$\f{(-1)^\f{n+1}*10}{10^n}$
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lunar lintel
ocean sealBOT
Hoesmad
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fringe sleet
and you can rewrite $(-1)^{n+1}$ to $(-1)^{n-1}$
ocean sealBOT
Duh Hello
lunar lintel
$\f{-1^(n+1)}*10}{10^n}$
ocean sealBOT
Hoesmad
Compile Error! Click the reaction for more information.
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fringe sleet
then you have same exponent on both and can put them under the same one and use geometric series from there
ocean sealBOT
Hoesmad
Compile Error! Click the reaction for more information.
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fringe sleet
$\frac{(-1)^{n+1}*10}{10^n}$
ocean sealBOT
Duh Hello
fringe sleet
you dont have the \f shortcut
lunar lintel
oh lol
lunar lintel
**Duh Hello**
ok so this is the same thing no?
fringe sleet
yeah it is, you wanna get it on geometric form tho
fringe sleet
only reason to use ast is to prove that it converges
fringe sleet
to find what the sum is you need to use geometric series sum
lunar lintel
yea ok
fringe sleet
its just a collorary to the fact that it converges and at some point the remainder must be less than the next term
lunar lintel
yea
fringe sleet
something along those lines
dont really know this theorem, i guess you could use it to find which n that is true for. not sure how to do it, i just saw that this is a geometric series so you can use that instead
oh wait, seems it holds for all n
so its just find the first n where $a_{n+1}\leq 10^{-6}$
ocean sealBOT
Duh Hello
fringe sleet
ok nvm yeah is see what you are supposed to do. much faster than using geometric series
then you just use the $A_n$ you found to solve this inequality
ocean sealBOT
Duh Hello
fringe sleet
**Duh Hello**
yeah, then use this
i got really confused about what you were writing here. seems like you were using eulers number and it was $A_n+1$ and not $A_{n+1}$
ocean sealBOT
Duh Hello
fringe sleet
so i thought you wrote $A_n+1=e^{-6}$ and i couldnt see the relevance to the problem lol
ocean sealBOT
Duh Hello
fringe sleet
but yeah now you just need to solve the inequality $$\f1{10^n}\leq10^{-6}$$
ocean sealBOT
Duh Hello
alpine sable
Hey, I know this might be a bit too simple math, but does anybody know accounting mathematics here?
alpine sable
Problem isn't with the actual math, but rather with what accounts to enter n stuff
.close
vast arrow
lone heartBOT
vast arrow
now I would like help sovling this however do want to try it on my own
for question A on this do I just subsitute for the value of 0
or since the function has the population for doubling every 3 months I need to adjust it for 8
modern sedge
the function N is defined, so just plug in 0
vast arrow
gotcha
vast arrow
the function N is defined, so just plug in 0
so just to double check I got 645
would I be correct
modern sedge
so just to double check I got 645
Yep
vast arrow
cool
then for B it would represent the initial population of the rabbit breed on the small island at the time of 0 months
awesome, now I am a bit confused on C
so I do need some help here
modern sedge
Okay, do you know what solving for t means?
vast arrow
no
modern sedge
It means getting t to one side and everythin else on other side
So then you plug in e.g. N=1000 and you will see when the population reached 1000
vast arrow
hmm I kind of understand but I dont get it fully
so when setting it up I would set it up as 2000 = 645(2)^(𝑡/3)
modern sedge
Now you would set it up as N=645(2)^(t/3)
then solve for t and you would get kind of function of N
vast arrow
hmmm
so I would have to get t alone
and see the equation for N
Should I start off diving both sides by 645
vast arrow
so I would have log₂(𝑁/645) = log₂(2^(𝑡/3))
and then
log₂(𝑁/645) = (𝑡/3)log₂(2)
which I could simipify into
log₂(𝑁/645) = 𝑡/3
correct?
modern sedge
Yep
vast arrow
which would give me 3log₂(𝑁/645) = 𝑡
modern sedge
and thats the solution
vast arrow
nice
modern sedge
just flip the sides
vast arrow
and from here do I have to do anything
ocean sealBOT
vast arrow
ummm
hold up
let me think
would it be a equation that relates the rabbits population to that specific time
modern sedge
Keep in mind that N(t) is a function that takes time as argument and returns population
modern sedge
Well so you started with N(t) = 2000
So this would represent that at some time t the population is 2000. Which doesnt tell too much. You solved that t=4.9 approximately.
modern sedge
Yep
vast arrow
thank you so much for your help, I have one more problem that I am going to test before taking my final
I might need help but ill make another ticket once I do
.close
leaden aspen
lone heartBOT
leaden aspen
I'm failing badly at understanding how these inductions are explained....
