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#help-0
safe tartan
cos(picosx)=0 for -pi/2 to pi/2, i tried rewriteing the domain for picosx
safe tartan
and i got x is larger than 0 but less than 0
safe tartan
i jsut did
picos(-pi/2) < picosx < picos(pi/2)
maybe you dont do this for when you apply cos but not sure
winter light
Can you send the original question? @safe tartan
winter light
cos(picosx)=0 for -pi/2 to pi/2 solve for x
Ah ok you have to solve it, so you can start with the outer cosine, whose argument must be π/2 + kπ since the result must be 0
near apex
It is.
safe tartan
Ah ok you have to solve it, so you can start with the outer cosine, whose argume...
picosx=pi/2 + kpi right
near apex
picos(-pi/2) < picosx < picos(pi/2)
That's why your reasoning here is wrong.
cosx isn't monotone in -pi/2 to pi/2.
near apex
picosx=pi/2 + kpi right
yes. This is the way to go.
safe tartan
monotone as in continuously decreasing/increasing?
near apex
monotone as in continuously decreasing/increasing?
yes
safe tartan
right
winter light
picosx=pi/2 + kpi right
So πcos(x) = π/2 + kπ, hence cos(x) = 1/2 + k. Since -1 ≤ cos ≤ 1, k (which is an integer) must be 0, giving you cos(x) = 1/2, that happens at x = ±π/3
safe tartan
k could be -1 right
near apex
So πcos(x) = π/2 + kπ, hence cos(x) = 1/2 + k. Since -1 ≤ cos ≤ 1, k (which is a...
You are not supposed to give solutions.
safe tartan
i mean im not doing it for answers though just tryna learn
winter light
I didn't just give the solutions, but also the method to get them
near apex
k could be -1 right
Yes
winter light
i mean im not doing it for answers though just tryna learn
Yeah, I know it, didn't want to break the rules sorry
near apex
Either just directly find solutions from your domain.
Or find general solutions and take intersection with domain.
alpine sable
lone heartBOT
alpine sable
I have no idea how to solve this
my idea was taking two arbitrary points
then measuring the surface area with both and seeing if i get teh same result
but idk if that's correct
near apex
You are on right track. Just take two varible points (x1,y1) and (x2,y2) and calculate surface area for both.
You'll come to see that their area is same.
alpine sable
oh so it's right
near apex
Surface area of triangle is just area of triangle or perimeter ?
alpine sable
1/2 x b x h
alpine sable
Alright another question but simpler
I managed to find the point where the two lines cross but
nimble latch
Then yeah, do that.
but i dont think showing two points is true shows that all the points are true
alpine sable
how do i find the tangent line equation's slope
alpine sable
but i dont think showing two points is true shows that all the points are true
i just checked my answers and apparently
near apex
but i dont think showing two points is true shows that all the points are true
Points are arbitrary. I'm not saying put values in there. Just in form of variables.
nimble latch
right, i see
vale crag
Same value, and same derivative at the intersection
That's what the condition for two graphs touching boiks down to
alpine sable
yeah but
what i did was plug -1 into y = x^2
and then did 1 = (-1)(-1) + b which is wrong i think
like i managed to find the point by equating the derivatives
then plugging -1 into the original formulas
yeah idk where to go from here
vale crag
Yeah idk what you're trying to do here
Just check the two functions have the same derivative for x=-1
If they do, you won
alpine sable
@vale crag
I wanna find the tangent line
that relates to these two points
but i have no clue how
vale crag
Yeah
thick monolith
i have question about definition of f(x)=e^x
lone heartBOT
i have question about definition of f(x)=e^x
tardy tapir
yes?
thick monolith
So in a math book im studying from rn I get the definition for f(x)=e^x where all real x values are allowed and result definition as y > 0
im not sure if the word definition is correct here btw, studying in swedish
foggy copper
definition is fine here yea
median oar
So in a math book im studying from rn I get the definition for f(x)=e^x where al...
