#help-23
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Wdym?
What do I do here
Well for A the elements are all of the x that can solve the equation 2x+1=6
This is pretty easy ngl
Just find the values of x that solve the equations
And then check if they're from the right set
And ur done ig
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Hello, i need help with the Convert vertex form to general normal form (Quadratic equations)
Do you have a specific question ?
I have exam tomorow and i just want to understand it. as my teacher wrote that on the board i didnt understand anything
btw i use translator for Technical terms
ok show us
I dont have a question, i just want a Crash course
If i had f(x)= (X^2-3) + 1 how would i do that ?
Its not vertex form is it ?
Vertex form is a(x-k)² + h
Just simplify the expression
Square the brackets, then collect like terms
Can we have a Picture ?
1 min
"e" should be "c" so ignore it
I understand how they shift but not how to convert them to the general normal form
Well do you agree that it is y = (x+d)² + c
ok
Actually about the shifting you just consider the min point and you slide the parabola
but how do i do the converting, my teacher said something about "binomic formuls" or a "Pq" formul
for (x+d)² + c, the min point will be (-d,c)
why minus?
i have to learn that formul?
Yeah
is there comming more or was that all?
Going from one form to another is better for both of us that you watch a video first and then maybe come with questions about the examples they show
ok
Like its something to see rather than read
wait
Hang on
.close
Closed by @gentle void
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Converting from $f(x) = a \cdot (x - d)^2 + c$ to $f(x) = ax^2 + bx + c$
USS-Enterprise
✅ Original question: #help-23 message
thats not that
But this was your question
.
If there's no a in front of (x-d)^2 it implies the leading coefficient of the quadratic function is always 1
Oh I see
wait, a means its wide, small, upside and downside right?
You are working with the leading coefficient being 1 constantly
a is called the leading coefficient
we learned a but never used it really, we just know what that is
Hm
Well a, the leading coefficient tells two things
- Vertical stretching or compression
- Direction of the parabola (facing or opening upwards or downwards)
But it's interesting you don't learn about that
i know that but we never use a in our formuls
So your vertex form is of $f(x) = (x + d)^2 + e$
USS-Enterprise
yes
And what is the General form?
but the + was a minus!
I don't see it in the photo
i remember
well if the x got shifted to the left its minus but if its shifted to the right, then plus
If d > 0, the parabola shifts left
Hmm
bye!
The quadratic with vertex form / Scheitelpunktform y = (x - d)^2 + e has vertex (d, e) / Scheitelpunkt (d | e)
Similarly the quadratic with vertex form y = (x + d)^2 + e has vertex (-d, e)
👀
yes thats what we learned but not the second
ok
Going from the vertex form to the general form should be the easier direction (you should be able to expand brackets)
can u maybe give me an example and i try to slove it?
Sub-question - Expand the brackets (x + 4)^2
I still don't quite understand why leave out the leading coefficient, because then you just take in a very special case of parabolas. Also no clue why + inside the brackets, everywhere else I've seen it has been a minus as convention
¯_(ツ)_/¯
Yeah, https://de.wikipedia.org/wiki/Quadratische_Funktion#Scheitelpunkt has the leading coeff. as well
SCHEISSE that's a large embed
😂
(x+4)(x+4)
x^2+4x+4x+16
f(x)= x^2+8x+16
thats how we learned
8+2?
just check what 4 mal 4 is?
better
Okay... and why the 2?
becuase it was (x+4)^2?
I mean, why have you got a +2 there?
(spielst du Uno oder was
)
-# (you playing Uno or sth?
)
can u speak german?
I mean there's a reason I looked for this in German 
well.
Was this correct ?
