i would but they are rly dumb, i made a trest for them, the first question was 'what is 1/4+1/4+1/2' they answered with 3/10
#help-0
dreamy parrot
buoyant saddle
i would but they are rly dumb, i made a trest for them, the first question was '...
how old
like middle school?
in middle school we were just taught to be able to regurgitate the pythagorean theorem tbh
i was never shown a proof or an intuitive explanation
just accepted it as fact
lavish cave
just accepted it as fact
sad
buoyant saddle
indeed
buoyant saddle
yea i didnt see that until after though
pythagorean theorem was a meme throughout elementary school
but in early middle school i didnt see that
alpine sable
Hiii so questionn here. I'm trying to find the derivative of 2^-0.274a
alpine sable
the rule is b^x = b^(x)lnb
and so I see that and i would just think
it's 2^(-0.274a) * ln2
where does the -2.74 come in from?
I've had to use this rule multiple times in class before but there's never been this third number that just appears
mortal magnet
Hiii so questionn here. I'm trying to find the derivative of 2^-0.274a
feels like a mistake, the derivative of 2^(-0.274a) is (-0.274) 2^(-0.274a) ln 2
alpine sable
where does the (-0.274) in front come from?
mortal magnet
thats from chain rule
the outside function in 2^(-0.274a) is 2^x
the inside function is -0.274a
mortal magnet
np
alpine sable
Nevermind that was the wrong answer apparently 
I guess this is the full question
but i'm trying to find the derivative at a=7
i tried plugging 7 into this equation
and then converted it to seconds
mortal magnet
that is because I guessed what T was since you didnt tell me
the derivative of 2^(-0.274a) is (-0.274) 2^(-0.274a) ln 2
so the derivative of 10 * 2^(-0.274a) is 10 * (-0.274) 2^(-0.274a) ln 2
or (-2.74) 2^(-0.274a) ln 2
alpine sable
oh sorry
mortal magnet
nw
mortal magnet
is there more to (c)?
mortal magnet
though i tried (-2.74)(2^-0.274a)(ln2) at a=7
dont get how this is wrong
just to be sure, can you screenshot this little bit of blue text below the (c)'s answer box
mortal magnet
nw, I didnt notice either
I didnt look too closely at the screenshot and I saw the = as a ≈
crude mortar
im confused here lim x-->x_0 f(x) = f(x_0)
so what does this mean
severe portal
What part aren't you sure about?
crude mortar
What part aren't you sure about?
i dont get what this means
severe portal
i dont get what this means
Well, it means the limit of f(x) as x approaches x_0 is equal to f(x_0)
In practice, if that equality holds, it means the function f(x) is continuous at x_0
crude mortar
so it means this is true only for continous functions?
crude mortar
Well, it means the limit of f(x) as x approaches x_0 is equal to f(x_0)
In prac...
.
i mean limits
or functions actually
high cargo
It’s true for functions continuous at x_0
crude mortar
It’s true for functions continuous at x_0
bruh thats what i thought at first but for some reaosn in another group, someone told me it was for discontinued functions
keen plinth
you can take it to be the definition of continuity
crude mortar
anyways i have another may i ask that rn as well?
So there is a theorem that if a function is differentiable, then it's continuous, and to prove it, there is an equation like this. So I was confused as to how proving this equation right will let us prove the statement.
keen plinth
because f(x0) is a constant, you can add it to the right hand side
,, \lim_{x \to x_0} (f(x) - f(x_0)) = 0 \Implies \lim_{x \to x_0} f(x) = f(x_0)
ocean sealBOT
crude mortar
oh we can do this even with limits?
keen plinth
yes
crude mortar
ok so if this true, this must mean this is continous but how can prove that its differntiable then?
keen plinth
hopefully you have learnt some "algebra of limits" properties
continuous does not imply differentiable
you have a differentiable function, and you can prove that it must also be continuous
crude mortar
how can we do that using the equation aobve?
in other words
can u explain me this
why did that expresison have to be 0 in the firstp place to prove that f(x) is differntiable?
and please ping me if someone helps
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slim laurel
I dont understand this, where did the 0 come from. Like why did you multiply it by 0. Why not just cross out thr (x-x_o)
crude mortar
I dont understand this, where did the 0 come from. Like why did you multiply it ...
so he said the limit of the first time is f'(x_0) and the limit of the other term is 0
so it becomes 0
so even i dont get why he did this and how he did this
primal bobcat
ok so if this true, this must mean this is continous but how can prove that its ...
A function being continuous doesn't imply it's differentiable
crude mortar
A function being continuous doesn't imply it's differentiable
but vice versa?
primal bobcat
but vice versa?
But a function being differentiable imply that it's continuous, yes
crude mortar
But a function being differentiable imply that it's continuous, yes
so we need to proove that
crude mortar
and apparently this is the proof for it
and i dont get how this proves that
the first expresison is just the fact that the function is continous
i donget get anything else
primal bobcat
and apparently this is the proof for it
The second expression proves the first expression
you have to prove that f(x) - f(x_0) = 0 as x approaches x_0 but you can't immediately do so
crude mortar
but why do we need to prove that
we need to prove that do show that f(x) is continous/
primal bobcat
but why do we need to prove that
You need to prove the continuity, given that it's differentiable
primal bobcat
You need to prove the continuity, given that it's differentiable
Which is equal to proving the first sentence
primal bobcat
you have to prove that f(x) - f(x_0) = 0 as x approaches x_0 but you can't immed...
