The answer is A but I still don’t understand
#help-19
dawn roost
odd edgeBOT
The answer is A but I still don’t understand
wooden python
ok so do you know the definition of logarithm
the most basic one:
the number $\log_a(b)$ answers the question ``$a$ raised to \textbf{what power} gives $b$?''
clever fjordBOT
Ann
ripe robin
The answer is A but I still don’t understand
What is log3 actually telling u
dawn roost
What is log3 actually telling u
10 to the power of x = 3
wooden python
so
you have this number x for which 10^x = 3
so when you raise 10 to the power of this x
what do you get?
dawn roost
so when you raise 10 to the power of this x
I don’t really get this part 🥹
wooden python
$\log_{10}(3)$ is (by definition!) the solution of $10^x = 3$. do you understand this? Y/N
clever fjordBOT
Ann
ripe robin
10 to the power of x = 3
Yes pretty much and when u evaluate this, and do 10^ of it u get back to 3
But u don’t actually have to evaluate it bc ur just reversing the process
wooden python
yeah so
when we take the x which satisfies 10^x = 3,
and work out 10^x,
we get...?
wide pollen
hey
wooden python
(translate?)
wide pollen
(translate?)
i need to prove that this function has only 3 roots so i used intermediate value theorem to show that there are 3 roots but i need to prove there cant be more than 3
any hint (no full answer) will be great
wooden python
(the verb is "to prove" btw)
wide pollen
roole
wide pollen
(the verb is "to prove" btw)
ok thx
wooden python
can you show how you found 3 roots
wide pollen
yep
@wooden python
first i said that f is cont for every x which isnt equal to 0
then i just did the IVT for specific intervals
for example theres a solution in (1,e)
wooden python
ok right
wide pollen
but plz hint cuz ig i need to try alone first
wooden python
you can look at f' and show it is monotone on each of these intervals
wide pollen
you can look at f' and show it is monotone on each of these intervals
u mean for example that in [1,e] f' is always - or + ?
so theres no way for one more f(x)=0 in (1,e)?
wooden python
you wanted a hint, this is my hint
wide pollen
ure right
wooden python
any two roots of a differentiable function on an interval must be separated by an extremum
in practice, they may instead end up separated by a point of non-differentiability or nonexistence of the function itself!
wide pollen
@wooden python this worked thx for saving my degree !
wooden python
your degree hinged on that problem?!
odd edgeBOT
Available help channel!
shrewd trellis
Why am I getting a negative answer? The answer they provided was positive.
shrewd trellis
wooden python
x - (x^2 - 2) not x - x^2 - 2
shrewd trellis
wooden python
under the integral, you forgor these brackets
... and you also turned the 2 into 2x.
for no good reason.
these are your two mistakes.
fix them.
potent nexus
Area doesn’t always correspond to the integral
wooden python
Area doesn’t always correspond to the integral
not the issue at hand here!
unkempt lichen
atm, i'd rather not confuse the OP
wooden python
i already outlined exactly what the issue is.
unkempt lichen
he's already a little careless and fumbling with reading and rereading as it is
wooden python
there is nothing else to it, and OP needs to fix his algebra fumbles.
unkempt lichen
throwing yet another wrench into his calculus is not exactly constructive at this moment, until he comes across them in his course
wooden python
throwing yet another wrench into his calculus is not exactly constructive at thi...
ms. underscore also attempted to yap to him about improper integrals, which i thankfully was around to shoot down.
unkempt lichen
oh dear.
shrewd trellis
ms. underscore also attempted to yap to him about improper integrals, which i th...
life saver fr
potent nexus
I mean, it’s good insight to know that the Area does not correspond to the integral always. The improper integral was mentioned first by h but yeah sorry ig
unkempt lichen
I mean, it’s good insight to know that the Area does not correspond to the integ...
i... don't exactly wish to think of the next two hours if OP decides to ask "then what else can solve part b if not a definite integral?"
potent nexus
Well obviously you’d still use a definite integral
shrewd trellis
I mean, it’s good insight to know that the Area does not correspond to the integ...
what level is this?
potent nexus
Just that in future if the integral he solves is not positive, perhaps it’s not an error he made but just an additional step he forgot
Or overlooked
wooden python
here's how i would lay the work out, in a "skip no steps" kinda way
one thing to note is that i deliberately delay any "complicated" fraction additions and am also extremely careful with signs and brackets.
shrewd trellis
here's how i would lay the work out, in a "skip no steps" kinda way
this is for me right?
wooden python
yes, it's for your question
would normally fall under !nosols but given you shared your work and we've established the fuckup is just arithmetic i think it is best shown rather than told how to do it better
shrewd trellis
here's how i would lay the work out, in a "skip no steps" kinda way
but in an exam or a test, its better to just let your calculator do the work
also Im a bit confused about this
unkempt lichen
i don't think you should get so used to the calculator you forget to show your steps
remember that showing your steps also allows you to cross-check yourself
wooden python
also Im a bit confused about this
is my handwriting unclear?
shrewd trellis
It is very clear but I dont get your point
wooden python
it is a good habit to write your polynomials with terms in a consistent order by degree
shrewd trellis
i don't think you should get so used to the calculator you forget to show your s...
