<@&286206848099549185>
#help-23
burnt sequoia
slender pendant
!15m
safe radishBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
kind forge
!status
safe radishBOT
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
drowsy dragon
1
safe radishBOT
drowsy dragon
Oh I want the answer
thin bridge
claim your own channel
thin bridge
we don't do that here
drowsy dragon
Ok I will tag u in my channel
thin bridge
PLS don't
drowsy dragon
Why
thin bridge
I don't like your attitude, abide by the rules, someone may help if they're free
candid panther
Sorry for that let me requestion my question
I can.
drowsy dragon
U can what
candid panther
Where is the question?
drowsy dragon
.
safe radishBOT
Available help channel!
gentle sedge
i do it how i normally do it, but i keep getting my answer wrong according to the answers
safe radishBOT
i do it how i normally do it, but i keep getting my answer wrong according to th...
hard crest
these numbers are very tricky because they're fractions, so it's understandable that you might have made an arithmetic mistake
what could be helpful is to start by multiplying each equation by its common denominator to remove complexity, although that will result in some large numbers so be aware of that
gentle sedge
what could be helpful is to start by multiplying each equation by its common den...
yeah i tried that it keeps failing
is there like a quick way to do thi?
rustic goblet
theres not really a quicker way to do this than the normal way tbh
the system is quite annoying though
could you show your work?
perhaps we can identify the arithmetic error
gentle sedge
i finally worked it out
rustic goblet
nice!
safe radishBOT
safe radishBOT
Available help channel!
strange plaza
safe radishBOT
strange plaza
Using Pareto, it should be Swim and FB right?
safe radishBOT
@strange plaza Has your question been resolved?
strange plaza
<@&286206848099549185>
plucky elk
Using Pareto, it should be Swim and FB right?
What's the pareto principle
safe radishBOT
@strange plaza Has your question been resolved?
strange plaza
What's the pareto principle
80/20 rule
To my understanding, you find the biggest causes by looking at the left of the vert line
hybrid plover
hi
hybrid plover
Laugh at this: AHAHA + TEHE = TEHAW. It resulted from substituting a code letter for each digit of a simple example in addition, and it is required to identify the letters and prove the solution unique.
what does "substituting a code... example in addition" mean?
i dont need a solution, i just need clarification
terse lichen
i dont need a solution, i just need clarification
all of those letters are digits
and you want to find what those digits are
hybrid plover
all of those letters are digits
oh so AHAHA means something like 12121?
terse lichen
yes
safe radishBOT
safe radishBOT
Available help channel!
dark cloak
safe radishBOT
dark cloak
safe radishBOT
@dark cloak Has your question been resolved?
safe radishBOT
@dark cloak Has your question been resolved?
dark cloak
.
safe radishBOT
@dark cloak Has your question been resolved?
safe radishBOT
@dark cloak Has your question been resolved?
cunning patio
Hard to read what is going on, but I would do it like this: Notice that $y=(1+x^2)^{2/3} = \left((1+x^2)^{3/2}\right)^{4/9}$. You want to find the derivative of this function wrt. $(1+x^2)^{3/2}$, so putting $u = (1+x^2)^{3/2}$, you see that your function reduces to $u^{4/9}$.
So you want the derivative of $y(u) = u^{4/9}$ wrt. $u$. The answer is $y'(u) = \frac{4}{9}u^{-5/9}$. Pop back in the expression for $u$.
$$\frac{dy}{d\left((1+x^2)^{3/2}\right)} = \frac{4}{9}\left((1+x^2)^{3/2}\right)^{-5/9} = \frac{4}{9}(1+x^2)^{-5/6}$$
safe radishBOT
@dark cloak Has your question been resolved?
lavish storm
safe radishBOT
lavish storm
How to solve without substitution and integration by parts
lean otter
hint: t = 2x+1
lavish storm
hint: t = 2x+1
No substitution
lean otter
oh i see uh
lavish storm
hint: t = 2x+1
Kinda obv
lean otter
well you want to eliminate that polynomial, x
so choose that to differentiate
and the square root to integrate
lavish storm
and the square root to integrate
No integration by parts
lean otter
what do you want to use then?
lavish storm
x = 2x + 1 - 1
@lean otter
lean otter
what?
