#help-17
vocal sleetBOT
elfin moon
I thought it would be 1 but it is 4
Because the limit doesn't exist
Can anyone clear this doubt
keen umbra
outer warren
consider the one sided limits
lethal plank
we have integers x,y,z where 17x+5y-2z=0
thin vale
lethal plank
closed the other
prove that A∈N
and that A is a perfect square
honestly hardcore 💀
lethal plank
<:this:489575168314966026>
got any idea on this one?
thin vale
do your natural numbers include 0?
thin vale
good
lethal plank
so A cannot be 0
thin vale
not true
lethal plank
what?
thin vale
y=-3 z=1 x=1. Then 17x+5y-2z=0. Then (3x+y)=0 then A=0
mild flower
if x = z then A = 0
mild flower
nu uh
lethal plank
yu uh
thin vale
HAH!
mild flower
slander
lethal plank
alr stop fighting
thin vale
Sorry, Hayley gets like that sometimes. super distracting
worldly crow
mild flower
i'm suing
thin vale
mhm
lethal plank
and i have no idea how
thin vale
use induction
urban edge
I think you prove each one is a multiple of a diff factor of 210
thin vale
I think you prove each one is a multiple of a diff factor of 210
yes, the perfect square 210
lethal plank
210 aint a perfect square
thin vale
twas sarcasm
thin vale
well the sarcasm was directed at garlic
you were supposed to jump in
like we did to Hayley
worldly crow
it'd be a calculus longer than my forehead
How long is your forehead??
lethal plank
💀
thin vale
the real solution here is to get a longer forehead I think
lethal plank
gotta go to walmart for that
thin vale
well
I have a tidbit
your problem boils down to proving A is a perfect square
because that implies that A is a natural number
agreed?
lethal plank
yep
thin vale
so you must show that A=n^2 for some n in N
lethal plank
yep
thin vale
why did you prime factorize 210
lethal plank
why not
thin vale
fair
worldly crow
You’re so close
lethal plank
but also nothing
lethal plank
thin vale
maybe we should apologize to garlic and hayley and beg them for their help again
thin vale
https://tenor.com/view/ricardosambasuwu-gif-21856144
this hurts my eyes
worldly crow
It tickles my eyeballs
lethal plank
@mild flower
Dear Hayley,
I want to sincerely apologize from the depths of my heart for any hurt or pain I have caused you. My words or actions may have crossed boundaries, disregarded your feelings, or let you down in some way. I deeply regret my behavior and the impact it has had on you.
Please know that I take full responsibility for my actions and I understand the importance of acknowledging and learning from my mistakes. I am genuinely sorry for any distress I may have caused you, and I want you to know that it was never my intention to hurt you.
I value our relationship and the connection we share, and I truly hope that you can find it in your heart to forgive me. I am committed to making amends and working towards being a better person. Your happiness and well-being are important to me, and I will do everything in my power to ensure that I never repeat the same mistakes again.
now help me finish this exercise please 🙏
mild flower
what was the gpt prompt
lethal plank
doesn't matter
lethal plank
NoOoO
mild flower
Dear [Sender's Name],
Thank you for reaching out and expressing your sincere apology. I appreciate your willingness to take responsibility for your actions and acknowledge the hurt they may have caused me. It takes courage to admit when we have crossed boundaries and hurt someone we care about.
While I cannot deny the pain that I experienced, I believe in the power of forgiveness and personal growth. It's important for us to learn from our mistakes and strive to become better individuals. Your commitment to making amends and working towards personal improvement is commendable.
Forgiveness is a process, and it may take time for me to fully heal and rebuild trust. However, I want you to know that I value our relationship too, and I'm open to the possibility of moving forward. I hope that we can both learn from this experience and create a healthier, more respectful connection.
Let's communicate openly and honestly about our feelings and expectations moving forward. It's crucial for us to establish boundaries, address any concerns, and foster a supportive and understanding environment. Together, we can work towards building a stronger relationship based on trust, empathy, and mutual respect.
Thank you for your apology and your commitment to personal growth. I believe in the potential for positive change, and I hope that we can find a path towards healing and strengthening our connection.
Sincerely,
Hayley
lethal plank
that's menacing
thin vale
[Sender's name]
lethal plank
slender's name
glad python
Can we find x,y,z in terms of a common variable?
paper depot
passing off GPT as your own math
i think it's also not very kosher to pass off gpt-written apologies as your own
glad python
Using CRT?
thin vale
critical race theory doesn't belong here
mild flower
btw i have no idea how to do this problem
thin vale
btw i have no idea how to do this problem
same
glad python
yum geo
mild flower
best guess is solve that 17 equation for [pick a variable] and then substitute it in and hope
glad python
First let’s do this tho
glad python
best guess is solve that 17 equation for [pick a variable] and then substitute i...
