5
6
#help-13
queen ice
Make sure the order stays the same, it’s important here
Now how about the fourth
tame sleet
add 2 to sides add 1 to length?
queen ice
Indeed
Can you express the two with a formula? One for the sides and one for the bottom
In terms of n
tame sleet
n +1 n + 2
queen ice
Not quite
n isn’t the last element
n is the index of the element
So if you have a formula n+2 for example, the first element would be 3 (cause n=1), the second 4 (cause n=2) etc
But the +2 is already quite close. For the first element, how many times have we added 2 to 0?
Considering that the first element is 2
tame sleet
?
queen ice
So we have
Bottom length: 3 4 5 6
Side length: 2 4 6 8
Just to kinda speed things up: the formulas here are 2 + n and 2*n respectively. Try to understand why. Then use that to get the formula of how many cubes there are (with a rectangle like this, you can calculate the number of cubes from just the side lengths)
@tame sleet
cedar kilnBOT
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burnt siren
the final answer was 3 sqrt 21 for both SU and TU, but squareroot 189 isn’t 3 x 21? 9 x 21 equals 189 so how did it simplify that way?
burnt siren
in the sense of, how did square root 189 simplify into 3 sqrt 21?
cedar kilnBOT
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brave nimbus
in the sense of, how did square root 189 simplify into 3 sqrt 21?
Since square root 189 is a whole square root number , you can simplify it to 3 square root of 21, because two factors of 189 is: 9 x 21
And since 9 is a perfect square , you just have to square root it , so it will be outside the square root symbol
This same rule applies to other sqrts as well !
compact gulch
Can someone tell me why when proving the Probability Generating function of a Binomial and Poisson distribution they take the summation from r = 0
compact gulch
But for Geometric and Uniform distribution it is from r = 1
drifting marlin
I assume those latter two are such that P(X=0) = 0
cedar kilnBOT
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cedar kilnBOT
solar vector
.reopen
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devout zealot
Is this normal
cedar kilnBOT
Is this normal
devout zealot
Click to see full picture
hollow trail
well if you get an equation that is always true at the end, then the solutions to that equation are all x (for which the equation makes sense in the first place)
devout zealot
So all x greater than 0
azure swift
yeah
which should make sense
since the rules you used as an equality are true for all positive x
this in turn i think might give a helpful perspective on the rules
as theyre merely equations that holds for most x's
devout zealot
thank you
tall brook
Is my notation correct? I'm trying to define two parameters for a dataset (x). The first is "the percent of datapoints below 6" and the second is "the number of datapoints where both that point and the next point are below 6".
vivid wadi
as long as you clarify, any notation is correct
tall brook
Oh, is that right? Sorry, math isn't my major so I assumed this sort of thing was more rigid ^^;
Thanks!
.close
cedar kilnBOT
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stark bronze
Why is the third term dervied to 0? Is it because it has no x term and is treated as a constant?
mortal grove
Why is the third term dervied to 0? Is it because it has no x term and is treate...
yes
hollow trail
yes, 7y^2 is a constant for the purposes of differentiating with respect to x
cedar kilnBOT
lucid escarp
How do I get this last value
hollow trail
use the x-intercept
lucid escarp
yes but idk how to use it
hollow trail
well you know that (1/4, 0) is a point on your graph
lucid escarp
is it just 1/2
hollow trail
how do you get 1/2?
lucid escarp
so how should i approach this
hollow trail
plug in x = 1/4, and set your function equal to 0
because x = 1/4, y = 0 is a point on your function
lucid escarp
How do I get this last value
do i keep my placeholder y in that process
like as a variable
hollow trail
maybe you should call it something else, but you are trying to solve for it
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compact quest
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heady gate
Hm
cedar kilnBOT
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orchid jewel
what does defines the function mean?
cedar kilnBOT
what does defines the function mean?
south tundra
In this case it means which equation describes the assignment rule of f, i.e., what formula does f(x) have
orchid jewel
In this case it means which equation describes the assignment rule of f, i.e., w...
does that mean the formula that draw the line in the picture is the correct answer?
south tundra
Yes, the picture shows the graph of y = f(x) and you are asked to find the f(x)
orchid jewel
Yes, the picture shows the graph of y = f(x) and you are asked to find the f(x)
is C correct?
south tundra
Yeah
orchid jewel
Yeah
it says thats not correct
Im confused about this too
this is from my SAT practice test
south tundra
Ah they are showing the graph of y = f(x) + 14, I misread that
So you need to subtract 14 from -x/4 + 2
orchid jewel
So you need to subtract 14 from -x/4 + 2
-1/4x?
south tundra
Same thing
south tundra
Again, it's not supposed to be the same
The picture shows the graph of y = f(x) + 14
orchid jewel
The picture shows the graph of y = f(x) + 14
oh so I need to get it into Y=Mx + B formula?
south tundra
Yes, and subtracting 14 from that will give you f(x)
orchid jewel
is it asking me what turns y = f(x) + 14 into Y=Mx + B formula??
if so I understand now
south tundra
Where y = mx + b gives you the given graph, yes
cedar kilnBOT
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junior stratus
cedar kilnBOT
junior stratus
How.
noble stump
how do i calculate a sum of n factorials?
junior stratus
, rotate
wraith daggerBOT
junior stratus
how do i calculate a sum of n factorials?
