Member: reinout-g

Vraces:
I need to understand why for example
[A radioactive kalashnikov gets less radioactive every year. After 60 years only 25% of the radio-activeness remains. What is the yearly reducing of radio-activeness in percent?]

I'm wondering. Since(Based on my assumption) 0.75^(1/60) should be in english: 75% of of the radioactiveness in one year. Since 75% was removed during 60 years shouldn't 0.75^(1/60) be the answer?[1 - 0.25^(1/60) = 0.75^(1/60)? ] And also. Why should it be ^(1/60) and not the percentage divided by 60?What does ^(1/60) actually mean? What happens when it calculates? I'm aware it multiples itself the times stated. For example: 3^3 = 27 ; 3^3(1/3) = 9 I must understand these things. It's good to know how to solve something, but if you don't know the meaning of it you can't solve another thing. I'm going to guess only Melody could explain this, but others are also welcome. IF you actually know the significance. Do not guess while trying to explain as it would only confuse me. And by the way, I may have confused you a little bit with what I'm trying to say. Good luck and thanks.

Dear Vraces,

I understand your confusion, and since Melody has just called it a day, I will do my best to give you the most clear and understandable explanation I can give you.

First let me calculate the following things for you;

a) 0.75/60 = 0.0125

b) 0.25^(1/60) = 0.9771599684342459

Suppose we have 100 kilograms of radioactive material, then we know that after 60 years only 25 kilograms will be left.

the first percentage is what we use if something reduces with 0.0125 of the original amount each year.

So in the case of the radioactive material this would mean that after 1 year the radioactive material would be

100-100*0.0125 = 98.75

after year 2 it would be

98.75 - 100*0.0125 = 97.5

which is the same as

100 - 100*0.0125 - 100*0.0125 = 97.5

which is the same as

100 - 2 * 100*0.0125 = 97.5

so after the 60 years it would be

100 - 60*100*0.0125 = 25 kg

As you can see, the radioactive material would then reduce with an amount of 1.25 kg each year

However, this is not what actually happens, because what actually happens is that the radioactive material reduces with the same percentage each year

If we calculate the percentage that is reduced each year in the above case we get;
1.25/100 * 100% = 1.25%
1.25/98.75 * 100% = 1.27%
1.25/97.5 * 100% = 1.28%
etc.

We want to reduce the material with a percentage per year,
Now let me give an example which will make you understand,

Suppose the radioactive material reduces with 2% each year
Then after 1 year we know we have 100kg * (1-0.02) = 100kg * 0.98 = 98kg
After 2 years we know we have 98kg*(1-0.02) = 98kg*0.98 = 96.04kg
or we can calculate it as 100kg * (1-0.02) ² = 96.04kg
After 5 years we know we have 100kg * (1-0.02) ⁵ = 90.39kg

(remember 2% reduction means 98% remains, which is why it is (1-0.02)=0.98)

Now lets turn the question around,
Suppose we do not know by how many percent the radioactive material reduces per year but we do know that after 5 years there is only 90.39 kg of 100kg left.

Then we know 100kg * (the percentage that is left per year) ⁵ = 90.39
We can rewrite this to (the percentage that is left per year) ⁵ = 90.39/100
and finally (the percentage per year) = (90.39/100) ^(1/5) = 0.98 = 1-0.02
So 1-(90.39/100) ^(1/5) gives us the percentage the radioactive material reduces by each year!

Now to get back to your question,

we know that in 60 years only 25% will be left, hence to calculate what percentage will be left every year we have (0.25) ^(1/60) = 0.977

Suppose again we have 100kg, in year 1 the amount that will be left can be calculated by
100*0.977 = 97.7 (so it reduced by 2.3 kg)

in year 2 the amount that will be left can be calculated by

100*(0.997) ² = 95.5 (so this year it reduced by 2.2 kg)

As you can see, the amount that it reduces by is now different, yet the percentage it reduces by is the same, which is 1-0.977 = 0.023%

Now for why i use 0.25^(1/60) instead of 0.75(1/60), 0.25 stands for, 25 percentage is left after 60 years, while 0.75 stands for 75 percent remains after 60 years,

This is exactly the difference between 0.25^(1/60) and 1-(0.75/60)

I hope this helps you

reinout-gJan 29, 2014

+2353

Melody:
reinout-g:
Little logic's puzzle for whoever is interested,

You are on a quest from Proqzanthar to Krighontyr but find a T-crossing and don't know which way to go.
At the T-crossing there are two twin brothers of which one is always true and the other is always false, but you don't know which one is which.
You can ask only 1 question to either of the two brothers.
Which question do you need to ask to know whether to go left or right?

