what do you think P, r, and t is for Account A
#help-10
azure anchor
fallen inlet
what do you think P, r, and t is for Account A
I’m not sure :(
azure anchor
what's the amount of money in Account A
fallen inlet
1000
fallen inlet
Ok
azure anchor
now what is the rate of interest?
fallen inlet
3%
azure anchor
very good. but you see that % symbol?
that means /100 in math terms
so its really 3/100 or 0.03
fallen inlet
3 years
azure anchor
good, so we will compound this amount 3 times.
so t = 3
we have all our values. now multiply P * r * t
fallen inlet
1000 x 0.03 x 3 ?
azure anchor
yes
azure anchor
mmmm im having doubts we are using the right formula, looking at your problem more.
fallen inlet
1000 x 0.03 x 3 ?
This isn’t right ?
azure anchor
right. i was thinking too simple
fallen inlet
Ok
azure anchor
we have to use a bigger formula
azure anchor
actually
we can use that simple formula but using the new value every time. you may not have been taught the bigger formula yet
so we compound it each year using simple interest
1000 x 0.03
,calc 1000*0.03
warm shaleBOT
Result:
30
so 1000 + 30 = year 1 balance
now for year two we have 1030 in the account
1030 * 0.03
azure anchor
so 1030 + 30.9 = year 2 balance
now we do it one final time for the third year's ending balance
fallen inlet
1,060.9 x 0.03
azure anchor
,calc 1060.9 * 0.03
warm shaleBOT
Result:
31.827
,calc 1060.9 + 31.827
warm shaleBOT
Result:
1092.727
you see how we got there?
fallen inlet
you see how we got there?
Yes!
obtuse pebbleBOT
@fallen inlet Has your question been resolved?
obtuse pebbleBOT
i forgot what should the last numbers be
tardy epoch
i forgot what should the last numbers be
Even numbers means divisible by 2
tame rivet
Even numbers means divisible by 2
so it is 256, 324, 1296, 5476, 373758?
tardy epoch
Take the square root of them and check
plush lava
hi how do i solve this
obtuse pebbleBOT
hi how do i solve this
plush lava
i think the textbook wants me to use this way
problem is the answer is 68 not 34
so idk what im going wrong
timid silo
ima solve it rq on my own way and see if it matches up
just gimme a quick second if you dont mind
plush lava
oki
timid silo
yeah im getting 68
plush lava
yeeaaa
timid silo
Ok so
Area of trapezoid is (b1+b2)/2 times change in x or you can call it height
Do you know what b1 and b2 and h are?
plush lava
oh
timid silo
yeah
plush lava
1?
timid silo
Those are ur 4 trapezoids
plush lava
yes
timid silo
They combined it all into one
timid silo
yw
plush lava
.close
dawn thunder
obtuse pebbleBOT
dawn thunder
for 25
I set r equal to each other to find alpha and beta to solve the area integral formula
but my bounds were pi/2 and -pi/2
but here
I don't know what they did here
obtuse pebbleBOT
@dawn thunder Has your question been resolved?
obtuse pebbleBOT
@dawn thunder Has your question been resolved?
hollow anvil
I tried to solve this with Integration by substitution, as I set "t = 1-x^2", but the answer does not match textbook answer and wolfram alpha
obtuse pebbleBOT
I tried to solve this with Integration by substitution, as I set "t = 1-x^2", bu...
hollow anvil
this is my answer↓
but wolfram and textbook answer says
How this can happen? and are there way to solve this problem through Integration by parts?
latent walrus
your answer is fine
polar fossil
i don't see the error but those aren't equal even by a constant
latent walrus
presumably factoring out $(1-x^2)^\frac{3}{2}$
$$(1-x^2)^\frac{3}{2}\left[-\frac{1}{3}+\frac{2}{5}(1-x^2)-\frac{1}{7} (1-x^2)^2\right]$$
$$(1-x^2)^{\frac{3}{2}}\left[-\frac{8}{105}-\frac{4}{35}x^2-\frac{1}{7}x^4\right]$$
warm shaleBOT
AℤØ
latent walrus
then factor back in
hollow anvil
Wooha thanks,that makes sense!
but can I lead to the 2nd answer directly through Integration by parts?
polar fossil
i think once you have $\int (1-t)^2 \sqrt t \dd{t}$ you could use IBP on that
warm shaleBOT
hayley
obtuse pebbleBOT
@hollow anvil Has your question been resolved?
hollow anvil
Without substitution, I can't solve with IBP?
hollow anvil
I see, I just wonder why the author put this problem in "Integration by parts" section
hollow anvil
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
ocean snow
obtuse pebbleBOT
ocean snow
I have to find the area under the curve
I am having trouble finding the bottom left area since it requires the inctercepts of all 3 equations
im unsure if I did step 1 correctly
stone spoke
the screenshot is really low resolution for me
ocean snow
just kidding this is wrong
so integral below the green and above the red
.close
austere dragon
Can i use the sandwich theorem or i should use the L`Hopitals Rule
obtuse pebbleBOT
Can i use the sandwich theorem or i should use the L`Hopitals Rule
worn yoke
you could, in principle, use both, although it may be tricky to come up with functions to compare to for the sandwich theorem, so L'Hopital's is probably easier
austere dragon
you could, in principle, use both, although it may be tricky to come up with fun...