What I was thinking, maybe it will reveal some symmetry
lethal plank
i'll think about it
anyways, here's the other problem
Let ABC be an acute-angled triangle with angle ACB = 50 and angle ABC = 70. The bisector of angle ACB intersects side AB at point D. The circumcircle of triangle ADC intersects side BC at distinct points C and E. The line parallel through B to line AE at intersects point F .Prove that FA=FB.
glad python
Ok let me try it
There’s nothing special about this problem. Just angle chasing
Do you know properties of cyclic quads?
@lethal plank
lethal plank
yep
lethal plank
ill try
glad python
the problem is the same as showing FBA=FAB (angles)
lethal plank
the problem is the same as showing FBA=FAB (angles)
the thing is that we don't know that ADEC is a cyclic quad
i gotta prove that
glad python
??
lethal plank
like
glad python
By definition it’s cyclic
lethal plank
it's not in the ipothesis
glad python
4 points lie on a cirvlhe?
lethal plank
yes, but that's in the drawing
glad python
“Circumcircle of ADC intersects BC at E”
glad python
That means E lies on circle ADC
lethal plank
yep
glad python
Big hint: ||BAE=FBA so FBAC is cyclic|| @lethal plank
civic drift
Hey maybe this might work too
You could prove FARB is a rhombus
By showing the triangles are congruent
Since diagonals of a rhombus divide it into 4 congruent triangle
vocal sleetBOT
Available help channel!
obtuse radish
latex banzai
vocal sleetBOT
latex banzai
obtuse radish
$\int_{0}^{\frac{\pi}{2}} \sqrt{(4sin(t)cos(t))^{2} + (3cos^{2}(t)sin(t))^{2} + (3sin^{2}(t)cos(t))^{2}} \delta t$
urban edge
dt where
obtuse radish
yep
urban edge
You can factor some stuff out
twin meteorBOT
shah821
obtuse radish
umm and take into the parts formula?
urban edge
Factors some stuff out first
obtuse radish
also how do i distance that dt thing? it almost seems inside the root
urban edge
It will work out really nicely
obtuse radish
Factors some stuff out first
i tried that once sin^2(t)cos^2(t) then out of the root
and use integration by parts but no end in sight
urban edge
Show your work
obtuse radish
i kinda cut it all; what should i do abt the root tho?
vocal sleetBOT
Please read #❓how-to-get-help
urban edge
You were right in factoring out the sin^2(t)cos^2(t)
obtuse radish
ok wait my work is utterly wrong; i literally ignored the root
urban edge
You get $\sqrt{sin^2(t)cos^2(t)} \times \sqrt{4^2+(3sin(t))^2+(3cos(t))^2}$
twin meteorBOT
garlicbredfries
vocal sleetBOT
vocal sleetBOT
Available help channel!
tight isle
I need to ascertain whether $\mathbb{Z}_2\times\mathbb{Z}_2$ and $\mathbb{Z}_4$ are isomorphic but the question doesn't give the exact operation that defined on both of these groups. Given groups $(G,\ast)$ and $(H,\circ)$, the question defines the operation on the direct product of two groups $G\times H$ as $(g_1,h_1)(g_2,h_2)=(g_1\ast g_2,h_1\circ h_2)$. I got an idea for a bijective map $\phi:\mathbb{Z}_2\times\mathbb{Z}_2\rightarrow\mathbb{Z}_4$ defined $\phi((x,y))\coloneqq 2x+y$ but I need to know the exact operation of the individual groups to prove the map is homomorphic
vocal sleetBOT
I need to ascertain whether $\mathbb{Z}_2\times\mathbb{Z}_2$ and $\mathbb{Z}_4$ ...
tight isle
apologies i miswrote the question hang on
twin meteorBOT
bostock123
tight isle
it says $\mathbb{Z}_n$ is the cyclic group of order $n$
twin meteorBOT
bostock123
cyan talon
if you think about it for non-prime n, (Z_n, *) isn't even cyclic
so the name would make no sense if the group was multiplicative
or just by definition I guess
tight isle
i see that makes sense
empty frigate
...(Z_n, *) isn't even a group for any n > 1
or at least not if you're counting 0 as being an element of Z_n
tight isle
that's what i thought of
empty frigate
what you can do is take the group of integers coprime to n with multiplication mod n as the operation
vocal sleetBOT
cyan talon
@tight isle I mean we haven't even gotten to the heart of your question tbf
tight isle
but my question was about the operation on the individual groups
i've got the rest of it down, i think
cyan talon
ah alright, I thought you wanted help for the whole thing
cyan talon
btw they're not isomorphic
tight isle
i'm confident about homomorphy
cyan talon
in another chan tho, cause you deleted your message again :/
vocal sleetBOT
Available help channel!
empty linden
how did this professor get the points for sin and cos?
vocal sleetBOT
how did this professor get the points for sin and cos?
empty linden
theres no triangle to work with either so
i cant use pythagorean property
ive been stuck on this since yesterday
ornate ember
directly plugging in t. For example y = cos(t), when t = 0, then cos(0) = 1. Similarly, y = sin(t), when t = 0, then sin(0) = 0.
cobalt stream
these are commonly used
outer warren
the values can be read off the unit circle
river minnow
Expected a professor not to know those?
