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Robin =72
Dravid = 98
Azhar = 22
Sachine = 98
Total score = 290
Iron and steel
(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
19
ans: none
let it may be any number the square cant end in 8
let x be lenghth of candles.
thicker one—- in 1 hr 1/6th will go.
thinner one— in 1 hr 1/4th will go.
let he lit for n hrs.
so in n hrs thicker one goes n/6.
and thinner one goes n/4.
so remainini length are x-n/6 and x-n/4.so x-n/6=2(x-n/4)
implie n=3x. if x=1 n=3hrs.
99/1020
X-340 = X x 4 x 8/ 100
100X – 34000 = 32X
68X = 34000
X = 34000/68
X= 500.
X+x+2+x+3=42
3x+6=42
3x=42-6=36
X=12
X+2=14
X+3=15
Middle number 14
90 inches
Slab = 6(x) where x is each step
Slab = 5(x + 3)
6(x) = 5(x + 3)
6(x) = 5(x) + 15
x = 15 inches
So 6(x) = 6(15) = 90
Check: 5( x + 3) = 5(18) = 90
Slab size is 90 inches
Suppose that total 100 employees are in company….. out of that 35 are man and remaining 65 are women.
20% of man 35 = 20*35/100
40% of women = 40*65/100
total employees = 7+26 = 33 out of 100
so, Ans = 33 %
TOTAL NUMBER OF BOOKS 40+40=80
ISSUED BOOKS 30
REMAINING BOOKS 80-30=50
RATE=50/80=5/8