I see why the left side becomes 2^k+1
why does the right side become 2 * k! and not (k+1)!
My first thought would be to do (k+1)! and then k!(k+1)
jagged cobalt
in the induction the assumption that 2^k<k! has been made so 2*2^k<2 k!
leaden aspen
the 2k! is tripping me up
so for this example k+1 is just dropped and then reintroduced later in the problem?
jagged cobalt
its not necessarily that its dropped, it was just reexpressed, theyre just slowly setting up inequalities that can then get to (k+1)!
leaden aspen
is there anything wrong with my approach at just saying RHS = (k+1)! ?
It just seems more in line with the process I've been practicing in my head
jagged cobalt
is there anything wrong with my approach at just saying RHS = (k+1)! ?
where?
leaden aspen
In most of the previous examples I've worked LHS = 2^k+1
I was then doing the same thing to the RHS .... (k+1)!
just increasing the iterator by 1 each time
so 2^k+1 < (k+1)!
errr
jagged cobalt
you cant just state or assume that in induction
you have to prove it with logical steps
leaden aspen
the logical step being : 22^k on the LHS and 2k! on the right?
jagged cobalt
the 2 2^k and 2k! are on the same side
but the assumption that 2^k<k! implies that 2(2^k)<2(k!)
thats a logical step that is founded in what is written before it
leaden aspen
I'm just confused why proving p(k) ---> p(k+1) is seemingly switched to proving 2 * 2^k < 2(k!)
To me these should be going like the last ones ...
2^k+1 < (k+1)!
jagged cobalt
which are shown here
it may make more sense to you if theyre written like this maybe
$2^{k+1}=2\cdot2^k<2\cdot(k!)<(k+1)k!=(k+1)!$
therefore $2^{k+1}<(k+1)!$
oops, one moment
ocean sealBOT
AℤØ
leaden aspen
I'm still really confused on why 2k! is brought into the mix
can we contrast with this example :
the IH here just goes ar^(k+1) -a / r -1 ....+ ar^k+1
A really basic question I have too is am I just working on the wrong side??? should I be showing the left equals this ?
Sorry i've been cracking at these for like a week and a half and no explanation has really set in to make them intuitive
jagged cobalt
there is no equals going on here though. ultimately youre showing 2^(k+1)<(k+1)!
the logic thats used to do the question above is ultimately the same as here but its just not the same kind of question, that is a series summation
this is proving an inequality - its not the same
jagged cobalt
**AℤØ**
the 2(k!) comes in because we assumed that 2^k<k!, theres nothing more to it then that
2^(k+1)=2(2^k)
we did that to introduce an inequality that gets built on
2(2^k)<2(k!) because 2^k<k!
2(k!)<(k+1)k! because k>=4
(k+1)k!=(k+1)!
this whole process gives you 2^(k+1)<(k+1)! which is what youre showing
leaden aspen
Thanks - I'm just really lost on these problems. Might just chalk it up to an L!
lone heartBOT
@leaden aspen Has your question been resolved?
lone heartBOT
@leaden aspen Has your question been resolved?
leaden aspen
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high wolf
How did he get dv = 1 dx?
lone heartBOT
How did he get dv = 1 dx?
high wolf
There's an imaginary 1 in front of the dx?
surreal meadow
There's an imaginary 1 in front of the dx?
a = a * 1
in general
you can always bring out a factor of 1
rocky condor
How did he get dv = 1 dx?
lol just ignore the 1
lone heartBOT
@high wolf Has your question been resolved?
high wolf
lol just ignore the 1
Okay..I was able to solve it. How would I solve a problem like this using integration by parts? Does it involve u substitution?
high wolf
assuming that's meant to say ln^2(x)
Yeah it was..but if that's the case where does integration by parts come into play?
it just seems like straight u substitution to me..
surreal meadow
i think you can do it with IBP but you can just do substitution
high wolf
not sure if im missing anything..
high wolf
i think you can do it with IBP but you can just do substitution
Thanks. Okay, this is my last last question...it's on this problem:
confused on how they got that last answer..
this is what I got:
the rectangled red part is my final answer
so somewhat close..but I didn't get 2/27cos(3x) at all..
lone heartBOT
@high wolf Has your question been resolved?
split swift
I have to make a board of the variations of f(x) but delta<0 so it’s impossible…?
lone heartBOT
I have to make a board of the variations of f(x) but delta<0 so it’s impossible…...
tacit arch
I have to make a board of the variations of f(x) but delta<0 so it’s impossible…...
