The speed of a boat in still water is 11 km/hr. It can go 12 km upstream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the stream.
A sector of circle of radius equal to one fourth of the diagonal of square is cut from the square taking one corner of the square as centre. If side of the square is 4 cm. then area of the remaining part is
Diagonal of the square = 4√2 cm.
Hence radius of the circle = 4√2/4 cm. = √2 cm.
Area of the sector of circle = 1/4 (π* radius2)
= 1/4 (π* (√2)2 )
= π/2
Area of the square = 4*4 = =16 cm.2
Hence area of remaining part = 16- (π/2) cm.2
= 14.43 cm^2
Multiply first factor with last and second with third factor to get
(x^2+5x+4)(x^2+5x+6)+1 = 0
Let x^2+5x = t
then
(t+4)(t+6)+1 = 0
Solve
(t+5)^2 = 0
t = -5
x^2+5x = -5
x^2+5x+5 = 0
Solve
Option 1)
Two train, Each 80 m long, passes each other on parallel lines. If they are going in same direction, the faster train takes one minute to pass the other completely. If they are going in the opposite directions, they over take each other in three second. Find the rate of each train in meter per second.
Let the speed of faster train be x m/sec and other train be y m/sec
Since
T = D/S
Then we get
x - y = 8/3 (i)
x + y = 160/3 (ii)
Now solving (i) and (ii)
x=28 m/sec and y=76/3 m/sec
When I fill, I am alone & a lot of haze in my life. I close myself in a room with a mathematics book. It fills a thrill in my mind..!
Ravi Ranjan Ojha
Six is a number perfect in itself, and not because God created the world in six days; rather the contrary is true. God created the world in six days because this number is perfect, and it would remain perfect, even if the work of the six days did not exis