सदस्य: Melody

kimberlydawn:
you want to purchase a car in 8 years and the cost is 87,000 and the APR is 6.5%. if you make monthly deposits, how much should you deposit each month to end up with 87,000 in 8 years

Ok Let me try to get this question straight.

You want to buy a car in 8 years. At the moment is costs $87,000 but each year the price will go up by 6.5%.
You make monthly deposits at the beginning of each month. You don't get any interest on you deposits. (This is a little strange, I wouldn't put my money in that bank account)
how much should you deposit every month to end up with $87,000 in 8 years.?

First you need to work out how much the car is going to cost in 8 yrs. This is a compound interest question so you have to use the compound interest formula. S=P(1+r) ⁿ
2'nd you need to know how many months are in 8 years.
Lastly you will need to divide the amount of money that you will need by how many months you have to save it in.

Now, see if you can do it yourself
If you can't you can post again but you will need to tell me what your problem is.

Melody23 Jan 2014

#15

+118691

Thank you Walt,
there is a simpler way of putting your answer. Have a think about it.

And as for your question, you are welcome. I am lucky to have good maths friends that will help me out.

Melody23 Jan 2014

#13

+118691

Guest:
Well, if I have a big number like 234, it is the same as 2x100 + 3x10 + 4 = 2x99 + 3x9 + 2 + 3 + 4.
The part 2x99 + 3x9 can obviously be divided by 9.
So if we can also divide 2 + 3 + 4 (the sum of the digits) by 9, the whole number can be divided by 9.

Melody23 Jan 2014

#10

+118691

4th response from Bob (again)

2^{5} x 3^{3} x 5 x 7 x 11 x 13 x 17 = 73513440,

has

6 x 4 x 2 x 2 x 2 x 2 x 2 = 768

divisors.

Any further offers ?

Melody23 Jan 2014

+118691

3rd response from ebaines

Building from BobP's good work, I think a better mix of values for a, b, c, etc are:

a=3, b=3, c= 2, d=1, e=1, f=1, and g=1. This gives:

2^3 x 3^3 x 5^2 x 7 x 11 x 13 x 17 = 91891800.

with total number of factors = 4 x 4 x 3 x 2 x 2 x 2 x 2 = 768.

The strategy is to use higher powers for lower primes, as long as the prime raised to that value is less than the next highest prime that would otherwise be needed. For example 2^3 = 8 is smaller than adding more primes (19, 23, etc). It would be nice to be ableto use 2^4, but then (a+1) = (4+1) = 5, and that does not divide into 768, so we/re limited to 2^3. Notice that one of the divisors of 768 is 3, so one of the primes is going to have to have a power of 2. So we need to see which works better: 3^2 and include 19 or 3^3, 5^2 and not include 19. I foind the latter gives a lower value.

Melody23 Jan 2014

+118691

2nd response from Bob

If you were to use the suggested 2^{x}.3^{y}.5^{z}, a divisor would be the product of 0,1,2,... or x 2's, 0,1,2,... or y 3's and 0,1,2,... or z 5's.
That would give you a possible (x+1)(y+1)(z+1) divisors. You would need that to equal 768.

I think though it's necessary to include higher primes.

If we assume that the divisors are of the form 2^{a}.3^{b}.5^{c}.7^{d}...... then we would need

(a+1)(b+1)(c+1)(d+1) ..... = 768.

Since 768=2^{8}.3, the best that I can come up with for the moment, subject to further investigation, is,

a=2, b=c=d=e=f=g=h=I=1 which produces the number 2^{2}.3.5.7.11.13.17.19.23=446185740.

My (Melody) response
Thanks Bob,
I wasn't suggesting that 5 would be the highest prime, (I actually put, etc, in my question)
I've got to think about your answer. I don't understand the logic you have used. I'm tired now. It might make more sense tomorrow.
Does your list really have 768 distinct combinations. (I hope i got my wording right that time) I did a quick calculation of my own and it could do. Still, I thought there would be more low prime numbers than that.
I'll be back

Melody23 Jan 2014

+118691

1st 'answer' from Romsek

I would think it's the product of the first 768 primes... 2*3*5*7*11*13.... *5489

You do mean unique divisors I assume. Otherwise i guess it would be 2^768.

My response (Melody)

I do mean unique.

Think about 2^5. By my logic this should have 6 distict divisors
1*2*2*2*2*2

1,2,4,8,16,32 See it has 6 distict divisors.

The reason I know that this is not the smallest one is demonstrated as follows
2^3=8, this has 4 factors, 1,2,4,and 8
but
6 is a smaller number with 4 factors, that is 1,2,3, and 6

Melody23 Jan 2014

+118691

Hi Walt.
I have asked my friends to take a look at you questions (next time it would be better if you put your questions as 2 different posts.
Since we have made no headway with the other one yet maybe you could repost it by itself. Just a thought.

I was going to give you a summary version of their answers but I think it might be better if you see the thought processes that everyone is havin.
This was my original question.

Hi everybody,
What is the smallest positive integer with exactly 768 divisors?

I think that 2^767 might have 768 divisors, but I think there would be a smaller one.
I'm thinking that it would be some product of prime numbers.

Like 2^x * 3^y * 5^z etc

Anyone got any ideas.
Thanks.

Melody23 Jan 2014

+118691

Guest:
Given a length of a line, and a rotation degree, what is the length of the axis-aligned bounding box for the rotated line ?

That is just a trickily worded trig question.

It is really an interval that is being rotated. Let the interval be h units long.

Draw the interval on a co-ordinate plane (in the 1'st quadrant, where x and y are both positive) such that it starts at (0,0) and it is rotated about the x axis.

Now drop a perpendicular down from the end of the line so that it intersects with the x axis.

Put theta where it belongs in the triangle that you now should see before you.

do you see why I told you to make the interval h units long?

Can you take it from here?

Melody23 Jan 2014

+118691

Vraces:
0.25 = 1(1-r)^n
0.25 = (1-r)^60
-0.75 = r^60
r = - 0.75^(1/60) = 0.016666...7
r = [Incorrect]
My calculation and understanding is completely off. If you spoke to me in math maybe I could understand better.

And sandwich man, your answer is incorrect, I thought that too at first. That is almost the answer, but almost doesn't cut it if we're talking math. Thanks for trying though.

--------------------------------------------------------------------------------------------------------
Your calculation and understanding are not completely off! You just took away the bracket too soon. I don't know why you did that
If I spoke to you in person you could understand much more easily. I am an excellent teacher. (That's what I think anyway)
But there is always a time delay on the web that slows everything down and makes learning (and teaching) harder.
However;
Sometimes I think that things are remembered better if the learning part is more of a trial.

0.25 = (1-r )^60
0.25^(1/60) = 1-r
r = 1 - (0.25)^(1/60)
r = 0.022840031
r = 2.28% (3 significant figures)

Melody23 Jan 2014

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