lavish storm
Here's the way I think
safe radishBOT
safe radishBOT
safe radishBOT
✅
main mural
it's w+1
w = e^2x - 1
w+1 = e^2x
yep
er not quite
your denominator is w
because you set it to be that
$\frac{1}{2} dw = (w+1) dx$
flat frigateBOT
artemetra
main mural
so $dx = \frac{dw}{2(w+1)}$
flat frigateBOT
artemetra
flat frigateBOT
artemetra
main mural
your denominator is w
yeah that's an oopsie
you can
no
1/(w^2 + w)
oh
partial fractions you mean?
yep
this type of stuff
mhm
uuuh
no
did you do that?
bro
$\frac{1}{w^2 + w} \neq \frac{1}{w^2} + \frac{1}{w}$
flat frigateBOT
artemetra
main mural
you can't just split fractions like that
you can only do that when it's in the denominator
main mural
you gotta use this
look up partial fraction decomposition
many tutorials
but i'll guide you
this is a simple one
no
lavish storm
Newton
main mural
revise algebra
lol
look
suppose $\frac{1}{w(w+1)} = \frac{A}{w} + \frac{B}{w+1}$ where $A, B$ are some variables we are going to find
flat frigateBOT
artemetra
main mural
still no
$\frac{A}{w} + \frac{B}{w+1} = \frac{A(w+1)}{w(w+1)} + \frac{Bw}{w(w+1)} = \frac{A(w+1)+Bw}{w(w+1)}$
flat frigateBOT
artemetra
main mural
does this make sense?
just adding two fractions
now recall that this is the same as 1/w(w+1) as we said
so $A(w+1) + Bw = 1$
flat frigateBOT
artemetra
main mural
(the denominators match so the numerators must match too)
okay maybe that was a bit of a jump
yes!
so now
$\int \frac{1}{w} - \frac{1}{w+1} dw$
flat frigateBOT
artemetra
main mural
from here proceed as usual
mhm
the second one is similar
mhm
eh
yeah but no need to here
not worth it
safe radishBOT
junior smelt
.Also a tiny comment, you could multiply numerator and denominator here by e^{-2x}
safe radishBOT
Available help channel!
sinful crown
safe radishBOT
sinful crown
how would you solve this?
safe radishBOT
how would you solve this?
sinful crown
im confused on how to use natural log here
main mural
divide both sides by 19 first
you get $e^{\text{something}} = \frac{12}{19}$
so that means you can take ln of both sides
flat frigateBOT
artemetra
safe radishBOT
Available help channel!
oak quest
could anyone help me wit this problem?
safe radishBOT
could anyone help me wit this problem?
oak quest
do the blocks have the same curve
would the blocks velocitys be going upwards till t1 and then become constant at t1-t2?
does their mass affect their velocity
safe radishBOT
@oak quest Has your question been resolved?
safe radishBOT
@oak quest Has your question been resolved?
safe radishBOT
@oak quest Has your question been resolved?
safe radishBOT
@oak quest Has your question been resolved?
vague urchin
do the blocks have the same curve
No
vague urchin
would the blocks velocitys be going upwards till t1 and then become constant at ...
Yes
vague urchin
does their mass affect their velocity
Yes (recall a=f/m)
The amount of momentum imparted, however, is just force*time, which is the same for both
safe radishBOT
@oak quest Has your question been resolved?
stone sedge
safe radishBOT
stone sedge
I’m not sure if I did the question right but I gave it a go!
any tips?
Thank you ren for guiding me too btw
stone sedge
Eek 😭 sorry it’s my first time doing these restriction questions
lean otter
you have to also realise that you need to be considering your domain from start to finish
for example, at the beginning, you couldn't have x = 0
stone sedge
Do I have to list the beginning as well?
lean otter
well yeah at the end of the day it's the total amount of restrictions
seemingly you were just missing x = 0 tho
otherwise its okay
lean otter
yk FOIL?
