#help-0
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how did they get to the next step?
the 16m on the first line is meant to be 16^m i believe
They factored out (m-1)/m all to the m-1 power
what about these two lines?
how did the remove the 16s on the right of the first line
whats 16 with an exponent
16^1?
wouldnt that become 16^m then?
oh wait thats not correct what i said
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working on this problem -- already figured out H3 and H5, but i'm blanking on what to do next for the error bound
here's what i have so far:
cant upper bound the 3rd derivative function -- this is what it looks like
@dim plaza Has your question been resolved?
@dim plaza Has your question been resolved?
all lines are flat
actualyl wait i used a different theorem
i used this representation:
i used this iwth the divided differences table
for the H_j functions? those ive gotten already but im stuck on the bounds i have no idea where to go from the pic i sent
the H functions i got:
yeah, this is the formula for E(x)
i just don't know where to go from here
^reference
it's asking for the bound, doesn't that mean a general expression? not a specific f(1.25)-H_j(1.25)?
how do i know what a and b are bounded by? is it just the data points?
ah yeah that was a typo i copied the quetsion down
oh okay
so in this case the max of f''' would be at the rightmost node?
awesome
okay
ill work on that
thank u so much
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$(\sqrt{3} cos\theta)^2$
hello can anyone tell me if this is correct
too late
putridplanet
how do you solve this
what is your question?
separately
answering me ?
(ab)^2=a^2b^2
no
then wuts the right ans or way 2 do it?
draw a straight line through y=1 @alpine sable
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wut do i hv 2 do next?
reflect it over that line
isnt that wut i did?
she can have it im done
no to get what you drew you need a function
oh i line i drew is that x=1?
no the blue line you drew is y =1
the U^2 point mirrored will be where the W^1 is
(4,3) is where the mirrored D point will be
This geometry video tutorial focuses on translations reflections and rotations of geometric figures such as triangles and quadrilaterals. Transformations include horizontal and vertical translations, reflection about a line of symmetry such as the x-axis, y-axis and origin as well as rotating a figure clockwise and counterclockwise by 90 degree...
watch this
ty i appreciate it
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idk if this belongs here but does anyone know how to calculate square roots of complex numebrs with the casio fx-991ex? i know how to do it on paper but i thought something as simple as that should be able to be done by a calculator like that?
i was in the mde that lets me use imaginary numbers, but it just says Math Error when i try to calculate it
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need explanation with the graph of {e^x}, where {.} represents the fractional part function.
And what's confusing you about the graph of {e^x}?
how to make the graph?
I actually want to conclude whether its one one or many one
so I need help with the graph
do you know what the graph of e^x itself looks like
yes
you don't need the graph for this goal btw
You definitely don't need a graph for that
consider for example
call your function f(x) = {e^x}
what is f(ln(2))?
and what is f(ln(3))?
do u mean this?
yes
careful
can u understand this?
0
and that of 3?
0
are you now able to draw the conclusion for your actual original problem
btw did you actually put your entire bday in your username 🤨
wait let me understand
see my pp, i made a smiley with a graph
the two do not seem related
i mean ok like you leave some ambiguity as to whether it's nov 6 or jun 11 but still 
oh it means that the above function has two roots, so we can conclude that it is many one?
June 11
dd/mm/yyyy
it has a lot more than two roots, but yes, we can conclude that it's not one-to-one.
it is not significant that they are roots
you can use the definition of injectivity to show this, or show a counter example like Ann asked you to
but the value of y=0 at those points? so why isn't it necessary that they are roots?
read my message please
i said "significant", not "necessary".
these two are not at all the same.
why isn't it significant that they are roots?
because it is only significant that the function has the same output at these two different inputs.
i could have had you calculate f(ln(2.5)) and f(ln(3.5)) for example
it would have been a counterexample to injectivity all the same, but ln(2.5) and ln(3.5) aren't roots of f.
the fact that f happens to output 0 at the two points i gave is only a coincidence.
oh okay
i understand what roots are, so it wouldn't have confused me
but thankss sis
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find all natural n such that result is integer number
so result of dividion should be {...-3,-2,-1,0,1,2,3...}
this type of number
and n is Natural
what do you mean by dividion?
this whole expression should be integer
so you mean division?
