How would I integrate it?
#help-10
slate hamlet
Do i have to square both sides in one of the function and rewrite both the equations in terms of one variable?
slate hamlet
No
quick merlin
Oh
restive gorge
This is the original question
you can convert -sqrt(-y) into -x^2
then find the intersection points of -sqrt(-x) and -x^2
should be from -1 to 0
slate hamlet
Gotcha, so its okay to square both sides?
restive gorge
the upper function is -x^2 and lower -sqrt(-x)
restive gorge
Gotcha, so its okay to square both sides?
that works basically
quick merlin
Whats the answer?
slate hamlet
that works basically
How do I justify keeping the - sign?
restive gorge
multiply by -1 first both sides
quick merlin
How do I justify keeping the - sign?
Yo what is the answer of this question?
slate hamlet
There isnt a answer key
restive gorge
,, \int_{-1}^0 (-x^2) - (-\sqrt{-x}) : : \dd x
warm shaleBOT
bacc (unhelpful)
quick merlin
The answer is 1/3
warm shaleBOT
warm shaleBOT
quick merlin
, rotate
warm shaleBOT
restive gorge
bro stop spamming
quick merlin
,rotate
warm shaleBOT
restive gorge
helpee already got the idea
slate hamlet
All right, thanks guys I understood
quick merlin
helpee already got the idea
Wdym?
tropic seal
Hi! I'm newly doing asymptotes and I'm still abit confused with the exact concepts. There's no Horizontal Asymptote in this function right? Also how do you find the f(x) of the vertical Asymptotes such as in this function?
obtuse pebbleBOT
Hi! I'm newly doing asymptotes and I'm still abit confused with the exact concep...
restive gorge
Hi! I'm newly doing asymptotes and I'm still abit confused with the exact concep...
there are
tropic seal
How so? Can you explain it to me?
restive gorge
find the first two limits
tropic seal
Alright
restive gorge
you will see it approaches a constant number as x->oo (same with -oo)
and that constant number resembles then a horizontal asymptote, the function approaches it but never reaches it
deep schooner
We consider n a natural whole number. Prove that the greatest common divider of n+1 and n+2 is 1
obtuse pebbleBOT
We consider n a natural whole number. Prove that the greatest common divider of ...
cobalt ocean
Let the greatest common divider of n+1 and n+2 =a, then, a|(n+2-(n+1))
=>a|1 <=>a=1
deep schooner
How do we demonstrate that a divides n+2-(n+1) ?
cobalt ocean
(n+1)=ak, if a does not divide n+2-(n+1), then n+2-(n+1)=ax+b where b<a
=>n+2=a(k+x)+b, which means a does not divide n+2
deep schooner
Ok tnx
cobalt ocean
np
glad arch
hello
karmic whale
We consider n a natural whole number. Prove that the greatest common divider of ...
Use Euler
obtuse pebbleBOT
@deep schooner Has your question been resolved?
civic nimbus
Hey
civic nimbus
Lim x-> 0 (1-cosx) / x(2^x-1) is
timid silo
what have you done uptill now?
warm shaleBOT
Edmund Cloudsley
timid silo
!status
obtuse pebbleBOT
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
No 1
timid silo
gotcha
well if you directly substitute 0, you would get 0/0 which is in indeterminate form correct?
therefore we can't do that
have you heard of L'Hôpital's rule?
civic nimbus
Yes
civic nimbus
Wait
lost tree
u cud also probably use the taylor expansion of 2^x
civic nimbus
Should I use log ??
timid silo
u cud also probably use the taylor expansion of 2^x
yup yup
timid silo
Should I use log ??
I don't think so?
civic nimbus
If I use , answer is getting 1/2 log2 e
timid silo
what are you logging tho <3
civic nimbus
Sorry ??
timid silo
how are you using the log function?
obtuse pebbleBOT
civic nimbus
.unlisted
obtuse pebbleBOT
Available help channel!
scarlet basalt
is this a set of numbers 1, 2 3 4 5 6?
obtuse pebbleBOT
is this a set of numbers 1, 2 3 4 5 6?
scarlet basalt
or what it means
rocky goblet
what's the context?
carmine hare
its a group....maybe
scarlet basalt
i have to test is sth is a group
and i have given set Z7
check if operation (x+y) mod 7 is an group[
but i don't know that exactly is in the set X
fallow wharf
is this a set of numbers 1, 2 3 4 5 6?
you ned to include 0
fallow wharf
0 and 7 are in the same equivalence class
carmine hare
cyclic group....
fallow wharf
so either is acceptable
scarlet basalt
so it is the set of the rests from devision by 7 right?