Now it is, yee
-# is your keyboard French or sth why've you got a space before the ? there
when a is for example 5,3 is the parable stretched or small?=
it is f(x)= ax"2
5x"2 + 4 for example
it tells when it is downwards, upwards, and the widh
well, if you take no translation, and stay with y = ax^2
Supposing a>0:
You can probably see that, if x is positive and we fix that value, then as a increases, then so does y
That is, a larger a forces the y values to shoot up faster
if a is a "0,2" number the parable is supposed to be wide
That is, the graph gets narrow af
but if a is a full number it should be small
-# "Parabel" ins mathematische Englische wird "parabola" sein
i understand it but i just wanted to know what happens if the number was 4,2 for example
-# "parable" ist wie vom Bibel
f(x)= 4,2x^2 + 1 for example
is it wide or thin the parable?
i just want to know that
larger a means narrower parabola
so it is stretched?
I feel like dividing the quadratic function into this many parts "no leading coefficient first; then no linear coefficient" leads to just more confusion than starting with the whole thing
soll ichs auf Deutsch
Wird a grösser, wird die Parabel enger
Yes or no?
ohhh
ok
thx
that was all
we can close this now?
So sagen auch die Beispiele hier
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why are we supposed to take only taller than 20-feet trees in the denominator
they said that "a tree from one of these rows will be selected at random"
what does that line really mean here?
you are told it will be selected a random, but you are given more information later
I see
but technically if were to take only 20-feet taller trees in the denominator, then wouldn't it violate the statement where they say that it is selected at random?
no, you are given that information is true
idk if it helps, but you can imagine parallel universes where each specific tree is selected a random
if you are given that the tree is tall, the parallel universes where a short tree was picked cannot exist
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this video explains it quite well
despite the shitty thumbnail
good luck on your SAT jug
@placid flower Has your question been resolved?
oh wow thank you so much
thanks
I see, thanks
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FTC: Part I and II
They exist, yes
I need help with them.
Remember:
• Ask your math question in a clear, concise manner.
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I don’t understand how indefinite integrals relate to derivatives
I would just like an explanation of them
I will ask such questions along the way
Just conceptually.
Okay. Sorry, I can't do that because I need to go to sleep 🙂
But yeah just wait around a bit
Someone will show up
Although it is preferred if direct questions are asked, perhaps someone will walk you through it. I would however still suggest going over material you have available that covers this
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For vertical asymptote we have sqrt(x^2 + 3x) + x = 0
sqrt(x^2 + 3x) = -x
x^2 + 3x = (-x)^2
3x = 0
x = 0
For the vertical asymptote we have the highest degree of x in the denom > highest degree in the numerator so we have y = 0
And no oblique asymptotes either if im not mistaken
So we only have x = 0 and y = 0 right?
But im not sure what a one-sided asymptote or 2 sided one is
Just use one-sided limits
I dont mean to be rude but id like to know whats wrong with my approach rather than being told 'just do this' 😅
I think they mean that that's what differentiates one sided and two sided asymptotes
You use the one-sided limits and see how many of those go to the value you need
Oh ok
If both, two sided asymptote. If one, one sided
Im not really sure how to do that tho
Btw I figured out about the HA
If you sub in x = infinity you get infinity, if you sub in x = -infinity you get infinity again
So it approaches from the top but not the bottom, right?
If thats what you meant
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is this available?
yep
show what you plugged in and where
alright then
what's pert? Because what you put in doesn't match what I think it is
A=Pe^rt
is
a is the amount acfter time t
p is the principle
r is the annual interest rate
and t is the time in years
so if you tried to make use of this pert, why is there no e in your answer?
so A=prt?
you've already concluded that's wrong
you said "I tried pert" then showed an attempt that doesn't look like pert
i dont know what to basically do after i turned the percent into a decimal
so it would be like 520e^.045t
indeed
and then would i seperate it into 520(e^.045)^t
sure
when i did the e i got 1.046
did the e?
,calc e^0.45
Result:
1.5683121854902
Result:
1.0460278599087
cool
and then would my decimal then be .046
decimal for what?
i assume you're asking about the second part now
yeah
looks good
tysm
my dogshit teacher just throws questions at me and answers them herself
so im so lost
oh one possible wrinkle
thanks!
note how many decimals they want
wym
read the question again in full
indeed
Alright
@sturdy drift Has your question been resolved?
