#help-49
1 messages · Page 31 of 1
@torpid silo Has your question been resolved?
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Why is the set of all real valued polynomials $\mathbb{P}$ a vector space? What are the vectors? It doesn't have to be linear?
determinate
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The vectors are polynomials themselves
It’s a space of functions
@last slate
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.close
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how do you do the following:
for what values of m will y=mx-8 be a tangent to the parabola y=x^2-5
do you know calculus
no
yeah i already did that
The line $y = mx-8 $ is tangent to the parabola $y=x^2-5$ only when the line touches the parabola at one point only.
In other words, m must be such that this equation:
$mx - 8 = x^2-5$
Has a unique solution
Daddy_314
k
@gritty holly Has your question been resolved?
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hello
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Guys help how do i calculate the f(0,52)
what module?
We don't know what f refers to here. We might need more context.
This is the task
Okay so f refers to the normal distribution
You probably have a table for it somewhere
The pdf can be calculated with any calculator, as long as you know the formula
Do you know the formula?
@thorny geyser Has your question been resolved?
@thorny geyser Has your question been resolved?
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hi
is it too small?
i got the first one right and 36 * 24 = 864 but apperently thats incorrect)
@unique cedar Has your question been resolved?
@unique cedar Has your question been resolved?
@unique cedar Has your question been resolved?
36 is the width of the larger part, and the 864 is the area of the small section inside the poster
so 864=(36-2*6)*(h-2*9)
gets you 54
which makes sense because the post is supposed to be taller than wide and at about a 3:2 ratio
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how do I solve this
like do I do cross multiple with sin(x)
like how do I single out the x
to find the angle
this is my process rn
but idk what’s next
$\arcsin(\sin(x))=x$
Afi
oh o tysm
do I put 78 to the X at the front o the equal sign?
You should write it in this way
sinx = c
Then
x=arcsinc
Basically arcsin is the inverse of sin
which returns the value of x
$\sin(x)=\frac{\sqrt{3}}{2} \
x=\arcsin(\frac{\sqrt{3}}{2})$
Afi
Is the RHS 78?
whats RHS?
Right Hand Side
What’s the value of the number
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Wondering if answers are correct
@umbral rampart Has your question been resolved?
.
How did you get b and c and what are the units?
volume of big - vol of small
flipped diagram upside down and used pythagoras for big cone and small cone then subtracted
I haven’t calculated it but that’s the right method
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Im stuck can skmeone uelp
is it $\frac{\sin(2x)}{1-\sin^2(x)}$
The Prophet Of The Damned
I’m assuming you’re solving for theta, correct?
Or x, you ended up with a combination of them throughout your question
@wintry plover Has your question been resolved?
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Find the definite integral of y = sec^2 (pi x/2) using the graph. The answer the teacher gave was 3.464 units^2 but I got undefined, so i'm not sure if the question itself is wrong or I did something wrong
Can you show your work
Oh I think you’ll need to do the limit as it approaches 1 I think
Actually I think I’m thinking of something else
lim (sec^2 (pix/2) when x is approaching 1 is infinity
or maybe the answer provided is just wrong 🤔
How did you get the area of 1/X from 0 to 1 then
I’m pretty sure there’s a value I remember seeing a video or something lol
I have no idea 😭
Can I see the original problem
it’s called a divergent integral
the one you have I think
@keen pebble Has your question been resolved?
@keen pebble Has your question been resolved?
,w integrate (sec(pi*x/2))^2 from 0 to 2pi/3
Looks like it diverges
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Have I made a mistake anywhere
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can someone explain this please? i rearranged to $\frac{dy}{dx} = \frac{y^2 -2xy} {x^2}$ and have $F(t) = t^2-2t$. Im stuck from what to do here. If anyone can help with this, that'd be great
lewis_f04
true answer its 2
??
Try u=y/x
@toxic flower Has your question been resolved?
i think thats what ive done? $\frac{dy}{dx} = F(\frac{y}{x})$
lewis_f04
Then you need to transform dy/dx into the expression of du/dx、u and x
I have no idea how to do that can you help me with that please?
u=y/x→xu=y
Differentiate both sides with respect of x
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Hi. could someone help with this? I tried several methods of splitting this up and none worked
@neon dune Has your question been resolved?
what are you trying to find?