Wdym
slender ginkgo
do i just use gamma function?
junior stratus
It’s just rewriting
Thats the point
How
I cant conjugate or apply new terms
It comes out diff
junior stratus
It’s splitting fraction
Wait. Lemme think abt it
vague sparrow
I think of it as adding 0 in a fancy was in the numerator as: sqrt(5) - sqrt(5)
junior stratus
I think of it as adding 0 in a fancy was in the numerator as: sqrt(5) - sqrt(5)
I mean
Now why the fuck did I not think of that
vague sparrow
dont be so harsh on yourself, math has a lot of tricks
slender ginkgo
<:catshrug:563818735085944843> dont be so harsh on yourself, math has a lot of t...
true
cedar kilnBOT
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junior stratus
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stoic crystal
cedar kilnBOT
stoic crystal
Determine if the series ( \sum_{n=1}^{\infty} \left( \frac{4^n}{9^{n+1}} - \frac{3^{n+1}}{4^n} \right) ) is convergent, and if so, calculate its sum.
wraith daggerBOT
938c2cc0dcc05f2b68c4287040cfcf71
stoic crystal
,, \sum_{n=1}^{\infty} \left( \frac{4^n}{9^{n+1}} - \frac{3^{n+1}}{4^n} \right) \ \frac{1}{9}\sum_{n = 1}^{\infty} \left(\frac{4}{9}\right)^n - 3\sum_{n=1}^{\infty} \left(\frac{3}{4}\right)^n \ \textbf{I am trying to calculate the sum of the geometric series }
a1 = 1/9 x 4/9
a2 = 3 x 3/4
r1 = 4/9
r2 = 3/4
wraith daggerBOT
938c2cc0dcc05f2b68c4287040cfcf71
stoic crystal
,, \begin{cases} a_1 = \frac{1}{9} \cdot \frac{4}{9} \\ a_2 = 3 \cdot \frac{3}{4} \\ r_1 = \frac{4}{9} \\ r_2 = \frac{3}{4} \end{cases}
,, \textbf{sum of infinte geometric series} \ = \frac{a}{1-r}
stoic crystal
,, \textbf{sum :} \ \frac{1}{9} \cdot \frac{4/81}{1 - \frac{4}{9}} -3 \frac{9/4}{ 1 - \frac{3}{4}} \ = \left[\frac{1}{9} \cdot \frac{4}{81} \cdot \frac{1}{1-\frac{4}{9}} \right] - \left[3 \cdot \frac{9}{4} \cdot \frac{1}{1- \frac{3}{4}}\right] \ = \left[\frac{1}{9} \cdot \frac{4}{81} \cdot \frac{9}{5} \right] - \left[ 3 \cdot \frac{9}{4} \cdot 4 \right] \ = \left[ \frac{4}{81} \cdot \frac{1}{5} \right] - \left[3 \cdot 9 \right] \ = \frac{4}{81 \cdot 5} - 27 = - \frac{10931}{405}
,, \textbf{Auxiliary Calculation 1: } \ \frac{1}{1 - \frac{4}{9}} = \frac{9}{5} \ \textbf{Auxiliary Calculation 2: } \ \frac{1}{1-\frac{3}{4}} = 4
wraith daggerBOT
938c2cc0dcc05f2b68c4287040cfcf71
stoic crystal
,calc -401/45
wraith daggerBOT
Result:
-8.9111111111111
@stoic crystal Has your question been resolved?
cedar kilnBOT
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dreamy void
,w Sum[(4^n/9^(n+1)-3^(n+1)/4^n),{n,1,inf}]
wraith daggerBOT
dreamy void
,calc 4/81 * (1/(1-4/9)) - 9/4 *(1/(1-3/4))
wraith daggerBOT
Result:
-8.9111111111111
dreamy void
**938c2cc0dcc05f2b68c4287040cfcf71**
You already multiplied 1/9 and 3 here.
Now you did it here a second time which lead to the wrong result
half glacier
hello
half glacier
need help for this
i transformed to 2sin(2x-pi/6)<=-1
x = 0+2kpi and 2pi/3 + 2kpi then idk what to do
pastel vault
x = 0+2kpi and 2pi/3 + 2kpi then idk what to do
you're nearly there but a small note
first of all, the period of this equation is pi, cause 2pi/2 = pi
so should be x = 0 + kpi and x = 2pi/3 + kpi
since 2 is positive, that means we have a normal-looking sine graph, so it increases from x = 0
(cause when x = pi/6, you get y = 0)
so we don't want the region between x = 0 and 2pi/3
we want the region between 2pi/3 and pi
so 2pi/3 + pi k <= x <= pi k is our answer, for $k \in \mathbb Z$
wraith daggerBOT
south's secret twin brother
pastel vault
since 2 is positive, that means we have a normal-looking sine graph, so it incre...
a better way is to test a value of x in (0, 2pi/3) actually
if the y value is above -1 we exclude the region
if it's below -1 we include it
we didn't have to test x = pi/6 specifically: any nice value works
half glacier
hmm
half glacier
first of all, the period of this equation is pi, cause 2pi/2 = pi
the period is pi because of the 2 in 2x ?
pastel vault
the period is pi because of the 2 in 2x ?
mhm
half glacier
i dont get why the period is pi
clear ember
i dont get why the period is pi
consider one period of sin(x)
which has a period of 2pi
half glacier
yes
clear ember
sin(2x) is sin(x) but compressed
so whatever that used to happen at pi (for example)
now happens at pi/2
so the whole "cycle" is just half of what it used to be
half glacier
yeah so the period is pi because of the 2 in 2x ?
clear ember
yeah so the period is pi because of the 2 in 2x ?
i mean yes
if you're concerned with the formula
wraith daggerBOT
mmmm7
half glacier
yeah whats the formula
clear ember
the period = 2pi/(coefficient of x) or 2pi/b
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proven stirrup
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proven stirrup
<@&286206848099549185>
the function isnt surjective right so does that mean that the inverted funciton doesnt exist?
cedar kilnBOT
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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
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cedar rampart
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gray sleet
Each different letter in this addition problem stands for a different digit. A letter stands for the same digit everywhere it appears. Find the value of TEST. HE+SET+THE = TEST
cedar kilnBOT
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proven stirrup
Each different letter in this addition problem stands for a different digit. A l...
