back to ginger
#help-13
wraith daggerBOT
limber dawn
this also shows the "trick" - x is just a certain percentage more than s
fallow drift
All t lol
limber dawn
this means that x's rate of change is the same percentage more than s
$\dv{x}{t} = \frac{15.5}{9.2}\dv{s}{t}$
wraith daggerBOT
back to ginger
limber dawn
you've seen this property of derivatives right?
fallow drift
Ye
limber dawn
🎉
so that's the answer that you found with math, and can also be visualized
(the problem tells you ds/dt = 5.5, and asks for dx/dt. they are related by the factor 15.5/9.2 as above)
limber dawn
ok
limber dawn
yeah it is
limber dawn
yes
fallow drift
Isn’t the 15.5 ft also relative to the ground
fallow drift
1705/126
limber dawn
15.5/(15.5 - 6.3) is another way to write it
fallow drift
ok wait
I still
DONT rlly get why it’s 6.3
If they’re both measured relative to the ground
limber dawn
that came from your math
fallow drift
Should t you use 6.3
limber dawn
it's solving this triangle
for x in terms of s
you set up the ratios correctly
with the 2 similar triangles
limber dawn
maybe yeah
fallow drift
how do I get good at related rates
limber dawn
ig whenever it's like they tell you one rate and ask for another
we do what we did here
we call one rate ds/dt
and the other dx/dt
then we find the equation for s and x first, then take the derivative finally
limber dawn
yes i think
fallow drift
okay
limber dawn
by equation 1 you mean in the image of your work?
fallow drift
ugh this is so hard
fallow drift
by equation 1 you mean in the image of your work?
Yea relate the 2 variables
limber dawn
yes exactly 👍
fallow drift
what math are you doing
limber dawn
idk i do physics now
fallow drift
huh
limber dawn
i'm a phd student
limber dawn
i haven't taken math classes specifically for a while
fallow drift
wow
limber dawn
physics major?
yeahh
fallow drift
🔥
limber dawn
this is the same idea overall
limber dawn
the angle is an extra kinda thing on top of it
fallow drift
ang le
limber dawn
but same idea
limber dawn
so we can still say the plane's speed is ds/dt = 4
fallow drift
so we can still say the plane's speed is ds/dt = 4
ok
limber dawn
and they want dx/dt, where x is the distance of the plane from the station thing
so we can start again just by making an equation with s and x
a diagram is probably needed
here actually the angle just comes up for the diagram
limber dawn
ok 👍
fallow drift
what even is this quesiton asking
what is the speed of the plane 5 mins later?
Why is it kinda weird
limber dawn
yeah it is phrased weirdly lol
fallow drift
Is this right
limber dawn
ok perfect
now actually the plane's positoin is changing
and we are asked to relate its rate of change 5 minutes later
so it will help to draw the plane on the diagram at some time later too
like this for example https://excalidraw.com/#room=49834d5ed31d037c98ef,lcUOBaMlsceDM5dxr2uIBg
fallow drift
like this for example https://excalidraw.com/#room=49834d5ed31d037c98ef,lcUOBaMl...
Hu
Huh
limber dawn
can you see it
limber dawn
weird
limber dawn
ok yeah that's it
fallow drift
Okok
limber dawn
Is everything that l wrote to far correct
yeah looks perfect
except it looks like you wrote "velocity function -> 4t" idk what the 4t means
fallow drift
except it looks like you wrote "velocity function -> 4t" idk what the 4t means
Like
Weren’t u told the plane moves at 4 km/min
So like
I wrote 4t
limber dawn
ah gotcha
fallow drift
Is that right
limber dawn
also i believe that would apply to s, rather than x
(like last time, we're using the letter s for the known/given rate)
fallow drift
also i believe that would apply to s, rather than x
Wdym
oh
ok I fixed it
It’s true that we want dw/dt right
Dx
limber dawn
last time the given rate was 5.5, so we had ds/dt = 5.5
limber dawn
It’s true that we want dw/dt right
w 😮
but yeah, here, we can say ds/dt = 4 is given
then s = 4t + constant (the constant may matter in general, but here it will turn out to just be zero)
fallow drift
Do we need trig for this question
fallow drift
mainly one equation (the "cosine law")
oh
limber dawn
By s you mean x?