Knowing those by heart usually is a result of happening to use them quite frequently
ornate ember
directly plugging in `t`. For example `y = cos(t)`, when `t = 0`, then `cos(0) =...
On top of that they're using known identities found in the unit circle on the top right:
outer warren
cos(t) gives the x coord on the unit circle at that angle
sin(t) gives the y coord on the unit circle at that angle
empty linden
cos(t) gives the x coord on the unit circle at that angle
sin(t) gives the y coo...
yeah but
howd they get the sqroot 3/2
i only got that answer when a triangle was involved
with a hyp of 1
river minnow
And yeah the symmetry helps with memorisation, it's then narrowed down to knowing just 3-4 values if not less
outer warren
as in you want to know how the values on the unit circle itself come from?
empty linden
yeah, and how their values related to the graph to plot points
should we first convert the radians to degrees, then find the sin of that degree?
because pi/6 is 30 degrees
empty linden
i got the decimal values for the fractions but
idk how they got the fraction
wait
outer warren
the exact values can be derived from special triangles
empty linden
the exact values can be derived from special triangles
yeah but i was confused since there was no triangle
because i got those fractions when a triangle was involved
outer warren
but refer to the unit circle defintions of sine and cos
empty linden
with a hyp of 1
outer warren
i mentioned above
empty linden
OHHHH WAIT
on the unit circle definitions
the hypotenuse is 1
so i can just do sin(theta) = opp/hyp
then use pythag theorem to find the opposite
i feel more comfortable working with degrees, so i convert pi/6 to 30 deg
sin(30)^2 + x^2 = 1
wait
i feel like somethings wrong
0.5^2 + x^2 = 1
that looks better
empty linden
i mentioned above
ok so now i figured out how to get the values but
instead of sqroot 3/2
wait
wait no something isnt right
ok so i got 0.5 for sin 30
should i convert that to fraction?
outer warren
that would be ideal
empty linden
yeah because i ended up getting sqroot 0.75 when i solved it with decimals
ill make sure to convert to fractions right away
the decimals can work but the fractions are more ideal
empty linden
the decimals can work but the fractions are more ideal
since 0.75 for sin(30) is incorrect
thats the value for cos(30)
well, i think i kinda get it now
thanks for the help
ok so...
i tried the same method with 11pi/12
and my answer was way off
outer warren
show work
empty linden
i cant, im using a pc
the most i can do is type it down
11pi/12 = 165 degrees
sin(165) = 0.25819045
outer warren
their values for 11pi/12 are wrong btw
empty linden
for some reason, my calculator couldnt convert it to a fraction
so i just went with it as it is
0.2581905^2 + x^2 = 1
outer warren
it was probably a typo and they intended
11pi/6
empty linden
x^2 = 1-0.2581905^2
empty linden
it was probably a typo and they intended
11pi/6
i see
empty linden
x^2 = 1-0.2581905^2
then i squarerooted it
outer warren
there are ways to get exact values for sin(11pi/12), cos(11pi/12)
which involve stuff like compound angle / half angle identites which you probably aren't up to yet
empty linden
and got 0.9695 to 4 decimal places
empty linden
and got 0.9695 to 4 decimal places
but i feel like this is the value for cos(t) and not sin(t)
empty linden
there are ways to get exact values for sin(11pi/12), cos(11pi/12)
which involve ...
not up to that part yet
im only at graphing special angles of sin and cos
pre calc
outer warren
sin(165°) is approx 0.2581905...
cos(165°) is approx **-**0.9695
beware of signs (note that cos is negative in Q2)
empty linden
cos(165°) is approx **-**0.9695
beware of signs (note that cos is negative in Q2...
wait a minute
so whyd i get the cosine value when i did sin(t)?
outer warren
because you're not keeping track of what's what
0.2581905^2 + x^2 = 1
how did you even obtain that value of0.2581905
empty linden
> 0.2581905^2 + x^2 = 1
how did you even obtain that value of `0.2581905`
i did sin(165) on the calculator
empty linden
thats all?
outer warren
using y for the sine value
x is the cosine value
and if you have access to the calculator...
you could use to to calculate cos(165°) as well
though it won't give you exact values here
(unless you have a really good one)
empty linden
i know chatgpt isnt the most reputable source but
empty linden
yeah it got many of my questions wrong haha
anyways
if i have the calculator, just plug in the values for t and thats all, right?
outer warren
depends if you want and/or are expected to give exact values
empty linden
but what if i dont have a calculator
or rather
the question said to not use it
i should just assume that the value for sin(t) is actually cos(t)?
outer warren
if you have access to a unit circle, you can literally just read the common values off it
if you know quadrant 1 and properties / symmetry of the unit circle, you can derive values in other quadrants applying those
if you don't know Q1, those can be derived from special 30,60,90 and 45,45,90 triangles and the right triangle definitions of sine and cos
outer warren
i should just assume that the value for sin(t) is actually cos(t)?
