It’s on that line
#help-0
oak perch
alpine sable
how
oak perch
|AP|+|PB| is minimal iff P is on line segment AB ?
alpine sable
ok
oak perch
|AP|+|PB|>|AQ|+|QB|
By you know who
Can’t spell his name bad at English
Rest is obvious
alpine sable
|AP|+|PB|>|AQ|+|QB|
okk
oak perch
Pytha guy
deft kettle
oh wow i made such a stupid mistake
never mind
thanks for your time
shall i close the channel are you guys still discussin?
alpine sable
close it
oak perch
I don’t have questions to ask
deft kettle
oh alright
oak perch
Your choice, I think it’s finished
weak valve
Hi not too sure how to do this question
lone heartBOT
Hi not too sure how to do this question
hushed whale
number 1 is incorrect
i can't give you explanation because i know nothing about matrix and the way i solve it is pull up the wikipedia and read
oak perch
i can't give you explanation because i know nothing about matrix and the way i s...
x=A^-1b
I only came here to correct you, no intention to answer him… tired, he needs to pick one option he doesn’t understand…
Anyway I answer option 4 I leave, I believe he can find rest in his textbook
Consider $A=\begin{pmatrix}1&0\1&1\end{pmatrix}$ and $B=\begin{pmatrix}1&1\0&1\end{pmatrix}$
ocean sealBOT
Cogwheels of the mind
vocal tapir
"With 2 3 4 5 and 9 are written all possible three-digit numbers. Find the possibility of a randomly picked to be even or odd"
vocal tapir
ok so all outcomes are V(5; 3)
V(3!; 5!)=60
I don't understand how the favorable outcomes are 2*V(2!; 4!)
I mean ok 2! because the even numbers are 2 and 4
but why 4!
Shouldn't it be V(2!; 3!) ?
cuz it's three-digit numbers
and why multiplied 2 times
urban pine
what is V ?
vocal tapir
what is `V` ?
Variations
the formula being V(k; n) k - elements n - classes
so V=n!/(n-k)!
vocal tapir
nope
urban pine
it says no repeated digits in the original question? because above you didn't specify
urban pine
ok np
vocal tapir
<@&286206848099549185>
urban pine
are you taking cases for how many even or odd numbers you've already placed in the other digits?
like there are no outcomes for an even number with digits EEE since you only have two even numbers w/o replacement
copper stone
I don't understand how the favorable outcomes are 2*V(2!; 4!)
because there are 4 numbers left
you took out one even number
oak perch
Odd: (3C1)(4)(3), even: (2C1)(4)(3)
copper stone
so you have to choose a 2 digits number with your 4 digits left
and mulitply by two bc you have 2 even numbers
vocal tapir
so you have to choose a 2 digits number with your 4 digits left
I understood this, but
now for odd
it's 3* V(2!; 4!)
copper stone
bc same as before you have to make a 2 digits number with your 4 numbers left
but this time you multiply by 3 bc we have 3 odd numbers
brittle hedge
Can someone help me out with this problem
lone heartBOT
Can someone help me out with this problem
brittle hedge
Yeah it would start like this
I did some algebra and I couldn’t finish with any of the listed answers
,rotate
ocean sealBOT
ember lava
lone heartBOT
@brittle hedge Has your question been resolved?
brittle hedge
<@&286206848099549185>
brittle hedge
x = sin theta
dx = cos theta dtheta
Oh really it’s not dtheta/costheta
So in this case the whole problem would just simplify to be tan^2theta
wary stream
No
wary stream
Rewrite the top line with cos theta dtheta
wary stream
So in this case the whole problem would just simplify to be tan^2theta
Wait, maybe you're right
Yeah, my bad, you're right
wary stream
So in this case the whole problem would just simplify to be tan^2theta
Yes, correct, this is correct
wary stream
Yes
lone heartBOT
@brittle hedge Has your question been resolved?
nocturne dove
lone heartBOT
nocturne dove
Help
tacit arch
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
nocturne dove
Looking at the options I judged that we needed to find the function fx and I'm not very sure how do I do that.
I know about rolles theorem and LMVT but I don't know how useful they are here.
How do I even get f(4)-f(1) in the first place 
wary stream
Mhm but it will be of no significance.
It's more significant to see what you tried and assist you at where you got stuck, and to see what knowledge you have on this
nocturne dove
It's more significant to see what you tried and assist you at where you got stuc...