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am i doing this right
@fair forge Has your question been resolved?
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my brain aint functioning anymore pls help
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Can i get some suggestions on how to deal with this? I think, to first solve the x equation, it would be the t root of that equation, yes? but how would i eliminate t in that circumstance?
you don't want roots here, you want logarithms
from x = 3e^t, divide by 3, then take logarithms
get t = ln(x/3)
show where you got thus far?
oh wait huh. i just saw the other written direction, my bad.
they want an exponential not a log
my bad
no worries
do you have any way to work it with the exponential?
i had thought i just misunderstood that written direciton lol
isolate t in the y equation first.
yes
should i then try to solve for y = something, as some simpler equations have it? because that feels wrong in my heart
i just put it in as is, and it was right! success
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Hey
hiya. got a question for the channel?
Yes
Please
Alright
sure thing. what are you stuck on?
got an example question?
mhm, inclusion-exclusion
Idk how to get it
and thus we return to this question. do you have an example question that applies this but one that you don't get A \cap B?
I don’t
He just put it on the board
Said it’s a rule
I just don’t know how to get AintersectB
It’s like
He gave an example with 3 ven diagrams
your teacher is right in that inclusion-exclusion is indeed a rule, but if A \cap B is not given then A \cup B cannot be determined uniquely
total number 34
21 play football
12 play basketball
10 play volleyball
8 play football and basketball not volleyball
5 play basketball and volleyball but not football
4 play football and volley but not basketball
there we go
oh
well yea the numbers here do not make sense
Gulp
but I get the general idea of what you're pointing at
Yes
Art of Problem Solving's Richard Rusczyk introduces 2-circle Venn diagrams, and using subtraction as a counting technique.
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I’m in class
I cant
Watch that
.
wait then finish your class first
I have math after
can always ask later
ask your teacher?
And I have an exam
your exam is today?
I’m not in math class rn and when I asked he didn’t explain it the best but I have the exam next session
session can mean anything, didn't know it meant period in that case
Oh
It’s next period then
Which is in 35 minutes
Like semester?
I know everything in set
Oh nvm
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Only the part I mentioned
just put on subtitles
It’s mixing me up
and mute it
you’re welcome
good luck
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oh ok, cool
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2x + 1/3x = 5 then what’s the value of 4x^2 + 1/9x^2
aight hol up
Try squaring what they gave ya
do you mean:
\begin{enumerate}[a)]
\item $2x + \frac{1}{3}x$?
\item $2x + \frac{1}{3x}$?
\item $\frac{2x+1}{3x}$?
\end{enumerate}
Ann
never appropriate to say in a help channel
My bad
B
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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
actually I wanna change the question
given the first condition what’s the value of 21/(6x^2-15x+8)
do i have to !status again or can you tell us your status without
1
you have to send "1" 17 more times for it to be formally registered.
anyway okay
can you do some algebruh to 2x + 1/(3x) = 5 to write it as a quadratic in x
dont solve the quadratic but just get it to that form
so I write x=..
Yep
Now get rid of the denominator
Now take a look at the denominator at this question
Compare it to what you have now
It’s +7
Yes!
At this point, i think you can do this yourself now
$6x^L$?
Ann
my handwriting is that bad 😭
what's this capital L doing there
$6x^2$
1 divided by 0 equals Infinity
Go fix your handwriting or Ann's going to be your judge in your math exam
I did
Yessir
21/7 no?
Anymore questions?
So 3?
