yep sure
#help-0
minor needle
alpine sable
dang thats a nice method
@minor needle Is the answer clear or should I like equate it to the question to show that it is the final answer
minor needle
It could be better, but it's not bad
alpine sable
should I continue to simplify or is it alright
minor needle
,w d/dx (4x^2+9)^5/40
ocean sealBOT
alpine sable
okay so it is correct
minor needle
np, you did everything, I've only checked your work
alpine sable
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long niche
hi
echo socket
Product to sum identities would help I think
long niche
you mean this?
echo socket
Looks familiar, but no, I meant something else
long niche
could you please explain more?
ocean sealBOT
A Lonely Bean
terse sundial
lim (x-> +oo) √(x^2-x) - x
lone heartBOT
lim (x-> +oo) √(x^2-x) - x
ruby current
infinity - infinity is an indeterminate form
convert it to a fraction and apply l'hopital
left aurora
terse sundial
convert it to a fraction and apply l'hopital
ill be honest with u brother no clue waht lhopitals rule is
timber tusk
ill be honest with u brother no clue waht lhopitals rule is
l'hopital rule also known as Bernoulli's rule its a rule that says you can solve limits by using derivatives
gray isle
multiply by conjugate/conjguate
terse sundial
dont i just get x / √(x^2-x) + x
waiitttt i could try
IT WORKS
thank u
any tips, that on an exam i dont just note down +infinity, like how do i know?
gray isle
rationalisation / conjugates
are common techniques for limit questions
trying to direct plug gets
inf - inf,
ad indeterminate form indicating the need for more work
past gull
guys is any st. line that cut through any graph and touchs 2 or more points of that graph a secant line?
random relic
guys is any st. line that cut through any graph and touchs 2 or more points of t...
That’s pretty much the definition
past gull
,w secant line
lone heartBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
@past gull Has your question been resolved?
wicked radish
Hello
I'm totally new here
Please help me in solving some math sums
Who would like to accompany me with that ?
In this 2nd and 3rd questions
wicked radish
yes
rotund crater
why is cm^2/cm
lone heartBOT
why is cm^2/cm
long axle
The unit of surface area is cm^2 and the unit of radius is cm, thus, as it says, dS/dr is given by square centimeters(area) upon centimeters(length)
rotund crater
oka thx\
lone heartBOT
@rotund crater Has your question been resolved?
honest wind
I need help I don't really get how I can do fractions if they are like this
vale wigeon
,rcw
ocean sealBOT
vale wigeon
what exactly do you mean by "like this"?
is it the placement of fractions and decimals side by side that bothers you?
honest wind
yep
vale wigeon
then write 0.5 as 1/2 instead.
opal glade
can someone help me with b. c. and d.
lone heartBOT
can someone help me with b. c. and d.
@opal glade Has your question been resolved?
opal glade
<@&286206848099549185>
cinder warren
lone heartBOT
@opal glade Has your question been resolved?
lone heartBOT
@opal glade Has your question been resolved?
opal glade
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plain hill
lone heartBOT
plain hill
I need help to find tan(alpha) and the straight line equation
echo socket
Recall that the tan(the angle made between a line and the right branch of x-axis from the intersection) = the slope of the line
Can you see what the slope is in this case?
plain hill
i should do like Δy/Δx?
echo socket
Yeah
Here, going from the y-intercept to the x-intercept, the delta y is -2 and delta x is 4
plain hill
so will be -1/2
echo socket
Yup
Meaning the equation of the line is also of the form y = -x/2 + c
Where c is the y-intercept
But, as you can see, c is given
It's simply 2
So the equation of the line is y = -x/2 + 2
plain hill
so y=(-1/2)x +2?
echo socket
Yup
plain hill
now i need to find tha tan of alpha
echo socket
As I already said, tan of alpha is equal to the slope
plain hill
-1/2?
echo socket
Yup
plain hill
so about this
?
is like -1/3
sorry i mean 1/3
ok someone can see if his correct: tan(alpha)=1/3 ---- y=1/3x -1
<@&286206848099549185>
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lone heartBOT
Available help channel!
onyx latch
Can someone walk me through solving this?
lone heartBOT
Can someone walk me through solving this?
