Huh what is it then
#help-13
half forge
what's the LCM?
I know what LCM stands for, I'm asking for what she got as the LCM of the denoms
tall saffron
Wouldn't it be x(x-3)(x-4)(x-5)
half forge
no, it would just be (x-3)(x-4)(x-5)
half forge
you're solutions doesn't even have "=" symbols bruh
obsidian coral
For starters, writing on a bigger piece of paper would help
tall saffron
okay should i write it and send it here
obsidian coral
Yes
wraith daggerBOT
tall saffron
<@&286206848099549185>
cedar kilnBOT
@tall saffron Has your question been resolved?
tall saffron
.close
frozen dome
cedar kilnBOT
clear berry
Use polynomial division
dense arch
cedar kilnBOT
Available help channel!
deep patrol
cedar kilnBOT
deep patrol
What is the left angle called?
Coterminal?
Forgot the name
It’s like 180-(the angle)
To get the left angle
I don’t believe it’s coterminal but smth else
crimson sedge
Reference angle? @deep patrol
deep patrol
Oooh
So the blue would be
The reference angle to the red?
Oh no
Its the other way around
The red would be the reference angle of the blue
I see
austere sierra
Hi. I want to know what actually does it mean by "Closed form Solution" in the context of integration.
crimson delta
roughly speaking, a finite combination of all the usual functions you know
crimson sedge
a closed form solution is a formula that gives an explicit expression for the definite integral of a function
crimson delta
polynomials, trigonometric stuff, exponential, logarithms, ...
crimson sedge
it just basically doesn't have non-elementary functions
usually
A closed form solution provides a way to calculate the area under a curve without having to resort to numerical methods such as Riemann sums, basically. Or whatever other numerical methods there are out there
austere sierra
polynomials, trigonometric stuff, exponential, logarithms, ...
If I write my answer as a series... like, $$\int \sqrt[n]{\tan{x}} \ dx = n \sum_{k=0}^\infty(-1)^k \frac{(\tan x)^{2k +\frac{n+1}n}}{2nk +n+1} + C$$.
Is it a closed form?
wraith daggerBOT
innocently.innocent.soul
crimson delta
no
crimson sedge
no
austere sierra
Why? There are all basic functions... trig and polynomial
crimson sedge
a series representation of an integral is not closed form
crimson delta
but its a series
austere sierra
Ohh
crimson sedge
you can rewrite all integrals to be infinite series, doesn't mean they all will be closed forms
austere sierra
it just basically doesn't have non-elementary functions
What are non-elementary functions btw? Like gamma, beta, hypergeometric functions, etc...?
austere sierra
you can rewrite all integrals to be infinite series, doesn't mean they all will ...
oh... I didn't know that.
crimson sedge
yeah sure
austere sierra
**innocently.innocent.soul**
Can I convert it into closed form?
crimson sedge
you can rewrite all integrals to be infinite series, doesn't mean they all will ...
Eh well ignore this actually
austere sierra
Eh well ignore this actually
Ok
crimson sedge
**innocently.innocent.soul**
I dont know if you can find a closed formula for that
that's usually very difficult to do
austere sierra
https://www.wolframalpha.com/input?i=Closed+form+for+integral+of+(tanx)^1%2Fn
This is the closed form for the above integral.... but it involved hypergeometric function which is non-elementary.
crimson sedge
thats why i said earlier that closed forms are usually given with elementary functions
you can still find one using non-elementary functions
crimson sedge
https://www.wolframalpha.com/input?i=Closed+form+for+integral+of+%28tanx%29%5E1%...
but whatever that is...I have no clue how Wolfram gets to that
austere sierra
How would I know that it is closed form?
You said usually.... what are the other ways to classify the solution as closed form?
crimson sedge
no i meant for the elementary/non elementary part
crimson sedge
How would I know that it is closed form?
Expressibility is usually the biggest give away
if you have a definite answer that is expressed using a finite number of mathematical operations, such as addition, subtraction, multiplication, division, etc. then it should be closed form
A closed form solution is typically expressed using elementary functions, such as polynomials, exponentials, logarithms, trigonometric functions, etc. but not always
austere sierra
A closed form solution is *typically* expressed using elementary functions, such...
"but not always" what about that case?
austere sierra
https://www.wolframalpha.com/input?i=Closed+form+for+integral+of+%28tanx%29%5E1%...