Note that n has to divide 52
Okay maybe going through all natural divisors of 52 is tedious
I would try solving for n in the equation
That doesn't solve the problem
Unless you have a bunch of free time
So n must be divisor of 52 ?
Yes
why?
not ncessarily
Because of the 2? 
Do polynomial long division
$\frac{52-3n^{2}+3n}{2n}=\frac{26}{n}-\frac{3}{2}n+\frac{3}{2}$
beard420
I didn't say it could be any divisor of 52
U sure bout that one?
,w (52 - 3 * 52^2 + 3 * 52)/(2 * 52)
I would break into cases of n even or odd
$\frac{26}{n}-\frac{3}{2}n+\frac{3}{2}=\frac{1}{2}\left(\frac{52}{n}-3n+3\right)$
This should prove that $\left(\frac{52}{n}-3n+3\right)$ is even and thus $\left(\frac{52}{n}-3n\right)$ must be odd
beard420
Beard you gotta slow down and let the helpee think a lil
agree
so we should find all divisors of 52 such that 52/n-3n is odd number?
I guess
Okay will try
13 is also a divisor of 52
Yep, that seems correct
so all n are : 1,4,13,52
Yes
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Im trying to divide hexadecimal numbers , I have AB:2 , I know using converters online that 55,8 should come out , but I cannot figure out how to get that ,8.
do you know how to divide AB0 / 2 ?
I look at how often 2 fits in A , that would be 5 times, then I look the same for B , it's 5 rest 1
so i have 55 written down
and i get stuck here
ok lets take a step back and go back to base 10. if I ask you to divide 30/4, what do you do
I just look at how often the 4 fits into 30 , it's 7 times , i multiply with 7 and subtract the result with 30
i then see that I can't fit 4 into the result , therefore I write a comma
I bring down a zero
I look how often the 4 fits in 20
it's 5 times
then I'm done
It comes out to be 55,5
but if i convert AB in decimal it comes out to be 171
and 171 /2 is 85.5
85.5 in hexa is 55.8
well you cant divide the 0 as if it was in base 10
youre welcome
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zero
identify the angles where the y-coord is -0.5
sin x = -0.5
x = sin-1(-0.5)
= -30
is it?
@ebon heath Has your question been resolved?
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how many maxima and/or minima does f(x) = x^2 - 3x + 2 have?
cus I get only one stationary point i.e. x = 3/2
,w plot x^2 - 3x + 2
yes
because it can have only one as i know
since a>0 it cant have maxima
and it can only have minima
formula is (4ac-b^2)/4a
aight
how'd you get 2 though
no
Akira
krishiv youre asking minimum value that can get right?
or maximum
whichever it has
the number of minimas and/or maxima that's associated with the function yeah
you use the quadratic formula to find the solutions of f(x)=0, not the stationary points of a function
those are different features
you sure?
very
and how can even function have 2 minimum values
,w calc x^2 - 3x + 2
well if f(x) had a degree of 4, it would have two local minima
you're correct saying a function can only have one global maxima/minima
but im assuming Krishiv is asking about local stationary points
anyways general rule of thumb is that a polynomial of degree N has at most N-1 stationary points
the amount of them yeah
ah okay
yeah that makes sense
if it has say 2 stationary points, does it necessarily mean it has a maxima and a minima?
like does it alternate between maximas and minimas and vice versa
,w plot x^3 + 2x^2
like this?
yeah they usually alternate
there are special cases but its best to sketch a graph and see for yourself
ah okay
also if I may ask
when do you know the first stationary point is a minima or a maxima
uh
regarding just polynomials?
because theres a way to tell if a stationary point is a maxima or minima for any function
which is evaluating f''(x) and plugging in the x values where there are stationary points
say a stationary point occours at x_0, then if f''(x_0)>0 the stationary point is a minima, f''(x_0)<0 means the stationary point is a maxima
ah okay okay
yeah that clears that thanks a ton
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I dont get this proof?
what can we get from (n + 6)(n +7)?
It implies that n^2 + 13n + 42 is a product of two integers both larger than 1, hence n^2 + 13n + 42 is never prime
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Howdy, this is my little brothers homework. I have never understood math and cannot help him. He's stuck on part B, would anyone be able to explain?
its a pie chart so the formula is frequency of data/ 90x360 for city athletics
to find for a) divide 132/360 x90
do the same for others
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i’m confused how to treat y gamma
like do is solve it as if it was e bc that’s eulers constant or do i treat it like it’s a random variable k or something that’s a constant idk
gamma is a constant like pi
okay
that kinda makes sense
wait is it like e tho like since the derivative of e^x = e^x does gamma^x = gamma^x? or is it gamma^x ln(gamma)?