sin(t) is sin(t),
cos(t) is cos(t)
if you tell a calc to calculate sin(whatever) that's what the calculator gives you
empty linden
i should just assume that the value for sin(t) is actually cos(t)?
ait
wait
i think i know why
i know why i got to that conclusion
i mustve used the pythag property by mistake
empty linden
0.2581905^2 + x^2 = 1
this is basiclly saying sin^2 + cos^2 = 1
outer warren
its applicable, you're just not keeping track of what your variables represent and reaching the wrong conclusions
empty linden
its applicable, you're just not keeping track of what your variables represent a...
yeah
outer warren
as mentioned earlier
empty linden
mhm
now that i think about it
i really shouldve memorized the special angles
ill do that right away
i was going through the lecture video too quickly
gaunt apex
vocal sleetBOT
vocal sleetBOT
vocal sleetBOT
Available help channel!
digital wave
if x lies between [0, 2 pi], then find the number of solutions of the equation sin 2x = cos 3x
vocal sleetBOT
if x lies between [0, 2 pi], then find the number of solutions of the equation s...
pallid zenith
if x lies between [0, 2 pi], then find the number of solutions of the equation s...
maybe you can use a phase shift identity?
wrong image
shrewd dagger
you could try sketching it
digital wave
maybe you can use a phase shift identity?
i dunno that identity
digital wave
you could try sketching it
that's what i tried.
i got 2x lies between [0, 4 pi]
and 3x lies between [0, 6 pi]
shrewd dagger
that's what i tried.
i got 2x lies between [0, 4 pi]
and 3x lies between [0, 6 p...
yes, but this is just the domain
you know a few important points for cos and sin
cos(0) = 1
sin(0) = 0
and so on
the 2 and 3x multipliers just get you there a bit faster
digital wave
you know a few important points for cos and sin
should i draw their individual graphs and get their intersection points?
digital wave
alr
digital wave
this is just my thought
u mean like, $cos 3x = cos(\frac{\pi}{2} - 2x)$ ?
twin meteorBOT
omniscientzenith
vocal sleetBOT
@digital wave Has your question been resolved?
digital wave
youre gonna have domain problems with the inverse
alr tq
vast shale
vocal sleetBOT
vast shale
I am stuck
vocal sleetBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
sterile trail
Where are you stuck @vast shale? Any work you have done so far?
vast shale
Where are you stuck <@456226577798135808>? Any work you have done so far?
im on step 1
karmic imp
Do you know how to isolate for a variable?
vast shale
not really
karmic imp
I suggest watching something like https://www.youtube.com/watch?v=fDMxOiS5g7k&ab_channel=MikeDeVor
sterile trail
I also found some good advice for harder one! Might wanna look at them
vast shale
I suggest watching something like https://www.youtube.com/watch?v=fDMxOiS5g7k&ab...
sure
vocal sleetBOT
@vast shale Has your question been resolved?
vast shale
Solution
3b - 5 = 7 (2-3b)
3b -5 = 14 - 21b
14 + 5 = 21b + 3b
19 = 24b
b = 19/24
vast shale
ya?
lime gorge
It’s not good to give solutions like that
vast shale
why?
lime gorge
It’s cuz it’s not conducive to peak learning
vast shale
oo
lime gorge
It’s okay I forgive you 👍
vocal sleetBOT
Solution
3b - 5 = 7 (2-3b)
3b -5 = 14 - 21b
14 + 5 = 21b + 3b
19 = 24b
b = 19/2...
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
@vast shale Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
sudden compass
Hey so we have a lottery which has P(Win)=25% and P(loss)=75%.
If I spin 9 times, what would be the number of wins apporximately? 9*0.25 right
dark sleet
vocal sleetBOT
dark sleet
I don't understand how he got 17.5, and 7.5
i have a slightly different version of this problem but if i can understand how he got that i can do the rest
i cant grasp what he did that resulted in 17.5
from the 100 plus minus 40 over 8
dense stump
what step are you confused on?
dark sleet
iirc im up to the same part as he is but i dont understand how he got 17.5 and 7.5
dense stump
from the 100 plus minus 40 over 8
well you just explained it lol..