Where did y come from
vale wigeon
you're using the word in two different senses
the INPUT set of e^x is the entire number line.
thick monolith
Df=xeR and Vf=f(x)>0
vale wigeon
the OUTPUTS on the other hand are only positive
thick monolith
right, outputs ill use that word
vale wigeon
in english they're called domain and range respectively
thick monolith
Okay so outputs allowed are defined as greater than 0
foggy copper
provided your input was real, yes
thick monolith
but than I have a function f(x)=e^x-1
vale wigeon
$e^x - 1$ or $e^{x-1}$?
ocean sealBOT
Ann
thick monolith
first one
vale wigeon
ok
thick monolith
So output should now be greater than or equal to 0
vale wigeon
no
foggy copper
no
vale wigeon
that's only for e^x itself
thick monolith
i think, since if I set x=0 than I get f(x)=0
vale wigeon
no, the range of e^x itself is (0, +∞).
but the range of e^x - 1 is obviously shifted down by 1 from that, so (-1, +∞).
foggy copper
thick monolith
(0, +∞) <- dont really understand this part
vale wigeon
it's the interval from 0 to +infinity
do you know about interval notation
if not i will have to translate that back into inequalities
foggy copper
it's the interval from 0 to +infinity
(not including either of those)
vale wigeon
the range of e^x itself is y > 0
thick monolith
right
thick monolith
okay that makes sense
and now I also see I actually misread one of the solutions in the book
thank you for the help :d
lone heartBOT
@thick monolith Has your question been resolved?
dapper verge
lone heartBOT
dapper verge
Could I get help on question 14?
vale wigeon
Four steel discs, each with radius 1 cm, are placed in a square frame as shown.
(a) Find the length of the sides of this frame.
(b) In order to brace the frame, a diagonal support is to be added to the frame. Find the length of this support.
(c) Find the length of material needed to build the frame, including the diagonal brace.
which part is troubling you?
dapper verge
I dont get how'd you find the length of the frame? Would I add the 1cm together or ?
and then apply pythag?
vale wigeon
are you talking about part a or part b here or what
dapper verge
are you talking about part a or part b here or what
A
vale wigeon
right
you don't need pythag for part a just yet
it is just visible that the side of the outer square is twice the diameter of each circle
dapper verge
half the circle
vale wigeon
you're not only not answering my question, you're also wrong.
dapper verge
isnt the diameter just a straight line that goes through it?
vale wigeon
"it"
vale wigeon
...
no, "a straight line that goes through the circle" does not describe the diameter.
and you still haven't answered my question:
what is [the length of] the diameter of a circle whose radius is 1cm?
dapper verge
2 cm
dapper verge
4cm
vale wigeon
exactly
dapper verge
and for be would it be:
c^2 = 8^2 + 8^2
c^2 = 64 + 64
c^2 = 128
dapper verge
as its four wouldnt u double it for each side?
vale wigeon
that sounds a lot better now
dapper verge
that sounds a lot better now
thank you, im sorry aha i just struggle to articulate what im thinking! thanks for the help
.end
.close
crisp moon
Imagine a gambling game, my probability of losing is 1/25, I have to play this game 10000 times. What is my probability of losing at least 240 times?
near apex
!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
1
near apex
How many ways can you lose 240 games out of 10000 games ?
crisp moon
My chance of losing each round is 1/25 (4%) im playing this game 10000 rounds. What is the probability of me losing at least 240 times in total?
Briefly chance of losing at least 240 out of 10000 rounds
near apex
Do you know what losing at least 240 games imply ?
crisp moon
it means all my money is gone
near apex
Lol. I meant what cases does it include.
crisp moon
Sorry im not a mathematician xD
near apex
I just want to ensure that you understand this:
Losing at least 240 games means that you lost 240 or more games.
Not exactly 240.
crisp moon
"Losing at least 240 games means that you lost 240 or more games." yes this is
not 240
near apex
is that clear?
crisp moon
yes
near apex
Good.