yh true
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
ember frost
Given 2 squares both have a side of 5cm, overlaid on each other such that the vertex X of one square is the center of the other (illustration below). Find the volume of the shape created by rotating the figure around XY.
obtuse pebbleBOT
Given 2 squares both have a side of 5cm, overlaid on each other such that the ve...
ember frost
my approach is to divide the 3d shape into 3 parts consisting of a cylinder, a truncated cone and a cone, find the volume of each part and sum
i would like to get my calculations checked because the solution i got isnt any of the listed 4 options
(i chose A because its the closest to the sum i got)
warm linden
obtuse pebbleBOT
@ember frost Has your question been resolved?
polar fossil
at a guess you confused radius and diameter
or incorrectly calculated the height of something
nice drawing though, looks good
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
sand cipher
hello,
i have the function f(n) = [f(n-1)*(n-1+r)]/n, where f(1)=a
how can i solve this? does it converge or diverge? im not quite sure how i can go abou this. The answer on wolfram alpha seems too complicated
obtuse pebbleBOT
hello,
i have the function `f(n) = [f(n-1)*(n-1+r)]/n`, where `f(1)=a`
how can ...
sand cipher
please @ me ^^
obtuse pebbleBOT
@sand cipher Has your question been resolved?
sand cipher
.close
timid silo
obtuse pebbleBOT
final thunder
which one?
timid silo
a b and c if u can please
fierce vale
how would u explain that though :p
timid silo
no i have no idea
native inlet
f(a) is the output if we put in x=a
native inlet
final plaza
lmao
timid silo
c will be 6/5 supposedly
obtuse pebbleBOT
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
timid silo
nice one line4ar but
Shush pure!
timid silo
https://tenor.com/view/doobadoo-akechi-gif-2793590102668434387
Eagle eye!
I wonder why ain't this channel closed yet?
obtuse pebbleBOT
@kindred forge Has your question been resolved?
smoky vigil
what is the question being asked? is it if this expression is just simplifiable?
obtuse pebbleBOT
@fading zodiac Has your question been resolved?
stone prism
tan theta = -1
how to find theta
obtuse pebbleBOT
tan theta = -1
how to find theta
winter surge
$\arctan-1$ also known as $\tan^{-1}-1$
royal basin
$\arctan-1$ also known as $\tan^{-1}-1$
formally correct but please don't call the input of arctan by the letter theta
makes you think it's an angle when it isn't
warm shaleBOT
Xerunox
winter surge
ah
final thunder
$\arctan(x)$ also known as $\tan^{-1}(x)$
warm shaleBOT
Pure
final thunder
drifting roost
winter surge
**Xerunox**
note tan repeats every $180^{\circ}$ or $\pi$ depending on your choose of angle representation
warm shaleBOT
Xerunox
stone prism
what's arctan 💀
final thunder
Also note that tan being equal to 1 is one of the standard trig values
drifting roost
arctan has range of (-pi/2, pi/2]
winter surge
what's arctan 💀
same thing as $\tan^{-1}$, just a more preferred representation for a lot of people
drifting roost
so arctan(-1) = -pi/4 and the periodicity doesn't matter i guess
warm shaleBOT
Xerunox
winter surge
also known as "inverse tan"
winter surge
what aren't you getting specifically
winter surge
if $\tan(\theta) = -1$ then $\arctan(-1) = \theta$
warm shaleBOT
Xerunox
drifting roost
tan(theta) could be the slope, but why is that relevant here?
final thunder
!xy
obtuse pebbleBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
winter surge
**Xerunox**
you can just plug $\arctan(-1)$ into your calculator, it might be written as $\tan^{-1}$ instead of $\arctan$ on it
warm shaleBOT
Xerunox
winter surge
tan theta = m = -1
sounds like a trick question, it gives you the answer
stone prism
sounds like a trick question, it gives you the answer
answer is 135, and sir, it's not a trick question thank you
winter surge
if you can call it please don't call me sir, and i now know its not a trick question but i would've known that if i had the full question
gradient = $\frac{y_2 - y_1}{x_2-x_1}$
warm shaleBOT
Xerunox
winter surge
$\frac{(-2) - (-1)}{4 - 3}$
stone prism
okay, ma'am perhaps ?
warm shaleBOT
Xerunox
winter surge
okay, ma'am perhaps ?
would much prefer thanks
winter surge
allow me to restate
stone prism
okay
winter surge
$\tan(\theta) = -1 \therefore \arctan(-1) = \theta$
warm shaleBOT
Xerunox
winter surge
are you allowed to use your calculator?
