huh
#help-27
solid osprey
supple knot
like you did here
deep elbow
d-1
10(c-1)
100(b-1)
1000(a-1)
These are all the same in mod 7
d-1
3(c-1)
2(b-1)
6(a-1)
These are all the same in mod 7
solid osprey
ab0d+10 mod 7=0
ab0d+3 mod 7=0
ab0d mod 7=4
supple knot
oh duh yes
placid minnow
yep 5694 is the largest 4 digit thingy
solid osprey
like you did here
abc0+1 mod 7=0
abc0 mod 7=6
placid minnow
def largest_divisible_number():
# Start from the largest 4-digit number
for num in range(9999, 0, -1):
# Convert the number to a string to easily replace digits
num_str = str(num)
# Check if replacing any digit with 1 makes the number divisible by 7
count = 0
for i in range(4):
# Replace the digit at position i with 1
new_num_str = num_str[:i] + '1' + num_str[i+1:]
new_num = int(new_num_str)
# Check if the new number is divisible by 7
if new_num % 7 == 0:
count += 1
if count == 4:
return num
print(largest_divisible_number())
we need proof tho, you cant try all the numbers like the computer
placid minnow
unless i misunderstood the problem again
dense lynx
unnecessary
this is a past problem from a mathematics competition and solutions are posted online
placid minnow
we need proof tho, you cant try all the numbers like the computer
i mean its more efficient this way since we're given such a small window of numbers this is way faster
solid osprey
this is a past problem from a mathematics competition and solutions are posted o...
hi mqnic did you get the same when you helped copter?
dense lynx
hi mqnic did you get the same when you helped copter?
the same answer? 5694 is correct
placid minnow
told ya
solid osprey
alr thanks
solid osprey
this is a past problem from a mathematics competition and solutions are posted o...
what competition is this?
dense lynx
what competition is this?
2024 AIME II #7
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floral sequoia
njuv h\\
placid minnow
what
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@restive river Has your question been resolved?
signal shore
hey sorry but I haven´t seen that yet I only know rn like basics
dusty pier
what are we trying to find
dusty pier
i see M but not K
signal shore
ok
like at the center?
yea
ok
what was the lenght of bc?
ok
ac or ab?
ok
m is in th middle if I know
ok
the same length of bc is the length of nc
like 4
what do you mean bye "prove it in english"?
by*
english is not ur main asccsent?
wich one?
ok I don´t know it
may I know what is the lenght of b and d
?
ok
yes
my pointer is moving a los
lot*
I can´t move it right
the pointer
I´m doing the thing u asked
and I can´t do it well
it suddenly just went crazy the pointer
wait
wait
look at the pointer
wait
it dosen´t sems to capt it
yes
sorry
sorry
but you don´t know the length of bd?
ok
if I´m right
the lenght of mk looks the same as am or bm
look at the picture and see it well
ok
I understand
ok
so
I only can see the thing of mk=am=bm
but
with the aproval
I think that would be on ur own if it´s ok
if not I will see hoe to help u
how*
I think I know someone
just let me ask him
ok
wait a minute
ok he dosen´twant to help me
but there is another person
if not I´m gonna see how to help you ok
I want you to sleep
o god
oh*
shit
ok
he is helping
ok he is not good at math i´m asking someone else
ok
so he no good to
so
u said u need an explication and prove it
like explicate ur answere
ok
sorry for not helping well
I´m actually in 1st grade
ok
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late root
I need help with my physic question
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I need help with my physic question
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/
late root
late root
i dont understand your question
lunar harbor
What can you discern from that
Hint: ||think of acceleration|| and then ||Newton’s second law||
late root
f=ma
if the object is moving in a constant speed, that means the normal force=weight, right?
thus, Fy=n=mg (?)
lunar harbor
if the object is moving in a constant speed, that means the normal force=weight,...
What’s the acceleration if speed is constant
late root
im sorry, im asking for question a)
we have to find the coeffecient of kinetic friction,
lunar harbor
I’m getting there
lunar harbor
What’s the acceleration if speed is constant
Until you figure this out, you kinda can’t do anything
lunar harbor
Until you figure this out, you kinda can’t do anything
Since you’re not engaging with my attempt to guide you, I don’t think it’s worth it for me to engage in this conversation anymore. I’ll pass the torch with someone else to help with this.
late root
i dont get it bro
like what do u want me to do
u just wanted me to find acceleration to a question that says speed is constant ??
how can i find acceleration when speed is constant?
Oh please don't leave me...I really need help on this question
Can u just explain to me about the forces on the y-axis
Why is it fn-1000-300sin20 ? When fn=mg,? So that means Fy=mg (?)