stone sedge
oh yeah
lean otter
yeah
lean otter
nw
stone sedge
.close
stuck crest
safe radishBOT
stuck crest
this seems so off what am i doing wrong
winged barn
Why didn't you substitute into the perfects of squares technique
(a - b)^2 = a^2 - 2ab + b^2
stuck crest
i did that for a previous question but it looked wrong so i wanted to foil here
thin bridge
how are you getting 56 in the denominator
thin bridge
how is that leading to 56
winged barn
7 x 9 is 63
thin bridge
you also apply the definition of squaring directly
without having to go through sqrt(9) and sqrt(49)
thin bridge
yeh
thin bridge
wrong signs in q3, also not a good idea to use a,b to represent different things
its recommended that you swap out the variables in the identity
note that if you're choosing to use
(p - q)^2 = p^2 - 2pq + + q^2
stuck crest
oh because it matches the variables used in the question
okok
wdym wrong signs though
thin bridge
then q represents the value being subtracted,
which in this case will be just the sqrt(2),
not -sqrt(2)
stuck crest
ohhhh
stuck crest
oh why so
thin bridge
because p + (-sqrt(2)) is p - sqrt(2)
stuck crest
ohhhh
thin bridge
in the denominator, yes
stuck crest
is this better?
thin bridge
yeh
stuck crest
any faster way to do it?
safe radishBOT
Available help channel!
hard shore
a in R, a != 0
for which a values W = U?
safe radishBOT
a in R, a != 0
for which a values W = U?
hard shore
so I want to begin by finding a base for each span right?
I tried to start with W but I am a bit stuck
proper crypt
Try to find an equivalent condition of what it means for W to be equal to U
Each of these are just the span of a single vector
safe radishBOT
@hard shore Has your question been resolved?
proper crypt
1 variable
4 equations
How would you do it if you had more variables?
This should be the same
proper crypt
You should have just 2 columns
hard shore
should I not write the As?
proper crypt
That's 3 columns
I meant 2 in total
1 for the varaible coefficients
1 for the a^-1, a, a, a^3
proper crypt
I can see that
hard shore
and your explanation is very clear
however
I dunno
so
one colomn for a^-1, a, a, a^3
proper crypt
I haven't really explained anything to be honest
I'm trying to let you figure it out
hard shore
proper crypt
You might want to look at examples from your book if you have one
If you just blindly remember what to put in the matrix, it shows you don't really understand it
hard shore
If you just blindly remember what to put in the matrix, it shows you don't reall...
facts
proper crypt
Here is an example
And we usually write this for short
And then perform row operations, which don't change the solution set.
First column is all coefficients of the variable x
Second column is all coefficients of the variable y
hard shore
thats not 2 colomns but this feels correct
I just wrote it like that
and each colomn represents a diffrent degree
proper crypt
You need a 4x2 matrix
Don't split it into degrees
a is not your variable
It's a parameter, some number
t is your variable
proper crypt
Ok, promising
hard shore
hard shore
Remove the negatives on the right column
wait exblain
why should I remove the negatives?
proper crypt
You don't move the constants to the left
Keep them on the right side of the equals
Again, look at the example I sent
proper crypt
Yes
proper crypt
Sure that works
Make sure you apply this to the right-most column aswell
And tell me what you get
hard shore
proper crypt
So when does this have a solution?
hard shore
I got these 3 equations
sry I really gtg but I think I got past the hard part
thank you so much for your help @proper crypt 
.close
safe radishBOT
proper crypt
Np
safe radishBOT
Available help channel!
inner scaffold
Okay, 1-1+1-1+1-…=½, but what about 1*(-1)*1*(-1)*1*…=?
safe radishBOT
Okay, 1-1+1-1+1-…=½, but what about 1\*(-1)\*1\*(-1)\*1\*…=?
proper crypt
1 - 1 + 1 - 1 + ... is not 1/2
inner scaffold
why
proper crypt
It diverges
inner scaffold
1-1+1-1+1-1+…=1-(1-1+1-1+1-…)
let`s 1-1+1-1+1-1+…=A
A=1-A
2A=1
A=½
proper crypt
You can't manipulate a series like that if it doesn't converge
lean otter
you are assuming convergence with that
you can come up with all sorts of crankery using similar logic
proper crypt
For the same reason, this product you gave diverges aswell
inner scaffold
okay
desert pasture
For the same reason, this product you gave diverges aswell
isn't the product not deinfed as (-1)^infty isn't defined either
inner scaffold
isn't the product not deinfed as (-1)^infty isn't defined either
it`s not same
proper crypt
It doesn't converge because the partial products don't approach anything as n goes to infinity
inner scaffold
1^∞ can be every number
Because
Infinity root of x(if x≠∞ or zero) =1
Like
infinity root of 2
=2^1/∞
inner scaffold
=2^0=1
proper crypt
Again, that's not a very mathematical way of saying it
And no, it can't "be" anything
inner scaffold
so, (inf_root(2))^∞=1^∞
And here must be two
We can do with inf root of 3
=1 and again 1^∞ here must be 3
hmmm
A=1*(-1)*(-1)*(-1)*…
-1*(-1*(-1)*(-1)*(-1))=A
-1*A=A
-A=A
Okay, are you asking a question?
