namely multiply stuff by something potentially 0, ignoring domain restrictions etc
#help-36
final tangle
the answer to the question of whether the point
(p,0) is an x-intercept is the same answer to
is g(p) equal to 0
glad basalt
gotcha
so the only point they have here that is simple is the y int and the hole
how do you go about getting the other points
final tangle
sub in values of x (whatever you want, as many as you want)
into your function equation
to get the respective y values
glad basalt
so any other number would also give the same graph
final tangle
the same with all other graphs
if you want to find the y-coord when x=1, you sub x=1 into the equation
glad basalt
is there any logic
final tangle
if you for some reason wanted the y-coord when x = 420,
sub that into the equation
glad basalt
like pick the number closest to y int
final tangle
pick whatever you want
pick nice meaningful values if you don't want to make life hard for yourself
tranquil pine
I am not sure how to approach this question.
final saddleBOT
I am not sure how to approach this question.
tranquil pine
I know that tension will face upwards the string, the weight acts downwards.
I'm guessing that I'd have to resolve forces and equate.
final saddleBOT
@tranquil pine Has your question been resolved?
final saddleBOT
@tranquil pine Has your question been resolved?
final saddleBOT
@tranquil pine Has your question been resolved?
muted trout
i did is as g=10 and found that f =1kg*g so if g=10 it would be 10 but if its 9,81 the asnwer would be 9,81
tension of string is 2sqrt3*a which is sqrt3 of g so tension would be sqrt3 kg g where g represents gravitinial acceleration
fathom stream
Could someone please explain structural induction
final saddleBOT
Could someone please explain structural induction
fathom stream
like whats the difference between structural and regular induction
and when do we use structural induction
final saddleBOT
@fathom stream Has your question been resolved?
violet rune
i wanna show that this series converge
final saddleBOT
i wanna show that this series converge
violet rune
i know that the same sum but with k=1 converge
tiny gorge
if you start at n+1 you're summing the tail of the series
any tail of a convergent series is also convergent
because it differs from the whole series by only finitely many terms
tiny gorge
why do you have to calculate the sum
you just want to know if the sequence R_n converges
violet rune
the exercie ask for it x)
tiny gorge
where? show the whole question
violet rune
no it's the next question
violet rune
yes
i don't see how to apply taylor here
to be precise i said calculate the sum, not the limit which is not the same
tiny gorge
try using
violet rune
x=1?
tiny gorge
yes?
tiny gorge
yes
violet rune
i know what it is don't worry
final saddleBOT
@violet rune Has your question been resolved?
final saddleBOT
@violet rune Has your question been resolved?
chilly beacon
can someone help
final saddleBOT
can someone help
wet warren
Yeah for x
But we want the value for y
But take the real value for x before rounding and apply it to the equation then round
chilly beacon
okay so what would that equal to
wet warren
Apply it the function
To get the maximum profit
,calc -25001.91.9 + 9500*1.9 - 7426
soft zealotBOT
Result:
1599
okay that was pretty easy bgl idk why it went over my head
chilly beacon
yes imma put it in the system now n see how it’s gonna rest
say
so
for c it’s b
and for for d
what would i do then
wet warren
To solve the third question
Obviously the first choice won't output the same maximum profit as the x value would still be the same but the maximum profit is less by 3 dollars
So it is the second one
To test that out just substitute (x-3) to x and apply what you applied already to get a and b
wet warren
Can you compare between the maximum profit
And the best price that produces the best profit?
chilly beacon
i’m
wet warren
The second one is what you get out of applying the derivative to the function and equating it to zero to get the x value
The first one is applying that x value to the function to get the maximum profit
chilly beacon
okay
so
it’s the same thing we did for the first question but plug in (x-3)?
it’s 4.90?
wet warren
$$-2500(x-3)^2 + 9500(x-3) - 7426$$
$$-2500x^2 + 15000x - 22500 + 9500x - 28500 - 7426$$
Take derivative
$$-5000x + 15000 + 9500$$
Equate to zero
$$-5000x + 24500 = 0$$
$$-5000x = -24500$$
soft zealotBOT
Sherif Player
wet warren
,calc 24500/5000
soft zealotBOT
Result:
4.9
Yeah correct
And for the final question
It will be the same as b
But add 50
As x doesn't change and we are adding to the whole profit
chilly beacon
no that’s it ty
wet warren
Don't forget to close the channel using
.close@chilly beacon
chilly beacon
.close
timid estuary
final saddleBOT
timid estuary
so these are the problems i need to do and im like 99.9% sure the answer is x but i dont know how to get there
sweet summit
for f(g(x)), you and remove the parentheses around the cuberoot of x - 2, then the 2's will cancel each other out. Then you have the cube root to a cubic power, so then you're just left with x. Similar logic with g(f(x))
timid estuary
is there a way u could like write that down
like so i can visually see it but if u cant thats fine
actually nevermind its alright and thank u so much!!
