the function definition already requires the entire domain to have an image
#help-42
viscid silo
hallow stirrup
yes true
viscid silo
surjectivity just means the preimage of the codomain is a subset of the domain
hallow stirrup
subset? not the domain itself?
viscid silo
does not necessarily have to be the domain
hallow stirrup
but every value in domain has to have an image right
viscid silo
read the definition of surjectivity carefully
hallow stirrup
subset also means the domain itself right
carmine sorrel
it can, yes
hallow stirrup
oh ok
carmine sorrel
what you said about surjective is correct. every element of the codomain is the image of an element in the domain.
This pre-image does not have to be the whole domain
hallow stirrup
i see
but wont that go against the defined domains
what i mean is, if the pre-images ≠ domain, that implies that some values in domain do not have an image in co-domain
which is wrong
carmine sorrel
hallow stirrup
i havent gotten to inverse functions yet
carmine sorrel
it's not the inverse. it's reused notation. it means the pre-image here
sick cloak
wait this server is for all ages, right?
hallow stirrup
yes
sick cloak
k
carmine sorrel
13+ i believe
carmine sorrel
pls help me with problem 2
read #❓how-to-get-help
open your own channel. and upload an image of the question
hallow stirrup
it's not the inverse. it's reused notation. it means the pre-image here
oh ok
carmine sorrel
i havent gotten to inverse functions yet
Basically,
If I have {1,2,3,4} -> {1,2,3} with f(x) = x for x=1,2,3 and f(4) = 1
Then the preimage of {1,2,3} can be {1,2,3}
it can also be {2,3,4}
hallow stirrup
https://mathworld.wolfram.com/Pre-Image.html
i find the notations very confusing
carmine sorrel
yeah..... it's dumb
hallow stirrup
Basically,
If I have {1,2,3,4} -> {1,2,3} with f(x) = x for x=1,2,3 and f(4) = 1...
my brain has just stopped working ill break it down for my own sanity:
f(1) = 1
f(2) = 2
f(3) =3
f(4) = 1
oh i see what you mean
kind of
thats a onto function right, all of the co-domain values have a pre image in domain
still unclear on why the set of pre-images ≠ domain
calm coralBOT
@hallow stirrup Has your question been resolved?
strange juniper
calm coralBOT
strange juniper
confused how to solve this?
naive owl
for a function to be differentiable, what must it also be?
strange juniper
if a point exists..?
naive owl
well yes, but it must also be continuous
implying that at x=0, the top expression and the bottom expression must be equal for it to be differentiable
and since it asks what makes it not differentiable, they must not be equal
i.e. breaking continuity breaks differentiability
strange juniper
oh because kind of like limits? left and right of 0 must be equal
naive owl
sort of, though there are situations where the limit exists at a point but it is not differentiable at that same point
take for instance $\lim_{x\to 0}\abs{x}$
potent lotusBOT
a disappointing son
naive owl
that limit exists and is equal to 0, but |x| is not differentiable at x=0
naive owl
and since it asks what makes it ***not*** differentiable, they must ***not*** be...
the main takeaway being this
naive owl
sounds like a good idea to me
naive owl
well recall that you're trying to see if they're equal at the point x=0
so you should be plugging x=0 into both expressions
strange juniper
but the second one x > 0
naive owl
right, but it gets infinitely close to the point x=0
therefore implying continuity if it is equal to the expression above it at that point
strange juniper
so its the right side 0+
naive owl
that is one way of thinking of it
naive owl
hm well i think more than 1 of them work
which is odd because the question doesn't seem phrased in a way to select multiple answers
strange juniper
oh
bc for a and b i said it is both diff bc both =0
then c i think both = 5?
then d for me i got -1 is not = to 0
strange juniper
okkk
i also um need help with this
i graphed c(t) and b(t)?
but am i supposed to do derivative of them?
and find max and min
<@&286206848099549185> :< sorryyy
valid carbon
Which one is cubic formula equation? I'm so confused
calm coralBOT
Which one is cubic formula equation? I'm so confused
languid dragon
A cubic equation is an equation that can be represented in the form a x 3 + b x 2 + c x + d = 0 ax^3+bx^2+cx+d=0 ax3+bx2+cx+d=0, where a, b, c, d a,b,c,d a,b,c,d are complex numbers and a is non-zero. By the fundamental theorem of algebra, a cubic equation always has 3 roots, some of which might be equal.
This is how you would know if it is one or not.
If you can't figure it out, come back.
steel karma
Who even uses that 
languid dragon
Me
valid carbon
Thank You
golden quartz
A cubic equation is an equation that can be represented in the form a x 3 + b x ...