Is this better?
wooden python
either low to high or high to low
unkempt lichen
this part was ok up to the last line, where you just chunked everything
wooden python
like would you rather hear someone say
twenty, five thousand, three and seven hundred
or
five thousand, seven hundred, and twenty-three
unkempt lichen
but i guess it's at the point where you can chunk it into the calculator so
shrewd trellis
like would you rather hear someone say
> twenty, five thousand, three and seven ...
2nd
wooden python
that's right.
so just as we arrange the components of a spoken-aloud number from big to small,
so too should you arrange terms in a polynomial from "big" (high degree) to "small" (low degree).
i must stress this isn't an absolute requirement and it won't by itself be a mistake if you don't do it
but i think it's better to stay organized when doing calculations.
amber veldt
it's like code hygiene, if you've come across that phrase in programming
odd edgeBOT
shrewd trellis
.reopen
odd edgeBOT
✅
shrewd trellis
wait
the reason why I did that was because there is a negative infront of the term
so woudnt it be considered more neater if it was to come later?
unkempt lichen
there's nothing wrong with the first term having a negative
in fact, it reveals the shape of a graph too
or at least, helps reveal it
viscid flint
i would consider -3x^2 + 2x + 7 to be more useful than 2x - 3x^2 + 7
shrewd trellis
i would consider -3x^2 + 2x + 7 to be more useful than 2x - 3x^2 + 7
thats true
wooden python
so woudnt it be considered more neater if it was to come later?
meh, "sort terms by degree" trumps "don't have a negative term leading" imo
viscid flint
négative numbers are just numbers imo
cerulean lynx
the reason why I did that was because there is a negative infront of the term
Nothing wrong with a negative term at the front
Makes it easier to understand really
shrewd trellis
I get it now, its much of an etiqquite and useful to do it in ascending order
unkempt lichen
I get it now, its much of an etiqquite and useful to do it in ascending order
etiquette*
less of an "etiquette" as i know the word, more of a useful habit
wooden python
yeah ig there is somewhat of an etiquette angle to it
unkempt lichen
ah nvm
wooden python
tho i would consider that secondary to organization
shrewd trellis
I mean its a goood idea to not force it, it might just be time consuming really
swapping this terms around when you can spend that time putting it in a calc
ocean bramble
it's not so much "etiquette" as it makes you make significantly less mistakes if you got them ordered
wooden python
yeah, as i said: organization.
ocean bramble
it's particularly useful if you need to do more steps with them later
wooden python
swapping this terms around when you can spend that time putting it in a calc
the idea is you'd only need to swap them before you even bothered with the double-substitution
cerulean lynx
swapping this terms around when you can spend that time putting it in a calc
I mean thats just computation, we are talking moreso for terms with variables
wooden python
ie the F(b)-F(a) thing
cerulean lynx
the idea is you'd only need to swap them _before_ you even bothered with the dou...
Yeah
shrewd trellis
I mean thats just computation, we are talking moreso for terms with variables
single terms like no fractions?
wooden python
you organize yourself from the get-go rather than only remembering it 19 steps deep in the shit
ocean bramble
swapping this terms around when you can spend that time putting it in a calc
honestly, most of the time a calculator is slower
unkempt lichen
swapping this terms around when you can spend that time putting it in a calc
you're talking about swapping the terms in the red step. we're talking about reordering the terms in the green step itself
where there's much less clutter
wooden python
where there's much less clutter
and that's also where i did the swap in my demo, too.
shrewd trellis
you're talking about swapping the terms in the red step. we're talking about reo...
yea I get Ann's point
ocean bramble
being organized in your calcs can speed it up a whole order of magnitude, you should ALWAYS put some effort into being tidy
shrewd trellis
I coudve did it earlier
ocean bramble
same with simplifications
hidden token
odd edgeBOT
hidden token
,rccw
clever fjordBOT
hidden token
I just don't know what to do
Btw, the hint is referring to a previous book which I do not have
nocturne brook
it could be useful to express the foci in terms of a and b
hidden token
Do you mean OQ and OR?
nocturne brook
I did mean Q and R as points, but since O is the origin, it's the same
kinda
I also wonder if there's something to do if you consider the point P, but rotated about the origin of the plane 180 degrees
hidden token
I just got something that may be important?
|PQ+PR| = 2|OP| => a^2 = x1^2 + y1^2
<@&286206848099549185>
golden sonnet
odd edgeBOT
@hidden token Has your question been resolved?
