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(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
Greatest number of 5 digits=99, 999
Smallest number of 5 digits=10, 000
And their sum=99, 999+10, 000=109, 999
FYI
3;4
99/1020
time is inversely proportional to speed.
So if speed taken is 4/5 of usual speed, time taken will be 5/4 of usual time
and the difference between time is 10 min
So,
(5/4)t -t=10 min
usual time,t=40 min
late time=40+10=50 min
1997
For optimal size of a project team..
the % increase in staff size should be “Zero”
reason:
additional member directly proportional to increase in
staff size..
b
Answer: z and u
Explanation:
Y is to the right of U and exactly in front of V. Therefore,
U Y
V
Z is behind W and W and X are at extreme ends. So, W has to be to the right of Y. The final arrangement is as follows.
U Y W
X V Z Therefore, Z and U are at extreme ends is true.
Perimeter of semi circular = πr+2r
Where r is radius , π = 22/7
πr+2r= 144 (given)
(22/7)r +2r = 144
22r+14r = 144*7 (multiply both sides by 7)
36r = 144*7
r= 144*7/36 = 28
radius =28 cm
Area =( 1/2)πr^2
Area=( 1/2 )*(22/7)*28*28
= 1232cm^2
Ans : area is 1232 cm^2
w, l=2w , area of square =8^2 = 64
area of rectangle = l*b
so w*2w = 8*64
w=16
length = 32
The rational number that does not have a reciprocal 0 because reciprocal of 0 is undefined.
maternal grand mother
T is the last speaker.
accountant trainee at thenational board of accountants and auditors