fallow wharf
yeah usually people just go with {0,1,2,3,4,5,6} so let's just stick with that since those are usually what people think of when they say remainder by 7
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
scarlet basalt
So i have
scarlet basalt
to check
if this is an group
the answear claims that its even an abelic group
X is a set of all the subsets of an unempty set P
and the equation is the common part of both set
what it the symetric element in this case?
because i think the neutral element is the set of all the subsets, but i don't see the symetrical element to exist
obtuse pebbleBOT
@scarlet basalt Has your question been resolved?
scarlet basalt
?
dreamy cove
if this is an group
youre gonna need to translate this
obtuse pebbleBOT
@scarlet basalt Has your question been resolved?
worn coyote
because i think the neutral element is the set of all the subsets, but i don't s...
The neutral element in this case is P
Because for any $S \subset P$ we have $S \cap P = P \cap S = S$
warm shaleBOT
EQUENOS
obtuse pebbleBOT
@scarlet basalt Has your question been resolved?
scarlet basalt
The neutral element in this case is P
i know what is neutral element
i am asking for
an alement that gives the neutral as solution
but i think it does not exist
worn coyote
an alement that gives the neutral as solution
I don't think I understand
What do you call it in your native language?
element odwrotny?
The inverse element indeed doesn't exist for proper subsets, because $\forall S, T \subset P$ we always have $S \cap T \subset S \neq P$
warm shaleBOT
EQUENOS
scarlet basalt
I don't think I understand
What do you call it in your native language?
element symetryczny
worn coyote
I'm assuming that's what you call $g^{-1}$?
warm shaleBOT
EQUENOS
worn coyote
If so, then you probably mean the inverse element
grand relic
obtuse pebbleBOT
obtuse pebbleBOT
@grand relic Has your question been resolved?
hardy widget
Note that the given expression is the square of the distance between two points on two different curves
grand relic
Note that the given expression is the square of the distance between two points ...
Yes but how do i proceed
I forgor what to do after deducing them as points for distance formula
hardy widget
Yes but how do i proceed
recall the shortest distance between two curves is taken along their common normal
grand relic
recall the shortest distance between two curves is taken along their common norm...
AHHHH RIGHT
so the points in question are dist between (x1,5-2x1) (x2, rt(1-x2²))
Wait how again do u represent it as eqn of curve 😭
Im fr forgetting
hardy widget
I have no idea what you're trying to ask
you have the distance between a line and a curve
the line gives you what the slope of the normal must be
grand relic
you have the distance between a line and a curve
Thats what im trying to find no?
hardy widget
Thats what im trying to find no?
fine just
forget I said that message
and move on from that
you can still understand with that
grand relic
Like what do i do with those points now
hardy widget
the line gives you what the slope of the normal must be
.
you can find the point on the second curve where the normal has the required slope
grand relic
The slope between those two points is x2²-2x1+4/x1-x2
Is that what ur referring to 😭
hardy widget
The slope between those two points is x2²-2x1+4/x1-x2
...
the normal is perpendicular to both curves
and is hence perpendicular to y = 5-2x
hardy widget
$y=5-2x$ and $y=\sqrt{1-x^2}$
warm shaleBOT
Civil Service Pigeon
hardy widget
grand relic
OHHH so u just parametrize the coordinates
oooh thanks now i got it : D
Sorry for annoying u
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
summer jolt
dont understand why this is wrong
obtuse pebbleBOT
dont understand why this is wrong
summer jolt
can i have some help with this
hardy widget
dont understand why this is wrong
recall the domains of arccos x and arcsin x
,w domain of arccos x
,w domain of arcsin x
summer jolt
is that in degrees or radians?
polar fossil
neither
worn yoke
the domain of inverse sin and cos is the same for degrees and radians, the range is what's different
bc they take a unitless ratio as input and return an angle as output
hardy widget
(the angle can be in degrees or radians tho)
slate hamlet
$Sin^{-1}(/sqrt{2}) =? $
summer jolt
idk
hardy widget
$\sin^{-1} \left(\sqrt{2} \right)=\text{?}$
warm shaleBOT
Civil Service Pigeon
$\sin^{-1} \left(\sqrt{2} \right)=\text{?}$
slate hamlet
Ty
slate hamlet
Do you know what the range of Sin x is?
hardy widget
recall the domains of arccos x and arcsin x
@slate hamlet
hardy widget
im using this image as reference
The point we're trying to make is that $x=\sqrt{2}$ isn't in the domain of $\sin^{-1} (x)$
summer jolt
Do you know what the range of Sin x is?
yea -1 to 1 inclusive
warm shaleBOT
Civil Service Pigeon
hardy widget
summer jolt
ohh so it be impossible?
