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:- Replace each letter by a digit. Each letter must be represented by the same digit and no beginning letter of a word can be 0.
Ques:- There are so many big companies like Reliance, Satyam,Infosys etc…But, y do u want to work for our company only?
Ques:- What are the soft skills training?
Ques:- India faces frequent power cut. Still why don’t the mosquito repellent companies(like All Out,Good Night) don’t provide an additional option of battery which will be used when the power is cut?
Ques:- There are 150 weights. Some are 1 kg weights and some are 2 kg weights. The sum of the weights is 260. What is the number of 1kg weights?
Ques:- What would you say are areas needing improvement?
Ques:- 80% pass in english, 70%pass in maths , 10%fail in both , 144 pass in both . How many all appeared to the test?
Recent Answer : Added by Admin On 2020-05-17 12:01:09:
pass English =80%
fail=100-80=20%
pass Math = 70%
fail in Math=100-70=30%
fail in both=10%
total fail students= fail in Eng+fail in Math-common
= 20+30-10=40%
if 40% fail then 60% will pass
let total students=x
hence
60% 0f (total students)=144
60/100 of (x)= 144
x=(144×100)/60
X=240
total students=240
Ques:- What is the next number in the series 1, 2, 4, 13, 31, 112 ..
Recent Answer : Added by Hamiss On 2022-09-29 16:38:01:
Answer is 274 .
Let the required term be x.
Pattern :- 1) Find the difference between consecutive terms as :
2 – 1 = 1
4 – 2 = 2
13 – 4 = 9
31 – 13 = 18
112 – 31 = 81
2) Now write the above numbers obtained by differences in series as :
1, 2, 9, 18, 81, y
(Suppose y be next term after 81.)
3) Look the difference series carefully and it follows the below pattern as :
(9 * 2)/1 = 18
(18 * 9)/2 = 81
(81 * 18)/9 = 162 = y (the next term after 81)
Thus the required answer is :
x = 112 + y
x = 112 +162 =274
Ques:- TEll abt yrself
Ques:- Think of the 8 vertices of a given cube. You are allowed to join three vertices to form a triangle. How many such unique acute triangles can you make ??
Ques:- What do u do after losing current job withougt information ?
Recent Answer : Added by Shaik Mohammad Javeed On 2021-11-18 17:15:42:
C)1440
2*2=4
4*3=12
12*4=48
48*5=240
240*6=1440
Ques:- Evaluate the sum of all even integers between 99 and 301?
Recent Answer : Added by Jagadeesh On 2022-09-15 16:37:00:
Summation of 301 – summation of 99
=41550
Summation of n=((n*n+1)/2)
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) Rose (b) Lily (c) Lotus (d) Marigold (e) Apple
Recent Answer : Added by Admin On 2020-05-17 12:03:34:
( e ) Apple
Ques:- From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is -.
Recent Answer : Added by Admin On 2022-09-29 19:02:13:
Explanation:
Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 ∩ E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13 = 1/26
Ques:- My mother’s sister’s son’s father’s mother-in-law is related to me as
Recent Answer : Added by Nisha On 2021-03-24 18:26:14:
maternal grand mother
Ques:- Why you want to change organization
Ques:- May 6, 1993 was Thursday. What day of the week was on May 6, 1992?
A. Tuesday
B. Wednesday
C. Friday
D. Saturday
Recent Answer : Added by Karthikraj S Nadar On 2022-08-14 16:42:06:
A. Tuesday
Ques:- How to define ourself?what format should be followed when interview ask define yourself?
Ques:- My personal life
Ques:- A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Recent Answer : Added by Peter Chibam Ebo On 2022-04-29 14:25:18:
325
Ques:- India?s largest electronics and home appliances company is :
A. Philips
B. Videocon
C. BPL
D. None of these
Recent Answer : Added by Sowmiya Sowmiya On 2023-07-06 06:58:48:
Phillips
Ques:- Why you r leave the priveous job
Ques:- Brief me something about yourself?
Ques:- A number exceeds by 25 from its 3/8 part. Then What is the number ?
Recent Answer : Added by Keshav Kumar On 2021-08-15 14:42:41:
40
Ques:- About the related field .
Ques:- TELL ABOUT YOUSELF?
Ques:- What are the kind of expectations you have from your first job?
Ques:- A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9% p.a. in 5 years. What is the sum?
Recent Answer : Added by ajay On 2022-03-18 09:20:17:
To provide the best experiences, we use technologies like cookies to store and/or access device information. Consenting to these technologies will allow us to process data such as browsing behavior or unique IDs on this site. Not consenting or withdrawing consent, may adversely affect certain features and functions.
Functional
Always active
The technical storage or access is strictly necessary for the legitimate purpose of enabling the use of a specific service explicitly requested by the subscriber or user, or for the sole purpose of carrying out the transmission of a communication over an electronic communications network.
Preferences
The technical storage or access is necessary for the legitimate purpose of storing preferences that are not requested by the subscriber or user.
Statistics
The technical storage or access that is used exclusively for statistical purposes.The technical storage or access that is used exclusively for anonymous statistical purposes. Without a subpoena, voluntary compliance on the part of your Internet Service Provider, or additional records from a third party, information stored or retrieved for this purpose alone cannot usually be used to identify you.
Marketing
The technical storage or access is required to create user profiles to send advertising, or to track the user on a website or across several websites for similar marketing purposes.
(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