if ur not allowed to use a graphing calculator u can always plug in ur x values
#help-36
glacial rock
wait does it want u to graph the inverse or the regular function
heres the full question
yk if the sketching is 1 mark
i might just ditch it
LOL
cuz i aint going through all that to just get 1 mark
pliant shore
i might just ditch it
it's much easier to find the domain and range after you sketch though
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glacial rock
.reopen
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glacial rock
i thought the Piecewise Function was matrices
pliant shore
i thought the Piecewise Function was matrices
lmao.....
glacial rock
ok let me just do my long division in peace and come back to this topic 💀
it was a long wait till i realized i was responded to for my long divison now that u guys are here
long division looks so much easier and nicer now that i've seen a matrices cut in half
it's like seeing a person sliced in half
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@glacial rock Has your question been resolved?
glacial rock
redid my long division in a better way
ok wheres the cut in half matrices 
wait imma do ii)
glacial rock
wait imma do ii)
not yet still in polynomials
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severe canyon
You just need to use the remainder theorem
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lunar grove
how do i solve for (b)
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how do i solve for (b)
lunar grove
answer for (a) is 5
wary copper
how do i solve for (b)
what do you know about parallel vectors
wary copper
ok well like
im not asking for you to just reguritate the fact they are parallel
what can u say algebraically for parallel vectors
lunar grove
o
wary copper
does the concept of them being scalar multiples to each other make sense?
wary copper
ok
so lets apply that concept here
for p+q to be parallel to the x-axis, it must be a scalar multiple of a vector that is on the x-axis
there are infinite numbers of vectors on the x-axis
so it doesn't really matter even what vector on x-axis u pick
u just need to realise what makes a vector lie on the x-axis
hint: ||any vector, lets say (x,y,) will be on x-axis if its of the form (x,0)||
lunar grove
hint: ||any vector, lets say (x,y,) will be on x-axis if its of the form (x,0)||
so we can say its x intercept i believe?
wary copper
so we can say its x intercept i believe?
i mean it doesn't relaly make sense in this context but if it helps u understand it, sure
really, any vector with a non-zero horizontal component and a 0 vertical component will be parallel to x-axis
so u just have to find a vector q, such that p + q = (x,0)
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modest bobcat
"True or False: If null(A - λI) = {0}, then A is not diagonalisable"
My thinking is that this statement means that Ax = λx has only the trivial solution, but then I am not sure where to go from there?
final saddleBOT
"True or False: If null(A - λI) = {0}, then A is not diagonalisable"
My thinking...
desert mantle
what is lambda
modest bobcat
Some constant I imagine. It doesn't specify whether or not it is an eigenvalue
desert mantle
can you give a picture
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@modest bobcat Has your question been resolved?
modest bobcat
can you give a picture
desert mantle
ok just ignore. the question isnt even a statement that could have a true false value, because it is not specified what lambda is
halcyon garnet
$$\lim_{x \to - infty} \frac{2-3x}{\sqrt{3+4x^2}}$$
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$$\lim_{x \to - infty} \frac{2-3x}{\sqrt{3+4x^2}}$$
soft zealotBOT
Mythicility
halcyon garnet
i got my answer as -3/2 , but apparently its 3/2?
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halcyon garnet
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halcyon garnet
The bottom is pos always
how would i write it tho
like i cant write , answer = 3/2
limpid egret
square of negative is always positive
that's why bottom denominator is always positive
halcyon garnet
yeah
limpid egret
square of negative is always positive
writing this is enough
halcyon garnet
but like how would i write it
i did it by , dividing top with x and bottom with sqrt x^2
runic tulip
x² makes it positive always
halcyon garnet
and then simplified , giving me -3/sqrt4 , so 3/2
halcyon garnet
yeah , i understand those
but do i just write it like that?
runic tulip
Honestly you can just say because of under root it's +ve (roots open with +ve only)
limpid egret
you can just write it as a statement
halcyon garnet
you can just write it as a statement
thats what i was asking , k
ill just write something , ty
.close
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limpid egret
"square of negative is always positive
that's why bottom denominator is always positive"
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wide frigate
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runic needle
X = AX^2, Y = AY^2
I = X - Y = A(X^2 - Y^2) = A(X - Y)(X + Y) = A(X + Y) so
X + Y = A^-1 = A
X = (A + I)/2, Y = (A - I)/2
runic needle
alright well the problem is done, idk what else you want
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barren saffron
i have problem understanding the difference between these types of counting:
count the ways to put:
10 distinguishable balls in 6 distinguishable buckets
10 distinguishable balls in 6 indistinguishable buckets
10 indistinguishable balls in 6 distinguishable buckets
10 indistinguishable balls in 6 indistinguishable buckets
@barren saffron Has your question been resolved?
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prisma mirage
how to continue
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how to continue
prisma mirage
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vague loom
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neon blade
translation 😭 ?
tranquil pine
I can speak the language, so I can maybe help
tranquil pine
شو التمرين الي بدك مساعدة فيه؟
vague loom
ذا كله تمرين واحد
vague loom
كله 😭
vague loom
شو المشكلة عندك حاليا؟
السؤال الاول مكعرفتش اذا مركب الدوال للواحد اي حساب مفكك دالة f او مركب الدالتين معا
tranquil pine
ثانية وحدة بس رح حاول ترجم المصطلحات للانجليزي لاني ما درستهم من قبل بالعربي
tranquil pine
السؤال الاول مكعرفتش اذا مركب الدوال للواحد اي حساب مفكك دالة f او مركب الدالتين...