lost jungle
Square both sides, bring all non square root parts to one side
And then square the new equation again
You then can bring like terms together and you have a quadratic
kindred vale
just a q @lost jungle
lost jungle
Yeah?
kindred vale
isn't squaring hte right side is multiplying it by hte sqrt(7x+2)
lost jungle
Yes
kindred vale
and the left side by (1+suqr(3x+3))
lost jungle
Yes
kindred vale
can you do that
lost jungle
Yeah
kindred vale
hm
lost jungle
Because those are the same thing as given in the equation
kindred vale
yes i'm dumb
kindred vale
i was reconsidering my life lmao
regal stag
i believe in you @kindred vale
dont let math scare you like it has for 28 years of my life
keep grinding
kindred vale
it's because x² is a strictly growing bijection from R+ to R+
regal stag
best of luck!
onyx latch
So it would look like this?
kindred vale
So it would look like this?
nah put brackets on the entire left expression and then square it all
onyx latch
lone heartBOT
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onyx latch
<@&286206848099549185>
nimble fern
lone heartBOT
@onyx latch Has your question been resolved?
zenith flax
Hello!
I’m currently on circular functions in my pre-calc 12 course and I’m really confused about the following
So in the first pic, we’re getting the domain from the argument, right? Then solve for x, pretty simple
But then in the second one, we don’t follow the same steps? For some reason we divide by 4, unlike in the first situation where we applied 2 to the terms within the bracket?
I asked my math teacher for help, and she said “cot and tan have periods of pie, other functions have periods of 2pie”, but I’m unsure how that applies exactly?
Thanks in advance for the help 🙂
minor needle
csc isn't same as cot
cot(x) = cos(x)/sin(x)
hence sin(x) isn't 0
4(x-pi/6) ≠ n * pi
x - pi/6 ≠ n * pi/4
x ≠ pi/6 + n * pi/4
as they highlighted in blue
you can do it same way as in the 1st one
it doesn't matter
zenith flax
you can do it same way as in the 1st one
ohhhhh okok
I was just real confused why the first step was a bit different
thank you :))
.close
lone heartBOT
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Available help channel!
jolly owl
I need to find the coefficient of this function
lone heartBOT
I need to find the coefficient of this function
jolly owl
but in the formula I need to use 2 times the period
and I have no clue what to do if the period given is 2π
is it 2 x 2π?
lone heartBOT
@jolly owl Has your question been resolved?
lone heartBOT
@jolly owl Has your question been resolved?
gusty gorge
honestly not sure, do they not tell you anything about what g(x) is for x > pi?
lone heartBOT
@jolly owl Has your question been resolved?
jolly owl
honestly not sure, do they not tell you anything about what g(x) is for x > pi?
Nope
I guess I'll have to ask the teacher to clarify that
primal dew
assuming ∞-1≠∞ (but still exists) would it be still be correct to say everything positive less than ∞ is finite
worn fox
how are you defining $\infty - 1$
ocean sealBOT
ΣAC
primal dew
how are you defining $\infty - 1$
Uhhhh
just act as if ∞ is a number
go one less than it
slender marten
Don’t use the infinity symbol to represent a number. Use any other symbol.
primal dew
Don’t use the infinity symbol to represent a number. Use any other symbol.
but what if it is infinitely large
slender marten
Then it’s not a number. For, infinity is not a number but more of a concept.
slender marten
There is no number at the end of the number line to be. Therefore infinity - 1 is certainly not a number either.
primal dew
so no number can be infinitely large?
gusty gorge
depends on what you mean by number
real numbers? no
there is always a real number above any given real number
slender marten
so no number can be infinitely large?
No. It’s a concept which can be useful for certain calculations, for example, limits.
You can make a interval arbitrarily fine by dividing it “infinitely” many times.
primal dew
I don't see why the two must be mutually exclusive
gusty gorge
no certainly we do talk about infinities as "numbers" of a sort
like infinite ordinals and infinite cardinals
slender marten
like infinite ordinals and infinite cardinals
I don’t even know what they are so I doubt they do. Must be an American thing. I ain’t ever heard of them.
slender marten
I don't see why the two must be mutually exclusive
The interval of course can’t really be divided up infinitely many times. It’s just a concept of making the fineness of the interval arbitrary small. In the sense of infinity being a number, you could just say infinity means you can choose a number arbitrarily large.
gusty gorge
I don’t even know what they are so I doubt they do. Must be an American thing. I...
set theory stuff
primal dew
The interval of course can’t really be divided up infinitely many times. It’s ju...