toxic rose
oh my bad
well here some thoughts. i think u have found the slope of the tangent passing through P already. then u can find the angle PF_2 and PF_1 make with x-axis. From there try to use those angles to express PF_1 and PF_2 and then use the definition of an ellipse (sum of pf_1 + pf_2 = constant, so maybe theres some differentiation shenanigans u can do here)
hidden token
Hmm
young ridge
u have 3 lines the tangent at p , pf1 and pf2 . we can get slopes of them . by finding angle made bt pf1 with tangent and equate to pf2 and tangent anf prove?
hidden token
Ok I will try these
young ridge
yeah get euations of pf1 and pf2
and then find slopes and use angle btw lines using slope formula that tan theta one
is it physics of mathematics what a good problem. i like applications like these
young ridge
Ok I will try these
worked?
hidden token
One sec
I got equation of PF2 as $$y = \tan (180 - \beta - \theta) x -\tan (180 - \beta -\theta)c$$
PF1 as $$y = \tan (\alpha - \theta)x + \tan (\alpha - \theta)c$$
clever fjordBOT
Sarin
hidden token
Now I find the angle between these?
Ok I got, find the angle between the slope of tangent and PF1 and slope of tangent line and PF2 and check if they are equal
Lemme try that
young ridge
Ok I got, find the angle between the slope of tangent and PF1 and slope of tange...
yeah
u done
hidden token
No not yet
odd edgeBOT
kind smelt
what i did f(x) = x^2(x^2 -1) + ax^2 + bx^2 + cx + d (by remainder theorem) put x = 1 4 = a + b + c + d which aint in the options lmao what did i do wrong
where did i go wrong
wooden python
!occupied
weary pelican
!occupied
odd edgeBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
proven comet
it is g(x)=ax^3 or ax^2
summer wave
what i did f(x) = x^2(x^2 -1) + ax^2 + bx^2 + cx + d (by remainder theorem) put ...
f(1) =3 no?
bleak dagger
odd edgeBOT
bleak dagger
I get that if the pivot falls into the middle half, then there are at least n/4-1 (rounded up) less than it or greater than it. I also get that after partitioning, the number of elements remaining in play will be at most n- n/4 (rounded up) elements. I don't get how tf it equals to 3n/4 rounded down
bleak dagger
I just realized something. If n is full, and we take away 1 quarter of it, then we're left with 3 quarters of it
.close
odd edgeBOT
Available help channel!
sage helm
In this case, what does the phrase "in lambda" means?
sage helm
quasi sparrow
In this case, what does the phrase "in lambda" means?
holding all else constant
for p = x + y^2, is a polynomial of degree 2 in y, but degree 1 polynomial in x
odd edgeBOT
odd edgeBOT
Available help channel!
vagrant talon
I am confused on the following
odd edgeBOT
I am confused on the following
ivory grove
,rotate
clever fjordBOT
ivory grove
I am confused on the following
do you need the numerical value or the algebraic one
vagrant talon
the measure of angle ABE
ivory grove
yes, in numbers? or in terms of n
vagrant talon
in numbers
ivory grove
then I don't think this is enough information—are there previous parts to the problem?
vagrant talon
nope
Thats what I was thinking because I was trying to use the angle addition postulate
but none of the angle postulates would apply to this instance
can you also help me with another problem too
It is from the same worksheet
ivory grove
can you also help me with another problem too
sure, but one at a time
are you sure there is no information about F? because the answer would vary depending on where it is
wait
vagrant talon
yea there is no information about f
vagrant talon
yes but I need to find the angle
by solving for n and then plugging that into 2n + 7
ivory grove
right, the numerical value. I forgot. so it can't be solved because there's no information on F
unless this picture is to scale
vagrant talon
This is the sheet
ivory grove
unless this picture is to scale
and the ray for F is the angle bisector of EBH
ivory grove
it looks like EBF = FBH
vagrant talon
and plus we cannot say that ray F is the angle bisctor of angle EBH without proof
ivory grove
yeah
vagrant talon
it looks like EBF = FBH
my teacher says we have to have proof in order to show that this is true
but yea
idk if there is another rule I can apply to check if any other angles are equal to eachother
I am only in unit 1
ivory grove
so therefore there is not enough information and you can't solve this. because if you move F a little bit to the right or left, the answer will change
clever fjordBOT
ivory grove
you know both the values of ABE and EBF; you also know that ABE+EBF=ABF so you can make an equation and solve for n
unless they're entirely different problems?
oh yeah it seems like they're different
vagrant talon
yea they are different
BUT
Ray BH still bisects angle EBC
I don't think there would be an answer for this question also
vagrant talon
Can we also go over num 41
vagrant talon
is that a valid response?
I am not sure
because my teacher's homework always has distinct answers
but I will look into it
I might send him an email
or ask during advisory
,rotate
clever fjordBOT
vagrant talon
number 41
ivory grove
number 41
this looks similar to the previous one, I'm not sure it has a solution either 
vagrant talon
this looks similar to the previous one, I'm not sure it has a solution either <:...
yea lol
bro we went over intensive content in class and most of the homework answers don't have answers 😭
TYSM tho
I appreciate the help astraea
have a good one!!!
ivory grove
you're welcome, you too!
odd edgeBOT
@vagrant talon Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
turbid wing
how do i get the probability of repeated chances ae (50% chance to output 2 and then a 10% ontop of that to output 4) would that just be 2^1*10^1 or whatever?
west light
You do multiply them, so 0.50 * 0.10.