همم اسفين ما قدرت تجرمه منيح صراحة، هل تقدري يمكن تحاولي ترجميه لو الانجليزي تبعك كويس؟
vague loom
تعرفين مصادر يمكن يساعدوني يوتيوب ؟ بالدوال
tranquil pine
ايه في كثير اماكن تحكي عن الدوال
vague loom
همم اسفين ما قدرت تجرمه منيح صراحة، هل تقدري يمكن تحاولي ترجميه لو الانجليزي تبع...
السوال الاول اكتب g و f على شكل Composite functions ثم rate of change على المجالات المقدمة
tranquil pine
السوال الاول اكتب g و f على شكل Composite functions ثم rate of change على المجال...
ببساطة عم تحوالي تلاقي f o g؟
vague loom
معرف اذا استعمل fog او uوv لكل وحدة
لان مكتوب مركب دوال بسيط
والسؤال للcomposistions رقم 3
لل gok
vague loom
تفكيك دوال لتركيبها
tranquil pine
وجيني شو قصدك يعني
باعتقد صعب علي شوي اعرف شو عم تحكي عنه بما انه في اختلاف كبير بطريقة استخدام المصطلحات 😅
vague loom
مافي سيرفر رياضيات عربي بديسكورد؟ 😭
tranquil pine
متأكد فيه بس يعني مافي اشهر من السيرفرات الانجليزية طبعا
mellow oxide
<@&286206848099549185>
final patio
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@vague loom Has your question been resolved?
tranquil pine
اوك طلع ما قدرت لاقي ناس اسفين @vague loom وما باعتقد الانجليز هون رح يعرفوا يتواصلوا معك
topaz chasm
@rose
في السؤال ١ ,أ
نحتاج ايجاد المشتقة للدالتين f و g ..
ثم نعوض في المشتقة بالصفر لايجاد النقاط الحرجة ... ثم نعوض باي رقم في المجالات بين تلك النقاط الحرجة لمعرفة ما اذا كانت الدالة تتزايد او تتناقص
vague loom
المشتقة لم تدرس في البرنامج
topaz chasm
كيف يعني اي برنامج؟
topaz chasm
اها
غريبة .. سلوك الدوال يعرف عبر المشتقة الاولى🤔
طيب ايش هي الدروس اللي قبل هذا الدرس؟
void yarrow
المشتقة لم تدرس في البرنامج
final saddleBOT
vague loom
طيب ايش هي الدروس اللي قبل هذا الدرس؟
مركب دوال / تساوي دوال / العمليات الجبرية على دوال..
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proper viper
?
worn iron
Wait you didn't write this?
worn iron
especially the 2nd part of the proof
For the second part they show that ]0,5] is included in the union
proper viper
For the second part they show that ]0,5] is included in the union
and how do they assume a is equal or larger than 1
worn iron
and how do they assume a is equal or larger than 1
Do you know the concept of proof by exhaustion?
proper viper
no idea
worn iron
no idea
Basically if "a" is a real in (0,5] then there is only two case for a right?
Either a>=1 or a<1
So if prove the property for both case then you proved it for all "a"
worn iron
but why a >= 1 or a < 1
Well it's convenient in this case :v
proper viper
how do you know when which a is convenient
worn iron
how do you know when which a is convenient
Well "x" varies from 0 to 1 and is the left endpoint of the interval in the union right?
proper viper
i guess
worn iron
Well you can chose any x here because it's the union :v
So might as well chose an x that isn't too complicated and is on a relatively simple case :p
Here the case x=1 is one of the simpler case :p
So you take a>=1 so you can corroborate it to the x=1 case
proper viper
hm
worn iron
Honestly this sort of insight is built on practice.
It's kinda hard to explain why such a case disjunction is better than another (outside of some cases where it's obvious).
Basically try to look at your problem and spot if there are any privileged value that you can divide thing around 
worn iron
and what happens here?
Well we know a>0 right
and now we suppose a<1 so it's in (0,1)
In which case because x€(0,1] we can just take the interval where x=a (which exists because x takes ALL value between 0 and 1 so because "a" is between 0 and 1 then "x" takes the value of "a" for one interval in the union)
And then a is in that interval
Because the interval in general are [x,3x+2) so for x=a you have [a,3a+2) and like a is in [a,3a+2)
If you don't understand don't hesitate to tell me
worn iron
i think i get what u mean
Ah that's nice :p
Do you have any other questions? :v
proper viper
Ah that's nice :p
Do you have any other questions? :v
i would but they are about an integral and not this.. 😅
worn iron
i would but they are about an integral and not this.. 😅
Well you can always ask away ^^
worn iron
Ig it's the b) section :p
proper viper
i didnt understand what they did here but this is a totally different question to the integral
worn iron
Can you post the question then ^^'
worn iron
Ah well you should try it before reading the correction :v
worn iron
More proof by exhaustion it appears 
proper viper
for x >= 1 all are positive
proper viper
my question would be for x < 0
worn iron
ah ok
worn iron
ah
well x=<0 right? so x is negative
So |x| = -x
You replace:
|x|/|x-1| (|x-1| is also below zero so it's also negative)
you get:
-x/(-(x-1))
Then you simplify the -1 and you get
x/(x-1) again
proper viper
ohh do you need to put a minus on both sides of a bracket ?
worn iron
Which bracket?
worn iron
well yeah
so like x and x-1 are both negative number right? (if x<0)
so even by default x/x-1 is a positive number actually
worn iron
yes
worn iron
ah well it works for x=0 as well
worn iron
wouldnt that be 0/-(x-1)
well that's just 0
0/a, a being literally anything that isn't 0 is 0
so here both side of the equation are equal to 0
actually 0 solves the equation lol
worn iron
ill just rememeber that then
do you have any more question? :p
if you don't remember to close the thread
.close :p
proper viper
do you have any more question? :p
i think i have bothered u way too much alreadu
worn iron
i think i have bothered u way too much alreadu
Dworry lol, it was nice
proper viper
thank you for your help
worn iron
thank you for your help
just type ".close" when you are done :v (so the thread closes and other people can use it)
proper viper
.close
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tepid mortar
How do you factor x^4 + 5x^3 + 6x^2
final saddleBOT
How do you factor x^4 + 5x^3 + 6x^2
rocky tusk
factor x^2 first
then it should be a regular quadratic that you hopefully know how to factor
tepid mortar
Oh
At first I thought it would be a complex number
is x^2[(x+2)(x+3)] correct?