This is math. We can let somthing happen if we just say it can happen.
just need to add a extra axiom to let it happen
worn fox
just need to add a extra axiom to let it happen
this is exactly how you arrive at an inconsistent list of axioms in which point you literally can't do maths with them
slender marten
just need to add a extra axiom to let it happen
Tell me the axiom you’re adding.
primal dew
this is exactly how you arrive at an inconsistent list of axioms in which point ...
you only arrive at an inconsistent list of axioms if you add inconsistent axioms lol
worn fox
which you frequently do
primal dew
irrelevant
gusty gorge
well you can add infinity tbf you just have to give up things like additive inverses
the extended reals are a thing
but it's like super weak and you don't do much with them
primal dew
well you can add infinity tbf you just have to give up things like additive inve...
why would you have to give up additive inverses?
gusty gorge
because you can't say that infinity + (-infinity) = 0
primal dew
why not?
gusty gorge
leads to way too many inconsistencies
surreal meadow
why not?
didnt we talk about this gt
your definition of infinity broke down a bit
tacit arch
Just a bit
primal dew
your definition of infinity broke down a bit
"my definition of infinity" (not actually a definition) is irrelevant to the question I have
surreal meadow
well it's sort of very relevant
not your definition
but a definition is kind of necessary
tacit arch
Asks question about an equation with infinity.
Refuses to accept the common definition of infinity and also refuses to define a consistent definition of infinity
subtle mantle
Google “the projective line”
surreal meadow
if you can give us the definition of infinity you intend to use this discussion can go somewhere productive, otherwise it's just a bunch of back and forth not really talking about anything
lone heartBOT
@primal dew Has your question been resolved?
latent venture
A guitar string is plucked at time t = 0. Twelve seconds later the sound has faded so as to be inaudible. Assume that the sound can be modeled by a damped cosine curve and that the initial volume is represented by an amplitude of 54 and the threshold of audibility is represented by an amplitude of 1. The note is an A which vibrates 110 times per second. Write a possible equation that models the sound. Show your work and write a brief paragraph explaining how you found your equation.
dusky tiger
A guitar string is plucked at time t = 0. Twelve seconds later the sound has fad...
What's your initial thoughts to solve it?
latent venture
Honestly, I don't know
I understand that the amplitude is 54
and the curve is damped, meaning that it will follow the path of another function
lone heartBOT
@latent venture Has your question been resolved?
latent venture
<@&286206848099549185>
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noble ermine
How do u do 10?
lone heartBOT
How do u do 10?
brisk heath
$x.y = |x| . |y| . cos(x,y)$
ocean sealBOT
Amer
brisk heath
i don't know how to use vectors in texit 🤷♂️
lone heartBOT
@noble ermine Has your question been resolved?
ocean sealBOT
Saccharine
lone heartBOT
lone heartBOT
Available help channel!
upper trout
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upper trout
Is this right notation
I'm trying to say there exists some vector u belonging to the 2nd dimension (or whatever R^2 means) such that vector u=<u1,u2> and that u is a linear combination of those vectors such that the constants belong to real numbers
I feel like using 3 such that's is wrong but idk what else I would use and I'm just now learning logic notation (and logic in general)
lone heartBOT
@upper trout Has your question been resolved?