So you multiply the expression by (x-x_0)/(x-x_0)
primal bobcat
then?
Then the limit becomes ( f(x) - f(x_0)/(x-x_0) )*(x-x_0) which evaluates to f'(x)(x-x_0)
So now we can plug x in as x_0 so the second term is 0, making the expression 0
crude mortar
so basically he converted the first equation in a form that it can also simultaneouly be a derivative * 0?
primal bobcat
Yeah
crude mortar
Then the limit becomes ( f(x) - f(x_0)/(x-x_0) )*(x-x_0) which evaluates to f'(x...
.
oh ok
got it tysm for ur help
.close
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raw jetty
$\frac{\sum^{399}{k=1}\sqrt{20+\sqrt{k}}}{\sum^{399}{k=1}\sqrt{20-\sqrt{k}}}$
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Skill_Issue
raw jetty
i neee to find the value if this
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raw jetty
errrrr
$$S=\frac{\sum^{399}{k=1}\sqrt{20+\sqrt{k}}}{\sum^{399}{k=1}\sqrt{20-\sqrt{k}}}$$
$$S+\frac{1}{S}=\frac{\sum^{399}{k=1}\sqrt{20+\sqrt{k}}}{\sum^{399}{k=1}\sqrt{20-\sqrt{k}}}+\frac{\sum^{399}{k=1}\sqrt{20-\sqrt{k}}}{\sum^{399}{k=1}\sqrt{20+\sqrt{k}}}$$
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Skill_Issue
gritty bramble
cross multiply
raw jetty
$$S+\frac{1}{S}=\frac{(\sum^{399}{k=1}\sqrt{20+\sqrt{k}})^2+(\sum^{399}{k=1}\sqrt{20-\sqrt{k}})^2}{\sum^{399}{k=1}\sqrt{20+\sqrt{k}}\cdot\sum^{399}{k=1}\sqrt{20+\sqrt{k}}}}$$
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Skill_Issue
Compile Error! Click the 
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gritty bramble
**Skill\_Issue**
numerator = x, denominator = y, find x+y
yeah this will work
looks much easier too
gritty bramble
this is also a direct result i think
raw jetty
this?
gritty bramble
$\frac{\sum_{k=1}^{m^2-1} \sqrt{m+\sqrt{k}}}{\sum_{k=1}^{m^2-1} \sqrt{m-\sqrt{k}}} = 1+ \sqrt{2}$ for $m\ge 2$
uh
raw jetty
yea its correct but how did you get that
ocean sealBOT
Astar777
gritty bramble
so $\sqrt{2}\sum_{k=1}^{399}\sqrt{20+\sqrt{400-k}}$
ocean sealBOT
Astar777
raw jetty
how did you get sqrt2
gritty bramble
take 2 common
raw jetty
o
gritty bramble
and $x = \sum_{k=1}^{399}\sqrt{20+\sqrt{k}}$
ocean sealBOT
Astar777
gritty bramble
do you notice anything
gritty bramble
so $x+y = \sqrt{2}x$
ocean sealBOT
Astar777
raw jetty
right
gritty bramble
**Astar777**
get x/y from here
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raw jetty
if say theres a polynomial with roots like say a,b,c is there an easy way to change the roots to a+1, b+1, c+1
raw jetty
like say its x^3-x+1=0
patent grotto
Hola math geeks
raw jetty
like say i dont know the roots nor the cubic formula, if the x^3-x+1=0 has roots a,b,c, can i easily somehow change it to a polynomial
raw jetty
er wait yeah
unique dune
indigo solar
Anyone able to help with probability and statistics (mainly using R)
indigo solar
the programming language?
Yes
unique dune
sorry, i do js
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severe edge
Yo
severe edge
Can anyone help me do 5-8 it's for a group activity idk how to do it
<@&286206848099549185>
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<@&286206848099549185>
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worldly coyote
Can sb help me with this?
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Can sb help me with this?
worldly coyote
this is a drawing to this task
And i know that the quadrilaterals LNDF and CMKE are similar to each other
But idk what,s next
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steep wing
Hello
steep wing
I need help calculating an inverse function
It is defined on D=[-2,0]
And its values are on [-30,2]
Sorry if my math termimology is bad, I've never stidied maths in english
Im trying to figure out b rn
alpine sable
to get the inverse, u can replace f(x) by y , put it in the expression of f(x) and solve for x
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steep wing
to get the inverse, u can replace f(x) by y , put it in the expression of f(x) a...
I did that and i got a wrong answer
But i am alsmost sure i did all the solvimg steps correctly, but its wrong, i think its because there is a very specific definition of the functuin, its only supposed to be defined on 2 elements
Look on the pic, the correct answwr is way more complicated than just solving for x
Or what am i missing?
