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#help-49
midnight plankBOT
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jade jackal
is there a derivative version of the super hexagon ?
midnight plankBOT
is there a derivative version of the super hexagon ?
jade jackal
it would save braincells
jagged saffron
context for people like me who had no idea what a super hexagon was: https://www.mathsisfun.com/algebra/trig-magic-hexagon.html
jade jackal
well anyways
if x = cosec theta and y = cosec theta + cot theta and if theta was 2 get the tangent line
.close
fair depot
How do you write correct notation for domain of a function
how would you write this in correct notation
midnight plankBOT
Available help channel!
vocal sand
Need help finding derivative with respect to x
midnight plankBOT
Need help finding derivative with respect to x
tender cove
chain rule
vocal sand
I’m just stuck on how to do it
midnight plankBOT
@vocal sand Has your question been resolved?
vocal sand
chain rule
R u able to show me how you’d solve it?
tender cove
what have you tried
vocal sand
I tried flipping the hyperbolic sine to the top and applied product rule
And at this point I’m not sure if my derivative is wrong or the way I’m using this equation
midnight plankBOT
@vocal sand Has your question been resolved?
midnight plankBOT
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alpine wolf
I’m struggling to find A and B…
midnight plankBOT
I’m struggling to find A and B…
midnight plankBOT
I’m struggling to find A and B…
Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.
alpine wolf
^ I accidentally closed the channel…
potent veldt
Is n not dependent on the index i?
alpine wolf
n = 1 sorry
potent veldt
OK well try doing partial fractions on $(n + 1)!$ and $n! $ instead
grand pondBOT
992qqoloy
alpine wolf
How did u come up with that
potent veldt
well u want the denominators to have a difference of degree $1$
grand pondBOT
992qqoloy
potent veldt
for there to be an n in the numerator
potent veldt
U can think of $(n+1)!$ as a degree $n+1$ poly and $n!$ as degree $n$ polynomial if u write as $n(n - 1)...(n - (n - 1))$,etc.
grand pondBOT
992qqoloy
potent veldt
Other than that I just figured if they were like that then u could maybe get some nice telescope
inland jewel
wronskian test of linear independence proof approach
midnight plankBOT
wronskian test of linear independence proof approach
inland jewel
hom eq. y'' + py' + qy = 0 has slns y1,y2
y1,y2 are differentiable on (a,b)
prove for every x in (a,b), Wy1,y2 != 0 ----> y1, y2 are linearly independent on (a,b)
i was thinking of using a contrapositive to prove it
wondering if that is the right approach
W[f, g] = fg' - f'g
<@&286206848099549185>
midnight plankBOT
@inland jewel Has your question been resolved?
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@inland jewel Has your question been resolved?
fathom herald
midnight plankBOT
fathom herald
What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the
horizontal axis for X. Shade the region corresponding to the probability. Find the probability.
how do i do this wit the above information
tulip cypress
on a book shelf there are four math books, 3 science books, 2 geography books, and 4 history books. the books are all different. In how many ways can the books be arranged so that the books of the same subject are grouped together?
midnight plankBOT
on a book shelf there are four math books, 3 science books, 2 geography books, a...
steep ledge
math, science, geography and history are 4 subjects
first, choose the order of the subjects
then choose the order of the math book between themselves
then same for science etc
tulip cypress
does there have to be an order? the question does not specify
steep ledge
counting arrangements is knowing how many choices you have
to arrange them
count how many choices you have at each step
tulip cypress
I think i need a breakdown of what the question is asking of me
if the books are arranged so that they're all part of the same subject, wouldnt that make each subject a single entity?
steep ledge
it does, but this entity can then be changed
steep ledge
because first math book before second is not the same as 2nd before first
you forget that if you switch books of the same subject it's not the same
tulip cypress
so like the sub arrangements matter?
steep ledge
yes
steep ledge
that's for the sub arrangements, but now you're forgetting your original choice of order for subjects
a 4! is missing for your final result
tulip cypress
sorry could you elaborate
steep ledge
(AAAA)(BB)(CCC)(DDDD)
if you don't care about sub arrangements, you have 4! choices of arrangements
inside each of the 4!
you have 4! * 2! * 3! * 4! sub arrangements (4! for A, 2! for B...)
so, in total, you have 4! * (4! * 2! * 3! * 4!) arrangements
limpid oyster
Hello im currently working on this homework and I am quite stuck and the notes from class are not helping. Problems 6 and 7. I showed how I went about solving 6, but I think it might be incorrect. This is in discrete math, and we are suppose to be using nHk, nCk, and nPk.
midnight plankBOT
Hello im currently working on this homework and I am quite stuck and the notes f...