bronze lotus
help
median oar
ask your question
bronze lotus
so here is the question
v+6 over 18v^2 + 18v + v-5 over 18v^2 + 18v
so they have the same denominator
but When do I know when I have to factor out a number in the denominator cause sometimes you do and sometimes you dont I guess
example
median oar
if the denominators arent the same
make them the same by multiplying by k/k where k is what you're missing
then just add them together first
then factor and simplify
OR, if you see how you factor first you can do that as well
bronze lotus
the denominators are the same
see how on the first question the denominator is factored from 18v but not on the second question. I am just wondering how do I know when I need to factor out the denominator with the gcf
median oar
$\frac{v+6}{18v^2+18v}+\frac{v-5}{18v^2+18v}\
=\frac{1}{18v}\left(\frac{v+6}{v+1}+\frac{v-5}{v+1}\right)\
=\frac{1}{18v}\cdot \frac{v+6+v-5}{v+1}\
=\frac{1}{18v}\cdot \frac{2v+1}{v+1}\
=\frac{1}{18v}\left( \frac{v}{v+1}+\frac{v+1}{v+1}\right)\
=\frac{1}{9(v+1)}+\frac{1}{18v(v+1)}\$
ocean sealBOT
Frosst
bronze lotus
according to the math key thats not what it wants the answer to be
it says the answer is this
so why would it not be 2v+1 over 18v squared + 18v
median oar
example
well this side isn't fully simplified on the right
i think that doesn't matter
i would argue factored form is "simplier"
so the 2nd question will still need to be simplified by cancelling a common factor of 2
bronze lotus
where?
on v-4 or the whole denominator
or I see, the whole answer
So why on question one do they factor out 18v from the denominator
but on question 2 they dont do that for 4v
done
bronze lotus
k I need help
bronze lotus
look
why isnt the denominator supposed to be simplified
that is the answer to this question
bronze lotus
well the math teacher must just be a smoothbrain
why isnt this simplified on the top?
merry depot
simplified how?
bronze lotus
like coudnt you factor 2 out and get 2(k+7)
merry depot
again, you can. but the answer is the same either way.
merry depot
i doubt it
but i'm not your teacher, so you should be asking them. Not random strangers on the internet
bronze lotus
I have the act on tuesday which is where normally I would have my math class
so I cant talk to him then
and the last day to do any tests is on thursday
merry depot
isn't the act multiple choice?
bronze lotus
Yah this isnt for the act this is just for my class
Im all behind and crap
you dont care tho so Ill spare the details 😂
vale wigeon
but if i put that on the test it would be wrong
do you know that for a fact?
merry depot
if this is the way the answers are written in the notes, I would assume that this is an acceptable answer on any exam.
bronze lotus
I can go see on the online thing real quick
vale wigeon
do you know for a fact that your teacher will mark as wrong any and all deviations, no matter how slight, from the way he does things?
bronze lotus
well he woudnt even check it just goes into some program
and then it gives me the score
merry depot
You've angered Ann... I'll be leaving before she sees your smoothbrain comment.
bronze lotus
ok lol
serene junco
Unless there are instructions specifically telling you to express the result in a given form, you should definitely not get marked wrong for something like that
I've seen some bad teachers, but that would be a whole different level
lone heartBOT
@bronze lotus Has your question been resolved?
summer stratus
lone heartBOT
wind cloak
$\frac{a - b}{b} \neq a - 1$
ocean sealBOT
NEONPerseus
wind cloak
You need to group the xs together
frank merlin
why is this wrong
lone heartBOT
why is this wrong
sly mantle
why is this wrong
show work for the bases
lone heartBOT
@frank merlin Has your question been resolved?
frank merlin
i think this question doesn't work? bc the bases should be the same as the p matrix
sly mantle
you may need to put the vectors in ()
lone heartBOT
sly mantle
np
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Available help channel!
wanton beacon
wanton beacon
Oops
Could u plz look at where I’ve written “right answer?”
Does that look right?
lone heartBOT
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@wanton beacon Has your question been resolved?
lone heartBOT
@wanton beacon Has your question been resolved?
stiff night
Two Cards Are Selected at random from a bag containing 10 cards , A to J. Whats the probability of selecting at least 1 vowel
woven plaza
How many vowels are there from a to j
stiff night
3
stiff night
yeah
woven plaza
So you can do 1- (probability of finding no vowels)
lone heartBOT
@stiff night Has your question been resolved?
vale wigeon
@woven plaza you did not account for the fact that two cards are drawn.
@stiff night there are 3 vowels and 7 consonants in the bag. NOT selecting at least one vowel means selecting two consonants.
find the number of ways to do that, then divide by the number of ways to draw two cards unrestricted.
lucid glen
I want to draw a pattern similar to the pic with functions in polar form, where do I start, are there example functions?
lone heartBOT
I want to draw a pattern similar to the pic with functions in polar form, where ...