worn yoke
yea -1 to 1 inclusive
so the domain of the inverse function is the same as the range of the original function
summer jolt
so it the answer no solutions then?
hardy widget
ohh so it be impossible?
better to say it "doesn't exist"
and same for the expression as a whole
obtuse pebbleBOT
@summer jolt Has your question been resolved?
opaque dome
Sin(x) = -sqrt(2)/2
Cos(x) = -sqrt(2)/2
[Knowing that sqrt(2)/2 is the same as 1/sqrt(2)]
deft ginkgo
The arcsin term does eval to -pi/4, but the arccos term evals to 3pi/4
Arcsin and arccos are the same as the -1 notation btw, just in case you're not familiar
opaque dome
!noans :)
obtuse pebbleBOT
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
deft ginkgo
Bruh I mean what else can u do here 😂
U can validate using your unit circle, and asking yourself what angle gives me the value inside the arc function
This is something you might want to memorize, it's gonna hunt you till college unless you go the humanities route
obtuse pebbleBOT
@summer jolt Has your question been resolved?
hazy scroll
need help
latent walrus
im not surprised it doesnt like that format
coarse ibex
Looks correct, maybe they just want it simplified
hazy scroll
what can i do to simplify it
coarse ibex
what's (1+5)/2
summer jolt
still confused
obtuse pebbleBOT
still confused
summer jolt
where did i go wrong
latent walrus
why are you writing the values twice?
the arcsin comes to -pi/4, the arccos comes to 3pi/4 this much i agree
dim yacht
where did i go wrong
And why did you change both -pi/4 to 3pi/4
summer jolt
because the range fore sin and cos is -1<=x<=1, so i need to subtract and do pi - pi/4
is that not correct?
latent walrus
the outputs of inverse trig functions are in the domain of the trig functions (albeit restricted), nothing to do with the range of them
the inputs of the inverse trig functions are in the range of the trig functions
think you have some concepts confused
latent walrus
the arcsin comes to -pi/4, the arccos comes to 3pi/4 this much i agree
just work directly from this
no trickery
obtuse pebbleBOT
@summer jolt Has your question been resolved?
summer jolt
<@&286206848099549185> so is it pi/2?
obtuse pebbleBOT
summer jolt
.reopen
obtuse pebbleBOT
✅
latent walrus
sounds reasonable
summer jolt
or maybe the chain rule?
latent walrus
you know it
summer jolt
https://tenor.com/view/thor-battle-ropes-working-out-work-out-chains-gif-2543160...
lol ok
can you tell me what it is again
its a bit confusing in my notes
obtuse pebbleBOT
@summer jolt Has your question been resolved?
obtuse pebbleBOT
@summer jolt Has your question been resolved?
summer jolt
<@&286206848099549185>
terse comet
All except the first part
summer jolt
wdym
terse comet
It’s sec^2(1-cosx) sin x
summer jolt
is that part of the rule
terse comet
Yeah Bc the chain rule you keep the inside of the parentheses
summer jolt
can u type what exactly this chain rule is
terse comet
The chain rule is used when you have a function inside another function
Like sin(cosx)
terse comet
summer jolt
maybe i need to do some more simplifying?
summer jolt
Where did the square come from
terse comet
Because d/dx tan u = sec^2 u
hoary lynx
(sec(1-cos(x))^2
summer jolt
ohh
terse comet
Or sec(1-cosx)
summer jolt
wait why
terse comet
Ok so
hoary lynx
for tan(1 - cos x) make 1 - cosx equal u
then the derivative of tan u equals (sec u) ^ 2
then plug 1 - cos x back in and get (sec (1 - cos x)) ^ 2
then multiply by the derivative of 1 - cos x
((sec (1 - cos x)) ^ 2) * (sin x)
terse comet
Yeah that looks right
hoary lynx
yes, that's all correct
hoary lynx
oh wait you might want to check what the original function was
hoary lynx
the work is correct but on the picture it shows that y is a different function
hoary lynx
yeah but that would be the right answer if you were differentiating what you wrote down
hoary lynx
yes
if you make x - 2 equal to u and differentiate e^u and x - 2 and multiply them together you get e^u which is still e^(x -2)
hoary lynx
for the domain of y you have to check for what x values does y not exist
the same thing for y'
hoary lynx
yes
if there was something like 1 / (x - 1) then x couldn't be 1 since you would have 1/0 which is undefined
hoary lynx
no you would still have to do chain rule
if you have e^2x then you would have to do chain rule
if you try solving this then you'll find out that it's not just e^2x
summer jolt
Ok so if I had e^arcsin x
Then outer function would be e^x
And inner would be arcsin x
hoary lynx
yeah
summer jolt
Right?
