Ques:- When x is real what is the least value of (x**2-6*x+5)/(x**2+2*x+1)
Recent Answer : Added by Admin On 2020-05-17 12:01:23:
(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
Ques:- What is the least number to be subtracted from 696 to make it a perfect square?
Recent Answer : Added by Amicah Maina On 2022-08-14 16:43:30:
20
Ques:- Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group?
A. Fruit
B. Leaf
C. Flower
D. Tree
E. Trunk
Recent Answer : Added by Susanna On 2021-08-10 15:21:36:
Tree
Ques:- After working for 6 days, Ashok finds that only 1/3 rd of the work has been done. He employs Ravi who is 60% as efficient as Ashok. How many days more would Ravi take to complete the work?
Ques:- Tell me something about your family background?
Ques:- X, Y and Z started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of Y is Rs. 1500. The difference between the profit shares of X and Z is?
Recent Answer : Added by Roop On 2021-09-18 16:12:08:
Profit ratio will be : 4:5:6
5x=150
X=300
X share is 1200
Y share is 1800
Difference will be = x-y =600
Ques:- A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is?
Recent Answer : Added by Shitoshe Wangatia On 2021-12-11 15:07:20:
854=P(1+4r)
P+4r=854
Solve the sums using Elimination method.
P+4r=854
P+3r=815
r=39.
Toget Principal
P+4r=854
P+4*39=854
P=854-117
P=698
Ques:- A worker earns a 5% raise. A year later, the worker receives a 2.5% cut in pay, & now his salary is Rs.22702.68
What was his salary to begin with?
Recent Answer : Added by Admin On 2020-05-17 12:01:03:
Assume his salary was Rs. X
He earns 5% raise. So his salary is (105*X)/100
A year later he receives 2.5% cut.
So his salary is ((105*X)/100)*(97.5/100)
which is Rs. 22702.68
So Ans is Rs.22176
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Ques:- Any Recent Movie you Saw Tell Me Story in Short ?
Ques:- Are you willing to work at night?
Recent Answer : Added by jackson On 2022-11-29 17:07:09:
Recent Answer : Added by jag On 2022-01-08 16:05:38:
-1
Ques:- Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
Ques:- How many figures are required for numbering the pages of a book containing 1000 pages?
Recent Answer : Added by MG On 2022-03-09 16:28:41:
pages # figures
1000 1000 4
from 999 to 100 (999-99)*3 2700
from 99 to 10 (99-9)*2 180
from 9 to 1 (9-0)*1 9
total sum= 2893
Ques:- In your opinion, what is the most beautiful math equation ever derived?
Recent Answer : Added by Admin On 2020-05-17 12:01:49:
obvious
e^(i*pi) + 1 = 0
Ques:- 3 persons started placementpapers with a capital of Rs.3000 . B invest Rs.600 less than A, C invest Rs.300 less than B. Then what is the share amount of B in a profit of Rs.886 ?
Recent Answer : Added by Admin On 2020-05-17 12:04:24:
Rs.265.80
Ques:- What will you do if our competitor offered you a higher salary?
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Ques:- Why haven’t you done your PG?
Ques:- ?Laterite Soil? is found in India in:(a) Western Ghats(b) Eastern Ghats(c) Deccan Plateau(d) Satpura region in Madhya Pradesh
Ques:- The town of Paranda is located on Green Lake. The town of Akram is west of Paranda. Tokhada is east of Akram but west of Paranda. Kakran is east of Bopri but west of Tokhada and Akram. If they are all in the same district, which town is the farthest west?
Recent Answer : Added by Emily Tilden On 2022-08-14 16:43:10:
Bopri is farthest to the west followed by Kakran, Akram, Tokhada, and Paranda to the east.
Ques:- Jack & Jill went to the hill….In going to hill (upword Direction)…Jack went to the hill first nd waited for Jill for “x” hours.. Jack’s speed was then twice of Jill.. In the down word direction Jill can go 3km in a hour, while Jack can go 1km in 1 hour.. Jill reach the ground 1st nd waited for Jack for “x” hours.. Total journey they traveled is 6 km.. Find the speed of Jack…
Recent Answer : Added by Admin On 2020-05-17 12:03:21:
previous ans wrong again..!!!!
first find x its 2 hours
total journey 6 hrs 3km up and also down
jill takes one hr to come down and jack takes 3 hrs so x
is 2 hours….
And while going up jack goes at 1.5km/hr and jill goes at
0.75 km hr so to travel 3 km they take 2 hrs and 4 hrs
respectively…!!! x again is 2 hrs…
so jack totally takes 5 hrs to travel 6 km
therfore speed is 6/5 km per hour
thats is 1.2 km per hour is the correct answer
Ques:- Why u want to join as a m.r?
Ques:- If you found 10 million dollars that belongs to nobody, what would you do?
Recent Answer : Added by Prajapati mitesh On 2022-08-14 16:41:51:
I will try to find that person
Or give that bag to police ..
Ques:- How many years experience you have in this field?
Ques:- There are 9 cities numbered 1 to 9. From how many cities the flight can start so as to reach the city 8 either directly or indirectly such the path formed is divisible by 3.
(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