@lucid glen Has your question been resolved?
lucid glen
<@&286206848099549185>
lone heartBOT
@lucid glen Has your question been resolved?
solid turtle
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echo plinth
I have a small inquiry concerning differential equations
Observing this differential equation
one is tempted to find an Exact pair of functions to perform a u and a v sub, and then turn this bad boy into a seperable differential equation
I'm struggling to find an exact pair of functions
an exact pair of functions: two exact differentials representing two functions
lone heartBOT
I have a small inquiry concerning differential equations
Observing this differen...
@echo plinth Has your question been resolved?
echo plinth
<@&286206848099549185>
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subtle birch
x^(1/6)-x^(1/4)=x^(1/4)-x^(1/2)
subtle birch
solve for x
It is clear that 0 and 1 are solutiona
But there is one more solution
pseudo ice
Hmm, well if you e.g. made the substitution $u = x^{\frac{1}{12}}$, then you can transform your equation into $u^{6} - 2u^{3} + u^{2} = u^{2} (u^{4} - 2u + 1) = 0$, from where $u=0$ and $u = 1$ are solutions of course (and correspond to $x=0$ and $x = 1$ \
The $u = 1$ solution implies that $u - 1$ is a factor of $u^{4} - 2u + 1$, and so you get that you can factor into
[
u^{2} (u - 1) (u^{3} + u^{2} + u - 1) = 0
]
but the latter factor doesn't look so nice
ocean sealBOT
@pseudo ice
pseudo ice
,w u^3 + u^2 + u - 1 = 0
lone heartBOT
@subtle birch Has your question been resolved?
tender wigeon
subtle birch
whatever this simplifies to is the 3rd solution
It simplifies to 0.00066712
@pseudo ice
How do I reach to this
pseudo ice
,calc 0.54369^12
ocean sealBOT
Result:
6.6713871180584e-4
Hmm It is the one
pseudo ice
In terms of an exact solution, I'm not sure atm 
rapid notch
lone heartBOT
rapid notch
\begin{align*}
T3(x) &= \cos(0) + \cos'(0) x + \frac{\cos''(0)}{2!} x^2 + \frac{\cos'''(0)}{3!} x^3
&= 1 - \frac{x^2}{2} + \frac{x^3}{6}
\end{align*}
ocean sealBOT
san
lone heartBOT
errant idol
<@1048516518587150396>
ask
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Available help channel!
long spindle
Hi can someone let me know if I’m doing this right?
lone heartBOT
Hi can someone let me know if I’m doing this right?
long spindle
Should I have differentiated applying ln to both sides?
gray isle
work looks fine
ocean sealBOT
lone heartBOT
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dark ibex
lim t/sint = 1?
t->0^-
lone heartBOT
lim t/sint = 1?
t->0^-
wet nest
lim t/sint = 1?
t->0^-
True
ocean sealBOT
MathIsAlwaysRight
modern sedge
It actually doesnt matter wheter it's from negative or positive in this case
both are =1
lament granite
i need help pls
dark ibex
both are =1
if x approaches to 0 from both sides is equal to 1 does that mean that x approaches from the left or right is 1 too?
dark ibex
i need help pls
go to the help channerls that are not occupied
lone heartBOT
i need help pls
Please read #❓how-to-get-help
wet nest
This is true
wet nest
Yes, that is the definition of a limit
karmic osprey
lone heartBOT
karmic osprey
gimmi a sec
imma figure out what i got stuck on
okay
got it
so basically
its increasing from the after -2,- 2 to 0
based on what they gave
and decreasing from 0 to 3 to whatevers after 3
concave up from whatever is after -2, to -2 to 0
concave down from 0 to 3 to after 3
but
how do i know what y axis to put? because the above is information for x axis i think
like
is there anything im mising
velvet cliff
karmic osprey
but
apparently i graphed it wrong somehow
based on the information i got from the problem
and im not sure what i got wrong
what determines where the stuff goes
fast lichen
can you put what you drew
karmic osprey
okay
hold up
phone being laggy
i know that graph is wrong
im thinking maybe the entire thing needs to be under the x=0?
im not sure how id make the graph based on the number line i made
fast lichen
its not necessary to shift up or down it dont matter
your -2 to 3 bit looks alright if it was drawn a lil better. like at some point near 3 it just stops deaccelerating?