I feel like I'm missing something here but wait I'll send my attempt.
nocturne dove
, rcw
ocean sealBOT
nocturne dove
Part c may be true of some cases
But I'm not sure
Is it necessary for f'(2) to be an integer and be equal to 3?
lone heartBOT
@nocturne dove Has your question been resolved?
lone heartBOT
@nocturne dove Has your question been resolved?
raw stream
Why cant you do this? its the square root of 1 right?
lone heartBOT
Why cant you do this? its the square root of 1 right?
chrome plank
Yes
violet bear
Why cant you do this? its the square root of 1 right?
you can't do it because it's -1 which is undefined
only positive real numbers under the radical have solutions
chrome plank
$\sqrt{(-1)^2} =\
= \sqrt{1}$
ocean sealBOT
Nonna
chrome plank
You can't do $\sqrt{-1}$ and $\left(\sqrt{-1}\right)^2$
ocean sealBOT
Nonna
chrome plank
it's (-1)²
chrome plank
(-1)² is 1
violet bear
unless you do factorization but that's not happening here
it is without the radical
when it's under a radical it becomes imaginary
chrome plank
$\sqrt{(n)^2}$ is the same as $|n|$
ocean sealBOT
Nonna
violet bear
if n is a positive real number
chrome plank
no, try pluggin in sqrt(x^2) into desmos
(-1)² = 1
and sqrt(1) = 1
so that's just 1
violet bear
then why is it undefined according to desmos
chrome plank
if n is a positive real number
Also if that were for positive numbers only there wouldn't be any reason to define absolute values in the first place
Bruh
violet bear
ah you got me
chrome plank
**Nonna**
@raw stream the expression you posted is completely fine, maybe are you confusing it with these?
lone heartBOT
@raw stream Has your question been resolved?
raw stream
You can't do $\sqrt{-1}$ and $\left(\sqrt{-1}\right)^2$
I know that... cuz the square root of -1 is i
alpine sable
Please help A manufacturer packages soap powder in containers of three different sizes. The amount of soap powder in a full large container could fill exactly 3 of the medium containers or exactly 5 of the small containers. If an equal number of small and large containers are to be filled with the amount of soap powder that would fill 90 medium containers, how many small containers will be filled?
alpine sable
I got 150
Cause if 3 medium are equal to 5 small then 90 medium should be equal to (90*5)/3
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
<@&286206848099549185>
If an equal number of small and **large **containers...
Ahhh okay I'm so dumb
Lemme try again
Got it, thanks a lot!
.close
agile salmon
lone heartBOT
agile salmon
oh and the answers i have selected i dont know if they are correct and i dont even think so
chrome plank
What's the definition of domain?
agile salmon
What's the definition of domain?
im not sure
chrome plank
It's the set of all x values you can plug into a function without breaking stuff basically
As an example, if f(x) = 1/x, you can't plug in 0, because then you are dividing by 0, so 0 is not in the domain of the function
Do you understand what I mean?
agile salmon
As an example, if f(x) = 1/x, you can't plug in 0, because then you are dividing...
ohh yes
chrome plank
Ok nice
So in this case, f(x) = -2x² -4x + 6, will anything break maths if it were plugged in?
agile salmon
So in this case, f(x) = -2x² -4x + 6, will anything break maths if it were plugg...
no
chrome plank
So what real numbers can we plug in?
agile salmon
So what real numbers can we plug in?
im not sure what you mean
plugging in for what
chrome plank
I mean, what numbers can we substitute to x without breaking maths
agile salmon
I mean, what numbers can we substitute to x without breaking maths
infinity?
agile salmon
ohhh
chrome plank
So what's the domain?
agile salmon
infinity?
chrome plank
agile salmon
how is it not?
chrome plank
Infinity is not a number, it's more like a concept
If I say that the domain of a function is 2 < x < 4, that means that I can plug in every real number in the interval between 2 and 4 and not make undefined calculations like dividing by 0 or taking square roots of negative numbers
In this case you can pick any number in the interval between...?