The derivative of e^x is technically e^x×ln(e)
But ln(e)=1 so the derivative is e^x
To answer your question, gamma^x×ln(gamma)
ah i forgot yeah that makes sense thank you
Because you can write it as e^(x*ln(gamma))
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Topic: Derivatves
Class: Calculus 1
I struggle to understand how we got the last equation
d/dx turns into f'(x), but then shouldn't it be [ f'(x) multiplied by xf(x) ] ? Where did the + come from?
By product rule, f(x)=f(x), g(x)=x
there's a bit of confusion in your statement. $\dv{x}$ is an operator, it can be applied to an expression such as $x^2$ or $xf(x)$ and means ``take the derivative of this thing with respect to x''
Hayley
oh so d/dx isn't a fancy way of writing f'(x)? I thought it meant the thing
$f'(x)$ is the derivative of $f(x)$ with respect to $x$, and could also be written as $\dv{x}f(x)$
Hayley
oh
or, rarely, $\dv{f(x)}{x}$ and if you've set $y=f(x)$ then you could say that's $\dv{y}{x}$
Hayley
in this case we care about $\dv{x} [x\cdot f(x)]$ and to take the derivative of a compound expression like this we need to use the product rule, given in that first red circle
Hayley
but where does the g(x) and g'(x) go? In the second expression they just dissapear? Are we allowed to take them off if they arent present?
we set $g(x) = x$ (to make the product rule match our expression), and the reason $g'(x)$ seems to disappear is because $g'(x) = \dv{x}g(x) = \dv{x}x = 1$
Hayley
hmm
Interesting, thank you sm for all the info. I think I need to go and revisit the product rule by a youtube video. At least I know what to look for now, thank you!
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you might try practicing the product rule to differentiate things like x*sin(x), or x^2 * e^x
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Hey! I'd like some help with finding the inverse of this function. I've been getting y = 1 + v(x-1) and the answer is ||y = 1 - v(x+1)||. I've redone it four times and still can't figure out what's wrong... I'm sure it's something silly but I can't see it myself.
what is the question
We ought to pick the negative root because the it should be <= 1
Find the inverse
Wait seriously
Yes, after switching x with y you get not only the equation x = y^2 - 2y, but also the inequality y <= 1
So after you complete the square and take square root of both sides, it becomes sqrt(x + 1) = |y - 1| = 1 - y
why absolute value?
In general, sqrt(a^2) = |a| for all real numbers a
@fair hedge Has your question been resolved?
why x + 1? shouldn't it be x-1 since we added 1 to the other side?
x = y^2 - 2y
x + 1 = y^2 - 2y + 1
x + 1 = (y - 1)^2
if you add to one side doesn't it mean you have to subtract it from the other?
1 = 1
1 - 1 = 1 + 1
0 = 2
?
Whatever you do to one side shall also be done to the other
Thank you
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Determine all possible sets of 6 consecutive positive integers such that the product of 2 of them added to the product of another 2 of them is equal to the product of the remaining 2 numbers.
i got about as far letting the 6 integeres be x-5,x-3,......x+3,x+5
how would we know which of the pairs are being added and which pair is the sum?
these aren't consecutive are they?
oh damn im a moron
That too.
ap with diff 1
yeah
i think brute force would work... just try the combinations; probly a smarter way tho
@hard aspen Has your question been resolved?
think i got it! thank you
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I am stuck on this one
I got the derivative but I dont know what to do next
Normally I would then set the derivative equal to zero and then solve to get the critical points but its not really possible with this
Cause of all of the e's and x's
My derivative is (8x^7)(e^-4x)+(-4e^-4x)(x^8)
Like how tf do I solve this shit, is there no other way?
Take 4e^-4x common factor
4e^-4x(2x^7 + x^8)
if you cant equate it to zero trying checking if the function is increasing or decreasing
How do I do that
Take x^7 common factor
Why not
4 is always 4
whats the origina equation
e to the power of anything can't make it equal to zero
So you can just cancel the e term
x^8*e^-4x
Ah didnt know that rule
or take (4.x^7.*e^-4) common you will be left with -2+x
Nah just in general there is no special case where a power can make a number equal zero afaik
So the only way to make the equation equate to zero is if this equals zero
then equate it to zero you will get x=2
OH didnt know this either
And what about the other bit
Ah yeah you doing the same thing I did
That bit can only equal zero if x = 0
you dont have to worry about the other bit
Why not?
