All Answers 358101 Answers

3/8 is the lowest term itself , it cant be reduced to a lowest term any further !

If you are repaying a loan then your first payment will be due at the end of the first payment period.

This is referred to as a "A present value of an ordinary annuity"

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If you are putting money in the bank at regular intervals then you would normally put the money in the bank at the beginning of the first time period.  

what it grows to is referred to a "The future value of an annuity due"

CPHill used the annuity due method - his answer is a better. (Although the question did not state when the first deposit was made)

1) How to access a web address that is written in a post (if you have a windows operating system)

Put the curser anywhere over the address, right click, choose 'open link in new tab'

2) How to copy and paste web addresses (if you have a windows operating system)

Use the calculator on this site and type this in just as you have written it here; then press Enter.

If you save money in a bank, the bank uses Melody's method to decide how much to pay you back.  If the bank loans you money it uses Chris's method to decide how much you must pay back.

No, ignore me; I'm just being cynical!!

I always draw a right angled triangle when I answer questions like this.

CPhill's answer is approximate.  It is easy to get the exact answer 

Let the angle be θ

for starters sinθ is positive (1st or 2nd quad) so cotθ can be positive or neg. 

From the diagram it can be seen that Cot θ= sqrt(5)/2

$$cot(sin^{-1}\left(\frac{2}{3}\right))=\frac{\sqrt{5}}{2}$$

Thanks Ninja,

That wiki page is really good and copying the diagram into the forum was an excellent idea.

I have added the address of this thread the sticky topic "Information Pages worth Keeping and Developing"

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Before this thread is closed I just want to make it very clear;

pi is an irrational number. This means that it cannot be exactly represented as a fraction and hence it it cannot be exactly represented by a terminating or a recurring fraction.

ANY number value that is assigned to pi is an approximation.

Saturday 14/6/14

What is the value of pi 

I have added this one's address to the sticky topic "Information pages worth keeping or developing"

$${\frac{{{\mathtt{10}}}^{{\mathtt{6}}}}{{{\mathtt{10}}}^{{\mathtt{7}}}}}$$

also, if you just think about it for a moment.  You have got 6 tens on the top and 7 tens on the bottom when you cancel you will be left with just 1 ten and it will be on the bottom.  The top cancels out to 1

$$\frac{10^6}{10^7}=\frac{10*10*10*10*10*10}{10*10*10*10*10*10*10}=\frac{1}{10}$$

Also as CPhill said

$$\frac{10^6}{10^7} = 10^{6-7}=10^{-1}$$

therefore

$$10^{-1}=\frac{1}{10}$$

Look here for more info on indices - especially negative indices.

Thank you.

I added that page (mathisfun etc) to the information pages worth keeping and developing.  I think answerers all use the mathisfun sites a lot but this may help remind people.

Great web pages

Solving Inequalities.

It is a 2nd function on the web2calc

First put one digit in front of the point

4.42166041

it is a big number so the power will be positive.

I moved the point over 8 digits so the power is 8

4.42166041 X 10⁸

You fill it up with water using measuring containers and see how many ml it holds.

(my container is water proof)

1ml =1cm³

There you go - that is one way.  

I don't, I love trains.  My trains do not run on one track and they do not crash each other to bits.  They just pass each other politely.  

Oh! what am I saying - where is the fun in that!??

Thanks CPhill,

I actually learned some of this myself while looking at the wikipedia page.

I didn't know the whole circumference/diameter thing before reading it.

The picture is also from the wiki page :)

This equation is technically incorrect, because there is two equal signs in it...

I'm thinking you didn't mean for the second one to actually be part of the equation. In this case, here's how you'd solve it. 

N=5.54(102)2/(10)2

N = 565.08(2)/(10)(2)

N = 1130.16/10*2

N = 113.016*2

N = 226.032

You also could have meant...

N=5.54(102)²/(10)²

...Which would give you a different answer.

Please be very carefull when typing in questions, so you can guarantee a good answer. :)

Very impressive graphics, ND.......amazing, really  !!!

Yup, CPhill's answer in correct.

Another way you can think of this is with fractions, if it helps you visualize it better.

$$\left({\frac{{\mathtt{99}}}{{\mathtt{100}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{50}}}{{\mathtt{1}}}}\right)$$

99/100 is 99%

$${\frac{{\mathtt{4\,950}}}{{\mathtt{100}}}}$$

divide the top and bottom by 100

$${\frac{{\mathtt{49.5}}}{{\mathtt{1}}}}$$

$49.5

Well...3/8 can't be reduced, so 3/8 is it's lowest term.

Pi = 3.14159265359, or usually shorted to something like 3.14

Actually, pi is proven to just keep going forever with decimal digits. This pattern is also unrepetitive, or having no patern to it.

Or as Wikipedia says it, "It's [pi's] decimal representation never ends and never settles into a permanent repeating pattern. The digits appear to be randomly distributed although no proof of this has yet been discovered."

Pi is a ratio of a circle's circumference to it's diameter, as shown below.

This means that a circle's circumference is a little over 3 times as big as it's diameter.

This also means that you can write pi as pi = circumference/diameter:

Because of this, you will often use pi when your dealing with circles.

99% = .99    

"of" means  "multiply"   

So we have

.99 * 50  =  $49.50

cot(sin^-1(2/3))

First, let's evaluate sin^-1 (2/3) = 41.810314895779°

So..........cot(41.810314895779) = 1.118033988749441

Notice that if this angle could also lie in the second quadrant..... there, the cotangent would be........ (-1.118033988749441)