if you can clear the denominator of the fraction it'll be great right
#help-39
cosmic charm
buoyant garnet
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buoyant garnet
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cosmic charm
yep
buoyant garnet
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heady finch
buoyant garnet
yep
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cosmic charm
but since you multiply b on the top you need to multiply b on the bottom also
so (a/b) / c = a/(b*c)
if thats your question idk
buoyant garnet
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cosmic charm
you said you dont understand it so i gave an explanation why that is
buoyant garnet
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cosmic charm
uh huh yep
buoyant garnet
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cosmic charm
1-1 is?
buoyant garnet
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cosmic charm
and 0+h is?
buoyant garnet
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cosmic charm
yep
buoyant garnet
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cosmic charm
exactly
cosmic charm
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you have h on the top
h on the bottom
cancel em out
1/1+h
buoyant garnet
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pearl pondBOT
pearl pondBOT
Available help channel!
polar crypt
pearl pondBOT
polar crypt
What did i do wrong?
The 12 one
i got it now
sorry for bothering
close
,close
how do i close it
nvm
teal wyvern
.close
gusty prism
pearl pondBOT
gusty prism
do i need to use some type of
length times width formula or something
like they give me the volume dimensions
22 times 3.8 ???? 😭
v=83.6cm^2
gusty prism
ah
gusty prism
hm so
oh
ok
perfect then
and still use d=m/v?
and which ever is heavier will alarm the belll
sinful nebula
oh density *volume = mass
gusty prism
based on the mass for the can of sand
sinful nebula
and which ever is heavier will alarm the belll
yes
gusty prism
o
sinful nebula
calculate the mass of those both first
rose silo
Sand should not be lighter or heavier
sinful nebula
if mass of sand does not equal that of gold
rose silo
It should be same mass as gold to not set off the alarm
sinful nebula
then it should trigger the alarm
rose silo
Yes
rose silo
np
sinful nebula
yea I got a little confused too
rose silo
The dimensions are same but densities are different so the alarm will go off
gusty prism
pi(r^2)h
like
what ever answer u get
from this formula
it must still be in cm right
sinful nebula
ye
gusty prism
ok
sinful nebula
bc radius and height are in cm
it would be in cm^3
clearly density of gold is greater than that of sand
for question b
sinful nebula
yes
midnight haven
What's difference between a function and a equation
A linear equation is there, by adding subtracting stuff on both sides I can get a function
But let's say I have a degree 2 equation
I can't write it as a dependent and independent variable
Like
y -mx = c
y = mx + c
It's a function right
But
x^2 + 2xy + y^2
I can't right it as y = bla bla
So this brings me back to question
What is function and what is equation
violet tundra
in simple terms, a function is something which maps an x value to only one y value
leaden wadi
An equation has an expression on either side of an equal sign.
A function explicitly designates a variable(s) to be a dependent variable.
f(x) explicitly designates x to be a dependent variable.
midnight haven
An equation has an expression on either side of an equal sign.
Again
x + y = 5
y = -x+5
In both the case i get same graph and second one is function too
So here equation and function are same right
leaden wadi
In the latter case, you are explicitly solving for y with x being a dependent variable.
midnight haven
In the latter case, you are explicitly solving for **y** with **x** being a depe...
Hmm makes sense
midnight haven
In the latter case, you are explicitly solving for **y** with **x** being a depe...
x - 3y = 5
x = 3y + 5
f(y) = 3y + 5
Is it also a function
leaden wadi
Yes.
midnight haven
Cool
pearl pondBOT
@midnight haven Has your question been resolved?
midnight haven
@leaden wadi again sorry
x² - y² = 4
y = √(4+x²)
So again
I can write all equation in form of functions
Then what's the difference between them
leaden wadi
With a function, one of the variables is explicitly the dependent variable.
x - y = 0 would be an expression because neither variable is explicitly designated as the dependent variable.
x = y would be a function because y is the dependent variable.
It's mostly semantics.
midnight haven
Oh cool
pearl pondBOT
@midnight haven Has your question been resolved?
charred sorrel
How can I work out 5^2 +5^2 - 2x5x5xCos(30) without a calculator? I know that Cos30 is √3/2 . But how can I get it to be 50-25√3 thanks.
edgy wren
What’s 5^2 ?
charred sorrel
25
frosty ravine
charred sorrel
Can I get it In the form r-s√3?
pearl pondBOT
pearl pondBOT
Available help channel!
midnight haven
how to determine the
pearl pondBOT
how to determine the
midnight haven
minimum of x^x
it's not 1
How to get the value?
damn
derivative?