How would I know this is closed form? At first glance, seeing hypergeometric stuffs, I just can't think that it is closed form.
cedar kilnBOT
@austere sierra Has your question been resolved?
torn notch
Lets say I want to apply the definition of limit in order to test if the limit I've found is correct, for example:
torn notch
$\lim_{x \to \infty}\frac{6x^5+7x^2}{7x^5-4}=\frac{6}{7}$
wraith daggerBOT
supMarco
torn notch
thus by applying the definition:
$\frac{6x^5+7x^2}{7x^5-4} - \frac{6}{7} < \varepsilon$
wraith daggerBOT
supMarco
torn notch
How do I realize (in case) that the limit isn't correct in that inequality (eg: if I use 5/7)? I understand it graphically
cedar kilnBOT
vagrant elbow
Yes
crimson delta
well assuming A and B are positive
high spruce
(a/b)^k = a^k/b^k
crimson delta
(ignoring complex numbers for a second)
high spruce
👍
vagrant elbow
well assuming A and B are positive
How would it affect though 
crimson delta
well if they are both negative then the sign on the LHS cancels but doesnt on the RHS
vagrant elbow
Can't you just cancel i on the RHS
crimson delta
(ignoring complex numbers for a second)
.
crimson delta
Yes but I’m still curious, why can’t we cancel i?
at a level where people ask these questions, sqrts of negative numbers probably just aren't allowed. so I'm going with that and saying that while the expression on the left might be ok, the expression on the right might not be allowed
unborn pike
at a level where people ask these questions, sqrts of negative numbers probably ...
Oh ok thanks
unborn pike
at a level where people ask these questions, sqrts of negative numbers probably ...
You don’t need to remove it
Try factorising
crimson delta
sqrt is continuous which means that you can pull the limit inside
unborn pike
You don’t need to remove it
Oops replied to the wrong msg
crimson delta
$\lim \sqrt{\ldots} = \sqrt{\lim \ldots}$
wraith daggerBOT
Denascite
unborn pike
Factorise
crimson sedge
i put one sqrt up and one sqrt down then i multiply by the denominator sqrt ?
buoyant latch
i mean
unborn pike
Factorise the numerator and denominators
crimson sedge
how do i remove the sqrt
buoyant latch
we do but we dont really
unborn pike
(x+4) cancels out
unborn pike
how do i remove the sqrt
You don’t need to
unborn pike
but then how i remove the sqrt
You don’t need to
crimson sedge
why i dont need to
unborn pike
Because (x+4) cancels
Denominator is (x-3)
Its not indeterminate anymore
Just substitute
buoyant latch
well assuming A and B are positive
$\sqrt{\frac{-a}{-b}} = \sqrt{\frac{a}{b}}\
{\frac{\sqrt{-a}}{\sqrt{-b}}=\frac{\sqrt{-1\cdot a}}{\sqrt{-1 \cdot b}} = \frac{\sqrt{-1}\cdot \sqrt{a}}{\sqrt{-1}\cdot \sqrt{b}}$
wraith daggerBOT
Frosst
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
buoyant latch
you can still just cancel the √-1's
crimson delta
without complex numbers this expression is just not allowed
jeez I really didn't wanna have this discussion
crimson sedge
@unborn pike but when i replace the x by -4 i get sqrt of 0/-7
vagrant elbow
i dont know this formula
It's just the quadratic formula
unborn pike
<@826856329712500857> but when i replace the x by -4 i get sqrt of 0/-7
Yeah
So thats 0 right?
crimson sedge
yes
unborn pike
So thats the answer
crimson sedge
so there is no limit ?
crimson sedge
but for x>-4 x<-4 ?
cedar kilnBOT
@crimson sedge Has your question been resolved?
lunar warren
cedar kilnBOT
lunar warren
Oh have to go to school.
cedar kilnBOT
@lunar warren Has your question been resolved?
bronze briar
For 8a, is it just that "All rabbits can hop"
cedar kilnBOT
For 8a, is it just that "All rabbits can hop"
bronze briar
it's a weird question, it's for discrete math
hasty fulcrum
i dont know about saying if it "can" hop
crimson sedge
i dont know about saying if it "can" hop
x hops <=> x can hop
bronze briar
i dont know about saying if it "can" hop
how about "all rabbits hop?"
final glen
I think its B
bronze briar
it's not multiple choice, the question has 4 parts
crimson sedge
I think its B
ah so you think everything is a rabbit
hasty fulcrum
x hops <=> x can hop
adding the word can adds only a possibility, not that it will
hasty fulcrum
how about "all rabbits hop?"
all animals that are rabbits hop
final glen
ah so you think everything is a rabbit
Mb lol
hasty fulcrum
i think is better
crimson sedge
adding the word can adds only a possibility, not that it *will*
i am saying thats what they probably meant
hasty fulcrum
i am saying thats what they probably meant
oh yeah thats what i meant as in we probably shouldnt write can
i hate logical sentences :| now im confusing myself
hasty fulcrum
its not multiple choice
bronze briar
all animals that are rabbits hop
oh okay, thank you. And i need a little bit of help with 8b too. Could I say "all animals are rabbits and can hop" ?
crimson sedge
its not multiple choice
huh?