Okk
This is what I got
A bit stuck when figuring out derivative of g(x)
hoary lynx
arcsin x is just one of those derivatives you memorize like the derivative of tan equals sec^2
there's no special rule for figuring it out. In the future just know that it equals 1 / sqrt(1 - x^2)
hoary lynx
yes
hoary lynx
no problem
summer jolt
can you help me with this too
i have done similar problems but its been a while
i first have to find the derivative of the equation right
but the notation is confusing me
it looks like its x * arcsin(y)?
hoary lynx
yeah
summer jolt
do i take derivative of both sides
hoary lynx
since we need to know dy/dx we need to derive with respect to x
this means that if we take the derivative of something like x^2 we get 2x but if we derive y^2 we would have to multiply it by dy/dx
the derivative of y^2 with respect to x would be 2y * dy/dx
summer jolt
ok i think im understanding this in two different ways
i have attached two lines for the nxt step... which one is correct
hoary lynx
mb I explained it wrong the first time
so you don't multiply it by dy/dx when you start taking the derivative
you do that at the end
so y^2
the derivative would be 2y * dy/dx
summer jolt
so this is the 1st step?
hoary lynx
yes but on the left side you forgot about the product rule
hoary lynx
yes
summer jolt
what should i do with the rhs
hoary lynx
take the derivative also
hoary lynx
yep
hoary lynx
yeah dy/dx
hoary lynx
well for arcsin y you took the derivative of x and not arcsin so since you didn't differentiate a y variable you don't put it there
for x / sqrt(1 - y^2) you did differentiate arcsin y so you multiply dy/dx
hoary lynx
yes but you didn't do the derivative of it since it's still arcsin of y
hoary lynx
yeah
summer jolt
and what abt rhs
hoary lynx
rhs you took the derivative of y^2 which has y so you multiply it by dy/dx
hoary lynx
the 2y disappeared after the second step
hoary lynx
can I see what you wrote down?
summer jolt
yea sure
its a bit messy
do i need to simplify it or smth
or it just supposed to be like that
summer jolt
shoot right
ok
ill add that in
anyways the question asks for the slope at (1,0)
so do i need to plug something into the dy/dx
hoary lynx
yea
since x is 1 and y is 0 then you just plug in 1 for x and 0 for y and solve for dy/dx
hoary lynx
radians
though it's the same either way lol
oh wait mb that only applies for sin
not arcsin
but yeah always use radians for calculus
unless they specifically ask for degrees
summer jolt
kk
ohh that makes sense
cuz i also used to use degrees for trig
and now everything is in radians
and thats probly becuz its calc
@hoary lynx i tried to solve a similar problem and got it wrong
hoary lynx
can I see your work?
hoary lynx
what did you plug in for y?
summer jolt
-0.5
hoary lynx
yeah that should be the answer
also want to know an alternate way you could have solved it?
summer jolt
sure
summer jolt
right
yea that makes sense
also i just realized the problem asks to find the equation not the line
summer jolt
and isnt that kind of hard to do
hoary lynx
well I would set it up differently
since it's a line the equation for a line is y = mx +b
hoary lynx
but the other way of writing this is y - y1 = m(x - x1)
y1 and x1 being the coordinates
summer jolt
is that way better
hoary lynx
yes because you just plug in the coordinates, move the y1 to the right and you're done
hoary lynx
when you took the derivative you changed 2x + 1 to 2x - 1
summer jolt
yea
hoary lynx
also the 2x - 1 needs to be squared since the derivative of arcsin is 1 / sqrt(1 - x^2)
summer jolt
when you took the derivative you changed 2x + 1 to 2x - 1
but that becuz its 1 - (2x+1)
i dont get it
hoary lynx
oh yeah nvrmind you're right
summer jolt
ohh its the minus
hoary lynx
but it still needs to be squared
summer jolt
but its not impossible
summer jolt
but it still needs to be squared
where
hoary lynx
1 - (2x + 1)^2
summer jolt
ohh yea its part of the formula
hoary lynx
also since it's chain rule you also still have to multiply by the derivative of 2x + 1
summer jolt
also since it's chain rule you also still have to multiply by the derivative of ...
what
r u serious
hoary lynx
yeah
hoary lynx
also you did (2x - 1)^2 instead of (2x + 1)^2
hoary lynx
I might be busy but I'll try
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
olive echo
french math help pls
obtuse pebbleBOT
french math help pls
ember frost
send the question, and translate it to english please
ember frost
i mean, there might be, but for the time being its best for you to translate the question
olive echo
A machine can break down. The probability of a breakdown is 0.01 each time the machine is used. The machine must be used 100 times.