Yes
Okay one more
Alr
What will be the sum of the two angles produced when one side of a right angled triangle is extended on both sides
💀
I actually just don’t understand what it means
Maybe an English issue
.
my bad, im sorry
what are you translating from
also can you send an image of the q
cause rn it sounds like you're trying to put your questions in plain text and not being very good at it
Now extend one side, example AB
it’s in diabolical form but if you insist
so we are confused at wtf you mean
ok sure
diabolical or not
if it's diabolical then we at least know it isnt your fault
,rccw
that paper is so bent
prob not related, but 1) how does this cmd work, and 2) are there any similar cmds?
and they also dont tell us if we are extending a leg or the hypotenuse
yeah that’s why I type it out
,rccw grabs the last image sent in chat and then rotates it counterclockwise
- rotates the picture counterclockwise
- ,rcw rotates clockwise
there is ,rcw for clockwise or ,rotate [angle] for arbitrary rotations
but if extend the hypotenuse, then it isn't a rught triangle anymore
i think the question is unanswerable without this info
Now draw AB longer than a bit
by that logic it isnt a right triangle if either leg is extended either
how do you know it's AB we are extending and not BC
So it’s 270 degree or so what
split into cases
Place a RULER onto AB, and then draw a longer line towards B
if we simply extend the legs in a straight line, then the right angle won't be disturbed
done
are we not expected to give one answer only?
neither will it be disturbed if the hypotenuse is extended
yeah
i dont understand wtf is meant to be inferred
You just further proved my point why we should extend AB
if we dont know whether we are extending a leg or the hypotenuse then the answer can range anywhere in (180, 270]
but why AB
extending a leg gives an unfindable answer
AB or AC
WHY A LEG
nobody is answering this question, how do we know the problem wants us to extend a leg
y'all are so happy to just yap yap yap yap yap without understanding that the q is wrong
*me when im looking for the edge case in my coding comp
*
anyway im out
no
also does the sum refer to other the other angles beside the right one?
in a triangle ABC angle B is 60 degree , Angle C is 40 degree and the bisectors of angle B and C mets at O, angle BOC is what
I’ve drawn it
Oh wait
Show it
Is it 130
PLEASE LET US HAVE A DAMN MOMENT
Show us the diagram
no need to act bc ann's out lol
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i have a question about graphs. (its written in norwegian sorry for that) Task A is different function exressions. And which one is the correct one to the graph? I know its not F(x) but i dont understand if its g(x) og h(x)? Can someone explain it to me? I did the -b/2a formula and got -1 as an answer...
ill suggest use completing the square method to find the standard equation of the parabola
Another suggestion: Try using -b/2a on both g and h. That will help in this case
i did that, but i dont understand what i do with the answer...
do you know what the answer represents?
i have heard about it, but i dont know it yet. Is it worth to take the time to learn it?
not exactly
its the x-coordinate of the vertex of the parabola, aka the lowest (or highest) point
absolutely when you are given such equations and you need to find the graph its useful its useful even in quadratic equations and calculus
i think the quickest way to find the graph would be completing the square here but if you got another formula you can use it too
OH!! Well now i understand it. I drew both equations and the lowest point on h(x) is +1 on the x-axis. And on g(x) it is -1! TYSM!!
You're welcome! thats also what the -b/2a expression is telling you
also definitely worth learning
yeah. I knew the formula but didn't know what i were supposed to do with it. But know i know!
I will learn the completing the square next!
Thank you so much for your time!
go ahead and ask here if you need anything concerning that
that would be .close
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Okay be honest here does this really deserve a 46%?
Is the professor just unable to understand the proof the way I wrote it or is it genuinely just wrong
@median drift Has your question been resolved?
you want to know whether you deserve a marking?
every teacher is different
just practice and the bias of the teacher will vanish too
The last step (taking the limit as m goes to infinity of the sequence) subsumes that you know the sequence converges already.
@median drift Has your question been resolved?