dark sleet
i swear i checked it and it wasnt right
maybe im just tired
Ok I feel like an idiot now
I am definitely tired
thank u
vocal sleetBOT
@dark sleet Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
north glacier
help
north glacier
i need help in solving a math problem
dreamy viper
dreamy viper
make a sketch
north glacier
im confused if i should be using cosine or sine method to use it
do u know how to solve it
dreamy viper
i do, make a sketch and visualize it
dreamy viper
looks right
north glacier
and the other right angle would be automatically 90
north glacier
oooh ok
dreamy viper
wait
no
the 34 degree angle is in the other corner
cause its from the boat
and youre looking up at the base of the lighthouse
it would still be opp/adj though
dreamy viper
yeah
north glacier
34 C/ 150?
north glacier
wait is it like
dreamy viper
what trig function is opp/adj
north glacier
tangent
dreamy viper
sohcahtoa
right
so tan(39) = opp/adj
plug in your opp and adj and solve for C as you denoted it
north glacier
so i get the tan(34) and then multiply is to 150
dreamy viper
adj=opp/tan34
twin meteorBOT
Hayley
dreamy viper
^
north glacier
they didnt really specify
i found a solution online
and they subtracted 37-45
= -8
and added 360
i dont really get why they added 360 tho
mild flower
they added 360 because negative headings aren't a thing
mild flower
37 degrees from the y axis?
the way headings work is that north = 0° = 360° and it goes clockwise, so east is 90°
dreamy viper
ah
north glacier
ooh ok
north glacier
yes thank u
vocal sleetBOT
Available help channel!
north glacier
hello i need help again hjhfd
vocal sleetBOT
hello i need help again hjhfd
next sleet
what does ms-1 mean
they meant ms^-1=m/s=meters per second
north glacier
so it just means meters per second right?
next sleet
yes
north glacier
ooh thanks
idle yoke
why is it xln(x) and not xln(2) ??
vocal sleetBOT
why is it x*ln(x) and not x*ln(2) ??
viral copper
Should be xln 2
idle yoke
can i send link to the vid?
6:30
is it a mistake then?
is nvm he then rewrite it
thanks
.close
unique musk
vocal sleetBOT
unique musk
can anyone help me@with these two i’m really bad at questions like this
merry python
what have you tried?
unique musk
i’ve tried imaging them into three separate triangles to find the similar sides but it just isn’t working for me
n i always get confused about which leg matches up with what
calm light
try using angles to prove similarity
unique musk
for the first one idk how to solve it cus
ik the hypotenuse of the biggest triangle is 15
merry python
i’ve tried imaging them into three separate triangles to find the similar sides ...
To get the correct similarity let one angle be x and find rest of angles in terms of x
unique musk
huh
the three from the little triangle has no corresponding side length we know in the bigger triangle
merry python
i’ve tried imaging them into three separate triangles to find the similar sides ...
or better show your work
calm light
alright so take the 2nd picture and label all the right angles
then pick any of the remaining angles and assign it the variable x
merry python
this may help
place the two triangles (for eg: ADB and DBC) in such a way that their x angle would coincide when superposed and same with the angle (90-x)
vocal sleetBOT
@unique musk Has your question been resolved?
unique musk
place the two triangles (for eg: ADB and DBC) in such a way that their x angle w...
yeah thanks bro i did what u said earlier and i figured it out
marble kettle
I need help with 4 I found my answer but it has multiple values
vocal sleetBOT
I need help with 4 I found my answer but it has multiple values
marble kettle
vocal sleetBOT
@marble kettle Has your question been resolved?
marble kettle
.close
vocal sleetBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
@vast shale Has your question been resolved?
vocal sleetBOT
@vast shale Has your question been resolved?
real gale
vocal sleetBOT
twin meteorBOT
Ann
real gale
$\norm{proj_{B}(A)}=\norm{\frac{A^T B}{A^T A}} = \abs{\frac{1}{A^T A}} \norm{A^T B} = 5$
twin meteorBOT
real gale
@paper depot Is that correct?
paper depot
that now looks more sensible.
bleak prawn
vocal sleetBOT
https://i.imgur.com/nhvoRnK.png
bleak prawn
Not really sure what to do here
bleak prawn
Normally I would just divide all of the terms by x and then get the answer that way, but the numerator already has -5/x so I dont really know if thats the correct way to do it?
I thought that they were both y=0, so I tried that but only the first one was correct
flat whale
do you see the horizontal and vertical asymptotes here
bleak prawn
Ye I see them
flat whale
oh
bleak prawn
I tried to solve without looking at the graph
flat whale
the function isn't even defined at negative values of x
so i don't understand the question
bleak prawn
Like just solving it with the maths to make sure I understand it
flat whale
last sentence
bleak prawn
But how do you know that its none sry?
bleak prawn
the function isn't even defined at negative values of x
Ohhh
I see now haha
Okok makes sense
Thats all I wanted to ask thank you!