More generally, P(AB) = P(A) P(B|A)
Where in your case, A = "output a 2 first" and B = "output a 4 second"
(Fixed a typo)
drifting parrot
<@&286206848099549185> hi can someone help me with my algebra? I js got into freshman year and i dont understand this (forgot how to do all of it and my teacher isnt helping) its simplifying and evaluating and i just dont understand the process of either
autumn cliff
<@&286206848099549185> hi can someone help me with my algebra? I js got into fre...
hey im in geo
vivid wyvern
!15m
odd edgeBOT
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.
autumn cliff
what do u need help with
drifting parrot
Simplifying 10x-8x+2+10 and then evaluating when x=2. I js need the process explained to me
autumn cliff
ok
so what would the first step be in this?
at least what do you think it would be
drifting parrot
Well my teacher said to first add up my variables or something
autumn cliff
ok
drifting parrot
Idk if its addition because of the -8x
autumn cliff
so lets combine both variables
its not add its combine
so, lets combine 10x and -8x
10-8=2
there is 2x left
correct?
drifting parrot
Yes
drifting parrot
12
drifting parrot
12 and 2x ?
drifting parrot
2x+12?
drifting parrot
2
soft terrace
drifting parrot
so to plug in the value of x, what would you plug in?
2 ??
autumn cliff
right so plug it in
drifting parrot
X=2 ?
autumn cliff
yes plug that into your equation 2x+12
drifting parrot
Okay give me sec
tidal matrix
I dont understand what u mean
Start with the equation: $$2x + 12$$ Put brackets around each $x:$ $$2(x) + 12$$ Replace each $x$ with the value you want, 2: $$2(2) + 12$$ I wanted to stress placing the brackets, otherwise things get wrong when you substitute negative numbers, for example
clever fjordBOT
haseeb
autumn cliff
yo help me with my prob haseeb
tidal matrix
yo help me with my prob haseeb
im thinkin about it, if i have any good ideas ill pop in 🫡
autumn cliff
alr thx
drifting parrot
Is the value supposed to be the same number i got for the equation
autumn cliff
yes
drifting parrot
? Idk if i did it rigt
drifting parrot
22
drifting parrot
3?
drifting parrot
So 22(3)+20
autumn cliff
yep
drifting parrot
86?
drifting parrot
HOORAY
autumn cliff
one more or do u think ur good
autumn cliff
alr gl
drifting parrot
Tyy
autumn cliff
dm me if u need anything
drifting parrot
Okay!
drifting parrot
.close
odd edgeBOT
drifting parrot
only OPs and Helpful+ can close channels
Sorry didnt know this
odd edgeBOT
Available help channel!
mystic saffron
How do I solve this? Problem 33, I tried to add up all the x and degrees to keep x on one side but it just doesn’t look right. Is there a method I have to use when it comes to triangles like this?
mystic saffron
vivid wyvern
How do I solve this? Problem 33, I tried to add up all the x and degrees to keep...
Sum of all three angles of a triangle=180
shrewd trellis
What did i do wrong
odd edgeBOT
What did i do wrong
shrewd trellis
shrewd trellis
i had to square it
unkempt lichen
think you copied the equation wrong in the first place
wooden python
also why did you write
sqrt(y) = sqrt(x-1)
at all
unkempt lichen
why is the y square rooted
amber schooner
clever fjordBOT
wooden python
the bounds are not the issue
the issue is that your integrand is/was completely wrong
your bounds were from 0 to 2 and that is actually correct, but you have to fix the algebra for isolating x in terms of y
have you done so already? yes or no.
fathom harness
Hello I’m a 16 year old currently learning calculus, however I realized when it comes to my algebra and trigonometry, and units that I haven’t touched on for a while, I need an example problem first to retrieve my memory and then instantly remember the material, however I wanna go to an understanding where Algebra and trigonometry are known to me like the back of the hand. What questions should I be asking or what ways of study should I channel into.
unkempt lichen
i don't get this question
odd edgeBOT
@fathom harness Has your question been resolved?
untold plume
Hi I’m new here, is there a specific channel to get help with statistics?
unkempt lichen
#probability-statistics #advanced-stats i suppose, or you can send your question here too
odd edgeBOT
@untold plume Has your question been resolved?
hushed acorn
I have no idea how to do this and I know it explains it but I’m just very confused is there any way someone could give me an example question like this so I can figure it out?
unkempt lichen
,rccw
clever fjordBOT
wise pilot
Let's say the line AB starts at (0,0) and ends at (10,10). What would be a point P so that AP:PB is 2:3?
Now suppose the line starts at (-1,-1) and ends at (9,9). What would be P then?