hasty fulcrum
you have to translate each sentence
into real words
there are four logical statements
and we have to translate each into regular english
crimson sedge
oh
hasty fulcrum
oh okay, thank you. And i need a little bit of help with 8b too. Could I say "al...
that sounds good
crimson pasture
Looking for feedback on this proof for (a)
cedar kilnBOT
Looking for feedback on this proof for (a)
@crimson pasture Has your question been resolved?
halcyon glacier
That’s some god tier handwriting
cedar kilnBOT
@crimson pasture Has your question been resolved?
crimson pasture
That’s some god tier handwriting
Ha thank you
cedar kilnBOT
@crimson pasture Has your question been resolved?
cedar kilnBOT
@crimson pasture Has your question been resolved?
untold copper
am i miss understating the question there should be an inner and outer radii to solve this problem.
it seems to be the same Q as the top problem part B.
If its an infinitely thin plane, whats the diff between part A & B.
cedar kilnBOT
am i miss understating the question there should be an inner and outer radii to ...
@untold copper Has your question been resolved?
cedar kilnBOT
@untold copper Has your question been resolved?
cedar kilnBOT
@untold copper Has your question been resolved?
untold copper
closed
dire geode
.close
gilded fractal
hey just had a quick question about the difference quotient/derivative formula
gilded fractal
what exactly does h represent
cosmic steppe
Change in x
gilded fractal
change in x from where the point on tan line is?
cosmic steppe
Well just some change in x
Like 2 -> 3, h is 1
And since we read functions left to right, h is gonna be positive
gilded fractal
.close
woeful torrent
cedar kilnBOT
woeful torrent
can someone help me if this is correct or not
royal loom
does x2 mean 2x? or x^2
woeful torrent
i dont know
royal loom
lol well that might be important
woeful torrent
i think its x^2
royal loom
okay
well, assuming it is x^2 this problem is going to involve the the product rule and the chain rule. if our first function is the cuberoot of x^2, we can simplify that to x^2/3 and leave our second function as (2x-x^2)
obsidian coral
can someone help me if this is correct or not
Can you post your work on how you got that?
royal loom
using the product rule we get that the derivative should be the derivative of [x^(2/3)] * (2x-x^2) + the derivative [(2x-x^2)] * x^(2/3). So take those derivatives and make sure to not forget to use the chain rule and see if your answer works out to be a.
cedar kilnBOT
@woeful torrent Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
calm hornet
cedar kilnBOT
calm hornet
What is this notation? It's for probability and statistics
fading narwhal
probability of some random variable x greater than or equal to 2 given x greater than or equal to 0
calm hornet
does the bar just mean given?
fading narwhal
yeah
calm hornet
that's the most confusing part
okay cool
just had no idea what that symbol was supposed to represent
calm hornet
no not off the top of my head
calm hornet
wow this is very helpful thanks! also it's dependent on my knowledge of intersection I see, intersection is like the middle of a Venn diagram right? what the two sets have in common?
fading narwhal
gl
calm hornet
thanks!
cedar kilnBOT
@calm hornet Has your question been resolved?
marsh venture
Can someone help me
cedar kilnBOT
Can someone help me
violet flume
just ask!
livid shell
bro what chapter is this
livid shell
ive never seen this in my lif
marsh venture
It’s unit 10 for ap calc bc
livid shell
ah
marsh venture
Infinite sequences and series
marsh venture
You’re supposed to
livid shell
oh ok
marsh venture
It’s the formula
livid shell
i think you can solve it using sum of arithmetic series formula
marsh venture
Uhh well calculator says converges
livid shell
let me checl
signal yoke
Check the order of your denominator
marsh venture
What
livid shell
oh yea it does converge
marsh venture
Yeah idk what I did wrong
signal yoke
Oh wait hm you wrote it wrong but your idea was right that it'd be 4/3 in the limit
marsh venture
Wdym I wrote it wrong
signal yoke
I'd check the a_{n+1}/a_n calculation again if anything
In your last bit of writing you had 3n^2 in the denominator but I think you realized it should be 3n^3
marsh venture
My teacher did this
However I don’t know where the ^2 on the n+1 went
See how it’s in the top right limit
But then in the bottom left one
It’s gone
That’s probably why mine is diverging but idk where the ^2 went
signal yoke
No you're right that (n+1) should be squared
marsh venture
Wait so how can I see the proper steps to that?
signal yoke
If I'm reading this right it may just be a small mistake on your teacher's part then
marsh venture
Is there online calculators?
marsh venture
If I'm reading this right it may just be a small mistake on your teacher's part ...
But i mean his answer gave him converges
cerulean sail
,w sum ( 4^(1 + n/2) n^2 )/(3^(2 + n) (n + 3)), n from 2 to inf
wraith daggerBOT
signal yoke
I know but this shows that it converges to some finite value
cerulean sail
Get 2/3
marsh venture
What
cerulean sail
Think you might have forgotten to square root 4 somewhere
marsh venture
Wdym
signal yoke
Yeah 2/3 should be your ratio
marsh venture
How
cerulean sail
How'd you cancel this?
signal yoke
When you're canceling the powers of 4 be careful abt exponents
marsh venture
How'd you cancel this?