?
isnt there anyone who is sure of an answer
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velvet mauve
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velvet mauve
Look at 3a, i have the vertical and horizontal asymptotes
As well as the x and y intercepts
But im confused on how to actually graph the function
Could someone explain it to me?
cedar kilnBOT
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signal grail
Hello, everyone,
Could anyone please help me out to understand, is it possible to complete this task without plotting ? I dont really want to relay only on plotting, I hope there is some algebraic way to complete this
cedar kilnBOT
Hello, everyone,
Could anyone please help me out to understand, is it possible t...
@signal grail Has your question been resolved?
signal grail
<@&286206848099549185>
vivid wadi
as 9 is part of the domain, it should be continuous at 9, but the limit as x approaches 9 of f(x) from the left is different from the limit as it approaches from the right
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sturdy parcel
<@&286206848099549185> can u guys explain proportionality to me?
versed nova
We model a speed control system for a bicycle using a chain, a front sprocket (P) with a radius R = 10 cm, and several rear sprockets (P₁) with different radii r₁ between 2 cm and 8 cm. The front and rear sprockets are connected by a non-slip chain. (See Figure 1)
- Let ω be the angular velocity of the front sprocket (P) and ω₁ the angular velocity of a rear sprocket (P₁) with radius r₁.
Show that: ω₁ = (R/r₁)ω (1 pt) - 2.1. Calculate the number of turns n₁ made by the rear sprocket P₁ with radius r₁ = 2 cm when the front sprocket makes one turn.
2.2. Let nᵢ be the number of turns made by the rear sprocket (Pᵢ) with radius rᵢ corresponding to the maximum value of rᵢ. Calculate nᵢ
versed nova
<@&286206848099549185>
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versed nova
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celest seal
please dont ping mods for math help
have you considered posting what you've tried and where you're stuck so people know how to help you?
dark mason
Need help with induction proof.
dark mason
<@&286206848099549185>
cedar kilnBOT
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ancient vector
cedar kilnBOT
ancient vector
How to proceed?
hollow trail
are there any simplifications you could apply to the numerator?
ancient vector
I'm trying to cancel out the h on the bottom but unsure what to do
Can't just shove in 0
It's been a while since I used this method. Totally forget what I can do
hollow trail
ok well are there any subtractions that might be performed?
ancient vector
Not sure what ur asking to be honest
hollow trail
if i had 3 + x - 3, could you simplify that?
ancient vector
I think I need to do something to top n bottom
Ok simplify
Multiply top n bottom by conjugate?
hollow trail
great 👍
ancient vector
.close
cedar kilnBOT
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cursive perch
Trig questions, How would you solve this question? I don't understand what ratio to use since its not a right angle triangle
crimson sedge
Hello is this the right chat to ask statistics questions? Please educate me
dreamy void
Hello is this the right chat to ask statistics questions? Please educate me
too late
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crimson sedge
Can someone please help me with my assignment?
cedar kilnBOT
Can someone please help me with my assignment?
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).
vivid radish
Trig questions, How would you solve this question? I don't understand what ratio...
How to find the area of triangle using sin?
cursive perch
How to find the area of triangle using sin?
Idk how to solve 😭 Im just stuck, i need help understanding how to solve it
vivid radish
cedar kilnBOT
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calm trail
When water freezes, its volume increases by 10.1%. a) If 150 L of water freezes, what is the increase in volume? b) Estimate the original volume of water frozen if the increase in volume is 22 L.
merry solstice
<@&286206848099549185>
which part
calm trail
b)
b) Estimate the original volume of water frozen if the increase in volume is 22 L.
merry solstice
let the amount of water be X
calm trail
ok
merry solstice
we knnow it expands by 10.1%
calm trail
ye
merry solstice
<@&286206848099549185>
we can write a same equation
but substitute 150 as x cause it's given
150+10.1%*150=(volume)
volume=16.51
calm trail
Isnt the increase of volume 15.15?
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@calm trail Has your question been resolved?
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@calm trail Has your question been resolved?
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oak kayak
S
swift badger
hello.
oak kayak
How do I express this quadratic step by step into vertex form?
mossy cloud
How do I express this quadratic step by step into vertex form?
vertex form ?
i'm sorry im french so our expressions are different
oh you mean la forme canonique ?
oak kayak
vertex form ?
Yes
oak kayak
oh you mean *la forme canonique* ?
What
dense grove
How do I express this quadratic step by step into vertex form?