well it really doesn't matter what letters we use
but last time we used s or ds/dt for the known rate
and x or dx/dt for what we want to solve for
fallow drift
like are we talking abt the same thing is what im concerned abt 😭
limber dawn
i was going to get to labeling s and x on the diagrams :p
that really is what determines it
limber dawn
npnp
it is a good time to do that now then
we can use your diagram if you added the plane at the second location
it might be easier on the whiteboard thing tho
where we both can draw
fallow drift
your writing is neater
fallow drift
where we both can draw
oh we can?
limber dawn
yes 👍
limber dawn
lol
cedar kilnBOT
@fallow drift Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
✅
limber dawn
does the whiteboard still work
fallow drift
can we actually differentiate tho
fallow drift
does the whiteboard still work
ya
fallow drift
cuz DONT we want dx/dt? there no t
limber dawn
you could try doing it the "implicit" way just to see how it works
so this is the chain rule part
you might remember
derivative of $x$ with respect to time is $\dv{x}{t}$ of course
wraith daggerBOT
back to ginger
limber dawn
derivative of $x^2$ with respect to time is $2x \dv{x}{t}$ via the chain rule
wraith daggerBOT
back to ginger
fallow drift
wait tho
limber dawn
so we'll get an equation that we can solve for dx/dt
limber dawn
npp
fallow drift
can we do d/dt even tho t isn’t even in the function tho
wraith daggerBOT
back to ginger
fallow drift
limber dawn
$\dv{f(t)}{t} = 2 x(t) \dv{x(t)}{t}$
wraith daggerBOT
back to ginger
fallow drift
ill stick to the first method.
fallow drift
technically everything in these equations are functions of t
Oh
Even tho t DOESNT even;appear
limber dawn
if you stare at it i think you'd get it
limber dawn
we're almost there
so we're just plugging in specific values for s, x, etc. now
we said before s = 4t, that's basically how we get s
oh you can only open one tab
cedar kilnBOT
@fallow drift Has your question been resolved?
cedar kilnBOT
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Available help channel!
main stratus
I am working on a program where I need to take the derivative of a normal polynomial via the power rule. I don't believe there is, but would there be any case where the derivative would be longer than the original expression? I'm wondering this for memory buffer reasons.
low edge
I am working on a program where I need to take the derivative of a normal polyno...
When you say longer, do you mean with more terms?
if you do, then no way. in the unfactorized expression it can be at most the same number of terms. If the original polynomial has no constants, then its derivative will have as many terms as the first one, but one order below of course
crisp lynx
cedar kilnBOT
buoyant latch
What have you tried
crisp lynx
dusty wren
Sum of roots is -b/a, not b/a
royal finch
You will have an easier time thinking about this problem if wlog you set a = 1.
cedar kilnBOT
@crisp lynx Has your question been resolved?
dire geode
still i dont understand what to do from here
did you use vieta's
cedar kilnBOT
@crisp lynx Has your question been resolved?
crisp lynx
did you use vieta's
yes
crisp lynx
ah i understand
cedar kilnBOT
ah i understand
crisp lynx
that was rought
cedar kilnBOT
Available help channel!
rustic bane
I’m taking discrete math and we are learning about recursive functions to explicit functions
In this we have a recursive function which has a particular solution. What I don’t understand is how is B = 5 and where did the function for B come from.
Thank you
rustic bane
Oh wait I just realized why it is equal to 5, but where did the function come from
.close
violet flume
its usually helpful to start defining quantities
you are given two pieces of information
so you expect to have 2 unknowns, probably
so a good first step is to define a couple variables
that represent what you need to know
then express the information youre given
in terms of those variables
yea
A = weight of bag a in grams
B = weight of bag b in grams
like this 
okay, next step
write your first piece of information
in terms of A and B
you know what the : means in terms of arithmetic operations?
i just mean you can get an equation out
nah i just mean
can you use the equation
thats all
yea, it means 4a to 1b
sup e4
wicked mantle
Not functions, the : sign tells you the portion of two bags, which you can get an equation from it
violet flume
okay, you got the flow yet?
can you tell the next step
im gonna go put my pizza in the oven
wicked mantle
Do you know why?
violet flume
oh, yea, youre right
wicked mantle
Ya want me to explain it to you?
wicked mantle
Pleaseee
violet flume
just kidding
wicked mantle
It’s always not a bad thing to learn more
violet flume
the next step is to express the next piece of information
you have another piece of information
u need to express it in terms of A and B
brb pizza
wicked mantle
are you looking for the ratio between a and b?
violet flume
yea
here's how these usually go
you write the equations in terms of normal arithmetic operations
you solve one equation for one variable
then, you substitute that into the other
like, check this out
say we had
x-y = 4
x + y = 6
we'd solve the first equation for x = 4+y
then substitute it in
(4+y) + y = 6
okay
well you have your equations
you can proceed with this step
unless you need help
yea fractions
then just the normal ol process
whats up
the normal trick is to make the first step getting rid of any fractions
we do it like this
$\frac ax = \frac by$
wraith daggerBOT
jan Niku
violet flume
say you got something like this
its important theres one fraction on each side
no problem
wicked mantle
Before you leave, can you tell us what’ve you learnt?
rapid mauve
?
wicked mantle
…..
