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:- A sum of Rs. 64 is made up of 80 coins which are either 100 paise or 50 paise coins. How many coins are of 50 paise?
A. 22
B. 32
C. 42
D. 52
Recent Answer : Added by Avisikta On 2021-12-09 18:39:36:
Let’s say,
I have x coins of 50 paise and (80-x) coins of 100 paise,so the equation is like this ,
50x + (80-x)*100 = 64*100
x = 32
So ,I have 32 coins of 50 paise
Ques:- Find out the wrong number in each sequence:
36, 54, 18, 27, 9, 18.5, 4.5
A. 4.5
B. 8.5
C. 18.5
D. 18
Recent Answer : Added by Abhishek On 2022-08-14 16:32:18:
C
Ques:- In a race if A beat B by 15m, A beat C by 25m and in a race between B and C, B beat C by 15m.Find the length of the tracks.
Ques:- Name the extra co-curricular activities you participated in and how many awards did you win?
Ques:- If Re.1 amounts to Rs.9 over a period of 20 years.Evaluate the rate of simple interest?
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Ques:- I participated in a race.1/5th of those who are before me are equal to 5/6th of those behind me. What were the total number of contestants in the race?
Ques:- consider expresion ‘ab’ . what happens when ‘a’ is divided by ‘c’ & ‘b’ is multiplied by ‘c’.
Recent Answer : Added by tsion On 2022-03-19 16:02:17:
exactly
Ques:- A person’s present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old id the mother at present?
Recent Answer : Added by MAMIDI LIJITA SREE On 2023-01-21 17:36:34:
40
Ques:- How are see your future in industrial environment.
Ques:- Find the average of the series : 312, 162, 132, 142 and 122?
Recent Answer : Added by L.Lalitha priya On 2022-05-17 08:56:37:
Sum of all numbers in series= 870 (I.e 312+162+132+142+122)
Average=sum of numbers/count of numbers
Average= 870/5
= 174
Ques:- Asked about my family details?
Ques:- If in a certain language FASHION is coded as FOIHSAN, how is PROBLEM coded in that code ?
Recent Answer : Added by Sowji On 2022-05-17 08:54:19:
FASHION= FOIHSAN
It is F-ASHIO-N to F-OIHSA-N.
So PROBLEM will be P-ROBLE-M,
the answer is PELBORM.
Ques:- A room is 15m long, 4m broad and 3m height. Find the cost of white washing its four walls at 50p per m2Â ?
Recent Answer : Added by Sourabh Singh Rawat On 2021-10-10 19:03:37:
2*3(15+4)=114
114*1/2=57 rs
Ques:- A worker pay 20/- day , he works 1, 1/3,2/3,1/8.3/4 in a week. what is the total amount paid for that worker
Recent Answer : Added by Admin On 2020-05-17 11:59:30:
20/- per day
So, if he work one day
So,1*20=20
1/3*20=20/3
2/3*20=40/3
1/8*20=5/2
3/4*20=15
so,
20+20/3+40/3+5/2+15=57.5
So ans is 57.5 is the ans
Ques:- The sum of the first four primes is
A. 10
B. 11
C. 16
D. 17
Recent Answer : Added by Anjum Parveen On 2022-03-09 16:31:39:
the sum of first 4 primes numbers =2+3+5+7 =>17
Ques:- BEST MEMORABLE WORTH EXPERIENCE IN THE CAREER
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Ques:- A cube of side 4cm is painted with colors red,blue,green in such a way that opposite sides are painted in the same colour . this cube is now cut into 64 cubes of equal size .then 1) how many have atleast two sides painted in different colours.
Ques:- Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest?
Recent Answer : Added by Karan Chavan On 2022-03-13 16:35:27:
Ans 635.5
4000
1 year 5 % 200 rs int
Total 4200
2 year 5 % 210 ra int
Total 4410
4410-2210 = 2200
1 year 5% 110
Total 2310
2 year 5 % 115.5 rs int
Total 2425.5
Total interest paid
200 +210+ 110+115.5. = 635.5
Ques:- Why do you need this job ?
Ques:- What is the average of first 10 natural numbers ?
Recent Answer : Added by Vaishali Singh On 2021-08-11 19:02:52:
n(n+1)/2
=10*11/2
55
Ques:- In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?
Recent Answer : Added by JAQ On 2021-06-21 17:40:13:
time = distance / speed
speed = 36*(5/18) m/s=10m/s
distance = 100m
time=100/10s = 10sec
Ques:- it takes 8 , 12 and 16 days for A , B and C to complete to task . how many days will it take if A works on the job for 2 days and then B works on it until 25 % of the job is left for C to do , and C completes the work ?
Recent Answer : Added by Abhishek Chabri On 2022-10-08 07:25:40:
C will take 4 days and the total number of days taken by a,b and c will be 12 days.
Ques:- Find out the wrong number in the series:
15, 16, 34, 105, 424, 2124, 12576
A. 34
B. 105
C. 424
D. 2124
Recent Answer : Added by G S Dheeraj On 2022-08-14 16:33:59:
The series is 15, 16, 34, 105, 424, 2124, 12576
1) (15*1) + 1 = 16
2) (16*1) + 2 = 34
3) (34*3) + 3 = 105
4) (105*4) + 4 = 424
5) (424*5) + 5 = 2125
Clearly, they gave 2124 instead of 2125, so it is the wrong number in the series.
Ques:- Why you are looking for change ?
Ques:- The H.C.F. and L.C.M. of two numbers are 12 and 336 respectively. If one of the numbers is 84, the other is
A. 24
B. 36
C. 48
D. 72
Recent Answer : Added by anonymous On 2022-03-09 16:38:02:
12*336/84=48
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Ques:- If $ stands for triple and # for negation, what is the value of #$#3-#5
(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