Completing the square?
mossy cloud
mossy cloud
@oak kayak
mossy cloud
i forgor a parenthesis on the 3rd line too
cedar kilnBOT
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echo timber
need help
echo timber
Pick 2 coordinates apply the formula
Whats the slope?
vivid wadi
Whats the slope?
a measure of how upwards or downwards a line is pointing, basically its steepness
it's calculated with rise/run
where rise is change in y and run is change in x
echo timber
5 and 7?
vivid wadi
m=y2-y1/x2-x1
and use the formula
echo timber
0,5 and 7,0
Yes
vivid wadi
vivid wadi
you can use this point
onyx reef
Apply the formula
cedar kilnBOT
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lone lagoon
cedar kilnBOT
lone lagoon
I'm stuck with this one.
urban pulsar
What do you need to find
lone lagoon
Well, I get 7/√35* √5
And the problem is, yeah, I can replace that with √7*5
BUT THAT'S NOT A NOTABLE ANGLE!
urban pulsar
I am working
urban pulsar
7 cannot be cancelled with √7
7 equals root 7*root 7
crude quest
yes what formula are you using?
urban pulsar
0.490883 radian
lone lagoon
yes what formula are you using?
Cos= (V x U)/|V| x |U|
crude quest
wouldnt it be dot product, not cross
lone lagoon
Based
Yeah.
afaik, it would be dot product
mostly because
the formula is based on doc product
Cross code doesn't involve cos, so you wouldn't be able to use the
urban pulsar
You can do it with cross also if you use sin
crude quest
yeah but its easier to do it with dot
crude quest
ud prolly just leave it as a function of arccos if u cant use a calculator tho
im assuming on an exam
lone lagoon
Yeah.
@urban pulsar are derivates and primitives and integrals going to kill me
=[
lone lagoon
BASED
cedar kilnBOT
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onyx pollen
if $X$ and $Y$ are banach spaces is the closed and bounded ball ${\Lambda\in B(X,Y)|,||\Lambda||\leq M}$ compact
wraith daggerBOT
goat
onyx pollen
i think this follows from banach steinhaus but im not sure
if not true in general then what about the case where Y=C so we are looking at a ball in the dual of some banach space (especially an Lp space)
real analysis is so hard
dire geode
Try uhhh #real-complex-analysis or #advanced-analysis
dire geode
And that's because you asked generically where to ask questions
onyx pollen
okay
onyx pollen
**goat**
<@&286206848099549185> it has been 15 minutes this is my 15 minute ping to <@&286206848099549185> please help me with this problem
feral ice
¿Qué onda?
onyx pollen
¿Qué onda?
i only speak english sorry
pallid knoll
What can I help you with?
onyx pollen
What can I help you with?
if $X$ and $Y$ are banach spaces is the closed and bounded ball ${\Lambda\in B(X,Y)|,||\Lambda||\leq M}$ compact
wraith daggerBOT
goat
pallid knoll
Oh shit
onyx pollen
basically does bounded imply totally bounded in this setting? if not what about when we require Y=C or Y=R or X=Lp
i think it should follow from banach steinhaus but im not sure
pallid knoll
What area of math is this?
onyx pollen
calculus
im kidding its real analysis
but people told me real analysis is meant to just be calculus so this is probably just calculus eventually
pallid knoll
The first calc class in my uni program had a little real analysis sprinkled in
onyx pollen
this class is real analysis class
but my friend told me real analysis is just calculus
pallid knoll
but people told me real analysis is meant to just be calculus so this is probabl...
so I agree w this
onyx pollen
so maybe my calculus class just didnt do enough
because i dont remember learning about bounded operators in calculus
but i also skipped calculus 1 so maybe thats where you learn it
pallid knoll
bruh first time even hearing that word
onyx pollen
no nevermind heine borel is just Rn
pallid knoll
isn’t real analysis usually associated with like PhD studies?
like one of the final bosses of math
onyx pollen
i dont know im in this class because my friend told me its easy
basically just calculus
<@&286206848099549185> it has been 15 minutes again
swift badger
wsp
arctic hare
fr
onyx pollen
wsp
if $X$ and $Y$ are banach spaces is the closed and bounded ball ${\Lambda\in B(X,Y)|,||\Lambda||\leq M}$ compact
wraith daggerBOT
goat
round nacelle
isn’t real analysis usually associated with like PhD studies?
real analysis is undergraduate level. it's the first proof-heavy class math students take, unless their school adds proofs to linear algebra, discrete math, or has a dedicated intro to proofs class.
cedar kilnBOT
@onyx pollen Has your question been resolved?
onyx pollen
<@1293262180195504191> Has your question been resolved?
not yet
no it hasnt been resolved yet
<@&286206848099549185> another 15 minutes
onyx pollen
wsp*
if $X$ and $Y$ are banach spaces is the closed and bounded ball ${\Lambda\in B(X,Y)|,||\Lambda||\leq M}$ compact
wraith daggerBOT
goat
onyx pollen
it doesnt hold in general metric spaces i know but is it false in all infinte dimensional spaces
swift badger
idk what else t say
cedar kilnBOT
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brisk shell
Can someone help me with this question pls is it just trial and error if so I’ve found 4 solutions do you think that’s all of the possible solutions?
brisk shell
<@&286206848099549185>
jovial marlin
what a weird question, what is this class called?
and by weird question i mean the M4 question. not ur question of asking for help
austere dune
!status
cedar kilnBOT
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
ngl I have never seen a question ask about the correct decimal place of some number in an addition problem
brisk shell
Oh alr
jovial marlin
its such a weird question to ask someone
brisk shell
True ig
jovial marlin
sorry chief, I hope someone else can help u out
brisk shell
Ty anyway
crimson sedge
Can someone help me with this question pls is it just trial and error if so I’ve...