the summation of (2r+3)/3^r(r+1) from r = 1 to n
in terms of n
im still stuck lol
,w sum from r=1 to n of (2r+3)/(3^r*(r+1))
The Lerch transcendent is generalization of the Hurwitz zeta function and polylogarithm function. Many sums of reciprocal powers can be expressed in terms of it. It is classically defined by Phi(z,s,a)=sum_(k=0)^infty(z^k)/((a+k)^s), (1) for |z|<1 and a!=0, -1, .... It is implemented in this form as HurwitzLerchPhi[z, s, a] in the Wolfram La...
do u have any working
i don't think you can reasonably be expected to find such a formula yourself
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can someone explain local maximum and local minimum in a way I would understand?
what about them? the definition?
well i'm given this:
and i need to figure out where local minimum and maximum is
i'm guessing it's where it's low and begins going up
and where it's high and begins going down?
local maximum means the graph has a peak, or highest point, in some region.
local minimum means it has a valley, or lowest point, in some region
so in this case, the local minima would be (-2,1)
So if you see a " downwards peak " it is a local minimum and an " upwards peak " is a local maximum
cause that's the lowest point i'm given
Ye
Well did you understand how to find the minima and maxima graphically?
any of you happen to know what monotonicity is?
yeah! thanks!
i had this in school but was sick ://
Yeah
If a function is strictly increasing or decreasing all across its domain it's monotonic
so this case is not strictly increasing or decreasing
okay, perfect, thanks
An example of a monotonic function is a linear function
very tough to remember haha
Or e^x
yeah I was about to ask about that
but like uh
the graph for sinus?
that goes like up and down
Sine isn't monotonic
Cause the slope isn't strictly increasing or decreasing in the domain
Yeee
i've got one last question tho
what is definitionamount?
wait let me figure out the proper english word
domain and range i think?
Domain is basically all the values that you can define a function for
Example, √x
Here the domain is x≥0
Square root of x
oh
So, negative square roots aren't defined in the real numbers
So √x you can only input values greater than or equal to 0
why not negative numbers tho?
The domain is all the values the computer can accept
Because no real number squared gives a negative number. For example, (-1)²=1
And the range is all the values the computer gives to you
Noo
and your domain would be x?
Your range will be all the possible values of y
ohhhhhhhhh
And your domain will be all the possible values of x
For all linear functions, both domain and range are all real numbers
This looks like a cubic to me so assuming it is, yes
hmmm
i wasn't fiven much information about this lol
but if i have
the sine thingy
then there would only be some range
Yeah
cause it's not infinitely tall
But the domain is all reals
but there would be infinite domains
Spot on!
Well the tangent function doesn't have a domain of all reals
it doesnt?
It's undefined for integer multiples of π/2
uhhh in english please? 😂
uhhhhh 1?
Well
Yes
You should know it only for 5 angles tho
Just memorise the sin values of
0, π/6,π/4,π/3,π/2
uhm... how...
Well you can find " tricks " online
well for 0 it would just be 0, no?
Yeah!
hmmm
i'm still a bit confused
when in math do you use this? Like under which subject?
Trigonometry
Maybe it's called something diff in ur country?
Well it's more so for triangles
Oh
we had about sine, cosine and tangent awhile ago aswell
but we had like how to utilize it etc
using cas
anyway it's unimportant
i still don't get why tan(x) wouldn't have infinite domains?
Undefined for π/2 and it's multiples
all good 😄
Its range is all reals tho
wait
sorry about that
OH SHI
no worries 😄
wait
wait
domain = all possible x's?
range = all possible y's?
then yeah the range is all possible values, my bad
cause i drew it
and these are all possible y's
not x's
Ye
yeah my bad
But u see how it's asymptote when x=π/2 or its multiple
asymptote???
yeah the y?
No
1.6?
It's 0
oop
Ye
but yes i figure you understand what I meant lmao
so it's undefined because it doesn't have an answer?
but wouldn't 1/0 = 0?
wait am i failing elementary school math holdups
nevermind
shush
This implies that 1=0
Ye
Yw
Dw u can, i was confused same time last year while learning trigo
haha thanks
we have about functions now
i missed one day in half a year and i felt so confused when my teacher said all this was homework
What grade are u in if I may ask?
well here it would be inbetween highschool and college
Couldn't be me, i had a 75% attendance in my previous academic year ( the bare minimum )
ah yeah us aswell
Cause everyday we have all the subjects
ohhhhhhh
Where are u from?
Oh I'm indian
dang that's far away
Ye
i'm thinking of studying abroad
oh you're at your bachelors?
