Double check
#help-0
ocean sealBOT
Umbraleviathan
last ether
Understand?
last ether
How did 12a = -1.2 go to a = -0.1
I put 0 in for x
Like what I said
Because there's a point (0, -1.2)
last ether
How did 12a = -1.2 go to a = -0.1
Also I divided by 12
soft needle
Also I divided by 12
O
last ether
So $f(x) = -0.1(x-1.5)(x-8)$
soft needle
Well that unconfuses me a little now
ocean sealBOT
Umbraleviathan
last ether
You can leave it like that
To find the vertex (highest point), you can either use a graphing calculator and using the "maximum" program
soft needle
You can leave it like that
That's the f function?
last ether
That's the f function?
Yes
Wait is that drunk Barney
I just realized what he was holding
last ether
They say the 15th shot hits harder than the first
soft needle
Unfortunately cannot relate I'm still a 15 year old mess
last ether
b. Expand f(x), and use your vertex-abscissa formula
Or whatever your class calls it
$$\frac{-b}{2a}$$
ocean sealBOT
Umbraleviathan
soft needle
Or whatever your class calls it
I don't remember absolutely anything, we learned this right at the beginningn of the year
soft needle
How to expand?
last ether
FOIL it
soft needle
How to foil it
soft needle
Got it
last ether
x^2 -9.5x+12.0
Multiply this by -0.1
Because a = -0.1
You just foiled (x-1.5)(x-8) but you also need to multiply by -0.1
Then use -b/2a
soft needle
You just foiled (x-1.5)(x-8) but you also need to multiply by -0.1
I got x^2 - 10.7
soft needle
Then use -b/2a
0
last ether
I got x^2 - 10.7
Should be $-0.1x^2+0.95x-1.2$
ocean sealBOT
Umbraleviathan
last ether
$$b = 0.95$$
$$a = -0.1$$
soft needle
ocean sealBOT
Umbraleviathan
last ether
That's your x-value for the vertex
Plug -b/2a into f(x) to get the vertex y- value (the answer)
waxen jungle
hey there, can someone explain to me how factoring
lone heartBOT
hey there, can someone explain to me how factoring
abstract fractal
What have you tried?
waxen jungle
uhhh well 12/2 is 6 and 4/2 is 2
but I don't get how that resolved in x+6 and x-2
and what happened to the exponent on the first x
abstract fractal
Do you know how to factor quadratics?
waxen jungle
no
abstract fractal
Gimme a sec
alpine sable
waxen jungle
thank you !
abstract fractal
Damn, beat me to it
alpine sable
x^2 + 4x - 12
quadratics can be solved thru middle term factorization , completing the square and also by using the general quadratic formula which would be the easiest and I learned to solve thru this video as well
waxen jungle
ohh finding two numbers that multiply to the one number and add to the other
i'm taking a math course for the first time in 8 years
can someone explain to me why we set the equation to
(equation) = 0 ??
why is the zero relevant
abstract fractal
It wouldn't be an equation otherwise
It'd just be an expression
You can also factor expressions, I suppose, but it's the same process
Normally, the whole reason you factor is to find solutions to when the equation is 0
waxen jungle
so why do the numbers have to multiply to the last term and add to the second term?
like what if the equation was x^2 - 12 + 4x
would factorization still be (x+6) (x-2)?
abstract fractal
It would be, because it's the same equation just reordered
Try going backwards: what happens if you expand (x + a)(x + b)?
abstract fractal
Yep. Expand it some more
waxen jungle
x^2 + a + xb +ab ?
abstract fractal
You missed an x on the a
Anyway, the expansion is x² + ax + bx + ab, right?
What if you factor out an x from those middle two terms?
waxen jungle
then it's x + a + b +ab?
slender gull
ax + bx = (a+b)x
waxen jungle
ugh so many letters and symbols
abstract fractal
Anyway, you get that (x + a)(x + b) = x² + (a + b)x + ab
So if we're gonna factor a quadratic into (x + a)(x + b), we better have it so that the last term is a*b and the middle coefficient is a + b
waxen jungle
so in my equation
x^2 +4x - 12
- 12 is ab
OH BECAUSE IT'S 6*2
dshfjslgdfl
GOT IT
thanks
abstract fractal
Well, 6 * -2
abstract fractal
Only if you're lucky, I'm afraid
I've seen many people's questions go unanswered and die
waxen jungle
damn I've had like 7 answered today
i have this fun equation here
is my factoring correct for the denominator
(x + 8) (x - 8)
because the way I got it was by plugging in a 0x
simple turtle
is my factoring correct for the denominator
no
simple turtle
4X4=16
waxen jungle
oh wait i got confused
yeah you're right
but my thing about the *pretending there is a 0x was correct?
simple turtle
What's the question. you are looking for where denominator is undefined?
abstract fractal
but my thing about the *pretending there is a 0x was correct?