Because what you are saying is just completely nonsense
It's not true
normal portal
yo
normal portal
.close
safe radishBOT
normal portal
.disown
safe radishBOT
Available help channel!
leaden scaffold
I'm still confused.
safe radishBOT
I'm still confused.
leaden scaffold
Is the answer not 4?
lean otter
Is the answer not 4?
thats the number of elements
rustic goblet
When measuring cardinality we don’t count the same element twice
Since 0 appears twice, we only count it once
split ether
The number of elements is irrevelant to the size of a matrix
A matrix with a rows and b columns is said to have size axb
So this matrix has size 1x4
rustic goblet
oh is this not just a set?
split ether
No, it's a matrix
rustic goblet
ah I see
rustic goblet
true, I guess I’m not paying enough attention lol
eternal carbon
and you can’t have a repeated element in a set to begin with
rustic goblet
I just haven’t seen anyone talk about the “size” of a matrix before
rustic goblet
and you can’t have a repeated element in a set to begin with
Yeah that’s what I said
eternal carbon
no
split ether
and you can’t have a repeated element in a set to begin with
Depends on whom you ask, some authors prefer to allow repeated elements but to still count them as one
That would, for example, make {0, 0} and {0} the same
eternal carbon
Depends on whom you ask, some authors prefer to allow repeated elements but to s...
interesting notation
split ether
Anyway, I have answered this person's question in dms so I will be closing the channel now
.close
waxen flare
Help
waxen flare
IVE BEEN LOOKING AT THIS FOR 4 HOURS
I need just the answer I’m too stupid for this
rustic goblet
it’s as the others have stated before, they have given you everything you need, and also plugged in the numbers into the formula
Your only task is to do the final computation
And put it in the boxes
waxen flare
Can I have the answer pretty please with the cherry on top
rustic goblet
I can’t give you it, but if you take out a calculator
You can easily punch in the values
safe radishBOT
safe radishBOT
Available help channel!
strange copper
this is a (financeish) question, but hopefully I can still ask it. I would like to say no, but im not sure how you would tell for part B. Ik if the sum of xi is > a the RoR is positive, but i dont believe i can put sum xi > 1.1a, as i dont think that would necessarily imply the RoR is > 10%
safe radishBOT
this is a (financeish) question, but hopefully I can still ask it. I would like ...
@strange copper Has your question been resolved?
safe radishBOT
@strange copper Has your question been resolved?
pallid mirage
stuck on a question and mark scheme doesnt show working, how would i do x- 4x^-2
plucky elk
stuck on a question and mark scheme doesnt show working, how would i do x- 4x^-2
what's the question asking
"do x-4x^-2" isn't a question
pallid mirage
dy/dx is 6x-24x^-2
find the values to which it is increasing
so i just factorised to make it x - 4x^-2
0
obsidian oracle
you want to know when this is > 0. Try to find when it's = 0 and then deduce the signs in between
be careful: there is a discontinuity point to consider as well
pallid mirage
yeah i get that as well but im not even sure how id solve for x even if it was +
=
obsidian oracle
how to solve $x - \frac{4}{x^2} = 0$
flat frigateBOT
rafilou2003
obsidian oracle
get rid of the denominator
obsidian oracle
yes
safe radishBOT
safe radishBOT
Available help channel!
spark wing
Why are initial conditions plugged into only the complimentary but not y_c + y_p
safe radishBOT
safe radishBOT
Available help channel!
supple nexus
...
lean hound
is this a periodic function?
safe radishBOT
is this a periodic function?
lean hound
I'm looking at the graph on desmos and looks close to periodic but never so and can't understand how to figure it out without having a graphing calculator
placid oak
it feels like it shouldn't be, because the inputs to cos and sin in this function differ by an irrational factor
maybe it does work though hmm
lean hound
well I just checked and yeah you're right it's not periodic because both period don't have a common factor
.close
safe radishBOT
safe radishBOT
Available help channel!