What’s your solution
(This is really just trial and error)
brisk shell
It’s not rly a proper solution I just did trial and error and got
Oh okay ty
I’ll send it now
1 second
jovial marlin
What’s your solution
im trying to see if there is a way to solve it without iterations
jovial marlin
hmm
oo nvm i misinterprete dthe question
oof
i was thinking that one decimal is incorrect and u need to change only one of them, not 4 out of the five
cedar kilnBOT
@brisk shell Has your question been resolved?
jovial marlin
in class did u learn anything that could help u solve this? have u done similar problems before? I feel like there should be a way to solve this without brute forcing it
dire geode
,rotate
wraith daggerBOT
dire geode
pain
austere dune
<@&286206848099549185>
arctic hare
what seems to be the problem
austere dune
read the prev msg
arctic hare
'couldnt find an attached image in the last 10 messages'
austere dune
Can someone help me with this question pls is it just trial and error if so I’ve...
^^^ 😭
arctic hare
oh damn thats long ago
austere dune
ye
arctic hare
Can someone help me with this question pls is it just trial and error if so I’ve...
well first of all
the answer will have 3 decimal places not 2
austere dune
there r multiple answers
but is there any other way to approach this question without using brute forcing
?
austere dune
there has to be bcuz i think there r abt 576 combinations where u can switch the decimal places around
using combinatorics
arctic hare
uh
austere dune
and i don't think brute forcing is an efficient way
arctic hare
actually waait no its not gonna be 3 decimal places the decimal in 38.627 is wrong should be 386.27
austere dune
it can also be 3.8627
arctic hare
i doubt it
wait maybe not
there is infact a lot of ways to do this
wait no
it HAS to be 386.27
right???
yes
wait or the 4000 one
im confsuing myself
but also only 386.27 is the decimal assuming 4508.57 is the correct decimal
or vice versa
im gonna stop talikng
jovial marlin
This question is soo weird
I cant find an easy way to solve it without brute forcing it by guessing and checking
Sorry that i couldnt help :<
shy ice
Maybe go through the ways for each of the 4 cases where one is the correct decimal, so eg find out the ways when the 1st is the correct, then the 2nd, then 3rd then 4th. So considering the case where the 1st is correct, you can just add it on to the result (4508.57+47.5=4556.07) and then work out the possible shifts in the other 3. Then do the same for rest. I guess this doesn't really explain how to find all the ways without trial and error but it at least simplifies it a bit.
jovial marlin
for the higher math helpers that want to take a crack at the problem. I generalized the problem and got the following
where chi and C are just some constants that we can determine based on the given starting numbers of the question
so essentially the problem becomes solving for each n in this part of the math, since we know what each x and what C is. (also each n is an integer and represents the number of digits u need to shift each decmial point)
I cannot find a way to solve this without guessing and checking
I don't think it's possible to solve this question without brute force
@brisk shell u don't have to follow what I just did there, im using more advanced tools to solve the problem so other higher math people can see it better at a glance
hopefully someone can see this and maybe come up with a solution that doesnt involve guessing
<@&286206848099549185>
do u know what textbook/workbook this problem came from? I wana figure out what the purpose of this question is
also technically from what I see there are technically inifnite ways to shift the decimals for 4 of the numbers to make the sum work out x.x
so i really don't know what the prof wants you to do here
cedar kilnBOT
@brisk shell Has your question been resolved?
cedar kilnBOT
austere dune
.reopen
cedar kilnBOT
Available help channel!
austere dune
Can someone help me with this question pls is it just trial and error if so I’ve...
^^^ <@&286206848099549185>
cedar kilnBOT
@austere dune Has your question been resolved?
cedar kilnBOT
@austere dune Has your question been resolved?
austere dune
<@&286206848099549185>
crimson sedge
You are cheating. <@1277260016725917859>
Caught in 4k 😭
cedar kilnBOT
@austere dune Has your question been resolved?
crimson sedge
hey yall i got a quick question on where I can find a video on this to help me out or someone to explain it to me
crimson sedge
some examples
i have a test tmmrow and i was sick for a long time so I wasnt able to study, so some quick help would be appreciated
i actually prefer video format because i learn better that way
end behavior of piecewise functions is the topic
crimson sedge
end behavior of piecewise functions is the topic
right but the functions are set up in a weirder way
so im confused
ye
those are piece wise functions
basically, different x-value domains have different functions associated with them
based on your limit, you need to figure out which function you need to use
for example in the first one, you would 1/(x+2) for the limit to -infinity and 1/(x-2) for the limit to +infinity
does that make sense?
cedar kilnBOT
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cedar kilnBOT
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bitter lily
im doing this question, but im kinda stuck,
i know i have to use Pythagorus theorem but im just unsure on how to do the equation
i dont want to use ai to help me, i just need someone to explain how i would do this so i understand and can do this equation fluently
cedar kilnBOT
im doing this question, but im kinda stuck,
i know i have to use Pythagorus th...
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).
bleak viper
im doing this question, but im kinda stuck,
i know i have to use Pythagorus th...
where are u stuck
2 triangles
use pythagoras theorem for each
bitter lily
do i need to do 14m for the base or just their respective bases?
bleak viper
respective bases
oblique flare
do i need to do 14m for the base or just their respective bases?
you can put a point D that is 5m from C and 9m from A
bitter lily
respective bases
so for BC it would be (12)v2 + (9)v2
bitter lily
you can put a point D that is 5m from C and 9m from A
oh yeah your right
wraith daggerBOT
Astar777
cedar kilnBOT
thank you guys
If you are done with this channel, please mark your problem as solved by typing .close
bitter lily
.close
rough scroll
Hello! I'm currently working on a Trig question for my pre calculus 11 course and am unsure of how to solve this specific question (it is using Sine/Cosine law). I apologize for my photo being a bit low quality! I cannot figure out how to find X for this equation.
crimson sedge
Hello! I'm currently working on a Trig question for my pre calculus 11 course an...
what was the original information given?
seems to be a law of cosines problem though
rough scroll
what was the original information given?