Yes. There's also a formula to factor a² - b², but it's the same principle
simple turtle
Ok, same thing. everything except denominator = 0
a² - b² is good. (x+4)(x-4) = x² - 4²
simple turtle
Yes. There's also a formula to factor a² - b², but it's the same principle
sorry. reply to wrong person.
lone heartBOT
@waxen jungle Has your question been resolved?
dull stone
Lines r and s both pass through the point (k; 9). Line r has a gradient of -4/3 and passes through the point (5;-3).
Find the value of k.
Please help me understand this
dull stone
Are you replacing the b with the k or ?
dull stone
Oh.
tender dew
I substituted k in place of x
dull stone
Isn't K x ?
tender dew
?
iron jungle
I wanted to ask that why is 0 allowed in the domain of the exponential function say f(x) = 2^x? f(0) = 2^0 = 1 which makes it a constant function right? Then why is it allowed in the domain?
zenith lodge
I wanted to ask that why is 0 allowed in the domain of the exponential function ...
f(0) is a constant function
???
iron jungle
Oops sorry, I mean to ask why is it allowed, my mistake
It makes f(x) a constant function ryt?
tacit arch
,calc 2^0
ocean sealBOT
Result:
1
gray ingot
oh I read it is as not allowed 💀
zenith lodge
It makes f(x) a constant function ryt?
*why??
just because f(0) is a constant doesn't mean it's a constant function
iron jungle
just because f(0) is a constant doesn't mean it's a constant function
So what makes a function a constant function?
zenith lodge
So what makes a function a constant function?
f(x) = some constant for all x
iron jungle
Hmm,
I thought if there is a single image for all pre-images of the input set, then the function is called a constant function...
zenith lodge
Hmm,
I thought if there is a single image for all pre-images of the input set, t...
that's also true
alpine sable
lone heartBOT
alpine sable
i tried to solve the integral using both binomial and power rule but i get different answers
can anyone check
heady hill
whats the original q?
abstract fractal
They didn't do u sub though
If they kept it as u⁵/5, you'd be right
But they have (x - 2)⁵/5
alpine sable
q8 was the original question
the first integral is right but the second integral is wrong according to the answers
-288/5 is wrong but i dont see anything wrong with my working out
,rotate
ocean sealBOT
ocean sealBOT
harsh girder
it's +16 not -16
mystic socket
lone heartBOT
Available help channel!
distant chasm
can you use disc method in a problem with 2 functions?
lone heartBOT
can you use disc method in a problem with 2 functions?
alpine sable
Of course, but it has a special name called a washer.
distant chasm
Of course, but it has a special name called a washer.
It's not disc then it's washer
alpine sable
yup but you can think of a washer as a special type of disc with a hole cut through it
lone heartBOT
@distant chasm Has your question been resolved?
frank steeple
Tips to solve using squeeze theorem?
lone heartBOT
Tips to solve using squeeze theorem?
flat ore
isn't this equivalent to $\lim_{r \to 0} \frac{r^2}{\sqrt{r^2+1} - 1}$
ocean sealBOT
ホタル
frank steeple
Was the only way I was taught to solve these types of questions
But that works too
Thanks!
flat ore
I'm used to doing these by converting to polar form
raw sigil
just use L hopital rule?
flat ore
just use L hopital rule?
yeah after converting to polar form you can just use l'hopital
raw sigil
yeah after converting to polar form you can just use l'hopital
maybe I have not studied polar form, any link for such theory? I am in 12th grade right now 😓
flat ore
maybe I have not studied polar form, any link for such theory? I am in 12th grad...
a cartesian point (x,y) can be represented by (rsina, rcosa) where r is the distance of that point from the origin
harsh girder
you can multiply $\frac{\sqrt{r^2+1}+1}{\sqrt{r^2+1}+1}$
ocean sealBOT
秋水
raw sigil
a cartesian point (x,y) can be represented by (rsina, rcosa) where r is the dist...
oh, this polar form, I thought something else
flat ore
i was going to directly apply in this
you cant
flat ore
i can after I rationalise I guess
l'hopitals rule doesnt work for multivariable limits
how would you do it?