.
i never use that 💀
valid carbon
.close
sudden patio
f(x) is in blue on the left and g(x) is in red on the right, how would i go about finding the limit at x->1 for g(x)?
leaden heron
So we both struggling with Calc1000B huh.
calm coralBOT
@sudden patio Has your question been resolved?
sudden patio
<@&286206848099549185>
sudden patio
f(x) is in blue and g(x) is in red, what happens when adding limits where one doesn't exist or one is equal to infinity?
calm coralBOT
@sudden patio Has your question been resolved?
gusty oak
what is the equilibrium quantity? apparently my answer is incorrect
gusty oak
here is what they told me to do, and i did exactly what they asked and still got that incorrect number
velvet osprey
your answer for the equilibrium quantity is incorrect
hm. ok wait
the numbers do check out
oh but look at the rounding instructions for the quantity @gusty oak
gusty oak
cant lol
plus, didnt it say one answer was correct? thus format also good?
i could get rid of the .5 but i doubt it will work out
but id have to do to both
oh sht..
ur right
welp didnt work
took out the .5
.5 doesnt round up
velvet osprey
on the contrary, you round up on five
gusty oak
i spent like an hour this set of problems
until question e
can we have someone else confirm
i have 1 try left
velvet osprey
so rounding down didn't work...?
gusty oak
.5 is middle
i googled it and you dont round up or down
i took out the .5
got it incorrect
mymathlab program is so bad lmao
do i round up or down?
.5
.close
proper shell
I need help with this i see youre supposed to factor it but the numbers are so weird and so is the equation compared to everything online
proper shell
please @ me if someone is willing to help as I have discord alt tabbed and very forgetful
calm coralBOT
@proper shell Has your question been resolved?
obtuse pendant
let f(x) = 2/x - x - sqrt(x) ; the question become to show that f(x) = 0 has a root in the interval (2,3) you can know just do the steps of the IVT to prove that
@proper shell
proper shell
let f(x) = 2/x - x - sqrt(x) ; the question become to show that f(x) = 0 has a r...
Wouldn't it be f(x) = 2x - xsqrt(x) - 2 though
To make it so that 0 = to 2x - xsqrt(x) - 2
obtuse pendant
Wouldn't it be f(x) = 2x - xsqrt(x) - 2 though
how did you get it like that ?
proper shell
Just multiplying by x on the 2/x side to move it then minusing 2 so that 1 side was 0
Opposite operations pretty much
proper shell
You'll have to multiply x by the sqrt(x) and 2 no?
I mean
X
Oh wait I think I got it
Hey thanks man
.close
calm coralBOT
calm coralBOT
Available help channel!
rotund birch
ln e^2 no calculator
calm coralBOT
ln e^2 no calculator
rotund birch
I wasn't in class and our teacher didn't give us enough information
I have no clue what ln is and my friend said it was just memorization
I wasn't there so I don't know what to memorize
solemn plover
do you know what e is?
solemn plover
hmm
solemn plover
ln e^2 no calculator
yeah so you can do this using the definition of log, or with log properties
rotund birch
I know how to do log but for some reason I can't figure this out
velvet osprey
you in fact do not need to know the value of e in order to calculate ln(e^2)
have you been introduced to logarithms in general?
rotund birch
by the few notes she gave us 🤩
sorry I'm a little frustrated with my teacher right now JKL;GFJ
I know how to evaluate without a calculator at least
that makes sense
gleaming scarab
by the few notes she gave us 🤩
Are you familiar with the properties of logarithms?
rotund birch
I don't think so
gleaming scarab
I don't think so
I mean stuff like log(a/b)=log(a)-log(b) or log(ab)=log(a)+log(b).
rotund birch
no I don't
gleaming scarab
Well, then you clearly lack the tools to solve this problem.
rotund birch
yeah, she didn't give us very much to work with
rotund birch
have you been introduced to logarithms in general?
not really
velvet osprey
wow, that's shitty of her.
rotund birch
she sent us a few videos and there's some stuff in a packet we got but hardly anything about ln and it's hard to understand anyways
somehow she's the math chair leader or something and she changed from our algebra book to this shitty book that she doesn't even have a teacher edition of
the answers are only the fully simplified version and there are only answers for the odd problems 🥰
she's so silly
ok I give up thank youu
.close
visual wigeon
calm coralBOT
visual wigeon
i have tried
but no one has helped
for the first one i get 0
but how do i work out sin theta
gleaming scarab
but how do i work out sin theta
Subsitute sin(theta) with x, and find the solutions of this equation.
Observe that once we substitute sin theta with x we end up with the same expression given in part 1.