Now suppose A is (-2,-1). B is (8,9). Now what is P?
Do you see how the coordinates of A and B affect P?
hushed acorn
yeah but how do I find the coordinates of P?
shell haven
If AP:PB is a:b then AP:AB is a:a+b
sonic widget
If P splits a line AB with the ratio 3:4, then AP is 3 parts and PB is 4 parts. Now you have 7 segments. so AP is 3/7 of AB and PB is 4/7 of AB. Right?
hushed acorn
yeah
sonic widget
More general, if P spilts AB with ratio x:y AP is x : (x+y) and PB is y : (x+y)
or as a fraction AP is x/(x+y) of AB and PB is y/(x+y) of AB
This work for the horizontal distance (run) and vertical distance (rise) seperately.
hushed acorn
so for AP i would do 3:(-2 + (-1))?
sonic widget
No, here the ratio is 1:3, so AP is one part and AB are (1+3)=4 parts, so AP is 1/4 of AB.
hushed acorn
yeah
sonic widget
What is the horizontal distance between A and B?
hushed acorn
12 units
sonic widget
Waht is 1/4 of 12 units?
hushed acorn
3
sonic widget
Add this to the x-coordinate of A and you have the x-coordinate of P.
Same in y direction
hushed acorn
so
3 plus -5 = -2
for the X coordinate?
and then 3 + -1 = 2? for the y coordinate?
do i add anything to point B?
sonic widget
and then 3 + -1 = 2? for the y coordinate?
Np, the distance i the y-direction has to be calculated with the ratio again. It is not 3.
sonic widget
Yes.
sonic widget
correct.
hushed acorn
and the coordinates would be (-2, 1) for P
sonic widget
Yes. But be aware, that the directions matter. If for example B is on the left of A, you have to subtract the distance from the x-coordinate of A and so on.
sonic widget
No, it would be -5 - 3, start with the coordinate of A and then add or subtract the distances.
sonic widget
np
hushed acorn
could you stay for a minute so i can try the second problem myself?
just to make sure i fully understand
if thats okay?
ok thanks
ok
so
this one is like what you just told me
the letters are reversed
i messed up somewhere but do not know where
sonic widget
5/6 of 12 is not 15 and 5/6 of 6 is not 7.5
sonic widget
If you want to calculate 5/6 of 12, you can divide 12 by 6 and then multiply by 5.
sonic widget
Looks good.
hushed acorn
YAY
THANK YOU
IVE BEEN STRUGGLING WITH THIS STUPID PROBLEM FOR TWO HOURS
THANK YOU
I ACTUALLY GET IT NOW
odd edgeBOT
odd edgeBOT
Available help channel!
whole pendant
just doing revision of year 12 maths and im stuck on trying to find the answer for B
whole pendant
the mark scheme says its -360 but ive got -960 and i have no clue where i went wrong
my working out
ah wait nvm i onmly found the first 2 terms
i forgot about the 3rd x^2 term
.close
odd edgeBOT
odd edgeBOT
Available help channel!
agile ore
can anyone help me on this ? any number helps, dont need to do all T_T thanks
unkempt lichen
what have you tried and what do you understand about this problem?
agile ore
what have you tried and what do you understand about this problem?
tried and finished all a
i cant do b eeuueueu
unkempt lichen
how many people are there in total?
agile ore
how many people are there in total?
150
unkempt lichen
and what's 40% of that
unkempt lichen
and we want the top 60 people who spent the longest time
so where on the graph should we look?
agile ore
do i see the t of the 60 ppl
unkempt lichen
yeah, but how far up the y-axis should we look?
agile ore
what 💔
unkempt lichen
we want the 40% who spent longer than k minutes, not shorter
agile ore
hold on let me think 😭
agile ore
if we start from 60 and look up we'd get the top 90 people
ok tbf i dont know what that means
unkempt lichen
think of it this way
if you spend more than k minutes, you'd be above k on the graph
40% of such people are above k, and there's no upper limit, so we want the top 40%
and you worked out that 40% = 60 people
so you want the top 60 people
if you took y = 60, however
since we want those that spent longer than k minutes to be 40%, starting at y = 60 (and going up, or to the right) gives us a total of 150-60 = 90 people included
that's not what we want. that's the top 90. we want the top 60
unkempt lichen
did i miss a message? or did you stop at the "like"?
unkempt lichen
correct
agile ore
like from the graph
unkempt lichen
you count 60 from the top
that's what it means to be top 60 anyway
so what's the time at y = 90?
agile ore
6.8 or 6.9 ish ?
unkempt lichen
close enough
unkempt lichen
the gap is too obvious for me to call it 7
but i can't help but notice that it's a 3-mark question, so make sure you draw the lines that allowed you to get this value
just in case, if nothing else
agile ore
alright
our teacher js told us to assume the answer so i guess its around that much...?