- The number of breakdowns observed is a random variable X. Calculate the probabilities of obtaining X=0, X=2, X=3 and X≥ 4.
- The cost of a repair is estimated at 500 euros; the expenditure, expressed in euros, on repairs to the machine is a random variable Y. Calculate the expected value of Y and its standard deviation.
olive echo
i mean, there might be, but for the time being its best for you to translate the...
there
ember frost
hm, seems to be outside of my knowledge. i cannot help you then
meanwhile you can wait for other people
olive echo
alright
red ice
it's binomial probability
for example, $P(X = 0) = {100 \choose 0} * 0.01^0 * 0.99^{100}$
warm shaleBOT
south's secret twin brother
olive echo
it's binomial probability
for example, $P(X = 0) = {100 \choose 0} * 0.01^0 * 0....
so how do i calculte de expected value of y and its standard deviation
red ice
so how do i calculte de expected value of y and its standard deviation
cool, so you have to remember that the expected value is np, and the variance is np(1 - p)
where p is the proability of success
that's 0.01 in this question, cause you're measuring the number of breakdowns
and n is the number of trials, so 100
olive echo
okokk
btw this is for a friend so id understand anything
he's in college im still in high school 😭
obtuse pebbleBOT
@olive echo Has your question been resolved?
old hollow
Can someone explain what Shearing is in Matrices? Aren't we technically just scaling them in a certain direction?
obtuse pebbleBOT
Can someone explain what Shearing is in Matrices? Aren't we technically just sca...
light flume
Can someone explain what Shearing is in Matrices? Aren't we technically just sca...
im not sure how u think of 'scaling in a certain' direction but to me, the english makes sense
old hollow
Lol I'm watching that exact video right now.
light flume
u might find the visual representation more intuitive
old hollow
We are just shifting everything in a certain direction
Like scaling and shifting in a direction
I am not sure if I am misunderstanding or something.
light flume
i think u probably understand it but just dont confuse it with rotation
old hollow
Yeah, it's different, I just don't how to describe it.
light flume
Yeah, it's different, I just don't how to describe it.
im not in uni yet so my explanation or 'description' of it is not osmething to be taken as 'acceptable' as anything formal
but
thinking of a gradient
like in 2D, you are slanted to the other unit vecotr
or the other way i thought of it was that each point described was a certain signed distance away from the axis
which is equivalent to just what gradient really describes
old hollow
Shear's in essencen are like gradients.
obtuse pebbleBOT
@old hollow Has your question been resolved?
gloomy pelican
I need to find a lower and upper bound on this $\sum_{i=1}^{n} \frac{a_i}{a_i + a_{i+1}} \quad (\text{cyclic with } a_{n+1} = a_1, , a_i > 0 \text{ for all } i)$ I tried induction and AM-GM but that doesnt work and i noticed that this expression is homogenous so we can take the sum to be 1, I think the minimum is when all terms are equal and we get $n/2$ I need some help/a hint on which inequalities to use (I cant use Jensen tho)
obtuse pebbleBOT
I need to find a lower and upper bound on this $\sum_{i=1}^{n} \frac{a_i}{a_i + ...
warm shaleBOT
ω
obtuse pebbleBOT
@gloomy pelican Has your question been resolved?
gloomy pelican
<@&286206848099549185>
gloomy pelican
okay induction works on the upper bound and i got <=n-1, but I still have to prove that its the best upper bound
obtuse pebbleBOT
@gloomy pelican Has your question been resolved?
obtuse pebbleBOT
@gloomy pelican Has your question been resolved?
obtuse pebbleBOT
gloomy pelican
.reopen
hearty citrus
How to solve
obtuse pebbleBOT
How to solve
orchid wind
calc allowed?
obtuse pebbleBOT
@hearty citrus Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
novel solstice
hello! im currently struggling with the quadratic formula, specifically on what to do if the b isnt a perfect square. (im not extactly the best at matth but i would like to get good at it)
obtuse pebbleBOT
hello! im currently struggling with the quadratic formula, specifically on what ...
novel solstice
did i do something wrong with my process?
dusk widget
hello! im currently struggling with the quadratic formula, specifically on what ...
if b isn’t a square, then it’s just not a square 
novel solstice
oh no
dusk widget
the quadratic formula will always give you the roots, but it doesn’t always have to be a pretty clean number
it can be super ugly too
but, you haven’t actually checked whether or not this is the case
novel solstice
what do i do then if its an ugly number?