<@&286206848099549185>
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robust phoenix
Going over first weeks hw and I’m confused on where to start we’re supposed to do every other odd numbered question
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Going over first weeks hw and I’m confused on where to start we’re supposed to d...
placid minnow
Going over first weeks hw and I’m confused on where to start we’re supposed to d...
is there a specific question you want to start with cause they all kinda encompass different things
or ask for* not encompass
robust phoenix
yes im on number nine
placid minnow
alright what dont you get?
robust phoenix
just the way to start it ive never been particularly great with math , if a voice call is easier for you we can do that aswell
placid minnow
I dont have a mic lol
robust phoenix
oof its okay
placid minnow
anyways what you always want to do with these problems is isolate x
meaning get x by itself
youre looking at 2x + 5 = - 17 right?
robust phoenix
yes
placid minnow
you always want to have no operations on x
you usually want to start this in the order opposite of PEMDAS
so in this case what is the lowest operation being done on the side that x is on?
robust phoenix
5 ?
placid minnow
yep, it is adding 5
so to isolate x you want to get rid of that
and to get rid of that you can move it to the other side of the equation
to do this what operation will you do to both sides of the equation? (Hint: it is the opposite of what you just said)
robust phoenix
Like literally?
placid minnow
well right now you have:
2x + 5 = -17
You want to get rid of the +5
to do this you want to do the opposite of +5 on both sides
which in this case is -5
so if you subtract 5 from both sides of the equation:
2x + 5 - 5 = -17 - 5
The +5 and the -5 cancel out to 0, and the right side is -17 -5 which is -22
so you are then left with:
2x = -22
Now what is the operation that is being done on x?
robust phoenix
so we are going to add 22 to the other side ?
empty inlet
No
flat stratus
*u want to isolate x
placid minnow
We are trying to get x by itself
flat stratus
*make the equation into x = something
placid minnow
what is the operation being done on the variable "x"
flat stratus
u mean '2x'
placid minnow
there are no operations being done on 2x, there is, however, an operation being done on x
placid minnow
so we are going to add 22 to the other side ?
alright if you want I can get on my phone and call you if thats easier
placid minnow
taking a while longer than i thought
robust phoenix
alright if you want I can get on my phone and call you if thats easier
yea that might work better
placid minnow
yea that might work better
dms
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jolly nebula
i would like for someone to give me a hand walking through some homework for my buisness and social science math class. I have just started the year and i am learning virtually and ive lost my footing in the book and cant really get a grasp from where to start, some help would be appreciated but really i just dont understand the question i am being asked. Thanks in advance!
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i would like for someone to give me a hand walking through some homework for my ...
torn vessel
what question
jolly nebula
the question says "List the degree of the given polynomial, its coefficients, and its constant term. " 6.8x^4 -5x^3+6x^2-5x+6.6
are we able to meet in a call so you could walk me through your process or is it just on basis of text ?
torn vessel
text
degree is just the highest exponent of a polynomial
so the degree of x^5+3x^3+2x is 5, because x is raised to the fifth
jolly nebula
so the degree in this case would be 4? or would the degree be 6.8x because its raised to the fourth power ?
jolly nebula
ok so the degree is always an exponent got it
torn vessel
it's under algebra right
jolly nebula
would it fall into pre calculus or college algebra?
jolly nebula
it's under algebra right
thats the problem lol i have access to two books and i dont see a clear answer
torn vessel
precalc
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torn vessel
thanks again !
np!
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abstract sonnet
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severe sparrow
can someone explain how it's 4??
what points do you count on it?
abstract sonnet
what points do you count on it?
wdym
severe sparrow
what points do you see on the semi circle?
abstract sonnet
like the ones on the semicircle?
severe sparrow
yes
abstract sonnet
what points do you see on the semi circle?
tbh in the beginning i thought it was 7
i was counting K C S N P Q and R
severe sparrow
can someone explain how it's 4??
also i don't think it's 4?
i guess the question is only considering the arc KQN
viral cloud
In January 20204, a brand-new smartphone was unveiled, with an initial price tag of $5,000.00 It is anticipated that the cost of the cellphone will decrease to 4, 512.50 in 2026 after depreciating to just 4, 750.00 in 2025. How much would a cellphone cost in 20 years if its depreciation keeps up at current rate?
severe sparrow
which is kinda stupid
severe sparrow
In January 20204, a brand-new smartphone was unveiled, with an initial price tag...
post your question in an avaiable channel, this one is occupied
abstract sonnet
i guess the question is only considering the arc KQN
if they were asking for the semicircle then
what would be the answer?
abstract sonnet
i believe just K C S N Q R so 6
so P wouldn't count?
severe sparrow
no
cold ledge
hi
abstract sonnet
.close
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cold ledge
all the servers that i go no one helps😒
cold ledge
ohhhhhhhhhhhhhhhhh
severe sparrow
all the servers that i go no one helps😒
also "hi" isn't suggestive of needing help
just saying
cold ledge
also "hi" isn't suggestive of needing help
k
quaint citrus
Its all good bro I forgive u
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dusk granite
hello, firstly i want to state that this is a problem from a mathematical modelling competition i join, it was not prohibited for me to discuss the problem with others, as long as the journal for the model was made by me only. So i want yall opinion where to start to think what kind of model i need to make for the problem, here's the problem
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hello, firstly i want to state that this is a problem from a mathematical modell...
dusk granite
here's the data they give me, there is 3 data, from Company X, Y and the individual
i kind of confuse where to start, like how to approach the problem
one of the thing that confuses me the most, is the column t in the excel, it was in terms day right?