❤️
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floral crow
im not sure where to start
vocal sleetBOT
im not sure where to start
hushed pewter
im not sure where to start
find a k such that f(f(x))=1 for every x
glossy maple
you mean f(f(x)) = x
first try to simplify the expression f(f(x))
plugging 2/(x-k) - 1 into the function as the input
then equate that to x
hushed pewter
you mean f(f(x)) = x
Oops right. Thanks
glossy maple
👍
granite wing
snlsmsmsmsmla
vocal sleetBOT
snlsmsmsmsmla
granite wing
hiya
terse forum
Turkish 
granite wing
Turkish <:catKing:812386361297862747>
oop
granite wing
Turkish <:catKing:812386361297862747>
tell me if you'd translate differently
granite wing
I can't understand your handwriting
oh
i suppose other people might have difficulty as well then
i'll write again
on my pc
here we go
so i'll explain my thought process
since dividing by 12 means
wait-
it doesn't divide 12...
oke oke so the last digit should be one more...
worthy citrus
3A4B are just the digits of a number?
granite wing
yep
tho i got it nevermind
wait it's not right??
i got 17+1 = 18
but the answer is 9
granite wing
How could one of them be 17
not one of them a+b
the question asks a+b
if it divides 12 then it has to divide 3 and 4
dividing by 3 means
3+a+4+b= 3k
and by 4 means:
4b=4k
granite wing
and by 4 means:
4b=4k
with this k=b=0,4,8
and if b=8,
15+a=3k
a can be 9
so 3948
a=9,b=8 a+b= 9+8 = 17
but since its one more (see the division)
should be 18
well that's what i thought
vocal sleetBOT
@granite wing Has your question been resolved?
granite wing
<@&286206848099549185>
vocal sleetBOT
@granite wing Has your question been resolved?
vocal sleetBOT
@granite wing Has your question been resolved?
granite wing
no botty no
<@&286206848099549185>
at least tell me if you're getting the same answer guys anyone?
just look at this:
QUESTION:
And my trial:
topaz sparrow
Is this prove right
Ques: σ(p^m) = 1 + p * σ(p^(m−1))
Ans: 1 + p*(p^(m-1)) = 1+p^m
flat whale
Is this prove right
Ques: σ(p^m) = 1 + p * σ(p^(m−1))
Ans: 1 + p*(p^(m-1)) = 1...
!help
vocal sleetBOT
Is this prove right
Ques: σ(p^m) = 1 + p * σ(p^(m−1))
Ans: 1 + p*(p^(m-1)) = 1...
Please read #❓how-to-get-help
vocal sleetBOT
@granite wing Has your question been resolved?
iron flax
vocal sleetBOT
iron flax
help me solve please
waxen harness
try to do some algebra with janet's solution and check if it s the same with antonio's
vocal sleetBOT
@iron flax Has your question been resolved?
vocal sleetBOT
Available help channel!
mossy mantle
can someone explain this please
vocal sleetBOT
can someone explain this please
ornate ember
Basically, it has to do with scale as n gets bigger and bigger. When I was learning this I would consider "which one of these are growing faster"? e^n grows so much faster than n^2 that as it increases to infinity, it diverges.
As an example, let's use n = 100 in their example.
e^100 = 2.69 x 10^43 and (100)^2 = 10000. It grows sooooo much faster that it doesn't converge
austere storm
because power is more powerful than a regular nubmer getting squared
raising something to infinity will go faster than squaring infiity
think of an exponential graph
and then think of a quadratic
exponential grows faster
mossy mantle
so infinity is correct because anything greater or equal to 1 its positive and it allows it to "grow fast"
1 is not entirely correct but can be used instead of 100?
ornate ember
well you have to be careful there
with the limit going to infinity, we're looking at "end behavior"
mossy mantle
Basically, it has to do with scale as n gets bigger and bigger. When I was learn...
right? becasue of 0 < |r|<1 ?
ornate ember
for example, consider which one grows faster: x^2 or x^10?
If you were to check values from 0 < x < 1, then x^2 would be larger than values of x^10, but for x > 1, that behavior changes.
austere storm
you're plugging in infinity for the limit
ornate ember
so basically the explanation they gave they were using 100 as an example
pastel swan
Open.
pastel swan
regal bane
You also need to know approximately where that root is. Huh.
sly sierra
well first, do you know how to see if it has a real root?
pastel swan
Do you know how to determine if a quadratic has a (edit: real) root?
Yes. Discriminant must be greater or equal zero.
regal bane
Oh lol nvm it's not so bad. Remember that you can plug a root into the equation.
sly sierra
i cannot confirm that
waxen harness
converges absolutely means that abs(an) converges for the LHS and it means that abs((-1)^n*an) converges for the RHS, but abs((-1)^n an)=abs(an)
sly sierra
what do you get if you take the absolute values of the terms in each series?
covert salmon
the same series
waxen harness
so it s just asking you "If abs(an) converges , then abs(an) converges"
vast shale
Help
lyric fossil
@thin vale
cobalt imp
if the right side is square root x-4 you would just substitute values for x and solve
so for example 4-4=0
then square root 0 = 0
lyric fossil
what 21 savage is suggesting is that you pick values for x and plug them into sqrt(x-4)
vast shale
what 21 savage is suggesting is that you pick values for x and plug them into sq...
Need to perfect square right?
lyric fossil
preferably
lyric fossil
where did 12 come from
also what you want to be a perfect square is the thing under the square root
vast shale
16myb
lyric fossil
ok let me ask a different question, do you know what the graph of sqrt(x-4) - 2 looks like
vast shale
No
vast shale
ok let me ask a different question, do you know what the graph of sqrt(x-4) - 2 ...
