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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
 one year ago
 one year 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
 one year ago
 one year ago

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

AryangBest 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..
 one year ago

mukushlaBest ResponseYou've already chosen the best response.1
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
 one year ago

AryangBest ResponseYou've already chosen the best response.0
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..
 one year ago

AryangBest ResponseYou've already chosen the best response.0
not professors, teachers..
 one year ago

ZarkonBest 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
 one year ago

AryangBest 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..
 one year ago

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

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

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

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

waterineyesBest ResponseYou've already chosen the best response.0
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..
 one year ago

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

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

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

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

soty2013Best ResponseYou've already chosen the best response.0
is it an IIT question ?
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.2
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,.,
 one year ago

bdh9800Best ResponseYou've already chosen the best response.0
I got\[x \approx 10.04351766\]
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.0
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
 one year ago

robtobeyBest 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.
 one year ago
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