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dusk granite
ooh
okay wait a minute
for the data, there's so many so, let me just ss a little bit
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cunning lily
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cunning lily
idk what comes after this
cold bone
Both degrees and radians☠️
definition of "cursed"
faint gorge
idk what comes after this
,rccw
woven radishBOT
faint gorge
tf
cunning lily
Both degrees and radians☠️
definition of "cursed"
so is it doable
faint gorge
two tangents
cold bone
can't distribtute tangent function like that
cold bone
so is it doable
of-course
faint gorge
tangent not log
cunning lily
oh
cold bone
tangent not log
even log can't☠️
chrome isle
cold bone
either way to avoid any further confusions you should find the Range of x in degrees
chrome isle
even log can't☠️
Linear
faint gorge
20° = π/9
faint gorge
let's better work with degrees
What about 3x
chrome isle
tan(3x-20) = -√3
faint gorge
Maybe it's 20⁰ = 1 😂
cunning lily
either way to avoid any further confusions you should find the Range of x in deg...
0 < x < 180° like that? (whats range cuz english not my first languange)
cold bone
0 < x < 180° like that? (whats range cuz english not my first languange)
yeah exactly
(english is my 3rd language btw)
cunning lily
yeah exactly
(english is my 3rd language btw)
yea ur lot smarter than me
cunning lily
tan(3x-20) = -√3
where does that come from
cold bone
yea ur lot smarter than me
ofcourse not
cold bone
where does that come from
re-arranging the equation
chrome isle
tan(3x-20) = -√3
tan(3x-20) = tan(2pi/3)
Use the gen formula
tan(a) = tan(b)
a = npi + b
faint gorge
tan(3x-20) = -√3
Shouldnt it be -3/sqrt(3) ?
cold bone
but it's incorrect kinda
chrome isle
Shouldnt it be -3/sqrt(3) ?
Ohh fck mb
Yea do the rearrangement
And use the gen sol formula
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chrome isle
Yup now use the condition given to u for x
cunning lily
Yup now use the condition given to u for x
oh so just ignore it?
cunning lily
is it good to go
cunning lily
Mb it's now not no
look look
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hidden pier
quick question what did i do wrong here
devout snowBOT
quick question what did i do wrong here
hidden pier
show your work
its all in my noggin
winter patrol
do the work on paper, not your head
hidden pier
how do u calculate these type of problems
hidden pier
the process you applied to get `x-2`
it looks like y=x down 2
hidden pier
how do I do that
winter patrol
use a point on your line to determine the value of b
hidden pier
how though
its not intercepting any y
oh i just realized what you mean
you want me to plug in let say 3,3 and solve for b
ok
ok i got -3
what do i do with d y intercept though
would it be x - 3
cause its x down to d y intercept
winter patrol
you now have the value of b
hidden pier
oh poop
winter patrol
y = 2/1x +b
replace the b with that value
and you'll have your equation
(simplify that 2/1 too)
chrome isle
is it good to go
Yea it's good but use the fact given to u in the ques that x lies between 0 and pi and find all values of x that satisfy
winter patrol
y = 2 -3
where's that coming from?
what happened to the x
hidden pier
y= 2x-3
winter patrol
yes
hidden pier
is the answer to that 2x-3
winter patrol
yes
hidden pier
i cant check if its right so are u 100 percent sure
winter patrol
yes
winter patrol
no
winter patrol
that's what you want your domain to be
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manic pawn
not a question per se but like how would you think of something like this? i was trying to guess the proof myself before reading it but i would’ve never come up with something like this myself. in what scenario would it be good to use this repeated bisection method?
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not a question per se but like how would you think of something like this? i was...
manic pawn
its alot easier for me to understand a proof if it’s something i could come up with myself hence why im asking lol
https://en.m.wikipedia.org/wiki/Bisection_method hmmm this doesn’t really answer my q but there is a wiki page on it
so i guess it works here because you know its between the set A and the set of upper bounds of A but dont know where
this method is also used in bolzano-weierstrass so clearly it’s something worth knowing when to use
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wicked rover
not my channel, im answering @manic pawn
devout snowBOT
not my channel, im answering <@1192550094776569987>
wicked rover
the proof strategy is to "home in on" a certain point, in this case the supremum, and we do that via sequences increasing from below and decreasing from above
thats what bisection essentially is
so whenever you have the task of "homing in on" certain points, a famous example being roots of a function, a less famous one being a subsequence limit in bolzano weierstrass, you should think of bisection
heavy current
runic prawn
so whenever you have the task of "homing in on" certain points, a famous example...