Suppose I don't have any knowledge about them
it's a very sus value
its
${\frac{1}{e}}$
jolly parrotBOT
icannotdoanymorecauchy
midnight haven
magic
chrome plank
let f(x) = x^x. if f(x) is always curving upwards, the minimum is where f'(x) is flat.
midnight haven
Is this always curving upwards?
chrome plank
Is this always curving upwards?
(assume) I don't know. how would you find out?
midnight haven
Idk by inspection
midnight haven
Yes
chrome plank
is x^3 always curving upwards?
midnight haven
i think
midnight haven
then what is it
chrome plank
what do I mean by "curving upwards"?
chrome plank
it's increasing yes, but it's not always curving upwards
midnight haven
curving is like convex and concave, no?
chrome plank
look at the left of the y axis, it's curving downwards there
chrome plank
curving is like convex and concave, no?
yep
midnight haven
look at the left of the y axis, it's curving downwards there
I got it
chrome plank
what tools do you know in maths that could help?
chrome plank
without drawing anything XD
midnight haven
I can't think of any
chrome plank
well, how would you define "curving" mathematically?
midnight haven
calculus not allowed here ):
chrome plank
calculus not allowed here ):
OOOOOOOOOH
midnight haven
yea
chrome plank
chrome plank
that changes things
jolly parrotBOT
icannotdoanymorecauchy
pearl pondBOT
chrome plank
ye, go learn some calc XD
midnight haven
**icannotdoanymorecauchy**
no, that's not min, (1/e)^(1/e) is min value of x^x
chrome plank
I suppose you could look at it, and propose the minimum is x. then, look a little to the left or right and show f(x+d) (for any d, positive or negative) is bigger than f(x).
you won't be able to calculate the minimum this way, but you can show some value iof x is indeed a minimum.
pearl pondBOT
Available help channel!
high steppe
avg = total we counted/total variable?
pearl pondBOT
avg = total we counted/total variable?
high steppe
for example 1+2+3+4+5
avg = 1+2+3+4+5/5
midnight haven
The average of 1, 2, 3, 4 and 5, is sum(1+2.....5)/(5), not of 1+2+3+4+5, because this simplifies to a single term.
tomorrow's my maths exam
high steppe
_The average of 1, 2, 3, 4 and 5_, is sum(1+2.....5)/(5), not of _1+2+3+4+5_, be...
i dont understand
midnight haven
the average of 1, 2, 3, 4 and 5 is (1+2+3+4+5)/5 = 3
high steppe
isnt that what i said?
midnight haven
avg = total we counted/total variable?
not total variables, total terms
midnight haven
avg = total we counted/total variable?
..
midnight haven
the sum is at the top and the number of terms is at the bottom
high steppe
wat
midnight haven
avg = 1+2+3+4+5/5
you forgot brackets
high steppe
avg = (1+2+3+4+5)/5
right?
high steppe
wat words
midnight haven
avg = total we counted/total variable?
this is very ambiguous
midnight haven
wat
high steppe
so avg = (4+4+4+3+4+4+4+3)/8 right
midnight haven
yes good
high steppe
dude tell me the words
midnight haven
pearl pondBOT
@high steppe Has your question been resolved?
spark shuttle
hey do you have an advise for studying math?
pearl pondBOT
pearl pondBOT
Available help channel!
shadow monolith
I'm trying to follow the following proof. How are they getting to it's false that Pr(e | A & ~T) is many times greater than Pr(e | T)?
pearl pondBOT
I'm trying to follow the following proof. How are they getting to it's false tha...
@shadow monolith Has your question been resolved?
pearl pondBOT
@shadow monolith Has your question been resolved?
pearl pondBOT
@shadow monolith Has your question been resolved?
worthy drift
What’s wrong with this question
plush bramble
What’s wrong with this question
!occupied
pearl pondBOT
What’s wrong with this question
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).
pearl pondBOT
@shadow monolith Has your question been resolved?
pearl pondBOT
@shadow monolith Has your question been resolved?
dusty heart
i need help with a complicated exercise using derivatives (theres also my attempt to solve it). What the exercise asks for is the minimal value of the function. Which would obviously imply using derivatives and, but i seem to be very far of from any of the multiple choice answers.
dusty heart
if you've got any question about my solution or what im trying to do id be more than glad to try and explain
pearl pondBOT
@dusty heart Has your question been resolved?
leaden wadi
I think you did a lot more work than you needed to do.
leaden wadi
Completing the Square was unnecessary.