pliant fossil
hello, why does parenthesis work and not brackets?
safe radishBOT
hello, why does parenthesis work and not brackets?
pliant fossil
there is a closed point at x= 3, i thought closed circles meant brackets?
obtuse jackal
How about this for an explanation ?
pliant fossil
my mind completely skipped that part, i was only looking at the graph visually and determined that the closed circle meant bracket
pliant fossil
How about this for an explanation ?
could you explain this further if possible? i cant quite understand 🥲
obtuse jackal
it asks for an open interval
So give it an open interval
even if technically you could close it on one side
pliant fossil
its still open regardless
but why
is it the line that passes through it? what makes it open 🧍♂️
obtuse jackal
open and closed is about containing its boundary
though since infinity is not a point, an interval that goes to infinity
is open since it doesn't contain infinity
is closed since there's no point on the boundary that could be included to close it
(on that side at least, it could be open/closed on the other side regardless)
pliant fossil
oh, hence the parabola function?
pliant fossil
would there be a point on a porabola that would be considered closed ever?
pliant fossil
though since infinity is not a point, an interval that goes to infinity
is open ...
makes sense
obtuse jackal
would there be a point on a porabola that would be considered closed ever?
what does it mean for a point to be closed ?
pliant fossil
what does it mean for a point to be closed ?
for it to stop and not contain infinity. i wasnt taught the reason, just the meaning behind the dots
obtuse jackal
though since infinity is not a point, an interval that goes to infinity
is open ...
as for why these choices are made, as they may seem arbitrary, and the names arbitrary too
This is somewhat modern notation that makes a lot of sense when viewed under the lenses of topology, a topic from undergraduate math that cares about this sorts of things
pliant fossil
as for why these choices are made, as they may seem arbitrary, and the names arb...
🙃sounds scary
obtuse jackal
as for why these choices are made, as they may seem arbitrary, and the names arb...
open means for all point, there's a small surrounding that is contained: no matter where you are in an open set, you can still walk a bit in any direction and still be there, nothing is stopping you, so it's open
Closed is when you can find yourself at that edge: you can choose a direction, and no matter how little you walk in that direction, you'll leave the closed set: you're on the boundary/at the door
but this is topology content so you don't need to worry about it
pliant fossil
that makes a lot of sense. professor said if we could explain it we’d get extra points. even if a problem is correct, i cant find myself leaving it behind without knowing why
thank you for the help!
.close
safe radishBOT
safe radishBOT
Available help channel!
hexed tree
hello! does anyone know how to do this? im trying to help my friend with her math homework and to be honest i dont remember covering this topic :')
safe radishBOT
hello! does anyone know how to do this? im trying to help my friend with her mat...
icy lance
do the words transformation, translation or shift ring a bell
its also important to know what a graph of just cos(x) would look like
safe radishBOT
@hexed tree Has your question been resolved?
tame raft
it's not as bad as it looks
basically you can make it into something like c + id = 0
so you need both c = 0 and d = 0
for c + id = 0
no
eternal carbon
is that "i." part of the question
tame raft
a little maybe
generally it should be yeah
it's worth learning at some point
idk how fast you learn, it's nice for me but i already know it
safe radishBOT
safe radishBOT
Available help channel!
lyric dragon
safe radishBOT
lyric dragon
How do i solve this
icy lance
have you seen the unit circle before
lyric dragon
Ya
icy lance
what do the coordinates usually represent
lyric dragon
Dunno
icy lance
they represent the value of (cos, sin) at that point
following from cos^2+sin^2=1
(x^2+y^2=1)
icy lance
(x,y)~(cos(t), sin(t))
lyric dragon
Ohh
Wait
So
Is t the same
Bc its not the same when im doing it
I got t= 2.65 and t= 0.4899
For cos then sin
icy lance
you dont need to bother about t from what it says
however just keep in mind trig functions are not one-one
one output will have several (infinite really) possible inputs
icy lance
its literally just asking you what sin(t), cos(t) and presumably tan(t) are
lyric dragon
I did cos-1 of the number
icy lance
thats not what its asking, at least not in what you showed me
just want the values of the trig functions, not t
lyric dragon
How do u find taht
icy lance
its right there
icy lance
(x,y)~(cos(t), sin(t))
^
safe radishBOT
@lyric dragon Has your question been resolved?