Typo
pure lodge
alright
tepid mortar
If I made it (x^2)(x+2)(x+3) is it still correct
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@tepid mortar Has your question been resolved?
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@tepid mortar Has your question been resolved?
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vocal grove
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vocal grove
determine the limit for lim x->infinity f(x) and lim x->-infinity f(x) if they exist
vital crag
how are you supposed to show this? epsilon-N proof?
vocal grove
how are you supposed to show this? epsilon-N proof?
i got no clue what that is
<@&286206848099549185>
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wanton olive
Hey ! I have a question why when you change the variable to « ln(x^2) » doesn’t the fonction become 1/xt ? Where did the 2 came ?
final saddleBOT
Hey ! I have a question why when you change the variable to « ln(x^2) » doesn’t...
daring tusk
chain rule
so 2/x dx would be dt
so you multiply divide with 2
in order to get 2/x
coarse thistle
Hey ! I have a question why when you change the variable to « ln(x^2) » doesn’t...
$$t=ln(x^2)$$
$$\frac{dt}{dx}=\frac{2x}{x^2}=\frac{2}{x}$$
$$dx=\frac{dt}{\frac{2}{x}}=\frac{x}{2}dt$$
$$\int \frac{1}{x*t} \frac{x}{2}dt$$
$$=\int \frac{1}{2t};dt$$
soft zealotBOT
MESSIAHOFALL69
wanton olive
oh i get it now , thank you very much !
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oak arrow
if i have an equation in the form of ( (x ± 0.5) - (y ± 0.5) ) / t, is that equivalent to (x-y)/t + 1/t?
final saddleBOT
if i have an equation in the form of ( (x ± 0.5) - (y ± 0.5) ) / t, is that equi...
oak arrow
please @ me if anyone responds
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oak arrow
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urban burrow
where are you stuck on?
oak arrow
where are you stuck on?
im not stuck, i just want to make sure I add the uncertainty properly.
so first I did (x - y)/t, and then the uncertainty is now just 1/t. So the equation can be simplified to (x-y)/t ± 1/t, right?
oak arrow
<@&286206848099549185>
oak arrow
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neat schooner
Determine the domain and range of each of the following function.
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Determine the domain and range of each of the following function.
undone sedge
i’m pretty sure you have to factor that not solve for x
are there any other directions ?
neat schooner
i’m pretty sure you have to factor that not solve for x
oh i see
neat schooner
are there any other directions ?
wdym direction?
undone sedge
for factoring trinomials (ax^2 + bx + c) you have to find two numbers that will have a sum of b but a product of c
neat schooner
im really weak with this stuff
undone sedge
wdym direction?
no i js wanted to make sure it was factoring and not anything else
neat schooner
no i js wanted to make sure it was factoring and not anything else
oh i see
i did this stuff in grade 11 and i absolutely sucked at it
now aswell
what do you factor?
undone sedge
for factoring trinomials (ax^2 + bx + c) you have to find two numbers that will ...
so in this case ur b is -4 and ur c is 3
oh wait woopsy
one sec lemme edit that
okay
undone sedge
so your goal is finding two numbers that will multiply to get 3 but also have sum of -4
neat schooner
(x ) (x )
neat schooner
so try to think of 2 numbers that can meet the criteria
got it
undone sedge
if ur ever unsure abt ur answer u can always multiply ur factors out and see if it matches the original equation, it’s a really good way to check ur factors
neat schooner
-3x-1?
undone sedge
ur numbers are right but not the format
neat schooner
if ur ever unsure abt ur answer u can always multiply ur factors out and see if ...
oh ok
neat schooner
ur numbers are right but not the format
oh
neat schooner
go back t o this
yeah -3x-1 is all i could manage
undone sedge
ya ur numbers are right but the correct answer would be (x-3)(x-1)
neat schooner
:((
undone sedge
u just have to format it correctly
neat schooner
i see
undone sedge
finding ur factors is the hardest part so u did a good job at that !
undone sedge
yeah
neat schooner
finding ur factors is the hardest part so u did a good job at that !
oh really?
les go
ahhh got it
so how would you get the domain and range now?
undone sedge
oh wow
uhhh
personally i would put the equation in a graphing calc if ur allowed to do that
neat schooner
i probably wont be able to do that
undone sedge
hmmm
i’m not completely sure then 😞 i would assume it has something to do with the constant value 3
since this is a quadratic equation with a leading exponent of 2, it will just be a parabola
neat schooner
oh is that so
undone sedge
parabolas have a domain of all real numbers or negative infinity to infinity
the constant number determines the range in believe
neat schooner
is the domain {XER}?