@limpid oyster Has your question been resolved?
limpid oyster
Here is some of the examples in the notes. I just dont understand how Uniform randomness effects this problem.
<@&286206848099549185>
Oops i think im in the wrong place.
.close
midnight plankBOT
@obtuse sinew Has your question been resolved?
fallow surge
midnight plankBOT
fallow surge
why (a) is not a proper subset but (b) is
main current
Where do you see a subset symbol in (b)?
fallow surge
Where do you see a subset symbol in (b)?
wait i said the exact opposite thing
why (a) is proper subset but (b) is equal to each other
oh wait i think i get it.
because for (a), the set represented by LHS and RHS might be a bit different, same elements in general but might have double counting
therefore is not exactly the same thus cannot use the equal sign
i guess?
hollow cobalt
Guys would anyone mind explaining?
midnight plankBOT
Guys would anyone mind explaining?
nocturne lynx
Wait.
nocturne lynx
Let me think how to explain it.
Nah it's my fault, I learned this in a different language.
Kind of like this.
hollow cobalt
ohh how do i go from that step to the next step?
nocturne lynx
The first line of the solution means they have the same k.
And you can solve for a.
Then b.
midnight plankBOT
midnight plankBOT
Available help channel!
gleaming atlas
,w integral 6/(x^2 +9)
midnight plankBOT
,w integral 6/(x^2 +9)
grand pondBOT
gleaming atlas
[\int\frac{6}{x^2+9}]
[6\int\frac{1}{x^2+9}]
[6(\frac{1}{9})\int\frac{1}{\frac{x}{9}+9}]
[\frac{2}{3}\int\frac{1}{x^2+9}]
[\frac{2}{3}\int\frac{1}{x^2+9}]
[\frac{2}{3}\int\frac{1}{u^2+1}\frac{1}{3}dx]
[\frac{2}{3}(\frac{1}{3})\int\frac{1}{u^2+1}dx]
[\frac{2}{9}\int\frac{1}{u^2+1}dx]
[\frac{2}{9}\arctan(x)]
grand pondBOT
dopediscorduser
gleaming atlas
I did something wrong, not sure what?
dense idol
$[6(\frac{1}{9})\int\frac{1}{\frac{x}{9}+9}]$ what is this
grand pondBOT
chlamydia
gleaming atlas
A typo
dense idol
$6(\frac{1}{9})\int\frac{1}{\frac{x^2}{9}+1}$ if you take the 9 out properly
grand pondBOT
chlamydia
gleaming atlas
Right
gleaming atlas
$6(\frac{1}{9})\int\frac{1}{\frac{x^2}{9}+1}$ if you take the 9 out properly
Sorry this is what I meant to put
[\int\frac{6}{x^2+9}]
[6\int\frac{1}{x^2+9}]
[6(\frac{1}{9})\int\frac{1}{\frac{x^2}{9}+1}]
[\frac{2}{3}\int\frac{1}{\frac{x^2}{9}+1}}]
[\frac{2}{3}\int\frac{1}{\frac{x^2}{9}+1}}]
[u = \frac{x^}{3}]
[du = \frac{1}{3}dx]
[\frac{2}{3}\int\frac{1}{u^2+1}*\frac{1}{3}dx]
[\frac{2}{3}(\frac{1}{3})\int\frac{1}{u^2+1}dx]
[\frac{2}{9}\int\frac{1}{u^2+1}dx]
[\frac{2}{9}\arctan(x)]
grand pondBOT
dopediscorduser
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
gleaming atlas
$6(\frac{1}{9})\int\frac{1}{\frac{x^2}{9}+1}$ if you take the 9 out properly
This is what I meant originally
dense idol
how are you integrating 1/(u^2+1) with respect to x
gleaming atlas
how are you integrating 1/(u^2+1) with respect to x
Right, another typo, I meant du not dx
[\int\frac{6}{x^2+9}]
[6\int\frac{1}{x^2+9}]
[6(\frac{1}{9})\int\frac{1}{\frac{x^2}{9}+1}]
[\frac{2}{3}\int\frac{1}{\frac{x^2}{9}+1}}]
[\frac{2}{3}\int\frac{1}{\frac{x^2}{9}+1}}]
[u = \frac{x^}{3}]
[du = \frac{1}{3}dx]