raw sigil
l'hopitals rule doesnt work for multivariable limits
😳 🙏 , didn't know that, sorry
in our course it only involves single variable calculus
flat ore
yeah once you convert to single variable you can apply it
flat ore
Was the only way I was taught to solve these types of questions
yeah apparently this method isn't taught in most places which i find much easier to use
frank steeple
yeah I didn't realise I could use it
flat ore
btw you can close this if you're satisfied with the answer
frank steeple
But I was taught polar coordinates like 10 weeks after I was taught limits
flat ore
I see
frank steeple
.close
late moss
lone heartBOT
harsh girder
you can factor it
late moss
i m practicing completion of square rn
i dont wanna factor it
and btw if we do square root of (4-2root3)
do we write it as (2-root3)
or whole underoot(4-2root3)
harsh girder
you mean you want to simplify $\sqrt{4-2 \sqrt{3}}$ ?
ocean sealBOT
秋水
late moss
yes
harsh girder
notice $4-2 \sqrt{3} = 1+3-2\sqrt{3}$
ocean sealBOT
秋水
late moss
idk why am i getting shitty dobuts like this suddenly
harsh girder
$4-2 \sqrt{3} = 1+3-2\sqrt{3} = (\sqrt{3}-1)^2$
ocean sealBOT
秋水
harsh girder
so
$$\sqrt{4-2 \sqrt{3}} = \sqrt{3}-1$$
ocean sealBOT
秋水
harsh girder
do you know $$(a-b)^2 = a^2-2ab+b^2$$
ocean sealBOT
秋水
alpine sable
i never thought like this
what's confusing in that
late moss
idk i just never thought like that
harsh girder
$4-2 \sqrt{3} = 1+3-2\sqrt{3} = (\sqrt{3})^2 -2 \times \sqrt{3} \times 1 + 1^2$
ocean sealBOT
秋水
alpine sable
so
$\sqrt{4-2 \sqrt{3}} = \sqrt{1^2+\sqrt{3}^2-2\sqrt{3}}=\sqrt{(\sqrt{3}-1)^2}=|\sqrt{3}-1|$
ocean sealBOT
sqrt(-1) is approx -30
alpine sable
as sqrt(3) > 1 we can remove the abs
alpine sable
$\sqrt{36-4\sqrt{7}}$?
ocean sealBOT
sqrt(-1) is approx -30
late moss
yes
alpine sable
well then the thing inside the sqrt isnt a square or something
I mean
u can't put it into the forma of (a+b)^2 or (a-b)^2
signal jackal
Its not possible for all of them
late moss
suddenly i m having doubts with sqr roots and oppening brackets
alpine sable
whaaat?
harsh girder
how did u guys
you can let $4-2\sqrt{3} = (a-b \sqrt{3})^2$, then to solve $a,b$
ocean sealBOT
秋水
late moss
i m gonna sleep for 10 mins
my head is gonna bombard
i have been doing maths from 3 hrs now
i m getting confused more and more
even with solving brackets
lmfoa
lone heartBOT
@late moss Has your question been resolved?
alpine sable
[
\sum_{n=1}^\infty \frac{1}{2\sqrt{n}e^{\sqrt{n}}}
]
lone heartBOT
\[
\sum_{n=1}^\infty \frac{1}{2\sqrt{n}e^{\sqrt{n}}}
\]
ocean sealBOT
mahmooz
alpine sable
ye it diverges but that doesnt mean a smaller series would diverge
im trying the root test
\begin{align*}
\lim_{n\to\infty} \sqrt[n]{a_n} &= \lim_{n\to\infty} \sqrt[n]{\frac{1}{2\sqrt{n}e^{\sqrt{n}}}}
\end{align*}
willow canopy
ye it diverges but that doesnt mean a smaller series would diverge
nah I was talking about the solution someone was coming up here
ocean sealBOT
mahmooz
alpine sable
hmmm yeah imma try that since Root test seems useless
the hell is the integral of sqrt(x)
1/sqrt(x) i mean
willow canopy
x^(-1/2)
alpine sable
got it
willow canopy
yup
integral test works