for this question?
if so you have the answer already
stone prism
are you allowed to use your calculator?
no ?
warm shaleBOT
Xerunox
stone prism
**Xerunox**
yes ? 1 ?
winter surge
correct
and, for $0^{\circ} \le \theta < 360^{\circ}$, $-\theta = 180 - \theta$ in $\tan(x)$?
warm shaleBOT
Xerunox
stone prism
how does -theta = 180- theta work ?
winter surge
how does -theta = 180- theta work ?
tan is symmetric from the x-axis, but also an odd function
which means $\tan(x) = -\tan(-x)$
warm shaleBOT
Xerunox
winter surge
actually i dont know if thats related
i don't know how to exactly prove it but tan just works like that
similar with sin, actually
stone prism
actually i dont know if thats related
that's exactly what i was thinking
winter surge
that's exactly what i was thinking <:sadcat:547124024585486359>
my bad brother
stone prism
my bad brother
it's fine, dw dw
winter surge
but yeah for tan just remember that $\tan(-\theta) = \tan(180 - \theta)$
warm shaleBOT
Xerunox
winter surge
or in radians, $-\theta = \pi - \theta$
warm shaleBOT
Xerunox
winter surge
brb
stone prism
but yeah for tan just remember that $\tan(-\theta) = \tan(180 - \theta)$
yes, I know that haha
dreamy veldt
Can someone please help with this question. Particularly part B.
winter surge
Can someone please help with this question. Particularly part B.
not how this works
dreamy veldt
Sorry. How does it work I’m new here
winter surge
read #❓how-to-get-help
dreamy veldt
Thanks.
obtuse pebbleBOT
@stone prism Has your question been resolved?
obtuse pebbleBOT
@stone prism Has your question been resolved?
obtuse pebbleBOT
@stone prism Has your question been resolved?
obtuse pebbleBOT
@stone prism Has your question been resolved?
knotty temple
help
dark stirrup
what do i do to get angle A
the two triangles are congruent
dark stirrup
do you know what it means for two triangles to be congruent?
knotty temple
yea i do
dark stirrup
So if triangles ABC and DEF are congruent, what can you say about angle A?
knotty temple
its congruent to D
knotty temple
(12y +3)
obtuse pebbleBOT
@knotty temple Has your question been resolved?
stiff knoll
How exactly do i do this question? can i get the steps listed out in a clear way?
obtuse pebbleBOT
How exactly do i do this question? can i get the steps listed out in a clear way...
daring sorrel
How exactly do i do this question? can i get the steps listed out in a clear way...
Do you know what the power rule is
elder nebula
A) is the first derivative and b) is the second derivative, aka taking the derivative of the first derivative, apply power rule once for a and again for b
stiff knoll
Do you know what the power rule is
Not by that name but perhaps i've learned it, still, explaining it would be great
daring sorrel
$\frac{d}{dx}x^n=nx^{n-1}$
elder nebula
It's essentially just the slope of the function
elder nebula
Just apply it again
daring sorrel
True
warm shaleBOT
Anton Yakunin.
stiff knoll
Just apply it again
sorry for my silliness, but, how do you mean apply? i'm a little tired today, my sincerest apologies
elder nebula
Okay so do the power rule to find the first derivative
stiff knoll
yes, understood
elder nebula
And then do the power rule on the first derivative to find the second
stiff knoll
oh, so hold on, ill work out the first one rq, then i just, do the power rule to that answer?
elder nebula
Yes
stiff knoll
ok, let me try that rq,
apologies for my english, it's not my first language
thanks, that works
.close
autumn otter
obtuse pebbleBOT
cobalt shuttle
it might help if you write down what each of those things means first because as such that f' and f" you've drawn aren't compatible
so the first sentence says f is increasing if x < 0 and f is decreasing if x > 0
and the second item says f is concave up if x < 0 and f is concave down if x is > 0
that should hellp!
obtuse pebbleBOT
@autumn otter Has your question been resolved?
autumn otter
and the second item says f is concave up if x < 0 and f is concave down if x is ...
Ahhh tysm
gritty swallow
hello I have a question about surface integrals, how come in this problem https://tutorial.math.lamar.edu/Solutions/CalcIII/SurfaceIntegrals/Prob2.aspx we integrate using ds, but in this problem https://tutorial.math.lamar.edu/Solutions/CalcIII/SurfaceIntegrals/Prob3.aspx we parametrize the surface and integrate using the normal vector?
obtuse pebbleBOT
hello I have a question about surface integrals, how come in this problem https:...
gritty swallow
how do you know when to use which method
cobalt shuttle
It depends on how you're presented the surface!