You can just square both sides to eliminate the radical.
dusty heart
wdum completing the square?
leaden wadi
Hmm, some terminology lost in translation.
dusty heart
english is not my first language so thats why im asking
leaden wadi
dusty heart
which i feel like it did kinda make my calculations easier
leaden wadi
Squaring both sides gets a better result that can then be simplified through polynomial division.
dusty heart
yup, thats what you would get by just raising them to the 2nd power
dusty heart
Squaring both sides gets a better result that can then be simplified through pol...
u wanna divide those polynomials together?
i mean, its an idea
leaden wadi
leaden wadi
Yes, and the end result does match up with one of the possible answers.
dusty heart
yup
same problem here
but these are some exercises for the entrance exam at a university so, it cant be that theyre wrong
it says its a)
so 14 sqrt 2
oh wait, did you plug the values u got for x in the function?
cuz thats what it asks for
leaden wadi
Yes
dusty heart
oh
leaden wadi
Solve for x and you will get two results. Only one of which gives a Real answer that lies inside of the interval you found earlier.
dusty heart
okay let me solve it too
ill see what i get
oh btw, random question, are u a helper that works for this discord server, or are you just a dude who likes math and decided to help
leaden wadi
I like to help others to help myself improve my own understanding of math.
And to learn about areas of mathematics that I do not know by observing some of the questions asked here.
leaden wadi
I'm good. You should be able to get the answer relatively easy now.
dusty heart
the final polynomial is 28x^2 + 700x + 343=0?
dusty heart
I'm good. You should be able to get the answer relatively easy now.
i feel like its nowhere close tho
let me check again
wait, no way, the delta is 672, thats amazing
sorry, i meant sqrt delta
sinful solar
Would Componendo and Dividendo have been a bad idea at the start of the question ._.
dusty heart
whats that?
sinful solar
well,
if a/b = c/d , then
(a-b)/(a+b) = (c-d)/(c+d)
y'all prolly have a different name for it but yeah
dusty heart
i see what u mean
sinful solar
Would that just make it tedius or something as it'd get heavy in the denominator
dusty heart
so, u mean after we got rid of the square root?
or where are u suggesting that we should have done that
dusty heart
yea no prob
sinful solar
Componendo Dividendo could be done in the 3rd step though here
dusty heart
alright so f(x) = sqrt 73 + 8*sqrt2?
this is what i got
but the thing is that theres obvi no choice like that
leaden wadi
What two values of x did you get?
dusty heart
nvm i solved it
finally
ill send you a pic
its really messy tho,
here ya go
i got more exercises that are hard btw
if yall interested
these entrance exam exercises are no joke
leaden wadi
Feel free to post more questions. Just make sure you start a new channel.
leaden wadi
Type .close
dusty heart
.close
fringe yoke
- PQRS overlap OLMN. Area of PQRS = 30cm^2. Find the shaded region's perimeter.
- Triangle ABD is a right angled triangle, angle ABC = 90. Point D is between line AC.
BD is perpendicular to AC. AD = 1 12/13, DC = 11 1/13, if the triangle's area is 30cm^2, find the length of AB.
pearl pondBOT
1) PQRS overlap OLMN. Area of PQRS = 30cm^2. Find the shaded region's perimeter....
@fringe yoke Has your question been resolved?
gleaming musk
pearl pondBOT
gleaming musk
im not really sure where i went wrong
context is highschool math, hyperbolic trig is not a substitution technique i have learnt
my handwriting isn't the neatest, so please lmk if there is any part u are finding hard to read
i somehow got 0
(manifesting rishabh to appear 🙏 again)
rough forge
easiest high school exercises
gleaming musk
easiest high school exercises
honestly the educaiton system here lets you choose the level of math u want to do
i did this to myself
i cant even complain anymore
next dove
It might be some visibility error but I don't see any negative sign with du
gleaming musk
It might be some visibility error but I don't see any negative sign with du
i might havej ust flipped bounds without showing the negative isgn
*sign
gleaming musk
where?
next dove
line just after u sub
it was cos(pi-u) so it will be -cosu right?
so a negative from this and a negative from du
gleaming musk
oh that is a pretty egreious
i just evaporated a negative sign
hold up let me redo this
next dove
kk
next dove
last line is just by parts?
yeah
next dove
dont u get stuck in a loop tho?