[\frac{2}{3}\int\frac{1}{u^2+1}*\frac{1}{3}du]
[\frac{2}{3}(\frac{1}{3})\int\frac{1}{u^2+1}du]
[\frac{2}{9}\int\frac{1}{u^2+1}du]
[\frac{2}{9}\arctan(x)]
grand pondBOT
dopediscorduser
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
last slate
what is bro writing
dense idol
lmao
last slate
$$\frac{du}{\frac{1}{3}} = 3 du$$
grand pondBOT
SherLocked's Assistant
last slate
$du = \frac{1}{3} dx $ $$\frac{du}{\frac{1}{3}} = dx$$
gleaming atlas
Ah
grand pondBOT
SherLocked's Assistant
grand pondBOT
SherLocked's Assistant
midnight plankBOT
@gleaming atlas Has your question been resolved?
wispy jackal
why is he solving for dx and then changing the the limits. my question is Find the arclength of y = 2x^2 + 4 on 0 ≤ x ≤ 1. cant i just keep u = 4x and a = 1 and then intergrade? hes just doing extra work
midnight plankBOT
why is he solving for dx and then changing the the limits. my question is Find t...
wispy jackal
$Find the arclength of y = 2x^2 + 4 on 0 ≤ x ≤ 1$
grand pondBOT
Flamester7 Tv
midnight plankBOT
@wispy jackal Has your question been resolved?
midnight plankBOT
@wispy jackal Has your question been resolved?
pseudo bear
midnight plankBOT
pseudo bear
Answer key says incorrect I say otherwise
Need a second opinion to ensure I’m not tripping
hearty rune
,rccw
grand pondBOT
hearty rune
whats your opinion
pseudo bear
I think it’s correct, answer key says incorrect
hearty rune
are the domains the same?
pseudo bear
I graphed x^2 and the other one on desmos and they overlap perfectly
I think the word for it is coincide
hearty rune
if you plugged 0 directly into f(x)=x^3/x without change youd get 0/0
the fact x is in the denominator implies x cant be 0 here
pseudo bear
Oh I get it
hearty rune
whereas theres no issue for just x^2
pseudo bear
Thanks a lot
That sounds sarcastic some reason but it’s not
hearty rune
no problemo
hearty rune
I graphed x^2 and the other one on desmos and they overlap perfectly
you can see it on desmos if you highlight the point x=0
just a side note
pseudo bear
you can see it on desmos if you highlight the point x=0
Yea just realised
So just curious what quotient of two functions would give me x^2
grand pondBOT
AℤØ
hearty rune
=$\frac{x^2(x+i)(x-i)}{(x+i)(x-i)}=x^2$
grand pondBOT
AℤØ
hearty rune
x cant be i or -i since its real so should be okay i think (i presume x is real)
theres probably a better answer but meh
midnight plankBOT
@pseudo bear Has your question been resolved?
pseudo bear
Thanks
waxen silo
can someone explain to me why tan^-1(-12/5) is in quadrant 4?
midnight plankBOT
can someone explain to me why tan^-1(-12/5) is in quadrant 4?
steep ledge
tan^-1 takes values only in Q4 and Q1
but since -12/5 is negative, it's Q4
since it's in Q4 that cos and sine are of opposite sign, contrary to Q1
midnight plankBOT
@waxen silo Has your question been resolved?
waxen silo
but since -12/5 is negative, it's Q4
sorry for long reply, but I am confused, since -12/5 is negative, why is it ony in quadrant 4?
steep ledge
tan(x) = sin(x)/cos(x)
in Q1 and Q4, cos(x) >= 0
so tan(x) is negative when sine is negative and vice versa
waxen silo
tanx is negative when sine is negative..