what's board of variations
lunar nova
tacit arch
https://imgur.com/a/XHdvnOj
!help
lone heartBOT
https://imgur.com/a/XHdvnOj
Please read #❓how-to-get-help
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lone heartBOT
@split swift Has your question been resolved?
warped cargo
Hi, can someone help me with this pls? Im mainly confusd beceause the sf is a negative number, so I'm not sure what to do
velvet cliff
it's negative because it goes the opposite direction from the centre of enlargement
warped cargo
oh
alpine sable
What's sf
warped cargo
scale factor
warped cargo
its still wrong
oh, I drew it in the wrong pos
Where am i supposed to draw it
@alpine sable
velvet cliff
draw lines connecting each corner of the original rectangle to the centre of enlargement
the enlarged shape's corners will lie on these lines
warped cargo
How do ik how long the line should be?
velvet cliff
using the scale factor
I'll illustrate one sec
you see how after the scale factor it goes twice the distance down and to the right because it's scale factor 2
warped cargo
shouldn't it be a diag line tho, from a to center or does it not matter
velvet cliff
shouldn't it be a diag line tho, from a to center or does it not matter
it is I just didn't draw the line
that's a straight line
warped cargo
Ohhk
And then I make the shape 2 timies bigger right
hold up, how would tht fit on the page then
warped cargo
How would it fit tho
because wont the hight need to be 4 blocks?
Would the top right corner be here? @velvet cliff
velvet cliff
yes
warped cargo
But wouldn't the hight be 4, wouldn't that be off the grid?
warped cargo
because the top right corner would be at tht red dot, and the hiehgt is 4
like I'm not able to go any further
velvet cliff
it doesn't go down though
show your work
where are you getting that it goes off the grid from
the top right corner gets inverted to the bottom left corner
as it's negative scale factor
warped cargo
like this then?
velvet cliff
no
velvet cliff
that's a straight line
just do this method for every corner
before trying to do it quiclky
warped cargo
The lines
velvet cliff
yes, do the corners you drew make a straight lien going through the centre?
velvet cliff
like here
just do the same process
count how many steps you take in each direction to get form a corner to the centre and then from the centre double it
or alternatively
if the point A I constructed is the bottom left corner
from there you can make the whole rectangle
warped cargo
So wouldn't it be like this?
velvet cliff
no
velvet cliff
yes
velvet cliff
np
hollow quail
i have no clue on this, i tried use the binominal coefficient with 50 and then subtract the binomial coefficient of 48, but im not sure if is okay
lone heartBOT
i have no clue on this, i tried use the binominal coefficient with 50 and then s...
@hollow quail Has your question been resolved?
hollow quail
<@&286206848099549185>
potent garnet
so let the people be A and B
if these people are together in the council, i believe there are 7 ways to place them into the roles
(i) both are untitled which gives us 1 way
(ii) one is untitled while the other is president which gives us 2 ways
(iii) one is untitled while the other is secretary which gives us 2 ways
(iv) one is president while the other is secretary which gives us 2 ways
for (i), there are 48 * 47 * 46 ways to choose the remaing members of the council
for (ii), there are 48c2*46 ways to choose the remaing members of the council
for (iii), there are also 48c2*46 ways to choose the remaining members
for (iv), there are 48c3 ways to choose the remaing members
hence, there are 1 * 48 * 47 * 46 + 2 * 24 * 47 * 46+ 2 * 24 * 47 * 46 + 2 * 17296 ways for A and B to be together
@hollow quail do you understand this so far?
potent garnet
finally we need to subtract this from 50c5
your welcome i will let you do the computations
lone heartBOT
@hollow quail Has your question been resolved?
rustic heath
Mrs. Morco gets 12% commission for selling an education plan. How much will she receive as a commission i she sold an education plan worth 250,000$? (Solution)
sharp thorn
$250000 \times \frac{12}{100}$
ocean sealBOT
bettim
sharp thorn
$2500\cancel{00} \times \frac{12}{\cancel{100}}$
ocean sealBOT
bettim
sharp thorn
$2500 \times 12$
ocean sealBOT
bettim
sharp thorn
this i hope you can do by yourself
fervent lantern
lone heartBOT
gleaming granite
k
fervent lantern
.close
stiff badge
What method could I use to show this series converge or not?
tacit arch
Alternating series test
lone heartBOT
@stiff badge Has your question been resolved?
ivory pendant
3 please
ivory pendant
Clearer picture
ocean sealBOT
bettim
craggy spade
Can u guys know this find the X ,RO,El in this trapezoid
ivory pendant
Can u guys know this find the X ,RO,El in this trapezoid
Already took this channel big bro
craggy spade
Already took this channel big bro
Ok
ivory pendant
Like the v question
sharp thorn
yes
ivory pendant
One more thing
What would we do when we are multiplying a variable by a negative exponent fraction?