unkempt lichen
well since you're given permission to estimate, take a shot at it
unkempt lichen
there's nothing much i can do for c)i) other than to tell you to look at the graph
it's pretty straightforward what they want you to do
there are several time intervals, and you are asked to find the number of people in each time interval
sounds to me you should probably start drawing some lines on the graph and doing some subtraction
agile ore
is it the same as finding its cumulative frequency ?
unkempt lichen
not exactly
this no longer has much to do with cumulative frequency
but you'll need the cumulative frequency graph shown there to get the number of people in each interval
hint: look at what the second interval is doing
the interval is $2 \leq t \leq 4$
clever fjordBOT
Hanako
agile ore
mhm
unkempt lichen
yet there are only 23 people listed - a fair few short of the 33 you see at t = 4
but you also see that the first interval has 10 people, exactly the number missing from the next interval up to get the value on the cumulative freq graph
that should be a pretty good hint what you need to do
clever fjordBOT
lyn
unkempt lichen
you don't need to subtract it from the first frequency
see, as the graph moves to the right, more people are included because the interval is getting larger. but these are cumulative
so if you know that, for instance, a total of 70 people took less than 6 minutes, but only 45 of them took less than 4 minutes (while maybe, say, 20 people took less than 2 minutes)
kindred pike
Anyone here was at the imo?
unkempt lichen
to find the number of people taking anywhere between 4 and 6 minutes, just take the number of people who took less than 6 minutes, and subtract the number of people who take less than 4 minutes
unkempt lichen
Anyone here was at the imo?
for chatting and stuff, you may head to #discussion, or #competition-math if you wish to ask about the IMO
this channel is currently occupied by a helpee
kindred pike
Aight mb im new srry
unkempt lichen
nps
unkempt lichen
correct
the same methodology applies for all subsequent intervals
this is what i meant when i said you needed to draw some lines and do some subtractions
agile ore
ohh
thank so much
😭
rlly helped
for the last one, do i find the mean from the frequencies i did b4
unkempt lichen
yes
unkempt lichen
don't throw me just the numbers - show how you got them too
and what are these anyway
unkempt lichen
i did not get 36 for the last one
the other two are correct
once i tell you the other two are correct, you probably don't even need the graph to find the last one
but use it anyway
agile ore
no cuz i only got it correct for 37
i have the answer sheet but im trying to figure out what i did wrong
unkempt lichen
40 is correct for the second blank
agile ore
im thinking that the second one was like 110 - 70 = 40
unkempt lichen
if you are told it's wrong, show the answer
agile ore
answer key
unkempt lichen
then i must be damn blind
i got 40 and 25 for the last two blanks
this is why you draw lines on the graph
so that you show you did not just randomly eyeball stuff
if i were the one doing i'd stick with 40 and 25
but your 36 is way out
agile ore
nah vro cuz ts is like printed later on our exan i cant js draw lines i would turn the whole graph black 💔
unkempt lichen
??
agile ore
yea
unkempt lichen
have you heard of dotted lines?
agile ore
i triedd
unkempt lichen
ok if you say drawing lines turns the whole graph black
what if i can do it while keeping the graph easy to read?
unkempt lichen
unkempt lichen
i printed ts thing
i can do the same with a 0.5mm ballpoint pen
and let's be honest, it's the last subsection of the question
i don't mind getting the graph a little dirty
more importantly i'm showing my work on the graph
agile ore
thats true
unkempt lichen
ok wait i also got 40 and 25
tbh if i were you i'd just draw the lines on the graph, circle the 110 point, and call it a day
if anyone else asks, point to the graph
agile ore
tbh if i were you i'd just draw the lines on the graph, circle the 110 point, an...
ok same my eyes hurts looking at ts thing 💔
okay, i think im done
thank you so much, im sorry for my stupid ahh 😭
have a nice day/night ! @unkempt lichen
.close
odd edgeBOT
odd edgeBOT
Available help channel!
somber river
odd edgeBOT
shut nymph
Do you have any ideas so far?
shut nymph
the two equations are pretty similar right?
and whats annoying is the exponent for each one, can you try to combine them to try to simplify?
somber river
yaaa...... ig
shut nymph
you know how exponents work right? like for example 1/x = x^(-1) and stuff like that
somber river
so i got
x+y )^y =2
so Ig x+y =2 , and y = 1 is one soltuion
And ig x=1
ohhh well one of the solutions is 2
what about others
shut nymph
you need to essentially find x+y in all cases
somber river
I mean there may some other values of x and y that satisfy
somber river
x+y)^y)/2=1?
shut nymph
you know how exponents work right? like for example 1/x = x^(-1) and stuff like ...
as I said here
somber river
ok..... where are ya going witht htis
shut nymph
what you want to do is have everything with the same exponent
that way it is easier to work
so you would like to have ((x+y) * 2) ^ something
and you can get that by combining both equations in a certain way
somber river
What.......