So we need this probability actually.
probability of losing exactly 240 games + probability of losing exactly 241 games + probability of losing exactly 242 games + ... + probability of losing exactly 10000 games
crisp moon
oh you better do it i'm not very good at math
near apex
Oh. I can't do it for you fully. I can only guide you.
near apex
probability of losing exactly 240 games + probability of losing exactly 241 games + probability of losing exactly 242 games + ... + probability of losing exactly 10000 games
Here, let's try to compute the first term i.e.
probability of losing exactly 240 games = ?
crisp moon
i found it as 0.67%
crisp moon
Yes, it seems like a very high number to me.
crisp moon
How did you get that ?
an ai
near apex
Woah. Lol
crisp moon
xD
near apex
Let's just do it via maths. I haven't computed it myself. So, i can't say if it's that or not with certainty.
crisp moon
Isn't the probability of every number between 1 and 10000 equal anyway?
like isnt the probabilty of losing 240 times and 241 times equal?
near apex
Isn't the probability of every number between 1 and 10000 equal anyway?
It is. But there are different number of ways for losing n number of games.
near apex
like isnt the probabilty of losing 240 times and 241 times equal?
They are equal.
But you can lose 241 games in more number of ways than you can lose 240 games.
crisp moon
Oh i didnt know that
near apex
Think this way: Let's say you play 4 games.
How many ways can you lose exactly one game ?
crisp moon
4?
near apex
Yes
Either you lose the first one, or the second one, or the third one, or the fourth one.
crisp moon
I got it
near apex
Now, how many ways can you lose exactly two games?
near apex
It's 6.
crisp moon
yes
near apex
How are you getting two?
crisp moon
it was a misunderstanding nvm
near apex
Possibilities of losing exactly two games out of 4:
first and second
First and third
First and fourth
second and third
second and fourth
Third and fourth.
Thus 6 ways.
near apex
it was a misunderstanding nvm
Okay. Good
So, we have established that there are different ways of losing 240 games and 241 games. Right?
crisp moon
Yeah thanks
near apex
Okay. Now, how many ways are there of losing 240 games out of 10000?
near apex
like isnt the probabilty of losing 240 times and 241 times equal?
btw, i just noticed this. No, they aren't same. They could have been same if probability of losing or winning was same i.e. 50% each. But it's not in your question.
crisp moon
true
near apex
btw, i just noticed this. No, they aren't same. They could have been same if pro...
Also even if probability of losing or winning was same i.e. 50% each, they'd only be same if we disregard number of ways we can lose those many games. Which we dont.
So, technically, it's never equal by default.
near apex
I couldn't find it. is there a formula?
yes.
near apex
So, basically, losing 240 games out of 10000 is like choosing 240 games out of 10000 which we'll then lose.
So, we need to see how many ways can we choose 240 games out of 10000.
Are you familiar with formula for choosing r objects out of n ?
crisp moon
formula looks better
near apex
Do you know the formula ?
crisp moon
no
near apex
Okay. Fine.
crisp moon
if i took too much of your time i can close the channel then i get help from someone else
or later
near apex
For, now i'll just tell you the formula. You can watch a video on it later and understand better.
near apex
if i took too much of your time i can close the channel then i get help from som...
no, we are almost there.
crisp moon
haha thanks
near apex
So, number of ways of choosing r things out of n is ${n \choose r}$.
Damn it.
I dunno latex well. Brb
crisp moon
Okayy
ocean sealBOT
Enemagneto
near apex
**Enemagneto**
Now,
$${n \choose r} = \frac {n!}{r! \cdot (n-r)!}$$
ocean sealBOT
Enemagneto
near apex
This is basically the number of ways of choosing r things out of n.
@crisp moon Are you familiar with factorials ?
crisp moon
No actually im not familiar with complete maths
near apex
Umm... It's then almost impossible to do without that. Try watching a video on what factorials are.
Also what's number of ways of choosing r things out of n.
crisp moon
Ok then, i will save this chat, is there anything more to say about this ?
or will this chat help me
near apex
There's some more about the probability computation.
Okay, let's finish it then.
So, for now, we'll assume that number of ways of losing 240 games is some m.
Now, let's try to calculate probability of losing 240 games out of 10000 disregarding the order.
So, to lose one game - probability is 1/25.
To lose another game at top of that - probability = 1/25 * 1/25 = 1/(25^2)
Similarly for losing 240 games, it'll be 1/(25^240).
However, if exactly 240 are lost so rest 9760 must be won.