(Edit: better wording)
agile salmon
In this case you can pick any number in the interval between...?
im sorry i dont know
chrome plank
All real numbers are in the interval (-inf, +inf)
agile salmon
All real numbers are in the interval (-inf, +inf)
ohhh
i thought it was that
but im really confused on the range
chrome plank
What's the definition of range?
chrome plank
All real numbers are in the interval (-inf, +inf)
(Note: -inf and inf are not included)
chrome plank
:/ you googled that
And also that's not what a range of a function is referring to
A range is all the numbers that the function can give as outputs
agile salmon
:/ you googled that
yeah i had no idea
chrome plank
yeah i had no idea
That's ok, next time just say it 👍
agile salmon
my teacher never gave any definitions
agile salmon
A range is all the numbers that the function can give as outputs
oh okay i see
chrome plank
Let's do a little recap:
Domain → All values that a function can take as input
Range → All values that a function can give as output
agile salmon
Let's do a little recap:
Domain → All values that a function can take as input
R...
yes
chrome plank
If you were to pick any point on this function, how high or low (y value) could it get?
agile salmon
If you were to pick any point on this function, how high or low (y value) could ...
it would have to be lower than 8 correct?
chrome plank
Yes exactly
agile salmon
oh i see now
chrome plank
is 8 included?
agile salmon
yes it is
chrome plank
Nice!
Then for the last two
It's very intuitive to find when a function is increasing and decreasing
Increasing means that the function is going up
Decreasing means that the function is going down
The intervals are read from left to right
And that's pretty much it
So when is the function decreasing?
agile salmon
So when is the function decreasing?
anything below 8 i believe
chrome plank
Notice that the increasing-decreasing is based on the x axis
And as I mentioned, read from left to right
Starting from the left and going to the right, at first, is our function increasing or decreasing?
chrome plank
like in (x,x),(x,x)
what do you mean?
chrome plank
An example (not related to this) is that I can say that a function is increasing when x > 12
That means that if I pick any x value bigger than 12, the y value at that new point will be surely bigger than the y value at x = 12
chrome plank
or just 1 and -3
Just 1 and -3
agile salmon
Just 1 and -3
oh okay
agile salmon
Just 1 and -3
?
agile salmon
alright
agile salmon
The sketch isn't perfect, but hopefully it's understandable
so its the y intercept?
im confused
chrome plank
so its the y intercept?
No, that doesn't matter
I think you are overthinking this
Start from the far left
slowly go to the right, at the beginning, is the function going up or down? (in the function of your exercise)
agile salmon
Start from the far left
slowly go to the right, at the beginning, is the functio...
dowm
down
wait
no up
chrome plank
Ok, it's going up
But the question is asking when it's decreasing
So, does it decrease at a certain point or does it keep getting bigger?
agile salmon
So, does it decrease at a certain point or does it keep getting bigger?
it gets bigger
wait no it decreases at 8
or after 8
agile salmon
So that's when our function is decreasing
ohhhh
agile salmon
So that's when our function is decreasing
wait so where does it turn positive
chrome plank
is that another question from the exercise?
agile salmon
wait so where does it turn positive
or how do i find it
chrome plank
Ok, you tell me
For which values of x is the y value bigger than 0?
agile salmon
Ok, you tell me
For which values of x is the y value bigger than 0?
i have no idea what youre asking
chrome plank
Let's say I only need positive values of y.
I give the function any value of x I want
You have to make sure that I'm getting positive values of y, for example (not related to this function) you could say "Oh, if you pick an x value bigger than 19, it's y value will be negative, so make sure you only pick x < 19"
agile salmon
Ok, you tell me
For which values of x is the y value bigger than 0?
anything above -3 and 1
chrome plank
I think you understood, but can you express your answer more clearly?
what is "anything", and what is "above" referring to
agile salmon
what is "anything", and what is "above" referring to
any value greater than -3 and 1
y value greater than -3 and 1
i dont know how to word it
chrome plank
any value of what?
agile salmon
any value *of what*?
of x
chrome plank
Yes! Finally ahah, well done
So what's the answer that represents what you just said?
agile salmon
chrome plank
let's say I pick x = 4
4 is bigger than one
but it's never going to be smaller than -3
let's say I pick x = -4
-4 is smaller than -3
but it will never be bigger than 1
I end up with no possible values to choose from
[condition] and [condition]
means that both conditions have to be true
So the answer must be another one
agile salmon
chrome plank
Me too 
chrome plank
After 8
The mistake came because we confused the y axis with the x axis, should have checked, my bad
agile salmon
The mistake came because we confused the y axis with the x axis, should have che...
ohh its alright
chrome plank
oh and what does that x mean ive never seen it before
|x| means that whatever x value has, we only consider the positive version of it
|4| = 4
|-4| = 4
|-5| = 5
agile salmon
oh alright
chrome plank
For the third question
At which x value does the function start getting smaller y values?