*hone not home
wicked rover
*hone not home
ive seen both used but i believe in home as in homing missile
runic prawn
yeah actually home seems more correct
manic pawn
the proof strategy is to "home in on" a certain point, in this case the supremum...
uhhh alright thanks
there’s sm random tricks in analysis icl
half of which id never think of on my own
this is y algebra better lowkey
wicked rover
not sure if this helps explain the motivation any more but
manic pawn
yeah no it helps thanks
wicked rover
if you only construct the increasing u_n then you might overshoot the supremum
so you need a decreasing v_n to keep u_n bounded, then the monotone property applies
manic pawn
@wicked rover how would u think to use this for bolzano-weierstrass tho
like that seems so random cause ur not honing in on anything
ok i guess you are but i still would not have thought to use that
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wicked rover
<@150414892225134592> how would u think to use this for bolzano-weierstrass tho
maybe the phrasing isnt great
for bolzano weierstrass the end goal is find a subsequence limit but we should really think of bisecting according to which subinterval has infinitely many sequence members
yeah if you frame it that way you get a subsequence in nested intervals which are shrinking to zero width
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wicked rover
.reopen
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manic pawn
for bolzano weierstrass the end goal is find a subsequence limit but we should r...
makes sense thanks
wicked rover
np glad this helped!
opaque wadi
Show that $x_1, \ldots, x_n > 0$ and $n \in \mathbb{N}^*, \sum_{k=1}^nx_k \cdot \sum_{k=1}^n \dfrac{1}{x_k} \ge n^2$ using $\dfrac{x}{y}+\dfrac{y}{x} \ge 2$
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Show that $x_1, \ldots, x_n > 0$ and $n \in \mathbb{N}^*, \sum_{k=1}^nx_k \cdot ...
static ember
I don't really get the summation, what do the dots do?
opaque wadi
sorry
woven radishBOT
Akti
opaque wadi
that should be better
supple knot
Did you try induction
static ember
yes
opaque wadi
I was hoping for direct proof
static ember
I can at least confirm it works
multiplying it out directly will work out too though
static ember
can you write this product as a single sum?
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opaque wadi
can you write this product as a single sum?
Yes, with double sum
static ember
needs to be a single sum
serene steeple
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serene steeple
can someone please help explain the soluiton
why do we use maximum likelihood estimators for this
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solid osprey
how do i find the minimum of a quartic equation?
devout snowBOT
how do i find the minimum of a quartic equation?
solid hull
I mean you could do derivation
find turning points and then use second derivative to find minimum
solid osprey
how does second derivative find the minimum
solid hull
concavity
if second derivative is above 0 it indicates that the rate of change is increasing so it's a local minimum
and then vice versa
if = 0 it could be a stationary point of inflection
solid osprey
say the quartic equation is like x^4-8x^3-45x^2/2+162x-20
solid hull
first is to take derivative then find when rate of change = 0 (indicates point of inflection) and then you can either graph or find second derivative
solid hull
say the quartic equation is like x^4-8x^3-45x^2/2+162x-20
take the derivative and find when f'(x) = 0
solid osprey
derivatice is 4x^3-24x^2-45x+162
mighty skiff
couldn't you also find zeros of the derivative and plug them into the quartic and see which one is smallest
solid hull
derivatice is 4x^3-24x^2-45x+162
find where f'(x) = 0
solid hull
second derivative also works though
note that the quartic must be +ve otherwise it will go off to infinity
solid osprey
umm
solid hull
couldn't you also find zeros of the derivative and plug them into the quartic an...
Alternatively as this person mentioned you can also find f'(x) = 0 and then just substitute each value in
solid osprey
note that the quartic must be +ve otherwise it will go off to infinity
what is +ve?
solid hull
what is +ve?
positive
solid hull
umm
now you know the locations of the Points of inflection you can then take the second derivative and substitute these values in. If the value is over 0 it will be a local min and if it is <0 it will be a locaal max
solid osprey
second derivative is 12x^2-48x-45
x1 is local max, x2 is local min, x3 is local max
huh
shouldnt there be a local max and 2 mins?
oh nvm im dum
.close thanks
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solid osprey
.reopen
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solid osprey
wait that means theres 2 local mins, which one is the global min?
mighty skiff
whichever one is smallest
wooden wraith
Once you find the values for x that produce local mins, just plug them in and see which is the least
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restive river
In a continuous arithmetic proportion, the first and third terms are in the ratio of 5 to 4, respectively. If the extremes add up to 320, calculate the third differential.
A) 120
B) 110
C) 88
D) 40
E) 150
a - b = b - c
b = 160
c = 1280/9
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In a continuous arithmetic proportion, the first and third terms are in the rati...