just did it I think
the sqrt(n) cancels in the integrand when you a-ply integration by parts
wait but you’re left with $\int_1^{\infty} e^{-\sqrt{n}} dn$
ocean sealBOT
Azzurala
willow canopy
oh that one you can do comparison i think
willow canopy
yea it is
knotty spire
repeated application of l'hopital
harsh girder
when $x>0$, $e^x>1+x+\frac{x^2}{2}$,
so
$$\sum_{n=1}^\infty \frac{1}{2\sqrt{n}e^{\sqrt{n}}}<\sum_{n=1}^\infty \frac{1}{2\sqrt{n}(1+\sqrt{n}+\frac{n}{2})}<\sum_{n=1}^\infty \frac{1}{n\sqrt{n}}$$
ocean sealBOT
秋水
willow canopy
taylor series approx pog
alpine sable
ok im lost
i cant integrate e^(-sqrt(x))
how did u integrate by parts
i cant use taylor series
harsh girder
$$\int \frac{1}{2 \sqrt{x} e^{\sqrt{x}}} ,dx= \int \frac{1}{e^{\sqrt{x}}},d\sqrt{x} = -e^{-\sqrt{x}}+C$$
ocean sealBOT
秋水
alpine sable
im sorry for being so stupid but why did u move the sqrt(x) out
harsh girder
$$(\sqrt{x})' = \frac{1}{2 \sqrt{x}}$$
ocean sealBOT
秋水
placid zinc
That's u = √x
alpine sable
\begin{gather*}
t = \sqrt{x} \implies \text{dt} = \frac{1}{2\sqrt{x}} \text{ dx} \implies \text{dx} = 2\sqrt{x}\text{ dt}\
\int \frac{1}{2\sqrt{x}e^{\sqrt{x}}} \text{ dx} = \frac12 \int \frac{1}{te^t} 2\sqrt{x}\text{ dt} = \int e^{-t} \text{ dt}\
\int_1^\infty \frac{1}{2\sqrt{x}e^{\sqrt{x}}} = \underbrace{\int_1^\infty e^{-t} \text{ dt}}_{\text{convergent}}
\end{gather*}
ocean sealBOT
mahmooz
alpine sable
which means the series converges, right?
harsh girder
yes
alpine sable
brilliant thank you so much
[
\sum_{n=1}^\infty \frac1n \cdot \sin\frac{1}{\sqrt{n}}
]
ocean sealBOT
mahmooz
harsh girder
you can compare with $\sum \frac{1}{n \sqrt{n}}$
ocean sealBOT
秋水
alpine sable
what about sin
oh sin makes the expression even smaller
wait no but sin jumps from -1 to 1
harsh girder
1>=1/sqrt(n)>0, so sin(this)>0
harsh girder
I mean $0<\frac{1}{\sqrt{n}} \leq1$, so
$$\sin (\frac{1}{\sqrt{n}})>0$$
ocean sealBOT
秋水
alpine sable
ohhhhhhh
harsh girder
$$0<\sin (\frac{1}{\sqrt{n}})<\frac{1}{\sqrt{n}}$$
ocean sealBOT
秋水
alpine sable
ye and $\sum \frac{1}{n\sqrt{n}}$ converges which means our series converges
ocean sealBOT
mahmooz
alpine sable
do u think integral test would've worked here too?
harsh girder
I think you also need compare your integral to $\int_1 ^\infty \frac{1}{x\sqrt{x}} ,dx$
ocean sealBOT
秋水
alpine sable
\begin{gather*}
0 < \frac{1}{sqrt{n}} \leq 1 \implies 0 < \sin\frac{1}{\sqrt{n}} < \frac{1}{\sqrt{n}} \implies \sum \frac1n \cdot \sin\frac{1}{\sqrt{n}} < \sum \frac{1}{n\sqrt{n}}
\end{gather*}
ye done
ocean sealBOT
mahmooz
harsh girder
yeah
alpine sable
but its not instantly obvious that $sin \frac{1}{\sqrt{n}} < \frac{1}{\sqrt{n}}$
ocean sealBOT
mahmooz
alpine sable
i wouldve never known that without looking at the sin function in the interval 0,1
harsh girder
when $x>0$, we have $x>\sin x$
ocean sealBOT
秋水
alpine sable
lone heartBOT
alpine sable
Please help me out?
willow canopy
hint: sum of all angle in a 4-sided shape is 360 degree
sleek cargo
Please help me out?
are you cheating on your exam
willow canopy
oh boy 👀
alpine sable
are you cheating on your exam
No im homeschooled.
its my homework that my teacher set up for us.