This is the original information it is just written small so I wrote over it so it was more legible:).
crimson sedge
o ok cool
rough scroll
The only text given is to determine the length of X
I figured it was Cosine law but I am unsure of how to input the information into the formula with how the question is set up if that makes sense?
crimson sedge
The only text given is to determine the length of X
does it say x = 6?
bleak viper
i think thats b
rough scroll
small b, I apologize for my handwriting
crimson sedge
ah okay mb
rough scroll
Its ok!
rough scroll
LMAO thats evil😭
crimson sedge
yea 1 sec
rough scroll
All good! Take your time:)
rough scroll
Yes
rough scroll
That makes sense! I guess my only question would be how you got the angle for B?
crimson sedge
well
angles in a triangle add up to 180 and since you already have 2 the 3rd is easy to find
rough scroll
okok! that makes sense, thank you!:)
crimson sedge
perfect
rough scroll
I seem to have forgotten that...
crimson sedge
ye all good
rough scroll
I appreciate your help:)
cedar kilnBOT
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woeful flower
Can anyone explain to me on how to do this?
cedar kilnBOT
Can anyone explain to me on how to do this?
clear umbra
Can anyone explain to me on how to do this?
modal class?
cedar kilnBOT
@woeful flower Has your question been resolved?
woeful flower
modal class?
Yes
clear umbra
then find which class has the most data
ebon grove
how did we figure out the point of intersection?
cedar kilnBOT
how did we figure out the point of intersection?
hollow trail
solve for y in the equation above, then plug in to one of the curves to solve for x
ebon grove
solve for y in the equation above, then plug in to one of the curves to solve fo...
why are they the poitns of intersection tho
mighty shuttle
how did we figure out the point of intersection?
Is is stewarts;s calculus?
ebon grove
Is is stewarts;s calculus?
yea the appendix
mighty shuttle
yea the appendix
cool
cedar kilnBOT
Available help channel!
vernal sentinel
"a) find the number of ways in which alvaro can paint his back door and his front door in a different colour if he has 14 colours of paint to choose from.
b) in how many ways could alvaro do this if he also considered painting them the same colour?"
guys, for b, why is the answer 14^2 = 196? i don't understand why we need to square it
pulsar lily
14 choices for the front door, 14 choices for the back door, and the choices are independent
worn olive
For a:
Alvaro has 14 options for painting his back door. When it comes to painting his front door, he can choose any of the other 13 colours, except for the one he painted the back door with.
He has 14 different ways to paint the front door, and then 13 ways to paint the back door. So together, there's 14x13 total arrangements.
For b:
It's very similar, but since it allows repetition (the same colour on both doors), we don't have to take away the option we painted the first door with. Therefore, Alvaro has 14 ways to paint the front door, and 14 ways to paint the back door. That's 14x14 total arrangements
So the question doesn't usually prompt you to square anything, but in this case the total number of arrangements is just equal to 14^2
@vernal sentinel
vernal sentinel
OHHH
vernal sentinel
For b:
It's very similar, but since it allows repetition (the same colour on b...
thank you so much
vernal sentinel
14 choices for the front door, 14 choices for the back door, and the choices are...
thank youu
worn olive
!! you're okay !!
vernal sentinel
i understand it now
worn olive
good!
vernal sentinel
i always stick with using nPr without knowing the reason
worn olive
Yeah, that's one of the only types of questions where you can't use nPr haha
worn olive
Or I suppose you could do (14P1)^2 😆
vernal sentinel
"find how many of the arrangements of four letters from A, B, C, D, E and F contain the letter A"
vernal sentinel
Or I suppose you could do (14P1)^2 😆
oh well 😭
vernal sentinel
"find how many of the arrangements of four letters from A, B, C, D, E and F cont...
why is it 6P4*4/6 = 240
worn olive
So, the way I see it:
-. -. -. -.
That's your four options.
For the first, you have 6 choices
For the second, five choices
For the third, four choices
For the fourth, three choices
Hence 6P4
But since there's 6 letters and 4 spaces, one particular letter will only be chosen 4/6 (= 2/3) of the time
Or, putting it another way: Since there is 2/3 the amount of spaces compared to letters, a specific letter will only be in 2/3 the total number of arrangements
vernal sentinel
Or, putting it another way: Since there is 2/3 the amount of spaces compared to ...
wait i don't understand this
worn olive
Okay what about this:
Let's find the total number of arrangements. That's 6P4=360.
Now, let's remove A and put it to the side for now. That leaves us with {B, C, D, E, F}. We're going to arrange those five letters into the same four spaces
Let's find the total number of arrangements for those letters:
For the first space, you have 5 choices
For the second space, you have 4 choices
For the third space, you have 3 choices
For the fourth space, you have 2 choices
So that's 5P4, which is 120.
360 (total number of arrangements) - 120 (total number of arrangements when excluding the letter A) = 240 (total number of arrangements that include the letter A)
vernal sentinel
OHH I UNDERSTANDDD
vernal sentinel
360 (total number of arrangements) - 120 (total number of arrangements when excl...