And -0.5 makes that expression zero, which means that it will make our new expression zero as well.
So for x=-0.5 our expression becomes zero and we know that x=sin(theta).
calm coralBOT
@visual wigeon Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
crimson shadow
how do I solve this? lg x = 4
calm coralBOT
how do I solve this? lg x = 4
mellow crater
def. of log
crimson shadow
what does def meann?
potent lotusBOT
Modus
crimson shadow
okay thanks
pulsar knot
what does def meann?
Definition
mellow crater
if base isn't mentioned we usually treat it as 10
crimson shadow
so A is 10?
mellow crater
I'd say so
potent lotusBOT
A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
calm coralBOT
Available help channel!
karmic ridge
omg the channel closed sorry. could i get a hint.
calm coralBOT
omg the channel closed sorry. could i get a hint.
fathom shuttle
usually with problems like these it would be a good idea to list out at least 10 of the next terms
calm coralBOT
@karmic ridge Has your question been resolved?
karmic ridge
usually with problems like these it would be a good idea to list out at least 10...
from 11117?
like 11117, 11118, 11119,e tc
fathom shuttle
or actually
you dont need to
the sum of the numbers would be the change from the starting number to the ending number
karmic ridge
wait why
fathom shuttle
think about it
if you compute the difference from 5 to 3 to 7, its the same as the difference from 5 to 7
calm coralBOT
lapis blaze
shall i ping a fellow of ours
Dio "Toby" Brando?
he is well versed in Newtonian Things
sir, do you want assistance from the best there is, in the name of Toby?
Sir
please answer
hollow totem
depends on the concavity of the graph
lapis blaze
@remote mural
hollow totem
if it's linear (no concavity), you'll get the exact root after one iteration
hollow totem
if it's concave in the same direction that it's moving, you'll undershoot
pearl vigil
This Desmos may help https://www.desmos.com/calculator/k5l90pmit6 Just replace the equation
hollow totem
if it's concave in the opposite direction, you'll overshoot
but as long as you started close, you'll overshoot but still be a lot closer
the way i know this is not that i had it memorized but just that i'm imagining the graphs in my head
and looking at the example you gave
feel free to draw out the others
it's possible for it to
touch the actual root at some step
even in a not linear case
just "infinitely unlikely" in the general case
Computers stop applying newtons method after the last 2 iterations are within a certain tiny amount of each other
In this case the tiny amount would be 0
So it gets the same root twice and then stops
hollow totem
This Desmos may help https://www.desmos.com/calculator/k5l90pmit6 Just replace t...
Probably this one
lapis blaze
Fine. I'll look past this.
hollow totem
it's my pleasure
hollow totem
.close
calm coralBOT
lapis blaze
".close"
hollow totem
calm coralBOT
Available help channel!
cobalt scaffold
Can anyone explain why 0 isn't a vertical asymptote
calm coralBOT
Can anyone explain why 0 isn't a vertical asymptote
cobalt scaffold
so if the numerator wasnt that identity
then 0 would be a va?
say the numerator was 1
ahhhhh gotcha
yeah they're throwing some curve balls lol. thanks for the help!
.close
spring garnet
Can someone help me with geometry homework? It covers perpendicular and angle bisectors. Here is the question that I am currently trying to work on.
crystal forge
think triangles, it's given in the problem based on the definition of perpendicular bisector that you have some congruent segments and angles
if you prove that the two triangles are congruent it follows that their corresponding sides are congruent which is what you want to prove
spring garnet
think triangles, it's given in the problem based on the definition of perpendicu...
the perdendicular bisect or shows congruent segments?
oh wait yeah
so they are congruent due to SAS
crystal forge
exactly
crystal forge
sure, just post them here
crystal forge
equidistant just means same distance
spring garnet
yeah
crystal forge
honestly it's kinda fuzzy, i can't tell where the 2nd entrance even is, i only see one on the right side
or i guess those two arrows are two different entrances? i was interpreting at some sort of large door
crystal forge
well, if you're at A are you closer to one of the entrances than the other?
spring garnet
lol
well i have a different question then i guess
im confused on what the theorem means
like i dont understand what the 'sides of the angle' are
crystal forge
that's uh, sloppy problem writing to say the least
spring garnet
an angle bisector of an angle of a triangle divides the opposite side into two parts that are proportional to the other two sides of the triangle.
still dont understand lol
crystal forge
but what they mean is youve got this angle A opening up and kind of the "sides" of it : )
crystal forge
so they're talking about the angle A, like imagine you just had the red figure and the angle A
and then you are drawing AD, bisecting that angle into two congruent angles (equal measures)
crystal forge
yep
crystal forge
yes you can use that indeed
spring garnet
and then the two angles
so im not sure why we needed the theorem
like i didnt use it
or did i
idk
crystal forge
which theorem?
