Question

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

Answer 1

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.\[\huge 1035+ \sum_{\color{royalblue}{j}=0}^{45}\; \tan\left(\color{royalblue}{j}\frac{\pi}{180}\right) \quad = \quad 2^x\]

\[\huge x= \;\color{green}{?}\]

Answer 2

x = 22

Answer 3

@Compassionate nopes..though you were close on the logic i guess..
@zepdrix yep,,thats the right interpretation..

Answer 4

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

Answer 5

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..

Answer 6

not professors, teachers..

Answer 7

\[N\left[1035+\sum _{j=0}^{45} \text{Tan}\left[j*\frac{\pi }{180}\right],20\right]\]
Out[15]= 1055.3586583514306367

Answer 8

*

Answer 9

@mukushla yep that inequality is correct but how do you come to your conclusion ?
as according to me,,the question is perfectly fine..

Answer 10

@mukushla has proved your question wrong with his Extra ordinary thinking..

ha ha ha...

Answer 11

well i'd be glad if i am proved wrong..am waiting for him to reason this out..

Answer 12

He comes rarely online now a days ..

Answer 13

Uh, I got x=10.0435176596052.

Answer 14

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..

Answer 15

Something looks wrong to me..

Answer 16

Do you have given right choices there @Aryang

Answer 17

now that all of you are saying it,,even am smelling something fishy here..i'll confirm and get back here asap..

Answer 18

It is better now to confirm it..

Answer 19

is it an IIT question ?

Answer 20

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,.,

Answer 21

I got\[x \approx 10.04351766\]

Answer 22

*

Answer 23

as @mukushla said and there is no number which can be expressed as 2^x where x is a integer between 1035 and 1080