waxen silo
i'm imagining it like this
so if it wasn't negative, tan woud be positive in 1 and 3
but if its negative, it would be in 2 and 4
steep ledge
yes
waxen silo
but this example, its only negative in 4
steep ledge
because tan^-1 only goes to Q4 or Q1 by definition of tan^-1
waxen silo
I see ok
steep ledge
either it's tan^-1(positive thing), then it's something in Q1
either tan^-1(negative thing)
then in Q4
steep ledge
it's because tan is pi periodic
so it only need to be defined on two quadrants and not the four
and its inverse function
tan^-1
then takes value only in Q4 and Q1 by choice
because tan is the same elsewhere
waxen silo
I see
if I think of it like
tan inverse is only positive in quad 1 and 3
ok hold on
I'm still not getting it, sorry
steep ledge
tan inverse on quad 1 is equal to tan inverse on quad 3 because tan pi periodic
so you can't define tan inverse on both
so the decision mathematicians made was that tan inverse would be defined on quad 1 and not 3
and on quad 4 and not 2
for the same reason
steep ledge
take x in Q1
x+pi/2, which is then in Q2
x+pi, in Q3
x+pi/2 + pi, in Q4
tan(x) = tan(x+pi)
tan(x+pi/2) = tan(x+pi/2+pi)
so when you use tan, Q1 and Q3 becomes the same thing
and Q2 and Q4 becomes the same thing too
so now, if you use tan^-1
you can't give something from Q1 and Q3 at the same time
mathematicians had to choose if tan^-1(something) gives the x I took in Q1, or the x+pi in Q3
they chose Q1
and Q4 for negative value
since a choice had to be made for Q2 and Q4 for the same reason
waxen silo
oh I see
just to make sure I understand it, if there wasn't a square in there
would it be (-5/13)+(12/13)
since - - = +
steep ledge
what do you mean if there wasn't a square ?
waxen silo
well in the original image
steep ledge
waxen silo
they use cos^2(A)
waxen silo
yea but double angle
steep ledge
they say cos(2A) = cos²(A)-sin²(A)
waxen silo
so since cos^2(A) is squared, if it wasn't would it be -5/13
steep ledge
no, cos is positive in Q1 and Q4
waxen silo
well in relation to tan inverse
waxen silo
hmm
give me a moment to think about this
so what I've read from this conversation
tan^-1 when it has tan^-1(negative) it will always be in the 4th quadrant
steep ledge
tan^-1(negative thing) -> this tan^-1... is in Q4
tan^-1(positive thing) -> this tan^-1... is in Q1
waxen silo
ok so like hypothetically say I am just using tan^-1
if it was positive, it would only be positive in Q1 and negative everywhere else
if it was negative, it would be negative in Q4 and positive everywhere else
right?
steep ledge
for example, tan^-1(1) is in Q1 because 1 is positive
and tan^-1(-1) is in Q4 because -1 is negative
steep ledge
I gave an explanation about why it is like that
because tan is pi periodic blablabla
waxen silo
I know, mathematicians just decided that
steep ledge
they didn't really have a choice
waxen silo
yea
steep ledge
like, you have to choose a quadrant for positive and one for negative
they chose Q1 and Q4
waxen silo
DAMMMIT there a whole different thing i have to remember for inverse then
:((
alright... thanks for the help Melo
sorry for taking so much of your time
steep ledge
no problem, you're welcome
waxen silo
.close
flat spire
In the contexts of volumes of solids of revolution there is an example a) Find the volumes of solids generated when the following regions are rotated about the specificed lines:
The region bounded by $y = x^2$ and $y = 1$, rotated about the line y = 1
I'm confused as to why the volume would be $\int_{-1}^{1}\pi\left(1-x^{2}\right)^{2}$. Where does the 1 - come from?
midnight plankBOT
In the contexts of volumes of solids of revolution there is an example a) Find t...
grand pondBOT
water beam
midnight plankBOT
@flat spire Has your question been resolved?
flat spire
.close
midnight plankBOT
midnight plankBOT
Available help channel!
twin ridge
I am having difficult navigating my TI 89 calculator. The teacher recommends a TI 84 the class but I already had the TI 89, but the functions do not translate at all in terms of what buttons to press.
midnight plankBOT
I am having difficult navigating my TI 89 calculator. The teacher recommends a T...
twin ridge
I am attempting to find the standard deviation on my calculator but it keeps giving me incorrect values.
