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Harut

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  • 1 year later...
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Which deal would you take ...

 

... a $500 raise every 6 months?

... or a $2000 raise every year?

I tried to see the challenge in this question but could not. Seems simple - depends on the interest rate. I am assuming the raise amounts are per year. Am I missing something? :unsure:

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I think it's a matter of interpretation.

 

A 500$ raise (on an semiannual basis) is the equivalent of a 1000$ annual raise. If the premise is that you're getting it every six months, therefore 2 raises a year, then:

 

Looking at option 1, if you take the 500$ semi annual raise, and your salary is X, the chart shows your income at six month intervals (hence the annual salary of X dividedby 2)

X/2 + 500

(X+500)/2 + 500

(X+1000)/2 + 500

(X+1500)/2 + 500

(X+2000)/2 + 500

(X+2500)/2 + 500

 

So the total after 3 years gives us: 3X + 6750$, which works out to an annual increase of 2250$, a whole 250$ higher than the 2000$ offered as option 2.

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I dont get it Vava jan.

 

Assuming 50K salary to start after 10 years(each line is 6 months)

500    50500    0        50000
500    51000    2000    52000
500    51500    0        52000
500    52000    2000    54000
500    52500    0        54000
500    53000    2000    56000
500    53500    0        56000
500    54000    2000    58000
500    54500    0        58000
500    55000    2000    60000
500    55500    0        60000
500    56000    2000    62000
500    56500    0        62000
500    57000    2000    64000
500    57500    0        64000
500    58000    2000    66000
500    58500    0        66000
500    59000    2000    68000
500    59500    0        68000
500    60000    2000    70000

Edited by Azat
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Which deal would you take ...

 

... a $500 raise every 6 months?

... or a $2000 raise every year?

 

 

There's no interst. You are getting a lump sum either anually (like $10,000 a year) or sum/2 every six months ($5,000 + $5,000).

 

500 is not 2000/2

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i didn't calculate 500 vs 2000, but for x/2 semi-anually vb x anually...

basically, by the end of the year, your salary is the same, but during the second half of the year you have been paid with x/2 raise...

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        monthly        monthly    
48000    4000    48000    4000    month 1
        4000            4000    month 2
        4000            4000    month 3
        4000            4000    month 4
        4000            4000    month 5
        4000            4000    month 6
48500    4041.67        4000    month 7
        4041.67            4000    month 8
        4041.67            4000    month 9
        4041.67            4000    month 10
        4041.67            4000    month 11
        4041.67            4000    month 12
49000    4083.33    49000    4083.33    month 13
        4083.33            4083.33    month 14
        4083.33            4083.33    month 15
        4083.33            4083.33    month 16
        4083.33            4083.33    month 17
        4083.33            4083.33    month 18
49500    4125        4083.33    month 19
        4125            4083.33    month 20
        4125            4083.33    month 21
        4125            4083.33    month 22
        4125            4083.33    month 23
        4125            4083.33    month 24
sum    97500        97000    
        50000        50000

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        monthly        monthly    
48000    4000    48000    4000    month 1
        4000            4000    month 2
        4000            4000    month 3
        4000            4000    month 4
        4000            4000    month 5
        4000            4000    month 6
48500    4041.67        4000    month 7
        4041.67            4000    month 8
        4041.67            4000    month 9
        4041.67            4000    month 10
        4041.67            4000    month 11
        4041.67            4000    month 12
49000    4083.33    49000    4083.33    month 13
        4083.33            4083.33    month 14
        4083.33            4083.33    month 15
        4083.33            4083.33    month 16
        4083.33            4083.33    month 17
        4083.33            4083.33    month 18
49500    4125        4083.33    month 19
        4125            4083.33    month 20
        4125            4083.33    month 21
        4125            4083.33    month 22
        4125            4083.33    month 23
        4125            4083.33    month 24
sum    97500        97000    
        50000        50000

Harut jan the second column shoudl be 2000 increase and not 1000

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48000    4000    4000    48000    4000    4000
    4000    8000        4000    8000
    4000    12000        4000    12000
    4000    16000        4000    16000
    4000    20000        4000    20000
    4000    24000        4000    24000
48500    4042    28042    48000    4000    28000
    4042    32083        4000    32000
    4042    36125        4000    36000
    4042    40167        4000    40000
    4042    44208        4000    44000
    4042    48250        4000    48000
49000    4083    52333    50000    4167    52167
    4083    56417        4167    56333
    4083    60500        4167    60500
    4083    64583        4167    64667
    4083    68667        4167    68833
    4083    72750        4167    73000
49500    4125    76875    50000    4167    77167
    4125    81000        4167    81333
    4125    85125        4167    85500
    4125    89250        4167    89667
    4125    93375        4167    93833
    4125    97500        4167    98000
50000    4167    101667    52000    4333    102333
    4167    105833        4333    106667
    4167    110000        4333    111000
    4167    114167        4333    115333
    4167    118333        4333    119667
    4167    122500        4333    124000
50500    4208    126708    52000    4333    128333
    4208    130917        4333    132667
    4208    135125        4333    137000
    4208    139333        4333    141333
    4208    143542        4333    145667
    4208    147750        4333    150000

 

On teh 14th Month they the total salaries catch up

Edited by Azat
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Harut jan the second column shoudl be 2000 increase and not 1000

 

actually, i was going by Sip's second post, where he said full anually or half semi-anually... i thought he made a mistake on the first post...