shut nymph
and im trying to guide you to find how
somber river
and im trying to guide you to find how
Wow your thought is amazing
so should I do the same witht hte other eaution
shut nymph
no because the 2 is already on the left
you are trying to make them similar in a sense
shut nymph
thats not right
somber river
I mean (X+Y)/2}^X-Y+1 =1
somber river
I basically multiplied both equations
shut nymph
yes
somber river
X-Y+1 should be zero no?
shut nymph
no
somber river
cause anything to the power zero =1?
shut nymph
why should it?
shut nymph
cause anything to the power zero =1?
that is true
somber river
ig that is one case
shut nymph
you are almost there tho
somber river
hmmm
shut nymph
what other thing could give you 1
shut nymph
yes
shut nymph
:)
somber river
.close
odd edgeBOT
odd edgeBOT
Available help channel!
vagrant talon
Hi
vagrant talon
do you guys have any tips on doing geometry questions quick
because today we had a quiz and it was 5 questions and we have 6 minutes
I got like 2 wrong but my teacher is giving us 100s because we didn’t have enough time
do you guys know what I should in these instances
shut nymph
List out what you know, and try to find which theorems could be useful, (like if you have a right angle then think about pythagoras), then think about what would help you get what you want and try to get to that
those are just some general tips
vagrant talon
like bro I study a lot and stuff but when I did that quiz It all fell out
odd edgeBOT
@vagrant talon Has your question been resolved?
fluid stratus
how do i explain part c? the targets inbtwn the confidence thing n im out of chatgpt uses💔💔
fluid stratus
odd edgeBOT
@fluid stratus Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
frozen musk
how would I graph r=5-4cos(theta)?
odd edgeBOT
how would I graph r=5-4cos(theta)?
frozen musk
I converted to cartesian and got x^2 + y^2 + 4x = 5sqrt(x^2 + y^2)
idk if I was supposed to do that tho
strange aspen
I converted to cartesian and got x^2 + y^2 + 4x = 5sqrt(x^2 + y^2)
you could've multiplied first by r then converted
wait
carmine idol
how would I graph r=5-4cos(theta)?
One way: Plot points then connect the curve
frozen musk
One way: Plot points then connect the curve
how?
I think I need to plot (theta,y)
but making that cartesian into y= format seems really hard
well actually
yeah idk
strange aspen
how?
use some known cosine values cosine of 0 pi/6 pi/4 pi/3 pi/2
then you could find the r with each
bronze citrus
how would I graph r=5-4cos(theta)?
geogebra
frozen musk
use some known cosine values cosine of 0 pi/6 pi/4 pi/3 pi/2
then you could fi...
oh, so plug those into the r=5-4cos(theta) for theta?
okay so for example r=1 for theta=0
how do I use that 1?
strange aspen
how do I use that 1?
one is the radius from the origin remember
you plot the polar point (1,0)
strange aspen
what if I wanted to draw the cartesian graph?
go for it but is it really worth it considering you have to know the change of 2 variables at the same time to plot each point ?
frozen musk
go for it but is it really worth it considering you have to know the change of 2...
yeah, it's not
carmine idol
how?
Plug in a value for theta, then use that to compute r. Choose nice angles like 0, pi/3, pi/2...
Then figure out what the corresponding x, y coordinates are
strange aspen
yeah, it's not
for some cases yeah it's beneficial to know that the cartesian graph of a polar equation is some kind of conic sections which are easy to find directly in cartesian
frozen musk
Plug in a value for theta, then use that to compute r. Choose nice angles like 0...
figure out corresponding x and y coordinates via unit circle right? so for r=1 when plugging in theta=0 means the (x,y) is (1,0)?
strange aspen
figure out corresponding x and y coordinates via unit circle right? so for r=1 w...
you could do that but i think plotting in polar coords directly is not that hard to do
carmine idol
Yeah, or you can just plug into the formulas x=r cos theta (and for y)
frozen musk
for some cases yeah it's beneficial to know that the cartesian graph of a polar ...
right
frozen musk
yeah idk my prof likes to ask cartesian for whatever reason
carmine idol
Then you can just set your ruler at angle theta and figure how far from origin to draw
frozen musk
If your x and y have the same scale
wdym same scale?
carmine idol
wdym same scale?
Assuming (1,0) and (0,1) are physically the same distance from (0,0)
frozen musk
ah, I see
carmine idol
If they are of different distances then you can get into... some issues
frozen musk
right lol
is it worth memorizing the patterns for stuff like this
like for example r=10+20sin(theta) you know it'll open upwards. the mini circle will be max at y=10. and the max in general wil be 10+20=30
I have an exam in a couple hours on this so idk
carmine idol
is it worth memorizing the patterns for stuff like this
Usually not unless...