.close
final saddleBOT
final saddleBOT
Available help channel!
tranquil pine
How would you differentiate this?
$$1+\ln(5xy)=e^{5x-y}$$
final saddleBOT
How would you differentiate this?
$$1+\ln(5xy)=e^{5x-y}$$
soft zealotBOT
What should I do
final saddleBOT
@tranquil pine Has your question been resolved?
regal hamlet
**What should I do**
Respect to which variable are you trying to differentiate?
final saddleBOT
@tranquil pine Has your question been resolved?
final saddleBOT
@tranquil pine Has your question been resolved?
final saddleBOT
Available help channel!
unborn roost
This is a graph of a rational function. Use the function's graph to determine the equation for its formula
final saddleBOT
This is a graph of a rational function. Use the function's graph to determine t...
unborn roost
I do know that the function for rational functions is (ax+b) / (cx + d), and got some understanding of asymptotes, but I struggle to find the way of finding the values for the variables
$\frac{ax+b}{cx+d}$
hidden kernel
I do know that the function for rational functions is (ax+b) / (cx + d), and got...
are you familiar with limits?
steep sequoia
$\frac{ax+b}{cx+d}$
\frac{(ax+b)}{(cx+d)}
soft zealotBOT
Seed
unborn roost
\frac{(ax+b)}{(cx+d)}
thanks mate
unborn roost
are you familiar with limits?
Not that much, but I am aware that the x-value -2 cannot be present in the equation
stark lotus
Do you know homographique function ?
unborn roost
it's the vertical asymptote, and it's a sign that we have a denominator that is equal to zero when x = -2
unborn roost
Do you know homographique function ?
i do not know that
i have at least not heard the name
if you're refering to the functions for the vertical and horizontal asymptote, where horisontal is equal to a/c, and vertical is -b/a then yes i they are familiar
stark lotus
Ok no pb, it tells you that $\dfrac{ax+b}{cx+d}$ can be rewritten as $\dfrac{\alpha}{x-\beta}+\gamma$
soft zealotBOT
Joseph.P
stark lotus
if you're refering to the functions for the vertical and horizontal asymptote, w...
Ye this
unborn roost
**Joseph.P**
$\dfrac{\alpha}{x-\beta}+\gamma is unfamiliar to me$
soft zealotBOT
Seed
unborn roost
Ye this
it is my first time seeing the equation, but i am familiar of the ones i've writte
stark lotus
$\gamma$ is the limit of the function, $\beta$ the value when $x=\frac{-d}{c}$ and I forgot what is $\alpha$
soft zealotBOT
Joseph.P
unborn roost
okay
stark lotus
Here what would be beta and gamma ?
final saddleBOT
@unborn roost Has your question been resolved?
abstract mango
.this is cool
final saddleBOT
ancient thistle
Not sure where to start
final saddleBOT
Available help channel!
final saddleBOT
final saddleBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
winter sleet
nothing, just the guy saying you have to solve sounds a bit off
worldly vale
Substitute 4 for x, then simplify/evaluate and end up with a number for your final answer
stark lotus
nothing, just the guy saying you have to solve sounds a bit off
Ok, sorry for the ping then
winter sleet
Substitute 4 for x, then simplify/evaluate and end up with a number for your fin...