So youre left with x = 0 or 2
But what if it doesnt equal 0
its like for exampe you get sin x=2 its not possible its kinda like that
Wdym
yess right
That bit can only equal zero if x = 0
What if x isnt zero
dude if you equate x=0 or 2 the whole equation becomes zero so u dont have to worry about it
Oh ok
You are trying to final crit points where the equation = zero, we just found out the only values of x that make it equal zero are x=0 or 2
then x=2
No
no differentiate it again and then check at point its maximum or minimum
Or maybe don't, it's already an annoying derivative to work with
Crit points are points where no increase or decrease occurs
From this
When the derivative is negative it's decreasing, when it's positive it's increasing g, so yes
It's increasing from 0 to 2
no man the derivative it decreasing from 1 to 2 there the function is decreasing
The value of the derivative doesn't matter, only it's sign
Good job!
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I got sqrt(3x-1)*sqrt(6x+1)=0 and I've honestly got no idea where to start.
What is the question?
To solve the equation
Can you send a picture of the original question?
So, there are a few ways you could do this. But 1 method is to know that if you are multiplying 2 things together, the only way their product equals 0 is if 1 (or both) of them is zero
does that make sense?
austinu
solve for when this is equal to 0
so sqrt(1-3x)=0
another useful property that arises here is that sqrt(a)=0 only when a itself is equal to 0
the sq root are always positive therefore equate 1-3x>0 and 1+6x>0 and then intersect the common value
if there isnt any common range there there is no value for x
i was taught i could do 1-3x=0^2 after which it becomes 1-3x=0?
The question isn't asking for the domain @fickle hamlet
this also works, yes
Yes
i need 2 solutions
Now find the other solution by doing the same process with the other square root
what is it asking
It is asking to solve for the roots of the equation (i.e solve for the values of x for when this takes on 0)
But that's pretty easy this way
is it asking for an integer or what
i believe intersect is a function of the graphic calculator right
It is okay manuel, they thought you were asking a different question
Okay
This makes perfect sense t hough
But then I've got another one that is confusing me
sure
then the answer has got to be 1/3 or -1/6
yea
perfect
then i understand that
i understand all that must be done after that myself
i got one more that i wont be able to do
yeahhh
yeahhh
I'm getting the hang of it
but keep on checking the condition
that the equation or terms under the sq. root should be positive
btw what class are u in
idk what it is in english
I'm from the netherlands
thats why my english is horrible
especially with math related things
dw i m not an englishman either
well we got 8 years of like first school
when u are 4 years old u go there
till youre 12
then we have 3 levels basically
of education
basically practical education practical+theoretical and theoretical
ohhokayyokaayyy
practical is the lowest
practical theorethical is middle
i completed that this year
after 5 years
btw practical lasts 4, practical + theoretical 5, theoretical 6 years
and now im going to do fully theoretical and i must catch up this math stuff
But i don't have a teacher so it's all self study
wow it went over my head but best of luck man
Lol
it's so hard to explain education system
it's not going to make sense really
i think it's also not a good system but it's whatever
i finally understand this stuff aswell
that's really good
theres no good education system anywhere bro
Very true
some people are just later with development
and they get assigned to something that doesn't fit and they don't have a choice
u just gotta educate urself
Yeah
I'm doing that now
But it's hard with no teacher really so I'm trying to figure it all out
Kinda sucks
i dont really thing its the maths that help in our life i think its just
how we deal with prblm in our lives that maths or school actually teaches us
yes
school doesnt teach that much though
most is learning from experiences to me
that's what works better for me
also school forcing me to learn stuff definitely does not work
i remember till the test and then it's gone
pretty pointless
offfccccc i hate testss
metoo
although with enough stress i perform really well
idk what it is
the more stress the better i perform
if i were to make a choice i would def choode no exams, tests etc
me too
but some people would learn literally nothing
so i guess it has some use
it forces people to educate themself a bit
yupppp sometimes it also makes them humble idk how bt it does
It depends on the person definitely
i just solved another one of these
it went smooth
i am definitely understanding it
did u check the condition
I think the problem is i forgot also the parenthese (after making the sqrt go bye bye i should parenthese what was under it )
I don't think we get negatives
It's above our level of education
Right now at least
ohhitss finee then
broo i m giving like the hardest uni exams ever
you already in uni damn
thats why im doing this
i can't go to uni without this
so i must
But i get 2 more years of education before the exam
no dude i m preparing for uni
So i should be able to get it done
O
Me too
but for me it's 2 years left
I'm going for some high grades for math though
since i'll need to also study german and i'm horrible at it so i must compensate 😭
i got like 1 year left
i think we r of the same age cause i enrolled in the school 1 year before the others
i'm very early student aswell
but i got delayed 1 year since i'm switching the level of education to a higher one
it would've been 1 year left
so i'm probably a bit older actually
ohhhokayyokayy
It's whatever though some dude on my school finished this shit when he was 14
crazy guy
I'll be 18 when I'm done
Some people are genius
i respect it
i will be 17
me too actually
almost 18 though
i finish in july and my birthday is august
yeah but they put as much effort too
tell me ur birth year man
2006
nah its fineee u will atleast know everything that will be goin with u sister
whyy ??