dusk widget
you did sqrt(570)
that’s not what the quadratic formula wants
it wants sqrt(570^2 - 4 * 30 * (-14990))
,calc sqrt(570^2 - 4 * 30 * (-14990))
warm shaleBOT
Result:
1457.2920091732
ah, it’s also ugly 
novel solstice
oof
dusk widget
,calc (570^2 - 4 * 30 * (-14990))
novel solstice
im currently studdying someones soulution
warm shaleBOT
Result:
2.1237e+6
for a project (but im getting no responses)
dusk widget
what do i do then if its an ugly number?
we cry, and hope our tears will somehow make the number look nicer 
novel solstice
we cry, and hope our tears will somehow make the number look nicer <:blobcry:971...
maybe it could be because of the chosen a1 and Common difference
novel solstice
wait is it ok if i send somthing else? its still related to this math question
dusk widget
sure
novel solstice
im so sorry if im being a bit blurry
dusk widget
you’re okay
novel solstice
its a part of this bigger arithmetic problem
where i have to calculate expences
slate hamlet
Whats the question?
slate hamlet
From what I can tell you have to find the limiting value of n, and n shouldnt be a fraction
So you can round down i believe
novel solstice
A) How many weeks will you need to be able to save for your target amount?
i have to look for n
My Sn should be 14990
a1 is 600
D is 60
my groupmaate said they used the Sn=n/2(a1+a1+(n-1)d)
slate hamlet
<= is fine
novel solstice
method for getting the numbers for the quadratic equatuion
slate hamlet
I mean essentially yes
novel solstice
they said it was the same as Sn=n/2(a1+an)
slate hamlet
Yes that also works but you dont know an
Basically you have to solve the quadratic equation when your expenses are = 14990
If n is a fraction
You round down
slate hamlet
You dont have to apologize
novel solstice
i double checked my notes
slate hamlet
But then this formula doesnt make sense
Cause its the formula for sum
Is D the amount you are saving per week?
novel solstice
common difference is how much you are addding to a1 each week
slate hamlet
Or is it the extra amount you are saving per week like interest
Okay
No then sum is fine
14990 isnt an
Its the sum
novel solstice
oops
slate hamlet
Yea and when you solve this quadratic
You are getting 14.7 something?
You cant round up
Because you will end up saving more
Either leave it at 14.78 weeks
Or round down to 14 weeks
novel solstice
my groupmate rounded it down
slate hamlet
Well
You can also argue for rounding up
Because then you will eat the target amount and more
Either way your working is correct
novel solstice
ohh ok ok
my main problem with my groupmate's solutution is the complete soulution for the quadratic equation they skip over so many parts of it that i dont understand it
thats why im trying to solve it for myself
but at thw square rooting part when i did 570 it gave me a decimal
so i was thinking what i should do next
if i did something wrong because its not a perfect square
slate hamlet
It doesnt have to be a perfect square
novel solstice
hello! im currently struggling with the quadratic formula, specifically on what ...
this
novel solstice
It doesnt have to be a perfect square
oh?
what if it isnt a perfect square?
do i round it up?
it will become 24 if i do
slate hamlet
Was this your friends working?
novel solstice
Was this your friends working?
yes
slate hamlet
Oh
novel solstice
im trying to understand it
slate hamlet
This working isnt correct
novel solstice
This working isnt correct
what did i do wrong exactly so i know what to improve on
novel solstice
Are you allowed graphing calculators?
no sadly
slate hamlet
Wait
What did you plug into the calculator?
You have to plug in this entire thing
novel solstice
You have to plug in this entire thing
wait fr?
slate hamlet
Yea
novel solstice
i dont have a 2 liner calculator
slate hamlet
Then you have to plug it in one by one ig
Solve the sqrt first
Then the other stuff
novel solstice
ok
wait
lemme do that
sory wait im evaporatoimg
Wait so like this?
Hold up im so confused
Or is it the other way around
Kase ill still get the same decimal
*because
slate hamlet
Huh
Explain
You have to find this value
-570 + or - the sqrt expression
Divided by 60
novel solstice
OHHHHHH
SO IVE BEEN DOIIN IT WRONG
OK OK
I GETS IT
:DDDDDD
wait lemme solve the rest of ot
and ill show you
This is what i have rn
slate hamlet
Your 2 * 30 turned into 2 * 50 ig
novel solstice
oopd
slate hamlet
And then into 10?
slate hamlet
Also 570 is also divided by 60
novel solstice
Also 570 is also divided by 60
divide after squarerooting?