-4
worldly vale
^^
glad basalt
I am super fucking confused
final saddleBOT
I am super fucking confused
fickle crater
fickle crater
🗿🗿
fickle crater
ye
glad basalt
fickle crater
before we continue
stark lotus
You’re telling me there is no value of f(x) when x=4 ?
fickle crater
is this college or highschool or middle school
glad basalt
Why would I think of doing x = 4 tho
I mean I got 4 points kind of
Is it supposed to be symmetric
fickle crater
okay so you know limits
glad basalt
No
stark lotus
Why would I think of doing x = 4 tho
To know the graph maybe
fickle crater
not yet alright
glad basalt
To know the graph maybe
Why does x = 4 matter
To know the graph
Isnt what I have already plenty
How do I know when enough is enough
In future graphs
fickle crater
@glad basalt you know what you call the ratio function where x is in the denominator?
for example what's 1/x called
fickle crater
🗿🗿
glad basalt
Idk
stark lotus
Man I just saw something
stark lotus
Try simplifying your function
fickle crater
you get y=2
stark lotus
No
stark lotus
you get y=2
You get y=2
fickle crater
bro with the emojis 😭
glad basalt
Teach me 
fickle crater
you said it yourself
2(x+2)/(x+2)
simplify what you can after you find your holes
fickle crater
x+2=x+2
glad basalt
Fucki
fickle crater
so you are left with y=2 for any x expect x = -2
glad basalt
Oh divide x + 2
So this
fickle crater
idk what that means
glad basalt
When u div same stuff they cancel cmon
fickle crater
but you are already dividing initially
yeah but no extra division just simplicify the function after factoring
glad basalt
Damn that is
Hella
Fucking
Interesting
So I don’t need to annoy myself with plugging x’s
How do I pick my points
fickle crater
How do I pick my points
what does that mean
fickle crater
you delete it all
glad basalt
Ok
That was sending
It is deleted
Now what
??
My x int is 0 -2
y int 2,0
stark lotus
I have a question, what are all the points ?
stark lotus
What is the dotted line ?
stark lotus
The "hole" is the value of x when the denominator of your function is equal to 0
glad basalt
Is it-2, 2
stark lotus
Is it-2, 2
Is 2+2=0 ?
glad basalt
I was taught that to find the y of the hole’s x
You remove what creates the hole
I.e. x + 2
Then all I have left is 2
Why doesn’t that work here
stark lotus
This just simplifying the fraction no ?
glad basalt
Ye
stark lotus
But you can’t simplify a fraction of the denominator is equal to 0
stark lotus
No it wouldn’t work either, what if x=-2 ?
glad basalt
Fucking
So I should say no to simplifying
And just plug in my x
Into the function
is it -2, 0?
0/0
stark lotus
So I should say no to simplifying
No you can simplify but you need to be careful of when the denominator is equal to 0
glad basalt
Is it equal to zero after you simplify?
But if you were to divide x + 2 and x + 2 you would get 1 right
Why is it zero
stark lotus
It’s not defined when x=-2
glad basalt
So dem is zero when x = -2
stark lotus
In this example yes
glad basalt
Do I not plot a hole anywhere?
stark lotus
Yes you do plot one when the denominator is equal to 0 for a certain value of x that you just said
stark lotus
For which value of x (2x+4)/(x+2) is 0/0 ?
stark lotus
Is thst cuz a hole is undefined so it doesnt matter
Ye
glad basalt
Okkk now what
@stark lotus
Thats wrong
-2 still produces y = 2
The hole is -2, 2
stark lotus
Show your work please
stark lotus
I mean the graph
stark lotus
The hole is -2, 2
Ye
glad basalt
Yes you do plot one when the denominator is equal to 0 for a certain value of x ...
You just said
stark lotus
I sais you plot a hole when the denominator is equal to 0
Is it to hard to understand ?
glad basalt
glad basalt
No it wouldn’t work either, what if x=-2 ?
You literally said its not 2
That the y value of -2 is not 2
You said not to simplify
But if I did
I would get 2
stark lotus
I thought you meant x=-2 and x=2 so I didn’t understand
glad basalt
so you are left with y=2 for any x expect x = -2
Look at this
Y = 2 for any x expect -2
By y is 2 for -2
This is not making any sense
stark lotus
It’s not 2 for -2 this point is the hole
final saddleBOT
@glad basalt Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
tranquil pine
A quantum particle can be trapped in a one-dimensional potential well if the equation:
final saddleBOT
A quantum particle can be trapped in a one-dimensional potential well if the equ...
tranquil pine
has a solution for 0<y<lambda
Proof that there is at least one solution in the interval
soft zealotBOT
The following error occured while calculating:
Error: Colon : expected after object key (char 14)
final saddleBOT
@tranquil pine Has your question been resolved?
wet warren
A quantum particle can be trapped in a one-dimensional potential well if the equ...