Imagine it like this
You are walking across that function, you start from the left and you are going from the right, and you count your steps.
Each step is 1 unit on the x axis
How many steps do you have to take before you start going downhill?
lone heartBOT
@agile salmon Has your question been resolved?
proud heron
why does |x-3| move the function 3 units to the right instead of moving the function 3 units to the left
naive valley
if you plug in x=3 you get x-3 = 0, right?
thus x=3 is at the vertex
it's just the way it is
marsh rapids
If f is your function, f(x-a) = f(b) when x = b + a, thus offset by a to the right, not the left
You need to move in a way that cancels the offset, thus opposite it
Since negative is to the left, it thus shifts it to the right
urban pine
"offset" is the way i think of it too
i need to start with larger values of x to catch up to the same point as the parent function
another way is to ask when the inside is zero
|x|
x = 0
|x - 3|
x-3 = 0
x = 3
plucky beacon
How many positive integers less 10000 than are there which contain at least one 2 or at least one 3 (or both)?
lapis sluice
How many positive integers less 10000 than are there which contain at least one...
you could calculate this
you could think of the problem as writing the numbers as a string
0000, 0002, 0023, etc.
plucky beacon
I see
lapis sluice
so the next step would be to calculate the probabilites
plucky beacon
@lapis sluice for instance from 1 to 100 we have 10 + 9 + 10 + 9 = 38
contain 2 or 3 right?
@lapis sluice right?
lapis sluice
That might be correct, but I haven't counted
This is a problem which you should not brute force, it's much simpler to calculate the probabilities of the digits showing up at each index
plucky beacon
@lapis sluice containing here means that for instance 12 contain the digit 2 right /
?
lapis sluice
<@530781099995955200> containing here means that for instance 12 contain the dig...
yes
thats why it would be easier to think of the numbers as a string
lapis sluice
0000, 0002, 0023, etc.
like i refered to here
glad surge
lone heartBOT
glad surge
hi can i please get help on this statistics question
real gazelle
I like that $\mathbb V$ symbol haha
ocean sealBOT
Eric Tao (he/him)
real gazelle
do you know the equation variance = E[x^2] - (E[x])^2
glad surge
do you know the equation variance = E[x^2] - (E[x])^2
yeah i do
real gazelle
alright
do you also know the fact that variance(x + y) = variance(x) + variance(y)
and variance(c x) = c^2 variance(x)
glad surge
yep
glad surge
hmm
glad surge
how can you simplify var(2(x7 + x9) - x4)?
could i do ((x7+x9)-x4)^2 variance((x7+x9)-x4)?
real gazelle
how did you get that
glad surge
so in that question, would 2 be c?
glad surge
anything involving xs here is not a constant
would it be 4 variance((x7+x9))+ variance (-x4)?
real gazelle
why?
glad surge
because E[x^2] =mu_2 and (E[x])^2= mu_1
glad surge
how can you simplify variance(x7 + x9)?
variance(x7)+variance(x9)?
glad surge
-variance(x4)?
glad surge
hmm
real gazelle
so which property of variance can you use
glad surge
-1^2*variance(x4)?
glad surge
and variance(c x) = c^2 variance(x)
because of this?
glad surge
4 (variance(x7)+variance(x9)+ variance (x4))?
real gazelle
yup
so now
let's take a small detour
and figure out what variance(x_i) is
and then we can sub that in for all the variances (they are all the same)
so what is the equation for variance(x_i)?
glad surge
E[x^2] - (E[x])^2?
glad surge
so 4(mu_2) - (mu_1^2)?
real gazelle
where did you get the 4 from?
glad surge
so 4(variance(x7)+variance(x9)) + variance(x4)
.
real gazelle
oh okay
don't worry about that yet
we're trying to find variance(x_i) first
and then at the end we'll put everything together
so what is E[x_i^2]?
glad surge
okay
glad surge
so what is E[x_i^2]?
mu_2?
glad surge
yes sir
glad surge
yep
real gazelle
so variance(x7) = mu_2 - mu_1^2, variance(x9) = mu_2 - mu_1^2, etc
do you see how to solve from there
glad surge
so variance(x7) = mu_2 - mu_1^2, variance(x9) = mu_2 - mu_1^2, etc
i get this
but im confused onwards
real gazelle
what do you get if you plug those values in
real gazelle
so 4(variance(x7)+variance(x9)) + variance(x4)
to this equation
glad surge
what do you get if you plug those values in
for var(x7), would that be -42?