- Your teacher asked you to memorize
- You like these patterns so much that you want to be able to plot them quickly
- Some other similarly convincing reason
frozen musk
hmmm
yeah my prof doesn't rlly care
it's more about me wanting to make sure I do things correct
to check my work
carmine idol
As long as you stick to basics of "plot points you know how to plot" you can sketch the curve from that
frozen musk
okay cool, I'll worry more about understanding how to plot then
tysm for the help
.close
odd edgeBOT
odd edgeBOT
Available help channel!
keen scroll
i was wondering if theres a trick to dis or u just raw dawg it
keen scroll
if there is a trick - my nuts tell me it has something to do with ze prime factors or something
stable sequoia
not really, just find the largest possible square thats a divisor
stable sequoia
i mean, it's not that hard
keen scroll
ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssigma okay
.close
odd edgeBOT
keen scroll
ty @stable sequoia
stable sequoia
its not that hard if you focus on what you need
unkempt lichen
if there is a trick - my nuts tell me it has something to do with ze prime fact...
this would be a good way to find larger square divisors
but for smaller ones, just factor the numbers
keen scroll
yeeeeeeeeeeeeeeee
goitta lock in
i have a test day afte tmrw
shit lookde easy in class os i didnt study anyting
keen scroll
havent made this mistake in years....
upper bound lowre bound
indicies surds
standard form
hcf lcm
sets and venn diagrams
sequences
wish me luck
unkempt lichen
glgl
keen scroll
google maths solver hard carry
visual delta
what do you guys know about circle theorems
warped glacier
what do you guys know about circle theorems
do you need help with a circle theorems question
visual delta
do you need help with a circle theorems question
just circle theorems in general
odd edgeBOT
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
odd edgeBOT
Available help channel!
sweet venture
how to tell if an equation is linear?
odd edgeBOT
how to tell if an equation is linear?
strange aspen
how to tell if an equation is linear?
if it's in the form y=mx+b where m and b are real numbers
(there are some other forms that lead to the same equation)
sweet venture
so what does it mean if the graph shows a “U” type line
unkempt lichen
then it's not linear
but it's also unclear what degree it is, other than the fact that it's an even degree
tacit wasp
!xyproblem
odd edgeBOT
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.
@sweet venture Has your question been resolved?
vernal yacht
Type your questions here
odd edgeBOT
**Type your questions here**
vernal yacht
For demonstration, no questions here
wanton bison
Why did you open?
odd edgeBOT
solar peak
**Type your questions here**
hello swami ji
odd edgeBOT
Available help channel!
somber river
Hello
somber river
I am heere to ask for a proof
bronze citrus
wich
wooden python
!da2a
odd edgeBOT
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/
somber river
wooden python
,rccw
clever fjordBOT
somber river
Just wanna know the proof
I fiddled around with this shit
and got this
but how are they equal
clever fjordBOT
wooden python
so we are looking for the greatest integer $m$ such that $p\equiv q \equiv r \pmod{m}$?
clever fjordBOT
Ann
somber river
Ya
wooden python
well by the defn of modular congruence any such m will need to divide p-q, q-r and r-p 
somber river
Wth
wooden python
p ≡ q (mod m) means m divides p-q, yes?
somber river
yA
wooden python
same logic two more times
somber river
What.........
hmm
Well how will ya explain this when ya the student doesn't know
ehhhh modular arithmatic
properties
And another question ........ does it need to be in that order
P-Q , Q-R, R-P?
Why not P-R , Q-R , and R-Q?
odd edgeBOT
@somber river Has your question been resolved?
somber river
NO
midnight smelt
I'll butt in
the question asks to show that if m is the greatest int satisfying the system of congruences, then m is also the gcd of p-q, q-r, r-p
the order doesn't matter since you can show if it divides the three differences above then it also divides p-r, q-r, r-q
to show that m is the gcd, start with an arbitrary divisor of p-q, q-r, r-p and call it d
then d is also a solution to the system of congruences (and hence d is less than m since m is the largest solution by definition)
so we've shown that if d is a divisor, then it is less than or equal to m
therefore m is the gcd
odd edgeBOT
midnight smelt
(Actually I think I misread the question. It asks to show that you can find the largest solution to the system of congruences by finding the gcd of the differences)
The proof is similar though
If m is the gcd of the absolute values of p-q, q-r, r-p then it also divides the non-absolute values
so m is a solution to the system of congruences
if d is also a solution then d divides p-q, q-r, r-p
so d is less than or equal to m since m is the gcd of the three
thus any solution d is at most m, and therefore m is the largest solution
odd edgeBOT
Available help channel!
lone elbow
odd edgeBOT
jagged maple
what does "hallar" mean?
lone elbow
find
void yew
Determine whether the following functions are injective, subjective, or bijective. Find the inverse for the bijective functions. For the nonsurjective functions, find the image.
lone elbow
bioactive 
void yew
lol
jagged maple
for i), f is neither injective nor surjective: there's no x such that f(x) = -10, and f(-1) = f(1) = 7
ii), f is only surjective: for all z, there exists some real numbers x+y such that z=x+y. f isn't injective because you have f(1,0) = f(0,1) = 1
void yew
I should add for iv) "par" means even and "impar" means uneven
jagged maple
iii) for the same reason as to ii), f is only surjective