So i don't know anything about quantum physics
But I can help you solve the equation
First I think we need to define what tan(lambda) is
@tranquil pine
Cause you can easily set
y = √(lambda) and say that lambda has any 2nπ value (as n is an integer) that makes the equation correct
final saddleBOT
@tranquil pine Has your question been resolved?
upper sigil
how would i do part 2
final saddleBOT
how would i do part 2
tired walrus
wtf is this notation
upper sigil
my teacher told us its like the average rate of change but at a single moment
yeah
i guess so
tired walrus
well ok like. maybe you are in a calculus class that's about to get to that
idk how you are expected to find its exact value tho!
upper sigil
well usually i think id plug in values approaching p(12) from - and +
so like
y1(12) - y(11.999) / .001
or something
and then the same for the other direction and then find within 2 decimal of accuracy
or something like that
but when i do it for this it doesnt make sense
i get a positive value
when this is a decreasing function
worn knot
y1(12) - y(11.999) / .001
It should be (y(12) - y(11.999)) / 0.001
upper sigil
yes
worn knot
That should be negative
worn knot
This is what desmos gives me
valid atlas
final saddleBOT
valid atlas
I don't know where I am going wrong
vital crag
I don't know where I am going wrong
!show
final saddleBOT
I don't know where I am going wrong
Show your work, and if possible, explain where you are stuck.
valid atlas
!show
This is my best picture
Never mind i was trying to skip too steps ugh
.close
final saddleBOT
final saddleBOT
Available help channel!
fathom stream
@tired walrus this is what I ended up doing for the question earlier
fathom stream
is this good
tired walrus
i mean, extra work ig
tranquil pine
hello
final saddleBOT
hello
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).
tranquil pine
it's a good question
fathom stream
i mean, extra work ig
should I exclude the "modifying the rref" part
and instead
just put it as my claim
final saddleBOT
final saddleBOT
Available help channel!
valid atlas
valid atlas
need help
final saddleBOT
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.
@valid atlas Has your question been resolved?
valid atlas
.close
woeful anchor
i need help with this sheet
final saddleBOT
i need help with this sheet
worthy shale
!status
final saddleBOT
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
2
worthy shale
what about it?
worthy shale
thanks
you might've differentiated s(t) wrong
try splitting up the terms and differentiating them separately
$s(t)=\frac2t-\frac4{t^2}$
soft zealotBOT
chlamydia
worthy shale
$-2t^{-2}+8t^{-3}$
soft zealotBOT
chlamydia
woeful anchor
what about now
worthy shale
do you understand what the units are?
woeful anchor
uhh idk
worthy shale
it means that distance is measured in feet, and time in seconds
so your s(t), which measures distance, is in feet
what about velocity?
woeful anchor
is it seconds?
woeful anchor
yeah
worthy shale
so the velocity here is feet/second?
worthy shale
you could just write feet/s beside v(t) i guess
final saddleBOT
@woeful anchor Has your question been resolved?
final saddleBOT
woeful anchor
.reopen
final saddleBOT
✅
worthy shale
what else
worthy shale
it might be better to put the units at the end
woeful anchor
ok cool also i corrected 3b can u check if its right
woeful anchor
idk how to indicate the units for acceleration
worthy shale
velocity (ft/s) is the change in position (ft) over time
and acceleration is the change in velocity over time
woeful anchor
so acceleration ft/sec^2 ?
worthy shale
yeah
gritty drift
Imagine calculating in feet 🤢
worthy shale
fr
gritty drift
Meter >>>>>
woeful anchor
ok bet also i dont get c d e f i tried doing them when u were gone
worthy shale
yeah
woeful anchor
ok
worthy shale
does your teacher care about show all working?
because then you should show how you found positive speed t<4, etc.
woeful anchor
yea she put in directions that said " Answer each question below, showing all work as described in class. Include units where appropriate"
worthy shale
how does she describe it?