because 7 -7^2?
real gazelle
No
real gazelle
so variance(x7) = mu_2 - mu_1^2, variance(x9) = mu_2 - mu_1^2, etc
variance(x7) is this
neither mu_2 nor mu_1 are 7
they are just some number that you don't know
glad surge
ok
glad surge
what do you get if you plug those values in
so would this just be variance(x7) = mu_2 - mu_1^2?
real gazelle
yup
glad surge
kk
glad surge
so variance(x7) = mu_2 - mu_1^2, variance(x9) = mu_2 - mu_1^2, etc
so once this occurs, do i do 4* ((mu_2 - mu_1^2) + ( mu_2 - mu_1^2)) - var(x4)?
real gazelle
yep!
real gazelle
what is var(x4)?
glad surge
(E[x])^2
glad surge
so variance(x7) = mu_2 - mu_1^2, variance(x9) = mu_2 - mu_1^2, etc
but idk how to do it like this
glad surge
mu_2 - mu_1^2?
real gazelle
how did you get the ^2
glad surge
becuase (E[x])^2?
real gazelle
well
real gazelle
mu_2 - mu_1^2?
you already know var(xi) is equal to this for all values of i
so logically, what is var(x4) equal to
real gazelle
yep!
glad surge
ahh okay ty
real gazelle
no problem!!
glad surge
sorry so like
since i have this 4*( mu_2 - mu_1^2 + mu_2 - mu_1^2) + ( mu_2 - mu_1^2)
what is next?
glad surge
tyty @real gazelle
real gazelle
no problem!
formal rampart
.close
lone heartBOT
lone heartBOT
Available help channel!
native blaze
In a proof, if i have to assign some variable a value per an existential quantifier, can it be in the form x <= ? as opposed to x = ?
native blaze
Like a statement that says there exists x such that P(x)
lone heartBOT
@native blaze Has your question been resolved?
viscid urchin
ok I closed the chat a bit too soon 😅 so to solve this, I have to know what sin beta and cos alpha are. How do I find those out?
viscid urchin
i know the inequalities with theta are for determining the sign but thats all i know
im using the first identity shown here
urban pine
you'll need to draw some triangles to get cos a and sin b
then you can sub in those four values to the first identity there
urban pine
ya we should go in another channel tho
viscid urchin
Ok so I drew a triangle with angles a and b and gave it side lengths based on the angle. I don’t think this is the right approach idk
viscid urchin
right, so shouldnt they be the same?
since both sin alpha and cos beta are looking at the same sides
urban pine
alpha and beta don't need to be part of the same triangle
viscid urchin
how do i find the 3rd side length?
since the sin and cos show only 2 side lengths for their 2 respective triangles
urban pine
yep!
oh sorry didn't see the question.
since these are right triangles you can solve with the pythagorean theorem
viscid urchin
this is what not being in a math class for 2 years does to u smh
urban pine
use it or lose it! comes back faster than you think though 😜
urban pine
oh sorry big deal that the triangles are in the correct quadrant
we can have negative side lengths in a sense
viscid urchin
oh yeah i completely forgot about that part
so the only thing thatd change is the side with the length of 24 becomes negative?
urban pine
yep!
lone heartBOT
@viscid urchin Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
hushed tundra
lone heartBOT
hushed tundra
Is this a valid proof that the limit doesn’t exist?
tacit arch
Is this a valid proof that the limit doesn’t exist?
looks mostly fine. maybe explicitly pick 2 values of k where the limit is different
at this point it just depends on the grader
cloud python
I am a dum useless human being that dosent know how to do basic math help ? Please 🥲?
last ether
Just replace x with -10
cloud python
Yeah but idk the rest 😭🤚
gray isle
yes
gray isle
what's the question
lone heartBOT
@cloud python Has your question been resolved?
modern maple
Help
modern maple
Math
hard patio
post your qustion
modern maple
It’s a fraction problem
indigo furnace
send it
modern maple
hard patio
well you have been given a total number of treats
and the fraction of treats that contain nuts
you have to find the number of treats that contain nuts
hard patio
do you know what operation you have to use here?
alpine sable
yikes
modern maple
That isn’t helpful
native cloud
I recommend using ratios
native cloud
Or you can find LCD
naive valley
take 11 treats, add nuts to 3 of them, and set them aside. then repeat this process several times until you run out of nuts. then count how many have nuts at the end. you could have done this manually by now 😀
modern maple
Least common denominator
Idk what that means
native cloud
You can change 3/11 to 27/99
modern maple
I only know least common multiple
native cloud
You can change 3/11 to 27/99
Do you understand this?
modern maple
Yes
native cloud
Then what should we do?
