(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
I have seen a few say 25% as an answer to this. But looks
like their math isn’t good and is extremeley complex to
have an asnwer of 25% to this question. Consider – Rs.1.00/-
per mango; so 40 mangoes = Rs.40.00/-, implies Rs.4.00/-
extra at the end of the deal. So he’s left with Rs.44.00/-
after selling 40 mangoes implies a profit of Rs.4.00/- over
Rs.40.00 = 44/40 = 110% which means his profit is 10%.
Hope this helps…
Thanks.
only if the results are greater than my input
2637
4815
OR
2817
4635
130 years
1261
trick
(r/10)*(r/10)
(20/10)*(20/10)
4% decrese
Given:
In a group of 15 students,
7 have studied Latin,
8 have studied Greek,
3 have not studied either.
To find:
The number of students who studied both Latin and Greek.
Solution:
In a group of 15 students, have studied Latin, 8 have studied Greek, 3 have not studied either.
Therefore,
n(A∪B) = 15 – 3
n(A∪B) = 12
7 have studied Latin,
n(A) = 7
8 have studied Greek,
n(B) = 8
n(A∩B) is the number of students who studied both Latin and Greek.
n(A∩B) = n(A) + n(B) – n(A∪B)
n(A∩B) = 7 + 8 – 12
n(A∩B) = 15 – 12
n(A∩B) = 3
The number of students who studied both Latin and Greek is 3
Final answer:
3 of them studied both Latin and Greek.
Thus, the correct answer .3
Friday
In 3 hours thinker candle becomes half
In the same time thinner candle becomes one fourth. Now the
required condition is satisfied. So 3 Hours
8men=6days
Xmen=1/2days
M1=8,D1=6
M2=X,D2=1/2
Formula:
M1*D1=M2*D2
8*6=X*(1/2)
X=8*6*2
X=96
Answer=96
-Total /n=80
– x/5=40
x=200
Total/n=y/n
y-x/n-5=90
80n-200=90(n-5)
80n-200=90n-450
450-200=10n
n =25 (students) write exam
The first number is 10 and the second number is 5
i Guess 8 mtrs.
Rs.13.8677