We have a different curriculum, our grade 10 ( for kids who are 15 ) has basic trigo
ahhhhh
We domt have functions tho
lucky you
We have functions next year
it's painful
we have basic trigonometry last year aswell
but i went to the 7th worst school in denmark
so yeah i didnt learn shi lmao
Lmfao yeah my school isnt the best eitherz but I'm changing schools this year
For coaching
ohhhhh
Coaching is basically preparation for an exam which grants you entrance into most engineering degrees in the country in case u don't know
As well as some other bachelors
ah okay
And at 17-18 if you wanna pursue engineering you give an exam, which is what I'm gonna be coached for
It's a retrace honestly
ahhhh
that makes sense
it's kinda boring for me tho
we have one of the most prestigious schools for engineering in europe like
5 minutes away from me
Oh wow
but i wanna study abroad so ´bad lmao
I wanna study abroad mainly because I wanna leave the country someday
oh?
Why?
bored of the culture here in denmark, it's a bit too... spoiled?
Yeah India's slowly becoming shitty cause of our islamophobic and xenophobic govt
Yeah that's expected of Europe haha
yeah but people here are so spoiled
and entitled
and very racist
i grew up in a ghetto here
meaning most of my friends were of other ethnic backgrounds
and while going out with them they would always get racist comments
Same here
Oof that's rough
Yeah I'd assume the young people are more tolerant
idk how that correlates but wtv
Geez
they are, by far
but the people here were too rich for too long
so the second something bad happens, they put the blame on immigrants
First world problems 😭
bro it is fr 😭
Oh yeah I've heard of that
Europeans blaming immigrants for every issue under the sun
like even my family does
i went to my grandparents
who I love very much
and they're discussing like crime rates in denmark
and like atleast they're not that eyed towards one direction, but I see where they wanted to put the blame
Thats basically backhanded racism
Here, people are discriminatory too but more about religion than race
Like the Country has 80%+ Hinduism followers who hate all the Muslim ppls and blame them for the shortcomings of the country
of course
it's kinda the other way around here
like i'm an atheist
and so many people, especially islamics, have commented on why I am
even blamed me for not being muslim
and most of denmark is atheistic
or like they're christians, but it's more for the culture
Ay same here
oh ive got tons of that
it's kinda overboard but whatever
Sort of similar situation here
Here we have to declare our religion in all government papers along with our birth certificates, in all of those I'm a Hindu but practically I'm an atheist, a large portion of the population is like this where they're atheist but on paper they follow xyz religion
yeah exactly the same here
except we dont put it on papers
but they're christians who dont believe in christ
We have to declare it on paper cause skme religions get benefits by virtue of being a minority
It is
tbh all these countries are whatever
We have a lot of reservation in government institutes for minoritirs
And people who are in marginalised groups
Maybe 27% I think in government jobs and colleges
that's kinda weird, no?
also i found out how stupid the danish politicians were today
someone said that nigerian people go to denmark to fix their phones
and they said that there were no nuclear reactors in europe?
I'm trying to make sense of that but I'm having a very hard time
Yeah it is, i think we should have the benefits given to those who are financially handicapped and not given to people by virtue of their birth
one of the representants of one of the danish political visions said that people from Nigeria have to go to Denmark in order to fix their phones, which just isn't true
Any context?
yeah that makes far more sense
we had a political debate in school, and that was his example
Ye, sometimes here rich kids will get admissions into prestigious colleges that they don't deserve
Cause their great grandfather was part of a marginalized community
Example against immigrants?
Yeah it was implemented as a political tool
To gain support from that community
Oh here it's very unfs8r
uhhhh it was against sanctions against russia, idk how that correlates either
I can give u an example
yeah i mean it makes sense for them to do it, but not to uphold it
here anyone can get into any public school, highschool or university (we have 3 different schools)
but you have to have a certain grade in order to apply for the schools
for example I'll need an average of 7, which is just above average for my university
and they have systems like that for all universities, aswell as highschools
Here most highschools can decide whether or not they want to admit a child on a case by case basis
Sometimes they ask u for extra money
If ur kid isn't that good at acadmeixs
oh heere ur school grades don't matter a lot
In grade 12z the last year before graduation
We have a nation wide standardized exam
Most schools require that you get around 75% in that which isn't that good
And if u do get 75% you'll have to attempt another standardized exam depending on what u wanna pursue
And some schools require that u write their entry exam
ah kinda the same here, if your average isn't high enough
The example I was talking about, here we have an exam called JEE which has 2 stages - mains and advanced. Mains is common for most engineering courses in the country but advanced is for the IIT's which are basically the best in the whole country ( acceptance rate of 0.5% ). You need a certain percentile in the mains exam to even qualify for advanced. For most of us ( general category ) it's 90 percentile meaning u need to score more than 90% of testtakers but for certain groups it's only 50 percentile meaning they only need to score more than 50% of testtakers
that's kinda weird
ANYWAY
i've got a mad mad woman screaming at me
(my mother)
since it's a little late here in denmark lmao
and i've gotta be up again in less than 5 hours 💀
dang go to bed bro
For my new school
I'm in bed but I just can't fall asleep 😭
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(Op A PAU junio 2014) It is known that the graph of $f(x) = ax^2 + b$ has a horizontal tangent line at the point $(2, 4)$. Determine the values of $a$ and $b$.