<@&286206848099549185>
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solemn stream
Can you please translate this into English?
wispy mulch
yo guy
wispy mulch
guys
i gotta simplify
x^3/x^3+2x
so what i do here is i make it
x(x^2)/x(x^2+2)?
but then i cant do anythng
manic wyvern
!xy
lone heartBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
wispy mulch
x^3/x^3+2x
.
well yea
i mean after that
wait
thats the solution in the solutions
wispy mulch
☠️
manic wyvern
Yeah
wispy mulch
what about
manic wyvern
!status
lone heartBOT
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
12x^2-12x/2x-2
manic wyvern
Cancel 2
wispy mulch
ohh alright i will start doing iut and then ill ask
wispy mulch
How did you reach there?
what
wispy mulch
Is that a different question?
ye
okay now idk what should i do
should i do ruffini?
i got 6x^2-6x/x-1
or should i do long division?
manic wyvern
!1q
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It is suggested that you limit yourself to one question per help channel, opening a new one once your original question is answered and your original channel has been closed. This is to make your channel easier to follow for potential helpers and can bring attention to the fact that your question has changed.
manic wyvern
Bro is on a roll lmao
wispy mulch
It is suggested that you limit yourself to one question per help channel, openin...
ohh
my bad
didnt know that
manic wyvern
Can you take anything common in the numerator?
After this q close this and occupy a new one lol
wispy mulch
Can you take anything common in the numerator?
no? i guess/
manic wyvern
It starts with S
wispy mulch
where did you get 5
manic wyvern
Also it comes before y
wispy mulch
now sjould i divide thwt?
manic wyvern
Lmao
manic wyvern
Lmao
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pale jackal
I apologise for shitty handwriting n blue shit, but did I fuck up because the coefficient of x in the numerator is a negative, whence I had to flip signs at some point?
pale jackal
😂😂😂😂😂😂
proud pine
Kool aid 🔥
azure needle
pale jackal
I acc have 0 clue how that got there, I looked down at my paper n it somehow was there n coated multiple pages. I’m not even playing
I have nothing blue on my desk, this shit just denatured r sum
Anywayssss thooo, -3x = flip of signs?
Ohhhhhhhhhhhh
ty ty
.solved
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alpine sable
how do i figure this out im in 8th grade trying to start calc
tacit arch
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round canyon
don’t understand this..any help?
lone heartBOT
don’t understand this..any help?
arctic lintel
m is the midpoint so its halfway between A and B
round canyon
right, what is the formula and how would i solve it?
arctic lintel
(A+B)/2 = M
round canyon
no no i meant how to solve for b
arctic lintel
well rearrange it
round canyon
okay..does (a+m)/2 work?
arctic lintel
no, thats the midpoint between a and m
round canyon
ohh
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rocky cape
Is that simply just a reference to the classic sohcahtoa stuff ?
rocky cape
We have to show that dy/dx (left side), is equal to the cos(t)/-sin(t). I knew that we had to do the converting stuff but I didnt expect them to do x/-y
I'm just unclear how they transition from x/-y to -x/square root of 1-x^2
mortal magnet
Is that simply just a reference to the classic sohcahtoa stuff ?
post the original question
rocky cape
I was about to do cos divided by sin
mortal magnet
Is that simply just a reference to the classic sohcahtoa stuff ?
oh I see, then yea its a reference to that
if you have y as a function of x, then thats sort of "sin(t) as a function of cos(t)"
and sin(t) = sqrt(1 - cos(t)^2)
so y = sqrt(1 - x^2)
rocky cape
oh I see, then yea its a reference to that
if you have y as a function of x, th...
I see
just one thing more related to this whole thing
They do something similar in the following question
This part here, I just don't seem to know all the trig function computations and stuff
I searched it up and realised that tan pi/3 is actually 0, but also can be written as ( (negative square root of 3) / 2 )
They've done this with other stuff in the past such as square root of 2 over 2, but idk how they remember
I guess, i'm not sure how to sort of get ((negative square root of 3 )/ 2)
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fringe laurel
Trig proofs
lone heartBOT
Trig proofs
fringe laurel
vast beacon
can some help me pls
fringe laurel
gtfo
vast beacon
36x^{4}+60x^{3}-47x^{2}-60x+36, How do i graph this?
round canyon
36x^{4}+60x^{3}-47x^{2}-60x+36, How do i graph this?
why are you on here..go ask somewhere else
round canyon
i can try to help i have limited knowledge on this though
fringe laurel
thank you
vast beacon
why are you on here..go ask somewhere else
because i need math help...
fringe laurel
get ur own channel
rocky cape
Omg man why did my channel close 
fringe laurel
why is ninja coming to my channel
fringe laurel
its proofs
look at the full equation on the top of the first image, i have to prove that the left side is equal to right side
so basically simplify it until its the right side of eq
round canyon
so basically, you’re trying to say that 4. is equal to 5.?
fringe laurel
?
vast beacon
its proofs
how do i make my own channel
round canyon
OH SORRY i was looking at the wrong image
round canyon
in this case i don’t think i would know how to justify it, as i do not have much knowledge sorry
fringe laurel
no prob
fringe laurel
Trig proofs
anyone help w this^
heavy drift
8x^3 + 1
heavy drift
last time i did a sum of cubes it was x^3 + 27
but this is a bit different i still know the a^3 + b^3 = a^2 - a(b) + b^2 right?