woeful anchor
ill show u my notes from class
worthy shale
yup
woeful anchor
thanks man
worthy shale
np
woeful anchor
i alr finished the first page of the hw could u j check my answers before i leave
soft zealotBOT
chlamydia
worthy shale
second question is good
woeful anchor
i'm having trouble reading what the first line says
it says 3^x ln(3) + 1/(xy) (y+y'x)
worthy shale
$\frac d{dx}log_2(xy)=\frac1{ln2}\frac d{dx}ln(xy)$
soft zealotBOT
chlamydia
worthy shale
the logarithmic derivative only works for natural log
so from here it'd be more convenient to do:
$\frac d{dx}(lnx+lny)=\frac1x+\frac{y'}y$
soft zealotBOT
chlamydia
worthy shale
so you're missing a factor of $\frac1{ln2}$
soft zealotBOT
chlamydia
woeful anchor
where do i add it? im confused
worthy shale
**chlamydia**
times this
worthy shale
yeah
woeful anchor
so question #1 is good now?
worthy shale
after you fix that throughout the question, it should be fine
woeful anchor
wait do i have to fix the other lines too?
worthy shale
yeah because it's the same derivative?
woeful anchor
what do i do? just add (1/ln(2) to every line?
worthy shale
you know what, it might be better to just redo the question
keep the photo so you know what to do
woeful anchor
okay
could u help me do it step by step cus i have no clue how to solve this question
woeful anchor
oh ok
i'll try to fix problem with log_2 and get back to you in few minutes
yea i tried solving question #1 didn't get an answer for some reason
worthy shale
what do you mean
woeful anchor
i did it halfway through and i was stuck
worthy shale
$\frac{y'}{yln2}=-3^xln3-\frac1{xln2}$
soft zealotBOT
chlamydia
worthy shale
did you get this?
woeful anchor
could u help me do it step by step cus i have no clue how to solve this question
???
.close
tranquil pine
physics question, is this correct?
final saddleBOT
physics question, is this correct?
tranquil pine
i drew this on MS paint, i want to know if this is correct in terms of if its speeding up or slowing down (acceleration
ping if you have answer thank you
worthy shale
are those v-t graphs?
final saddleBOT
@tranquil pine Has your question been resolved?
tranquil pine
sorry i dont know
im trying to check my notes but no idea
i think it might be PT. sorry for wasting ur time my questoin doesnt make sense if i dont know what it is
worthy shale
what is pt
they're most likely velocity graphs:
keeping in mind that speed is the magnitude of velocity, all that matters is how far the curve moves away from the x-axis
if it moves away from the axis like in the first graph, then it's speeding up
but in the green part, it's moving towards 0, so it's slowing down
final saddleBOT
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Available help channel!
tranquil pine
final saddleBOT
tranquil pine
why isnt p(x<=6) also = (probability 7 students wont pass) + (probability 8 students wont pass) + (probability 9 students wont pass)
thinking about alternative ways to solve it
serene cradle
why isnt p(x<=6) also = (probability 7 students wont pass) + (probability 8 stud...
Well that's effectively the way you calculate it, isn't it? You find the probability that 7, 8, or 9 students (respectively) pass, and subtract it from 1 as we don't want to count those probabilities
Unless I misunderstood your question
indigo plover
final saddleBOT
indigo plover
uh i am having some trouble
So i found the distance between ab bc and ac
Using the formula for distance
and i recently found out a^2+B^2=c^2 is the therom
But i dont understand what they want here for the conclusion
serene cradle
and i recently found out a^2+B^2=c^2 is the therom
So for this theorem, c is the hypotenuse. You're essentially just substituting the letters (a, b, and c) with the corresponding edges from the triangle in the graph
serene cradle
Your value for AC seems wrong
serene cradle
I plug them in
But also no, you don't have to plug them in just yet, you just have to find which distances are equal to a, b, and c in the formula
indigo plover
oh
serene cradle
And there's one main restriction that you have to respect: c must be the hypotenuse, which is defined as the longest edge in the triangle, or the side that is directly opposite the right angle
final saddleBOT
Available help channel!
tawny frigate
final saddleBOT
tawny frigate
How do I find the parametric equations?
final saddleBOT
@tawny frigate Has your question been resolved?
final saddleBOT
@tawny frigate Has your question been resolved?
final saddleBOT
@tawny frigate Has your question been resolved?
final saddleBOT
@tawny frigate Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
tepid forum
I dont need help with a problem per say, but in general I know if you have polynom you can turn x^4 and x^2 into t^2 and t.
final saddleBOT
I dont need help with a problem per say, but in general I know if you have polyn...
final saddleBOT
final saddleBOT
Available help channel!
glad mango
Hello! I have to show using the power method, which of these converge and their lambdas / eigenvalues throughout the iterations
final saddleBOT
Hello! I have to show using the power method, which of these converge and their ...
glad mango
For the top 1, I get this plot:
And for the bottom one:
My question is then: Using the power method, what determines whether they will converge or not? I have run the simulation with 10mil iterations with no apparent convergence.