undone sedge
i believe so since there’s no other restrictions for the x axis
undone sedge
for the range you start from the lowest point (or vertex) i’m pretty sure
the constant value determines how many units it goes up or down on the y axis
so i believe it will be [3, ♾️)
undone sedge
because this parabola is positive (no negative sign on the outside) so it would just keep increasing
yes
undone sedge
i was taught to do domain write (-♾️,♾️) and range write [3,♾️)
i’m not sure if that’s how ur teacher wants u to
neat schooner
i think so
undone sedge
i’m not the best with domain and range but that’s how i was doing it
neat schooner
i’m not the best with domain and range but that’s how i was doing it
i see
im not good either
well thanks a lot
really appreciate it
undone sedge
ur welcome !
neat schooner
have a good day
undone sedge
u toooo
neat schooner
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spare moth
i have to show that f(theta) = tan(theta)
but i dont know how to decide which double angle identity should be used in numerator and denominator for the cos2theta
i did it with trial and error but in exam i wont have that much time, does anyone have any tips to know which one to use
final saddleBOT
i have to show that f(theta) = tan(theta)
but i dont know how to decide which d...
subtle ginkgo
i have to show that f(theta) = tan(theta)
but i dont know how to decide which d...
i would split '1' up into sin^2 + cos^2
then use cos2a = cos^2 (a) - sin^2 (a)
and sin2a = 2sinacosa
and probably the same for the denominator
and just simplify
yeah and then all you need to do is like combine like terms, factor, then things should cancel out down to sin/cos
spare moth
yeah and then all you need to do is like combine like terms, factor, then things...
thank you but could you also explain your thinking process like how u know which identity to use: -)
subtle ginkgo
thank you but could you also explain your thinking process like how u know which...
youre just trying to use the identities that get you to the same kind of terms
so in this case sin and cos and their squared versions
not sure if that makes sense but this is how i always did it and it seemed to come out fine each time, im just trying to find things that would be easy to factor or combine later on
spare moth
not sure if that makes sense but this is how i always did it and it seemed to co...
That makes sense, thank you!
.close
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drowsy seal
is there a faster way to factor this without polynomial long division
frigid hawk
do you know synthetic division?
royal swan
do you know synthetic division?
That's almost same as long division
frigid hawk
it’s much quicker due to only using coefficients
drowsy seal
no i havent but is it really much quicker?
steel tinsel
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steel tinsel
Want to show the last bit
I assume that f is continuous and Riemann intégrable on [0,2pie] and that <f,f> is = 0
Want to show that this => f = 0
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olive maple
hello can someone pls help me solve this exponential function problem?
tacit oak
hello can someone pls help me solve this exponential function problem?
try starting off by changing the 5^(x+4) into 5^x times 5^4, same with the other one and try factoring and maybe it’ll start to look clearer!
olive maple
try starting off by changing the 5^(x+4) into 5^x times 5^4, same with the other...
oki I'll try that
olive maple
try starting off by changing the 5^(x+4) into 5^x times 5^4, same with the other...
should I continue and solve for x or should I combine like terms first?
tacit oak
what have u done so far?
olive maple
what have u done so far?
5^x(5^4)+5^x(5^6)=26
tacit oak
do u see any common factors? (hint: theres one!)
olive maple
5 and 2??
tacit oak
(1+5) inside?
it would be 5^4 + 5^6 in the inside
tacit oak
tacit oak
so it'll look like (5^4+5^6)5x?
5^x *
tacit oak
does this make sense?
olive maple
yes it doess
tacit oak
ur able to take ojt the 5^x out of the 2 terms since both terms are multiplied with 5^x
and then the insides are added up
olive maple
so now I just need to make the constant or the base the same, right?
olive maple
Well, it says here in the process that I have to make the bases the same
tacit oak
yes but u can’t rlly do that yet right?
olive maple
I need to simplify it further, then?
tacit oak
what do u think ur next step is in order to attempt making x by itself
tacit oak
I need to simplify it further, then?
how so?
tacit oak
5^x(5^10) =26
u can only add powers if the same bases are multiplied together
olive maple
ah
tacit oak
5^4 + 5^6 ≠ 5^10
5^4 times 5^6 =5^10
tacit oak
my next step would be, u can divide both sides by (5^4 + 5^6)
so it’ll leave u with
5^x on the LHS
and a number on the RHS
yes?
tacit oak
yess
so u went from
5^x(5^4 + 5^6) =26
divided both sides by (5^4 + 5^6)
you’ll now end up with
5^x = 26/(5^4 + 5^6)
which is just
5^x = 1/625
yes?
olive maple
yes
olive maple
you can use the formula for exponential function for that, right?
tacit oak
which formula?
olive maple
1/a^n
tacit oak
yessss
olive maple
it's gonna be 5^-⁴ right?
tacit oak
is that _ a negative
olive maple
yes
olive maple
-4?
tacit oak
u got 5^x = 5^(-4)
olive maple
wow
tacit oak
🔥🔥🔥
olive maple
You're such a great teacher!!
olive maple
I'm sorry that u had a hard time teaching me, I'm kinda slow 😅😅😅, Thanks so much again!!
tacit oak
noo it’s okay nwwss
i use to be pretty slow too
just keep up the effort and try to understand it and slowly you’ll improve significantly
tacit oak
goodluck!! i mean you’ll prob be able to from a few months to a year
olive maple
Thx againnn, I'll do my best to get better!!
tacit oak
goodluck!🫡
olive maple
.close
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ember tartan
tried solving many times
lament vale
Maybe integration by parts will help
ember tartan
yeah i tried doing that but there was this one step that was cauing me probems to figure it out
lament vale
nice
ember tartan
I j dont understand how they get into u -1 /u for that
ember tartan
so they cubed that x = sqrt(u-1)/7 i see
lament vale
yep
ember tartan
so how do we conclude it to be the int of u -1 / u
lament vale
You also have dx
dx = d(sqrt(u-1)/7) = du / (14 sqrt(u-1))
Hence x^3 dx = (u - 1) / (7^3 * 14)
7^3 * 14 = 4802
ember tartan
ur one kind of a genius lol!