spring garnet
angle bisector theorem
crystal forge
well read the problem again, they're essentially asking you to prove the theorem
not use it
spring garnet
so how would i do that
crystal forge
you just did lol
spring garnet
oh alright
ill send a picture of the completed proof and lmk
also
would angle b and c be congruent
just cause it shows it
it doesnt say it but it shows it
crystal forge
basically proving that BD = DC is equivalent to proving the theorem because thats what the theorem says is that the point D is the same distance from the two sides
so when you are talking about distance from a point to a line
spring garnet
what
crystal forge
or line segment
spring garnet
okay
crystal forge
spring garnet
so what do i do about angle b and c
whats the reason for them being congruent?
given?
even though it doesnt say
spring garnet
okay
crystal forge
when you are talking about distance from a point to that segment
its basically the path you take from the point thats at a right angle to the segment
intuitively, that's the shortest path right?
spring garnet
yeah
crystal forge
like imagine you are in a field next to a road, and you want to take shortest walk to the road
youre going to end up walking into the road perpendicular to it right?
spring garnet
yeah
crystal forge
so since the whole thing you are trying to prove is that the DISTANCE from that point D to the two sides is equal
thats why BD and CD are drawn in such a way that they make a right angle to their two respective sides (see in the original figure?)
so yes of course those angles in the triangles are congruent as well since they are both right angles
spring garnet
so okay
crystal forge
so they couldve given you just this figure to begin with and told you ok we have an angle, an angle bisector and some point on that bisector
spring garnet
crystal forge
and asked you, prove that the distance between that point and the left red segment and red right segment is equal
but they were nice and already drew those segments at right angles for you...
but it would have been enough to just show you my figure because you wouldve thought to yourself "oh we are looking at the distance between this point and this segment, ill draw a new segment from the point to the red segment at a right angle"
spring garnet
is my proof right?
crystal forge
looks good
spring garnet
ALRIGHT
crystal forge
what does cpctc stand for anyway?
crystal forge
corresponding parts of congruent triangles are congruent?
spring garnet
yeah
its dumb
but my teacher adds the extra c
I have to go for an hour, but can you help me when I get back?
crystal forge
probably wont be around but just make a channel and someone will help you im sure
calm coralBOT
@spring garnet Has your question been resolved?
gray knoll
calm coralBOT
gray knoll
need some help
muted marlin
!help
calm coralBOT
Please read #❓how-to-get-help
gray knoll
i got what x is
muted marlin
how did you do that?
gray knoll
yeah thats the issue
muted marlin
ok when you say you solved for x do you mean you solved in terms of y or did you somehow get a number
what did you get for x
gray knoll
0.75y
gray knoll
60 each
gray knoll
not rlly
muted marlin
ok so the final equation comes from the angle
you know that the angle is just 60 degrees
you can plug in x and solve for y with the last equation
remote mural
It becomes a system of equations with two equations and two variables
gray knoll
ah alright
muted marlin
can you finish from here?
gray knoll
.close
calm coralBOT
calm coralBOT
Available help channel!
icy otter
calm coralBOT
wanton wave
Do you know the pythagorean identities?
wanton wave
for 93, you're given sin(theta) and asked for cos(theta)
So do you see which one of those identities we want to use
icy otter
maybe sin + cos = 1
wanton wave
so plug in the value you have for sin(theta), and what do you get
icy otter
okkk!!
for the square do you multipy the whole fraction by itself or just the top and bottom to get 9/25
(3/5)2 + cos2 = 1
wanton wave
either way should be the same. 9/25 is good
icy otter
is 16/25
wanton wave
no, that's cos^2
wanton wave
Right, but be careful
icy otter
YESSSSSSSSSSSSSSSSSSSS
wanton wave
It could be 4/5 or -4/5
icy otter
wait why
wanton wave
(4/5)^2 = 16/25. And (-4/5)^2 = 16/25
Whenever you apply a square root to both sides of an equation, you get a positive and negative solution
icy otter
ohhhhhhhhhhhhhh
wanton wave
But
You can figure out which one is right
since they told you which quadrant theta is in
icy otter
how
icy otter
Yes itmeans they're in the 2nd box thing on graph
remote mural
Quadrant
icy otter
yess
remote mural
Different of the functions are in different quadrant
wanton wave
And is the cos positive or negative in that quadrant?
icy otter
hmmmmmmm
wanton wave
hmmmmmmm
remember the cos represents the x value of the angle. In quadrant 2, that is negative
wanton wave
Yep you got it 👍
calm coralBOT
@icy otter Has your question been resolved?
icy otter
THANK YOU SO MUCH
calm coralBOT
calm coralBOT
Available help channel!
tulip sail
I need to verify are these are the answers for the principle solution for the sin theta = -1/2
tulip sail
naive owl
your answers in degrees are correct but you converted to radians incorrectly
though you showed the correct formula for converting
tulip sail
Ohh thank you. I didn't notice that. It should be 11π/6.