So far, I've read that it depends on the start vector and the complexity of the eigenvalues, but I am not sure how any of those apply to my example. The second one has a pretty fractionized eigenvalue, but I need some clarity / help please
final saddleBOT
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glad mango
.close
dense garnet
Consider $F(x)=(x,\sqrt{1+x^2})$. What conditions on $x$ do I need to impose in order for $F$ to be Lipschitz continuous on some $A\subseteq\mathbb R$?
final saddleBOT
Consider $F(x)=(x,\sqrt{1+x^2})$. What conditions on $x$ do I need to impose in ...
soft zealotBOT
sunside
teal hamlet
dense garnet
.close
keen dragon
hellooo
final saddleBOT
@keen dragon Has your question been resolved?
final saddleBOT
@keen dragon Has your question been resolved?
keen dragon
.close
charred pebble
Hi
charred pebble
rancid idol
,calc 8 + 9 * 6
soft zealotBOT
Result:
62
youve swapped the positions of both numbers in both diagonals
thats not how the 2x2 inverse works
rancid idol
youve misremembered
charred pebble
Okay no so
Finding the inverse cant you just find matrix of cofactors
Then multiple by 1/det
rancid idol
uh maybe!? but i sure as hell wouldnt be doing that for a 2x2 matrix
charred pebble
Or that doesnt work for 2x2
rancid idol
ofc it would work
charred pebble
But the matrix of cofactors for this matrix is not that
rancid idol
in practice, most people do not use that method to compute determinants, i dont
maybe someone can help in #linear-algebra
i would personally row reduce, if anything
strange palm
in practice, most people do not use that method to compute determinants, i dont
sir can u help me
rancid idol
sir can u help me
not your channel.
strange palm
not your channel.
wdym
drowsy scroll
you only have to swap across one diagonal
rancid idol
i dont know this method, honestly
drowsy scroll
not the other one
drowsy scroll
the one with the negation doesn’t swap
charred pebble
Can some call?
worldly vale
one step in the cofactor method is you transpose the matrix
charred pebble
Okay the method I was taught
charred pebble
Is that the matrix of minor is all the entries that are not in the row and column of the entry your finding the minor for
Then the cofactor is just differing signs of the minor
charred pebble
You have to transpose to find inv?
Oh shit
Yeah thats what I forgot
But thay is the cofactor rightt
.close
near gull
robust mulch
What us the length of the big hypotenuse using pythagorean theorem?
robust mulch
big hyptenuse = 3 × small hypotenuse
tranquil pine
please send in png
plucky raptor
,rotate
soft zealotBOT
craggy orchid
anyone working on it ?
plucky raptor
what did you try?
craggy orchid
idk u can see my working out there i had no idea what i was doing
plucky raptor
you mean that work was just guessing ?
final saddleBOT
Available help channel!
plucky raptor
?
plucky raptor
idk why it closed
anyways
ok so he travels for some amount of hours, call it t, with an average of 90, then he travels for another hour, making the total driving hours t+1. and he traveled for 30 km. making the average 78
rancid idol
.
craggy orchid
ohhh
plucky raptor
if you want to write the formula of the average speed for his entire journey
craggy orchid
i kept writing 2t+1
plucky raptor
how would you do it?
craggy orchid
so speed is distance over time so therefore its 30km added on with the last distance
over t+1
but we dont know
the last distance
verbal pendant
Are you on the first or second part rn?
craggy orchid
first
verbal pendant
Ok gotchu
plucky raptor
the question said, he travel for t hours, with an average speed of 90
can you get the distance from this?
an expression that eqauls the distance
craggy orchid
90t
plucky raptor
there you go
craggy orchid
totoal distance is 90t +30
craggy orchid
90t+30 over
plucky raptor
for the average speed of the entire journey
craggy orchid
t+1
plucky raptor
which is equal to?
plucky raptor
look at the question again
craggy orchid
78
plucky raptor
yaeh
plucky raptor
why?