I am typing stdDev({0,1,2,3},{14,28,12,1}) but it is giving me 0.7454 instead of what I am supposed to be getting.
Also I do not have very long as my midterm is at 8 AM and it is 11:40 PM, so swift assistance would be very much appreciated.
<@&286206848099549185>
jolly hornet
so
The first list is the list of values, and the second list is the number of times each value appears in the original list.
hollow glade
gnarly
twin ridge
The first list is the list of values, and the second list is the number of times...
Correct.
I am trying to figure out why this list of values with frequencies is not giving the correct answer.
Is it assuming I'm doing a sample std instead of a pop?
It was indeed, I'm a dumb.
.close
safe field
midnight plankBOT
warm magnet
!status
midnight plankBOT
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
warm magnet
For which question
the first?
Isolate the x-term first
So subtract 1/9 from both sides
Then flip the fractions
safe field
For b
warm magnet
Oh
No need for common denominator stuff with x in it. Again, isolate the x term
Subtract both sides by 2/5, then flip the fractions on both sides
warm magnet
I told you to subtract both sides by 2/5 not 1/2
safe field
oh my b
done now what
nvm
so every time i just need the x alone
don’t do common demonator with the x right
pure seal
midnight plankBOT
@safe field Has your question been resolved?
last slate
midnight plankBOT
nova yoke
!status
midnight plankBOT
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
full prairie
A bit stuck on this limit, keep getting it converge at 1 but ik thats wrong
midnight plankBOT
A bit stuck on this limit, keep getting it converge at 1 but ik thats wrong
full prairie
lyric charm
show work
fading egret
full prairie
g'(x)/1/f'(x)
0/1/0
yeah thats what i mean
but dont i start at 0/0
im confused why the rule doesn't apply to 2e^x - 2 / x(e^x -1)
f(a) and g(a) both = 0 as lim-> a?
lyric charm
sjilgsdj
ok wait no
i would need to reread your work again to see if i imagined things
but i dont have the energy to do that rn
waxen silo
can someone help me figure out how they got 13/18 for part b
midnight plankBOT
can someone help me figure out how they got 13/18 for part b
lyric charm
your numbers in the venn diagram are wrong
7+12+5+10 is not 40
12+5 is not 20 and 5+10 is not 18
midnight plankBOT
@waxen silo Has your question been resolved?
waxen silo
sorry for late response
uh yes
this would be P(-H|G)
the -H is suppose to be H hat
<@&286206848099549185>
.close
midnight plankBOT
midnight plankBOT
Available help channel!
last slate
e
last slate
@sage helm
sage helm
yeah
last slate
period is 8 second
sage helm
right so what's a quarter of that
sage helm
and what phase corresponds to 2 s
last slate
and what phase corresponds to 2 s
what that mean
sage helm
$\omega = \frac{\Delta \varphi}{\Delta t}$
grand pondBOT
NEON
sage helm
correct?
last slate
Ok
sage helm
you know Δt = 2
sage helm
Sure
sage helm
yeah
midnight plankBOT
@last slate Has your question been resolved?
pure snow
How would i do this one?
midnight plankBOT
How would i do this one?
clever sedge
How would i do this one?
Is that h(3) + h(1)?
prisma idol
pure snow
I'm still pretty confused
clever sedge
h(x) is a function.
It takes an x, does things to it and outputs something.
In this particular case, h(x) = 2x - 5
This means it takes an x, multiplies it by 2 and then substracts 5 from it.
However, you can have a function like k(t)
For example k(t) = 3t + 1. Multiplies t by 3 and adds 1
In your case, you've got h(x) and you want to figure out what h(n) is
You do this by simply replacing the x with n.