Typically there's 3 different ways you might see it
- Explicit in xyz which is what's happening in the dS case
- Parametrized, then you'd use normals
there's a third way Implicit but typically you'd kind of end up doing some sort of parametrization anyway
gritty swallow
so for this problem it seems to give the surface in terms of xyz, but the key uses normals
i guess its just because its a cylinder so its easy to parametrize?
gritty swallow
yes, to make the double integral more simple
cobalt shuttle
thats nothing but a parametrization in disguise
Try it if you want! Try doing the first one using normals
you'll get the same answer
but typically sometimes you'll write it in an explicit way and it will be messy
and it turns out using differentc oordinates or parametrizing might make it cleaner
gritty swallow
so i actually did but managed to get an incorrect answer (and crossed it out sorry lol)
wait a minute i think i see a mistake right off the bat, y should be r squared
cobalt shuttle
I can't super read it but you can try parametrizing using polar coordinates by saying
x = r cos theta
z = r sin theta
then y = 3r^2
And this is parametrized by y = 3r^2, 0 ≤ r ≤ √2 (why?) and 0 ≤ theta ≤ 2π
and then you can try integrating ∫∫3r^2 |r_r x r_theta| dr dtheta
and you'll find that that cross product norm comes to r
gritty swallow
okay this is a lot more clear now, thank you 👍
cobalt shuttle
I think I messed something up or ovesimplified but that's the gist
obtuse pebbleBOT
@gritty swallow Has your question been resolved?
left kettle
Question 21
I’m so lost
obtuse pebbleBOT
Question 21
I’m so lost
left kettle
<@&286206848099549185>
left kettle
Oh! Ok thank you I wasn’t sure if anybody had seen it yet
left kettle
It’s less a solution based problem and more just proving it if that helps? My answer booklet is only answers so it says nothing for this question
tall wind
okay, so basically you want to represent the time for light to travel from P1 to P2
there's two lengths for this light to travel
from P1 to the water surface, and from the water surface to P2
you can easily find the lengths of these distances
because you have the measurements given
next, you have time = distance / speed
you are given the speeds in both mediums
left kettle
We don’t have any measurements though, it’s just variables? Do you mean in terms of the other variables or?
left kettle
Ok so yea in terms of other things not actual numbers
So distance from P1 to the water surface is root(a^2 + x^2) and water surface to P2 is root(bw^2 + (c-x)^2)
tall wind
what is w?
left kettle
a mistype ignore it
Or if you wanna use trig stuff it’s like P1 to water is x/sin(theta1) and water to P2 is (c-x)/sin(theta2)
The speed would be the velocities right?
So time would be P1 to water divided by v1 plus water to P2 divided by v2 ?
tall wind
yep that's good
However
theta1 and theta2 are both dependent on x
that means when you differentiate this function
you will have to apply the chain rule to theta too
which I don't recommend
the alternative is to just represent sin(theta1) in terms of x
and sin(theta2) in terms of x as well
left kettle
Sin(theta1) = x/root(a^2+x^2) ?
Sin(theta2) = (c-x)/root(b^2 + (c-w)^2)
Time = root(a^2 + x^2)/v1 + root(b^2 + (c-x)^2)/v2
Where would I go from here?
tall wind
now you can differentiate by x
left kettle
Would I treat a, b, c, v1 and v2 as all constants?
tall wind
the reason being that we want to choose x that minimises the amount of time taken for the light to travel between P1 and P2
treat everything else as constants
left kettle
I think I did it right but I just wanna check rq- I still need to simplify and what not though
Ignore the a=3 and b=4 parts that’s from a different questions
The bell just went for me to go home so I might take a bit to continue sorry
tall wind
you're nearly done
just simplify it as much as you can
and then you should see some very familiar looking fractions
wink wink
obtuse pebbleBOT
@left kettle Has your question been resolved?
left kettle
Alright! So I’ve simplified it down to T’ = Sin(theta1)/v1 + sin(theta2)/v2
So then the shortest time thing would be the minimum so a stationary point so when T’ = 0 ?
But where from there? I could put the sin(theta2)/v2 on the other side but then it would be negative
Do I need to go to the second derivative?
tall wind
Alright! So I’ve simplified it down to T’ = Sin(theta1)/v1 + sin(theta2)/v2
So t...
you're really close
You're missing a minus sign T’ = Sin(theta1)/v1 - sin(theta2)/v2
check your work
you can just set T' = 0
and you will be done in no time
if you want to verify that the only choice of x is a minimum, then you can go ahead and compute the second derivative
left kettle
Oh! I forgot to do the chain rule a second time with the (c-x)^2 since it would be 2(c-x) * -1
That’s where I went wrong
tall wind
although, theoretically, choosing x such that T'=0 must be a minimum point. Try moving the pivot point around (varying the length x) to maximise the time for the light to travel
you'll find that you can't choose a x such that the time travelled by the light is ever maximal
left kettle
Oh! So like as x approaches infinity so does the time so there is never a max it can just keep going
Thank you so much-
tall wind
It's not an X to infinity thing
It's more like a "I can choose a specific X and claim it maximises the time"
"unfortunately there is this other X that cause the time for the light to travel to be even bigger"
Does that make sense?