Split 4^3/2 into 4 and 4^1/2
To cancel with the bottom ones
cerulean sail
[sorry poor choice of blue]
marsh venture
Uhh
cerulean sail
Should it not be this?
signal yoke
Exactly what chartbit said but if it helps here's how to see it maybe in an earlier step
marsh venture
OH
So then it would be
Wait no
Wait what
Yeah so I’m left with 4^1/2 right
Which is 2
So then 2/3
Correct?
cerulean sail
Also suggestion is that the denom starts with n^3 in your work, if you meant you expanded
marsh venture
63/) it’s n^3
I just forgot to change it in pic
Which one of these looks the most difficult?
I have my exam tomorrow so I want to make sure I understand these good
cerulean sail
Hmmm they all seem about the same, having not yet tried them tbh
marsh venture
Alright can I try them and if I get stuck I can help ?
Everyone on the ap calc bc chat went to bed:(
cerulean sail
Top and bottom ones you can ignore the (-1)^{...} because of absolute value, but with them all I think it's being careful with steps?
cerulean sail
Alright can I try them and if I get stuck I can help ?
Sure sure, I may not be around myself but there are plenty of people who can help out 
marsh venture
:((
cerulean sail
I'm usually lurking though 
marsh venture
It’s 2 for me
cerulean sail
Just hope that this coffee has set in for me now 
cerulean sail
Haha I'm on like an hour and a bit of sleep
cerulean sail
Chart r u a boy
Can't disclose
cerulean sail
I don't know 
marsh venture
Help me with abstract algebra in 2 years
When I’m a senior
:))
And number theory
And analysis too lol
Actually gonna take those
Senior year
With discrete mathematics
cerulean sail
Analysis and abstract algebra 
cerulean sail
Hopefully not! Wish you best of luck! 📿
marsh venture
Maybe
22 APs plus 7 math classes might be enough
Hey
@cerulean sail
This one is inconclusive right?
wait
I’m stupid
I just ignore the 1^
N
Bc it’s gonna be -1 anyways
cerulean sail
I think it gets you inconclusive if you do it by ratio test
But you could check that it's absolutely convergent
Compare it to the series
$$\sum_{n} \frac{4}{n^2 + n + 1} \leq \sum_{n} \frac{4}{n^2}$$ (make denominator smaller)
marsh venture
Wait what
wraith daggerBOT
chartbit
marsh venture
Inconclusive by ratio test?
cerulean sail
If I've done my workings right, I get that it is [though I may have messed up of course!]
marsh venture
Oh yes
Bc it’s n^2 over n^2
Ah yes
No no dw this is a ratio test assignment so
It says there’s some that could be inconclusive by
Ratio test
cerulean sail
Ahhh fair, I was just about to ask whether they wanted you to use ratio test and then say it converges/diverges/inconclusive by it
cerulean sail
In fact I think for the first one you could even say that it's a decreasing positive sequence you're summing that's then made alternating, which would mean it's at least conditionally convergent
marsh venture
The first one I sent?
Ngl I only learned ab this stuff 1 hour ago so idk what that meant
cerulean sail
Ya this one, I'm just thinking out loud tho so if it doesn't make sense or you haven't come across what I'm saying ignore me 
cerulean sail
Lemme try it out too so I can check your steps better
marsh venture
Ok:)
cerulean sail
Odieeeeeee omg
marsh venture
?
marsh venture
Lol
cerulean sail
,w sum (6^(-2n) (n-4))/(4^(3 - 2n) (2 - n^2)) n from 3 to inf
wraith daggerBOT
cerulean sail
I get 16/36 I think
cerulean sail
This 6^(-2), what happened to it?
cerulean sail
No no, looks about right to me, I get inconclusive too!
marsh venture
U did it already?
cerulean sail
Did it earlier as I thought it would be inconclusive haha
cerulean sail
I only wish 
I'm not as good as I look most days haha
marsh venture
How old r u?
cerulean sail
Can't say either
marsh venture
R u in college?
cedar kilnBOT
@marsh venture Has your question been resolved?
marsh venture
Yes
tropic oxide
isn't that the same problem that you came here with half an hour or so ago?
and why are you consistently spelling it "Pennie's" and not "pennies", i wonder?
so, you have found that the students collected a total of 26,409 pennies, and you know that their goal is 30,000.
