Solving "A Trick Question - Find R Range & What Approach to Use

[vishal007win]

R=(30⁶⁵-29⁶⁵)/(30⁶⁴+29⁶⁴)

find the range of R?

can any please help me out..
what approach i need to attack this problem?

 

[tiny-tim]

R=(30⁶⁵-29⁶⁵)/(30⁶⁴+29⁶⁴)

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 …

(30⁶⁵-29⁶⁵)/(30⁶⁴+29⁶⁴) is a constant, so how can there be a range?

 

[vishal007win]

sorry the question was..
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

 

[retracell]

I think the question is asking for something else.

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

 

[vishal007win]

@retracell
how did you approached to this solution??

 

[hamster143]

yep, approximately 24.

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 $(1+x)^y \approx e^{xy}$, which holds with good accuracy if x is small and y is large.

 

[vishal007win]

yup after dividin by 30^65 both num. and den.
i get something like this
R=(1-y⁶⁵)/30*(1+y⁶⁴)

where y=29/30

now writing y=(1-x)
where x=1/30

$(1-(1-x)^{65})/30*(1+(1-x)^{64})$
now using this
$(1+x)^y \approx e^{xy}$
i got

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

which finally gives the answer R=0.024

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

 

[hamster143]

No, it should be

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

 

[vishal007win]

calculation mistake..

thnx
now i got it...