wants  the money in her account to last for exactly 20 years.
  Let An be the amount of money in her account after n years.
 
 
(i) Write down an expression for the amount left after two withdrawals. 1
 
 
(ii) Calculate the amount of each withdrawal. 3
 
 
(iii) After her tenth withdrawal, the bank changes its interest rate to 3% p.a. on  the balance remaining in her account. Interest is still compounded annually.
 Ashley changes the amount of her withdrawals so that they last the   remaining 10 years and are equal in value over these 10 years.
  What will be the new amount of each withdrawal in these last 10 years?        3

[RuiAce]

Hi, I'm having a lot of trouble with this q
pls help!!!

thank you so much

Ashley has just retired with $1 000 000 in her bank account. This account attracts  interest at a rate of 5% per annum compounded annually.    She intends to withdraw money in equal amounts at the end of each year, and wants  the money in her account to last for exactly 20 years.
  Let An be the amount of money in her account after n years.
 
 
(i) Write down an expression for the amount left after two withdrawals. 1
 
 
(ii) Calculate the amount of each withdrawal. 3
 
 
(iii) After her tenth withdrawal, the bank changes its interest rate to 3% p.a. on  the balance remaining in her account. Interest is still compounded annually.
 Ashley changes the amount of her withdrawals so that they last the   remaining 10 years and are equal in value over these 10 years.
  What will be the new amount of each withdrawal in these last 10 years?        3

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[Fahim486]

Hey I'm having trouble understanding simpson's rule and trying to apply them. Thanks!

[jakesilove]

Hey I'm having trouble understanding simpson's rule and trying to apply them. Thanks!

Hey! Simpson's rule states that


Where x0, x1 etc are evenly spaced intervals and h is the distance between such intervals. In this case, we only want three values, each spaced one unit apart. So,

Then, we simply plug in the values of the function (ie. f(2)=ln(2)) and use our calculator to find the answer!

[Fahim486]

Thanks Jake for that help and just as bad as I am at the Simpson's rule, I am equally bad at Trapezoidal rule so if you don't mind could you also show me how to do this question as well. Thanks!!!

[pikachu975]

Thanks Jake for that help and just as bad as I am at the Simpson's rule, I am equally bad at Trapezoidal rule so if you don't mind could you also show me how to do this question as well. Thanks!!!

4 strips means 5 function values, so x = 3, 3.5, 4, 4.5, 5 and h/2 = 1/4
A = 1/4 (f(3) + 2f(3.5) + 2f(4) + 2f(4.5) + f(5))
A = 1/4 (ln8 + 2ln11.25 + 2ln15 + 2ln19.25 + 24)

Sub into calculator for your answer

[Fahim486]

4 strips means 5 function values, so x = 3, 3.5, 4, 4.5, 5 and h/2 = 1/4
A = 1/4 (f(3) + 2f(3.5) + 2f(4) + 2f(4.5) + f(5))
A = 1/4 (ln8 + 2ln11.25 + 2ln15 + 2ln19.25 + 24)

Sub into calculator for your answer

Thanks for your help but may I ask where you got h/2 = 1/4 from?