@restive river Has your question been resolved?
fossil token
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faint zinc
You need to use the first step, that the triangles are similar. Then use the standard formula for the area of a triangle with base = BC and height = AD @fossil token
Hint: ||if the triangles are similar, what can we say about AD/AC? What other ratio is this equal to?||
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serene steeple
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https://media.discordapp.net/attachments/903430335474331698/1279649945091051542/...
serene steeple
can i get some help with (d) please
jovial surge
!status
devout snowBOT
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
shouldnt it be X (formerly Twitter)
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serene steeple
shouldnt it be X (formerly Twitter)
just don't get what to do
not sure what is the best to start
did U= X^2, V = Y^2
but after that not sure what to do next
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light niche
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light niche
what do i equate as u?
north roost
a^2 - r^2
light niche
hmm i see
light niche
then what will be the bounds of integration?
lunar kiln
that depends on what u sub
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lime star
How does this, translate to this
devout snowBOT
How does this, translate to this
lime star
can anyone explain
faint gorge
How does this, translate to this
Try to group and find common terms in the numerator in order to factorize
vague frigate
How does this, translate to this
9 - x can be written as 3sq. - sq. root x sq
and factorise the numerator
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hollow shoal
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winter patrol
can you show your work?
agile wraith
be careful of signs
hollow shoal
There is no work to show, you just follow the graph for this
agile wraith
and how the limit works
winter patrol
show how you're folloing the graph / which part of the graph you're looking at /reading
that's the work
hollow shoal
and how the limit works
I am reviewing my notes, and an example similar to this shows different answers and now I am super confused.
One shows DNE and the other shows an actual value
One second let me photograph the notes, maybe the professor did something wrong
agile wraith
try finding the limit from the left and right
using the fact that lim f(x)-g(x) = lim f(x) - lim g(x) what’s the limit from the left and right
hollow shoal
So if I am reading this correctly then,
a is not DNE because there is no jump, just a hole that with the fill-in directly above? at f(x)?
but b is DNE because of the jump at g(x)
agile wraith
not nessicarily
just consider the limit from the left and right and send your results
hollow shoal
I'm just going to write in DNE
Looks like that was the case.
If the function continues from left/right at that area unimpeded it still keeps that as the limit but if left/right has some sort of jump like in g(x) then it's DNE at that point of the jump
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sly marlin
hi, im computing limits, no calculator or lhospital
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hi, im computing limits, no calculator or lhospital
sly marlin
i tried expanding and got (cos/sin)(1/sin) which i split into (cosx)(1/sin^2x) or cos(x)csc^2(x)
can't seem to find out how to get rid of the sin from the denominator to not get 0
glossy dew
hidden notch
Yk the identity sin x/x =1 when limit tends to 0
placid minnow
hi, im computing limits, no calculator or lhospital
Simply evaluate the left and right hand limits
sly marlin
o
placid minnow
aka as theta approaches a little under or a little over pi
hidden notch
aka as theta approaches a little under or a little over pi
Can't he just multiply numerator and denominator by x² and call x²/sin²x =1?
hidden notch
Why?
winter patrol
the limit in question is for t→pi, not 0
placid minnow
^
hidden notch
Sin(pi) is 0 no?
We can use it as long as sinx/x is making indeterminate form as far as I've heard
winter patrol
yeh, but is sin(x)/x indeterminate when x=pi?
hidden notch
Ohhh im dum
sly marlin
mm i plugged in 5pi/6 and 7pi/6 and got -2sqrt3
for both
does that make it my limit
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sharp nimbus
sharp nimbus
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queen mason
i dont understand the third step
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i dont understand the third step
queen mason
what exactly do you do to get there
lunar harbor
what exactly do you do to get there
multiply the numerator and denominator by $i$
woven radishBOT
Civil Service Pigeon
lunar harbor
alternatively, it's common enough to see this to the point you can just memorise that $\frac{1}{i}=-i$
woven radishBOT
Civil Service Pigeon
lunar harbor
but it's not super necessary and it's not a major time saver anyway
queen mason
so the denominator becomes -1 and the numerator becomes 8-3i?
lunar harbor
so the denominator becomes -1 and the numerator becomes 8-3i?
numerator is -8+3i
then cancel a factor of -1 from the numerator and denominator
and you get 8-3i
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maiden tapir
are my answers correct for each question?
1- B - 2
2- **B- △ABC ∼△PQR **
3- B- 4
4- A - 5:4
eager nova
Your first answer doesn’t make sense
maiden tapir
Your first answer doesn’t make sense
are the others okay though?
eager nova
are the others okay though?