karmic osprey
uh
is there a rule im supposed to follow?
how do u connect the different parts of the conacve up x increasing, and decreasing concave down
like
why does it not look right
fast lichen
the thing after 3 is def wrong. its supposed to be decreasing after x>0, you cant have a turning point
which is why i just want to focus on -2 to 3 and get that right
first
fast lichen
karmic osprey
here's what i have
i realized i wrote the number line wrong
but i still dont see why the graph is wrong
changed the stuff down here
fast lichen
and the acceleration after 3 can nver 'turn'
karmic osprey
lemme draw new graph
fast lichen
because everything after 0 has to be decreasing
fast lichen
yea it looks ok. still a bit innaccurate some places but its a drawing so i dont think its a big deal
fast lichen
it looks slightly increasing after it passes the y-axis
it looks like there is slight deacceleration right before -2 thta little 'curve'
but like i said it really is nothing
karmic osprey
so
next time i make a graph like this
i remove the extra bumps?
and make it smooth?
fast lichen
yea sure
viral pagoda
Natural logarithm I.e
vague mirage
What's the Actual question is it
$1/2.\int_{5}^{10} t^{-1}dt$
ocean sealBOT
Offline due to exams
lone heartBOT
@viral pagoda Has your question been resolved?
lone heartBOT
Available help channel!
jagged forge
I need to find the solid made by rotating this about the y - axis
quasi vector
within what bounds?
jagged forge
The bounds are where the two lines intercept
quasi vector
ahh i see
jagged forge
"Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis."
jagged forge
yea
I just realized the shell method would be easier but this problem is in the disk and washer section
So i put in terms of Y since its around the y axis. And then its piR^2 - pi r^2
lone heartBOT
@jagged forge Has your question been resolved?
royal dawn
The question was “A spherical balloon is inflated at a rate of 4pi cm^3. At the moment the radius is 5pm, determine the rate of change of the surface area (hint: first, determine the rate of change of the radius) State an exact answer
royal dawn
I tried my best, on the left I found the rate of change of the radius, and used it to find the rate of change of the surface area. However the correct answer was 8pi/5. I don’t see what I did wrong and could use some help
Thanks!
long axle
What does it mean “radius is 5pm”
oak chasm
Also, is that 4pi cm^3/s?
long axle
Also, surface area of a sphere is given by 4pi * r^2
Not pi * r^2
That may fix ur issue
@royal dawn
royal dawn
What does it mean “radius is 5pm”
It’s supposed to be 5cm but my hand writing is messy lol
royal dawn
Also, is that 4pi cm^3/s?
Yes
long axle
Do u see what u did for SA
royal dawn
Also, surface area of a sphere is given by 4pi * r^2
Ohhh yea I didn’t see that, I’ll try this when I get home
long axle
Np
royal dawn
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swift mesa
I am trying to simplify the derivative d(f(x))/dt. Can I express it as d/dx(f(x)) * dx/dt?
swift mesa
Where x is not independent of t
oak chasm
Yes, that's done quite a bit.
lone heartBOT
@swift mesa Has your question been resolved?
alpine sable
if inverse proportion means as one variable increases the other one decreases, then why isn't y = -kx an example of inverse proportion?
limpid turret
That's still linear or direct proportion
alpine sable
but if x increases then y decreases
mortal trellis
alpine sable
im not following.. xD
wdym exactly
like why is it about absolute value
and not x = 1, y = -1
x = 2, y = -2
etc
lament forge
inverse proportion doesn't mean "as one variable increases the other decreases"
worn fox
if inverse proportion means as one variable increases the other one decreases, t...
this 'definition' of inverse proportion isnt entirely accurate is the problem, as you are currently discovering
alpine sable
then what is the true definition?
lament forge
one variable is (linearly) proportional to the reciprocal of the other
equivalently, the product of the two variables is constant
crimson pilot
For what value of m do we have a non trivial solution here? this is from a mock exam im studying from
limpid turret
Are you familiar with linear algebra?
crimson pilot
yea
drowsy grove
which term looks the easiest to eliminate?
crimson pilot
which term looks the easiest to eliminate?
i dont understand sorry
lone heartBOT
@crimson pilot Has your question been resolved?
crimson pilot
<@&286206848099549185> if possible a quick text explanation would really help out here, im not asking to solve the whole thing, just how it is different from the problem i solved earlier, thanks 🙂
ebon aspen
<@&286206848099549185> if possible a quick text explanation would really help ou...