Since I cant physicly go to the other side of south africa and get my homework.
and Im bad with geometry
languid bolt
i wanna answer e tbh
median oar
Please help me out?
try to write it down in math terms
your first hint about the sum of all interior angles in a 4 sided shape is 360 degrees should be where you want to start
languid bolt
360*
median oar
ty
alpine sable
angleP+angleS+angleQ+angleR = 360 degrees
lone heartBOT
@worldly wasp Has your question been resolved?
alpine sable
angle P + angle Q + angle S + angle R = 360............ all angles of any quadrilateral add up to 360
Angle P = 90
Angle = 90
Angle R = x-20
angle Q = x+10
..............................................Given information
90+90+(x-20)+(x+10)=360
180+(x-20)+(x+10)=360
(x-20)+(x+10)=360-180
(x-20)+(x+10)=180
x-20+x+10=180
x+x-20+1=180
2x-10=180
2x=190
x= 190/2
x=95
Hence, C is the answer
knotty wren
what is standard deviation?
lone heartBOT
what is standard deviation?
knotty wren
i cant find any good explanation on the internet
how is it different from variance
what does standard deviation tell us that variance doesn't or vice versa
median oar
sd is just sqrt of variance
worn fox
They both tell you the same thing, of course, you can argue standard deviation is "better" because it has the same units as your data, so it's more intuitive when talking about how far things are from the mean
median oar
what does standard deviation tell us that variance doesn't or vice versa
if u wanna look at the mean at say 6
then the sd is 1
and you have a value of 8
you know that's 2 sd away
kinda hard to say that in variance
not that you cant but it's a bit simplier in "sd"
median oar
how many sd away
knotty wren
sd?
knotty wren
whats a distribution
knotty wren
bruh
i swear they just jumprd straight to chebyshev's theorem right from calculating mean
they missed everything in between
median oar
how did you get to that
without knowing what distributions are
if you look at people's height
i think that's a normal distribution
knotty wren
i mean theres a formula for calculating mean
median oar
so most people are around the average with some outliers
knotty wren
so not much to do there
median oar
so let's say 170 is the average height
and let's say sd is 15
(im making these numbers up)
knotty wren
ok
knotty wren
okay
median oar
now variance is sd squared so it's not quite measured in cm
so it's somewhat "less" useful to know
median oar
i dont know how to adequately define it
knotty wren
hmm
worn fox
Very roughly a distribution just describes probabilities in a concise way
lone heartBOT
@knotty wren Has your question been resolved?
knotty wren
alright i dont get it but alright ig
shy briar
Could someone walk me through this excersize, I believe we must use the Bayes theorem.
shy briar
why is it not of good quality, I apologize for it
shy briar
.close
lament glen
I have no clue what this graph is, mostly confused as to what $v = v_0$ and $u = u_0$ is supposed to be (why have two different variables here?) and what $r$ is meant to be
ocean sealBOT
Doggo
lament glen
the book gives basically no previous context, it's the jacobian part
r was used for vector valued functions before when I was on that subject
but no clue what anything is here?
worn fox
u=u_0 and v=v_0 are lines in the u,v plane
worn fox
I assume you're doing multivariable calc
lament glen
yeah
worn fox
In which case here r: R^2 --> R
worn fox
Ah yeah you're right bc of the bold
lament glen
I tried reading the book but I can't really understand anything because it uses this graph to explain everything
and I have no clue what's going on here exactly
worn fox
So they're changing coordinates from u,v to x,y
And showing how the region S changes to the region R
lament glen
and how does r work here? is it taking the line u = u_0 and moving it to x,y coordinates?
why not use T directly?
worn fox
Hmm, what is T here
lament glen
T(u, v) = (x, y) as the book put it
so I think it just moves any point on uv to xy
oh hm wait I found some extra context that I missed on the book
ook so r is basically another way to write T from what I can see
ah I got it now
.close
lone heartBOT
lament glen
thanks
lone heartBOT
Available help channel!
gray flame
Let ABC be an acute triangle
BE & CF be the height of the triangle, they cut each other at H
M is the mid-point of BC
On the line EF, construct a point X such that the angle XMH= HAM
Proof that AH split MX in half
gray flame
Does someone have any idea how to solve this?
