Time taken (t) = 3 sec
Velocity of sound (v) = 332 m/s
Distance travelled (d) = ?

We know,

d = v x t = 332 x 3 = 996 m

Hence, the source of thunder is about 996 m far from the boy.

Log_2aa=x    then, a=(2a)^x  ......(1)

Log_3a2a=y    then,2a=(3a)^y ......(2)

Log_4a 3a=z  then, 3a=(4a)^z ......(3)

So, 

a=(2a)^x  [from (1)]

Or, a=(3a)^xy    [from(2)]

Or, a=(4a)^xyz     [from(3)]

Multiplying both sides by 4a,

4a.a=4a.(4a)^xyz  

Or,(2a)² =(4a)^{xyz + 1} 

Or,(3a)^2y =(4a)^xyz+1 

Or,(4a)^2yz =(4a)^xyz+1 

Or, 2yz = xyz+1 .proved.

#include<stdio.h>

#include<conio.h>

#include<string.h>

int main() {

int i, nextTerm;

int t1 = 2, t2 = 2;

nextTerm = t1+t2;

printf("%d, %d, ", t1, t2);

for (i = 3; i <= 10; ++i) {

printf("%d, ", nextTerm);

t1 = t2;

t2 = nextTerm;

nextTerm = t1 + t2;

}

return 0;

}

Yes, a vector which has zero magnitude is also a vector in case of two vectors travelling in opposite directions with equal magnitudes. At this case, the resultant vector has zero magnitude but it is still a vector. We call it a null vector.

a)When silver nitrate comes in contact with skin, it is reduced to white color metallic silver.In most cases, a black stain appears due to formation of finely divided silver which has black color.

The black color is due to the decomposition of the Ag+ ion into Ag, silver. Silver nitrate will slowly decompose with the silver ion reverting to elemental silver. The microscopic particles of silver are so small that they absorb light instead of reflecting it, and so appear black, instead of silver....

Here, the given equation of parabola is y²= 8x.

The equation of tangent to the parabola y²=8x is,

y= mx + 2/m

This tangent passes through the point (-2, 3)

So, 3 = -2m + 2/m

or, 3m + 2m² = 2

or, 2m²+3m - 2= 0

or, 2m² + (4 - 1)m -2 = 0

or, 2m² + 4m - m - 2 = 0

or, 2m(m + 2) - 1(m+2) = 0

or, (m + 2) (2m - 1) = 0

Either, Or,

m = -2 m = 1/2

Required angle is,