F -7/6
Nvm
ocean sealBOT
bettim
ivory pendant
What did you get for your answer?
sharp thorn
i didnt calclate
ivory pendant
I got 1.241
ocean sealBOT
sharp thorn
yes right
ivory pendant
Would I leave it as that?
sharp thorn
yes ig
ivory pendant
Because we are doing radicals and exponents
sharp thorn
no idea
ivory pendant
Thanks og
lone heartBOT
@ivory pendant Has your question been resolved?
tight sinew
lone heartBOT
whole shell
!status
lone heartBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
rough sphinx
I'm a bit confused about the proofs proving AB and BC, I tried to prove them through HL because of the right angles. But said these HL weren't proven congruent. Although SSS was in some I proved CPTC didn't count which is where I'm confused.
tight sinew
```
What step are you on?
1. I don't know where to begin
2. I have begun but got...
I got an answer but I'm told it's wrong
whole shell
I'm a bit confused about the proofs proving AB and BC, I tried to prove them thr...
!help
lone heartBOT
I'm a bit confused about the proofs proving AB and BC, I tried to prove them thr...
Please read #❓how-to-get-help
whole shell
I got an answer but I'm told it's wrong
what answer did you get
what was your working out
rough sphinx
delta math proofs
whole shell
i can see youve joined the server recently, pro tip is to not use a help channel someone else has already used
rough sphinx
just go to this
sorry, so I go to 27?
lone heartBOT
@tight sinew Has your question been resolved?
solar bridge
lone heartBOT
solar bridge
for #3, how would I separate the 28?
pseudo ice
What's the prime factorisation of 28? Do those numbers [in said prime factorisation] appear anywhere in what you're given?
peak mist
hello
peak mist
can someone explain why this works
and what is even about it and what is odd abou tit
ocean sealBOT
benevo
peak mist
i see whats the odd refeering too
quiet shadow
as far as I can tell there is an issue with the problem as for all positive n there should be an negative result when n is odd
wait no, this is correct.
peak mist
ok
quiet shadow
the reason that the limit does not have a result is that it does not converge
In this case as the approached (infinite) value cannot be assigned the even/odd property. The limit does not converge on one value with alternation between -1 and 1.
peak mist
oh so if i plug in n=1 the denominator and numerator are not going to be both even or both odd
quiet shadow
no, as the result approaches infinity odd values of n would approach -1 and even values of n approach 1.
is infinity even or odd?
peak mist
both
quiet shadow
would you like another example?
peak mist
yes please
quiet shadow
$\lim_{x \to +\infty} sin(x)$
ocean sealBOT
benevo
ocean sealBOT
benevo
quiet shadow
what about this?
peak mist
isnt it still one negative and positive but compressed
quiet shadow
could it be compressed enough to be considered one value?
peak mist
i dont see it
ocean sealBOT
benevo
peak mist
yes
quiet shadow
if we divide by some value, n...
$\frac{-1}{n} \le \frac{sin(x)}{n} \le \frac{1}{n}$
ocean sealBOT
benevo
peak mist
is this squeeze tehrom
quiet shadow
yes
peak mist
ok
quiet shadow
would you like me to continue?
peak mist
yes please
ocean sealBOT
benevo
quiet shadow
$\lim_{n \to +\infty} \frac{-1}{n} = 0$
ocean sealBOT
benevo
peak mist
i see
quiet shadow
and because the value of sine of x over x is between 0 and 0 it must also be 0
quiet shadow
of course, no problem.
broken finch
the problem states, write the inequality that shows the values of x for which the expression is defined but I dont really understand how to do it whatsoever
broken finch
um sorry I still dont really understand ;n;
vale wigeon
@alpine sable might not wanna yell?
alpine sable
<@456226577798135808> might not wanna yell?
am i being too loud
vale wigeon
you're being allcaps
@broken finch do you understand the idea of "square roots can only take nonnegative numbers as inputs"
broken finch
yeah I get that
vale wigeon
$5x^2 \geq 0$, $2x \geq 0$
you need both of these inequalities to be satisfied in order for your thing to not throw an error
ocean sealBOT
Ann
vale wigeon
5x^2 >= 0 is automatic and the other one is solved in one step
lone heartBOT
@broken finch Has your question been resolved?
storm tree
lone heartBOT
storm tree
rocky grove
storm tree
cant seem to get the correct answer
lone heartBOT
@storm tree Has your question been resolved?