@arctic stump
... no need to reply-ping me this often.
and you are one step away from the answer
they have 26,409 pennies but need 30,000. how many more pennies do they need?
no... that doesn't make any sense.
how can they need a greater number of pennies than they set their goal to
by your logic, if i asked you "You want to buy a book for 30 dollars, but you have 25 dollars in your wallet. How much are you missing?" you would answer "I am missing 55 dollars."
exactly, and how did you get 5?
you filled in the blank in 25 + __ = 30
...did you simply guess that, though? or did the idea of "subtraction" cross your mind at least once
so you did subtract 25 (the amount you have) from 30 (the amount you need), yes?
well then,
it's just the same with your penny-collectors.
there's the amount they have (26,409) and the amount they need (30,000) and you need to find the difference between these...
with all due respect, i've said it both directly and not already.
so YES YOU DO HAVE TO SUBTRACT.
you subtracted them the wrong way around
you should have had 30,000 - 26,409 = 3,591
it is really the same principle as with the "how many dollars short am i for that $30 book" problem
only the numbers are different
but the logic is the exact same
crimson sedge
do i have to multiply 4 * 2?
cedar kilnBOT
do i have to multiply 4 * 2?
crimson sedge
in this kind of a fraction
Depends on if it is $\ds \f{\f12}{4}$ or $\ds \f{1}{\f24}$
it's the former, I think
wraith daggerBOT
Depends on if it is $\ds \f{\f12}{4}$ or $\ds \f{1}{\f24}$
woeful totem
number 7
cedar kilnBOT
@woeful totem Has your question been resolved?
cedar kilnBOT
@woeful totem Has your question been resolved?
cedar kilnBOT
@woeful totem Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
crude fiber
Can anyone help me with this? I tried solving this I got angle YXZ as 25 and angle XPZ as 100
cedar kilnBOT
Can anyone help me with this? I tried solving this I got angle YXZ as 25 and ang...
@crude fiber Has your question been resolved?
crude fiber
Uhh guys
crude fiber
Yes
worthy mural
Part of circle xz) is 260
And xyz) is 100
crude fiber
Yes i already found that
worthy mural
Ok
crude fiber
but angle pxy
worthy mural
You can see xy) = yz) = 50
If i draw this pt
Yzt) is 130
Pxy angle is half it
Solution is 65
Got it?
crude fiber
yessssss
thanks
this is solved by construction
i am so dumb
i was joing p to z
Thanks @worthy mural
worthy mural
👍
crude fiber
.close
worthy mural
i was joing p to z
You can do with like this pxy=pzy=65
X=65 , p=100 , z=65 , y=130
Dont forget geo have more 1 solution
cedar kilnBOT
Available help channel!
untold abyss
Can somebody explain to me what I am doing wrong?
cedar kilnBOT
Can somebody explain to me what I am doing wrong?
untold abyss
Solution is supposed to be = 24/7
long arrow
why do did it separately
untold abyss
I thought it is easier to do it like that to find the geometric series
But I guess it just does not work
long arrow
after multiplying you would get r = -1/6
then 4 * 1/(1+1/6) = 4 * 6/7 = 24/7
what you did gives product of sums of two geometric series
untold abyss
Where exactly?
wraith daggerBOT
Modus
untold abyss
So I am using wrong brackets
cedar kilnBOT
@untold abyss Has your question been resolved?
untold abyss
.close
half forge
can you show your work?
I could point out to you where you made a mistake
first of all you should apply exponent laws to the constant, meaning you should do (-2)^2
also, 3 times 2 is 6, not 5
it's just using this rule
you need to apply ^2 to the constant (-2)
small gyro
hi i am confused on how to solve this
cedar kilnBOT
hi i am confused on how to solve this
small gyro
my thought proccess is that i
need to get the meters per minute first
so i did 5x60 to get 300 m/min
tropic oxide
you meant "i need to convert the speed into meters per minute"
calling it "the meters per minute" is like calling a distance "the feet"
small gyro
ya
tropic oxide
a bit silly at best
anyway yeah sure you do need to bring the units for time and speed into alignment
whether that's with s and m/s or min and m/min
so theres nothing wrong as such with what you wrote thus far
small gyro
but after that since the question says i need to only find the distance to the telephone pole dont i need to divide 15 by 2
to get 7.5
tropic oxide
what does the number 15 represent?
small gyro
how many minutes it takes for him to go to the telephone and back
tropic oxide
exactly, it's the time for the journey.
dividing it by 2 would again give a time, not a distance...
tropic oxide
i was going to get to that...
but you blurted out some nonsense i had to address.