But I am confused with some of my notes and some online reference where it says principle solution for this as -pi/6.
naive owl
iirc the principal solution is any solution between 0 and 2pi
tulip sail
naive owl
so i'm not sure
tulip sail
Can you verify the above pic if can
calm coralBOT
@tulip sail Has your question been resolved?
calm coralBOT
@tulip sail Has your question been resolved?
pearl skiff
hello, the range of principle solution may differ in different situation.
I think the principal solution required in your context would be
(-pi/2,pi/2] for sine
[0,pi) for cosine
(-pi/2,pi/2] for tangent
pearl skiff
Can you verify the above pic if can
would this help?
tulip sail
So is that the reason that solution is differ in the the printed image that I have sent.
I am stuck in here. There is no any context define in this note.
calm coralBOT
@tulip sail Has your question been resolved?
crisp glen
calm coralBOT
crisp glen
how do i figure this
velvet osprey
carefully expand (α+β+γ)^4
use the known values of α^2+β^2+γ^2 and α^3+β^3+γ^3, as well as vieta's formulas, to your advantage
remote mural
carefully expand (α+β+γ)^4
that sure is going to take a bit
use pascal's triangle
~~also hope you get better soon @velvet osprey ~~
crisp glen
carefully expand (α+β+γ)^4
i have no idea how to expand that
remote mural
use pascal's triangle
pascal's triangle is an option, for sure
velvet osprey
something something multinomial coefficients
remote mural
just assume β+γ = u and expand (α+u)^4 normally
just make sure to also double expand on the u too after u undo the sub
crisp glen
quite the time it may take
potent lotusBOT
remote mural
might take a bit
calm coralBOT
@crisp glen Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
desert bobcat
How exactly can I find an undetermined rate in regard to exponential growth and decay?
desert bobcat
.close
calm coralBOT
upper sparrow
Assume that p(x) = ax^2 + bx + c, and assume that T(p) is mapped to the zero vector
Have you shown that at least? If so then you've answered your original question by showing the kernel just consists of the zero polynomial
upper sparrow
Assume that p(x) = ax^2 + bx + c, and assume that T(p) is mapped to the zero vec...
If not, then try and see what T(p) looks like, then equate that to [0, 0, 0]
oblique current
well you shouldn't still have x's in those equations
blissful ermine
calm coralBOT
granite trout
What have you tried?
blissful ermine
What have you tried?
im not sure what to do. I have not treid anything
granite trout
im not sure what to do. I have not treid anything
What do you think you should try?
Also, I assume you have studied parallelograms?
blissful ermine
yeah ?
granite trout
Yes, I meant what are the values specifically?
blissful ermine
there is a right angle
blissful ermine
multiple accutes ?
granite trout
multiple accutes ?
There are 3 acute angles
Only one of them is known
60 degrees
Can you use that to find any other angle?
granite trout
Yeah so go ahead, which one?
blissful ermine
I mean thw left bottom angle looks the same
blissful ermine
yes
granite trout
Correct
blissful ermine
we have 45, 60, 60 degree angles so far
granite trout
Where did you get the 45 from?
blissful ermine
the right angle
granite trout
Can you send an image of your working?
blissful ermine
im doing this in my head
granite trout
the right angle
A right angle is 90 degrees?
blissful ermine
oh my bad
blissful ermine
yeah
granite trout
There is a straight line going up if you can see
Can you use that in any way?
Extend it to make a familiar shape?
granite trout
Exactly
Correct
Now
What kind of triangle???
I mean equilateral or isosceles or scalene or right angled?
blissful ermine
id have to say obtuse
granite trout
Something like that?
granite trout
id have to say obtuse
Can you draw what you are thinking on paper and send an image?
blissful ermine
im on a 70$ monitor
granite trout
Will the line, when you extend it, be perpendicular to the base of the parallelogram?
blissful ermine
yes
granite trout
Means one angle will be?
blissful ermine
scalein
granite trout
Well, those definitions are wrt sides
One angle will be 90 degrees, right?