uncut mulch
You could also from $\dd u = 98x ; \dd x$ see that,\
$\int \frac{x^{3}}{49x^{2} + 1} ; \dd x = \frac{1}{98} \int \frac{x^{2}}{49x^{2} + 1} ; \dd u$\
And then simply use the substitution $u = 49x^{2} + 1$ and the rewritten version $(u - 1)/49 = x^{2}$ to get the finale thing.
soft zealotBOT
ember tartan
dx = d(sqrt(u-1)/7) = du / (14 sqrt(u-1))
how did u get it to be 14?
ember tartan
ahh
ember tartan
That looks much simple and effective
final saddleBOT
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pastel hull
final saddleBOT
edgy burrow
complete the square
pastel hull
When we get x we need to plug it in the fraction bracket to find what x-intercept is
edgy burrow
yeah almost but you shouldnt have a x^2 in the brackets
its putting it in the form of (x + B/2)^2 + C
final tangle
you want to use (5/2)^2 not just 5/2
and also subtract at the end to balance it out
you also have the wrong sign for the 7, that should've been - as well
pastel hull
yeah almost but you shouldnt have a x^2 in the brackets
Sorry I didnt square root it yet
Ok thank you!!!
pastel hull
you want to use (5/2)^2 not just 5/2
and also subtract at the end to balance it ...
Ok thank you!!
pastel hull
you also have the wrong sign for the 7, that should've been - as well
Huh
Wdym I put the negative sign already
final tangle
you wrote + in your messages just now
pastel hull
Oops sry!
pastel hull
Ohhhh like (x^2+5x+5/2)+7+5/2
Now I get it😭😭 i misunderstood it as an equation
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compact echo
hello i have a question, what is the sum of all the divisors of the number 24 (it must be without remainder, and the sum must be two digits)
final saddleBOT
hello i have a question, what is the sum of all the divisors of the number 24 (i...
tranquil pine
24 = 1, 2, 3, 4, 6, 8, 12, 24
Sum = 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 = 60
tranquil pine
no prob
compact echo
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grave zenith
Does anyone know how to prove or disprove this logical statement?
x ⇒ y ∧ z ≡ (x ⇒ y) ∧ z ≡ x ∨ z
grave zenith
I've tried to start from the right side and work everthing out distributively but I keep getting stuck
it ends up like
(-x V y) ^ (-x V z) == (-x V y) ^ z
and I need to prove this equals
x v z
final saddleBOT
@grave zenith Has your question been resolved?
drowsy epoch
Does anyone know how to prove or disprove this logical statement?
x ⇒ y ∧ z ≡ ...
I think you can try to start with [ x \lor z \equiv (x \lor z ) \lor (y \land \neg y) ]
to somehow include $y$, however I would think a truth table would be the best, to test first if it's provable at all.
soft zealotBOT
bacc (unhelpful)
grave zenith
I think you can try to start with \[ x \lor z \equiv (x \lor z ) \lor (y \land \...
Can't use a truth table, I need to prove it mathematically. Ill try out your suggestion, I'm pretty sure it's provable though
drowsy epoch
Can't use a truth table, I need to prove it mathematically. Ill try out your sug...
You said to prove or disprove it. So it would be good to see first what the expected outcome would. Say it was equivalent, then you focus on proving it's true, instead of second guessing every time...
grave zenith
You said to prove or disprove it. So it would be good to see first what the expe...
Thanks for the answer, I tried it in a truth table and it appears there's one counterexample (0, 1, 1) for (x, y, z). Do you think this enough to solve the problem? Just use a truth table and show there's a counterexample? How else would I go about disproving this
Actually no, I think I messed up, a logic table online says it's true for all values
drowsy epoch
I see
I think I would try the approach to show that (x -> (y ∧ z) <-> (x -> y) ∧ z <-> x ∨ z) ≡ T
grave zenith
is <-> not the same as ≡ ? my exact question is worded like this
I put it in the truth table like that because there was no ≡
drowsy epoch
You basically have [ A \leftrightarrow B \leftrightarrow C ] and I would first try to get rid of the implication arrows using [ A \rightarrow B \equiv \neg A \lor B ]
soft zealotBOT
bacc (unhelpful)
drowsy epoch
is <-> not the same as ≡ ? my exact question is worded like this
I put it in the...
At my university we distinguish between -> and => (same with <-> and <=>)
basically => and <=> are tautological in that sense
e.g. if A -> B is always true then we say A => B
but it might be different at yours
grave zenith
here, => just means implies, we don't use -> at all (funmath is the notation im pretty sure)
grave zenith
can you just replace the ≡ with => (or -> for you) ? doesnt it have to go both ways?
because I tried this (in both ways) and failed / gave up after like 10 steps
drowsy epoch
≡ is the same as <=> for me
grave zenith
**bacc (unhelpful)**
can you just replace that with a singular implication, as shown here?
drowsy epoch
why would I?
grave zenith
I don't know lol, I'm lost.
drowsy epoch
i am trying this problem rn to see if it works out
grave zenith
thanks 🙏
olive crest
Can't use a truth table, I need to prove it mathematically. Ill try out your sug...
You need to provide details on what's allowed then. Creating a step-by-step truth table is a valid proof (via semantics).
grave zenith
You need to provide details on what's allowed then. Creating a step-by-step trut...
Provide a calculational proof (preferably without case analysis) if it is a tautology; give a counterexample if it is not a tautology.
drowsy epoch
I think I considered this now for long enough, and I think there is just the hard way, to simplify it using the laws
olive crest
calculational proof
What is that supposed to mean? Tools may vary between lectures and lecturers. Like, which rules of inference and which axioms are allowed..