Maybe subtraction?
Oh wait
We got the answer nvm
Because we are finding the amount that HAS nuts
Answer 27 nuts
agile condor
proove that
$6(a^3+b^3+c^3)^2 \leqslant (a^2+b^2+c^2)^3$
with $a+b+c=0$
agile condor
@oak perch
ocean sealBOT
what do i live for v2.0
agile condor
sorry
lone heartBOT
@agile condor Has your question been resolved?
agile condor
oak perch
Wait
Made a mistake, fixing
Let s_1=a+b+c, s_2=ab+bc+ca, s_3=abc, t_k=a^k+b^k+c^k
So we can obtain that
3s_3=t_3 and t_2=-2s_2
From
(s_1)^3=t_3+3(t_2s_1-t_3)+6s_3 and (s_1)^2=t_2+2s_2 respectively
Therefore you became proving (t_2)^3>=6(t_3)^2, , which is proving 54(s_3)^2+8(s_2)^3<=0
Which is proving 27(s_3)^2+4(s_2)^3<=0
Now
a,b,c are three real roots of polynomial x^3+s_2x-s_3=0
We recall that a cubic polynomial x^3+px+q has three real roots iff its discriminant -4p^3-27q^2>=0
Now plug in p=s_2,q=-s_3, so we have 27(s_3)^2+4(s_2)^3<=0
QED
agile condor
ok thnx
@oak perch
i have a lot of exercices these days if u want not the derangement
for me i have no problem
oak perch
Wait a second…
I am checking whether I made any mistake…
Yeah made one mistake
Editing
Done
agile condor
thnx
oak perch
Np
agile condor
<@826318983413366824>
i have a lot of exercices these days if u want not the der...
.
or u haven any pb
lone heartBOT
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agile fulcrum
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alpine sable
its a taylor remainder theorem problem i believe
Write the taylor series for this problem
Keep substituting till you get the value as far as the fourth decimal point
alpine sable
What
Yes
So you substitute x as 2
And then keep calculating until you get the 4th point right
That should make the error margin disappear
alpine sable
Yes yes
alpine sable
Is this wolfram?
agile fulcrum
yes
alpine sable
Send site link, please
agile fulcrum
and putting the upper bound at 400
results in a difference of
i doubt this problem need that many
alpine sable
Put the bound at 1000
agile fulcrum
i dont think this is how you do it
it cant be
i tried doing this way before i got it incorrect
alpine sable
Ohhhhhh
I get it I get it now!!
You've to use the remainder term in the Taylor series
agile fulcrum
please explain
alpine sable
agile fulcrum
what is c and x
alpine sable
ebon terrace
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polar fossil
uh when you say increased by 30% does it mean you add 30% to the amount or take the amount multipled by 30%
polar fossil
for example her savings were 50% of her income and next month it increased by 30%
is it 50% × ³⁰/100 or
50% + 30%
ionic trail
uh when you say increased by 30% does it mean you add 30% to the amount or take ...
Whats "it"? Savings amount or savings rate?
If you base it on savings amount, which is what I would do, then its 50% * 1.3 = 65% so her new savings rate is 65%
vale wigeon
@polar fossil do you have the question exactly as worded
polar fossil
<@789854796429000725> do you have the question exactly as worded
yes but i have problems with the english
vale wigeon
show the question
polar fossil
in july, mary spent 45% of her income on transport, 25% of it on food and kept the rest as savings. in august, her income increased by 10%. she spent the same amount of money on transport but increased her savings by 30% to $780 in august.
a) what was her income in july?
b) how much did she spend on food in august?
polar fossil
yes
vale wigeon
make a table.
frozen hare
,rotate
ocean sealBOT
vale wigeon
\begin{tabular}{c||c|ccc}
Month & Total & Transport & Food & Savings \
\hline\hline
July & & & & \
\hline
August & & & & 780
\end{tabular}
ocean sealBOT
Ann
vale wigeon
as a first step i suggest finding mary's July savings
vale wigeon
great, so what was the income for July?
