IIT JEE , AIEEE Forum - Mathematics , Algebra

shailesh_45

the internal angles of a polygon are in AP. the smallest angle is 120degree and the common difference is 5 degree . find the number of sides of the polygon and the sum of internal angles .

there are 25 trees at equal distance of 5 metres in a line with a well , the distance of a well from the nearest tree being 10 metres . a gardener waterws all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next . find the total distance the gardener will cover in order to water all trees.

a gentleman deposites one paise in a bank on the first of march . in the subsequent days he deposits two paise more than his balance with the bank till the previous day . what will be his balance at the end of the month .

there are n stones in a line , the distance between the consecutive stones being 1m,3m,5m, ,etc . tthere is a basket fixed at the first stone . a man starting from the basket collects all the stones in the basket one by one . find the total distance described by him in collecting all the stones .

rates assured , if not given nudge

akhil_o

1)
a=120,d=5
Sn=(n-2)180

Sn=n/2(2a+(n-1)d)
=n/2(240+(n-1)5)

180n-360=n/2(235+5n)
360n-720=235n+5n*n
n²-25n+144=0

or n=9 or 16

thanks to nadeemoidu...
n=16 has to be omitted since angle>180
so n=9 is the only solution

akhil_o

2) distance to the 'i'th tree is given by
d=10+(i-1)5
now for each plant the gardener travels twice the distance...
so
D=2d=10(2+i-1)=10(i+1)

so total distance=summation (i=1 to i=25)
5i(i+1)+10i
=5i²+15i

5(25)²+15(25)
=3500m
but he does not make last trip from last tree to well=120+10 =130 m

so min dist=3500-130=3370m

nadeemoidu

1)
@akhil
when n=16, one of the angles is 180 degree. since this is not possible , we have to remove this case . so the answer is n=9.

raulrag009

spideyunlimited

a gentleman deposites one paise in a bank on the first of march . in the subsequent days he deposits two paise more than his balance with the bank till the previous day . what will be his balance at the end of the month

he deposits...
1 then (1+2)
then 1 + (1+2) + 2. .. and so on

So he deposits (starting from day 1) :
1
3
6
12
24
48
96
....
and so on
as you can see after the first day, it is a GP with r = 2
..

Considering the month to be 30 days :
total balance at end of month =
1 + (3 + 3*2 + 3*2*2 + 3*2*2*2 ..... 3*2*2... with 28 2s)
= 1 + 3*(2^29 - 1) / (2 - 1)

= 1 + 3(536870912 - 1) / 1
= 1 + 3 (536870911)
= 1 + 1610612733 = 1610612734

shailesh_45

1)akhil how did u get Sn = (n-2)180

deedee

hey itz a knw formula

d sum of all interior angles of a polygon of n sides

is 180*(n-2)

2tone

Actually any 'n' sided regular polygon can be divided into 'n' equilateral triangles with their common vertex at the geo. centreof the polygon.

the sum of all the angles of the tri. is 180*n. Since 360deg is contributed by central angle,

sumof int angles of polygon is :

180*n - 360 = 180*(n-2)

shailesh_45

thanks

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