So, probability of winning 9760 games = (24/25)^(9760)
Now, probability of exactly losing 24 0 games(disregarding the order) = 1/(25^240) * (24/25)^(9760).
Taking the order into account, it is equal to:
$${10000 \choose 240} \cdot \frac{1}{25^{240}} \cdot \left (\frac {24}{25}\right )^{9760}$$
ocean sealBOT
Enemagneto
crisp moon
woah
crisp moon
Okay probably i can do with a program, thanks now i can close the channel
thank you btw
.close
buoyant mirage
Doing practice papers for NSAA and I’m stuck on how to do these two questions. The first one I’m not even sure where to start and the second one I think you have to do the next term in the sequence subtract the current one to get an equation which I did but now I’ve got no idea how it’s going to end up as a/3 or a/sqr3
quiet lynx
This may be an easy question but from the script my professor provided i couldn't figure this out. I need to find the singular points of a curve (0 = f(x,y) so multivariable function) and classify them with the help of the Hessian matrix. I was working on an example, in which i found singular point as 0,0 and the
Hf(0,0) = [2q^2 0, 0 -2]
I of course researched about how to classify them (double points, cusps and hermits?) but somehow I couldnt find how. Could you kindly explain to me what should I do after setting up the Hessian matrix?
lone heartBOT
This may be an easy question but from the script my professor provided i couldn'...
@quiet lynx Has your question been resolved?
dusty wigeon
The diagonal light can rotate about the point
lone heartBOT
The diagonal light can rotate about the point
dusty wigeon
Doing some engineering with cams and a hinge so I want to know how to do this
If the parameters of the diagonal was 1
At 45° the red line is at 0.5 on the X axis
wispy geyser
I can't decrypt what you've written on the paper
dusty wigeon
How does the height of follower (RED) correlate with theta
wispy geyser
Is it's position on the x axis fixed ?
dusty wigeon
The only thing that is moving is the follower up and the diagonal line rotating
wispy geyser
Does the follower move horizontaly ? Or Is at a fixed distance from the vertical line on the left
wispy geyser
And what do you want ?
dusty wigeon
To know how the height of the follower correlates with the angle of theta
wispy geyser
Do you have a length for the red Line ?
wispy geyser
You're problem isn't really clear
Yes but to know which one I need to better understand the question
dusty wigeon
So with the red follower when it goes up it makes the thing on top rotate as it’s fixed to a point
wispy geyser
But in it's initial state the red bar IS on the ground and 25mm in height right ?
dusty wigeon
Yea
wispy geyser
To solve this you need the difference in x coordinate from the hinge point to where the red bar is
This IS a constant because neither one IS moving sideways
dusty wigeon
Yea
wispy geyser
What do you know in trigonometry ?
wispy geyser
Ok then you really need to make a clear drawing of you're problem (see how I needed to Ask a lot of questions to even understand what you were trying to tell me)
dusty wigeon
Okay
wispy geyser
This should help you have a clear Idea any make a triangle appear on which you Can Do some trigonometry
dusty wigeon
Imma simplify this
Damn it’s easy to represent but putting it in its simplest form is hard
Wait I’m going to stop and try to understand how to represent this
So I will come back maybe in an hour
Wait I need to kill a spider
I killed the spider
And I think I have a bit of a better understanding
wispy geyser
Here's a nice drawing with :
H : the fixed height of your hinge point
d : the fixed lateral distance between your hinge point and the red bar
L : the fixed length of the bar
and two variables x the height at which the bar is and theta the angle
Now you can see the blue triangle and do trigonometry in that
wispy geyser
The key is to do a clear drawing
wispy geyser
paint
dusty wigeon
I drew by hand
wispy geyser
but use a sheet of paper that's better
dusty wigeon
So yea hopefully I can get a good cam toy
For my sister
So yea thx again
Now time to model
barren yacht
im getting 100/21 for some reason
tulip knoll
i got 21/31
barren yacht
oh hold up
fervent belfry
.
barren yacht
u sure its a whole num?
do u have the sol?
nah bro i checked online too
the ans is 109/19
its decimal
shut kayak
Do not spam, flood, or post unsolicited advertisements. Do not post responses written by ChatGPT or a similar AI tool.
barren yacht
where'd the 3 go?
there is supposed to be a 3
bro chatgpt is wrong 💀 💀
chatgpt high
the ans is 109/19
where did the 3 go?