I haven't gotten any progress so far
lone heartBOT
@gray flame Has your question been resolved?
gray flame
<@&286206848099549185>
lone heartBOT
@gray flame Has your question been resolved?
gray flame
<@&286206848099549185>
gray flame
The problem isn't exist in any competition though
gray flame
AH doesn't even touch MX
The intersection AH at MX is I
Prove that MI=IX
Another way to state it
last ether
Let's see what I can do
I can try breaking it down
H is the orthocenter of ABC
I'm honestly not sure how to do this lol
What have you tried
gray flame
I have no idea, especially the part "XMH= HAM"
I don't know how to use it
last ether
Yeah I don't think any helpers would wanna help with one too
Maybe ask your teacher
There's so many lines
gray flame
There's so many lines
I think we might have to construct something to use "XMH= HAM" part
last ether
Yeah I tried making triangle MAX
That doesn't help
Let's see
Lemme try using sumboblab
gray flame
good luck with it, cya later
lone heartBOT
@gray flame Has your question been resolved?
iron parcel
what grade material is this
lone heartBOT
what grade material is this
wide raven
try equating everything to lambda
thick yoke
It probably depends between different countries but where I live (Israel) I believe that in grade 8-9 pupils can solve this
iron parcel
quiz
wide raven
or any arbitrary constant
wide raven
It probably depends between different countries but where I live (Israel) I beli...
7-8 in mine
iron parcel
waht is lambda
wide raven
you can do directly but would be better if done with that
iron parcel
can u use 1
thick yoke
can u use 1
you need a letter, not a number
you can write c for example
or lambda which is a Greek letter
wide raven
or lambda which is a Greek letter
i kinda use it like a standard thing when dealing with ratios so i siggested that
iron parcel
you need a letter, not a number
ok ill try
gray isle
around grade 8
iron parcel
my teacher must have been sick cause she was absent for a week and didnt teach us this
lone heartBOT
@iron parcel Has your question been resolved?
north adder
around grade 8
thats very kind, I would say 5th grade
north adder
what grade is this stuf
do you need help or was this your question
iron parcel
a(a-b) =31
idkthis tho
iron parcel
do you need help or was this your question
do u know?
lone heartBOT
@iron parcel Has your question been resolved?
north adder
what is a+b
wait do you need a value?
untold knot
Would this be correct?
lone heartBOT
Would this be correct?
ocean sealBOT
real solar
Not correct
balmy warren
simplify the left hand side first
untold knot
So, would I have to expand?
balmy warren
the bottom part of the fractio
real solar
Yeah
untold knot
Okay
balmy warren
yes
lone heartBOT
untold knot
.reopen
lone heartBOT
✅
untold knot
Hold up
balmy warren
So I just have to expand
there is no expansion involved
untold knot
balmy warren
,rotate
untold knot
,rotate
ocean sealBOT
balmy warren
what is 1^2
untold knot
1
balmy warren
so therefore you have 1 / (x+2)^2
untold knot
What?
balmy warren
you have squared the one
untold knot
Oh okay
balmy warren
no point writing 1^2
balmy warren
$(\frac{1}{x+2})^2 = \frac{1^2}{(x+2)^2}$
ocean sealBOT
IntelligentCake
strange basin
Hello kind sirs/mams I have a curious question. Are these two equations the same ?
strange basin
I found the second one online but I'm not entirely sure it matches what I put in the calculator (1st one) and I just want to make sure (There's no way for me to check on the website that I got it from, I'm pretty sure)
tacit arch
yes they're the same
toxic flint
hi guys can someone explain to me whats going on here its not clicking
I derivate it and i have 3x^2+5 im stuck here
tacit arch
I derivate it and i have 3x^2+5 im stuck here
differentiate*
the question has nothing to do with derivatives
do you know what the notation $f^{-1}(x)$ means?
ocean sealBOT
riemann
toxic flint
yes
tacit arch
so trial and error some values for x in f(x) to find out which one equals 5
lone heartBOT
Available help channel!
alpine sable
lone heartBOT
tame hound
$$y=Ce^{-2x}+De^{-x}$$
$$y^{\prime \prime }+3y^{\prime }+2y=0$$
tame hound
Is this accurate?
ocean sealBOT
AuHasard
tame hound
I got $y=Ce^{{}^{-x}}+De^{-2x}$
ocean sealBOT
AuHasard
tacit arch
Did you plug in that y to your ODE?
tame hound
$y^{\prime \prime }+3y^{\prime }+2y=0\rightarrow y=e^{rx}\rightarrow r_{1}=-2,\ r_{2}=-1$
ocean sealBOT
AuHasard
tame hound
I am not sure how much it matters if -2 is r_1, or -1 is r_2
tacit arch
it doesn't
tame hound
$y=Ce^{r_{1}x}+De^{r_{2}x}$
ocean sealBOT
AuHasard
tame hound
This is how it's written, so if I write $y=Ce^{-2x}+De^{-x}$ is no different from $y=Ce^{-x}+De^{-2x}$?
ocean sealBOT
AuHasard
tacit arch
correct
raven oriole
lone heartBOT
tacit arch
yea
tacit arch
partial fractions
raven oriole
partial fractions
so it'll be ∫ A/x + ∫ B/(1-x)
tacit arch
right
lone heartBOT
@raven oriole Has your question been resolved?
lone heartBOT
@raven oriole Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
winged heron
Hey
winged heron
I'm looking for someone with a higher education than algebra which I'm in myself.