safe radishBOT
safe radishBOT
Available help channel!
gaunt inlet
safe radishBOT
gaunt inlet
this is what i tried so far but when i plug in 2/3 I dont get the answer ?
grand cedar
Could anyone explain how there was a right 6 and down 3? I understand the reason for stretches though
gaunt inlet
Could anyone explain how there was a right 6 and down 3? I understand the reason...
the (x-6) means that its moving right 6. when its in this form y = a(k(x-d) + c whatever is in the (x-d) the d value is the opposite of the sign. so for (x-6) d = 6 and it moves to 6 on the x axis. (x+6) means d = -6 and it moves to -6 on the x axis. the c value is -3 which means its going down 3, if it was positive 3 it would go up 3
.close
safe radishBOT
grand cedar
the (x-6) means that its moving right 6. when its in this form y = a(k(x-d) + c ...
I'm aware of that. I'm asking how there's those values of 6 and -3
gaunt inlet
I'm aware of that. I'm asking how there's those values of 6 and -3
oh
mb
they started the transformation from the origin point
look at the green points
violet mango
is this 15120?
kind forge
i thought the first one would just be 5 factorial
west hedge
So
plush crown
i thought the first one would just be 5 factorial
would it not be that for both?
violet mango
but you cant repeat so how would it be 5!
kind forge
would it not be that for both?
nah cause you don't get a five digit number with a leading 0
plush crown
but you cant repeat so how would it be 5!
5 options times 4 option x 3 options x 2 options x 1 option
kind forge
but you cant repeat so how would it be 5!
it's 5! precisely bc you can't repeat
otherwise it'd be 5^5
west hedge
So it can be seen as 5 people lining up
violet mango
how is the first iteration 5 options?
plush crown
nah cause you don't get a five digit number with a leading 0
if it is for a lock 0 can be used as the first number though
plush crown
how is the first iteration 5 options?
you can chose any of the 5 options to be the first number
kind forge
ok but
rose plume
is it from 0 to 9, where 1,3,5,7 and 9 can only be used exactly once, or you can only use 1,3,5,7 and 9's?
kind forge
nobody said anything about a lock
kind forge
is it from 0 to 9, where 1,3,5,7 and 9 can only be used exactly once, or you can...
question says "exactly one"
violet mango
you can chose any of the 5 options to be the first number
what 5 options?
kind forge
it just asks for "five digit numbers"
plush crown
what 5 options?
1, 3, 5, 7, and 9
kind forge
of which, say, 2468 is not a member
violet mango
1, 3, 5, 7, and 9
why cant i choose 2,4,6,8
plush crown
why cant i choose 2,4,6,8
thats for the optional part, focus on the part required for now
kind forge
and that's a four digit number anyway
violet mango
no othr digits right?
plush crown
all the odd single didget numbers
violet mango
i thought it was 0-9 and only use 1, 3, 5, 7, 9, once
lol
do you know what that would be anyway?
robust harness
but you cant repeat so how would it be 5!
Well, a factorial is meant to show those kind of combinations
Since it's just rearrangements of 1, 3, 5, 7, and 9
robust harness
Oh, you can only use each number exactly once tho
I think that would be right if you were able to use those numbers any amount of times
Do you understand that first part?
violet mango
i understand why its 5!
but
i thought it was 0-9 and only use 1, 3, 5, 7, 9, once
robust harness
Yeah, exactly once implies that you can't just not use one
Do you know how'd you approach the optional part?
violet mango
do you know how to answer 0-9, but only choose odd int once
robust harness
That one is more tricky to solve
I'm just gonna do my thinking over here
So there are 89999 combinations of 5 digit numbers, and all possible cases are okay unless there is more than one of the same odd integer
icy oxide
Hi, I am stuck on the following question;
safe radishBOT
Hi, I am stuck on the following question;
fluid token
where’d the sqrt go
hardy lion
you cant just fet rid of the sqrt like that
icy oxide
you cant just fet rid of the sqrt like that
oh
uh
im not good at this
i havent done algebra in so long
safe radishBOT
@icy oxide Has your question been resolved?