I am not sure that I understand the question.
If I can ask 1 brother 1 question and then ask the other brother a different question then I know how to do it.
Is this what you meant?

I edited it, Does that make it more understandable? So in total you can ask only 1 question and you have to pick one of the two brothers.

reinout-gJan 29, 2014

#65

+2353

Here is my version of the magic number (choose the one that is best suited to your ability level)
Rules:
You have to use some or all of the numbers to make the magic number. You are not allowed to use any of the numbers twice. (Unless one was written twice in the first place)
You can use brackets, +, -, x, or divide and that is it.

HARD ONE
2 2 5 7 17 20 and the magic number is 1994

EASIER ONE (not done yet)
3,5,2,4 and the magic number is 40

Happy calculations.

reinout-gJan 29, 2014

+2353

Fair point Melody,

I do agree 22.5%/12 is indeed more accurate for this question

reinout-gJan 29, 2014

#63

+2353

Melody:

(...)

Here are the next ones (choose the one that is best suited to your ability level)
Rules:
You have to use some or all of the numbers to make the magic number. You are not allowed to use any of the numbers twice. (Unless one was written twice in the first place)
You can use brackets, +, -, x, or divide and that is it.

HARD ONE
2,3,6,6,8,50 and the magic number is 972

EASIER ONE (not done yet)
3,5,2,4 and the magic number is 40

Happy calculations.

My answer is 6*3*(50+6-2)

Even though I cannot be sure whether the last computation is a multiplication, Unless I clearly see the number is not divisible I begin to check whether the number is divisible by any of the given numbers.
so 972/2 = 486, 972/3 = 324, 972/6 = 162

Then I check again with the numbers I have left, beginning with the smallest number (since it seems to be easier to get too)

Then 162/2 = 81, 162/3 = 54, 162/6 = 27

There is no way I can make 27 with the numbers 2,3,8,50
However, for 54 I find 54-50 = 4 and 4 = 6-2
Hence, 972/(6*3) - 50 + 2 - 6

Be aware that my method is a little trial and error.

I tried applying some other methods too such as, trying to find some numbers such that I could get 50*19 or 50*20.
This for instance gave me 50*(8*2+3), however this left me with 972-950 = 22, which I could not solve with only 6 and 6.

reinout-gJan 29, 2014

+2353

Zamarronics:
1 TB = 1048576 MB @ 1.5 MB/s = 1048576/1.5 = 699050.666667 seconds = 8.1 days

Hey Zamarronics, how do you get to 1048576 MB in 1 TB?
Unless there is some computer round off I am unaware about,tera literally means the fourth power of 1000 or 10 ¹² bytes.

Therefore I'd say that 1TB = 1000000 MB @ 1.5 MB/s = 6666666 2/3 seconds = 7.7 days

reinout-gJan 29, 2014

+2353

haha okay, fair enough,

Wouldn't really have figured that out myself,
but thanks for figuring it out for me.

reinout-gJan 29, 2014

+2353

AMaqueira3:
Trisha uses her credit card to pay for new tires that ended up totaling $527.89. She can pay off up to $200 a month. The card has an annual rate of 22.5%. How much will she pay in interest?

I will take a small detour before explaining the question to you,

Remember that if she'd borrow this amount for 3 years without paying off anything in the mean time, she would have to pay $527.89*(1.225) ³ at the end of the three years. The interest she'd have to pay in three years would then thus equal (1.225) ³-1 which is aproximately 0.838 or similarily 83.8%

Now we can do the same thing to calculate the interest Trisha has to pay every month. Since a year has 12 months, the interest per month will equal 1.225 ^(1/12)-1 = 0.017 or 1.7%.

To continue, look at it on a month to month basis

Then in month 0 she pays the $527.89

in month 1 she has interest of $527.89*0.017 = 9.00 which amounts her total debt to 536.89,
However she pays of 200 which makes her debt 336.89

Now for month 2 she has interest of $336.89*0.017 = 5.73 which amounts her total debt to ....

I think you can finish this part yourself from there on, stop when she has paid off all her debt.

Now to answer the question, you have to add up all the interest she has had to pay, so 9.00 + 5.73 + etc

Good luck

reinout-gJan 28, 2014

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