MortterGx
please
what have u tried
f'(x) = m = 0
f'(x) = 0 at what value of x?
$f'(x) = \frac{ax^2-b}{x^2}$
MortterGx
howd u get that?
in the function I have to substitute x,y in the values to clear point a or b
the statement is wrong
oh
$f(x) = \left(\frac{ax^2+b}{x}\right)$
MortterGx
this is still wrong
a
where
$\frac{2axx-1\cdot \left(ax^2+b\right)}{x^2}$
yes
MortterGx
no pasa nada
$\frac{4a+b}{2}$
plug in x = 2, and set equal to 0
MortterGx
howd u get this
u are using this?
Stephen
$f(x) = \left(\frac{ax^2+b}{x}\right) ; \frac{a2^2+b}{2}=0; a2^2+b=0$
MortterGx
Compile Error! Click the
reaction for more information.
(You may edit your message to recompile.)
$f'(x) = \frac{ax^2-b}{x^2}$
MortterGx
MortterGx
$16=:4a-b$
MortterGx
$a=:4-b$
MortterGx
Stephen
f'(2) = 0
use this
$4a-b:=0$
MortterGx
sip
$4a:=b$
MortterGx
asi ahora tenemos la primera equacion
eres español?
ok
sabes? como lo podemos hacer?
the second is by substituting in the initial function?
yes
2-a=b
howd u get that?
$\left(\frac{4a+b}{2}\right)$
MortterGx
=4
Stephen
$4a + b = 8$
$a=\frac{8-b}{4}$
Stephen
yes
a=1
yea
initial function, I substitute both x and y to clear one variable
we also know f'(2) = 0 because theres a horizontal tangent at x = 2
here we use the derivative function to create a second equation
then I do the derivative of the function to substitute only x and take out the variable again.
I solve the system and that's it
yea
that just simplifies to y = 4
thats the tangent line at x = 2 yes
but why do u need that?
just to remind myself
I have a global in little and tangent line exercises there are many types I think.
and I get quite confused
Do you think you can make another one with me?
ok
- (Op B EBAU sep 2020)
Find the values of a and b so that the line of equation y = 6x + a is tangent to the curve ... at the point of abscissa x = 0. Write the functions obtained.
ok have u tried anything?
MortterGx
derivating
we already know the slope at x = 0
$\frac{2b}{\left(bx+1\right)^2}$
MortterGx
ok
id understand
y = 6x + a is tangent to f(x) at x = 0, so f'(0) = 6
i see
ok so we have f'(x) here
set this equal to 6
and then plug in x = 0
$\frac{2b}{\left(bx+1\right)^2}=6$
MortterGx
MortterGx
so what is f(0)
-1
yes
b= 3
this one seemed easier
- (Op A PAU June 2015)
Consider the function f(x) = ln(x 1) defined on the interval [2, e + 1]. Determine the equation of the line tangent to the curve y = ln(x-1)
parallel to the line passing through the points P(2, 0) and Q(e + 1, 1).
i gotta get going now
oh ok
cya
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see it from this angle
i hope its clear in the picture
thats like its projection from that angle
but we dont know AC though
since A is not fixed
thats not AC that we want at the moment
here we can see that AD and AC both has a relation with DC, right?
alright, so 4r^2 = AB^2 + AC^2, so here is AB, we still need to get BC^2 into the eq.
can u find a relation between BC and AC?
notice that AC is the projection of BC here
i think i can actually find the diameter
since we are given sphere equation and the plane equation
ok, and whats after, u still dont know how to remove AC^2 from here and put BC^2
try to find a plane that has both AC and BC together
BC^2=AC^2+AB^2
right!
Damn
?
that should be 4r^2 = AD^2 + AC^2
as in the picture
the first eq shoud be AD^2 instead of AB^2
ahh i see now
ok brb imma do some calculations
64
seems correct too
@pearl kindle thanks!