Bro, I’m fr
Imma make sure you understand
Sure, but can you explain why 1:2 = 4:8
violet flume
you dont have to say anything lol
but i am curious
we can circle back to the original question
cedar kilnBOT
cedar kilnBOT
Available help channel!
void sand
if $K \subseteq M$ is compact and $U \subseteq K$ is open in $K$, is $\operatorname{cl}_M(U)$ compact in $M$?
wraith daggerBOT
higher!
void sand
if it matters, assume that M is Hausdorff because that's the only case I really care about anyways 
cl_M refers to the closure operation in M
void sand
**higher!**
so U being open in K means it's over the form U = K \cap V for some open V in M
so we can ask if $\operatorname{cl}_M(K \cap V)$ is compact in $M$ instead
wraith daggerBOT
higher!
void sand
but I'm not sure how to approach this at all now 
all I know is that K is compact (and thus closed if we assume M is Hausdorff), and that cl_M(U) is closed in M
well, one idea I had is to show that cl_M(U) is a closed subset of K, hence compact in K (and thus in M), but I don't know how to do that
it's my only idea thus far though, so I'd appreciate if somebody had a suggestion as to how I'd show that, or if this idea is wrong altogether
pallid slate
I would say consider interior of U vs the limit points
royal finch
Topology isn't really my thing, but the way I see it, M/K is an open set, and U has a finite subcover except for possibly its boundary which M/K would help you handle.
I didn't flesh out that thought very deeply, so grain of salt and all that
mint inlet
Topology isn't really my thing, but the way I see it, M/K is an open set, and U ...
but U isn't necessarily compact?
royal finch
Yeah sorry I misspoke, that was the line of thinking I had with the boundary part
pallid slate
well, one idea I had is to show that cl_M(U) is a closed subset of K, hence comp...
Well K is closed since M hausdorff
void sand
Well K is closed since M hausdorff
sure thing
pallid slate
And U subset of K so cl U is contained in K
void sand
I agree with that, but why is cl_M(U) closed in K?
pallid slate
Havent done this in a while but my intuition is the definition of closure being intersection of open sets containing U definition
void sand
you mean closed sets?
pallid slate
Like cl_M(U) = \bigcap_{V \supset U } V
void sand
mhm
pallid slate
lemme find it on wikipedia
dusk goblet
lemme find it on wikipedia
it’s just the intersection of all closed sets containing U
pallid slate
Bruh yeah
And since K is closed set containing U we have that
Idk why I thought it was opens
void sand
I agree that K contains cl_M(U) and that cl_M(U) is closed in M
but I don't see why it's closed in K
pallid slate
**higher!**
Wasnt this original question
void sand
I'm confused?
yeah
but the theorem says that compact subsets of Hausdorff spaces are closed
we don't know that cl_M(U) is compact in M yet
that's what we wanted to show, no? 
void sand
we don't know that cl_M(U) is compact in M yet
and yeah K is Hausdorff too
but we also don't know that cl_M(U) is compact in K either
that's what we want to show
dusk goblet
we don't know that cl_M(U) is compact in M yet
but you know it’s closed in M and a subset of a compact set
void sand
but you know it’s closed in M and a subset of a compact set
but it's not closed in K
dusk goblet
you’re showing it’s compact in M?
void sand
do we not wish to show it's compact in K first, from which it will follow that it's compact in M?
void sand
but you know it’s closed in M and a subset of a compact set
and I'm still kinda confused about what you mean by this
it's closed in M and a subset of K, why does that make it compact?
void sand
like, this doesn't apply, right?
because it's not a closed subset of K yet
we only know it's closed in M
hallow pelican
finite intersection property go brrrrrrrrr
pallid slate
because it's not a closed subset of K yet
Yeah isnt it the intersection thingy
void sand
what do you mean?
pallid slate
Like closed subset of K is using definition of subspace topology right
Is that what you mean?
void sand
yes
pallid slate
Like subspace topology of K wrt M and K is compact
cl_M(U) is closed in M implies cl_M(U) \cap K is closed wrt subspace topology.