@rotund grotto you will refrain from such vile behavior.
the man's journey consists of two legs: running toward the phone and back from the phone
we note that the distances of these two legs are of course the same, since it's the same space being covered.
however, the speeds are different (5 m/s there, but 4 m/s back), and so the times are different too.
that means you cannot simply divide the total time by 2 to find the time taken for each leg.
do you understand this?
small gyro
shit you are right
tropic oxide
i'll also work with seconds as my time unit, so the total time will be 900 seconds
\begin{tabular}{c||c|c|c}
Leg & Speed, m/s & Distance, m & Time, s \
\hline
Forward & 5 & & \
Back & 4 & & \
\hline
Total & --- & --- & 900
\end{tabular}
this is of course not yet a complete table
wraith daggerBOT
Ann
tropic oxide
please don't call me bro
sorry, i had to disappear for a few minutes
is there something that troubles you about this table?
small gyro
please don't call me bro
my bad
tropic oxide
mind you, this table is not yet complete. all i'm doing is filling in the immediately-known data.
small gyro
oh i see
so i am guessing what i have to figure is the distance for 5m/s and 4m/s
is that right?
tropic oxide
no
we'll get to this in a moment
the angle i want to suggest with this problem is as follows:
instead of finding the distance, let's find the time taken for each leg.
we do not yet know these times, but that's okay, since we can introduce a variable to represent one of them.
for example, let's use the letter t to represent the time for the forward leg.
\begin{tabular}{c||c|c|c}
Leg & Speed, m/s & Distance, m & Time, s \
\hline
Forward & 5 & & $t$ \
Back & 4 & & \
\hline
Total & --- & --- & 900
\end{tabular}
wraith daggerBOT
Ann
tropic oxide
like this
then, since the total time is known to be 900 seconds, the time for the back leg will of course be 900 - t.
\begin{tabular}{c||c|c|c}
Leg & Speed, m/s & Distance, m & Time, s \
\hline
Forward & 5 & & $t$ \
Back & 4 & & $900-t$ \
\hline
Total & --- & --- & 900
\end{tabular}
wraith daggerBOT
Ann
tropic oxide
do you understand this?
small gyro
ya i do
tropic oxide
okay
can you now tell me
what is the distance for the forward leg, in terms of t, based on this table?
tropic oxide
you know the formula distance = speed * time, yes...?
small gyro
ya i do
tropic oxide
right
small gyro
but i dont know t
tropic oxide
you don't know t, yes
but i said to answer in terms of t
this means that your answer to my question can (and should!) include the letter t
small gyro
4 * 900 - t
tropic oxide
careful
there's something in there you're missing
do you want to try and fix it yourself or do you want me to tell you what it is
small gyro
i dont know what i am missing
tropic oxide
you are missing parentheses around the 900-t
you meant 4(900-t), but the way you said it, only the 900 was being multiplied by 4,
tropic oxide
\begin{tabular}{c||c|c|c}
Leg & Speed, m/s & Distance, m & Time, s \
\hline
Forward & 5 & $5t$ & $t$ \
Back & 4 & $4(900-t)$ & $900-t$ \
\hline
Total & --- & --- & 900
\end{tabular}
wraith daggerBOT
Ann
tropic oxide
to bring the table back
and now,
we note that the distances of these two legs are of course the same, since it's the same space being covered.
can you write this as an equation?
small gyro
9 * 900
tropic oxide
this is not an equation and it is also pointless
small gyro
then what do i do
tropic oxide
the distances of these two legs are the same
tropic oxide
no
i want you to write an equation which says "The distances of the forward and back legs are the same."
i want you to write an equation which says "The distance of the forward leg equals the distance of the back leg."
i don't know how else to put it.
small gyro
how would i do that
tropic oxide
do you know how to solve linear equations in one variable?
small gyro
i think
dont i have to remove the t or something
oh ya i have to remove it on one side
so then i would get like 6t = 4* 900
6t = 4 * (900)
6t = 3600
6 * 600 = 3600
t = 600
ok i think i got that part
cedar kilnBOT
@small gyro Has your question been resolved?
small gyro
no
cedar kilnBOT
@small gyro Has your question been resolved?
tropic oxide
@small gyro sorry, was off to do irl things
dont i have to remove the t or something
oh ya i have to remove it on one side
so then i would get like 6t = 4* 900
this is incorrect
tropic oxide
well you were supposed to expand 4(900 - t) into 3600 - 4t
so you would then have 5t = 3600 - 4t
add 4t to both sides to get 9t = 3600
small gyro
oh
small gyro
ok i tried solving for a bit and got this
9/3600s = 400
t = 400
5 * 400 = 2000
4 * 500 = 2000
i am assuming that i was supposed to get 2000 for both equations
tropic oxide
i am assuming that i was supposed to get 2000 for both equations
yes, the fact that you got the same distance means everything worked out correctly
high salmon
(x+1)^2-(x^2+2x+1) factor this expression
cedar kilnBOT
(x+1)^2-(x^2+2x+1) factor this expression
obtuse sable
(x+1)^2-(x^2+2x+1) factor this expression
What have you done so far?