of course
round patio
A piece of advice,
You could have done the shift from x to -x to get another representation of I with same bounds
next dove
you assume this integral to be some I then after by parts you'll get I in some form
after that you can do some algebra to get I
round patio
That's much simpler
gleaming musk
A piece of advice,
You could have done the shift from x to -x to get another re...
what do u mean by that
round patio
what do u mean by that
sub u = -x
round patio
Then change the dummy variable to x again
round patio
that skips the 2 u subs i did
Yeah
gleaming musk
will keep that in mind
actually would that integral be nicer to crunch here?
since my u sub turns everything to integrating 0 to 2pi
your suggestion still keeps it from -pi to pi which might be nicer
round patio
How'd you do the thing on
gleaming musk
on?
gleaming musk
i split the integrla into 2 parts
and then use symmetry
like integrating f(x) = f(a-x)
squash the 2 together
round patio
It has e^(pi - u) + e^(u - pi)
gleaming musk
nw, i didnt write any justification either so thats a bit arbitrary to follow
wait idk how to do the last line by parts
my brain is cooked
T=T
actually nvm, let me try swapping
round patio
wait idk how to do the last line by parts
e^u-pi/2 can be split in e^u * e^-pi/2
gleaming musk
pi/2?
gleaming musk
oh
yeah i did that
i think i just need to swap what i let my differentials equals to for by parts
gleaming musk
ended up getting -[e^pi - e^(-pi) ]/2
wolfram got decimal approximation rounded to it so i think its right
at least its correct to 4dp
thx for all the help here
🙏
.close
lucid valley
Im very mathematically challenged and im very stuck on understanding the system of disequalities of this type overall i can't wrap my head around what steps I'm supposed to take or what the rules are since it somtimes brakes already established rules for example "solve whatever is in (...) first" my math teacher said there are no formulas for it and im not sure what the rules are and how im supposed to solve it
rough forge
Im very mathematically challenged and im very stuck on understanding the system ...
Are you referring to inequalities?
seems so
before we speak about a system, do you know how to approach one inequality, generally speaking?
lucid valley
the answer is supposed to involve some sort of system
i almost dont know anything
my mind sort of gets wiped when schools out ecpecially when it comes to math
lucid valley
before we speak about a system, do you know how to approach one inequality, gene...
nope
rough forge
Let's start with something simple i guess
jolly parrotBOT
bacc
lucid valley
it means some sort of random number squared is more than zero
or equal
lucid valley
x^2 is a default parabola
whats a parabola
jolly parrotBOT
lucid valley
so negative numbers don't exist in this case?
rough forge
negative outputs don't exist*
lucid valley
oh
rough forge
if you square a real number you always get a non-negative output
for example
(-2)(-2) = 4
lucid valley
coz - x - = +?
rough forge
yes
this was just an example so you get an intuition what an inequality means
you basically introduce more solutions
instead of asking x² = 0 (which the sol. is x = 0) you now also ask yourself when is x² > 0
which is true for all x unless x = 0
does this make sense?
lucid valley
instead of asking x² = 0 (which the sol. is x = 0) you now also ask yourself whe...
why js the solution of that 0
rough forge
you ask why x² = 0 gives x = 0 as solution?
lucid valley
yea
rough forge
try any other number
to satisfy this equation
you will always get a false statement
rough forge
you can see also on the graph that x² becomes 0 is x is 0. For all the other values of x it's above the x-axis aka positive
lucid valley
oh
rough forge
does this make sense?
lucid valley
sorta
rough forge
well thats bad i guess
lucid valley
well thats bad i guess
😭
rough forge
say you have two functions
lucid valley
ye
rough forge
i suppose you kinda have an idea of what that is
lucid valley
maybe im not English and im currently in a country where i dont speak the language fluently so i might or i might not
rough forge
this is a function
lucid valley
oh then yes
rough forge
polynomials
exponential functions
logarithms
trigonometric etc
rational functions
x, ln(x), e^x, sin(x), x/(x²-1) etc
such things
say we have two different functions
I call the one f(x) and the other g(x)
ok?
lucid valley
ok
rough forge
is there hope or did i lose you
lucid valley
is there hope or did i lose you
keep going we will see
rough forge
We can do the following
lucid valley
is there hope or did i lose you
i hope so😭
rough forge
We can ask ourselves if there is a common point among f(x) and g(x), an intersection for example
for example
,w plot x^2 and x
jolly parrotBOT
jolly parrotBOT
bacc
rough forge
We set them equal
we wanna find such x where y is the same in both functions
that's the idea of equations
any questions?