So you have what you want
void sand
cl_M(U) is closed in M implies cl_M(U) \cap K is closed wrt subspace topology.
ah. that works.
darn. I can't believe I forgot about that
oh hi c squared
turns out after all that, my issue was forgetting how the subspace topology works
more specifically, that cl_M(U) = K \cap cl_M(U) since cl_M(U) is contained in K
so it's closed in K
pallid slate
You can probably just use same proof for that property of compact sets to prove it too
Where you take open cover of cl U and then you union it with M-clU and then you realize its cover of K which you take finite subcover
analog steeple
if $K \subseteq M$ is compact and $U \subseteq K$ is open in $K$, is $\operatorn...
||K is closed in M because compact subsets of Hausdorff spaces are closed.||
|| cl_M(U) is contained in K because K is closed||
|| cl_M(U) is compact in K because closed subsets of compact spaces are compact||
|| cl_M(U) is compact in M because compactness is not a relative property||
pallid slate
||K is closed in M because compact subsets of Hausdorff spaces are closed.||
|| ...
Yes we pretty much did this
Just walk thru
analog steeple
yea, just summarizing
void sand
||K is closed in M because compact subsets of Hausdorff spaces are closed.||
|| ...
the third point is where my misunderstanding is, apparently
analog steeple
this is a good exercise
pallid slate
the third point is where my misunderstanding is, apparently
Its pretty much what I said here #help-13 message
void sand
we had to first show that it's contained in K, which lister boys did
void sand
Its pretty much what I said here https://discord.com/channels/268882317391429632...
I know this argument, dw 
I'm not concerned about the compactness in K vs compactness in M part
that I'm familiar with
I was concerned about closed in K vs closed in M part
analog steeple
cl_M(U) is closed in M, not K
cl_M(U) is closed in M, indeed, but it won't help you show that it is compact, because not all closed subsets of Hausdorff spaces are compact.
This proof relies on the fact that cl_M(U) is contained in a compact set
pallid slate
cl\_M(U) is closed in M, indeed, but it won't help you show that it is compact, ...
Counter example is closed ray
analog steeple
yes
pallid slate
[0,infty) closed but not compact
void sand
cl\_M(U) is closed in M, indeed, but it won't help you show that it is compact, ...
my problem lies precisely in the wording of this statement
pallid slate
Yeah its closed with respect to topology of compact space
analog steeple
what is your confusion?
void sand
"closed subset of a compact space" makes me think the closed subset must be closed in the compact space K
not in the ambient space M
analog steeple
it doesn't matter
pallid slate
"closed subset of a compact space" makes me think the closed subset must be clos...
It does need to be
analog steeple
because compactness is not a relative property
another exercise worth doing:
Let X ⊆ Y ⊆ Z. Show that X is compact relative to Y (i.e., in the subspace topology on Y) if and only if X is compact in Z
void sand
that's really the only one that was befuddling me here
void sand
because compactness is not a relative property
this is something that I didn't take a priori to be true, hm
void sand
more specifically, that cl_M(U) = K \cap cl_M(U) since cl_M(U) is contained in K
this is how I had to I justify it
every closed subset of a subspace S of X is of the form S \cap L, where L is closed in X
and cl_M(U) = K \cap cl_M(U), so it's closed in K
analog steeple
yea, that is one way to apply this lemma
void sand
then we can use the closed in compact thingy
analog steeple
mhm
analog steeple
another exercise worth doing:
> Let X ⊆ Y ⊆ Z. Show that X is compact relative t...
this lets you be a bit more care-free when dealing with compact spaces
if its compact, its compact no matter what space it sits in (with respect to the subspace topology, of course)
void sand
this is something I'll definitely have to keep in mind for the future
okay, thank you c squared, lister boys, knief, mango, and JessicaK
I appreciated this a lot 
.solved
cedar kilnBOT
cedar kilnBOT
Available help channel!
grand idol
I'm curious that how does this formula come out? And when do I gonna use it on my exams during trigonometry tho....
lusty osprey
I'm curious that how does this formula come out? And when do I gonna use it on m...
area = bh/2
now
draw a line perpendicular to a to the bottom right point
what's the length of this line?
grand idol
draw a line from the perpendicular you mean?
pastel vault
draw a line from the perpendicular you mean?
no, and what do you mean by that?