high salmon
I want to factorize this expression into a two-factor product
obtuse sable
Well
To start, x^2+2x+1 is a perfect square trionomial. (you can factor by decomposition, but this just skips that step)
high salmon
I want to factorize this expression into a two-factor product
latent bloom
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half yacht
cedar kilnBOT
half yacht
someone help ASAP due in 30 minutes
cedar kilnBOT
@half yacht Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
gentle perch
cedar kilnBOT
gentle perch
i need help
dull oxide
!status
cedar kilnBOT
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
!show
cedar kilnBOT
Show your work, and if possible, explain where you are stuck.
gentle perch
so I got (5x-1)(x+2-3i)(x+2+3i)
but i got 5x^3+19x^2+61x-13 after solving it
which isnt viable with any of the soltuions
gentle perch
so i just go x-1/5 and made it 5x-1
dull oxide
so I got (5x-1)(x+2-3i)(x+2+3i)
Double check your roots
gentle perch
and the 2+3i, i just did 2+3i and 2-3i
dull oxide
Your roots are 2+3i and 2-3i
gentle perch
ye
dull oxide
So why did you do (x+2+3i) and (x+2-3i)?
dull oxide
If so, then why did you do (5x-1) for your root of 1/5?
dull oxide
If a is a root of your polynomial, then (x-a) is its factor
gentle perch
so can u apply it to this
dull oxide
If I told you a quadratic had roots 3 and 5, how would you find its equation?
gentle perch
(x+3)(x+5)
gentle perch
is it because its x=3 and then x-3=0?
gentle perch
ok so now what
dull oxide
so I got (5x-1)(x+2-3i)(x+2+3i)
Figure out what you did wrong here
eager crane
cedar kilnBOT
cedar kilnBOT
Available help channel!
fleet wedge
The volume of a pyramid varies jointly as its base area and altitude. Find
the altitude of a pyramid whose base area is 12, and whose volume is the
sum of the volumes of two pyramids whose base areas are 6 and 9 and
whose altitudes are 3 and 6 respectively.
fleet wedge
I am unsure about how to solve this problem on variation
cedar kilnBOT
@fleet wedge Has your question been resolved?
sterile pecan
I have a question
cedar kilnBOT
I have a question
sterile pecan
Would the domain of the following piecewise function be [0,6]?
Since it's continuous at x=4
carmine bronze
Yes.
spring orchid
hi can someone help me with probability
cedar kilnBOT
hi can someone help me with probability
ancient lodge
lofty ridge
spring orchid
it’s translated that’s why the quality is bad
but can someone like walk me through this exercise 
spring orchid
LMAO WHAT
dire geode
The hell is the Monte Carlo method
dire geode
but can someone like walk me through this exercise <:nameitpls:10720409102898995...
a) involves programming
try #computing-software or find a server for your programming language
spring orchid
a) involves programming
sorry lol i was so confused cause i didn’t realize i needed excel or sth for this
but otherwise i do get it now
except the last one
oh no wait nvm
how do i close
cedar kilnBOT
cedar kilnBOT
Available help channel!
visual oyster
Hi I have a question where I am given cylindrical coordinates $\theta = \frac{3\pi}{2}, z=\sqrt{3}r, 0 <= r <= 3$ but have to describe them as spherical coordinates, how do I go about doing that?
wraith daggerBOT
windy
visual oyster
I think got it, if theres anyone willing to check $(2r, 0, \frac{\pi}{6})$
wraith daggerBOT
windy
cedar kilnBOT
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cedar kilnBOT
Available help channel!
Available help channel!
Available help channel!
crimson sedge
Hi I’m confused if you can do that to the denominator
cedar kilnBOT
Hi I’m confused if you can do that to the denominator
crimson sedge
<@&286206848099549185>
sudden olive
Yeah, you can. No problem
crimson sedge
Wth really?
How does the m get multipled by 2?
Oh
Thanks!
Have a nice day
.close
obsidian wasp
Geometry help
cedar kilnBOT
Geometry help
obsidian wasp
the top problem
“Antonio’s friend Jessica was also on The Screamer when it broke. Her seat was 65 ft above ground. What was her seat’s angle of rotation. Is there more than one possibility?”
how would I start this problem besides drawing the triangle with the height
I think we gotta use those special right triangles cuz teacher’s been talking a lot bout those that we NEED to learn them
from geometry but that sh was a year ago I don’t remember!
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
mild geyser
** Summation of squares as summation of product of two consecutive numbers
Sum of two nth powers expressed as a product of two consecutive integers**
I want to search a research paper similar to these topics, but whats the proper term for these kind of topics? tyia
cedar kilnBOT
** Summation of squares as summation of product of two consecutive numbers
...