she's a snitch
and i don't pay much attention in class
and a friend of mine switches also so we go together and have some fun
but she's not really into fun
she sees school as the shit
okayy thats sad then
man i wish i had a sis
i got more brains than my bro too
i can guarantee
I rather have like 4 brothers than 1 sister
But i have 0 brothers unfortunately
no man i m a girl if i had a sis i could take all her thinks
things*
But i guarantee you wouldnt want that
i got 2 sisters
my little little sister
doesn't want my older sister shit
because it's all seocnd hand
and she wants her own stuff
well i got 5 cousins sis we grew up tgt so i kinda know bt still
bt the good stuff uk
maybe
u can never leave the good stuff
but my little sister is almost taller than my older sister
I got messed up hard
for like 3 years i was smaller than my sister
now i'm taller fortunately
dw man puberty hits boys late
i m short tho and my mom is conctantly telling me that i have 1 yeah to grow an inch taller
1 year to grow an inch should be easy
so i kinda get u
i'm now pretty tall actually
hahahaha no not for me
i'm 185cm
but still nto that tall
i think my sleep schedule messed up my growth aswell
i shouldve been 190cm
man i m like a dwarf to u then cause i m like less than 160
i sleep 4 hours every day since i cant sleep
O
but females are often much smaller
My sister is 173cm
And not growign anymore
yeah it sucks
it depends where u are from ofcourse
wish i could be like this
i can sleep anywhere everywhere
here in the netherlands you would be fucked
at anytime
everything is built around tall people
No
my eyes burn always
but say i'm in sp ain
spain
see i m from india so u cant really say
i wish i was tall
India average height is not that high right tho
You are not far below average
how tall is your brother
he is young
yuppp
but i can reassure you
being 185cm already is pretty tall everywhere and it's not that useful anymore
i think 175cm is enouogh for men except in netherlands
in netherlands you wont be good
he will be tall thats what my aunt told me when she was looking at his feet
the supermarkets are built with very high places for items
still dk how tho
lol
I don't want to say anything about this but i will
My cousin
no no say it
has much smaller feet than me
but hes taller
5cm even
but im not done growing
so maybe your aunts theory will work out
is it a race then
I don't know
bro idk, idk half the stuff she says
but i dont think feet size and how tall you will be are that attached to each other
thats a question for my aunt
btw is that ur cat
why did u put it has ur pic then
uk a cat once scratched my mom
cats are not so smart i believe
ever since then i keep asking my mom for a cat
they are unpredictable
I don't like unpredictable
but they do look nice
and i think they can be nice
they are fine u give them their spave they give u urs
i have got atleast 12-13 dogs in our neighbourhood
and my brothers loves animals he is into dog too
but i m def gonna get a cat for my mom
Yea my mom aint beatin me no more
it's great to be taller than your parents
they can't do shit
I respect them
but i won't allow them to push me anymore
im not a little kid anymore
i wish i could do that
bt i kinda get where they are coming from
eyyyyy u the gym bro
man if u were infront of me rn i would def flex my muscles saying that line
I'm not the kind of guy that will go to the gym every day and take some steroids etc
yeah thats not goodd
it is totally not good
Low testostoron is a big issue but giving everyone hrt is not a good idea definitely
idk never went too gym not just didnt have the time too
make time
it really makes you have less problems in life
you will feel more secure
you can beat up some men if they harras you
i cant dude the uni exams gives me no time for nothing
It
i can still beat their ass
i think men in general are pretty scared of me
It's said that learning full time is less effective than learning for a bit then do something different relaxing and then do learn again
That's interesting statement
You have been to the gym
or you work out at home
or you are just strong from yourself
i dont work out man not my ting
it's no one things