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real
u = 1 - r^3 | du = -3r^2
integral of (9r^2)/(sqrt(u))(-3r^2)
integral of -3/(sqrt(u))
Oh wait I see my mistake 🤡
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oh okayy
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Can someone pls help me understand this
This is CRT
I understand the general idea of it, given like examples but I don’t get the intuition behind this
@thin lion Has your question been resolved?
what do you want to know
I don’t get what that remark is saying
do you have experience with groups
Yes I know congruence classes
ahhhh this is not what I meant
but nvm
The remark is saying that there is a bijection between these two sets
so anything you can say mod N you can say simultanuously for all n_i
and vice versa (this is the non trivial part)
so you can solve an equation modulo 6 by solving it modulo 3 and modulo 2
Is that like saying all integers can be in one of these sets [1]_3 [2]_3 [0]_3 ?
But in this case
Sorry bad wording
equivalence classes under modulo N
and 0, 1, ...., N - 1 form a complete set of representatives
Ah alright
likewise for Z/niZ
And this is bijection to f(x)
That’s the bijection right?
yes
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I am using gapminder to calculate some statistics. But I stumble across a problem where I'm one decimal off but can't figure out why. I am calculating death by measles for children per 1000 births for Nigeria. According to Gapminder it should be around 0.117
I use gapminder to get the data for total births in Nigeria, and total death by measles to make me own death by measles per 1000 births
I had 6 310 000 births, and 10800 total deaths for the same year
10800/6310 = 1.7 deaths per 1000
How am I one decimal off? I don't get it, I can link the gapminder data I'm looking at if someone could help
@mighty prism Has your question been resolved?
You should link the data. We can't determine why a calculator made a mistake without even seeing the input/output
This represents the total births, Nigeria is the big blue bubble in the middle https://www.gapminder.org/tools/#$model$markers$bubble$data$filter$dimensions$geo$/$nor@$world_4region$/$in@=asia&=americas;;;;;;;;&encoding$y$data$concept=new_births_total_number_estimated&space@=geo&=time;&source=sg;&scale$domain:null&zoomed:null&type:null;;&frame$value=2008;;;;;&chart-type=bubbles&url=v2
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@mighty prism Has your question been resolved?
Well first off
0.117 and 1.7 aren't 1 decimal off
Not completely, but some error is understandable since I'm using approximate numbers of total births and total deaths
so it not being exactly 0.117 isn't that big of a deal
but being a decimal off approximately is a bit of a bigger deal
I see, but still even if we move the 'correct' answer one decimal to the right we get 1.17, or rounding up to 1.2? Which is still a ~40% difference
Is this expected?
Sure
The numbers from gapminder is like 6.31 million
for total births
We wouldn't obviously have such an even number in reality
where it is exactly 6 310 000
So I'm expecting some error, as long as I'm within a 50% margin
Huge margin but I am in no way an expert about these things so okay
Well to me it seems a huge margin*
Also quick question
I mean could be, the issue is that I don't have any knowledge of knowing how gapminder estimates their values or what model they use. I'm just taking their numbers and data to try and ''rederive'' an answer they have
I haven't deep dived into the question really, but just off the face of it I see the statistics can be sorted by year
And I don't see you mentioning any year
Might the mistake be here?
Oh I see, yes
or if you prefer to open gapminder tools yourself and sort the y axis
I appreicate a new pair of eyes looking at it
Maybe I've tunnel visioned staring at this question for a while
I could also share my screen if that makes it easier
I doubt it 😅
Okay I looked at it
And best I can say is that either Gapminders statistics for measles death / 1000 births is calculated, or rather modeled differently than simply dividing the two quantities
Or, different sources were used
I tried to find the sources for the data since they typically link it
But the sites were unvailable
probably taken down after this many years
:/
But thanks I guess, I was kinda at the same conclusion as you. But I wanted another pair of eyes to analyse it with me
Yeah
I don't know, perhaps leave it open
For someone with more expertise in this area
But that would be my top guess after looking into it
Should I trust my number more or gapminder?