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fallen mortar
heavy drift
@fallen mortar i am trying to get help myself, helpers seem very busy right now, but and it doesn't look like any other help channels are open rightn ow
<@&286206848099549185>
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static wagon
why do multiply 1/6 x 1/6 rather than add them?
lone heartBOT
why do multiply 1/6 x 1/6 rather than add them?
static wagon
so when do we add then?
ionic jewel
so when do we add then?
whats the probability of rolling a 4 or a 6 on a single die roll?
static wagon
1/6
ionic jewel
no
static wagon
wait so u add them here?
ionic jewel
well there are 6 possible outcomes 1, 2, 3, 4, 5, 6, and you want to know the probability of rolling either 4 or 6, so thats 2 of the outcomes
so thats 2/6
ionic jewel
well i was trying to give you an example, what causes us to add in that case?
static wagon
when there are multiple outcomes in one situation?
or ig mutually non-exclusive events
like if u think of a venn diagram but there's nothing in the middle
ionic jewel
yes, generally whenever you have an "or" in the question
static wagon
alrlr
ionic jewel
the actual formula is P(A or B) = P(A) + P(B) - P(A and B)
static wagon
yea ive learnt that one
toxic fable
hi
toxic fable
sorry this is off topic but can anyone help with a grade 12 physics problem. I've been trying for days and sometimes I get 300N and other times I get 250N. The correct answer is 351 N. I would apreciate anyone attempting
fresh wedge
sorry this is off topic but can anyone help with a grade 12 physics problem. I'v...
You can paste your question, if someone knows they will respond
toxic fable
toxic fable
You can paste your question, if someone knows they will respond
thanks boss
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native hamlet
Is there any easy way to know how a graph would look? For example I have to know how the graph y=(0.5)^x
Would look like
limpid heart
how i know its decreasing?
or how i konw it would look like an exponential function
limpid heart
Decreasing its obvious cause it's less than one correct? Or I'm lost
yes
when the base is smaller than 1
native hamlet
or how i konw it would look like an exponential function
This
Just how it looks in general
cinder tundra
native hamlet
When it's ^x the graph will look that way? And the number just signifies where to "shove" it
limpid heart
shove in terms of being more or less steep
native hamlet
We know that it's a decreasing graph, but is there a way to know like which way it's going without graphing it?
Number 1.32
Without graphing I'd be stuck between option 2 and the last
Is there a way past it?
reef wren
check using values x=-1,x=0,x=1
native hamlet
Yes that would be graphing it, so there's no other way right?
limpid heart
lim
reef wren
Exponential functions in form a^x
won’t have values of y be negative
reef wren
so the answer should be ?
native hamlet
Б (the second one)
reef wren
yep
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candid swan
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candid swan
can someone explain a to me?
autumn salmon
can someone explain a to me?
the image is blur could you send again?
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primal zephyr
Hi can anyone help
lone heartBOT
Hi can anyone help
primal zephyr
let (x;y) belong to R2 / xy<1
show that:
arctan(x) + arctan (y ) = arctan(x+y/1-xy)
mystic swallow
ocean sealBOT
ren
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alpine sable
How do I check
lim x=>π/2 (k cosx)/π-2x
Without using L'hopital rule
barren orbit
unique dune
How do I check
lim x=>π/2 (k cosx)/π-2x
Without using L'hopital rule
$\lim_{x \to \frac{\pi}{2}} \frac{k\cos x}{\pi - 2x}$
ocean sealBOT
k
unique dune
is this correct?
alpine sable
Yep
unique dune
definition of derivative
sorry for the delay
${f'(x) = \lim_{x \to c}\frac{f(x) - f(c)}{x-c}}$
ocean sealBOT
k
unique dune
@alpine sable
alpine sable
Yeah
unique dune
u can use that
rearranging in such a way that it fits the limit definition of a derivative
alpine sable
How
alpine sable
Wait let me think
unique dune
wdym
unique dune
alpine sable
Got it, thank you so much for your efforts🙏
alpine sable
Alright
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tiny minnow
Can you help me out?
sure just ask
tiny minnow
alpine sable
yo she got the channel first you might need to get a new one lmao
NO LIKE HE ASK FIRST
hollow vapor
ik
alpine sable
AND I KINDA JUST STOLE IT
IM SO SORRY
I DIDN'T KNOW AND IM JUST NEW HERE
IM SO SORRY IM REALLY SORRY
hollow vapor
allg dw
alpine sable
the bot doesn't read a message with a "." at the start of it
hollow vapor
nah its better if he gets his own channel
alpine sable
yo she got the channel first you might need to get a new one lmao
Idk how this system works at all lol 🫠 i'm read the how-to channel
manic wyvern
Hmm
alpine sable
yo
alpine sable
LIKE IM OKAY IF HE ASK HERE HE GOT THIS FIRST
Nah you can go first
hollow vapor
Idk how this system works at all lol 🫠 i'm read the how-to channel
go to #help-34 and post your q
alpine sable
lmao
manic wyvern
Pov: you go to a polite competition and these ppl are your opponents 
alpine sable
go to <#908075848752590918> and post your q
Ok
hollow vapor
Pov: you go to a polite competition and these ppl are your opponents <:bleakkekw...
ive lost 💀
alpine sable
Nah you can go first
Thank you so much and I'm really sorry for taking this!!
manic wyvern
Pls ask your doubt now
alpine sable
Okay So..
manic wyvern
!da2a
lone heartBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
alpine sable
Can someone actually help me-
sour mica
ive lost 💀
Doctor of reverse psychology 👀
manic wyvern
alpine sable
Hello?? Can someone help me??
manic wyvern
Istg
sour mica
Just go ahead and ask the question
alpine sable
I'll just start placing each question
First is this
- MIKE and his friend are playing a number - guessing game. MIKE asks his
friend to think a positive number, then add four to the number. Next, square the
resulting number, and multiply the result by 3. Finally, divide the result by 2. If
you are his friend and you get a result of 50,
(a) write an inverse function that will give you the original number and
(b) determine the original number.