As a logician by profession, I haven't even heard that term before, and there are very few results.
For example, according to the paper https://www.sciencedirect.com/science/article/pii/S0168007201000598:
grave zenith
> calculational proof
What is that supposed to mean? Tools may vary between lect...
That's what our professor said, we're supposed to use the different laws (weakening, reflexivity, associativity, ...) to simplify and end up with something like 1 == 1 to prove it
grave zenith
I think I considered this now for long enough, and I think there is just the har...
Yeah, I tried it the hard way and it takes like 2 pages (and I have never seen a problem that long) thanks for the help though
I didn't even prove it either
olive crest
That's what our professor said, we're supposed to use the different laws (weaken...
And how was anyone trying to help you supposed to know that? ^^ Anyway, now maybe someone can help.
drowsy epoch
Can't use a truth table, I need to prove it mathematically. Ill try out your sug...
because he mentioned it here
scrolling helps
olive crest
No he didn't.
to prove it mathematically
Means something else entirely (and would include truth tables).
drowsy epoch
No he didn't.
> to prove it mathematically
Means something else entirely (and wo...
he did, i referred to it.
If Can't use a truth table isn't clear to you, I don't know what is.
grave zenith
It doesnt matter, my first language isn't english, I dont know how to translate the mathematical terms properly. Sorry for the confusion.
olive crest
If *Can't use a truth table* isn't clear to you, I don't know what is.
You can copy the entire argument of using a truth table without using a truth table. It doesn't matter.
But apparently it is not only restricted such that using the semantics is not allowed, but that only some "calculational proof" calculus is allowed.
olive crest
> calculational proof
What is that supposed to mean? Tools may vary between lect...
More precisely, the one from that image (I suppose).
grave zenith
More precisely, the one from that image (I suppose).
No I don't think that's it, I can send you an image of a proof I did in class, but my handwriting is dogshit so beware.
olive crest
People need to know precisely which rules are allowed in order for them being able to help you.
grave zenith
Well, I'm guessing all of them? we have like 3 pages of proven rules that we can use. Is the stuff I'm learning that unusual? haha
olive crest
Well, I'm guessing all of them? we have like 3 pages of proven rules that we can...
It's just random/arbitrary. Probably a good strategy of the professor to make it harder for you to find solutions online or get help.
grave zenith
It is indeed working, because I cannot find anything online
drowsy epoch
It is indeed working, because I cannot find anything online
I think I might have a last idea but I first need to try it out, before you close this
drowsy epoch
nah never mind i give up
final saddleBOT
@grave zenith Has your question been resolved?
jade tree
This may sound stupid but i’m getting a gift for my girlfriend and i need to work this out.
I basically need to work out what size jar i need to buy to fit 365 pills in it.
According to the image, the pills are 2cmX0.6cm but the depth or diameter of the inside isn’t shown.
I am buying 365 of these pills and want to put them all in a jar.
I’m wondering what size jar i will need to buy in order to fit them all in. I assume 500ml right? A bit of extra space in the jar is okay as i can fill the gaps but i want the closest possible result
final saddleBOT
This may sound stupid but i’m getting a gift for my girlfriend and i need to wor...
subtle ginkgo
Volume = π * radius^2 * height
The radius is half the diameter, so radius = 0.6cm / 2 = 0.3cm
The height is 2cm
Therefore, Volume = π * (0.3cm)^2 * 2cm = 0.56548667764cm^3
multiplying by 365 pills
warm ether
thats more complicated than you may think, but if you dont mind extra space its not so complicated
subtle ginkgo
206.4026373 cm^3
1 cm^3 is 1 mL so
206.4026373 mL worth of pills
even if we take into account the fact that you cant perfectly fit pills into that area
we still have like 88 mL of space left to work with if we have the worst possible scenario of the pills taking up 2x the space
so it should be fine
probably
subtle ginkgo
This may sound stupid but i’m getting a gift for my girlfriend and i need to wor...
tldr: you have quite a lot of wiggle room with 500mL so its fine probs
jade tree
tldr: you have quite a lot of wiggle room with 500mL so its fine probs
how many cm cubed of space do u think i’d have
subtle ginkgo
how many cm cubed of space do u think i’d have
1 cm^3 is 1 mL so 500 lol
jade tree
WHAT
jade tree
1 cm^3 is 1 mL so 500 lol
that’s how it works?😭😭😭
subtle ginkgo
subtle ginkgo
that’s how it works?😭😭😭
ye
subtle ginkgo
also a typical packing efficiency for cylindrical objects is around 60-70%.
so in all honesty you would still have like 180mL of space left over
jade tree
isn’t that too much😭
subtle ginkgo
yeah like over half lol
jade tree
how do i fill that much space haha
subtle ginkgo
wait sorry im dumb
jade tree
with 365 of them no way
jade tree
i thought i’d have around 100 left
subtle ginkgo
i thought i’d have around 100 left
206.4026373/.6
(aka worst case scenario of 60% packing efficiency)
will still leave you with:
500 - 344.0043955 = 155.9956045 mL of space
jade tree
206.4026373/.6
(aka worst case scenario of 60% packing efficiency)
will still ...
so ideally i get a smaller jar
jade tree
are you trying to like
but who would make a 400ml jar😭
subtle ginkgo
yeah basically all the way to the top
is it not an option to get more pills?
jade tree
is it not an option to get more pills?
sadly not i’m writing something in all of the pills😭
right i’ll stop bothering you, thank you for the info - i’ll try figure it out on my own
subtle ginkgo
right i’ll stop bothering you, thank you for the info - i’ll try figure it out o...