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@storm tree Has your question been resolved?
lone heartBOT
@storm tree Has your question been resolved?
hardy moth
cant seem to get the correct answer
Weird, i plugged it into desmos and it looks fine to me, could it be that your syntax is wrong?
Bruh. The question states D=(3,3) but the picture clearly shows D=(3,1)
Try to do the spline again but with D=(3,3), should be fine then
(Or im misunderstanding something, but it looks like it)
lone heartBOT
@storm tree Has your question been resolved?
alpine sable
(Can some one find the surface area for the top one.) and the volume and surface area for the bottom one I haven’t been at school I got Covid and I’m back and this is due tmrw morning and it’s night right now
alpine sable
hardy moth
(Can some one find the surface area for the top one.) and the volume and surface...
!help
lone heartBOT
(Can some one find the surface area for the top one.) and the volume and surface...
Please read #❓how-to-get-help
hardy moth
Also, no one is just gonna give you the answers
fickle oyster
lone heartBOT
echo socket
Would consider simplifying $\sum_{k=2}^n(8n - 4)$
ocean sealBOT
A Lonely Bean
fickle oyster
Would consider simplifying $\sum_{k=2}^n(8n - 4)$
would this not just be 0?
cus the rest of the terms are constants
echo socket
Why would a sum of positive integers be 0?
fickle oyster
and the degree of the variable is lower on the numerator than the denominator
fickle oyster
Why would a sum of positive integers be 0?
no like the limit of the whole thing
echo socket
Then you could argue that (n^2 + n)/2n^2 is 0
Because that's the same as (n(n+1)/2)/n^2
Which is (1 + 2 + ... + n)/n^2
And this would approach 0 if such logic worked in this case
echo socket
and the degree of the variable is lower on the numerator than the denominator
You can use that when you have polynomials
Here you need to turn the nominator into a polynomial first
fickle oyster
You can use that when you have polynomials
i see
echo socket
**A Lonely Bean**
Meant 8k - 4 here, my bad
fickle oyster
Here you need to turn the nominator into a polynomial first
how do i do that?
echo socket
Rewrite that as $8\sum_{k=2}^nk - \sum_{k=2}^n4$
ocean sealBOT
A Lonely Bean
echo socket
The latter sum is simply 4(n - 1)
And the first one is 4n(n + 1) - 8
So the denominator is actually 4(n^2 - 1)
fickle oyster
wait i need some time to think about this
echo socket
Would be quicker if I applied the general formula for arithmetic sums though
fickle oyster
fickle oyster
Would be quicker if I applied the general formula for arithmetic sums though
yeah i was thinking of that
i did that
i think the answer is 4
echo socket
Yup
fickle oyster
Yup
i had to open my old notebook of such formulas for this lol
thx for the help!
.close
alpine sable
I have this ratio:
R1 : R2 : R3 = 2 : 3 : 7
Anyway, when solved, it is equal to
4 : 6 : 14 = 2 : 3 : 7
My question is why I can't do basic math with it, or what's wrong with this approach:
(4/6) / 14 = (2/3) / 7
1/21 = 2/21
when I try to calculate this, I get inequality.
fickle oyster
4 : 6 : 14 = 2 : 3 : 7
is equivalent to
4/24 + 6/24 + 14/24 = 2/12 + 3/12 + 7/12
vale wigeon
three way ratios cannot be written as fractions this way
alpine sable
So this operator between these three numbers is not really division operator, it has some different meaning?
vale wigeon
i would not really call it an operator at all
alpine sable
how would you call it?
I guess the key point that I need to understand is that the ratio between 3 or more numbers is not actually a simple division, and symbol : is misleading.
Also, for ratio of two numbers, dividing them works and makes sense.
lone heartBOT
@alpine sable Has your question been resolved?
lilac basin
how do i determine the value of y
lone heartBOT
how do i determine the value of y
gray isle
did you determine x?
lone heartBOT
@lilac basin Has your question been resolved?
lilac basin
did you determine x?
yes , x=39
mellow grail
Good
mellow grail
how do i determine the value of y
Given ED is parallel to AB
gray isle
after finding x, (supposedly you also know 2x)
y can be determine from parallel line theorems
mellow grail
So By corresponding angles (we have transversal AF), y=? @lilac basin
pearl vine
pearl vine
no
lone heartBOT
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lone heartBOT
@pearl vine Has your question been resolved?