(c) graph
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alpine sable
I kinda know but the thing is..
It'll just look weird if I just do f(x) = 3(x + 4)^2 = 50
Looks very weird
manic wyvern
I'm gonna need help after this 💀
alpine sable
manic wyvern
It'll just look weird if I just do f(x) = 3(x + 4)^2 = 50
This is correct imo
sour mica
Looks very weird
thats because you forgot to divide by 2 in the end
alpine sable
thats because you forgot to divide by 2 in the end
No like this is the start.
Like the steps are
- Change f(x) to y
- Interchange x and y variable
- solve for y
manic wyvern
I stead of equation to 50
sour mica
No like this is the start.
I mean in the f(x) you got.
manic wyvern
Replace the x by y
sour mica
f(x) should be 3(x + 4)^2 / 2
manic wyvern
And keep 50 as x
alpine sable
f(x) should be 3(x + 4)^2 / 2
Is that how it's suppose to look like??
just.. 3(x + 4)^2 = 50
sour mica
x -> x+4 -> (x+4)^2 -> 3(x + 4)^2 -> 3(x + 4)^2 / 2
alpine sable
1. MIKE and his friend are playing a number - guessing game. MIKE asks his
frien...
But there's 50
sour mica
thats how you perform the operations
manic wyvern
But there's 50
You need a function in x and y
sour mica
"Finally, divide the result by 2."
manic wyvern
We will put the value of 50 in b part
alpine sable
what's a b part?-
manic wyvern
It is suggested that you limit yourself to one question per help channel, openin...
"Determine the original number "
💀
alpine sable
ok
alpine sable
Okay so
f(x) = 3(x + 4)^2/2
y = 3(x + 4)^2/2
x = 3(y + 4)^2/2
From '3(y + 4)^2/2', Do I use the foil method on 3(y + 4)?
alpine sable
No cause that'll only turn f-1(x)
manic wyvern
Hmm
alpine sable
Want me to show an example to better understand it?
manic wyvern
Want me to show an example to better understand it?
Yeah sure
alpine sable
Yeah sure
f(x) = 3x + 1
y = 3x + 1
x = 3y + 1
x - 1 = 3y
x - 1/3 = 3y/3
y = x - 1/3
f-1(x) = x - 1 /3
(from teacher)
alpine sable
Idk what am I gonna do next-
sour mica
x -> x+4 -> (x+4)^2 -> 3(x + 4)^2 -> 3(x + 4)^2 / 2
You understand how x becomes f(x) following this order of operations right?
hollow vapor
She's all yours
im right there with you brother
alpine sable
f(x) = 3x + 1
y = 3x + 1
x = 3y + 1
x - 1 = 3y
x - 1/3 = 3y/3
y = x - 1/3
f-1(x)...
Yeah but the design is suppose to be like this
sour mica
Now you have to figure a way to step back from f(x) to reach x
alpine sable
Okay so
f(x) = 3(x + 4)^2/2
y = 3(x + 4)^2/2
x = 3(y + 4)^2/2
From '3(y + 4)^2...
So what I did on the first step was correct
sour mica
so follow the operations backwards one step at a time, and then combine them together
alpine sable
im right there with you brother
IM NOT THAT DIFFICULT TO DEAL WITH STOP.
alpine sable
so follow the operations backwards one step at a time, and then combine them tog...
How do I do that?-
sour mica
Lets take a small step. x -> x+4
manic wyvern
theres been worse today
Real
sour mica
Now someone told you the number x+4, how do you get x from that?
manic wyvern
What country btw?
alpine sable
f(x) = 3(x + 4)^2/2
y = 3(x + 4)^2/2
x = 3(y + 4)^2/2
x = (3y + 12)^2/2
????
alpine sable
f(x) = 3(x + 4)^2/2
y = 3(x + 4)^2/2
x = 3(y + 4)^2/2
x = (3y + 12)^2/2
????
@sour mica
What are you trying to do
Finding the inverse of y?
alpine sable
What are you trying to do
Inverse Function. I'm trying to know what to do after x = 3(y + 4)^2/2
sour mica
Now someone told you the number x+4, how do you get x from that?
can you start with this? We can reach your problem step by step
sour mica
f(x) = 3(x + 4)^2/2
y = 3(x + 4)^2/2
x = 3(y + 4)^2/2
x = (3y + 12)^2/2
????
this is unnecessary
alpine sable
Now someone told you the number x+4, how do you get x from that?
