anonymous
  • anonymous
a challenge question for all if 1035 + summation( tan( j pi/180) ) from j =0 to 45 = 2^x then x= 1) 20 2)21 3)22 4)23
Mathematics
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SOLVED
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katieb
  • katieb
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zepdrix
  • zepdrix
I don't know the answer, but I thought I'd format this for you so it's a little easier to read. Hopefully I read it correctly.\[\huge 1035+ \sum_{\color{royalblue}{j}=0}^{45}\; \tan\left(\color{royalblue}{j}\frac{\pi}{180}\right) \quad = \quad 2^x\] \[\huge x= \;\color{green}{?}\]
Compassionate
  • Compassionate
x = 22
anonymous
  • anonymous
@Compassionate nopes..though you were close on the logic i guess.. @zepdrix yep,,thats the right interpretation..

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anonymous
  • anonymous
how can it be a power of 2 with ur options :) because\[\large \sum_{\color{royalblue}{j}=0}^{45}\; \tan\left(\color{royalblue}{j}\frac{\pi}{180}\right) \quad <45 \ \tan \frac{\pi}{4}=45 \]if im not wrong
anonymous
  • anonymous
please whosover sees it atleast bookmark it, so that if someone tells the solution or finally i tell the solution, you get to know that the solution really exists and is a genius one! :) note that i couldnt solve it either, but one of my professors did..
anonymous
  • anonymous
not professors, teachers..
Zarkon
  • Zarkon
\[N\left[1035+\sum _{j=0}^{45} \text{Tan}\left[j*\frac{\pi }{180}\right],20\right]\] Out[15]= 1055.3586583514306367
shubhamsrg
  • shubhamsrg
*
anonymous
  • anonymous
@mukushla yep that inequality is correct but how do you come to your conclusion ? as according to me,,the question is perfectly fine..
anonymous
  • anonymous
@mukushla has proved your question wrong with his Extra ordinary thinking.. ha ha ha...
anonymous
  • anonymous
well i'd be glad if i am proved wrong..am waiting for him to reason this out..
anonymous
  • anonymous
He comes rarely online now a days ..
queelius
  • queelius
Uh, I got x=10.0435176596052.
anonymous
  • anonymous
So, it means the term : \(\large \sum_{\color{royalblue}{j}=0}^{45}\; \tan\left(\color{royalblue}{j}\frac{\pi}{180}\right)\) can have one of the four values according to the choices given : 1047541 Or 2096117 Or 4193269 Or 8387573..
anonymous
  • anonymous
Something looks wrong to me..
anonymous
  • anonymous
Do you have given right choices there @Aryang
anonymous
  • anonymous
now that all of you are saying it,,even am smelling something fishy here..i'll confirm and get back here asap..
anonymous
  • anonymous
It is better now to confirm it..
anonymous
  • anonymous
is it an IIT question ?
shubhamsrg
  • shubhamsrg
well one thing i can easily make out is 1035 = summ( j) from j=0 to 45 so LHS on whole can be written as summation (j + tan(j pi/180) ) from j=0 to 45 my personal query is that, are you sure its summation there? if thats the product symbol there,,i can easily come to ans.otherwise i doubt,.,
anonymous
  • anonymous
I got\[x \approx 10.04351766\]
Callisto
  • Callisto
*
anonymous
  • anonymous
as @mukushla said |dw:1356354261761:dw| and there is no number which can be expressed as 2^x where x is a integer between 1035 and 1080
anonymous
  • anonymous
@bdh9800's numerical answer is correct. x = 10.0435176596051999738145449873985899460812855308 to 48 digits. Refer to the attached Mathematica solution.
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