left kettle
Ah! Yea it does!
obtuse pebbleBOT
tall wind
👍
obtuse pebbleBOT
Available help channel!
honest flicker
obtuse pebbleBOT
honest flicker
Uhhh
The midline is like
10.5
Right
Amplitude is 7.5
Uhhh
That one sentence says it's cosine right
Or no
Sine
Cuz like it's halfway
Maybe
Idk
Idk which one to use
Or how to get the period
Idk what define the function using radians means isnt it always defined by radians in the period part
obtuse pebbleBOT
@honest flicker Has your question been resolved?
honest flicker
I have
An idea
the 10 am and 10 pm both bring points at the midlinr
that's luke
Like
A 12 hour
Period
so π/6
Not sure which function to use
<@&286206848099549185>
7.5(idk trig function)(π/6(x))+10.5
Something like that
I think
I'm not completely sure
obtuse pebbleBOT
@honest flicker Has your question been resolved?
bold bane
Not sure which function to use
You can use either sine or cosine, the only difference is that there is a phase shift of pi/2 for cosine. The only real preference for one over the other is that the sine function starts at 0 when x = 0.
bold bane
Just use the sine function to keep things simple.
It's what you are most familiar with.
bold bane
Think about what the periodicity is.
honest flicker
uhh
honest flicker
Think about what the periodicity is.
12
honest flicker
How many hours in a day?
24
bold bane
Ok, let's actually start with the most basic information first. You know the amplitude and the center line. Make an initial equation using those two things that you know.
And just use sin(t) for the trig function.
honest flicker
Ok, let's actually start with the most basic information first. You know the am...
7.5sin(2π/P(t))+10.5
bold bane
That's a good start. You know what P is so substitute that value in.
honest flicker
7.5sin(π/12(x))+10.5
bold bane
Good. Now you just need to calculate the horizontal shift.
If you graph the function as is, this is what you get
Notice where the maximum value currently is.
You need to move that so that it occurs at x=10 so you need to change H which represents the horizontal shift.
honest flicker
7.5sin(π/12(t)-5π/6)+10.5
bold bane
Not quite. You don't need to guess here. You can solve this using math.
bold bane
At what time does the maximum temperature occur?
honest flicker
Idk
bold bane
You are given that information in the problem.
bold bane
One moment, I was reading the question wrong.
Ok, the problem states that the temperature is typically halfway between the daily high and the daily low at both 10am and 10pm. That means the center line of the wave occurs at those times.
bold bane
Doh, you were correct with the equation you came up with.
honest flicker
bold bane
Had a brain fart.
honest flicker
.close
balmy sand
obtuse pebbleBOT
balmy sand
does this work
obtuse pebbleBOT
@balmy sand Has your question been resolved?
balmy sand
balmy sand
what about this one @dark stirrup
dark stirrup
Looks good, but explicitly state the number of elements
balmy sand
ok
dark stirrup
3 is kind of trivial. It's a subset of N³, which is countable
balmy sand
like N x N x N
balmy sand
3 is kind of trivial. It's a subset of N³, which is countable
whats an example thats like non trivial
idk why my teacher makes us do all of this then
dark stirrup
proving rationals or N² is countable
proving that the set of all finite subsets of N is countable
balmy sand
proving rationals or N² is countable
wait so is this like non trivial
so i cant say this is a subset of N^2
dark stirrup
where is x?
balmy sand
idk ny teacher writes it like that
dark stirrup
so i cant say this is a subset of N^2
what is? the image of f?
balmy sand
where is x?
ah ok i think it should be 2^x here then
dark stirrup
or f(k) even better
balmy sand
right
dark stirrup
proof looks good
balmy sand
i just have one last question, thank you for the help so far
does this work
fta = fundamental thrm arithemtic
dark stirrup
so many words
balmy sand
ok
dark stirrup
if $21x^6=n^2$, then $3$ divides $n^2$ as it divides $21x^6$, but that means 3 divides $n$, which means $9$ divides $n^2$, which means $9$ divides $21x^6$, which means $3$ divides $7x^6$. But $3$ does not divide $7$, so $3$ divides $x^6$, which means $3$ divides $x$.
warm shaleBOT
SWR
dark stirrup
I'll let you consider the rest
regal sequoia
help
regal sequoia
polar fossil
they are if one is the center
polar fossil
extends from... to
empty cypress
in fact its actually actively not how i read that
but yeah anyways just write the formula for the circle with the right center, then use the other pt to solve for the constants
polar fossil
oh nvm ok this question is terrible
regal sequoia
x+3 y-13
regal sequoia
or his rending of it
not my writing
polar fossil
it's assuming the two points are two ends of a diameter
empty cypress
find the midpoint of the vector that goes between them, then use that as the center
then distance formula for radius
regal sequoia
find the midpoint of the vector that goes between them, then use that as the cen...
is that just midpoint formula
empty cypress
probably? havent heard it called that
empty cypress
ya
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
obtuse pebbleBOT
timid silo
This is a function of four variables that I've modeled. What's a good way to find a rough estimate of the equation?