plucky raptor
now solve for t and continue
craggy orchid
can u help with 9 as well
verbal pendant
All good
verbal pendant
Can we make the two amounts equal in some way
verbal pendant
Well let’s try to find an equality here
Firstly, what’s the original cut per winner
verbal pendant
Let’s set x as the amount of winners
verbal pendant
Can you write an expression for the amount of money each winner gets
verbal pendant
Yep
And then if we want to set them equal what do we have to do
Each person gets 66 less when there are 3 more winners
craggy orchid
lol i dont understand
thats the part where i get confused
do u take away 66 lots of 3 or something ?
verbal pendant
So what we want to do is what our two expressions be equal to each other
verbal pendant
do u take away 66 lots of 3 or something ?
Close
Remember we are calculating per winner
So 1540/x = 1540/(x+3) + what
craggy orchid
x-(66x3) ?
verbal pendant
How did you get that number
verbal pendant
I gtg for a few minutes sorry
craggy orchid
its okay
verbal pendant
Think about the difference per person, if you get 66 less with three more people how do you incorporate that into what we had above
Ok I’m back
craggy orchid
right side
verbal pendant
Add or subtract
verbal pendant
You would subtract from the left
craggy orchid
why?
verbal pendant
Subtracting from the right would mean when you add three winners, you gain 66 each. We subtract to equalize the equation
verbal pendant
Kinda yeah
The left side, each person gets 66 more, so we would need to subtract 66, and vise versa on the right
craggy orchid
why does each person get 66 more on tje left
verbal pendant
It’s just how the problem was set up
1540/x - 66 = 1540/(x + 3)
This should give an answer
craggy orchid
i see okay thank you
viscid badger
Im not understanding this question. I have f(x)=cot(x)-1/x. Now for all x ∈ R with x ̸ = nπ, n ∈ Z. how do i find lim x->π- ?
How am i do to it if x /= π?
final saddleBOT
Im not understanding this question. I have f(x)=cot(x)-1/x. Now for all x ∈ R wi...
viscid badger
<@&286206848099549185>
worthy shale
$\lim_{x\to\pi^-}(cotx-\frac1x)$
soft zealotBOT
chlamydia
worthy shale
it may help to consider the two terms separately
$\lim_{x\to\pi^-}cotx-\lim_{x\to\pi^-}\frac1x$
soft zealotBOT
chlamydia
viscid badger
Well. I have calculated it and gotten it to -infinity. But what is confusing me is for all x ∈ R with x ̸ = nπ, n ∈ Z
How would i write this in texit.
worthy shale
$\forall x\in\mathbb{R}, x\neq n\pi, n\in\mathbb{Z}$
soft zealotBOT
chlamydia
viscid badger
Dosnt that mean anything?
worthy shale
the limit's -infinity
that there's an asymptote
like cotx has
are you concerned about limiting to x=pi when it says x/=pi?
viscid badger
So it doesnt change the fact that cot(pi) approaches 0 infinitively close, so -infinty?
idk honestly
worthy shale
cot(pi) goes to -infinity though?
viscid badger
wait are you asking me now?
worthy shale
cot(pi) approaches 0 infinitively close
what do you mean by this
viscid badger
Well limx→π- (cot(x))
worthy shale
is -infinity
viscid badger
how so
worthy shale
the limit approaches 0 from negative, so it'll be -infinity
tanx: limit x->pi- means you get 0-
which turns into -infinity on cotx
but x->pi+ is +infinity
worthy shale
typically assuming 0 is positive
but you can't be certain without knowing how it approaches limit
depending on the function
viscid badger
but wait
the 2nd picture you send makes sense, i can see it forever getting closer, but the first one goes thorugh it, does it not?
worthy shale
yeah, which becomes the asymptote
viscid badger
idk why im so confused
worthy shale
if a function f(x) goes through 0, 1/f(x) will have an asymptote at that same place
depending on whether f(x) reached 0 from positive side or negative side, 1/f(x) will shoot to +infinity or -infinity
for both sides
it's the difference between what happens when it approaches, and what's actually there
worthy shale
for cot?
viscid badger
yeah
worthy shale
cot(pi) doesn't approach 0
viscid badger
I think i need to do some heavy reading on this, for i can for the love of god not understand
worthy shale
it approches pi
can you try to explain this?
worthy shale
for$\lim_{x\to\pi-}cotx$
soft zealotBOT
chlamydia