polar fossil
$2000
lone heartBOT
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vague cloak
can anyone help me😭
lone heartBOT
can anyone help me😭
vague cloak
it doesn't seem like a quadratic function to me, am i missing smtg?
winter rune
Its not quadratic, "in the form of the intercept" likely means in the style of f(x) = mx + b
winter rune
In this case, multiply -2 by (x + 1/4)
vague cloak
-2x-53/8 right?
winter rune
Yes I think so
vague cloak
this is just a straight line function right?
winter rune
Yes the function is linear
winter rune
What is the question on this one?
vague cloak
can anyone help me😭
this
winter rune
It seems the answer is already provided. Are you asking how to reach it?
winter rune
x*x = x^2
vague cloak
can anyone help me😭
but there's only 1 x here
winter rune
Yes that function is linear
The second one is not
They are different
In the second one, parenthesis next to each other imply multiplication
So when you multiply (x - 3/2)(x+2), you get an expression containing x^2
vague cloak
i understand that
vague cloak
i dont undertsand
i dont get how this is the answer for
vague cloak
can anyone help me😭
this
winter rune
It isnt, these seem to be two separate questions
vague cloak
i think i've been fooled by my tch
winter rune
If you only mean the two expressions shown in the second image though
I believe for quadratic functions, intercept form looks like f(x) = m(x - a)(x - b) where a and b are the two zeroes of the function found using the quadratic equation
m does not need to be calculated, its the same as the number next to x^2 in the first expression
winter rune
Yes
high granite
This is my first time seeing something like this, not sure where to begin
lone heartBOT
This is my first time seeing something like this, not sure where to begin
@high granite Has your question been resolved?
molten pivot
Let z = x+iy
winter rune
It seems its asking you to find an equality using the two real-valued parts of a complex expression (x and y in x+iy) to describe what points on the complex plane are satisfied by the complex equality
ionic trail
Thats the intersection of all intervals of the given form.
For x to be in set (i), it must hold, that x ∈ [-1/n, 1+1/n] for all n ∈ {1,2,3,...}
Similar for (r)
Looks good to me
Yes
Wait, is 0.5 in (r) ?
For n >= 3, 1-1/n is bigger than 0.5
So for 0.5 to be in (r), in particular 0.5 must be in (1-1/3 , 1 + 1/3) which it isn't
I don't think so🙂
We are looking for a number thats bigger than 1-1/n and smaller than 1+1/n for any n. Can it be bigger than 1? Can it be smaller than 1?
If not, it has to be 1.
So I think its {1}
Lets take some n >= 1 then 1/n <= 1 and -1/n >= -1
Give me a sec😅
Given n >= 1 we need to show:
(1) 1 - 1/n <= 1
(2) 1 + 1/n >= 1
(1) 1 - 1/n <= 1 <=> -1/n <= 0 <=> -1 <= 0 which is true
(2) 1 + 1/n >= 1 <=> 1/n >= 0 <=> 1 >= 0 which is true
Yes sorry, all brackets are < and >
This "infinity" thing is merely a notation of this set. We don't need to actually take limits here. We can say that 1/n > 0 for all n, but "at infinity" 1/n is not defined.
Best stick to the definition that says that an element needs to be in all of the sets that make it up.
And no other number except 1 is in this set. That is because if m != 1, than m is bigger or smaller than 1. Lets say m smaller. We show that m is not in this set. If m < 0 then it should be clear (because 1-1/n doesn't get smaller than 0). If m is between 0 and 1, then for sufficiently large n (say n=N) , 1-1/N gets bigger than m because it converges to 1 and so m can't be in the set (1-1/N , 1+1/N) and therefore can't be in (r). (Similar for if m > 1)
lone heartBOT
@silver tangle Has your question been resolved?
lone heartBOT
@fiery tide Has your question been resolved?
summer hornet
$\frac{x^2 + y^5}{1-\cos x +y^4}$
lone heartBOT
$\frac{x^2 + y^5}{1-\cos x +y^4}$
ocean sealBOT
cw26
oak perch
You asked last time and I answered right?