lucid valley
well why do people sometimes
move things around
like one number to the other side
lucid valley
how would that moving work and in what cases
jolly parrotBOT
bacc
rough forge
Question
can you immediately tell me the solution for x
(i dont wanna hear the actual solution)
but my point being
we wanna simplify the equation
until we can get obviously and immediately tell what x is
here you would kinda have to think or even guess
lucid valley
well if 2x-2=0 if somthing beinf like subtracted gives u the answer you can just add jt up to see what your subtracting from?
rough forge
how would that moving work and in what cases
To answer this:
You can always add,subtract things on both sides.
You can always multiply/divide things (except 0).
These are the very basic rules for solving equations/inequalities
rough forge
well if 2x-2=0 if somthing beinf like subtracted gives u the answer you can just...
The goal is to isolate x
So maybe you implied this
we could add 2 on both sides
jolly parrotBOT
bacc
rough forge
which gives us what
rough forge
yes
jolly parrotBOT
bacc
rough forge
we basically "moved" 2 on the other side
hmm
how can we get rid of the 2 multiplied with x on the left?
lucid valley
isnt that impossible
rough forge
haha no
lucid valley
coz you gotta always do multiplication first?
rough forge
remember you can divide things on both sides
lucid valley
but what about the rule that says you gotta multiply 😭
lucid valley
remember you can divide things on both sides
oh
lucid valley
pemdas?
rough forge
this has nothing to do right now
PEMDAS stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction
this is what you mean
order of calculating numbers
forget this here for a second
lucid valley
i thought it was universal
rough forge
our goal is to isolate x
rough forge
i thought it was universal
it is but it has nothing to do right now with our matter
jolly parrotBOT
bacc
rough forge
In order to get rid of the 2 multiplied with x
lucid valley
wait isnt 0 times anything 0
jolly parrotBOT
bacc
jolly parrotBOT
bacc
rough forge
this is the solution to the equation
jolly parrotBOT
bacc
lucid valley
oh
rough forge
**bacc**
then staring at this and asking what it could be
instead we work our way there
and we do this by isolating x from everything else
lucid valley
so how do we separate the X?
rough forge
luckily these rules for equations are also applicable for inequalities, there is just one more thing with inequalities that you need to keep in mind
lucid valley
what are those
rough forge
To answer this:
You can always add,subtract things on both sides.
You can always...
.
addition
subtraction
multiplication (except 0)
division (except 0)
there are a few more but we will stay with them for now
lucid valley
ok!
rough forge
so
lucid valley
ye
rough forge
before you touch inequalities
you have to get comfortable with equalties
with normal equations
the basic and hard ones
and i see that you are definitely not comfortable
that's an issue you have to accept for now
you should start from scratch
it's literally impossible to explain to you why inequalities and how you calculate with them
and then especially system of inequalities
that's too hardcore
that's just if you were level 1 this would be level 10
lucid valley
how do i get comfortable with equalitys
rough forge
practice
you master the very basic operations
addition
subtraction
multiplication (except 0)
division (except 0)
you can solve/isolate x fast without second guessing
that's something you have to do
you have to unlock this skill first
lucid valley
ok!
rough forge
so what you wanna do is this
lucid valley
ye?
lucid valley
ty
rough forge
then the next level
system of equations
you get a good understanding of what a system is now
If you watched, practiced and got the hang of this
then you can start with this
then from there it starts to get a bit easier
cause solving inequalities is not that different from normal equations
I recommend taking your time to watch and understand these, in the order i sent. Then to try and apply the knowledge you gained
and during that you can always come here and ask questions
rough forge
Im very mathematically challenged and im very stuck on understanding the system ...
but this, this is too overkill right now
rough forge
i almost dont know anything
especially if this is your level
lucid valley
i littrally dont even know how to find the percentage of somthing 😭
lucid valley
but this, this is too overkill right now
what do i start with then :(.
lucid valley
ok
rough forge
make a todo list
of what you need to cover
so you get a basic understanding of things
if necesary write down notes
and most of all practice
until you develop an intuition for things
otherwise you will stay there where you are, and you dont want that
the most important thing for you is acceptance and to stay calm
there maybe tons of doubts you have right now
which i cannot cover all up
but it's important to start somewhere with something
concentrate now on this topic
then if you did that
do percentages
lucid valley
ok
lucid valley
thank you
rough forge
just search and you will find
and if you struggle
you can ask here questions, always
i wish you good luck, and i hope we will see each other again
but when you are more ready
and more prepared
more equipped
lucid valley
you can ask here questions, **always**
ok thank you very much again!