You are correct on scalene btw
blissful ermine
yes
granite trout
We need angles though
blissful ermine
scalen obtuse, acute, right
granite trout
And I would suggest drawing now for the part after this one, grab any piece of paper near you
granite trout
scalen obtuse, acute, right
Okay, one angle you figured is 60 degrees, the other 90 degrees, right?
blissful ermine
yeah, the right one
blissful ermine
I have no idea
granite trout
What should it be? Can you use 2x and 3x to find the third angle?
blissful ermine
yeah
granite trout
You extended the straight line to make a right angled triangle
Now I STRONGLY suggest you draw
blissful ermine
yes
granite trout
Can you see any connection between 2x and 3x?
blissful ermine
yeah
granite trout
Know what vertically opposite angles are?
blissful ermine
ive heard of it
granite trout
Okay, I will try to explain it here in brief
Draw 2 intersecting lines wherever you are writing
And then see that 4 angles are formed
And each angle is equal to the one opposite to it
So 2 pairs of equal angles are formed
That is a vertically opposite angle
blissful ermine
i understand now
granite trout
Yes
blissful ermine
the line caused both of the angles
blissful ermine
so then 2x and 3x would have to qual the same
granite trout
No, actually
blissful ermine
oh
granite trout
If you have drawn it all
You will see that via vertically opposite angles
You can write it as 2x + x
And the angle x lies inside the triangle
That means, the angles of the triangle are 90 degrees, 60 degrees, and x
I think you know how to find x?
blissful ermine
subtract ?
granite trout
Do you know what the angles of a triangle sum to?
blissful ermine
150
granite trout
The sum of all angles of a triangle is 180 degrees
That means 90 + 60 + x = 180
You can solve this equation I guess
You will find x
blissful ermine
yay
granite trout
And I suggest doing the problem once again all on your own
blissful ermine
thank you for your help
granite trout
Geometry gets easier when you draw it
blissful ermine
I did not understand how to break it down
granite trout
thank you for your help
You're welcome but do not forget to redo it on your own
blissful ermine
yeah
granite trout
I did not understand how to break it down
Did you draw it?
blissful ermine
yes
granite trout
Good
remote mural
I’m also doing something similar but it deals with trigonometry. Can I ask the question?
granite trout
Now, just try to remember all you know about parallelograms and triangles
And analyze it
granite trout
I’m also doing something similar but it deals with trigonometry. Can I ask the q...
Hey Vegan, check out #❓how-to-get-help
blissful ermine
alright. Thanks for the help
granite trout
Or in short, ask in a help channel that is not occupied @remote mural
granite trout
alright. Thanks for the help
You're welcome, a little more effort and you will be able to do it on your own 👍
calm coralBOT
blissful ermine
calm coralBOT
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rugged stirrup
2x - 3y - 10 = 0;
X^2 + xy + y^2 + 2x + y - 6 = 0
Please I need workings for these simultaneous equations
quick glade
Express x in terms of y
rugged stirrup
i know, but im finding it difficult to arrive at the answer...
let me show you my workings
Somethibg must have been wrong somewhere but I can't figure it out
quick glade
Somethibg must have been wrong somewhere but I can't figure it out
I think you should multiply it by 9 to get rid of the factor, not by 3
rugged stirrup
Oh I see
calm coralBOT
@rugged stirrup Has your question been resolved?
rugged stirrup
the answers are x = 2 or 172/19 and y = -2 or 58/19
But the answer I got is different
vast stirrup
lemme read what happened here
rugged stirrup
Please read
vast stirrup
Ok imma try to work it myself and see
rugged stirrup
Thank you!!
vast stirrup
Thank you!!
I got x=2 and 8/19
vast stirrup
Thank you!!
Get out of bluestacks and get ur ass back here
rugged stirrup
lmao I actually used it for Whatsapp, now it says im playing a game😂
vast stirrup
lmao I actually used it for Whatsapp, now it says im playing a game😂
Whatsapp aint got lobbies what
rugged stirrup
vast stirrup
Alright
so what u do is
Multiply by 3
everything
Ok idk how to use the bot
U get this
Expand and u get this
then just use the quadratic formula
and u get the x vlaues
values
rugged stirrup
Yea i got it to this place after @quick glade made a correction. Both our answers are the same but it doesn't tally with the one in the textbook. It wasn't worked tho', just the answer. Is it possible the textbook answer is wrong??
@vast stirrup
vast stirrup
Whats the answer in the text book
vast stirrup
the answers are x = 2 or 172/19 and y = -2 or 58/19
this?
rugged stirrup
Hmmm, that's actually a problem if it's wrong, I gotta change textbook
@vast stirrup But is there a way to proof our answers
Cause its like plugging those answers in the equation doesn't do much in proving anything?