grand idol
draw a line perpendicular to a to the bottom right point
i dont quite understand about this
pastel vault
i dont quite understand about this
grand idol
much better. Thanks
livid hound
this also works
grand idol
so using pythagorus Theorm, then is going to be $b^2= \frac{1}{2} a^2 + (line)^2$
livid hound
no
wraith daggerBOT
Bleach_Enjoyer
livid hound
where's 1/2 a^2 coming from
grand idol
where's 1/2 a^2 coming from
isnt that half of its a length?
livid hound
no
also that'd be (1/2 a)^2, but still no
the perpendicular line isn't guaranteed to bisect a
also no need for pythag here
grand idol
perhaps sine rule?
grand idol
$sinC = \frac{line}{b}$
livid hound
use capital C for the angle
grand idol
use capital C for the angle
my bad i forgot the caps
wraith daggerBOT
Bleach_Enjoyer
livid hound
yes
grand idol
so line is going to be $b*sinC = line$
wraith daggerBOT
Bleach_Enjoyer
livid hound
yes
grand idol
**Bleach\_Enjoyer**
ok so how do i know from here
to find the area of triangle
since i know the line length is just that
pastel vault
since i know the line length is just that
that's the perpendicular height by our construction
livid hound
that line is the altitude relative to side a
from there its just
Area = 1/2 base * height
pastel vault
that height is perpendicular to side a
grand idol
that's the perpendicular height by our construction
ohh so thats the height?
the line is the height
livid hound
when considering a as the base
grand idol
put in we got $Area_of_triangle = \frac{1}{2} (a) (bsinC)$
livid hound
yeh
wraith daggerBOT
Bleach_Enjoyer
livid hound
And when do I gonna use it on my exams during trigonometry tho....
you can use this to find the area when you have two sides and the angle in between
grand idol
> And when do I gonna use it on my exams during trigonometry tho....
you can us...
Ok got it...
pastel vault
it's just as natural as the sine or cosine rules
it's like the other main formula for mensuration and trig
grand idol
it's just as natural as the sine or cosine rules
yea i was thinking that is very similar like finding the sides using sine rule
and also cosine rule
livid hound
(or form a relation to find one of the relevant sides / angle depending on what you're given)
cedar kilnBOT
cedar kilnBOT
Available help channel!
turbid bramble
How do I go on with this ( I am not a native English speaker so sorry if I say something incorrectly )
turbid bramble
Our teacher gave us this problem I have to do it by tomorrow I am stuck on this one I tried multiple methods none work
slender ginkgo
,rccw
wraith daggerBOT
turbid bramble
I can't get it still is there a formula or something?
turbid bramble
K
mighty shuttle
Need to prove $\frac{ sin(x)-cos(x)+1}{sin(x)-cos(x)-1} = \frac{1}{sec(x)-tan(x)}$?
wraith daggerBOT
wai
turbid bramble
Yeah
mighty shuttle
Start by wrting the right in terms of sin and cos
mighty shuttle
,rccw
wraith daggerBOT
turbid bramble
<@&286206848099549185>
I found this in a book and this makes no sense to me pls explain
glass sky
I found this in a book and this makes no sense to me pls explain
which part the start?
slender ginkgo
,eccentric
slender ginkgo
,rccw
wraith daggerBOT
turbid bramble
The book seems to solve lhs
slender ginkgo
It’s really conjugation
turbid bramble
I can't really understand what it soes
turbid bramble
It’s really conjugation
Tbh I don't know what that is
slender ginkgo
Rationalising
turbid bramble
Hmm
glass sky
Tbh I don't know what that is
x+y conjugate is x-y , so the act of multiplying dividing by conjugate is usually reffered as conjugation
turbid bramble
I just know sec is 1/cos and tan is sin/cos
turbid bramble
x+y conjugate is x-y , so the act of multiplying dividing by conjugate is usuall...
Oh
Rationalising te denominater
I see
glass sky
I just know sec is 1/cos and tan is sin/cos
yeah first turn they take cos theta comon from both numerator denominator
slender ginkgo
Rationalising te denominater
Yup
glass sky
is that clear?
glass sky
Rationalising te denominater
not exactly cause nothing is irrational here but yeah same idea
turbid bramble
Cos theta common?
turbid bramble
not exactly cause nothing is irrational here but yeah same idea
Hmm
turbid bramble
turbid bramble
What's this
turbid bramble
rearanging to group in conjugate
Oh
turbid bramble
Ahhhh I see it now
Makes sense
The book doesn't show full steps
Makes it kinda confusing for a guy like m
glass sky
it is an asspull of a question , going rhs to lhs was prol better
turbid bramble
Hmm
cedar kilnBOT
cedar kilnBOT
Available help channel!