3(1-3x) = 3 - 9x
where the 3 at 💀
i did it 3 times u got me trippin
chatgpt wrong
haha
k so
dont multiply 21 w everything
take the lhs and take 21 as lcm
simplify ull get (52 - 23x)/21 = 7 - 2x
u can do it later too doesnt matter
now take the 21 there and ye multiply
look
what nah
google is dumb
hold on leme understand how to type this
proly some prof
k so
look just whatever u typed earlier
not everything
add a + 3 before the -9x
then simplify
because 3 (1-3x)
equals to 3 - 9x
multiply 3 with both terms
yes
wdym
what about the variable
"x"
ye
u write the varible as it is
2 into 3x is 6x
2x into 3x is 6x^2
multiply constants with constants and varibles with varibles
only the varible "x" is sqaure
because there are 2 "x"
bro
m into m?
yes
just an example
2m into 3m is 6m^2
what grade u in?
damn
cool
im surpsied this hasnt been taugh earlier
trust me the q u did is nothing 💀
u got me trippin fr
i was questioning reality
fr bru
aint no way i cant do some algebra 😭
have u learnt trigno
oh
the chart?
like angles
sin 45?
bruh
cool
i really like trigno
i doubt you know the basics
im trash at teaching literally search 2- (2x+1)/3 + (1-3x)/7 = 7 -2x on google
youll find every step easily
uh
about algebra
m^5/m^2
??
lol
what
tf u on bro
lmfao no
bruh imma sleep
gn
m^5/m^2 = m^5 - m^ 2 = m^5-2 = m^3
add me imma talk later
barren portal
is $e^{-{(x^2+y^2)}}$ and even function of x?
lone heartBOT
is $e^{-{(x^2+y^2)}}$ and even function of x?
barren portal
What I mean by even function of x is to treat y constant
echo socket
{-x^2 + y^2}?
echo socket
What I mean by even function of x is to treat y constant
I mean, it clearly satisfies f(-x, y) = f(x, y)
stray estuary
i think they mean $e^{-(x^2 + y^2)}$
barren portal
I mean, it clearly satisfies f(-x, y) = f(x, y)
right so, clearly the I can use twice the integral property between -a to a right?
barren portal
$\int_{-1}^{1} $e^{-(x^2 + y^2)}dx$
ocean sealBOT
.doc
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
echo socket
$\int_{-1}^{1} e^{-(x^2 + y^2)}dx$
ocean sealBOT
A Lonely Bean
echo socket
Yeah sure you can use the property here
echo socket
Where?
barren portal
when i find the antiderivative
echo socket
Antiderivative of e^(-x^2) is nonelementary though, what do you mean
Try differentiating $\frac{e^{-(x^2 + y^2)}}{-2x}$
ocean sealBOT
A Lonely Bean
echo socket
Does it give you the integrand?
echo socket
Yeah, you can simple divide by the derivative of the inside only when the derivative is constant
barren portal
That’s what i meant
keen plinth
are you xy probleming here
like this integral is very suspicious
where did you even get it from
echo socket
Yeah I don't think you would be asked to evaluate that
barren portal
Why do you think it’s non elementary?
keen plinth
this is a well known result
barren portal
I can use substitution right?
naive valley
it's not elementary, in the sense that people had to define a function for it, namely the error function
barren portal
notice im differentating with fixed y
naive valley
but the error function is widely available in software and its properties are well known, so it's not really any worse to deal with than say sin or cos
barren portal
partial integral it is
naive valley
if you express the exponential as a product, you can pull the y part out as it's a contant with respect to the integral
keen plinth
why do you need this integral
keen plinth
this doesn't have a good answer
barren portal
thought to use even function property
keen plinth
well in 2 dimensions you want to respect the circular symmetry
barren portal
but hit the wall
keen plinth
but you've made the domain of integration a square
so you're gonna have a hard time doing it by hand
keen plinth
,w integral -1 to 1 integral -1 to 1 exp(-x^2 - y^2) dx dy
ocean sealBOT
keen plinth
erf is defined as the antiderivative of e^(-x^2) with some scaling factors
barren portal
Its non elementary double integral ig
what suprises me, is the inner integral is possible when limits are -1 to 1 but not when 0 to 1
ocean sealBOT
lone heartBOT
@barren portal Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
undone ledge
lone heartBOT
undone ledge
what should be the aproach to this question
im stuck
also in the last step
the equal has 18
fallen verge
undone ledge
hm?