I'm going to be on for a couple hours studying for the second part of my finals and would really enjoy some help
lone heartBOT
@winged heron Has your question been resolved?
winged heron
<@&286206848099549185> ?
winged heron
Idk I'm just waiting for someone to tell me if they can help cause I got alot of questions
placid zinc
You can feel free to ask, and anybody who knows the subject will answer!
winged heron
Well question 1
That'
That's just (9 r^3 s^9)(r^3 s^3)
And then that gets 27 r^6 s^12
correct?
placid zinc
Almost. 3^3 is 27, not 9
winged heron
Yeah just caught that
placid zinc
But all of that is the right idea
placid zinc
I actually can't quite read that
placid zinc
You just subtract the exponents
winged heron
and when the base is the same on division you subtract correct?
for question 3. it's 1/a^3 correct?
placid zinc
ye
winged heron
question 4. is I think 1/3^14
Question 5 is uh
81 a^-8
over
b^12
Final answer for question 5= 81/ a ^8 b^12
correct?
Soooo
<@&286206848099549185>.
im fucked lol
<@&286206848099549185>
winged heron
W
Arya how long would you bee able to help
Cause like
I got a whole packet
.close
lone dagger
Could some mathematician solve this
stone glen
,w solve (2n-1)(2^n)+1=950273
ocean sealBOT
lone dagger
Is there anyway to write that in simpler terms?
cuz I need the number of terms
with my work shown
stone glen
,w solve (2log_2(x) - 1)x+1=950273
ocean sealBOT
lone dagger
thanks bro
stone glen
Wait
lone dagger
but I need to show work as well
stone glen
That's not the n
lone dagger
We didnt do all that log stuff yet
lone dagger
okok gotchu
stone glen
,w 32768=2^n
ocean sealBOT
lone dagger
so how many terms will it be
stone glen
15?
lone dagger
ohhh my bad
But is there a way to simplify the shown work?
cuz I havent learnt this advanced stuff yet
stone glen
So the answer to part a is i guess one part of the general term is an Arithmetic sequence and the other part is a geometric so if we could call it AGS
$$(2n-1)(2^n)+1=950273$$
ocean sealBOT
Lelouch
ocean sealBOT
Lelouch
stone glen
@lone dagger paying attention?
lone dagger
Yes sir
ocean sealBOT
Lelouch
stone glen
**Lelouch**
Writing this in terms of x
stone glen
I cannot use log is what I was trying to say
Then it's a big big problem
:((
Log is simple
Learn it
lone dagger
ik but teacher gonna say I cheated lol
stone glen
So if we have $a=b^c$
ocean sealBOT
Lelouch
stone glen
ik but teacher gonna say I cheated lol
Screw the teacher, math is math ;(
lone dagger
hmm what if I say trial and error and write the series for 15 terms
Even B^c, i hav no clue what that is lol
stone glen
Don't learn because you want to impress your teacher, learn because you want to develope a skill
stone glen
hmm what if I say trial and error and write the series for 15 terms
That will take ages
lone dagger
I did fun fact, ended up with a 0 😦
no, cuz 6 terms r there
I can follow the pattern no
?
till the 15th
stone glen
You could but that would take alot of time and it's the "brute force " method
It's not very elegant of you to do thay
Also you didn't use the equation of sum so it doesn't count :3
lone dagger
Also you didn't use the equation of sum so it doesn't count :3
Is that in your books, or it actually doesnt count
stone glen
Disgusting ways
lone dagger
hahahah agreed
stone glen
stone glen
Is that in your books, or it actually doesnt count
It doenst count at all , because they give you the equation just because you should be using it
Otherwise why would they give you the equation://
lone dagger
well how would I use it then? If i cant use any of the advanced stuff
stone glen
well how would I use it then? If i cant use any of the advanced stuff
I don't know then, :/
little drum
:O
south anvil
hello?
waxen haven
what do you mean combine?
south anvil
what do you mean combine?
one second
I want the red line to subtract the green line
for x 1 y would be 1
for x 2 y would be 2
south anvil
yes
I will try to round it now
one second
wait
no
I will say one second
okay here you go
x: 0 would be bellow the x axis
hello?