slate hamlet
warm shaleBOT
novel solstice
oh lord
its fine, ill just try again tommorow i cant think when im so burnt out
@slate hamlet im so sorry if it was a pain, i really apreashate your patience
slate hamlet
its fine, ill just try again tommorow i cant think when im so burnt out
Its all right you are veryyy close
Something went wrong here
Cause the square root shouldnt be that big
novel solstice
weh? what do you think i did wrong?
slate hamlet
I dont know you must have entered a couple extra zeroes in the calculator
,w calculate (1314042)^2
warm shaleBOT
slate hamlet
Yea idk what you entered
novel solstice
Solve from here
0k ok
Oh wait
Im short circuiting
I cant keep my eyes open i think i moght have to stop
Im so sorry i cant keep mysef awake anymore ill have to stop but i have an idea how to solve tgis
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
queen sand
Can i get a step by step explanation preferably visually on how to solve this task?
obtuse pebbleBOT
Can i get a step by step explanation preferably visually on how to solve this ta...
queen sand
Determine the limit value
bold bane
Expand (4+h)^2 then simplify the expression.
obtuse pebbleBOT
@queen sand Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
cerulean umbra
i'm studying one-sided limits using the epsilon-delta definition of a limit, but im stuck on this question. so far i was able to write a statement saying (1 - x) + sqrt(1 - x) < epsilon. what should i do next?
obtuse pebbleBOT
i'm studying one-sided limits using the epsilon-delta definition of a limit, but...
cerulean umbra
this is what i have so far
obtuse pebbleBOT
@cerulean umbra Has your question been resolved?
cerulean umbra
<@&286206848099549185> i posted this almost an hour ago. some help would be great
past sand
I don't think the "for all x < 0" is any help
I think you can just take delta = epsilon here
cerulean umbra
would that satisfy it?
i wrote some more for it:
(1 - x) + sqrt(1 - x) < delta + sqrt(delta) < epsilon
past sand
I'm too rusty for this, damn
past sand
i wrote some more for it:
(1 - x) + sqrt(1 - x) < delta + sqrt(delta) < epsilon
That should work for x > 0 which is kind of given
What's left is to get delta in terms of epsilon I guess
unreal musk
(you might like to make it such that 1 - x is "small enough", potentially)
stray lily
how to make channel
obtuse pebbleBOT
how to make channel
marsh geyser
Do you want the definition of function?
stray lily
Do you want the definition of function?
yes
like types
and everything
im literally 0
math
marsh geyser
I will explain in an easy way
marsh geyser
Go ahead
stray lily
why or where do we use functions
marsh geyser
Very open question
stray lily
these rules and definitions r created to solve problems in the past
so what about functions
marsh geyser
Imagine a function is like a machine.
stray lily
okay
marsh geyser
That machine has some instructions inside
stray lily
input and output
marsh geyser
Right now we don’t care what are those instructions
marsh geyser
input and output
No
stray lily
okay
stray lily
okay
marsh geyser
The input goes inside the machine, does the instructions and give in the other side an output
Lets call the machine f(x)
stray lily
okay
marsh geyser
I will give this machine the following instructions
Whatever you receive as an imput, multiply by 2, add 3 and give the result as an output
f(x) = 2x+3
Remember
stray lily
done
marsh geyser
f(x) is the machine
stray lily
so lets say i put 4
stray lily
isee
marsh geyser
Go ahead
stray lily
like polynomial and square root functions
r these the types
or what
cuz i kinda dont understand this part
marsh geyser
We can have f(x) = sqrt(x) for example
The instructions now are, taking the square root of your input
stray lily
ik
marsh geyser
But sometimes the machine can break
marsh geyser
For example in this one
earnest scarab
But sometimes the machine can break
there are many types of functions, the basic difference of a function from any other graph is that; for each x value, there is its own y value
marsh geyser
If your input is negative and you are working in real numbers
When you do f(-1) = sqrt(-1)
stray lily
it wont work
marsh geyser
-1 is a real number but sqrt(-1) is not
So your input works, but instructions don’t know what to do
stray lily
Now, type of functions is your next question?
look in my book it says types r algebraic and non algebraic
what about bijective and surjective
stray lily
-1 is a real number but sqrt(-1) is not
isee
marsh geyser
Any variable that has a log, or trigonometric function like sin, cos or the ones with the exponent being the variable are non algebraic
f(x) = e^x is non algebraic for example
Or f(x) = tan(2x)
marsh geyser
Ok
marsh geyser
Maybe you are studying too many things in a very short period of time because you have a test soon?
stray lily
what is the diffrence between classification of functions and types
stray lily
Maybe you are studying too many things in a very short period of time because yo...