So if h(x) = 2x - 5, then h(n) = 2n - 5
pure snow
Oh thats it?
clever sedge
Yes.
clever sedge
Well now it's a function that takes n's
pure snow
So would it need like 2 answers one withe h(3) and do a superate one with the h(n)
clever sedge
You are simply adding h(3) to h(n)
This is done by first calculating h(3)
Then adding h(n) to that
What is h(3)?
grand pondBOT
USS-Enterprise
clever sedge
$h(3) = 6 - 5 = 1$
grand pondBOT
USS-Enterprise
pure snow
Just add?
pure snow
It's 1 right?
pure snow
So h(n) = 2n -5?
grand pondBOT
USS-Enterprise
clever sedge
To get f(k), we'd just replace every x with k
And we would end up with $f(k) = k^2 + 2k - 1$
grand pondBOT
USS-Enterprise
clever sedge
That's what you have to do
So now you've figured out what h(3) is and what h(n) is
Now just add them together
pure snow
So 2n -4?
clever sedge
Yes! $1 + (2n - 5)$
grand pondBOT
USS-Enterprise
grand pondBOT
USS-Enterprise
clever sedge
$2n - 4$
grand pondBOT
USS-Enterprise
clever sedge
And there's your answer!
pure snow
Do I have to do like h(3) + h(n) = then the answer?
clever sedge
h(3) + h(n) = 2n - 4
clever sedge
You should, 2n - 4 alone doesn't mean much 😅
pure snow
Thank you again
clever sedge
Hehe, no problem 🙃
pure snow
.close
quiet hazel
trying to prove c) but having trouble
midnight plankBOT
trying to prove c) but having trouble
quiet hazel
i have this so far
but im stuck because i cant say that X is necessarily a subset of A
midnight plankBOT
@quiet hazel Has your question been resolved?
quiet hazel
<@&286206848099549185>
chilly fern
Might be a very stupid question, but I have this weird problem in my math book
grand pondBOT
Feevo
chilly fern
$\sum_{n=1}^3 kx^k$
grand pondBOT
Feevo
boreal cliff
what did I do wrong?
chilly fern
get your own channel
boreal cliff
no I need help💀
chilly fern
YOU'RE IN MY HELP CHANNEL
send a message in the available channels
Anyways --
the first sum makes sense to me
$\sum_{k=1}^3 kx^k = x + 2x^2 + 3x^3$
$\sum_{n=1}^3 kx^k$ wtf is this?
grand pondBOT
Feevo
chilly fern
is it just $kx^k+kx^k+kx^k$ ?
grand pondBOT
Feevo
lethal owl
Do you know what the meaning of sigma notation?
chilly fern
This one makes sense, right?
lethal owl
But yeah that is correct if it is n
grand pondBOT
Feevo
wraith flower
Linear algebra
A system of three equations with three variables is homogeneous , and the determinant of the coefficient matrix is equal to three. If we interpret the equations as planes in the space , do they have a point in common ? and in this case, which one is it ?
midnight plankBOT
Linear algebra
A system of three equations with three variables is homogeneous ...
wraith flower
ok
so
I understand the representation
since the determinant is three
which is not equal to 0
it means that the system has a single solution
so it's one point
so , one point and three planes
it looks like this
What I don't understand, is how do I know which point is it ?
knowing the determinant is 3
nova yoke
the key is:
homogeneous
that means the equation is of the form Ax=0
what's the most obvious solution to that equation?
midnight plankBOT
wraith flower
midnight plankBOT
Available help channel!
errant blaze
suppose x^2-2x+y^2=8. prove that if x ≠4,-2 then y ≠ 0
midnight plankBOT
suppose x^2-2x+y^2=8. prove that if x ≠4,-2 then y ≠ 0
last slate
the question is basically saying prove that 4 and -2 are the roots to the question
errant blaze
like is the formatting right? still having a little trouble on solving using contradiction and not sure if something is right
last slate
according to the fundamental theorem of algebra, a quadratic polynomial can only have 2 roots maximum
,w (4)^2-2*4+(-2)^2
grand pondBOT
last slate
read the question wrong, lemme read ur proof
errant blaze
👍
last slate
You only proved that when x=-4,2, the y is 0
but you didnt prove why for any other values, it can't be 0
errant blaze
is it not asking to prove only when x ≠4,-2 then y=0
last slate
yeh but you just subbed the values of 4 and -2 in and obtained y=0
which part did you prove if you sub in 5, y cant be 0?