No
We haven’t learned something like that yet
We just using the table like this to graph
tulip forge
ok so
when x = 0
fill in the equation with x being 0
so its 0 on the right side after solving
or when x=1
fill in ur equation replacing x with 1
them solve
vast shale
ok so
when x = 0
fill in the equation with x being 0
are u able to write it on a paper so its more clear?
vocal sleetBOT
@vast shale Has your question been resolved?
vocal sleetBOT
@vast shale Has your question been resolved?
vocal sleetBOT
@vast shale Has your question been resolved?
thin vale
<@779131727338930196>
thin vale
A few people have already offered help to you
either be more clear in what your issue is, or stop pressing the ❌
You want to graph this?
get a few points
and then connect them
$$\sqrt{x-4}-2=0$$
twin meteorBOT
austinu
thin vale
I think it wants you to compare the graphs of $$y=\sqrt{x-4}$$ and $$y=2$$
twin meteorBOT
austinu
thin vale
you should very easily be able to graph y=2. It is a horizontal line
Now, to graph the top equation, you know that nothing under a square root can be negative, so x must be greater than or equal to 4
start with x=4 and grab a few points. When x=4, you get y=0, and then can plot the point (4, 0)
now grab some more points
brittle minnow
@vast shale are you even there?
thin vale
try ones that will make the thing under the square root easy to evaluate
I recommend that you next try x=8
thin vale
<@456226577798135808> are you even there?
.close
vocal sleetBOT
brittle minnow
thin vale
2 to go
brittle minnow
let's goooooo
vocal sleetBOT
Available help channel!
lost swift
vocal sleetBOT
vast shale
now grab some more points
How do u even grab more points?
vast shale
<@456226577798135808> are you even there?
I went to sleep bro
lost swift
I need help with part (i) not sure how to diffentiate it
vast shale
It was like 1:20am
lost swift
yep
molten rain
yes
u= 2x
v= e^(2x)
differentciate the power
the power remains the same
put the differenciated power infront
dv/dx = 2e^(2x)
u do
then send me
ill check
🦅
product rule is
u x dv/dx + v x du/dx
x is times here
lost swift
cool-
merry python
<@&268886789983436800>
molten rain
thanks
lost swift
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verbal merlin
vocal sleetBOT
verbal merlin
bernoulli
im stuck at this
@vast shale
btw its wrong qn
its dis one
homogenuous?
dk how to spell
vocal sleetBOT
@verbal merlin Has your question been resolved?
verbal merlin
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glad mirage
vocal sleetBOT
hasty pulsar
,rotate
twin meteorBOT
royal kestrel
or division first
it doesnt matter
its better to just go left to right since division and multiplication have the same level of priority
but your answer will still be the same
glad mirage
k ty
vocal sleetBOT
@glad mirage Has your question been resolved?
marsh coyote
vocal sleetBOT
marsh coyote
5.4.7, the highlighted text, the x<=y+\epsilon is abit strange right since
If x=y+\epsilon for some \epsilon, then the hypothesis wouldn't hold anymore
lyric fossil
yes, but it’s for all epsilon
so you can pick a smaller epsilon and it should still be true
wraith venture
If x=y+\epsilon for some \epsilon, then the hypothesis wouldn't hold anymore
Pre-exercise: prove the result doesn't change if you make the inequality strict
marsh coyote
Pre-exercise: prove the result doesn't change if you make the inequality strict
Could you elaborate abit
wraith venture
If you take the exercise and replace <= by < (in the epsilon part), show it doesn't change anything (i.e. the 2 hypotheses are equivalent)
marsh coyote
so you can pick a smaller epsilon and it should still be true
If x=y+\epsilon, then wouldn't a smaller epsilon make the hypothesis false since x>y+\epsilon/2 for e.g.
Oh thought you mean
Use exercise 6
wraith venture
Yes
wraith venture
If x=y+\epsilon, then wouldn't a smaller epsilon make the hypothesis false since...
Then epsilon/2 shows it's an impossible case
marsh coyote
But then wouldn't it be better to just leave the exercise x<y+epsilon for all epsilon?
Since the x=y+epsilon doesn't do anything
I understand the result will still hold eitherway
wraith venture
Yes. It doesn't matter.
marsh coyote
Oh wait that's what you mean by hypothesis ar equivalent
Ah okay got it thanks
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vocal sleetBOT
marsh coyote
.reopen
vocal sleetBOT
✅
marsh coyote
Wait just to confirm, this will mean that the statements x<=y+epsilon for all epsilon, and x<y+epsilon for all epsilon are exactly the same for all scenarios?