@crimson pilot you solve it exactly the same as before, the difference now is that your coefficients involve an unknown parameter m.
So when you find the déterminent, the solution and whether the Det is 0 or nonzero depends heavily on the value of m. You don't need to solve for m. You just need to take it into account when doing your elimination steps.
For the first two equations, I would start by multiplying the second one by -m and adding them together to eliminate x
alpine sable
help i am supposed to find graident of this but i dont know how
vapid shuttle
do you know what the gradient represents?
alpine sable
what does that mean
vapid shuttle
your question wants you to "find the gradient"
what is the gradient?
just in general
alpine sable
WHAT DOES GTHAT MEAN
limpid turret
gaganiga, Are you asking us what gradient means?
vapid shuttle
in reference to your question
alpine sable
no
like i dont know what do do
to do
i know how to find y intercept
but not gradiejt
dont give me asnwer i just need to know how to do
inner patio
Gradient is another way to say slope
alpine sable
how do i find it
limpid turret
(if you know)
alpine sable
the differnece between x and y
vapid shuttle
almost
alpine sable
uhg
vapid shuttle
the slope represents the rate of change
if the line is very steep
y is increasing fast
the slope can be thought of as
the change in y / the change in x
and the word slope and gradient are interchangeable here btw
so a steep slope would be a big number, and a low slope would be a small number
alpine sable
i dont know how to find it
ocean sealBOT
AustinU
vapid shuttle
pick two points on your graph there
find how much y increases in between them
and how much x increases in between them
then find the change in y divided by the change in x
that will be the "slope" / "gradient"
limpid turret
"rise over run" is the general saying
limpid turret
❤️
alpine sable
how to close dis
wary stream
how to close dis
.close
alpine sable
.close
vapid shuttle
If S is the subspace of R3 containing only the zero vector, what is S perp?
vapid shuttle
if S was instead spanned by <1,1,1> and <1,1,-1> what is a basis for S perp?
I find the row space of S to be <1,0,0> <0,1,0>
which givess
N(a)=<0,0,1> c
which would be a basis for s perp
yes o no?
worn fox
is (0,0,1) perpendicular to either of those vectors
vapid shuttle
yea to both
worn fox
to (1,1,1)?
vapid shuttle
oh
I want to find the column space then
instead
and then the left null space would be basis for s perp
not the normal ?
worn fox
if what you're doing is equivalent to just setting up the two equations that cause a vector to be perp to (1,1,1) and (1,1,-1) and solving it then sure
vapid shuttle
Okay
I find that the left null space is
<-1, 1,0> a + <0,1,-1> b
both of which are perp to S
but I am confused
how can S be two dimensional
vapid shuttle
S transpose
worn fox
S is a subspace
vapid shuttle
if you make it into a matrix though
and then transpose
that gives you the column space
the span of S
and then the null space of that matrix
worn fox
okay you should be clear thats what youre doing rather than talk about the null space of a subspace
vapid shuttle
would be all vectors perp to it
sorry
I made S into a matrix, and then transposed it. This matrix shows the span of S (the column space) , and the null space of this matrix contains all the vectors perp to S (because they are perp to the column space)
that was my method
is it improper?
worn fox
you were finding the nullspace of
1 1 1
1 1 -1 ?
vapid shuttle
yes
vapid shuttle
okay, so did I find it wrong then?
okay
so when I reduce I get
1, 1, 0 on top
and 0, 0, 1 on bottom
so I let x2 be itself
and then x1 has to be -1 and x3 0
or the opposite way around
is how I got those two vectors
worn fox
it is, and its telling you that x3 =0
worn fox
you made this:
$\begin{pmatrix} 1 & 1 & 0 \ 0 & 0 & 1 \end{pmatrix} \begin{pmatrix} x_1 \ x_2 \ x_3 \end{pmatrix} = 0$
ocean sealBOT
ΣAC
vapid shuttle
yes
vapid shuttle
oh
I see that now
I was wondering how I got a 2 dimensional null space
okay
sorry I don't know why I am so bad at this lol
thank you again
worn fox
lmao youre good dw
vapid shuttle
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zenith spoke
The volume V of a cone with base radius r inscribed on a sphere of radius R is equal to ? Someone Have any idea ?