yes
tbh
marsh geyser
That is a problem, because it is very possible that you forget absolutely everything tomorrow
But if you get the machine idea at least you know how a function works
stray lily
But if you get the machine idea at least you know how a function works
i get it
anyways tysm for the help
how to close this channel
obtuse pebbleBOT
If you are done with this channel, please mark your problem as solved by typing .close
stray lily
.close
obtuse pebbleBOT
stray lily
?
royal raptor
?
the channel is officailly closed now and can be used by another person
once the message is sent that its officially closed
obtuse pebbleBOT
Available help channel!
uneven sentinel
i wrote some more for it:
(1 - x) + sqrt(1 - x) < delta + sqrt(delta) < epsilon
| [ sqrt(1-x) - (1-x) ] / (1-x) |
= | 1/sqrt(1-x) -1 | < 1/sqrt(delta) - 1
Epsilon + 1 = 1/sqrt(delta)
Delta = 1/ (epsilon+1)²
U found ur delta and so its proven for any epsilon
obtuse pebbleBOT
| [ sqrt(1-x) - (1-x) ] / (1-x) |
= | 1/sqrt(1-x) -1 | < 1/sqrt(delta) - 1
Epsi...
@uneven sentinel Has your question been resolved?
left mesa
Hallo! I just need an explanation on why this is a one to one function
obtuse pebbleBOT
Hallo! I just need an explanation on why this is a one to one function
left mesa
I was a bit confused since this was the definition
Also how come the answer to this one is the last one?
I also don't get this, how did the denominator become 7/2
left mesa
Also how come the answer to this one is the last one?
This and the other one below is Rational Functions
coarse ibex
I was a bit confused since this was the definition
The definition they gave is $x_1 \neq x_2 \implies f(x_1) \neq f(x_2)$. This is equivalent to $f(x_1) = f(x_2) \implies x_1 = x_2$.
warm shaleBOT
Morrow
left mesa
How so?
coarse ibex
It's called "taking the contrapositive". In general "P implies Q" is equivalent to "not P implies not Q"
coarse ibex
Also how come the answer to this one is the last one?
For this question, "find the domain" just means "figure out for which values of x the function definition makes sense"
left mesa
how come it's not -2 then? is it because there's no x variable?
coarse ibex
In the first question, the expression "(3x-7)/2" makes sense for any (real) value of x, so the domain is all real numbers.
left mesa
o
left mesa
I also don't get this, how did the denominator become 7/2
then what about the second one
howd it become - 7/2
NVM
divide both sides by 2 after transposing 7
lol
I forgot it's like solving x
marsh geyser
What sides?
coarse ibex
I assume they mean when solving for denom=0
coarse ibex
yeah so with a rational function its domain is anywhere the denom is not 0
coarse ibex
you got a specific question?
left mesa
then teach me how to solve it
left mesa
you got a specific question?
no 😅
coarse ibex
$$3^{3x+1} = 9^x$$
coarse ibex
the bot?
warm shaleBOT
Morrow
left mesa
what will happen to the exponent x on the 9^x?
marsh geyser
anyways can u help me with this instead?
Some things must be specified here btw.
left mesa
I know 9 will be 3^2
coarse ibex
yeah
left mesa
Some things must be specified here btw.
I'm sorry 😭
marsh geyser
Not you, the image you shared
coarse ibex
so we can write it as $$3^{3x+1} = (3^2)^x$$
warm shaleBOT
Morrow
left mesa
Not you, the image you shared
Oh
left mesa
so we can write it as $$3^{3x+1} = (3^2)^x$$
ok then cancel both 3?
coarse ibex
**Morrow**
not yet, first you need to simplify the right-hand side so it looks like 3^something
left mesa
oh then 3^2x?
coarse ibex
yeah
then you just solve 3x+1 = 2x
(this should remind you of injectivity, btw)
one-to-one
left mesa
am I right? x (3-2) = -1?
left mesa
(this should remind you of injectivity, btw)
idk that 😭
coarse ibex
yeah x=-1
coarse ibex
idk that 😭
I mean one-to-one
coarse ibex
yeah one-to-one and injective are synonyms
coarse ibex
yeah
left mesa
oki thank u so much
coarse ibex
(this should remind you of injectivity, btw)
and what I meant by this is that you can do the cancellation because the function f(x) = 3^x is one-to-one
left mesa
and what I meant by this is that you can do the cancellation because the functio...
I'm a bit confused
oh is it bec its exponent is an odd number?
coarse ibex
no, it works for any positive base
left mesa
I'm told that if an exponent is an odd number then it's one-to-one
coarse ibex
you're thinking of the function x^k where k is odd
left mesa
you're thinking of the function x^k where k is odd
ye