So:
x<=y+epsilon for all epsilon iff x<y+epsilon for all epsilon
wraith venture
Yes
vocal sleetBOT
vocal sleetBOT
Available help channel!
trail shoal
help finding a please
vocal sleetBOT
help finding a please
mild flower
are you sure that should be f ' (0) = -1/sqrt3?
and not f (0)?
to me this looks like an initial value problem
vocal sleetBOT
@trail shoal Has your question been resolved?
trail shoal
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spark cloak
Question is a simplifiable rationale expression with 2 restrictions
spark cloak
i did $\frac{x^2+4x+4}{x^2-81}$
twin meteorBOT
deviousglxy
spark cloak
it turned out that it is not simplifiable
so what equation can be simplifialbe with 2 restrictions?
ruby vapor
so what equation can be simplifialbe with 2 restrictions?
Do you mean an equation with two "holes" in it? Basically so you have two things that cancel from the equation. You can construct one if you do something like: (x+1)(x+2)(x+3)/[(x+2)(x+3)]. x can't equal -2 or -3 but the equation can be simplified to x+1.
vocal sleetBOT
@spark cloak Has your question been resolved?
spark cloak
Do you mean an equation with two "holes" in it? Basically so you have two things...
ya
that works
Thanks
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vocal sleetBOT
vocal sleetBOT
Available help channel!
still anvil
Find 𝑑𝑦/𝑑𝑥 in terms of 𝑥 and 𝑦 if 3𝑥𝑦+4𝑥+𝑦=13
vocal sleetBOT
Find 𝑑𝑦/𝑑𝑥 in terms of 𝑥 and 𝑦 if 3𝑥𝑦+4𝑥+𝑦=13
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
so originally i tried taking derivative of left side and right side so i did product rule to split 3xy and got everything down to ( ((3)(y)+(3x)(y')) + 4 + y') = 0 then i got rlly confused and im questioning if i approached it correctly
twin meteorBOT
northsteve
still anvil
idk what to do about the two y' since the 3x is being multiplied to y'
cyan shadow
factor it out!
still anvil
o snap
lime gorge
First get all the terms with a y’ on one side and all the others on the other side
Then proceed with what bunny said
cyan shadow
<@307914411648090113> y'(3x+1)=-3y-4 ?
now how do you get the y' by itself?
still anvil
div by 3x+1
steady prawn
vocal sleetBOT
steady prawn
Also this question is very complicated I think
IDK
Read it all first though plz
Also the phsyics thing was for a diffrent discord server
Thats why I said physics which still was math but also science and you know
flat whale
this is a lot of words
can you ask ONE math question?
stars and black holes have nothing to do with how infinity is defined
steady prawn
Yeah I'll explain more in a second
Well basically the summary is that I think that ∞ should be able to be added, subtracted or whatever other things you could use and Hilbert's hotel paradox because I believe that if you add 1 to ∞ or in the paradox's case if you add 1 to a ∞ long hotel that's fully occupied you would just have to move all the guest one room over but I think that while they say it's still infinity it could be because the mind can't comprehend it and despite being well ∞ there's still more to it that you can add technically but it would still just be counted as ∞ and for the quasi stars it's just that a fraction of infinity could be possible even in the real world because we still don't know the rules of infinity and quasi-stars is a black hole with a star becoming a black hole but the black hole in the star is pushing back which should be infinitely forceful I guess you could say because of newtons and all that jazz but its only in power and since everything travels at the speed of light it took less long to create a black hole in the middle of the star then on the outside since the star would have to fully collapse in on itself to do so. that means also that the quasi-star is in a way semi-infinitely forceful like 0.5*∞. and black holes are negatively infintely forceful or powerful however you wanna describe it in the amount of newtons that gets pushed outwards. white holes have to do with this because there like black holes but opposite where they create things and one of the theories is that the create things that black holes destroy so they could be positively infitely powerful and that about sums it up.
NGL this definintly is a phsyics problem hes right.
flat whale
NGL this definintly is a phsyics problem hes right.
great go to #old-network for physics server
steady prawn
ok
vocal sleetBOT
@steady prawn Has your question been resolved?
vast shale
vocal sleetBOT
vast shale
I chose the x intercept to be 1,0 and the asymptote to be 2
And then y approaching 2 as well
But im confused on how to continue
rugged orchid
what about the rest
vast shale
likeee how would i do the y approching 2 part?
rugged orchid
how is it possible for a function to have both a vertical asymptote and only 1 x intercept whilst being odd or even
rugged orchid
it sounds impossible
vast shale
it doess
rugged orchid
you need it to either be odd or even
which means either f(-x) = f(x) or f(-x) = -f(x)
vast shale
i can cancel the odd or even part and explain that its impossible?
vast shale
which means either f(-x) = f(x) or f(-x) = -f(x)
soo f(1) = -f(1), for the 5th point?
rugged orchid
do you know what i mean by it's impossible
vast shale
that the graph wont work out?
regal slate
how about a rational function with x-intercept at 0,0
vast shale
how about a rational function with x-intercept at 0,0
hmm how would that work?
vast shale
yea
regal slate
hmm
rugged orchid
but then you cant have an asymptote on the same point as an x-intercept
vast shale
yea, theres that too