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  • 2 months later...

ok i've been banging my head for two days now without success over this.

 

i'm trying to get the square root of a number without using Math.sqrt or Math.pow functions in java.

does anyone know of a method to get the sqrt of a number without these?

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What kind of number? Any number? You can use some sort of iterative search to find the answer. One of the most common ways to do this is Newton's method. The basic iteration for doing Newton's method looks like this:

 

x_next = x_curr - f(x_curr) / f'(x_curr)

 

By starting from some x_curr, doing the iteration above repeatedly will eventually lead to an x such that f(x)=0, if such an x exists of course. To solve the square root problem, let f(x) = x*x - n where n is the number for which you want to find the square root. Then f'(x) in this case is 2x. Thus, the Newton's iteration becomes:

 

x_next = x_curr - (x_curr*x_curr-n) / (2*x_curr)

 

 

With a loop like this, you should be able to find a decent square root:

 

x=1;
while (abs( x * x - n) > 0.00001) {
  x = x - (x*x-n)/ (2*x);
}

 

Note that this thing will diverge if you let n=0 and will eventually cause a divide by 0 problem. But it should work fine for most cases. Also, you might be able to pick a better starting point than just 1. You may also wish to limit the total number of iterations as opposed to waiting for a certain accuracy (in this case 0.00001). The other things to watch out for is that you might end up at the negative square root of a number (depending on where you start) since each positive real number has potentially 2 real square roots. But that's an easy check on the final answer. Negative numbers for n will most likely cause problems too.

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thanks alot.

i forgot that i studied the newtons method in calc 2.

:P

actually i forgot the newtons method too. :sleep1:

 

this is exactly what i needed. to be able to decrease the error as much as i wanted for the sqrt.

 

tnx again.

Edited by hytga
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  • 3 weeks later...

If I may insert a challeng, here is it.

 

A car is travelling at a constant 120 km/h, it passes a cop on a motorcyle and the cop takes .2 seconds to take off after it. With an acceleration of 6 m/s/s, and a maximum speed of 150km/h, how long will it take for the cop to reach the car, and at what distance.

 

I dont know the answer yet, it was a refresher problem in my dynamics course. I have to work it out anyways, lets see how this goes.

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ok i've been banging my head for two days now without success over this.

 

i'm trying to get the square root of a number without using Math.sqrt or Math.pow functions in java.

does anyone know of a method to get the sqrt of a number without these?

runga kutta method works fastest, the equation should be on the net somewhere, its been a while, so i dont remember it percisely.

 

 

edit: Newton's method is good too, most simple to work.

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ok... this is nto a math puzzle but its pretty cool. It was on car talk recently. Please dont just Google for the answer.

 

---

Imagine that you and I are sitting opposite one other at a small round table at the kind you find at a bistro or a cafe, or some other place that sells overpriced beverages and desserts. Next to us is a supply, unlimited if need be, of soda pop bottles.

 

Here's the game we're going to play:

 

One of us is going to place a bottle on the table, upright. And then the other one's going to place a bottle on the table and that's going to end round one. The game consists of many rounds, perhaps.

 

The same person who went first is going to put another bottle on the table, then the person who went second is going to put his bottle on the table. So, if you go first, you'll place your bottle on the table, then I'll place my bottle. In round two you place your bottle and I place my bottle, etc. We're going to continue to do this until we black out!

 

Actually, we're going to continue to do this until somebody puts a bottle on the table that either doesn't fit, or falls off, or causes another bottle to fall off the table. The rule is that you can place your bottle anywhere on the table, but you can't move anyone else's bottle.

 

The question very simply is: Is there a strategy to win? And do you want to go first or second?

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Winning strategy:

 

When the table gets nearly full, and there at least one bottle close to the edge of the table - as your opponent has nearly placed his bottle on the table, you imperceptibly kick the table leg nearest you. That'll cause the table to jiggle slightly and "your opponent" will have disturbed the bottles - resulting in your win :D

 

:)

 

No just kidding - that would be cheating, and everyone knows that no Armenian would ever cheat. :o

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How about you go first.

You put your first bottle in the exact middle of the table.

For your second bottle, you place it symmetrically opposed to your opponents first bottle. I'm not sure if that's how you express it, but essentially, for every bottle your opponenent places on the table, you place your next bottle at the exact opposite spot with respect to the middle of the table. This pretty much guarantees that at the end of the game there will be an odd number of bottles on the table - you having gone first, would be the winner. :D :D :thumbsup: nice puzzle!!!

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