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 2 years ago
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
 2 years ago
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

This Question is Closed

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.0I 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.\[\huge 1035+ \sum_{\color{royalblue}{j}=0}^{45}\; \tan\left(\color{royalblue}{j}\frac{\pi}{180}\right) \quad = \quad 2^x\] \[\huge x= \;\color{green}{?}\]

Aryang
 2 years ago
Best ResponseYou've already chosen the best response.0@Compassionate nopes..though you were close on the logic i guess.. @zepdrix yep,,thats the right interpretation..

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.1how 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

Aryang
 2 years ago
Best ResponseYou've already chosen the best response.0please 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..

Aryang
 2 years ago
Best ResponseYou've already chosen the best response.0not professors, teachers..

Zarkon
 2 years ago
Best ResponseYou've already chosen the best response.0\[N\left[1035+\sum _{j=0}^{45} \text{Tan}\left[j*\frac{\pi }{180}\right],20\right]\] Out[15]= 1055.3586583514306367

Aryang
 one year ago
Best ResponseYou've already chosen the best response.0@mukushla yep that inequality is correct but how do you come to your conclusion ? as according to me,,the question is perfectly fine..

waterineyes
 one year ago
Best ResponseYou've already chosen the best response.0@mukushla has proved your question wrong with his Extra ordinary thinking.. ha ha ha...

Aryang
 one year ago
Best ResponseYou've already chosen the best response.0well i'd be glad if i am proved wrong..am waiting for him to reason this out..

waterineyes
 one year ago
Best ResponseYou've already chosen the best response.0He comes rarely online now a days ..

queelius
 one year ago
Best ResponseYou've already chosen the best response.0Uh, I got x=10.0435176596052.

waterineyes
 one year ago
Best ResponseYou've already chosen the best response.0So, 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..

waterineyes
 one year ago
Best ResponseYou've already chosen the best response.0Something looks wrong to me..

waterineyes
 one year ago
Best ResponseYou've already chosen the best response.0Do you have given right choices there @Aryang

Aryang
 one year ago
Best ResponseYou've already chosen the best response.0now that all of you are saying it,,even am smelling something fishy here..i'll confirm and get back here asap..

waterineyes
 one year ago
Best ResponseYou've already chosen the best response.0It is better now to confirm it..

soty2013
 one year ago
Best ResponseYou've already chosen the best response.0is it an IIT question ?

shubhamsrg
 one year ago
Best ResponseYou've already chosen the best response.2well 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,.,

bdh9800
 one year ago
Best ResponseYou've already chosen the best response.0I got\[x \approx 10.04351766\]

sauravshakya
 one year ago
Best ResponseYou've already chosen the best response.0as @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

robtobey
 one year ago
Best ResponseYou've already chosen the best response.0@bdh9800's numerical answer is correct. x = 10.0435176596051999738145449873985899460812855308 to 48 digits. Refer to the attached Mathematica solution.
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