Probably gapminder
I'll try to ask around a bit more just in case, before I decide to abandon my approach and use gapminder's numbers. I have a handin, if I'm lucky then my teacher won't ''fact check'' the calculations
and then question why the two numbers don't align
Because the data is probably modeled and corrected for things like underreporting, etc.
Most likely, it is valid what you are saying
My issue is that I then make a comparison to Germany and calculate the precentage difference. Since Gapminder says Germany has 0 deaths per 1000 births
Most likely because the number is so small they just rounded it to 0
so I had to ''get the real number'' myself by using their total deaths in 2008 + total births
and I was like ''fact checking'' to see if I would get the same number if I did it for Nigeria, but I didn't
so I could just calculate Germany's death per 1000 births, and then be like ''I took the data for Nigeria from Gapminder'' and do the comparison there
But that's risky business
You could try emailing them? It’s always messy business trying to reverse engineer how people got to the statistics they did
Especially real world data
Well looking at Germany specifically, 8 deaths have been registered from measles between 2001 and 2018
No age given
Would've probably worked if I had enough time to wait to exchange emails
Assuming an answer from them would be bestowed upon you
Ya, it's extremely rare. Which explain's gapminder's number of 0.13 total deaths by measles during 2008
You have a deadline? Is this like a project or something
Yeah
Well anyway, I should probably go to sleep, given that it's 00:26. Best of luck Basel!
Ya, a project
Thanks for the help
Well it’s still worth a try if you’re actually interested
Even if they respond after the deadline youd learn something if they respond
I can send the email anyways to see if I can get some information. Honestly seems like the data is very lacking when it comes to deaths per 1000 births
Since that is the ONLY year gapminder has any data on deaths per 1000 births for measles
You can't scroll or analyse it for any other year
And maybe their model takes other factors into consideration?
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gaaaaaaaaaaah
FIRSTLY, wtf is the $\kappa(\mathbf{v})(\mathbf{w})$ notation??
;(
well k(v) is supposedly a linear form in (K^n)*, so you can evaluate it on a vector in K^n
hence the k(v)(w)
@loud wren
@loud wren Has your question been resolved?
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this looks easy but i can't do it 😭
If the diagram is just for reference, I believe there are two solutions
Have you heard of sine law?
no i dont think so
What are you learning recently?
What topic or chapter does this question belong to?
idk we've been doing trig equations like cos theta= .8
im not sure its just a problem my teacher wants us to solve
Presumably you haven’t gotten in touch w sine/cosine law, right?
Right….are you allowed to use unlearned theorem or additional tools like a calculator?
If they’re allowed, I can introduce sine law rq
yeah they're allowed
Alright, let’s talk about sine law
So for every triangle\
\
$\frac{\text{its relative side}}{\sin(\text{certain angle})} = \frac{\text{its relative side}}{\sin(\text{the other certain angle})}$
i see
HungryChomper
Let’s take this triangle for example
9/sinA = 8/sinC
Do you have any doubt so far?
so it would be like 8/sin(34) = 9/sin(C)?
Exactly
Alright, anything else?
Feel free to post your work for verification after you’re done 
I could probably do it by myself but if you want could you help me solve for the angle of c?
Why not
Can you first isolate sinC for me?
ohh yeah
Ping me when you’re done
@magic junco sin(c)=4.5/8 i think
well i multiplied both sides by sin(34)
,w 8/sin(34 deg) = 9/sin(X) find X in degree
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ok, I give up using wolfram lol
sinC = 9/8*sin34?
yeah that works
but taking sin34 as 0.6 instead of 0.5 looks more precise imo
yeah also because it says to round to the nearest tenth
anyways once im there im not quite sure what to do
i use arcsin right?
use inverse function
yes
Be aware that there can be two possible answers
sin 120 deg = sin 60 deg
The angle can possibly be at second quadrant
when the angle is obtuse
.64?
from arcsin .6
yeah from arcsin(.6)=.64
.something is just 0.something if you're confused
oh i shouldve put the 0 in front lol
,w arcsin(9/8*0.6)
convert it to deg mode

As I mentioned, the value can possibly be (180-42.450443)
because they yield the same sine value
yeah so we have all the angles
but in the diagram, the angle C looks like an acute angle
which, by default, indicates that the other scenerio does not work
it's up to your teacher, tho. Idk if the diagram is just for reference
yeah
Just find angle B and play the same trick again
I believe that you can finish it from here on out 
yeah tysm
no worries, anything else?
