Burn Rope One first, it will burn in 30 mins.Mark 30 mins and at the end of 30 mins now burn second rope from both sides (15 mins it will take ),and simultaneously burn third and last rope until it is half left.30+15= 45 , Remaining time 7.5 mins.By this time last rope is burnt half ,and now burn it from both sides as well it will exhaust in 7.5 mins. 30+15+7.5=52.5 measured.
3 groups
48,400
1, 2, 4, 13, 31, 112,?
This series is written in base 5 numbers for decimal nos of 1,2,4,8,16,32,64
so next number is 224 .
224 in base 5 = 64 in base 10.
so 224 is next number.
15
“Since I’ve been working and gaining experience to get into this company, I’d like to stay a long time if I’m offered the job, since this is where I want to be. “ “As long as there’s a lot of work to do, then I’d be happy to stay for a long time. Since I’m a busybody, I like to being productive most of the time.”
length is 30 breadth is 12 and height is 12
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1
.——————————
1 .
1 .
1 10 .
1
1 .
1
1
1 30 .
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1
consider right angled triangle
so the distance= square root of (30*30+10*10)
2hrs
12 month=>900Rs+Uniform
1month:75 => 9month:675
675-650=25 =>price of Uniform
(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
D. Vice President