slower train – 48 kmph = 40/3 m/s
say faster train, v m/s
therefore, {v-(40/3)}*180 = 600, => v= 60 kmph
d
To determine how many consecutive zeros the product of S will end with, we need to find the highest power of 10 that divides the product. This is equivalent to finding the highest power of 5 that divides the product, since the number of factors of 2 will always be greater than the number of factors of 5.
The primes in S are {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}.
There are 24 primes in S, so the product of S is:
2 x 3 x 5 x 7 x 11 x 13 x 17 x 19 x 23 x 29 x 31 x 37 x 41 x 43 x 47 x 53 x 59 x 61 x 67 x 71 x 73 x 79 x 83 x 89 x 97
We need to find the highest power of 5 that divides this product. To do this, we count the number of factors of 5 in the prime factorization of each number in S.
5 appears once: 5
5 appears once: 25
5 appears once: 35
5 appears once: 55
5 appears once: 65
5 appears once: 85
So, there are six factors of 5 in the product of S. However, we also need to consider the powers of 5 that arise from the factors 25, 35, 55, and 65.
25 = 5 x 5 appears once: 25
35 = 5 x 7 appears once: 35
55 = 5 x 11 appears once: 55
65 = 5 x 13 appears once: 65
Each of these numbers contributes an additional factor of 5 to the product of S. Therefore, there are 6 + 4 = 10 factors of 5 in the product of S.
Since each factor of 5 corresponds to a factor of 10, we know that the product of S will end with 10 zeros. Therefore, the product of S will end with 10 consecutive zeros
999,919 = 991 × 1,009
Number of cats= 991
Number of mice killed by each cat=1,009
40
GERMANY
Country Name..
X= pigeon
Y= hares
X+Y= 200
2x+4y=580
By solving y= 90
X=110
So Hares= 90
ans: .1432 inch
1-3/4=1/4
1-1/12=11/12
1/8,1/4,11/12 are broken off
so
5/8
5/8/4
5*11/8/4/12
remaining .1432inch
Let the number be X,
Instead of dividing the number by 10, i.e.,X*10.
he got the result as 100,
so, (X*10)=100
X=100/10
X=10.
BUt he has to divide X by 10,
so, X/10=10/10=1.
obviously the answer is 1.
15a=45
3000(4x/100) + 5000(2x/100)=10