THANKYOU SO MUCH
vernal sentinel
(Don't worry I hated permutations when I was in high school)
HAHAHAH thanks for this 
worn olive
All good, hopefully that helps you
vernal sentinel
helped me alottt
worn olive
good to hear!
cedar kilnBOT
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Available help channel!
analog jackal
Given a geometric series with the 2nd term = 6 and the sum to infinity = 18. Determine the sum of the first 4 terms.
Can someone help? How are you supposed to use infinity in a math question???
pastel vault
Given a geometric series with the 2nd term = 6 and the sum to infinity = 18. Det...
oh sum to infinity = a/(1 - r)
analog jackal
oh sum to infinity = a/(1 - r)
a usually means the 1st term right?
pastel vault
a usually means the 1st term right?
yes
pastel vault
how are you supposed to find the first term using the ones at the top though?
well you have the system of equations $ar = 6$ and $\frac{a}{1 - r} = 18$
wraith daggerBOT
south's secret twin brother
pastel vault
try subbing in the 1st equation into the 2nd
(you need to rearrange the 1st equation to isolate a variable)
analog jackal
try subbing in the 1st equation into the 2nd
sorry, could you explain more?
pastel vault
sorry, could you explain more?
sub $a = \frac{6}{r}$ and you get $\frac{6/r}{1 - r} = 18$
or $6 = 18r(1 - r)$
wraith daggerBOT
south's secret twin brother
pastel vault
this is a quadratic!
now expand and solve for r
then you can find a
then the sum of the first 4 terms is $a + ar + ar^2 + ar^3 = \frac{a (1 - r^4)}{1 - r}$
wraith daggerBOT
south's secret twin brother
analog jackal
then the sum of the first 4 terms is $a + ar + ar^2 + ar^3 = \frac{a (1 - r^4)}{...
but sicne I still don't know what a is, how am i supposed to solve it
pastel vault
but sicne I still don't know what a is, how am i supposed to solve it
you need to solve for r first ofc
analog jackal
you need to solve for r first ofc
Ohhhh so r = 1/2 then how to find a
pastel vault
Ohhhh so r = 1/2 then how to find a
then a = 6/r remember
analog jackal
then a = 6/r remember
so 12?
pastel vault
Given a geometric series with the 2nd term = 6 and the sum to infinity = 18. Det...
,w a/(1-r)=18, ar=6
there's a problem with the question
wraith daggerBOT
analog jackal
???
pastel vault
???
yeah the question gives impossible values
impossible values as in not real numbers
analog jackal
impossible values as in not real numbers
then its unsolvable?
pastel vault
then its unsolvable?
yeah
cedar kilnBOT
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worn olive
I'm on the last question. Unsure as to what to do next.
cedar kilnBOT
I'm on the last question. Unsure as to what to do next.
worn olive
This is what I've got
cedar kilnBOT
@worn olive Has your question been resolved?
worn olive
<@&286206848099549185>
cedar kilnBOT
@worn olive Has your question been resolved?
cedar kilnBOT
@worn olive Has your question been resolved?
tardy remnant
cedar kilnBOT
@worn olive Has your question been resolved?
floral narwhal
Hi, i had a question my friend taught me to solve ( find x) this and he said the first step was to discard everything under the line (x + 5).
Is that true
fair geyser
maybe
he's saying that's the first step of his method, it's possible
he's just not mistaken about his own method
floral narwhal
yeah and then just solving the y = 4 * x + 1
floral narwhal
he's saying that's the first step of his method, it's possible
well, idk if its good to discard that, wouldnt it be relevant
fair geyser
maybe he introduces it back at sme point
floral narwhal
nah he just said it doesnt matter
fair geyser
ok tell him i said it's not true
floral narwhal
what would be the appropriate method
mental trail
If you're solving for (4x+1)/(x+5) = 0, then in THAT case the only way is for the numerator to be 0, so you would have 4x+1 = 0
when the other side is different from 0, you can't disregard the denominator
if you want to "get rid of" the denominator, you have to multiply it out on both sides
as for example (4x+1)/(x+5) = y
getting rid of the denominator means multiplying by it, so let's multiply both sides by x+5:
(x+5) * (4x+1)/(x+5) = (x+5)y
4x+1 = (x+5)y
then I'm assuming you want to solve for x, so now we can isolate x
so (.....) * x = ....
and the rest is hopefully straightforward
brave nimbus
Hi, i had a question my friend taught me to solve ( find x) this and he said the...
Is the numerator (4 multiplied by x) + 1 ? Or is it 4 multiplied by x+1 ?
mental trail
Is the numerator (4 multiplied by x) + 1 ? Or is it 4 multiplied by x+1 ?
PEMDAS/BODMAS says it's (4x) + 1
of course not accounting for potential omission of parentheses
formal nest
is t and 1/t linearly independant ?
cedar kilnBOT
is t and 1/t linearly independant ?
formal nest
the wronskian = -1/t^2
so yea they are
but k1 t + k2 1/t = 0
when k1=1 and k2=-1 with x=1 gives zero
mental trail
when k1=1 and k2=-1 with x=1 gives zero
so you found k1 and k2 that work for ONE value of x
but is the FUNCTION k1 t + k2 1/t equal to the zero function?
formal nest
i dont understand
formal nest
so you found k1 and k2 that work for ONE value of x
that means they are dependant
mental trail
is k1 t + k2 1/t = 0 for every t
formal nest
it has to be for every t ?