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@pearl vine Has your question been resolved?
slate monolith
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@pearl vine Has your question been resolved?
brazen berry
lone heartBOT
lone heartBOT
Available help channel!
normal holly
lone heartBOT
normal holly
What would the equation be?
tranquil wind
1.08x = 101,520
tranquil wind
yup
normal holly
tysm
solar tapir
Remember to mark the channel as closed
molten lotus
lone heartBOT
molten lotus
I dont get how this transitioned
long axle
Which specific part do u not get
molten lotus
The first part
halcyon mesa
its basically using the power rule on the first part (see how the -1 went to the front of the function and now the exponent is -2), then using chain rule
molten lotus
I get the left part of the first part
But then the right part
It uses chain rule?
halcyon mesa
yeah so both parts are from chain rule. its taking the original function multiplied by y prime
lone heartBOT
halcyon mesa
noice. good work! :)
lone heartBOT
Available help channel!
languid bolt
f(1) = 2286, f(1) + f(2) + f(3) + ... + f(n) = n^2 f(n)
find f(2287)
languid bolt
what the hell am i supposed to do here....
tacit arch
induct? f(1) + f(2) = 2^2 f(2) and solve for f(2)
languid bolt
oh wait...
oh that was what that means
ohhhhh
i thought it meant
S_n = n^2 f(n)
well it means that
i thought we need to find. n first nvm
ok thanks
.close
lone heartBOT
languid bolt
forgot
lone heartBOT
Available help channel!
jagged timber
lone heartBOT
jagged timber
does anyone know how I can set t's max to when f(x) = 0?
so the dotted line should stop at the x intercept
solar tapir
does anyone know how I can set t's max to when f(x) = 0?
Let me review something about parabolas
Nice avatar, BTW
whole shell
@jagged timber just use the quadratic equation no?
alpine sable
Hi whoever's here I know this is kind of late tho
lone heartBOT
Hi whoever's here I know this is kind of late tho
alpine sable
but Im struggling on the 5th and final problem of a worksheet that was handed out for honors math
It's Piecewise Functions
TBH our teacher taught us it in 1 day
im still confused
ooh the resolutions bad
nevermind ill just type it out
f(x)={x if x is lesss than -2
(top line
3 if -1 is less than or equal to or less than 6
second line
last line
is
3/4
oops
3/4x-6 if x is greater than or equal to 8
that was confusing
nevermind
vapid shuttle
I can see the question
I'd recommend graphing it like this
the piecewise functions splits it into 3 regions: 1) x<-2 2) -1<=x<6 3) x>=8
so first, find out where those regions are on your graph
maybe shade them, maybe just underline each one at the bottom
so you know which is which
and then graph in each region 1 at a time
start with the first region
x<-2
alpine sable
im getting a pencil almost
vapid shuttle
in there, the function is y=x
so graph that in the region provided
and then move onto to the other two regions
you got it
alpine sable
ok
thanks
here's my question though for 3/4x-6 if x is greater than or equal to 8 it does not intercept at 8 on the x axis when moving the slope
it intercepts at 7 on the x axis
vapid shuttle
the function y=(3/4)x -6
has a x-intercept at x=8
because y=(3/4)*8 - 6 = 24/4 - 6 = 6-6 = 0
alpine sable
huh!
are you sure we're both talking about piecewise functions
because i have not seen that 0 before
anywhere
alpine sable
alright
lemme try it out first
it worked
it hit the 8 on the x axis
turns out my line was slanted to the left
and i ran over 3 instead of 4
in rise over run
thanks
vapid shuttle
no problem
alpine sable
ill ask my teacher more about the equations you gave me
but shes honestly grumpy when you ask her
goodnight
vapid shuttle
what equations?
alpine sable
the ones you texted earlier "y=(3/4)*8 - 6 = 24/4 - 6 = 6-6 = 0"
vapid shuttle
that was showing where the x-intercept of the function is
an x-intercept is when y=0
you'd agree?
alpine sable
yeah
vapid shuttle
y=(3/4)x -6
so if we have this
we can find the x-intercept by setting y=0
and solving for x
alpine sable
oh
vapid shuttle
0=(3/4)x-6
which is what I did, but kind of in reverse order
just showing you that the x-intercept was at x=8
alpine sable
oh ok
i kinda get it now
do you know any good youtube videos that go into depth about it?
alpine sable
thnx
normal flower
Hey can I know what and all I need before starting Calculus? I know Trigno and linear functions. Any kind of algebra I need more to start?