icy oxide
<@&286206848099549185>
lean otter
you can do this
$sqrt(x) - 14 = 6 - x
\rightarrow sqrt(x) = 20 - x
\rightarrow (sqrt(x))^2 (20 - x)^2
\rightarrow x = x^2 - 40x + 400$
flat frigateBOT
TheGodfather
lean otter
$ sqrt(x) $
why is this not formatting right 😭
$sqrt(x)$
bruh
anyway you get my point
lean otter
i genuinely dont get it
so what i did first was i isolated the sqrt x
past hare
use {}
lean otter
$sqrt{x}$
flat frigateBOT
TheGodfather
past hare
with a slash before
lean otter
$/sqrt{x}$
flat frigateBOT
TheGodfather
flat frigateBOT
TheGodfather
lean otter
ahh there we go
thanks
$\sqrt{x} - 14 = 6 - x
\rightarrow \sqrt{x} = 20 - x
\rightarrow (\sqrt{x})^2 = (20 - x)^2
\rightarrow x = x^2 - 40x + 400$
flat frigateBOT
TheGodfather
lean otter
@icy oxide as i was saying
first i isolated the sqrt x by taking the -14 to the other side
then i squared both sides
and from there, you can subtract the x from the left side and set it as a quadratic equation and solve it that way
lean otter
ok
lean otter
yeah
icy oxide
okay one sec
lean otter
lmk what you get
icy oxide
lmk what you get
i have to set this to equal 0 right?
lean otter
i have to set this to equal 0 right?
yes
icy oxide
yes
so im technically looking for
0 = x^2 -40x + 400 - x
which would be
0 = x^2 - 41x + 400
so i'd be looking for what adds to -41 and multiplies to 400?
lean otter
so i'd be looking for what adds to -41 and multiplies to 400?
yes
lean otter
should be 16 and 25 i believe
icy oxide
well it cant be 2 positives? if it needs to add to -41?
lean otter
no
icy oxide
ok nvm i see
lean otter
yeah
icy oxide
so x = 16, x = 25
lean otter
however, you need to test if both values actually give you the same results when you plug it into f(x) and g(x)
lean otter
because 16 doesn't work
icy oxide
so i have to find another number?
lean otter
however, you need to test if both values actually give you the same results when...
^^
both roots are correct
but you had to see which root actually worked by plugging it back into f(x) and g(x)
lean otter
so like what do i do now? just find another factor?
you already found another factor
you forgot about 25
icy oxide
well doesnt it need to be 2 numbers?
lean otter
well doesnt it need to be 2 numbers?
no
icy oxide
okay so it was just 16
lean otter
yes
lean otter
what part do you not get
lean otter
entire thing
so basically
this question asked for what x value does f(x) = g(x)
and it gave us two equations for f(x) and g(x) respectively
icy oxide
right
flat frigateBOT
TheGodfather
lean otter
then i isolated the sqrt x
by doing this
$\sqrt{x} - 14 = 6 - x
\rightarrow \sqrt{x} = 20 - x$
flat frigateBOT
TheGodfather
icy oxide
right
lean otter
then i squared both sides
$\sqrt{x} = 20 - x
\rightarrow (\sqrt{x})^2 = (20 - x)^2
\rightarrow x = x^2 - 40x + 400$
flat frigateBOT
TheGodfather
icy oxide
ok then thats how u got quadratic formula
then = 0
which means -41
idk how 16 was sufficient though
lean otter
16 + 25 = 41
icy oxide
right
lean otter
which is how i got my two roots
icy oxide
but why isnt 25 a part of the answer
lean otter
but then to actually prove f(x) = g(x)
you had to plug in that x to both equations set equal to each other
if you did 25
you get this
icy oxide
well i thought factoring required 2 answers
which would be 16 and 25
so idk how 1 answer is sufficient
is what im confused on
lean otter
$\sqrt{25} - 14 = 6 - 25
\rightarrow 5 - 14 = 6 - 25
\rightarrow -9 = -19$
flat frigateBOT
TheGodfather
lean otter
well i thought factoring required 2 answers
not necessarily
lean otter
g(x) = f(y)
they'd probably not ask you something like that
icy oxide
i just do better with in person
but you have been tremendous help
like im just still lost on why there are 2 answers for a factor
but we only used 1
lean otter
so did you plug in 25 into the original equation for x?