errant blaze
didnt, typically in class we dont do that
errant blaze
i wasnt aware thats something that had to be done since it was asking to specifically prove if x≠4-2 then y≠0
last slate
do u see why y cant be 0?
for t=3
we have
9+y=9
y=0
for any value greater than 3
we have smth bigger than 9+y=9
last slate
i wasnt aware thats something that had to be done since it was asking to specifi...
ur proof would be correct if it's: if x=4, -2, then y=0
errant blaze
I get what your doing, its just something we havent explored in class. from my understanding, this is a sufficient proof for full marks at least
last slate
ok sure if thats good enough
steep ledge
suppose x^2-2x+y^2=8. prove that if x ≠4,-2 then y ≠ 0
the equation is equivalent to (x-1)²+y² = 9 by completing the square
y² = 3²-(x-1)² = (3-(x-1))(3+x-1) = (4-x)(2+x)
so if x =/= 4, -2, y =/= 0
is way easier
last slate
yeh this proof works
errant blaze
yea thank you, im still new to proof by contradiction so this is a great help
steep ledge
you can also just prove the contrapositive if the exercise doesn't say to not do it
the contrapositive is y = 0 implies x = 4 or -2
which is really easy to prove, like just plug in 0 and factor
errant blaze
yea, contradiction and contrapositives is what im working on. i understand it but i just wanna be more intuitive with it
thanks yall though
.close
ruby widget
How would i sketch this?
midnight plankBOT
How would i sketch this?
velvet oar
would you be more comfortable sketching the line in slope-intercept form? like y=mx+b
ruby widget
I mean yes, sorry i should've phrased it better but I do know how to sketch but im just curious as to why the stopped the line when profit is at 0
ruby widget
,rotate
grand pondBOT
velvet oar
not when the profit is zero, when the number of items manufactured is zero
You can't manufacture a negative amount of items
velvet oar
np 👍
ruby widget
.close
weary mural
does this mean all real numbers?
weary mural
oops
blissful pier
does this mean all real numbers?
midnight plankBOT
blissful pier
alright great thanksss
it is read as "y is an element of the set containing all real numbers" or smthn like, that are a few ways :)
weary mural
it is read as "y is an element of the set containing all real numbers" or smthn ...
ahhh gotcha
thank you so much
blissful pier
thank you so much
midnight plankBOT
Available help channel!
wraith hamlet
I need help
midnight plankBOT
I need help
wraith hamlet
$5^\frac{5}{7}$
grand pondBOT
Umbe
grand pondBOT
Umbe
abstract bridge
you could always put it in root form ngl
midnight plankBOT
midnight plankBOT
Available help channel!
arctic hollow
midnight plankBOT
arctic hollow
Don't know where to start
surreal grove
ok increased by 60% just literally means 160% because you increased by your amount + 60%
arctic hollow
So do I do 80/1.6
surreal grove
yes
sleek shell
could someone help me get the derivative of f(x)=(x+4)^{11} (x-5)^{6}
midnight plankBOT
could someone help me get the derivative of f(x)=(x+4)^{11} (x-5)^{6}
lyric charm
!status
midnight plankBOT
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
on at the beginning i was gonna to the product rule for it but its been a while since i've done derivatives
lyric charm
product rule? how were you gonna apply product rule exactly
oh
you didn't type the function fully
right ok yeah
product rule on (x+4)^11 (x-5)^6 makes sense
sleek shell
using the product rule i got $f'(x)=(x+4)^{11}6(x-5)^{5}+(x-5)^{6}11(x+4)^{10}$
now im not sure where to go from here, i need to find the critical points
grand pondBOT
Voiss
sleek shell
ty
midnight plankBOT
Available help channel!
thorny oasis
midnight plankBOT
hot fox
log(ab) = log a + log b
thorny oasis
okay so
thorny oasis
okay so um
4 log 2 will become log 2^4
so
log 2^4/log 10?
henh
can we do
log (2^4/10)?
is that legal?
hot fox
log 2^4/log 10?
no
hot fox
yep
hot fox
yes
thorny oasis
n den im done?