4x?
sour mica
no...
alpine sable
...
sour mica
you subtract 4 from x+4 to get x
alpine sable
x = 4...
sour mica
no, x = (x+4) - 4
alpine sable
oh
sour mica
this is how you get inverse for x+4
by subtracting the 4
doing the opposite operation of what we did before
hollow vapor
Wait isn't that a quadratic equation
theyre just doing small egs of what the q is aiming for, idk what quad youre talking about
alpine sable
f(x) = 3x + 1
y = 3x + 1
x = 3y + 1
x - 1 = 3y
x - 1/3 = 3y/3
y = x - 1/3
f-1(x)...
why can't we follow this example?-
sour mica
So what you have at hand right now is the function $f(x) = \frac{3 \cdot (x+4)^2}{2}$
ocean sealBOT
Bacter10Fr4g is not fr0g
hollow vapor
why can't we follow this example?-
cause the problem isnt the question, its the concept
sour mica
why can't we follow this example?-
if you notice, x+4 is a part of the problem
alpine sable
Can we just use foil method?
alpine sable
theyre just doing small egs of what the q is aiming for, idk what quad youre tal...
Sorry if I misunderstood his question . "Inverse Function. I'm trying to know what to do after x = 3(y + 4)^2/2"
I thought he is finding the inverse of y and it's a quadratic function which has two solutions I.e the inverse of y is not possible because it's not one-one .
sour mica
foil is not a method, it is the order of operations
we will use foil to get the inverse
Since you love foil so much, can you tell what is the first operation we should do here on $f(x) = \frac{3 \cdot (x+4)^2}{2}$ ?
ocean sealBOT
Bacter10Fr4g is not fr0g
sour mica
Can you tell when to use foil?
alpine sable
3 (x + 4)^2
3 ( x^2 + 16)
3x^2 + 48??
sour mica
FOIL is to be used when you actuallyy need to multiply two terms in brackets
alpine sable
...
sour mica
3 (x + 4)^2
3 ( x^2 + 16)
3x^2 + 48??
this is wrong
You need to use (a+b) ^ 2 formula. Which is something you dont need to do here
sour mica
And how does this help
alpine sable
To remove 3?
sour mica
that 3 hasnt disappeared. It simply moved from outsside the bracket to inside
we need that 3 on the side of y
so what you are doing is not necessary to solve the problem
When you are looking for the inverse, you have to follow the order of the problem in the reverse direction
thats why I kept mentioning x -> x+4 -> (x+4)^2 -> 3(x + 4)^2 -> 3(x + 4)^2 / 2 this
hollow vapor
Sorry if I misunderstood his question . "Inverse Function. I'm trying to know wh...
Check dms
alpine sable
but the steps state that
- Change f(x) to y
- Interchange x and y variable
- solve for y
Therefor,
f(x) = 3(x + 4)^2/2
y = 3(x + 4)^2/2
x = 3(y + 4)^2/2
sour mica
Yes, and the part of solving for y means you go back the way of the steps
and not foil
alpine sable
Hm...
sour mica
Constructing the function had a specific order of operations given in the problem
that you add 4 before you square the number and so on
alpine sable
okay..
sour mica
So, it is important we follow it in backwards direction
sour mica
how did you get 4y?
alpine sable
Add 4 (y + 4) = 4y?
alpine sable
I swear im bouta lose it
manic wyvern
Same
sour mica
this is how you get inverse for x+4
can you please read this?
sour mica
IM JUST GONNA GUESS EVERYTHING
not that you had logic backing stuff you did before
sour mica
y - 4 = -4y
y + 4 = 4y
y + 4 - 4 = y
this is better
alpine sable
WHAT?
manic wyvern
y - 4 = -4y
y + 4 = 4y
y + 4 - 4 = y
alpine sable
WHICH ONE??
sour mica
but still you seem to not know the difference between addition and multiplication
manic wyvern
Sorry 
alpine sable
but still you seem to not know the difference between addition and multiplicatio...
So..
sour mica
Addition and subtraction work in ways opposite to eachother
alpine sable
3 (y + 4 - 4)...?
sour mica
And multiplication and division do too
molten pewter
<:bleakkekw:913344117981999125>
please don't make fun of people in help channels, don't post if you aren't gonna be helpful
sour mica
Same way squaring something and taking square roots
sour mica
3 (y + 4 - 4)...?
now now, wait a moment. Like I said, you need to reverse the order of operations
Can you tell what was the last step that you did to the number? According to the question?
sour mica
I mean in the statement of the problem
I'll tell you: you divided by two
Finally, divide the result by 2.
So you start by undoing this
alpine sable
MIKE and his friend are playing a number - guessing game. MIKE asks his
friend to think a positive number, then add four to the number. Next, square the
resulting number, and multiply the result by 3. Finally, divide the result by 2. If
you are his friend and you get a result of 50,
(a) write an inverse function that will give you the original number and
(b) determine the original number.
(c) graph
So.. it'll be x = 3/2(y + 4)^2/2?
sour mica
You have an extra /2 in there
alpine sable
x = 3(y + 4)^2/2?
alpine sable
What do I do next?
sour mica
Now you can start by listing the operations you did starting from mike was told the number. I'll start
- Add 4 to the number
- ...
You fill the rest
alpine sable
Which number-
sour mica
MIKE and his friend are playing a number - guessing game. MIKE asks his
friend to think a positive number,
This number
sour mica
Why are you skipping stuff ahead
alpine sable
I THOUGHT OF A POSITIVE NUMBER.
sour mica
Can we just go in the order of what I ask you and you answer?
sour mica
I THOUGHT OF A POSITIVE NUMBER.
And then what? Write step by step
sour mica
Can you please wait? Clearly you havent understood anything I told you yet, and still you skip ahead without understanding anything...