obtuse pebbleBOT
@timid silo Has your question been resolved?
novel siren
what do I do for this? find derivative?
obtuse pebbleBOT
what do I do for this? find derivative?
high lily
yes
robust raven
what do I do for this? find derivative?
you have find the minimum of the derivative, which is a trinomial
novel siren
you have find the minimum of the derivative, which is a trinomial
how can I find the minimum of the derivative?
high lily
what's your derivative
novel siren
if I solve dy/dx =0 that'll only give the minimum value of y right
high lily
no
high lily
and to find the min of that, consider vertex of quadratics/parabola
or more differentiation
novel siren
can you pls elaborate?
high lily
do you know how to find local extrema of quadratic functions / parabolas
novel siren
do you know how to find local extrema of quadratic functions / parabolas
no honestly never heard of that
high lily
apply that here
novel siren
but not local extrema
high lily
local extrema refers to local min/max
novel siren
by finding second derivative?
high lily
i gave you two routes
since you have a quadratic function, you could apply your knowledge about the vertex
alternatively yes, you could differentiate again to find the local min of that here
novel siren
oh right
the minimum point of that quadratic is the same as minimum gradient of y
got it thanks
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
summer pond
Hello!
summer pond
homework I got wrong this week
Anyone know why I got all of them wrong?
the question is
chilly scroll
They all look right to me
outer moat
What you did is correct
summer pond
wait- I really don’t know
wary bobcat
did they want you to do something more with the final result that you forgot to do?
summer pond
Let me send a photo
outer moat
Maybe they wanted you to write (x-4)^2 instead of x^2-8x+16?
wary bobcat
Maybe they wanted you to write (x-4)^2 instead of x^2-8x+16?
they did write that
summer pond
outer moat
they did write that
Oh my bad, there is an empty line I thought its a new exercise
summer pond
wait do I contact teacher?
to ask about it?
because I really don’t know why I got 0/3 🥲
wary bobcat
oh i reckon they want you to factorise the completed square form using difference of 2 squares
so your end result should look like a(x-b)(x-c)
wary bobcat
eg, ||5((x-2)^2-5) = 5(x-2+sqrt(5))(x-2-sqrt(5))||
wary bobcat
So question 2 should be 5(x+2-5)(x+2+5)
might want to double check the numbers but thats the idea!
wary bobcat
youre welcome :)
dense geyser
Aw im late
summer pond
???
dense geyser
I wanted to help you
summer pond
Hello!
summer pond
Sorry, if you guys don’t mind me asking again 😭
How would I be able to put a into (x-b)(x-c) form?
Question A
Would it be + and - root 190
gritty iris
Lets say I have a bijection from A to C and B to D. Can I show that there must be a bijection from A x B to C x D (where x is the cartesian product)?
The approaches I have right now will be to define it element wise, although I'm not sure how that could go for uncountably infinite sets A B C and D
obtuse pebbleBOT
Lets say I have a bijection from A to C and B to D. Can I show that there must b...
eternal thistle
Lets say I have a bijection from A to C and B to D. Can I show that there must b...
Yes you can
gritty iris
I can do this with uncountable sets?
eternal thistle
Yes
gritty iris
for countable sets i can do something like map a1 b1 to c1 d1 etc
but for uncountable sets i can't do such a thing right
dark stirrup
for countable sets i can do something like map a1 b1 to c1 d1 etc
don't need that
no need to do different cases
Just use definitions of bijections
eternal thistle
f: A -> C, g: B -> D
h: A X B -> C X D
h(a,b) = (f(a), g(b))
gritty iris
bijective if surjective and injective
surjective because A x B can be mapped to C x D
injective because i don't have repeated images for different elements
ok now i just need to write this properly
dark stirrup
Assume h(a, b)=h(a', b). Prove (a, b)=(a', b')
gritty iris
then that is a proof of uniqueness
dark stirrup
Likewise, for any (c, d) in C X D, show there is an (a, b) in A X B such that h(a, b)=(c, d)
gritty iris
thanks i get it now. ill try and update you guys on the formalised proof. i don't know why i took this course, i'm not even a physics or math major
dark stirrup
way late for me, so gtg
gritty iris
way late for me, so gtg
take care. thank you
dark stirrup
but it looks like you understand the problem, so best of luck to you
midnight narwhal
obtuse pebbleBOT
midnight narwhal
my exam
in few hours
i need sleep
its 4am
Im begging any1 here can help
how do they get that matrix below
if any1 answers plz i will do anything
polar fossil
the one up top? that's A transpose times A
final thunder
I think you should sleep 
midnight narwhal
I think you should sleep <a:joyspin:690630295548067981>
I did that last night
for my data struct and algo class
and i had a 100 Mc exam
on data struct
😭
final thunder
Singular value decomposition
polar fossil
looks like it's just the eigenvalues on the main diagonal
midnight narwhal
what
how did they construct it
is what im confused about
like how do they know where 4 or root 6 goes
how how big the matrix is
final thunder
SVD is a diagonal matrix that contains all the singular values or the original matrix A.
same size as A.
midnight narwhal
SVD is a diagonal matrix that contains all the singular values or the original m...
ooh
ok
ty guys
loud harbor
Can something be a critical point if it doesn't lie on the curve?
obtuse pebbleBOT
Can something be a critical point if it doesn't lie on the curve?
loud harbor
For instance x^3+y^2+xy+y=0 has a critical points when f'(x)=0
I find them to be (1/2,-3/4) and (-1/3,-1/3) but they don't even lie on the the original curve did I make a mistake?