Both might actually results to 0 which is weird to me, but its maths yk
vast stirrup
<@605796165493194762> But is there a way to proof our answers
I mean its just simple math
rugged stirrup
Aiit, thanks for the help, really 'preciate
vast stirrup
Aiit, thanks for the help, really 'preciate
Ok u can go play now
calm coralBOT
vast stirrup
Yeah
calm coralBOT
Available help channel!
fervent matrix
Hello i have a probability question
calm coralBOT
Hello i have a probability question
fervent matrix
4 players play with a 32 card deck. We draw out 3 cards for each player. What’s the probability that each player gets an ace
Is it this or am i tripping ?
hollow furnace
Why do you have y in the expression????
remote mural
thats a 9 or a 4
fervent matrix
Woops no y haha
fervent matrix
give the aces to the players
Cmon bro 😂
remote mural
and after you do al that thats the number of possibilites that each player gets an ace
fervent matrix
Wait what ?
remote mural
and the total possibilites are just distributing everyone 3 cards
fervent matrix
and the total possibilites are just distributing everyone 3 cards
I don’t get it ?
remote mural
huh?
fervent matrix
The cards are distributed at random
fervent matrix
take out the aces
You can’t do this tho
fervent matrix
That defies the problem they’re asking ?
remote mural
like when u roll 2 dies
whats the probability the sum is 2?
the total possibility is 6*6
fervent matrix
whats the probability the sum is 2?
Sum of ?
remote mural
and the number of ways it give 2 is just forcibly rolling two 1's
remote mural
so your counting the number of ways each player gets an ace is the same as the counting if you give them the aces
so i give them the aces and count
also you have to account for have many ways you can give the acse
fervent matrix
remote mural
anyways the answer is $$(hello)$$
(number of ways to distribute the aceless card set to each player 2 cards) * (number of ways to give the players the aces) / (number of ways to distribute each player 3 cards)
potent lotusBOT
Jester
fervent matrix
I think i agree
How do you calculate the fist part of the product tho ? ( left side )
28C2 * 26C2 * 24C2 ?
@remote mural
remote mural
yeah sure
remote mural
I think i agree
i was personally thinking 28C6 * 6! / (2!)^3
but they maybe the same
fervent matrix
Where did you get that from haha ?
remote mural
just choose 6 cards to distribute
line them up
but every 2 card is counted 2! times in 1 hand
yeah i checked its the same
same with the total numebr
fervent matrix
Nice
Oh wait there are 4 players tho
So 28C2 * 26C2 * 24C2 * 22C2
How do you count the aces tho ?
4! ?
Yeah has to be
Right ? @remote mural
.close
calm coralBOT
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Available help channel!
fiery tide
calm coralBOT
fiery tide
i got the answer but i typed it into my calc manually
and it took forever
is there a quick way of doing this?
leaden thunder
Use demoivre's formula
fiery tide
or do i have to use calculator
fierce mulch
Complex numbers
fiery tide
.close
remote mural
(\sqrt(306))/(x)=(15)/(20)
calm coralBOT
(\sqrt(306))/(x)=(15)/(20)
remote mural
How would I simplify this equation
that looks weird
let me fix that
square root of 306/x = 15/20
[{\f{\s{306}}{x}} = \f{15}{20}] is this it
√ 306/x = 3/4
No the square root is only over the 306
potent lotusBOT
remote mural
yeah
that's it
multiply both sides by x first
so square root of 306 = 15x/20
√ 306 = 15x/20
which is simplified to √ 306 = 3x/4
Oh so looking at the answer key that's how I was supposed to do it
which would be 4√306 / 3 = x
Gotcha
I asked mathway to see what it got it and it gave me some weird bs
alright
.close
cunning ravine
does anyone know what the difference between a "y on x" line of best fit and a "x on y" one?
hasty fiber
The role of dependent and independent variable is switched
cunning ravine
but the line of best fit changes? I don't understand that part
hasty fiber
The equation does, yes
cunning ravine
in this question they already pre-defined the x and y
how?
we aren't changing the variables on the axis right?
hasty fiber
Because one is x plotted against y, the other is y plotted against x
Yes we are, that's exactly what we're doing
cunning ravine
oh ok
but
aren't line of best fits always expressed in terms of x and y
oh so you just write the equation one in
y = mx+c
the other in
x = my+c
form?
hasty fiber
It matches the usual references to x and y, but they're just letters
cunning ravine
wait what do you mean
say for y=2x
that would be "y on x" right
since you are measuring rise over run
hasty fiber
I'll admit I've never seen "y on x" verbatim so I don't know which direction that is
Ideally it'd be defined earlier
cunning ravine
yeah I'm also super confused, can't seem to find anything online either
cunning ravine
alright, thanks a lot!
calm coralBOT
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gilded drum
calm coralBOT
gilded drum
please can someone guide me through this question
do i do the (area x d) x centre of mass of each shape then add it up and divide by the total (area x d) to get the centre of mass for the wholle thing ?