pearl pondBOT
@lucid valley Has your question been resolved?
lucid valley
<@820324415732449286> Has your question been resolved?
i mean if i manage to understand later on maybe😭
rough forge
i mean if i manage to understand later on maybe😭
you will if you put in the work
pearl pondBOT
What does that even mean
placid zealot
so for a reflection
just imagine a line
if polygon a is reflected across that line to show polygon b, then it can be mapped only using reflections
something which uses something other than reflections would be scale factors, which would make a bigger or smaller
placid zealot
just imagine a line
in this case something like y=x
placid zealot
np
upbeat goblet
What about this one
This one kinda confused me
Because I thought I got it right but I guess I got it wrong
pearl pondBOT
@upbeat goblet Has your question been resolved?
pearl pondBOT
@upbeat goblet Has your question been resolved?
upbeat goblet
hexed cobalt
at the centre of a regular heaxagon we can see 6 equilateral triangle and taking about angles each angle should be 60 degrees
tropic estuary
let f be a function defined and continuous in R, prove that for every 2 real numbers a, b a real number d exists such that 3f(d) = 2f(a) + f(b)
plucky python
let f be a function defined and continuous in R, prove that for every 2 real num...
was this what the question was meant to be lol
(the one u sent in last time)
plucky python
let f be a function defined and continuous in R, prove that for every 2 real num...
anyway haven't thought about it fully but hint: ||IVT||
pearl pondBOT
@tropic estuary Has your question been resolved?
tropic estuary
anyway haven't thought about it fully but hint: ||IVT||
ik that
and I did smth kinda
i worked with max and min
it's pretty scuffed
I don't even understand what I did
plucky python
ah ok
well basically we'll have to do cases which is a bit boring
but here's the general idea:
let's sps a<b and that f(a) < f(b)
then (2f(a) + f(b)) / 3 is somewhere between f(a) and f(b)
so we finish by IVT
tropic estuary
oh btw
tropic estuary
was this what the question was meant to be lol
it's a different one
the other one was meant to be
7f(d)= 2f(a) + 2f(b) + 3 f(c)
plucky python
ah right
tropic estuary
it's not the same approach is it?
plucky python
7f(d)= 2f(a) + 2f(b) + 3 f(c)
i'll have to think abt it but i think the same approach should work?
tropic estuary
because we have 3 numbers here so we can't just say a<b and f(a)<f(b) ...
tropic estuary
i'll have to think abt it but i think the same approach should work?
also how do we conclude taht (2f(a)+f(b))/3 is between f(a) and f(b) just from the condition that f(a) < f(b)
plucky python
also how do we conclude taht (2f(a)+f(b))/3 is between f(a) and f(b) just from t...
bigger than f(a), less than f(b)
think intuitively - the average of a big number and small number is somewhere in-between
tropic estuary
.close
pearl pondBOT
cloud wren
pearl pondBOT
Available help channel!
plain quarry
Can someone help me out with these problems? I just need a guide
storm osprey
wich one do you need help with ?
pearl pondBOT
Can someone help me out with these problems? I just need a guide
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
All four, in terms of the choices the bot has given me im in the middle of one and two
storm osprey
You need to find what axis you should use in order to have a 4th rectangle wich is a reflection of A''B''C''D''
plain quarry
You need to find what axis you should use in order to have a 4th rectangle wich ...
Ohhh I see now
Is it the Y axis?
storm osprey
What rectangle would you reflect with the y axis ?
plain quarry
I don’t know
storm osprey
what triangle is one the left side of your y axis ?
plain quarry
what triangle is one the left side of your y axis ?
A B C?
plain quarry
Yeah I think I have to find where W”V”X”lies
storm osprey
yes
plain quarry
I believe W’V’X is already rotated right
So if it were to be rotated again would it be the first quadrant?
Or something I think 😭
storm osprey
it is rotating in the direction of the arrow
plain quarry
Oh so the fourth quadrant
storm osprey
yes
storm osprey
do you get the third one ?
storm osprey
if you say that P->P' is a rotation of 90 and P'->P'' is one of 45
try to find P->P''
plain quarry
try to find P->P''
Would it be something like 180 degrees or 270 degrees?
storm osprey
how did you get to that result ?
plain quarry
how did you get to that result ?