wind cloak
logarithms are important as well
normal flower
logarithms are important as well
I never knew but thank god I know it
wind cloak
not just linear though, probably up until cubics
atleast the basics
like knowing how to plot a cubic and quadratic graph
normal flower
not just linear though, probably up until cubics
Cubics as in? (Sorry I am new to this so)
normal flower
$f(x) = ax^3 + bx^2 + cx + d$
Yep got it
ocean sealBOT
NEONPerseus
normal flower
You should know limits
Getting that done too
normal flower
And summation
Got it
normal flower
Oh
median oar
It’ll be the first thing you learn if your course is comprehensive
whole shell
my school just taught me calculus raw
without limits
well very little interms of limits
normal flower
It’ll be the first thing you learn if your course is comprehensive
Interesting
slender gull
Really?
normal flower
I will do limits as well
median oar
You should be extremely proficient with algebra before going into calculus
normal flower
Will work on that
slender gull
I thought limits was like the formal introduction to calc after functions and whatnot.
One really should study limits first.
whole shell
you should also learn even and odd functions
median oar
That means expanding brackets, factorising, indicies, log laws, adding and multiplying fractions, conjugates
normal flower
That means expanding brackets, factorising, indicies, log laws, adding and multi...
Oh that I am perfect with
median oar
Those things should be second nature by the time you start calculus
normal flower
you should also learn even and odd functions
Adding it to to do list
normal flower
Those things should be second nature by the time you start calculus
I see
median oar
Later on in part 2 of calculus, integration
Knowing your trig identities is super important
normal flower
I see
normal flower
Knowing your trig identities is super important
I am good at trigno. Aced a trigno test
whole shell
yh, trig integration is the worst if you forget your identities
normal flower
yh, trig integration is the worst if you forget your identities
Agreed it gave me trouble on normal trigonometry while doing my homework one day lol
normal flower
Tan² + 1 = sec²
Yep
median oar
In differentiation I’d say factorising and fractions is what you really need to nail down absolutely
Along with exponent and log laws
normal flower
I see
Log I am pretty much saved
I solved few questions from JEE on log
Just the rest I am doomed for
Be back
median oar
In general a great understanding of algebra will be most useful
lone heartBOT
@normal flower Has your question been resolved?
ocean sealBOT
hibyehibye
alpine sable
So
alpine sable
Let |x|=t
alpine sable
Let |x|=t
hmm how does that help
Now, what you have to show simplifies to t² is greater than not equal to or whatever that sign is 3t+1
Now you can shift everything to rhs
So the problem is just
t²-3t-1 is greater than not equal to 0
well I cant change the thing I'm trying to prove
so I have 3t +1 < y and t^2 < y
alpine sable
well I cant change the thing I'm trying to prove
Its just for convinence
Yeah but I cant write that in my proof
alpine sable
so I have 3t +1 < y and t^2 < y
what do you do from here is what I'm confused with
You can do without that if you want doesnt matter
alpine sable
t²-3t-1 is greater than not equal to 0
That means it has no roots in short.
alpine sable
so I have 3t +1 < y and t^2 < y
What would you do after this step
alpine sable
well I cant change the thing I'm trying to prove
But i mean for this sake of understanding the logic, can we just assume that for now?
well that isn't what I'm gonna write so it doesnt really help
alpine sable
But i mean for this sake of understanding the logic, can we just assume that for...
So that you can understand the concept
Rest could be framed by you
alpine sable
well that isn't what I'm gonna write so it doesnt really help
👍i understand, but we are here to make you understand the concept, what is the logic, not to do your hw.
The logic your showing is flawed
I can't change the thing I'm trying to arrive at
I get you can make a quadratic inequality by reversing from the solution but that isn't what I want to do
alpine sable
I get you can make a quadratic inequality by reversing from the solution but tha...
Well that was just to convey the concept. from there, i was just trying to say that you just have to prove that for x less than 3+roo13/2 roots does not exist thats all, but you did not let me complete
the concept your showing doesnt help
alpine sable
the concept your showing doesnt help
Proof by contradiction exist dont they?
yes
It has to be a direct proof
alpine sable
so I have 3t +1 < y and t^2 < y
I just dont get what to do from here
plucky token
just to clarify, do you want strictly less than?
alpine sable
yes
well I want to show 3|x| + 1 \not \leq x^2 so I guess 3|x| + 1 > x^2
strictly greater than
alpine sable
It has to be a direct proof
I am not sure what do you mean by that
plucky token
maybe itll help to use |x| = sqrt(x^2)
alpine sable
hm
3 sqrt(x^2) + 1 < y and x^2 < y
i think I might have just gone about it all wrong
gusty gorge
hold up why is this true in the first place
alpine sable
hold up why is this true in the first place
Yeah thats what I was thinking
alpine sable
this is the original problem
gusty gorge
what about x = -1000
alpine sable
hm
plucky token
,w graph 3|x|+1 and x^2 on the same graph
ocean sealBOT
gusty gorge
did you mean |x| < (3+sqrt(13))/2?