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This is a question that I got incorrect on and exam I have already taken. I do not understand why I got it wrong. Could you help me figure out if its incorrectly marked wrong, or if I actually did it incorrectly?
We are specifically told to use the formula A = P((1+r/n)^nt -1) / (r/n)
Then what did you use to get your answer
,calc 95((1+.0625/12)^480 - 1) / (.0625/12)
yeah 202,531.68 rounded up is the answer I picked. So is it actually marked wrong incorrectly?
Yea I don't see any mistakes
It could be that they rounded early in between calculations but yours is correct
Are you kidding? This was a final.... okay thank you. I got to go write an email.
I used P=0 and C=95 and it matches your answer
Even if you of set P=95, you don't get any of the other answers
That question was the difference between a 92% and a 96%.
anyways thanks you
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Tried anything yet?
Can you show your work?
oh my god
i don't have camera.
Type it down
this the solution provided
my one:
after simplyfying : log3(log2a/log(1/2)b) = 1
= 3 = log2a/ -(log2b)
= -3 = logb a.
this give ab^3 = 1
u mean the solution is wrong?
The question asked log3(log2(a))
however in their solution it became log3(log3(a))
the solution is wrong.
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Wait @fast bolt
?
maybe they assumed
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test
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👀
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Can anyone please help with this question
How can we say that A,B,E will be collinear
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@green ivy Has your question been resolved?
its pretty easy to see that AB bisects CD (use the power of a point on the two circles about that point of intersection)
And from then on, you just play the fact that diagonals of a parallelogram bisect eachother to your advantage
use the power of a point on the two circles about that point of intersection, wdym by this ?
do you know a geometric result by the name of Power of a point?
Ohh tysm I got it the line AB acts as the radical axis
yep
Hence it passes through the mid point of the diagonal CD
And is collinear to point E due to that

😅 this was pretty self explanatory i guess my mind was just not working
Thanks!
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how can i solve the inequality
x^2 + 3x + 10 <= 0
when there isnt any real solutions to the quadratic
Then the statement is false for any real value of x
so should i just put down "no real solutions"?
that works
if we have the quadratic ax²+bx+c=<0, and D<0
we look at the sign of 'a'
- if a is negative, the expression is true for all real x, else if a is positive, the expression is false for all real x.
is it the same for just < not <=?
in set notation we write that as $x \in \phi \ or \ \left{ \right}$
$x \in \varnothing$
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south
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hey, in this question how can I solve this integrals? I tried to substitution but i found it hard to do
@patent laurel Has your question been resolved?
<@&286206848099549185>
Is this the exact question?
Like what is asked in yr question exactly?
Cause this integral's answer can't be expressed
The exect question is first linear order differential equations
But in the step is both integral both sides
i am being stuck
this seems to be of the form y' + Q(t)y = P(t) to me
try an integration factor perhaps
but you'd still have to integrate
hmm
$y(t) = A e^{-\int_{0}^{t} \sqrt{1+t^4},dt}$
all good here?
Now, as $y(0) = 0; \implies y(0) = A e^{-\int_{0}^{0}\sqrt{1+t^4},dt}$
@patent laurel Does this solve yr question?
ah yeh I got it, thanks a lot
@patent laurel Has your question been resolved?
Yes
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got stuck proving BxA^2 = (A^2)xB (square matrices) not sure where to go on from here
if not familiar |A| = det(A)
what are you trying to do