meager dock
[(6 ∛250x^5y^4)+(4 ∛54x^7y)]/∛2x^2y
cedar kilnBOT
[(6 ∛250x^5y^4)+(4 ∛54x^7y)]/∛2x^2y
meager dock
this guy challenged me to solve it
tropic oxide
this is not an equation and there's nothing to solve
also do you have a picture of the problem as originally stated
meager dock
nothing
ember heath
so u want us to solve it for u?
tropic oxide
full factorize
meager dock
help me solve it
tropic oxide
ok so uhhhhh
meager dock
please
tropic oxide
i guess we have to assume that this means $\frac{6 \sqrt[3]{250x^5y^4} + 4 \sqrt[3]{54x^7y}}{\sqrt[3]{2x^2y}}$ or something?
wraith daggerBOT
Ann
meager dock
i guess so yeah
ember heath
yeah its a little tough to understand whats inside the cube root and whats not
tropic oxide
is DMing the guy to clarify what is and isn't under the root an option
meager dock
yes
meager dock
"anything after the root is under"
tropic oxide
k then we just have to go with my reading
tropic oxide
no
what i would notice here is that $\sqrt[3]{250}$ factorizes as $\sqrt[3]{125 \cdot 2}$ and hence as $5 \sqrt[3]{2}$
wraith daggerBOT
Ann
meager dock
is the 6 outside of it part of the root
tropic oxide
it's outside
meager dock
or just there to be multiplied
tropic oxide
it is there to be multiplied
meager dock
okay okay
tropic oxide
it may also help to pull out perfect cubes on the variables i.e. to break x^5 as x^3 * x^2, x^7 as x^6 * x and similarly for the y's
wraith daggerBOT
Tan
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
blazing zephyr
3√ 2x into x into y
$\sqrt[3]{2x\cdot x\cdot y}$
wraith daggerBOT
ihave<skissue>
blazing zephyr
this?
meager dock
$2x\cdotx\cdoty$
wraith daggerBOT
Tan
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
blazing zephyr
add spaces
meager dock
really??
one time i added spaced
and it said
compile error
and then someone told me if u add spaces it wont understand
blazing zephyr
$2x\cdot x\cdot y$
wraith daggerBOT
ihave<skissue>
blazing zephyr
dont add it to the front
wraith daggerBOT
Tan
meager dock
oh!
meager dock
$\sqrt[3]{2x\cdot x\cdot y}$
how did u get this to cube root tho?? you just wrote sqrt
blazing zephyr
\cdot is like a command, if you make it \cdotx it tries to do the command "cdotx" which is an error, but if you do \cdot x it does the command "cdot" then adds an x
blazing zephyr
how did u get this to cube root tho?? you just wrote sqrt
theres a [3]
meager dock
isnt that in the fraction tho?
blazing zephyr
there is no fraction
meager dock
oh
blazing zephyr
unless you mean in the radical, it is not as it is before it
meager dock
can you help me solve it then
blazing zephyr
just divide
meager dock
$\frac{6 \sqrt[3]{250x^5y^4} + 4 \sqrt[3]{54x^7y}}{\sqrt[3]{2x^2y}}$
wraith daggerBOT
Tan
blazing zephyr
divide each term in the numerator with the denominator
wraith daggerBOT
Tan
blazing zephyr
then it wont be equal anymore
meager dock
wait its not an equation tho..
yeah
mb
can you help me solve this
find the values for which the curve y=x^2+kx+(4k-15) is completely above the x-axis.
"completely above the x axis
so D>0?
||<@&286206848099549185> ||
meager dock
:D
and then its just a quadratic you equate with zero right
the lesser value will be < and the bigger value will be >
blazing zephyr
i think0
wind meteor
For y=x^2+kx+(4k-15) to always be positive for all x ("above the x-axis"), the discriminant must be less than zero not greater.
wind meteor
A positive discriminant means there are roots, so the parabola is crossing the x axis. You dont want that (since you want the parabola to be completely above the x axis).
tough finch
Just take out (2x²y)^(1/3) in each term
meager dock
what is parabola
tough finch
Inside everything remains a whole cube
meager dock
is it the x intercepts
tough finch
what is parabola
The shape of the graph of a quadratic is called a parabola
meager dock
the part of the graph that instersects the x axis
meager dock
The shape of the graph of a quadratic is called a parabola
why do we not just say curve then?
is it like wrong
tough finch
why do we not just say curve then?