I mean your answer doesn’t make sense because you mixed options and solution
So idk if you mean B -2 or C -4
eager nova
Why do you say abc ~ pqr?
maiden tapir
Why do you say abc ~ pqr?
idk some smart classmate had it as his option earlier today when i was cheating o im assuming its that
eager nova
Not a very good strategy
maiden tapir
Not a very good strategy
so what is the correct option choice & why?
like do u mind explaining it to me?
dire forge
like do u mind explaining it to me?
what have you tried so far?
do you understand what the question is asking?
also yeah don't cheat
cheating is also banned on this server
maiden tapir
what have you tried so far?
i havent tried anything so far as the paper is from a diagnostic exam a couple years abck so theres no actual way to find answers and be able to understand the lesson
which is why im here
dire forge
do you know what "similar" means?
maiden tapir
yeah
dire forge
what does it mean
dire forge
yeah, can you be more specific? like what does it mean in math
when two triangles are similar
maiden tapir
they have 3 sides?
maiden tapir
corresponding angles are equal?
dire forge
yeah, more generally it's when two things have the same exact shape but they're different sizes
so, for triangles, having corresponding angles be equal is one way you can test if they're similar
that's called the AA test
maiden tapir
so its abc & xyz
dire forge
how come?
maiden tapir
theyre the same shap diffrent size
dire forge
it looks like they might be the same shape BUT you don't know what the length of XY is, you get what I mean?
like if it's really short or really long, they won't be the same shape anymore
what would the length of XY have to be in order for them to be similar?
maiden tapir
it looks like they might be the same shape BUT you don't know what the length of...
yeah
maiden tapir
what would the length of XY have to be in order for them to be similar?
not sure
maiden tapir
right
dire forge
yup!
so if you want the two triangles to be similar, what length would you want XY to be?
maiden tapir
it would need to follow the same ratio no?
dire forge
yup! exactly
but we don't know the length of XY so we can't conclude that they're similar
they could be but we don't know
maiden tapir
right
dire forge
do any of the other options seem similar
maiden tapir
ΔABC and ΔPQR are bcz of the side ratios
dire forge
okay, can you explain a bit more why they're similar
maiden tapir
because of the corresponding angles which are equal
so they make the triangles similar
and teh same side ratio
dire forge
how do you know the angles are equal? i don't think you're given any info about the angles of ABC and PQR
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twilit jasper
Can someone explain this to me fully
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Can someone explain this to me fully
timber pebble
Can someone explain this to me fully
do you understand what the terms mean?
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fair moat
how to do 7 cuz im js learning limits
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how to do 7 cuz im js learning limits
upper schooner
Do you know any way to rewrite cos(2x)?
fair moat
Do you know any way to rewrite cos(2x)?
i think 2cos^2 -1 would be best but not sure
magic sun
upper schooner
i think 2cos^2 -1 would be best but not sure
that's quite good, yep! There are the multiple forms, that one is the best here
fair moat
yeah let me test see what i can do from here thanks
upper schooner
Sure! If you need me, ping me 
fair moat
@upper schooner alr im stufk again i rewrote and i cant think of any ideas to do
can i cancel cos ^2(x-1)
upper schooner
can i cancel cos ^2(x-1)
How did you end up getting this?
fair moat
using the 3rd id
upper schooner
Putting that in should give $\frac{2\cos^2(x) - 2}{\cos(x) - 1}$, no?
woven radishBOT
@upper schooner
fair moat
oh i wtotr it wrong mb
fairs
fair moat
can i cancel cos^2(x) and cos x
fair moat
Which one did you mean, that you wanted to cancel?
can i cancel cos^2(x) and cos x
wait nvm thatll leave me with 0 on bottom
uhhh i have no idea where to go now
upper schooner
If, instead, you had $\frac{2a^2 - 2}{a - 1}$, would you have any ideas as to how to simplify that?
woven radishBOT
@upper schooner
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fair moat
If, instead, you had $\frac{2a^2 - 2}{a - 1}$, would you have any ideas as to ho...
yeah and once i simplify can i just plug in 0?
upper schooner
yeah and once i simplify can i just plug in 0?
You would be able to, if you did, yep
fair moat
alr thanks
upper schooner
But of course, it's with a = cos(x) and all 
restive river
i dont know where i went wrong because i got the maclaurin expansion right and then i just substituted in
devout snowBOT
i dont know where i went wrong because i got the maclaurin expansion right and t...
restive river
let $x = \left(g\dfrac{t}{c}\right)^2$
woven radishBOT
Derivative
restive river
and then $\sqrt{x+1}= 1 + \dfrac{x}{2} - \dfrac{x^2}{8} + \dfrac{x^3}{16} - \dfrac{5x^4}{128}$
woven radishBOT
Derivative
restive river
so then it should be that:
$d = \dfrac{c^2}{g}\left(1 + \dfrac{1}{2}\left(g\dfrac{t}{c}\right)^2- \dfrac{1}{8}\left(g\dfrac{t}{c}\right)^4 + \dfrac{1}{16}\left(g\dfrac{t}{c}\right)^6- \dfrac{5}{128}\left(g\dfrac{t}{c}\right)^8 - 1\right)$
woven radishBOT
Derivative
restive river
then you can simplifies this as you want but it should equal what i got
idk let me know
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gleaming heron
Can someone explain to me the step that took du from 10x to 1/10? This is the example telling me what to do but I don't understand this step. Yes I should understand U substition better than I do.