hot fox
yes
hot fox
same thing...
thorny oasis
wait what
but now its alphabets
2 log a + 3 log b - log c
log a^2 + log b^3 - log c
log a^2 x log (b^3/c)?
hot fox
how did the + become x
thorny oasis
log (a^2 x (b^3/c))
hot fox
well that's it
hot fox
what do you mean
thorny oasis
how do i do this
teal raptor
lol
thorny oasis
ION GET IT
thorny oasis
log 10 = 3 x log x?
hot fox
$\log_{10} x$
{10}
grand pondBOT
A_Note
hot fox
log 10 = 3 x log x?
how did you get this ?
thorny oasis
i took the log x to the other side
hot fox
what mathematical operation have you applied
hot fox
how would you get something like log_b(x) = ...
grand pondBOT
A_Note
hot fox
you use something formula
or you can just use basic fraction manipulation
thorny oasis
log x/log 10 = 3
hot fox
so log x = ?
hot fox
log x / log 10 = 3
thorny oasis
yes
hot fox
so log x = 3 log 10
hot fox
yep
hot fox
raise b to both powers
thorny oasis
wait isnt it just x = 1000
hot fox
np :)
thorny oasis
dont lol me im crying pls
grand pondBOT
A_Note
thorny oasis
huh
teal raptor
when you add as logarithm,
thorny oasis
can we do log x - log 1 + log x - log 9 = 2
teal raptor
?
thorny oasis
when you add as logarithm,
OH RIGH TMAKES SENSE
okay yes ignore what i said pls
log (x-1) + log (x-9) = 2
log (x-1)(x-9) = 2
log x^2-9x-x-9 = 2?
log x^2 - 10x - 9 = 2
i feel like
im going in a horribly wrong direction
teal raptor
yes.. you know that base is 3 right?
so
let's get the value
$\log_a b$, a is base
thorny oasis
yes okay
grand pondBOT
A_Note
thorny oasis
log_3 (x-1)(x-9) = 2
thorny oasis
yes how
teal raptor
the definition of logarithm be like:
thorny oasis
LOOK I DONT GET IT
teal raptor
$a^x = b$ , x =$\log_a b$
thorny oasis
OH RIGHT
grand pondBOT
A_Note
thorny oasis
log_3 (x-1)(x-9) = 2
3^2 = (x-1)(x-9)
teal raptor
yes?
thorny oasis
okay NOW what
teal raptor
solve the equation
thorny oasis
9 = x^2 - 10x - 9?
teal raptor
yess
thorny oasis
x^2 - 10x - 18? and then formula?
teal raptor
bruh
if you use formula, it's relatively complicated unless you're using a calculator
thorny oasis
then what
teal raptor
hmm... didn't you learn that?
ok whatsoever i'll tell
a(x-α)(x-β) = 0
we have the equation here
thorny oasis
im scared but go on
grand pondBOT
A_Note
thorny oasis
um ok
teal raptor
you get (α , β) that meets the condition αβ = -18
all of them
and find the one which meets the condition α+β=10
oh wait
teal raptor
there's nothing integar that meets the condition
in this case,
we should use formula..
(Lol)
thorny oasis
where did I go wrong
thorny oasis
do you know where did formula come from
no clue
teal raptor
well, do you want me to prove it
thorny oasis
WAIT NO BUT WHAT DID I DO WRONG
teal raptor
we were getting $x^2 - 10x - 18$ =0
grand pondBOT
A_Note
teal raptor
a = 1
thorny oasis
si
teal raptor
$-10^2$ isn't $(-10)^2$
grand pondBOT
A_Note
thorny oasis
ok now which one
thorny oasis
**A\_Note**
yes meesa wrong
teal raptor
due to definition of logarithm
lol
now you know how to solve..
without principals :trollface
thorny oasis
done yipee yahoo
thorny oasis
go awn
thorny oasis
my eyes hurt im just not gonna bother
teal raptor
hmm no
thorny oasis
das it
teal raptor
:
thorny oasis
7^x = 70
teal raptor
use definition of logarithm
thorny oasis
okeh
teal raptor
for the second question
thorny oasis
log _7 70 = x
teal raptor
so
thorny oasis
right