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Hi, I'm hoping to get some help with solving this equation:
I always do some kind of algebra which is like "illegal" so I usually end up getting the wrong answer. Can anyone offer some useful advice/tips when it comes to solving the bottom line for V_c1? When I look online it says to use the common denominator etc. but I actually don't know how to quickly work it out.
it would be easiest to just split the fractions then factor the Vc1 terms
then you dont actually have to find the common denominator
I think that's the process I typically do, and that's where I always end up doing something that I don't realise I'm not allowed to do, and I end up getting it wrong lol
hm, how would you do it here?
Just writing it out
Alright well I've worked it out and it's correct lol, but I got it wrong originally because I pressed something wrong in my calculator
Maybe I just have to be mindful that I'm putting it correctly into my calculator for exams
this was my working out for reference
always helps to double check what you type
or even just type it again with fresh eyes
yeah probably hey
but yeah that method will probs be the best one to do, I think I remember a tutor telling me last year in a different course to use that method as well
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I'm not sure why this wouldn't be the answer, I also tried make j as 1
are all vectors in V parallel to the y-axis?
I thought so?
because if x is whatever x is and y is 0 then its just pointing straight up i thought
are they pointing straight up?
or straight down
but i feel like maybe its not then 😭
but i dont understand why not
what is the unit vector that points straight up?
im not sure 
sorry let me check the notes
could it be just <1,0>?
OR NO
THATS SIDEWAYS
<0,1> or <0,y>
idk why i was thinking like that my bad
could you help me with this one too?
originally i said C A B (dumb idk why i did that), but does this make sense for my answers?
the gradient field always points in the direction of greatest change
the countour plots always go along the direction of no change
so, the gradient field is always perpendicular to the contours
ohhh?
i struggled with countor plots so its causing me problems again lol
let me think real quick
so far im sure that 3 is A
I'm thinking C B A
try to imagine the two images on top of each other. for which combinations is the vector field always perpendicular to the curves?
mmm okok
B C A
i felt confident so I submitted it and it was right 
thank you for your help! it was my last problem so i can sleep early tonight as a result!
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If I am asked to find the roots of the quadratic equation: y=-2(x-1)^2-3, you can get two values of x that incorporate the imaginary number i, but would those still count as roots as the quadratic?
Because if you graph the quadratic out there are no points that intercept with the x-axis
So I should still write them as the roots right, I wouldn’t just put “no roots” as the answer?
Well depends on what type of exercise it is?
Did they ask you specifically for real roots?
it only says roots:, but its only 9th grade math so im assuming my teacher wouldn’t be asking for something that complex
If you haven’t been taught complex numbers then I guess you don’t need to write those roots
Alright well thanks for clarifying, I just wanted to make sure the roots are still considered an answer although the graph doesn’t have any
🙏🙏
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Where error
,rotate
Why not
cuz
sin is kinda like a function probably
so like imagine sin function called f(x)
if it's sin^2
it's f^2(x)
not ( f(x))^2
try using
sin^2(x) = 1-cos2x/2 identy to finish
Is trig identity the same as rules for trigonometry
likely correct
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yes you can
its literally the same
$ \sin^{2}(x) = [\sin (x)]^2 $
👍
0<sin^-1(x)<1
i think thats the problem
you insert pie which is larger then 1 therefore it cant be
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Question: A is a set of straight lines. Write a statement that says that there is no pair of two lines in A that are parallel
Is this statement true?
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in this differential equation would the particular integral be:
Ax^2*e^-2x + Bx + C?
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i have tried differentiating this twice and subbing into the differential equation but like i can't do anything to find A B and C
like compare coefficients and stuff it's soo messy so I think im going wrong
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Am fine with question B, need help with A
all interior sum to 360
opposite pairs sum to 180
I don't understand what x+2y=160 and 2x+6=110 mean
i mean
i don't understand how for example x+2y=160 came about
by the second one
opposite pairs sum to 180
DAB and BCD
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Why is it safe to conclude the vertical U = 0 ?
It only says horizontal u = 21 but never mentions vertical u so why can we infer it is 0
Thanks
Shouldn't it have any vertical values though?
wdym
It has vertical values for acceleration
so why cant it have vertical values for initial velocity?
yea, its just saying initially, vertical velo is 0
But why can we infer that? It doesnt say it specifically in the question
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is that also the same for final velocity too?
Just want to make sure i understand it fully
well when it hits the ground, ofc vertical velocity is 0
no i mean just before
just before it hits the ground becuase it isnt written so i dont know
just before it hits the ground, it has nonzero vertical velocity
I need to finish this