@mild geyser Has your question been resolved?
mild geyser
<@&286206848099549185>
cedar kilnBOT
@mild geyser Has your question been resolved?
cedar kilnBOT
@mild geyser Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
covert ferry
cedar kilnBOT
covert ferry
why when factoring a quadratic equation, why does he multiply a times c?
what does the -45 have anything to do with it?
long arrow
is it some specific method?
crimson sedge
this is called the sum-product method
so original equation is 9x^2-12x-5=0, he decides to pull out a*c to help find your b value
9*-5=-45
list out all the multiples for -45
and find 2 multiples where the sum is your b constant
so in this case the 15*3 multiple is desired because -15+3=-12 which is exactly our b constant
from there, we have 9x^2-15x+3x-5=0. we group terms and factor out the greatest common multiple.
9x^2+3x would be grouped and -15x-5 would be grouped
greatest common multiple for both terms are 3x+1
factor 3x+1 from 9x^2+3x, we get 3x.
factoring 3x+1 from -15x-5, we get -5
(3x-5) (3x+1).
cedar kilnBOT
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cedar kilnBOT
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Available help channel!
crimson sedge
is this correct?
cedar kilnBOT
is this correct?
trail bridge
It's not, there's a mistake on your third last line
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
It's not, there's a mistake on your third last line
how
trail bridge
You plus seven on both sides to remove the -7, not just move the -7 straight to the right hand side
cedar kilnBOT
cedar kilnBOT
Available help channel!
alpine spire
help me
crimson sedge
- Don't occupy multiple help channels
- show what you have tried and explain your thought process
- have you made use of the hints given to you?
alpine spire
wrong. B is an integer
tropic oxide
!nosols
cedar kilnBOT
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.
tropic oxide
but also @alpine spire why did you choose to spam your problem across every single help channel
alpine spire
but also <@476909474351939605> why did you choose to spam your problem across ev...
cuz i once waited 5 days and no one helped
last year
sand wind
also the coefficient of the ln3 is not an intger if you calculate the whole thing, either
vagrant elbow
Such a travesty
rapid halo
@alpine spire reminder that this is your help channel
alpine spire
also the coefficient of the ln3 is not an intger if you calculate the whole thin...
the value of B is an integer. thats what the prof says
sand wind
what is the solution
cedar kilnBOT
@alpine spire Has your question been resolved?
cedar kilnBOT
@alpine spire Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
Algebra
crimson sedge
cedar kilnBOT
@crimson sedge Has your question been resolved?
bitter surge
Q.16
I don't know what to do to start. I notice that it has no roots(i cant find in factorization) and also there might hv no mid point (cus there has no roots). I don't know what n where to start with.
wraith daggerBOT
NEONPerseus
digital cliff
put it into vertex form
bitter surge
Value of h aka axis of symmetry
digital cliff
(x-3)^2-9+15=y, y=(x-3)^2+6 so h=3
vagrant elbow
Oh I didn't notice the edit I'm sorry
bitter surge
I wrote the answer besides the questions , i still hv no idea how
bitter surge
Oh I didn't notice the edit I'm sorry
is fine
vagrant elbow
Do you know how to differentiate
bitter surge
Since i dont understand that word i guess i don't
vagrant elbow
You don't need to but it would make life easy
vagrant elbow
Since i dont understand that word i guess i don't
Alright cool
As Azo said, put it into vertex form
Which is basically completing the squarw
digital cliff
for a quadratic of form $y=ax^2+bx+c$ (a is 1 here so ill just make typing this easier) $y=x^2+bx+c$ so $y=[(x+\frac{b}{2})^2-(\frac{b}{2})^2]+c$ then $y=(x+\frac{b}{2})^2 +[c-(\frac{b}{2})^2]$
wraith daggerBOT
Azo
bitter surge
Emm... i hv never seen that (in my place)
digital cliff
you could also solve the equation youve made here, you get x^2-6x+9=0 so (x-3)^2=0 so x=3 still
if thats easier?
bitter surge
Yes! but what about 9 ?
digital cliff
wdym?
digital cliff
np
bitter surge
.close
cedar kilnBOT
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long mauve
Anyone know how to solve this, answer is b
cedar kilnBOT
Anyone know how to solve this, answer is b
carmine pagoda
still not enough information
carmine pagoda
.close
scarlet garnet
.close
tired rain
Hi, I need some clarity on this question here.
by max and min, are they asking which sequence is larger and smaller respectively?
if they are, shouldn't lim->M and lim->m both exist? (Making 3rd option true)
gilded elm
no
theyre defining a sequence given by
taking the individual max
so for example M1 is max of x1 and y1
tired rain
ah, so they are forming a sequence M by taking the larger term of sequence x and y from every iteration?
Even then, both M and m should have limits since they will take the nth term of x and y which would be convergent
gilded elm
you should prove that
tired rain
I will try
I can make sense of statements in my head but I absolutely suck at writing proofs somehow
Anyways, thanks for the clarification
.close
tender valley
I thought that a fraction in front of the parenthesis was supposed to vertically shrink the parabola and but it looks like it horizontally stretched it when I plugged it into the graphing calculator. The first function is y=(x-4)^2 and the second one is y=1/3(x-4)^2