yeah u can say that
i dont really enjoy it either but after it feels good
so i keep going anyways and eventually it got into my rythm and now i dont mind
i dont think men fear me bcz of looks i just think it how i carry myself around them that makes it pretty intimidating
thats my goal after the uni one offc
my mom always tells me im intimidating
i dont really see it as a compliment though
For females its a compliment
but not for males i think
it makes you look arrogant
eh we can be the intimidating duo then
big ego
nah dude dont think it like that
flaunt it
Maybe
theres no maybe the answer is yes
I think its the combination of being tall and being pretty big in size
i got a big ego for a girl
185cm with 80kg
i aint thin either soo i get it
i used to be thin asf
never had that phase in my life
i just ate a lot
it wasnt a phase for me
i ate a lot
enough even
but i just wasnt gaining weight
so i just went to the gym and it made me big
and muscle is heavy
yeah ik people like that too
but i used to be the guy to eat the whole mcdonalds menu and be thin asf still
still dk a thing about gym\
udk how i wish to be u
uk i went to this celebration once with a sequin dress on
then i had just a plate of food
and i was preg with the food
Rip
but it's often
you get a bit bloated after eating
after couple hours it's gone
i have that too a bit
man i did the pregnant photoshop on that day it was fun
But i got a really really fast metabolism
its really opposite for me
my heart rate is at 90bpm
it's a big sign of fast metabolism
aswell as not being able to gain weight easy
kinda jealous rn
in rest
I dont think u want to be
my reason for fast metabolism is not good
I go to the doctor every month for it
cause i had some serious personalit issues or smt like that bt now
my heart function is horrible
eyyy thats sad man
yeah
but to be honest
the scars of the surgeries
some ppl stare at it
but i see it as a part of me you know
It's good
i got big self confidence
unhnnn i kinda get it its like my stretch marks
me tooooo
i have those on my back aswell
due to fast growing
those im less proud of actually
my scars are like serious scars
15cm in length
Those stretch marks on my back are like 5cm but 15x
its fine dudeee those represents u survive
but they are red
what else matters
not much
exactlyyyy
idkk dudee can i add u as a friend
Sure
whats ur id tho
brooooooooooooooooouu i wish we could change our abilities
i've been blessed and fucked
i wish u could do math and i could do comp
but we can both learn it
you can learn how to operate computers and i can learn how to do math
yeahh c++ is pretty hard to learn tho
yeah lets just help each other
bt first u need to help me with the discord i really dk how this shit works
Lol
How did u even end up here
You just made an account or googled for this server
or
lol
and the other person just left
yeah anyways u can ask me for your maths doubt anytime
from gaming competitions winning to programming programs and websites
But math is lacking
mann u r cool
I'll be sure to let you know any doubts
Yes but i suck at math
And honestly gaming isnt cool
too much hours went into it
not even close to worth it
yeee being good at maths is fine
yes
bt u got like the gym and the computer skill
ikkk bt still it is for me
you should definitely try the gym out this summer once you're done
i am bt my proffesor
it'll be great
yeah def i will
btw what uni are you applying for
math is hard for self studying if you dont understand youre fucked
for uni of amsterdam
uva
it's aclled
ohhokayyokayy
it is actually just have to keep doing it
man i m optinf for the cs branch bt who knows what i will get
its not a choice actually
What the heck
i've got free choice
A friend of mine who used to live in India moved to Australia for uni
if i get pretty good grades then i can bt if i dont i wouldnt be able to apply for it
he must have pretty good grades then
he's actually not that intelligent
maybe i think i will too bt lets see
are his parents cool with it
i dont really care about beautiful thing its fine for like a month bt then home is home
thats the problem my entire nighbourhood even my parents collegues and waiting for my result