oak perch
I said you approaches (0,0) on y^2=(t/2)x by different t will give you different limit
You didn’t say you didn’t understand
summer hornet
yea mb
oak perch
$=\frac{x^{2}+y^{5}}{2\sin^{2}(\frac{x}{2})+y^{4}}$
ocean sealBOT
Cogwheels of the mind
summer hornet
yep
oak perch
$=\frac{4+yt^{2}}{2(\frac{\sin(\frac{x}{2})}{\frac{x}{2}})^{2}+t^{2}}$
ocean sealBOT
Cogwheels of the mind
oak perch
Where $t=\frac{y^{2}}{\frac{x}{2}}$
ocean sealBOT
Cogwheels of the mind
oak perch
Is fixed
Limit of this is 4/(2+t^2)
Changes with choice of t
So limit doesn’t exist
oak perch
$\lim_{y \to 0}\frac{\sin(\frac{x}{2})}{\frac{x}{2}}=\lim_{y \to 0}\frac{\sin(\frac{y^{2}}{t})}{\frac{y^{2}}{t}}=1$
ocean sealBOT
Cogwheels of the mind
oak perch
In the end you can let t=1 and 2 respectively for example
This gives you two different 4/(2+t^2)
oak perch
Okay
summer hornet
sorry for the trouble
oak perch
Np
lone heartBOT
@summer hornet Has your question been resolved?
humble scroll
Hello
humble scroll
Could someone help me understand this
They have an explanation but I don’t understand that either
.close
alpine sable
is there a way i can memorize trigonometry ratios properly or are there any tips on how i can practice to keep it in my mind because i keep forgetting them
alpine sable
try some problems
there is like one way on how people memorize it is by saying “ some pol have curly brown hair through proper brushing “
im not sure if this works
you can draw a right triangle
and do it urself
humble scroll
Look up SOA CHA TOA
gray isle
soh cah toa
lean depot
It is indeed "soh cah toa," not with a "cha." This mnemonic seems weird but it works for myself and many other people. It's still how I remember the ratios.
However, here's another way to memorise it. If you know how sin and cos are defined -- as in this diagram -- the ratios are actually a consequence of this.
gray isle
son of hades can ask hades to obliterate antarctica
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strange fractal
help plz
alpine sable
Im gonna puke, just hold on
strange fractal
thx
alpine sable
Add number of rainwater and tap water users, rainwater and not tap water users, and not rainwater and tap water users. You get 59.
59/100 or 59%
Not currently doing venn diagram probability, so someone from <@&286206848099549185> pls confirm my answer for the question above.
strange fractal
Hi
strange fractal
Add number of rainwater and tap water users, rainwater and not tap water users, ...
?
If u add the number of rain water and tap water users u get 71
strange fractal
Oh i was looking at total
alpine sable
Dont worry, I experienced that whenever i have a big exam
strange fractal
I just started this topic today 😭😭
alpine sable
Did i answer your question and was i right?
lone heartBOT
tame willow
@strange fractal if you can’t behave in a help channel don’t use them at all
strange fractal
i dont get it wut i waited an hour its 11 pm and i have school tmr
tame willow
Doesn’t mean you get to ping us four times inside an hour
lone heartBOT
Available help channel!
north hamlet
Did i do somethin wrong?
The answer is sus
lone heartBOT
Did i do somethin wrong?
The answer is sus
alpine sable
x and u are related. You cant treat it as a constant when integrating
north hamlet
x and u are related. You cant treat it as a constant when integrating
I don't get it
alpine sable
if you changed x to u, then you should get rid of all the x's
north hamlet
That is the problem, i can't
burnt ravine
While substitute a variable (x replaced by u) you must have no x in final integration, only u
alpine sable
That is the problem, i can't
hence why integration by parts was suggested before
north hamlet
Ok
burnt ravine
Toby is right you interpreted x as a constant but x is not a constant because x depends of u (x = exp(u))
north hamlet
Also, do we have something called "inverse logs"?
wide raven
that'd be exponents
north hamlet
Oh my god i wanna commit suicide
I thought you were going to say somethin like ln(2x-x)
wide raven
no no
north hamlet
Huh?
north hamlet
Well, we need u, v, du, dv for parts
We already have u and dv
We need to find du and v
alpine sable
Did i do somethin wrong?
The answer is sus
IBP is only used when multiplying two things in an integrand, your problem here shows that you're only trying to find the integral of ln|x|
north hamlet
So, i shouldn't use parts?
alpine sable
No
north hamlet
Then what am i supposed to do?
alpine sable
wait, nevermind ignore what I said
I'm stupid, I got confused
Keep going with IBP
alpine sable
lemme solve it on paper real quick