devout snowBOT
Can someone explain to me the step that took du from 10x to 1/10? This is the ex...
misty crest
$dx = \frac{1}{10x}du$
the x in the integrand cancels with this x
and you’re left with 1/10
gleaming heron
so is it always just like the inverse? I don't really understand why that is done
misty crest
you have dx in your original integrand yes?
you’re looking to make a change of variables which means you need to be integrating du
so we rewrite dx in terms of du
woven radishBOT
knief
woven radishBOT
knief
misty crest
it’s algebra
gleaming heron
No. I don't think anyone ever explained dx/du etc to me. sometimes they're treated like a variable and sometimes ignored
gleaming heron
that notation
misty crest
$\frac{dx}{du}?$
woven radishBOT
knief
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west wing
I don't get it
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I don't get it
misty crest
!xy
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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.
wicked turtle
i assume you are allowed to choose more than one answer?
west wing
nvm I understood
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wicked turtle
you used the wrong angle convention
west wing
sorry?
west wing
wait so it's asking for "b"?
wicked turtle
that's how i read it anyway
wicked turtle
yea but you can see from the figure that b is in the 2nd quadrant
west wing
wait how
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west wing
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west wing
like the dotted lines is the x axis or
wicked turtle
pasting again to refer to it:
b is the angle between the dotted line and the diagonal line
visually you can see it's more than 90 degrees but less than 180
so that is an angle in quadrant 2
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agile night
Need help.
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Need help.
acoustic vault
chrome isle
Need help.
I believe there is a typo
It might have wanted to say g(x) = x² +1
And for fog(x) = f(g(x)) as hugaxi said
agile night
I don't even understand the Question The Teacher Just Sent That as Homework without Explaining anything, We Only Discuss about Piecewise function so idk.
chrome isle
I don't even understand the Question The Teacher Just Sent That as Homework with...
What is f(f(x))
agile night
Idk, 9x + 8 is the only thing i remember.
long pasture
I don't even understand the Question The Teacher Just Sent That as Homework with...
seems like you need to have some revision on how does a function works in order to complete this homework.
agile night
seems like you need to have some revision on how does a function works in order ...
You Know About how The Function Works?
long pasture
Do you recall something like:
Let f(x)=3x+2, what is f(1)?
long pasture
You Know About how The Function Works?
kinda, i can help with that.
agile night
Do you recall something like:
Let f(x)=3x+2, what is f(1)?
Hmmm, Wait let me Think.
long pasture
Hmmm, Wait let me Think.
sure
agile night
I'm still Finding My Notebook 😵
agile night
that'd be Great.
long pasture
sure
agile night
wait let me Read My notebook if i can Remember something
long pasture
Do you recall something like:
Let f(x)=3x+2, what is f(1)?
f(x)=3x+2
here: f(x), f is a called a function, where x will be the input.
so, for my question f(1), we input 1 into the function f.
next: 3x+2 is the output of the function, since our input is 1, we have 3(1)+2=5
long pasture
wait let me Read My notebook if i can Remember something
sure
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long pasture
it's okay
let's take a look at the example again
f(x)=3x+2
so, the x in f(x) is the input, while 3x+2 on the right is the output
we can put anything to replace the x as long as it's defined (in the domain)
e.g.
f(x)=3x+2
f(y)=3y+2
f(a)=3a+2
all good till here?
agile night
I'm Writing it on paper
long pasture
sure
agile night
e.g.
f(x)=3x+2
f(y)=3y+2
f(a)=3a+2
What's the difference in x,y,a?
long pasture
What's the difference in x,y,a?
they are just variables, it doesn't really matter which x or y or a you use
we just need to know
f( )
↑
this is where we put the input
and then change all the corresponding letter in the output 3( )+2
↑
agile night
Ohhh
long pasture
next, we can try with some numbers:
e.g. f(x)=3x+2
what is f(1)?
agile night
f(1) = 5?
agile night
f(3) = 11?
long pasture
correct, let's go to the next level then
agile night
Ohh wait
long pasture
yea?
agile night
so it's just adding and Stuff?
long pasture
not really
long pasture
Need help.
hmmm, if you're unsure, let's try with g(x)
agile night
Ok
long pasture
Let g(x)=x²+1
what is g(4)?
agile night
g(4) = 17?
long pasture
yea?
long pasture
let me grab a drink
sure
long pasture
okay, next
long pasture
we can put anything to replace the x as long as it's defined (in the domain)
.
so, if we put something weirder
again, let f(x)=3x+2
we can say
f(
)=3 +2
how about f(x+1)
we can do it like
f(x+1)=3(x+1)+2
so, do you know what can f(x+1) simplifies into?
long pasture
yep
agile night
idk if it's correct
long pasture
f(x+1)=3(x+1)+2=3x+3+2=3x+5
so you're correct
let's do another question
see if you really understand
again f(x)=3x+2
what is f(x^2+1)?
