- #1

vishal007win

- 79

- 0

^{65}-29

^{65})/(30

^{64}+29

^{64})

find the range of R?

can any please help me out..

what approach i need to attack this problem?

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- Thread starter vishal007win
- Start date

In summary, the value of R is approximately 24 and the approach used to find it was to divide the numerator and denominator by 30^65 and then use the approximation (1+x)^y \approx e^{xy}. This resulted in the equation 30 * (1-e^{-65x}) / (1+e^{-64x}) \approx 30 * 0.9 / 1.1 \approx 24.

- #1

vishal007win

- 79

- 0

find the range of R?

can any please help me out..

what approach i need to attack this problem?

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- #2

tiny-tim

Science Advisor

Homework Helper

- 25,839

- 258

vishal007win said:^{65}-29^{65})/(30^{64}+29^{64})

find the range of R?

can any please help me out..

what approach i need to attack this problem?

Hi vishal007win!

I don't understand …

(30

- #3

vishal007win

- 79

- 0

what is the range in which R lies?

is it

1. 0< R <0.1

2. 0.1< R < 0.5

3. 0.5< R <0.7

4 0.7< R <1

- #4

retracell

- 22

- 0

If you find the value of R, it ends up being approximately 24 and doesn't lie in any of those choices.

- #5

vishal007win

- 79

- 0

@retracell

how did you approached to this solution??

how did you approached to this solution??

- #6

hamster143

- 911

- 2

The easiest way to see that it's on the order of 30 is to divide the numerator and the denominator by 30^65 and to use the approximation [itex](1+x)^y \approx e^{xy}[/itex], which holds with good accuracy if x is small and y is large.

- #7

vishal007win

- 79

- 0

i get something like this

R=(1-y

where y=29/30

now writing y=(1-x)

where x=1/30

[itex]

(1-(1-x)^{65})/30*(1+(1-x)^{64})

[/itex]

now using this

[itex]

(1+x)^y \approx e^{xy}

[/itex]

i got

[itex]

(e^{65x} -1)/30*e^x*(e^{64x}+1)

[/itex]

which finally gives the answer R=0.024

now please check the solution...n point out my mistakes

- #8

hamster143

- 911

- 2

No, it should be

[tex] 30 * (1-e^{-65x}) / (1+e^{-64x}) \approx 30 * 0.9 / 1.1 \approx 24[/tex]

[tex] 30 * (1-e^{-65x}) / (1+e^{-64x}) \approx 30 * 0.9 / 1.1 \approx 24[/tex]

- #9

vishal007win

- 79

- 0

calculation mistake..

thnx

now i got it...

thnx

now i got it...

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