first can you tell me the approximate diameter and height of the jar?
i wanna try out my cool new thing i made
jade tree
hahha sure wait
jade tree
first can you tell me the approximate diameter and height of the jar?
this might hurt your feelings a little bit
would you like to see the shape of the jar😭
jade tree
subtle ginkgo
:p
jade tree
not even close to a cylinder lol
no it’s alright
subtle ginkgo
walp
jade tree
at first i was thinking of a love heart one😭😭😭
why am i telling you this 💀
diameter 10cm
height 11cm
including cork at the top
subtle ginkgo
ngl dude
i dont think my thing worked
xd
how the heck did it even do this
wait i think i forgot to set liquid to cylinder
subtle ginkgo
its supposed to be the volume lol
yeah its just a python program i made while in this help channel
jade tree
that’s so cool
subtle ginkgo
doesnt work tho xd
subtle ginkgo
i have no idea how to even do that so congrats 😭
¯_(ツ)_/¯
takes like 5 seconds, you can learn easily
anyways you can .close now lol, sorry for taking so much time
subtle ginkgo
dw tho one day i’ll get it💀
going into comp sci?
jade tree
definitely not
subtle ginkgo
rip
subtle ginkgo
nurp
jade tree
well
i’m studying maths throughout it
so i’ll get it eventually
not comp sci tho that doesn’t really interest me
see? i’m using my new terminology
jade tree
it is
jade tree
the applied knowledge is crazy
if you don’t mind me asking how old are you
subtle ginkgo
if you don’t mind me asking how old are you
well i learned how to code in python at like 16 ish if thats what you want to know
jade tree
well i learned how to code in python at like 16 ish if thats what you want to kn...
i see i see
that’s not really my thing
im studying maths, economics and psychology next
i’m aware psychology isn’t a great mix 😭
subtle ginkgo
ive heard that psychology is fun, but its just a crap load of writing
jade tree
ive heard that psychology is fun, but its just a crap load of writing
yeah the writing isn’t fun but i’m just too fascinated not to take it😭
subtle ginkgo
fair enough
jade tree
fair enough
anyway thanks for the help 😭
haughty vault
- If you will draw the graph of y = x * (x + 2) ^ 2 how will you sketch it with respect to the x-axis?
A. Sketch it crossing both (-2, 0) and (0, 0)
B. Sketch it crossing (-2, 0) and tangent at (0, 0)
C. Sketch it tangent at (-2, 0) and crossing (0, 0)
D. Sketch it tangent at both (-2, 0) and (0, 0)
final saddleBOT
9. If you will draw the graph of y = x * (x + 2) ^ 2 how will you sketch it with...
distant sleet
Is the answer c?
what makes you think it is/isn't c?
haughty vault
what makes you think it is/isn't c?
From a help I've gotten yesterday explaining the meaning of tangent
Where tangent is the point where the line doesn't intersect x
and from this observation, I could see that the line doesn't intersect x, meaning it's tangent at -2,0 crossing 0,0
and also the other method which of course is just the process of elimination
barren hound
yes - but i think you'll be required to do this without computer help in the future
haughty vault
yes - but i think you'll be required to do this without computer help in the fut...
does that mean c, is the answer?
final saddleBOT
@haughty vault Has your question been resolved?
haughty vault
<@&286206848099549185>
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haughty vault
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hollow garden
for a rational function, how do i find the end behavior if the denominator has a greater degree? please ping me if you respond!!!!
do i still subtract the denominator exponent from the numerator exponent? do I base the end behavior on the denominator instead? what do i do?
i dont have an example because i cant find any rn
final saddleBOT
for a rational function, how do i find the end behavior if the denominator has a...
subtle juniper
for a rational function, how do i find the end behavior if the denominator has a...
If the denominator has a greater degree then the end behavior will approach zero
since the magnitude of the denominator will grow a lot faster than the numerator
hollow garden
If the denominator has a greater degree then the end behavior will approach zero
thanks
.close
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broken idol
how do i do this? Im getting different answers from my friends and website
autumn geode
how do i do this? Im getting different answers from my friends and website
gotta ask the right friend
but what have you done so far
broken idol
but what have you done so far
tried adding them up for the standered deviation adding them up n divide by 81
autumn geode
tried adding them up for the standered deviation adding them up n divide by 81
add em up
and divide by sample size
broken idol
kk
autumn geode
get point estimae for mean
use this formula for standard error
find t critical to find margin of error rip
95% confidence interval t
autumn geode
ill try that
ofc
you wanna find urself a beauty friend
who can sauce you some help
onyx pike
i need help
onyx pike
oh sorry
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@onyx pike Has your question been resolved?
final saddleBOT
tacit cargo
use a calculator
glad harbor
send the problem
royal swan
2. Pair the triples
3. Replace these triplets with single number and get it out of cube root
4. Multiply the numbers out of the cube root ```³√81
³√3×3×3×3
³√(3×3×3)×3
3³√3```Well you gotta figure it out by yourself
If it's 27,81,243 , you can't use 2 , you need to use 3
Nope, break it down to smallest prime multiplication then take triplets
³√216
³√2×2×2×3×3×3
³√(2×2×2)×(3×3×3)
2×3³√1
6```
open silo
can someone help me find the concavity of y= 6x+sin(3x)
final saddleBOT
can someone help me find the concavity of y= 6x+sin(3x)
open silo
i found the 2nd derivative and solved for the inflection points but i'm getting intervals where the slope is negative
but when i plotted the original function it was all negative
help what do i do
drowsy epoch
i found the 2nd derivative and solved for the inflection points but i'm getting ...