And what you do is not even correct
alpine sable
I THOUGHT OF A POSITIVE NUMBER WHICH IS 2. I ADD IT TO 4 SO 4 + 2 IS 6
sour mica
clearly, you have misunderstood something and I am looking to correct that
alpine sable
WHAT AM I NOT GETTING??
sour mica
Then what exactly? Aren't I suppose to do
3(y + 4 + 2)^2/2
3(y + 6)^2/2?
why are you writing this then?
alpine sable
why are you writing this then?
BECAUSE I DID WHAT'S SUPPOSE TO HAPPEN
sour mica
No you dont have to do that. Clear everything you did from your head, and start from scratch. What is the first step?
- Add 4 to the number
What is the second step? - Square the resulting number.
What is the third step? -
Can you now answer something which should be in place of the ___ ?
We are breaking down the problem into managable parts that are relevent later
alpine sable
ADD 4 TO THE NUMBER
I PICKED 2 FOR THE POSITIVE NUMBER
ADDING 4... TO THE NUMBER (2)
4 + 2 !!!!!!!!
sour mica
GREAT
alpine sable
SO IT'S 6.
sour mica
BUT YOU STILL HAVE TO SQUARE IT AND SO ON
sour mica
ALSO FORGET ABOUT YOUR CHOICE OF NUMBER
alpine sable
f(x) = 3(x + 4)^2/2
y = 3(x + 4)^2/2
x = 3(y + 4)^2/2
x = 3(y + 4 + 2)^2/2
Finally
Now square
sour mica
Again you are skipping steps 😭
alpine sable
what.. DID I DO
sour mica
No you dont have to do that. Clear everything you did from your head, and start ...
can you just answer what to put in 3 here?
alpine sable
ADD 4 TO THE NUMBER
I PICKED 2 FOR THE POSITIVE NUMBER
ADDING 4... TO THE NUMBER...
I DID EXACTLY AS THIS
4 + 2!!!!!
hollow vapor
がんばれman you got this. reread the question
alpine sable
AIN'T NO WAY YOU JUST CHANGED YOUR MIND
sour mica
No you dont have to do that. Clear everything you did from your head, and start from scratch. What is the first step?
- Add 4 to the number
What is the second step? - Square the resulting number.
What is the third step? - Multiply by 3
alpine sable
STOP CHANGING YOUR MIND.
sour mica
I wanted the anwer multiply by 3
alpine sable
BUT THE WHAT?
sour mica
No you dont have to do that. Clear everything you did from your head, and start ...
Can you read what I wrote in the message I replied to?
alpine sable
ADD 4 TO THE NUMBER
I PICKED A POSITIVE 2
2.
ADD 4... TO THE NUMBER (2)
4 + 2
sour mica
I did not ask you to do anything, other than fill in the blank
alpine sable
Can you now answer something which should be in place of the ___ ?
3???
sour mica
- Add 4 to the number
- Square the resulting number
- Multiply the resulting number by 3
- Divide the resulting number by 2
Is it hard so understand I just want the question reformatted in this form?
hollow vapor
calm down kio
alpine sable
THIS THING IS KILLING ME
sour mica
In the question, when this fictional character of MIKE is told the number by fictional character that is his firend, that is what the friend does to the number
alpine sable
calm down kio
NO CAUSE IM DOING THE EXACTLY SAME INSTRUCTION AND THIS IS STILL NOT CORRECT.
sour mica
You are NOT SUPPOSED to multiply or add or whatever
alpine sable
I ADD 4 WHAT'S WRONG WITH WHAT IM DOING???
4 AND THEN A POSITIVE NUMBER
4 + 4?!?!
sour mica
Will you just stop adding when the text says Add. Stop and read stuff written before and after the word too
alpine sable
IT SAYS ADD 4
WHAT AM I SUPPOSE TO DO WITH THAT INFORMATION NOTHING???
JUST 4?
THERE
4
sour mica
Now you can start by listing the operations you did starting from mike was told ...
if you read this, its in the beginning, and no one asked you to start addition and multiplications and whatever
I clearly said start listing
it means write stuff down, not perform maths
alpine sable
IT SAYS ADD
alpine sable
THEN JUST SAY "OH PUT THE 4 IN STANDBY"
SIMPLE.
SO IT'S STILL LIKE THIS
f(x) = 3(x + 4)^2/2
y = 3(x + 4)^2/2
x = 3(y + 4)^2/2
sour mica
Ok
alpine sable
Okay Finally
sour mica
Now we put that function aside
alpine sable
Btw I kinda forgot to tell you
sour mica
WE PUT MATHS ON STANDBYE
sour mica
like that needed telling
alpine sable
Next step Square the resulting number
sour mica
ONLY WRITING
alpine sable
do i need to tell this again?
I DIDN'T DO ANYTHING YET
sour mica
Good
alpine sable
IT'S STILL LIKE THIS
f(x) = 3(x + 4)^2/2
y = 3(x + 4)^2/2
x = 3(y + 4)^2/2
NEXT STEP.
sour mica
We are writing down the original order of operations (WE WILL NOT DO MATHS YET)
- add 4 to the number (DO NOT ADD, I AM WRITING TEXT)
- Square the resulting number (DO NOT SQUARE I AM WRITING TEXT)
- Multiply result by 3 (DO NOT MULTIPLY I AM WRITING TEXT)
- Divide result by 2 (DO NOT DIVIDEI AM WRITING TEXT)
Ok?
