let the third no be x ,
then the first no is 3x ,
second no is 2*3x ie 6x
average is (3x+6x+x )/3 = 20
10x/3 = 20
x= 60/10 = 6
third no is 6 , second is 6x = 36, first no is 3x = 18
largest no is 36 i.e second no
35 km/h = 10 m/s
Speed = Distance/Time
Distance= (100+150)m = 250m
Speed = 10 m/s
Time= 250/10 = 25s
Pfull = 4 Hrs; Qfull = 5 Hrs
Assume velocity Vp = x then Vq = 4/5 x –> avg velocity = (5/5 + 4/5) / 2 = 0.9
If fastest time = 4hrs then the time it would take to fill up tank by alternating is 4/0.9 = 4.44 Hrs
26 rupees and 53 paise
take goat from one side and leave it another side and then come back another side and carry cabbage from one side leave it near goat and carry goat back to other side and then carry wolf leave it another side with cabbage come back to
goat side and carray goat to other side not all three are there on another side
10000*8:10000*12
2:3
5x=25000
x=5000
p:q
10000:15000
(x**2 – 6* x + 5) = (x-1)*(x-5)
(x**2 + 2 * x + 1) = (x + 1) * (x+1) = (x+1)**2
For what x is (x-1)*(x-5)/( (x+1)**2) a minimum?
One way to answer this question is by using calculus.
Take the derivative, and set to zero.
Since this is a fraction of polynomials, and a fraction is
zero only if it’s numerator is zero, we need calculate only
the numerator of the derivative and set it to zero.
The numerator of the
Derivative of (x-1)*(x-5)/( (x+1)**2) is
( (x-1) + (x-5) ) ( x+1)**2 – (x-1)(x-5)( 2 (x+1) )
= (2 x – 6) (x+1)**2 – (2) (x-1)(x-5) (x+1)
= 0
Divide through by 2 (x+1)
(x-3)(x+1) – (x-1)(x-5) = 0
(x**2 – 2 x – 3 ) – (x**2 – 6 x + 5) = 0
x**2 – x**2 – 2 x + 6 x – 3 – 5 = 0
4 x – 8 = 0
x = 2
Plugging in x = 2 into the original
(x**2-6*x+5)/(x**2+2*x+1)
gives us (2**2 – 6 * 2 + 5)/(2**2 + 2*2 + 1)
= (4 – 12 + 5) / (4 + 4 + 1) = -3/9 = -1/3
Least value is -1/3
A=P+SI——(1)
sum of money after 30 years = Double the money
A=2P———-(2)
Equate 1 and 2
P+SI=2P
SI=2P-P
SI=P————-(3)
WKT, SI= PTR/100
Equate 3 and SI
P=PTR/100
P=P*30*R/100
R=P*100/P*30
R=100/30 or 10/3 or 3(1/3) %
In a cube all the diagonal and sides are equal, we can go diagonally.
1+0^3=1
1+1^3=2
2+2^3=10
10+3^3=37
37+4^3=101
101+5^3=226
1,2,10,37,101,226……..
c