mental trail
well yeah
formal nest
hmm
mental trail
they're linearly independent functions
meaning any non-zero linear combination of the FUNCTIONS
will give you a function that isn't the 0 function
the 0 function being 0(x) = 0 for every x
formal nest
so its not the same thing as for vectors ?
mental trail
so its not the same thing as for vectors ?
it is the same thing as for vectors
functions are vectors
but for two vectors to be linearly independent
formal nest
when k1=1 and k2=-1 with x=1 gives zero
then what does this prouve
mental trail
then what does this prouve
same way it proves that in 2 dimensions for example, A = (1,1) and B = (1,2), for k1 = 1 and k2 = -1 we have that k1A + k2B has a zero coordinate
does this make k1A + k2B the zero vector?
formal nest
same way it proves that in 2 dimensions for example, A = (1,1) and B = (1,2), fo...
its not the zero function
it gives (0,-1)
mental trail
yup
formal nest
OOOOOOOO
mental trail
so just because you looked at the first coordinate and it was 0
doesn't make the whole thing the 0 vector
mental trail
yep
the wronskian already tells you if f and g are LI or not
if the wronskian is 0 anywhere, it's 0 everywhere and the functions aren't LI
otherwise, f and g are LI
meaning that for any k1 and k2
k1f + k2g cannot be the zero function (zero vector), except if k1 = k2 = 0
cedar kilnBOT
@formal nest Has your question been resolved?
wise galleon
is there a way to compress multiple numbers into one number and add something to it, a set of instructions as it were on how to decompress the numbers, like taking 209, 151, 102, adding them to get 462 and tacking on another number that can tell you how to get the original numbers from the 462?
distant kite
That's an encryption
distant kite
is there a way to compress multiple numbers into one number and add something to...
Not really I think, but you can create one, lol
wise galleon
if they were primes it would be super easy, but they can be any number
<@&286206848099549185>
cedar kilnBOT
@wise galleon Has your question been resolved?
languid forum
there's a GitHub for that in python, but I don't remember the name fuck
where they help you to convert à list of number into an encryption
cedar kilnBOT
@wise galleon Has your question been resolved?
cedar kilnBOT
@wise galleon Has your question been resolved?
potent fractal
is there a way to compress multiple numbers into one number and add something to...
Mathematically it's possible, because all finite sequences of integers form a countable set. In other words, you can assign a unique number to any finite sequence of integers
All elements of $\mathbb{Z}^n$ can be enumerated by "walking in spirals" from the origin (a common argument that is often used to prove that $\mathbb{Q}$ is countable, for example)
Denote $s_{n,k}$ the $k$-th element of $\mathbb{Z}^n$. We can write all $s_{n,k}$ in an infinite table like so:
$$s_{1,1} \ s_{1,2} \ s_{1,3} \ \dots$$
$$s_{2,1} \ s_{2,2} \ s_{2,3} \ \dots$$
$$s_{3,1} \ s_{3,2} \ s_{3,3} \ \dots$$
We can then repeat the spiral argument and assign a unique number to each $s_{n,k}$.
wraith daggerBOT
EQUENOS
potent fractal
However, this is far from a good algorithm. A more adequate approach in programming involves the fact that integers in applications are typically bounded
I'm pretty sure there're multiple efficient algorithms for different applications
wise galleon
so like find -or design- an algorithm that can assign single numbers to a whole set of numbers?
crimson sedge
cedar kilnBOT
crimson sedge
The directions are: “you are given the explicit formula for an arithmetic sequence. Find the first 3 terms of the sequence and the term named in the problem.
I know this is probably easy but i forgot
slender ginkgo
just plug n in
crimson sedge
?
celest void
sub 34 for n
celest void
lol
crimson sedge
thank you
celest void
np
spice jungle
how do i find the derivative of a function? like how does x² become 2x?
rare vault
how do i find the derivative of a function? like how does x² become 2x?
hello voiced velar approximant, almost as good as the voiced bilabial approximant. In this case, you apply something called the "power rule"
in general, there are a bunch of identities you can apply to find derivatives, but they are all fundementally from the "limit definition of the derivative"
spice jungle
in general, there are a bunch of identities you can apply to find derivatives, b...
cool, where can i learn them?
pseudo merlin
yt
spice jungle
nice
rare vault
first result is this, and it has a few useful ones
spice jungle
thank you so much
rare vault
you are ɰelcome
spice jungle
.close
cedar kilnBOT
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rare oasis
I want to solve the DE 1/2 y'' + 9/2 y = cos 3t. We get the complimentary solution y = a cos 3t + b sin 3t.
Variation of parameters is inconvenient to use for this problem, and I want to solve it with the annihilator method, but the annihilator for cos(3t) is D^2 + 9.
We rewrite the DE as y'' + 9y = 2 cos (3t)
When we multiply the annihilator to both sides of the DE we get (D^2 + 9)(D^2 + 9) y = 0.
I don't think I obtain any information about the form of the particular solution from the new DE, since the new roots introduced by the annihilator in the characteristic equation are the same as the roots that form the complimentary solution. Or, do I proceed with the repeated complex roots similar to repeated real roots? That is, is the solution to the new DE
y = a cos(3t) + b sin(3t) + c t cos(3t) + d t sin(3t) ?
If this does work, do I always proceed with repeated complex roots by multiplying on an extra t for each time it repeats?
cedar kilnBOT
I want to solve the DE 1/2 y'' + 9/2 y = cos 3t. We get the complimentary soluti...
@rare oasis Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
ocean robin
Where Do I start
cedar kilnBOT
Where Do I start
ocean robin
Work so far