Because if to get P->P’ is 45 degrees then P->P” must be 180?
Errr actually
Is it 135?
storm osprey
it is
plain quarry
Awesome sauce
storm osprey
do you understand the last one ?
plain quarry
Hell nah 💀
pearl pondBOT
@plain quarry Has your question been resolved?
weary dragon
Can someone check if this is right
pearl pondBOT
Can someone check if this is right
pearl pondBOT
@weary dragon Has your question been resolved?
eager flax
could someone help me to find out the anwser for that indetermination without l'hopital?
acoustic path
could someone help me to find out the anwser for that indetermination without l'...
consider the domains of those root functions
eager flax
I called a=sqrt[4]{2x} and b=1
so I find out after some conclusions 0/4, do you found out that?
I do that, is it right? @acoustic path ?
naive orbit
,rotate
jolly parrotBOT
eager flax
@acoustic path ?
pearl pondBOT
@eager flax Has your question been resolved?
half goblet
Yo someone wanna help me figure out how youd get 5d and 15c
pearl pondBOT
Yo someone wanna help me figure out how youd get 5d and 15c
light helm
did you do all the other parts?
light helm
did you do 5c?
light helm
exact same question, no
but the same idea applies when doing it
half goblet
Alr
light helm
they're pretty much all evaluating/simplifying
pearl pondBOT
@half goblet Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
craggy rivet
A group of physics students builds a catapult. They place it on the roof of a school, 18.0 m above the ground and launch a ball toward the east at 24.5 m/s [24° above horizontal]. When the ball hits the ground, how far away from the school will it be?
I am looking for t so I can do vc=dx/t
but none of the equations in the book let me find t
edgy wren
first get the vector components
pearl pondBOT
@craggy rivet Has your question been resolved?
uneven bear
but idk how I get time from that?
Let's say x is the horizontal axis and z the vertical. To get the time, you only need to figure out how long it takes for z to reach 0.
The general approach to such problems is to start with the equation of motion
$$F=m\ddot{z}$$
jolly parrotBOT
Kex
uneven bear
Then figure out what forces are involved
craggy rivet
I never got such an equation in my text book
uneven bear
$\ddot{z}$ is the z component of the acceleration vector
jolly parrotBOT
Kex
uneven bear
m is the mass of the object and F is the total force that is acting on it
craggy rivet
yeah never see that before, this is confusing me
jolly parrotBOT
Kex
uneven bear
Still who the heck would introduce such problems without teaching Newton's equation of motion first :/
craggy rivet
Have you seen this before at least?
What does z mean?
can i take pictures of the equations I have access to?
uneven bear
Just a distance. Probably the textbook has x or d or whatever
uneven bear
can i take pictures of the equations I have access to?
Sure, would help to get an idea what your background is
craggy rivet
Still who the heck would introduce such problems without teaching Newton's equat...
I live in Canada
@uneven bear
uneven bear
There it is 😄
Mine is just more general with the initial position/distance included
$$d=\frac{1}{2}at^2+v_0t+d_0$$
jolly parrotBOT
Kex
uneven bear
So again, we are just looking at the vertical component
$d_0$ is the initial height, $v_0$ is the z component of the initial velocity and $a$ will be $-g$ from gravity
jolly parrotBOT
Kex
uneven bear
And we want the time it takes for d to become 0, so you have to solve this quadratic equation to get t.
craggy rivet
There it is 😄
how do I get t though because there are 2
uneven bear
One solution is negative, so not physical meaningful
craggy rivet
im falling asleep a bit, how do you know that, and which solution?
uneven bear
midnight formula is your friend
obtuse plaza
You should see examples of that question the concept behind it on yt or smth
As you don't know anything about the laws of motion
craggy rivet
Those get introduced later
uneven bear
I agree with FlexO though. You can't really appreciate the solutions to these problems without understanding the laws of motion, so have a look already and it might give you an edge 😉
pearl pondBOT
@craggy rivet Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
north talon
There is a math test with 30 questions, where 3 students and 1 teacher is doing it. If each of the students can do atleast 3 questions, and the teacher can do no more than 15, how many ways can the 4 people complete the test?
north talon
ive never seen these types of questions before
cinder flower
can do atleast 3 questions
does that mean must do at least 3?
it doesn't read like that but why would it be there if it really just meant 'can' 
north talon
oh in the original question (i translated it) they used can so i dont really know
cinder flower
ok probably must do at least 3 then
north talon
alright
cinder flower
hm well i have a way of doing it but i don't think you'll like it
north talon
what is it?