To take the inverse, we need to follow the order in opposite way, so that we can undo the above operations
Do you understand this previous sentence?
alpine sable
...
Yes...
So this is still a stand by
f(x) = 3(x + 4)^2/2
y = 3(x + 4)^2/2
x = 3(y + 4)^2/2
sour mica
YES
alpine sable
Okay.. so that's the answer?-
sour mica
yes
So now we start inverting the function
Like I said, we have to undo the operations
MATHS TIME, TIME TO PULL STUFF OUT OF STANDBYE
alpine sable
Okay :3
sour mica
we start with step 4
Divide result by 2. (DO NOT DIVIDE)
To undo the division, what do we do?
UNDO the division
what is the name of operation that reverses the division?
alpine sable
Hmm... (2)x = 3(x + 4)^2/2 (2)?
sour mica
YES
alpine sable
2x = 3(y + 4)^2
alpine sable
Multiply..
sour mica
be more specific
alpine sable
2x = 3(y + 4)^2
2x = (3y + 12)^2
sour mica
😭 nooo
sour mica
once again, you started reading only half of the text
alpine sable
2x/3 = 3(x + 4)^2/3?
sour mica
Yes
alpine sable
2/3x = (x + 4)^2
sour mica
still there is y on right hand side
alpine sable
OH RIGHT
JUST LEMME REWRITE IT
f(x) = 3(x + 4)^2/2
y = 3(x + 4)^2/2
x = 3(y + 4)^2/2
(2) x = 3(y + 4)^2/2 (2)
2x = 3(y + 4)^2
(2/3)x = (y + 4)^2
There
sour mica
Opposite of square root..
opposite of square
alpine sable
2/3x = (2y + 8)??
primal bobcat
f(x) = 3(x + 4)^2/2
y = 3(x + 4)^2/2
x = 3(y + 4)^2/2
(2) x = 3(y + 4)^2/2 (2)
2...
-# (a minor mistake in 2/3x, it should be (2/3)x)
alpine sable
Huh? Why
sour mica
2/3x = (2y + 8)??
you have to take square root of both sides
alpine sable
you have to take square root of both sides
2/3x^2 = (y + 8)^2?
sour mica
2/3x^2 = (y + 8)^2?
nope
ocean sealBOT
Catgod
sour mica
f(x) = 3(x + 4)^2/2
y = 3(x + 4)^2/2
x = 3(y + 4)^2/2
(2) x = 3(y + 4)^2/2 (2)
2...
Back from here we start
alpine sable
**Catgod**
Yeah- aren't they both the same?
alpine sable
Back from here we start
Okay
sour mica
Yeah- aren't they both the same?
in first you divide by x, in second you multiply by x. Two are different
proven rivet
maybe this clarifies, they are both different functions
sour mica
undoing the squaring means taking the square root. There is no need to take the opposite of square root
alpine sable
undoing the squaring means taking the square root. There is no need to take the ...
I don't get it
sour mica
What's the opposite of square root-
what does this say? Opposite of square root.
We want opposite of SQUARE. which is different from square root
alpine sable
triangle-
sour mica
If you read it again, step 2 was
Square the resulting number (DO NOT SQUARE I AM WRITING TEXT)
We have to undo the square
This means, we have to take the square root
proven rivet
Sorry to interrupt, what problem are you trying to solve?
alpine sable
If you read it again, step 2 was
> Square the resulting number (DO NOT SQUARE I ...
So just do nothing?
alpine sable
HOW
proven rivet
MIKE and his friend are playing a number - guessing game. MIKE asks his
friend t...
this is the question you are trying to solve, right?
sour mica
If you read the sentence completely (I AM ONCE AGAIN ASKING YOU TO DO THIS) you would see
sqrt((y+4)^2) = y+4
THIS IS NOT THE SAME AS (y + 4)^2 = y + 4
(2/3)x^2 no one mentioned this anywhere
we did not take x^2 in previous steps
sour mica
THIS IS NOT THE SAME AS (y + 4)^2 = y + 4
This is EXTREMELY WRONG. DO NOT DO THIS ANYWHERE
alpine sable
WELL EXCUSE ME IF I DON'T KNOW WHAT IS A sqrt!
sour mica
square root
alpine sable
THANK YOU
proven rivet
maybe this helps?
the top is how you start from the original number and end up to the final number
alpine sable
√(2/3)x = √(y + 4)
sour mica
$\sqrt{\frac{2x}{3}} = \sqrt{(y+4)^2} = y+4$
ocean sealBOT
Bacter10Fr4g is not fr0g
sour mica
ok?
alpine sable
Where did y + 4 Why is there another y + 4?
sour mica
there is an equal sign there 😭 no new term
alpine sable
f(x) = 3(x + 4)^2/2
y = 3(x + 4)^2/2
x = 3(y + 4)^2/2
(2) x = 3(y + 4)^2/2 (2)
2x = 3(y + 4)^2
(2/3)x = (y + 4)^2
√(2/3)x = √(y + 4)^2 = y + 4
sour mica
yes
And now we invert the first step
back from y+4 to y
WE SUBTRACT 4 TO UNDO THE ADDITION
alpine sable
minus 4
alpine sable
y - 4?