plucky token
theres some intersection and x^2 overtakes at some point
yeah that makes more sense
alpine sable
hm
I have to show that
(3+sqrt(13))/2
is the smallest k value for which
3|x|+1 \leq x^2
urm it says smallest
gusty gorge
nvm
smallest
uh this is probably smallest in magnitude
it might be helpful to just assume x > 0 without loss of generality
alpine sable
3|x|+1 \leq x^2
I still dont get how to show that this doesnt work for a smaller k value tbh
And I'm blanking at highschool algebra lol
Uh i think the question is a bit incomplete as at x=-(3+root13)/2 equality does hold
Which is clearly less than the given bound
gusty gorge
I mean the idea here is that you can show that the function x^2 - 3x - 1 is increasing from zero, yeah?
alpine sable
Wavey curve works, but as said by the OP, i can not let 3|x|+1=x²
Or manupulate what we are tying to prove
alpine sable
I mean the idea here is that you can show that the function x^2 - 3x - 1 is incr...
urmm wdym
gusty gorge
,w solve x^2 - 3x - 1 = 0
ocean sealBOT
normal flower
In general a great understanding of algebra will be most useful
Yep got it
gusty gorge
yeah just as I suspected
alpine sable
If we could let 3|x|+1=x², we could have found its roots which is ±(3-root13/2)
plucky token
for 0<x<(3+root13)/2, x^2-3x-1>0
x^2 -3x-1 is just the difference between x^2 and 3|x|+1 since |x|=x on this interval
we can check similarly for -(3+root13)/2<x<0
alpine sable
If we could let 3|x|+1=x², we could have found its roots which is ±(3-root13/2)
And then we could simply say no roots for inequality between 0 and 3+root13/2 so hence x>3+root13/2
alpine sable
we can check similarly for -(3+root13)/2<x<0
can I say this by just putting without loss of generality?
hmm I think I got it
tysm
.close
sturdy yacht
really simple question just dont know how would I make an equation for this : The kangaroo A starts at stair number 0 and jumps up 5 steps each time, while the bunny B starts at stair number 24 and jumps down 3 steps at the same time, where will they meet
storm flower
I thought smthing like (0+5)x=(24-3)y
this problem comes down to making equation for 2 lines
and make them meet together
you know y = ax + b?
sturdy yacht
you know y = ax + b?
yea
storm flower
so make one for the kang, one for the bun
sturdy yacht
kang: y=x-3 bunny :y=x+5
storm flower
kang: y=x-3 bunny :y=x+5
eh no
sturdy yacht
whats wrong ?
storm flower
a = how many step each time, forward is +, backward is -
b = starting point
storm flower
bunny : y=0x +3 kang: y=24x-3
you reversed it
storm flower
yes, but remember to have x
storm flower
now thats the correct first step
sturdy yacht
Do i just add them now
sturdy yacht
when are the values going to be the same?
storm flower
exactly, so they will meet at the same location right
so how do you express that using an equation?
sturdy yacht
Y(rabbit)=y(kang) ?
sturdy yacht
sooo 5x+0 = -3x+24
robust dagger
how do i geometrically prove this? i know it has something to do with a phyiscal parallelogram proof, I know how to draw simple vectors but i dont know what the deal is with squares, etc
robust dagger
this is a vector quesiton btw
look in the unoccupied help channels
type in one of those
yes
type in there
no idk that
.close
lone heartBOT
vale wigeon
@alpine sable don't intrude in others' channels.
lone heartBOT
Available help channel!
quaint sleet
whats the greatest integer function of [4.99999999999......]
lone heartBOT
whats the greatest integer function of [4.99999999999......]
@quaint sleet Has your question been resolved?
prime badge
floor of 4.99... is 5
quaint sleet
floor of 4.99... is 5
wrong
its 4
greatest integer function returns the greatest integer smaller than or equal to the input
.close
lilac basin
how do i Determine the sizes of 𝑅𝑈O and 02
lone heartBOT
how do i Determine the sizes of 𝑅𝑈O and 02
lilac basin
lone heartBOT
@lilac basin Has your question been resolved?
lone heartBOT
lone heartBOT
✅
normal flower
I am gonna try my best
Lemme see
I am new to trigno too just started it yesterday
I solved it yeah
lone heartBOT
@lilac basin Has your question been resolved?
steel mantle
hello
mossy jetty
please explain how to do b)
lone heartBOT
please explain how to do b)