A rude person who doesn’t respect me
(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
21
length is 30 breadth is 12 and height is 12
——————————
1
.——————————
1 .
1 .
1 10 .
1
1 .
1
1
1 30 .
——————————-.
1
consider right angled triangle
so the distance= square root of (30*30+10*10)
2:3
2400
Simple interest Formula:
A=P(1+rt)
Therefore,
815=P(1+3r)
P+3r=815
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
we need to take half tabulate among the 4 tablets. den it ll be like 1 tabulate is of fever and one tabulate is of cough
Total=60reems
Utilized=40reems
Un utilized= 60-40=20
Percentage of remainder 20/60=.3333
0.33333*100=33.333%
Dear friends i ofcourse confused like you when i come
across to solve this problem. Really friends its very
simple if you understand the question clearly. First thing
is what is mean by “as many as” means its called ‘idiom and
phrase’ in english and it means “the same number of”. now
read the question “how many pairs of letters in STAINLESS
which has same number of letters between them in the word
as they have in english alphabet”.
In the alphabetical order, A-Z can be numbered as 1-26.
In A(INL)E which is same as in the alphabetical order A
(BCD)E. In both the cases E is in the Fourth position. so
we got one pair.
And in ST, there are no letters between them in the word
stainless. In alphabetical orer from A-Z also there is no
letters between them..so we got the second pair…
In STAINLESS it has two pairs ST and AE
ans=13.33
solution: (710/12)*8 – 460
number1*number2=lcm*hcf
so,
product of two numbers is ,
2025=lcm*15
lcm=2025/15
lcm=135