@waxen haven are you there, if not then I will ask another person
@waxen haven okay I am going to another help location, thanks for your time
tacit arch
.close
south anvil
I need help with this:
lone heartBOT
I need help with this:
south anvil
alpine sable
you don't need to close it when one of us can't help you
just wait for other people
lone heartBOT
@south anvil Has your question been resolved?
simple turtle
I don't understand your question.
spring jackal
lone heartBOT
spring jackal
For this question, when I put these values into the delta as (-k)^2 -4(x)(6)
alpine sable
Real roots exist when b^2 - 4ac > 0
alpine sable
as 1
spring jackal
How come?
alpine sable
yw
spring jackal
.close
lone heartBOT
lone heartBOT
Available help channel!
pseudo smelt
Hello the question says ( find the distance between the 2 " . " (-3 ; -2) ; (-5 ; -4 )
sullen agate
lone heartBOT
@pseudo smelt Has your question been resolved?
frosty lark
Hello 👋 I’ve got a linear algebra problem, just looking for help on where I went wrong on my homework problem, thanks.
crude rose
Hello 👋 I’ve got a linear algebra problem, just looking for help on where I wen...
You probably messed up somewhere in the algebra
For the set
Det
frosty lark
You probably messed up somewhere in the algebra
i cross referenced it with symbolab and its still the same result, are my entries wrong for (x-3)(x+4)(x+1)-(-2)(1)
crude rose
Hello 👋 I’ve got a linear algebra problem, just looking for help on where I wen...
I’m noticing u prematurely changed signs
Idk if that does anything weird
frosty lark
It would seem the algebra is correct
frosty lark
Thought the same thing then I did this and it got the correct answer so I don’t know what I’m doing wrong
waxen flame
lone heartBOT
@frosty lark Has your question been resolved?
frosty lark
id multiply both sides by (x-3)?
ocean sealBOT
Kookiemon
frosty lark
You forgot to multiply (-2)(1) by (x-3)
That’s not part of the determinant calculation though is it?
frosty lark
Wouldn’t you simply multiply your number by the minor and leave it at that
waxen flame
Yes, you sum the product of the diagonals from UL to BR and subtract the sum of the product of the diagonals from UR to BL.
frosty lark
Is this only for characteristic polynomials
waxen flame
You are calculating the determinant of A - λI, so yes.
frosty lark
You are calculating the determinant of **A - λI**, so yes.
Ah okay so it’s for that reason I see I see
lone heartBOT
@frosty lark Has your question been resolved?
low pewter
lone heartBOT
low pewter
Can someone please explain to me how to put any quadratic equation in to a square ?
eternal shale
you can write x^2-x+1/4 + 3/4
eternal shale
you can write x^2-x+1/4 + 3/4
and u notice that first 3 terms are (x-1/2)^2 and remains + 3/4
alpine siren
hi
alpine siren
For what values of p does the vertex of parabola y = $x^2 + 2px + 13$ lie at a distance of 5 from originorigin
ocean sealBOT
Darth Vader
alpine siren
How do i start?
i would try calculating distance by using vertex coordinates
-b/2a and -D/aa
Just one a*
ocean sealBOT
Categorist
lime bobcat
Well...
-b/2a = -2p/2 = -p
(-p)²+2p(-p)+13 = p²-2p²+13 = -p²+13
I calculate the first coordinate of the vertex -b/2a and then substitute y(-b/2a)
lone heartBOT
@alpine siren Has your question been resolved?
wispy salmon
lone heartBOT
wispy salmon
Im stuck at question 19 for over an hour and i cant find any proper info to help me out
This is how far i can take this before it falls apart
balmy warren
what is the question
wispy salmon
How do i get to the answer in the bottom, this is a derivative
balmy warren
you need to take derivative of this?
worn fox
Chain rule
wispy salmon
you need to take derivative of this?
Yes
wispy salmon
Chain rule
Im trying it doesn't work, im missing something
balmy warren
ok so start by writing it in power notation
worn fox
You shouldn't be differentiating the stuff under the root and leaving it there. You wanna do the power thing like you've done and leave the inside alone, then multiply the whole thing by the derivative of the inside
Using the quotient rule like you did
balmy warren
do it slowly, no need to do everything together all at once
dreamy shoal
lone heartBOT
dreamy shoal
How do you solve an inequality like this one?
vale wigeon
,rccw
ocean sealBOT
vale wigeon
are you solving for x or for w?