<@&286206848099549185>
calm coralBOT
@gilded drum Has your question been resolved?
gilded drum
<@&286206848099549185>
calm coralBOT
@gilded drum Has your question been resolved?
calm coralBOT
@gilded drum Has your question been resolved?
calm coralBOT
@gilded drum Has your question been resolved?
calm coralBOT
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Available help channel!
thorny whale
did i do this correctly?
calm coralBOT
did i do this correctly?
vagrant oak
did i do this correctly?
idk what's blank 1 and blank 2, but h and depth are correct
calm coralBOT
@thorny whale Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
tender current
,w 10 * 8 * 13 * 13
calm coralBOT
,w 10 * 8 * 13 * 13
potent lotusBOT
tender current
What am I doing wrong here?
I assumed this was a fundamental counting principle problem, but the book says the answer is 6240
low pumice
look closely at the two desserts
there will be times where the same meal happens twice
velvet osprey
are you sure that (a) choosing the same dessert is allowed, and (b) the order in which you choose desserts matters
tender current
are you sure that (a) choosing the same dessert is allowed, and (b) the order in...
No I'm not sure of either of those things
edgy raven
^
right now you say that {dessert1, dessert2} is different from {dessert2, dessert1}
though in reality you may choose which dessert gets served first and which gets served second, here I think you have to count out the order
tender current
I'm sorry I don't understand what you mean by count out the order?
edgy raven
pretend that there is no order
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Available help channel!
fierce cradle
Would I. E able to graph each scenario?
calm coralBOT
Would I. E able to graph each scenario?
fierce cradle
With the information given?
edgy raven
yes, they expect a general graph with both curves
fierce cradle
yes, they expect a general graph with both curves
I’d like to know whether I’m understanding the price right. For the 1st one, I know there would be a shift in the demand curve and it would be to the right because greater demand always shifts the curve rightwards…but my supply curve would shift leftwards and would be lower then my demand curve?
Anyone?
calm coralBOT
@fierce cradle Has your question been resolved?
remote mural
$8b^4+24b^3-2b^2-6b$
calm coralBOT
$8b^4+24b^3-2b^2-6b$
potent lotusBOT
AllUtility
remote mural
should i group or just factor out 2
sterile seal
Factor out 2b first
remote mural
$4b^3+12b^2-b-3$
potent lotusBOT
AllUtility
sterile seal
Yea now the factoring is pretty clear
remote mural
Yea now the factoring is pretty clear
lol
sterile seal
What
velvet osprey
$4b^3+12b^2-b-3$
you forgor the 2b you factored out 💀
it doesnt just vanish into thin air
sterile seal
forgor 💀
velvet osprey
potent lotusBOT
AllUtility
remote mural
is dis rite
velvet osprey
looks suspicious.
remote mural
$2b(2b-1)(2b+1)(b+3)$
amber basin
**AllUtility**
I think you mean $2b(4b^2-1)(b+3)$
amber basin
great
remote mural
.close
calm coralBOT
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shell granite
Hello, I am back after not recieving feedback. I think my handwriting wass probably too difficult.
shell granite
This is the original question - and here are my notes
I am getting the incorrect answer, and I am hoping to find out what I am doing wrong.
@heady karma
.close
remote mural
calm coralBOT
visual nimbus
B commutes with any 2x2 matrix A if AB - BA = 0
remote mural
The solution says: a = d, b = c = 0
visual nimbus
then great
remote mural
I'm not following
leaden thunder
The solution says: a = d, b = c = 0
Prove that using herels hint
remote mural
Am I on the right track here?
glass heart
and now choose specific values of w,x,y,z
remote mural
calm coralBOT
@remote mural Has your question been resolved?
paper bolt
I have expression a_1 + a_2 + a_3 + a_4 ... a_n, where each element is of form a_x = 1/(2k)! if k is odd, and -1/(2k!) if k is even
paper bolt
I would like to somehow simplify this expression since it can't be easily evaluated by computers
1/4! is already too little
Not to mention greater factorials
oblique current
$\sum_{k=1}^n (-1)^{k+1}\frac{1}{(2k)!}$
potent lotusBOT
ΣAC