0,0 is also one but that's the only one that lies on the curve
inland matrix
$3x^2 + 2yy' + xy' + y + y'=0$
warm shaleBOT
Lorentz
loud harbor
Yeah
inland matrix
$3x^2 + y =0$
warm shaleBOT
Lorentz
loud harbor
inland matrix
$x^3 + 9x^4 +x(-3x^2) -3x^2=0$
warm shaleBOT
Lorentz
loud harbor
Oj so you subbed y back into the original equation
inland matrix
Ye
loud harbor
And that finds the critical points for x?
inland matrix
I don't have a book atm so I was just typin it out
loud harbor
Damn thank you so much
inland matrix
**Lorentz**
This? Yeah
inland matrix
Ye and now put dy/dx = 0
loud harbor
Yeah
I was just trying to figure out what to do since there are two unknown variables
inland matrix
**Lorentz**
You get the same thing
loud harbor
Got it thanks Lorentz
inland matrix
Np
loud harbor
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
What is sin(infinity) considered?
Working on improper integrals rn and if they converge or diverge, and I don't know if putting infinity into trig functions is even possible let alone quantifiable
obtuse pebbleBOT
What is sin(infinity) considered?
Working on improper integrals rn and if they ...
robust raven
It cannot be explained this way. Better show an example, then we can dispel doubts.
timid silo
Pmuch gotta find out if this function converges or diverges
Which I simplified using u substitution and such- got -u cos(u) + sin(u)
Putting u cause i can't type out all this on mobile lol
timid silo
Which I simplified using u substitution and such- got -u cos(u) + sin(u)
So how do I plug infinity into this so I can subtract 2 and see if it converges or diverges?
robust raven
in this case, right, you may use untegration by parts, after substituion, and first one is divergent because:
$\lim_{t \to \infty } tsint\text{ }\text{ does not exist}$
warm shaleBOT
Joanna Angel
robust raven
but
such an integral
$\int_{0}^{\infty }\sin\left( x^{2} \right)dx=\frac{\sqrt{\pi}}{2\sqrt{2}}$
warm shaleBOT
Joanna Angel
robust raven
is convrgent
it is famous Fresnel's integral
adn admit
that is ivery similar to yorus
so we cant base some general opinions
on one such integral
the other example:
$\int_{0}^{1}\frac{sinxdx}{\sqrt{x}}$
warm shaleBOT
Joanna Angel
warm shaleBOT
Joanna Angel
obtuse pebbleBOT
@timid silo Has your question been resolved?
north mountain
anyone can prove this
obtuse pebbleBOT
anyone can prove this
spice citrus
what's the full question
north mountain
it says x,y,z is all positive and xyz=1
spice citrus
so, x^4 + y^4 + z^4 >= x^2y^2 + y^2z^2 + z^2x^2, right?
north mountain
how did you get that
spice citrus
from this identity: $$a^2 + b^2 + c^2 = \frac12 (a^2 + b^2) + \frac12 (b^2 + c^2) + \frac12 (a^2 + c^2) \geq ab + bc + ac$$ and then subbing $a = x^2, b = y^2, c = z^2$
warm shaleBOT
Jelle
north mountain
so, x^4 + y^4 + z^4 >= x^2y^2 + y^2z^2 + z^2x^2, right?
pls go on
north mountain
ok so a^2 + b^2 + c^2 >= ab+bc+ac= x^2yz+xy^2z+xyz^2= xyz(x+y+z)= x+y+z
is it correct
ok thanks for your help!!!
.close
torn ocean
obtuse pebbleBOT
inland matrix
!status
obtuse pebbleBOT
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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
@torn ocean Has your question been resolved?
torn ocean
obtuse pebbleBOT
@torn ocean Has your question been resolved?
naive wasp
can someone help me understand how a, c, and e is true? The only techniques I know for solving differential equations is integrating factor or if it is seperable, which the provided equation is neither. How does the fact that f(0)=0 help us solve this equation for a? just a direction or a hint would be really helpful
obtuse pebbleBOT
can someone help me understand how a, c, and e is true? The only techniques I kn...
@naive wasp Has your question been resolved?
naive wasp
<@&286206848099549185>
obtuse pebbleBOT
@naive wasp Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
spiral sleet
Hi I have to rate whether the proof is well written or not.