zenith spoke
possible answers
zenith spoke
<@&286206848099549185>
lone heartBOT
@zenith spoke Has your question been resolved?
lone heartBOT
@zenith spoke Has your question been resolved?
high rapids
,w volume of cone formula
ocean sealBOT
tall reef
lone heartBOT
tall reef
dont get it
rocky grove
Hmm
You know how things get repeated?
They're usually referred to as "frequent" things
Because they happen often
rocky grove
How did you find it?
lone heartBOT
@tall reef Has your question been resolved?
undone cove
would the answer be 18
as you can break up the integrals
and put the constant on the outside?
high rapids
Yeah
wheat crystal
lone heartBOT
wheat crystal
I subtracted 0.2864 from both sides
got cot x = -0.2864
then rewrote cot as 1/tan
i basically got to the point
That I have x = approximately -1.292
Im kinda confused how to find all the solutions tho
gray isle
consider the period of the tan function
wheat crystal
pi
But arent I supposed to like
sketch an angle or smth and see where the tangent is equivalent idk
pseudo ice
Well you could but you don’t have to
wheat crystal
HI
pseudo ice
If e.g. you used a calculator and found a value, you know that adding/subtracting multiples of pi would remain as a solution
pseudo ice
Yep 
wheat crystal
ah okay
pseudo ice
Just accept the ones that are in the interval you can find
pseudo ice
another value since the interval is [0, 2pi]
[in this case, this one!]
wheat crystal
Ok so -1.292 + pi would be our x value
x approx 1.849
Which is in interval
Ohhh and i add another pi because thats in the interval
Tysm!!
pseudo ice
Yep yep 
wheat crystal
.close
alpine sable
$\sqrt{(-4)^2}$
lone heartBOT
$\sqrt{(-4)^2}$
ocean sealBOT
okokok
alpine sable
simplify
limpid turret
!status
lone heartBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
!show
lone heartBOT
Show your work, and if possible, explain where you are stuck.
alpine sable
idk
limpid turret
Any guesses?
alpine sable
-2
limpid turret
How'd you arrive there?
ocean sealBOT
okokok
alpine sable
4
limpid turret
bingo
undone hornet
Hi, I am having an issue with one of my homework questions. Here is an image of the question:
undone hornet
I am not really sure how to get started, all I really know is that u + v = w, I am not sure if I am supposed to plug it in, distribute, and simplify or if there is a simpler way to solve this
My friend did it but he did u + v + w, but I don't know why w is positive when it is given to be negative
<@&286206848099549185>
wet bane
Add the x components together and the y together
undone hornet
What do you mean?
wet bane
Oh wait no
alpine sable
Hi, I am having an issue with one of my homework questions. Here is an image of...
idk how vectors work but is that even possible u+v=w when u and v cant equal 6 or -6?
Ohhh
i see
wait
nvm
i think this
is a substitution question
wet bane
Ok I'm still confused on how +/- 3 +/- 4 = +/- 6
alpine sable
yea
undone hornet
It is given that u + v = w, which is u + v - w = 0, this is a 0 vector
The magnitudes don't play a part just yet
wet bane
The magnitudes don't play a part just yet
See that's what I don’t understand, why not?
alpine sable
well at most i can reduce the 2nd equation to 36+uv
undone hornet
See that's what I don’t understand, why not?
That's because you are dotting different vectors that add up to be scalar, and there is no way in the given equation that the magnitudes can be plugged in
u, v, and w are vectors, the magnitudes of vectors in a 3D space is sqrt(a^2 + b^2 + c^2) and 2D is sqrt(a^2 + b^2) since we are working with algebraic vectors
wet bane
u, v, and w are vectors, the magnitudes of vectors in a 3D space is sqrt(a^2 + b...
Yes, I'm following
alpine sable
bro what, what math course is this
undone hornet
So you can't plug in scalar quantities into vectors