well because a curve can be anything, not just a parabola
all continuous graphs of an equation with real roots are curves
tough finch
[(6 ∛250x^5y^4)+(4 ∛54x^7y)]/∛2x^2y
This is the question right?
meager dock
well because a curve can be anything, not just a parabola
so a parapola is only a quadratic curve right
not a polynomial curve
meager dock
find the values for which the curve y=x^2+kx+(4k-15) is completely above the x-a...
this is the question
blazing zephyr
why do we not just say curve then?
a curve is very broad
cedar kilnBOT
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tawdry jasper
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tawdry jasper
Why am I discounting the already discounted 3000 dollar PDV? In picture 1 I find the PDV by dividing 150 by 0.05, which equals 3000. Later down in the text I discount it again by dividing with 1.05. Why?
cedar kilnBOT
@tawdry jasper Has your question been resolved?
tawdry jasper
.close
cedar kilnBOT
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Available help channel!
flat flax
need help with this question
cedar kilnBOT
need help with this question
rapid mauve
what have you tried so far?
blazing zephyr
need help with this question
try to find the area of the flowers with respect to x, and you know that it equals 100
flat flax
how to find the are of the flowers
rapid mauve
you have big rectangle and small rectangle. you are told that flowers are planted on area outside small rectangle
flat flax
yea
rapid mauve
so what is the area of the flowers in terms of the area of the rectangles?
flat flax
x+1m*x+2m?
rapid mauve
i see you're trying to find the area of the big rectangle, not the flowers (which is the unshaded region)
and that would also be incorrect unfortunately, because the length of the shaded region is not x
please look carefully at your question and see what the length of the shaded region is
flat flax
the length of the shaded rectangle is 2x and with is x so isnt x2x+(x+12x+2)=100
rapid mauve
i don't quite get your notation. could you write it out perhaps?
or use ^ to denote exponent/powers
flat flax
Xx2X+(X+1x2X+2)=100
rapid mauve
i'm sorry, i'm still confused
flint cape
the length of the shaded rectangle is 2x and with is x so isnt x*2x+(x+1*2x+2)=1...
I need to explicitly tell you right now that _ is NOT the minus sign
It's -
flat flax
ok wait
flint cape
i'm sorry, i'm still confused
He's using the _ key for minus, but that's also a markdown for italicising text, meaning that two of them in the same message end up cancelling each other out
Actually wait
No
rapid mauve
Xx2X+(X+1x2X+2)=100
i understand, but i mean this one
rapid mauve
He's using the `_` key for minus, but that's also a markdown for italicising tex...
also, that would be *
flint cape
They're using * for multiplication
flint cape
also, that would be *
(no, the _ does the same thing)
Discord underlining requires TWO underscores on either side
flint cape
He'd typed x*2x+(x+1*2x+2)=100
rapid mauve
yeah but even with this notation it's still unclear and i think he needs a couple more brackets
flat flax
rapid mauve
is this an x?
flat flax
Yes😅
rapid mauve
this is incorrect. where did the x(2x) come from?
flat flax
The area of the shaded rectangle
rapid mauve
but the area of the shaded rectangle is already included in the area of the big rectangle
you are counting that area twice now
flat flax
Ohh my bad,now i understand
rapid mauve
now try again
rapid mauve
what's your current quadratic
flat flax
x^2+2x-49=0
rapid mauve
do you know the quadratic formula?
flat flax
No
rapid mauve
completing the square?
cedar kilnBOT
@flat flax Has your question been resolved?
flat flax
Is this correct
cedar kilnBOT
flat flax
.reopen
cedar kilnBOT
✅
flat flax
Is this correct
?
wraith daggerBOT
ℝαμOmeganato5
rapid mauve
yeah that part is a bit confusing
flat flax
ohh ok
livid hound
its also a bit dodgy when / how the +- appeared and disappeared
flat flax
@rapid mauve @livid hound thx for the help
livid hound
$\pm$ shouldn't have appeared here
$$\sqrt{(x+1)^2} = \sqrt{50}$$
then
$$x+1 = \pm\sqrt{25}\cdot \sqrt{2}$$
wraith daggerBOT
ℝαμOmeganato5
hearty nexus
can i ask my doubt here
cedar kilnBOT
can i ask my doubt here
dusky panther
about
hearty nexus
integration
dusky panther
what's ur doubt
slender ginkgo
Any question in particular?
sacred iron
!da2a
cedar kilnBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
slender ginkgo
,rccw
wraith daggerBOT
slender ginkgo
Progress?