To prove (with contrapositive):
∀(a1, a2 ∈ A|(a1, a2) ∈ R → (a2, a1) ∉ R) ⇒ ∀(a3 ∈ A|(a3, a3) ∉ R)
- This is achieved by transforming the implication ((a ⇒ b) ⇔ (¬b ⇒ ¬a)) equivalent to:
∃(a3 ∈ A|(a3, a3) ∈ R) ⇒ ∃(a1, a2 ∈ A|¬((a1, a2) ∈ R → (a2, a1) ∉ R)) - This is achieved by the dissolution of the negation (¬(a → b) ⇔ (a ∧ ¬b)) is equivalent to:
∃(a3 ∈ A|(a3, a3) ∈ R) ⇒ ∃(a1, a2 ∈ A|(a1, a2) ∈ R ∧ (a2, a1) ∈ R) - You can choose a1 := a3 and a2 := a3. So if the left side is true, so is the right side is true.
Example: for R = {(1,2),(2,3),(4,5)}, A = {1,2,3,4,5} and a1,a2,a3 = 2
∃((a3, a3) ∈ R) ⇒ ∃((a1, a2) ∈ R ∧ (a2, a1) ∈ R)
∃((2, 2) ∈ R) ⇒ ∃((2, 2) ∈ R ∧ (2, 2) ∈ R)
Therefore, the subjunction as a whole is always true. The statement is thus proven.
My rating to it, is it good or not, what would you write?:
Overall, this submission is good because the proof type is correct, the proof was done correctly, and the Python code is correct. For example, he performed the method, proof of contrapositive correctly, since (A ⇒ B) ⇔ (¬B ⇒ ¬A) and for implications of form A ⇒ B are used. Thus, it has been shown that if (¬B ⇒ ¬A) is true, then the original statement is also true.
obtuse pebbleBOT
Hi I have to rate whether the proof is well written or not.
To prove (with cont...
spiral sleet
I also wrote, but it´s unneccessary for the proof method, so you can kinda can ignore that:
Also, the source of evidence is trustworthy, because it comes from a well-known university. In addition to the Python code, one could have added the definition of irreflexive and asymmetric from the textbook for a direct comparison to the code, e.g.: "A relation R on A is called irreflexive if for all a ∈ A holds: [a, a] ∉ R". In the case of the "1.3 Explanations" section, the comment was presumably cut out in the code when exported, which is not a big deal for understanding the proof.
obtuse pebbleBOT
@spiral sleet Has your question been resolved?
obtuse pebbleBOT
@spiral sleet Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
sand plover
obtuse pebbleBOT
obtuse pebbleBOT
Helpers are just people volunteering their time to help you. Be polite and patient.
obtuse pebbleBOT
Helpers are just people volunteering their time to help you. Be polite and patient.
sand plover
oh
polar fossil
your other equation will come from the amount of money received
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
Is anyone here familiar with StatCrunch? I have to use it for my statistics class and when I try to get summary stats for certain columns, it gets everything right but the variance which is a ridiclously huge number
obtuse pebbleBOT
Is anyone here familiar with StatCrunch? I have to use it for my statistics clas...
timid silo
https://www.statcrunch.com/app/index.html?dataid=4509444# i'm trying to calculate for the thousands column
tame narwhal
maybe ask in #probability-statistics or #computing-software
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
balmy sand
obtuse pebbleBOT
balmy sand
i feel like this is wrong because it says (power set) in the question right
so like the power set of this thing would be quite a few terms
idk
<@&286206848099549185>
obtuse pebbleBOT
Show your work, and if possible, explain where you are stuck.
brave bramble
Strange it says (power set) for basically no reason
Especially since it goes on to say this is a relation over X, not P(X)
balmy sand
i dont get it
brave bramble
Indeed I think that's a typo
balmy sand
alright ty then
golden sand
confirm with teach
balmy sand
i cant lol
balmy sand
its fine
brave bramble
It's a typo
balmy sand
.close
ebon dagger
The answer is D, but why is it that sometimes the geometric series converges when the r equals 1 and sometimes it diverges when it equals 1
obtuse pebbleBOT
The answer is D, but why is it that sometimes the geometric series converges whe...
tame acorn
What type of series is this
ebon dagger
I thought it had to be |r| < 1
tame acorn
For what type of series is that true
ebon dagger
Geometric
tame acorn
Is this geometric?
ebon dagger
If you remove put the 1/n^5 to the left and everything else u leave it as (r)^n yeah
How should I approach it then?
As a geometric or a combination or something else
tame acorn
I don't think these is a straight forward way rather than testing each (a), (b), (c) etc
ebon dagger
.close
obtuse pebbleBOT
worn yoke
ratio test to find the interval then test the endpoints
obtuse pebbleBOT
Available help channel!
royal walrus
can I get help solving out A, I understand I have to use the ratio test, but I dont know where to start
