What is the remainder when 13^13 is divided by 17?
@catahead said:What is the remainder when 13^13 is divided by 17?
13^2(6) x 13 / 17
1*13 / 17
=> 13 ?
@catahead said:What is the remainder when 13^13 is divided by 17?
13.
(13^2)^6 *13 /17
(-1)^6 * 13
1*13/17
R= 13
@ani6 said:Acc. to a plan a drilling team had to drill a depth of 270 mtrs. below the ground level. For the first 3 days the team drilled as per the plan. However subsequently finding that their resources were getting underutilized acc. to the plan, it started to drill 8 more mtrs. than the plan every day. therefore the day before the planned date they had drilled to a depth of 280 mtrs. how many mtrs of drilling was the plan for each day.
We can create equations....let x be metres per day and y be days...
Then xy = 270 and 3x + (x+8)(y-4) = 280 can be solved to give us the required answer.
OR
We know that metres and number of days are probably going to be factors of 270 So trial and error. Also from the numbers, metres > days. I got it on the second trial.
Try 27m x 10d, then 27*3 + 35 *6 is not 280
Try 30 x 9 then 30*3 + 38 *5 = 280. Hence 30 is the answer.
regards
scrabbler
Then xy = 270 and 3x + (x+8)(y-4) = 280 can be solved to give us the required answer.
OR
We know that metres and number of days are probably going to be factors of 270 So trial and error. Also from the numbers, metres > days. I got it on the second trial.
Try 27m x 10d, then 27*3 + 35 *6 is not 280
Try 30 x 9 then 30*3 + 38 *5 = 280. Hence 30 is the answer.
regards
scrabbler
1) The area of a circle curcumscribed about a
regular hexagon is 144 pi. What is the area of the hexagon ?
2) find the area of the triangle whose sides measure
sqrt(x+y)
sqrt(y+z)
sqrt(z+x)
regular hexagon is 144 pi. What is the area of the hexagon ?
2) find the area of the triangle whose sides measure
sqrt(x+y)
sqrt(y+z)
sqrt(z+x)
@ani6 said:plz help....Acc. to a plan a drilling team had to drill a depth of 270 mtrs. below the ground level. For the first 3 days the team drilled as per the plan. However subsequently finding that their resources were getting underutilized acc. to the plan, it started to drill 8 more mtrs. than the plan every day. therefore the day before the planned date they had drilled to a depth of 280 mtrs. how many mtrs of drilling was the plan for each day.ANS 30
30 mts.
Please do not post the OA with the question.
Approach :
let the diggin per day be a mts and let the number of days be n
na = 270
first 3 days amount dug = 3a
number of days before the last days = n-1-3
amount dug in these days = (n-4)(a+8)
so,
3a+(n-4)(a+8) = 280
soliving the two equations you will get a quadratic equation
:
8n^2 -42n -270 =0
on solving the number of days comes out to be 9
hence a = 270/9
= 30
@scrabbler
Then xy = 270 and 3x + (x+8)(y-4) = 280 can be solved to give us the required answer.
thanks...but why (y-4)???
Then xy = 270 and 3x + (x+8)(y-4) = 280 can be solved to give us the required answer.
thanks...but why (y-4)???
@ani6 said:@saurav205(13^2)^6 *13 /17(-1)^6 * 131*13/17R= 13how did you get -1??
13^2 = 169 which is 170-1.
Think of it as equivalent to -1 (since we could write it as 17k-1)
We could treat the above as (17k - 1)^6 * 13 = Now on binomial expansion, (17k-1)^6 will be [terms div by 17 + (-1)^6] i.e. 17m+1. Hence the remainder of this part is 1.
Hope it helps...
regards
scrabbler
Think of it as equivalent to -1 (since we could write it as 17k-1)
We could treat the above as (17k - 1)^6 * 13 = Now on binomial expansion, (17k-1)^6 will be [terms div by 17 + (-1)^6] i.e. 17m+1. Hence the remainder of this part is 1.
Hope it helps...
regards
scrabbler
@ani6 said:@saurav205(13^2)^6 *13 /17(-1)^6 * 131*13/17R= 13how did you get -1??
you have 13^2 as 169..
when divided by 17 it gives remainder of 16 or -1
@nole said:The area of a circle curcumscribed about a regular hexagon is 144 pi. What is the area of the hexagon ?
216*sqrt(3)???
@saurav205 Oh thanx a lot....was doing time and work stumbled upon this solution understand should again brush up numbers
@jain4444 said:Find fifth digit from the end of 5^(5^(5^(5^5)))
koi solve akro isko
Rem 123123123.....123 ( 300 digits) when divided by 99
Rem 123123123.....123 ( 300 digits) when divided by 99
Then xy = 270 and 3x + (x+8)(y-4) = 280 can be solved to give us the required answer.
how (y-4)
@ani6 said:@scrabblerThen xy = 270 and 3x + (x+8)(y-4) = 280 can be solved to give us the required answer. thanks...but why (y-4)???
3 days already gone at x per day, and now it is getting finished one day early, so there will be y-3-1 = y-4 days at x+8 waala speed.
regards
scrabbler
regards
scrabbler
@ani6 said:Then xy = 270 and 3x + (x+8)(y-4) = 280 can be solved to give us the required answer.how (y-4)
see 3 days were already utilised before they came uo with a new plan...after that they completed the work 1 day before the schedule..
so if n was the total number of days you gotta minus first 3 days and also the last day.
so after the first 3 days they dug for n-4 days.
@nole said:1) The area of a circle curcumscribed about a regular hexagon is 144 pi. What is the area of the hexagon ?2) find the area of the triangle whose sides measuresqrt(x+y)sqrt(y+z)sqrt(z+x)
1> Radius of circle = side of hexagon
pi * r^2 = 144 *pi
r=12
use Area of Hexagon =3*_/3/2 *a^2
pi * r^2 = 144 *pi
r=12
use Area of Hexagon =3*_/3/2 *a^2