yes
icy oxide
and when it didnt equal each other
lean otter
$\sqrt{x} - 14 = 6 - x$
icy oxide
that eliminated the number
flat frigateBOT
TheGodfather
lean otter
this one
icy oxide
as an option
lean otter
that eliminated the number
yep
lean otter
and 16 works
icy oxide
i wanna try 16
lean otter
alright
icy oxide
so sqrt of 2 = -10
lean otter
no
icy oxide
o
lean otter
the -14 is outside of the square root
lean otter
$\sqrt{16} - 14$
flat frigateBOT
TheGodfather
lean otter
yes
lean otter
on the right side you would have 6 -16 = -10
lean otter
on the left you would have sqrt(16) - 14 which equals to 4 - 14 which equals to -10
lean otter
oh i added the -14
i only did that in the original equation before we found x so it was much easier to square both sides
over here, you don't need to move the -14
icy oxide
also ik im supposed to make another help request but i have 2 more problems i need help with
icy oxide
over here, you don't need to move the -14
i see
okay makes sense
thank you brother like seriously
it means a lot
lean otter
thank you brother like seriously
no worries!
if you need anything else, reach out to me
safe radishBOT
lean otter
yes please
alr
safe radishBOT
Available help channel!
neon bridge
I do not know where to start. Like zero
safe radishBOT
I do not know where to start. Like zero
safe radishBOT
safe radishBOT
Available help channel!
bold torrent
safe radishBOT
bold torrent
4-30 is the problem
I'm not sure if my teacher wants me to use sigma notation
Regardless, I need some help starting the problem
safe radishBOT
@bold torrent Has your question been resolved?
bold torrent
<@&286206848099549185>
safe radishBOT
@bold torrent Has your question been resolved?
steady vault
safe radishBOT
steady vault
i calcualate days then (1-rt)P and its not correct apprantly like a 1% error
<@&286206848099549185>
safe radishBOT
@steady vault Has your question been resolved?
safe radishBOT
@steady vault Has your question been resolved?
rocky kraken
lets say you start from March 18, 2017 to March 17, 2018, that 365 days for 1750. The per day value is 1750/365
so if x is the number of days between March 18. 2017 and Febraury 25, 2018, the total value without discount fee up to Febraury 25 would be x*1750/365
now , the discount factor would be (1-0.163) therefore the final answer should be (1-0.163)x1750/365
you are basically applying composed rule of thirds to solve the first part and applying percentages to get the final answer
The rule of three in math is a proportion that states that if two ratios are equal, then the product of the means is equal to the product of the extremes. In other words, if a/b = c/d, then ad = bc.
The rule of three can be used to solve a variety of problems, including:
Finding a missing term in a proportion. For example, if you know that a/b = c/d and you know the values of a, b, and c, you can find the value of d by solving the equation ad = bc for d.
Comparing two ratios. For example, if you know that a/b > c/d, you can conclude that ad > bc.
Solving problems involving percentages. For example, if you know that a certain item is 20% off, you can use the rule of three to find the sale price of the item.
Here are some examples of how the rule of three can be used to solve problems:
Example 1: If a car travels 200 miles in 4 hours, how long will it take the car to travel 300 miles?
Solution: We can use the rule of three to set up a proportion:
200 miles / 4 hours = 300 miles / x hours
safe radishBOT
@steady vault Has your question been resolved?
winter pivot
Wtf?
stuck compass
hi i need some help with 11 and 12 please
safe radishBOT
hi i need some help with 11 and 12 please
twilit hare
for 11 so far i have
x(x^3+8x^2-x-8)
try making pairs first
hint:$(x^4+8x^3)+(-x^2-8x)$
flat frigateBOT
斯韋裡
stuck compass
(x^3+8x^2)-(-x-8)
twilit hare
now take terms common
violet cosmos
Take out an x^2 for the first one
twilit hare
there is an addition sign in between
violet cosmos
Take out a -1 for the second one
twilit hare
not multiplication
stuck compass
so x^4 and -x^2 are the common terms?
twilit hare
so x^4 and -x^2 are the common terms?
no.
twilit hare
another hint- like how you took x common from before, do the same thing here
ah I'll just tell you. you can take x^3 common from the first and x common from the second.
violet cosmos
so x^4 and -x^2 are the common terms?
Want me to show u my work?
stuck compass
ohh i see