(or if you can type ², what is f(x²+1)? )
agile night
Hmmm i think it's, f(x^2+1) = 3x^2 + 5.
agile night
Yes please
long pasture
we can put anything to replace the x as long as it's defined (in the domain)
again, recall
what if we put other functions inside the
f( )
↑
e.g.
Let
f(x)=3x+2
g(x)=x²+1
f(g(x)) will be f(x²+1)
while
g(f(x)) will be g(3x+2)
agile night
what if we put other functions inside the
f( )
↑
Well ahhh i forgot
I got a brain of a Goldfish.
long pasture
Let
f(x)=3x+2
g(x)=x²+1
f(g(x)) will be f(x²+1)
while
g(f(x)) will be g(3x+2)
f(x)=3x+2
g(x)=x²+1
\
|
|
↓ ↓
f( g(x) ) = f( x²+1 )
all good till here?
agile night
Yeah I'm still remembering things you taught me
long pasture
Hmmm i think it's, f(x^2+1) = 3x^2 + 5.
so
f( g(x) )
= f( x² + 1 )
= 3(x²+1)+2
= 3x²+5
agile night
Ohh wait I'm thinking About Wth is that dancing Legs
agile night
f(x)=3x+2
g(x)=x²+1
\ \
| \
| \
...
.
long pasture
Ohh wait I'm thinking About Wth is that dancing Legs
lol, it's just an arrow
i mean 2 arrows
I'm too lazy to draw😆
long pasture
do tell when it's ok to continue
agile night
Let
f(x)=3x+2
g(x)=x²+1
f(g(x)) will be f(x²+1)
while
g(f(x)) will be g(3x+2)
do the "f" change into "g" and "g" into "f" in the answer?
long pasture
do the "f" change into "g" and "g" into "f" in the answer?
nah
you can ignore that last part first if you don't understand for now
long pasture
so
f( g(x) )
= f( x² + 1 )
= 3(x²+1)+2
= 3x²+5
try to understand this first
long pasture
you can ignore that last part first if you don't understand for now
i bet i was going too fast there
agile night
let me Try to understand it all Give me some time.
compact summit
How should I proceed to solve this question?
devout snowBOT
How should I proceed to solve this question?
fair storm
First find AC by rearranging the lines and use AB^2 + BC^2 = AC^2
compact summit
First find AC by rearranging the lines and use AB^2 + BC^2 = AC^2
How can I find AC?
compact summit
Rearrange the lines, put them in different spots.
I don't get it. Could you please show a diagram?
fair storm
fair storm
Ohhh thanks
No problem.
compact summit
Is enough information given in this question? @fair storm
fair storm
Yes.
stoic minnow
Is enough information given in this question? <@1055368499964420139>
is this solved?
fair storm
is this solved?
Yes.
fair storm
How? I am getting multiple solutions for some reason.
Send me your workings.
compact summit
Send me your workings.
Is the answer (b) 8?
fair storm
Is the answer (b) 8?
Bravo, correct!
compact summit
For some reason I totally forgot to use the fact that the total time is 100 minutes
Can you also help me with a reasoning question?
stoic minnow
How should I proceed to solve this question?
what is the answer??
compact summit
what is the answer??
B
stoic minnow
what is the sequence??
compact summit
what is the answer??
Did you ask about the first question or the last one?
stoic minnow
this one
compact summit
Ok the answer is given B. But I can't understand the logic behind this.
stoic minnow
Ok the answer is given B. But I can't understand the logic behind this.
i am also thinking
fair storm
I don't know how to do this.
compact summit
I tried drawing some random lines on a plane but never got more than 12 regions. But the answer given is 16.
stoic minnow
I tried drawing some random lines on a plane but never got more than 12 regions....
same here
stoic minnow
How should I proceed to solve this question?
is the answer 150?
compact summit
No it's 160
stoic minnow
I tried drawing some random lines on a plane but never got more than 12 regions....
is it max num region or total number??
compact summit
Max
stoic minnow
i got a formula
compact summit
Please send if you get any proper solution. I need to leave right now. I'll check the messages later.
stoic minnow
i got a formula
u can use this formula here n=number of lines drawn in a plane
If there are no lines, there is just 1 region (the whole plane).
1 line: A single line divides the plane into 2 regions.
2 lines: If two lines intersect, they divide the plane into 4 regions.
3 lines: A third line that intersects both previous lines can create 7 regions.
4 lines: A fourth line can intersect the three previous lines, resulting in 11 regions.
5 lines: Adding a fifth line that intersects all four previous lines creates more regions.
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zenith forge
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