cursive wraith
I was thinking about stars and bars but the >= 0 version
cinder flower
the constraints are kinda annoying for a stars and bars approach
north talon
I was thinking about stars and bars but the >= 0 version
ive never heard of that what is it
cursive wraith
the constraints are kinda annoying for a stars and bars approach
we can get rid of teacher condition and then subtract amount of ways where teacher > 15
cursive wraith
ive never heard of that what is it
so you might not know by name
cursive wraith
but do you know how many ways can we choose x1,...,xk such that x1+...+xk = n
(x1,...,xk are non negative integers)
cinder flower
wait does complete the test mean just assign a number of questions to each person
north talon
no😭
cinder flower
or does which questions each person does matter
cursive wraith
oh yeah this is important
cinder flower
or does which questions each person does matter
this seems kinda hard
north talon
or does which questions each person does matter
it wasnt specified
i think this was like comp math from a month ago but ive found nobody doing it online
cinder flower
cursive wraith
wait does complete the test mean just assign a number of questions to each perso...
let us be in this configuration xdd
cinder flower
LOL yea i agree
you could just assign the 3 students 3 questions each, and then take cases on assigning the teacher 0 through 15 questions
then you just need to compute like compute 16 binomial coefficients
by stars and bars
north talon
they have to do a total of 30 questions
cursive wraith
then you just need to compute like compute 16 binomial coefficients
I only needed to compute 2 but
cinder flower
ohhhhh
cinder flower
we can get rid of teacher condition and then subtract amount of ways where teach...
yea that's so much better
cursive wraith
they have to do a total of 30 questions
alright so here's to you, formula that might be helpful
the number of ways to choose $x_1,...,x_k$ non-negative integers such that $x_1+...+x_k = n$
jolly parrotBOT
rafilou2003
cursive wraith
is $\binom{n+k-1}{k-1}$
jolly parrotBOT
rafilou2003
north talon
oh
cursive wraith
had you seen this before?
north talon
no sorry
cursive wraith
no worries
the visual proof that I use for this
you imagine that you have n stars to distribute between k bags
those bags are in a line, and there's bars between them to separate them
so after placing the stars, from left to right you will have a total of "n+k-1 objects"
the objects regrouping the stars and the bars
(n stars, k-1 bars)
north talon
ohh
cursive wraith
and to choose how many stars goes in each bag
all you have to do is choose where in that sequence you place the bars
north talon
makes sense
cursive wraith
**rafilou2003**
thus this value
so now to apply the formula
you can write for example s_1, s_2, s_3 and t the number of questions each person takes
so then you would be solving $s_1 + s_2 + s_3 + t = 30$
jolly parrotBOT
rafilou2003
cursive wraith
problem being, those can't be any non-negative integers
because each student must take at least 3 questions
north talon
yeah?
cursive wraith
so, instead of looking at the number of question each student takes
we're gonna look at the number of questions each student takes, minus 3
call these numbers x1,x2,x3
north talon
oh dang i was about to ask if that would work😭
cursive wraith
and we get $x_1 + x_2 + x_3 + t = 21$
jolly parrotBOT
rafilou2003
cursive wraith
so, if there were no restrictions on t, how many choices do we have?
north talon
24?
north talon
oh
cursive wraith
**rafilou2003**
how many bags do we have?
north talon
4
cursive wraith
and how many stars do we have to place in total?
north talon
this is where you're supposed to apply the formula
24C3?
north talon
oh nice
north talon
crazy
cursive wraith
ok so
unfortunately
there's not that many choices
because we overcounted the outcomes where the teacher had too many questions
for which values of t does that happen?
north talon
16 to 30
cursive wraith
**rafilou2003**
if everyone here is non negative, the max value of t would be
cursive wraith
to 21 maybe?
yes
what does matter is that we gotta get rid of the outcomes where t >= 16
north talon
would we subtract 16 then?
cursive wraith
we subtract 16 to what?
north talon
from t
north talon
hooray
north talon
x_1 + x_2 + x_3 + x_4 <= 5? im not sure
cursive wraith
almost
cursive wraith
**rafilou2003**
this is always gonna be true
so if you subtract 16 from both sides
not sure there's an "inferior or equal to"
north talon
o
cursive wraith
$x_1 + x_2 + x_3 + x_4 = 5$
jolly parrotBOT
rafilou2003
cursive wraith
alright