What is the 2nd derivative?
open silo
y''=-9sin3x
drowsy epoch
y''=-9sin3x
If you draw it you will find out that there are intervals where f" > 0 (concave up) and f" < 0 (concave down)
The period is 2π/b
So you can divide the sine function into four sections
And since it's -sine instead sine it starts off decreasing in the first quarter of its period
open silo
ohhh wait i think im misinterpreting the 2nd derivative. I'm not look at the value of y''
how would we write out the concavity
drowsy epoch
how would we write out the concavity
As I said, you plot the simple sine function, and find out when f'' > 0 (concave up) and when f'' < 0 (concave down).
The transformations from sin(x) -> -9sin(3x) are just that it's been reflected at the y-axis, stretched by 9 units vertically in both direction up/down and the period is 2pi/3.
final saddleBOT
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left quail
hi is anyone here to help?
final saddleBOT
hi is anyone here to help?
livid ice
Please post your question
left quail
ok, gimme a sec thanks
marsh temple
Among the longer secs I've encountered
left quail
sorry gimme 1 min
jagged flare
timer started
marsh temple
jagged flare
oop hold on it resetted :p
left quail
its sending
so i am taking a study guide test and was very confused on this topic, i was hoping someone could help?
I would prefer you would answer majority or half of them so i could understand the topic more clearly, thank you very much
just wanting to know is anyone working with me?
?
ivory vessel
just wanting to know is anyone working with me?
no, because this is a test
and you are not allowed to cheat
please close this channel
left quail
how
left quail
what
ivory vessel
do you want to close this channel?
left quail
ye
ivory vessel
.close
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shy grove
hi guys.
y = |x| is transformed to y = |2x| -3
is the transformation translation by vector (0, -3), followed by stretch on x axis by stretch factor (1/2)?
fleet granite
first the stretch, then the move
shy grove
ooooh
is the stretch factor correct?
bcs my book's answer key says it is stretch on y axis by stretch factor 2, but it might be wrong
tulip coyote
bcs my book's answer key says it is stretch on y axis by stretch factor 2, but i...
Same thing 
cause |2x| = 2|x| so you could see it either way
final saddleBOT
@shy grove Has your question been resolved?
shy grove
Same thing <a:nyaNana:586338925983957009> cause |2x| = 2|x| so you could see it ...
ohhhh i seee
thank you so much!!
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opaque stirrup
can anyone help me with this?
sharp root
can anyone help me with this?
what part
urban dust
can anyone help me with this?
just calculate the determinant using the laplace formula. have fun
raven marsh
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tranquil pine
i need help with derivation of [ \cos(\theta + \phi) = \cos \theta \cos \phi
- \sin \theta \sin \phi ]
from lhs to rhs
please don't answer me by saying google it i didn't find it on google
final saddleBOT
i need help with derivation of \[ \cos(\theta + \phi) = \cos \theta \cos \phi
-...
soft zealotBOT
Svaha
desert mantle
what are you allowed to take for granted
and frankly this really is something easily found with google
"addition theorem cos proof"
tranquil pine
and frankly this really is something easily found with google
fr
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tranquil pine
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thorn stump
A bright young executive with foresight but no initial capital makes
constant investments of D dollars per year at an annual interest rate of
100k percent. Assume that the investments are made continuously and
that interest is compounded continuously.
(a) Find the accumulated amount A at any time t.
i dont understand what this question is saying,
so like hes investing D dollars, so hes "depositing it" but then he will also get the money back at the specified interest right?
is this correct?
final saddleBOT
A bright young executive with foresight but no initial capital makes
constant in...
warm ether
100 000 percent??? good lord
He deposits D dollars per year
there is also an annual interest of (100k% really?)
thorn stump
100k per cent
so its just gonna cancel out 100k/100 to just be k
its for the sake of calculation i believe
warm ether
oh thank god
cyan kayak
k being a variable, makes sense
So let's think about this in terms of a differential equation.
thorn stump
yeah i mean i know that but i dont understand the situation
cyan kayak
Let's think about the change in A, dA/dt
It changes in two ways, first by addition of the continuous deposit, and then by the effects of compound interest.
dA/dt = ? + ?
Help me fill in the blanks
The first ? represents the deposits, so what should go here?
thorn stump
uhh it should be.... D
but D is deposited annualy
so like D/something?
cyan kayak
Let's put everything in units of years, so t = 1 is 1 year
So if that's the case, we have just D
thorn stump
kD?
cyan kayak
Not kD
Close though!
Compound interest affects the entire value, not just what was just being deposited
cyan kayak
No worries!
thorn stump
kD^t?
thorn stump
nah man, i have forgotten everything, wait up gimme a minute
cyan kayak
No worries
thorn stump
oohhh my bad man
it should be kA
cyan kayak
So dA/dt = D + kA
thorn stump
so should i solve for A now?
cyan kayak
This is a differential equation, it should be separable i think, and yeah you solve for A
thorn stump
okay
also, kinda dumb maybe but like
i dont CLEARLY understand why its kA, like on the definition of compound interest it takes interest on the current amount?
or is the reason completely different
cyan kayak
Yeah, the idea is compound interest gives you interest on the entire amount
final saddleBOT
thorn stump
.reopen
final saddleBOT
✅
thorn stump
@cyan kayak hey, just had a thought in mind, so the D + kA, that gives me the change in A right, but why is it so
like shouldnt it be the actual A instead?
and also
why cant i apply the
A = D + Dk^t thing over here
cyan kayak
What do you mean "apply the other ones?"
cyan kayak
You will get a result very similar to that
cyan kayak
It's slightly different
thorn stump
You will get a result very similar to that
yeah i got it