hearty nexus
its multi correct actually
hearty nexus
and how do i do that
modern estuary
Do you know how the find the area bounded by two curves?
hearty nexus
yea
modern estuary
Then it should be fairly straightforward
hearty nexus
f(x)-g(x)
hearty nexus
Then it should be fairly straightforward
oh okay
modern estuary
Tell me what expression you get for An and then which options follow from it
hearty nexus
u could also take n as a number say 2
you mean in the An expression?
ember heath
you mean in the An expression?
yes
slender ginkgo
Region above x-axis
modern estuary
Okay that works then
modern estuary
Did you check option C and D?
modern estuary
Okay
modern estuary
and see which option matches
Only helpful for seeing which ones dont match. The ones which match need to be confirmed and then you will end up doing this anyway
So there is no point in doing smaller cases if you know the method
ember heath
Only helpful for seeing which ones dont match. The ones which match need to be c...
yes i was just giving a suggestion
hearty nexus
yes i was just giving a suggestion
i did the way you told
its kinda easy substituting
but method is also imp
ember heath
but method is also imp
yeah exactly
so like in an exam if ur stuck u can do stuff like this
modern estuary
You can type .close if your question is solved @hearty nexus
cedar kilnBOT
@hearty nexus Has your question been resolved?
crisp lynx
cedar kilnBOT
void sand
you shouldn't assume k is anything yet
crisp lynx
i know
void sand
you need to find what k is equal to
crisp lynx
yes
void sand
any ideas? 
ember heath
do i assume k as 1 ?
how can u assume k value then what will u solve for
void sand
on how to proceed, that is
crisp lynx
it wouldve been easy if there was nothing in denominator
drifting cedar
try multiplying both sides by (3x + 1)
void sand
it wouldve been easy if there was nothing in denominator
you can get rid of the denominator by multiplying both sides by it 
ember heath
firstly @crisp lynx when does a quadratic equation have both roots real
crisp lynx
when its equal to 0 ?
crisp lynx
when its D>0
ember heath
when its D>0
yes correct..but it can be D>=0 also because they dont specify distinct roots
crisp lynx
okay yes
ember heath
try multiplying both sides by (3x + 1)
ok so now that we've clarified that, do this as ur first step
and tell me if u can see what comes next
ember heath
multiply what
void sand
@crisp lynx try to turn the given equation into a quadratic equation
you can then use properties of the discriminant to deduce the values of k for which the quadratic (and thus the original equation) have two real roots 
crisp lynx
void sand
,rotate
wraith daggerBOT
void sand
seems like you made a sign error here
crisp lynx
no?
oh
so now i have to use the quadratic formula on the quadratic i got from the determinant of the original eq
void sand
so now i have to use the quadratic formula on the quadratic i got from the deter...
idk what you mean by "the determinant of the original eq", but you're going to be using part of the quadratic formula on the new quadratic you found, yes
void sand
recall the following fact:
given a quadratic ax^2 + bx + c, the discriminant is the expression b^2 - 4ac
crisp lynx
thats right
void sand
if the discriminant is greater than 0, then the quadratic has two real roots
if it's equal to 0, then it has one real root
and if it's less than 0, then it has no real roots
this is what you really want to be using
cedar kilnBOT
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Available help channel!
normal seal
Remove all perfect squares from inside the square root, √175. I understand the factoring, but not how to add them together to get the final answer.
pseudo sage
Remove all perfect squares from inside the square root, √175. I understand the f...
can you clarify the question
I think I understand
so basically
175 is prime factorization 5 * 5 * 7
so we have sqrt(5^2 * 7)
We can separate the square roots, so sqrt(5^2) * sqrt(7)
Therefore the answer is 5 * sqrt(7)
normal seal
Do you need to put 5^2 for a reason or is it to simplyfy things? and how do you know which one ends up squared for the answer?
rapid mauve
So will prime numbers always be with the root?
quick reminder that because you're doing a prime factorization, there will always be a prime number under the root unless all prime factors have even powers
normal seal
Try sqrt(48)
4√3 ?
silk gust
yes, that's right
vocal minnow
sup
i need some help
i got finals in a week 😭
its 1 am rn i will come online tmmrow
slender ginkgo
!occupied
cedar kilnBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
vocal minnow
hopefully smeone will be here
fallen needle
8469x63564x27854x34724x27172x12511x9871x16058x5702x256x192360
wraith daggerBOT
Result:
1
Use this
wraith daggerBOT
Result:
7.8778707800612e+45
There we go