tardy stag
instead of doing ln do log2
undone ledge
oh?
alright i will try that
1 sec
OHH
Damn
thats it right?
so option (b)?
yeah cool got it
thanks
.close
undone ledge
i dont know how to start this question
lone heartBOT
i dont know how to start this question
ocean sealBOT
physicsrocks
mystic vortex
I believe they mean angles
lethal belfry
yeah, my bad, sorry
lethal belfry
LHS,if possible
undone ledge
ok i will try..
lethal belfry
I'm jus thorwing ideas that may work, I've not tried it myself
undone ledge
understandable
mystic vortex
Is the implication there that the equation is true for all values of a?
lethal belfry
Is the implication there that the equation is true for all values of a?
no, it's obviously not true when a=0. but I suggested that as the RHS iis purley in terms of cos(a)
mystic vortex
Hmm ok
I've never seen a problem like this but I'd agree trig identities seems like a good first step
Also, are k, w, and p all supposed to be integers?
undone ledge
hm??
mystic vortex
Cause it talks about factors, but it doesn't explicitly say
lethal belfry
ah,ok
undone ledge
2cos a . sin a = sin 2a
lone heartBOT
@undone ledge Has your question been resolved?
lone heartBOT
undone ledge
thanks
lone heartBOT
Available help channel!
undone ledge
lone heartBOT
alpine sable
how does this simplify to this
lone heartBOT
how does this simplify to this
ocean sealBOT
Modus
alpine sable
i suppose that makes sense
x-x/2 and if lets say x=5 then:
5-5/2= 5-2.5=2.5
5/2 = 2.5
minor needle
yes, but
this is how it works, I mean for every x, even for the expression like -voy^2/g
alpine sable
well
is is the same if what we talk about is constant
5, 20, (17/200)^2 or -vy^2/g
or so i suppose
lone heartBOT
@alpine sable Has your question been resolved?
lavish kelp
I am confused on how they got the maximum value
lone heartBOT
I am confused on how they got the maximum value
lavish kelp
I know for the minimum value, they just took the vertex
but how did they get the maximum value mathimatically
because it does not give me a graph
near garden
if the part of the graph given doesnt contain the vertex it would be the lower end of the arch
you just have the range of y value as the lower y of it and the upper y of it
however if the vertex is included only one side of the arch can be the maximum (or both be)
taking the coefficient of the squared term as positive that is
lavish kelp
so the maximum value is just the 2^2?
near garden
what
lavish kelp
I am as confused as you are
how did they get the numbers 4 and 6 for the maximum mathematically
near garden
or just take the two end points of the graph, plus the vertex if it's included in the range, and the lowest y and highest y would be the y bound over the range
lavish kelp
I am not given coordinates
near garden
how did they get the numbers 4 and 6 for the maximum mathematically
6 is the given x upper bound
near garden
I am not given coordinates
you don't need the coords to do that you just have to plug in the bounds and the x for the vertex in the original function to get the y values
near garden
huh
lavish kelp
im not given any numbers on my graph
near garden
wdym
lavish kelp
its just a raw graph with a parabola
near garden
how would you ahve the graph if you dont have the numbers
and the graph is drawn with the information given
both the formula for the function and the range
for you to find the y range
lavish kelp
let me take a photo
near garden
ok
near garden
yeah and?
lavish kelp
I have no clue on how to get the maximum value
near garden
from the minimum value of a quadratic, either going to the left or to the right the value should always be increasing if the coefficient of the squared term is positive
so the maximum value can only be at one end of the x range or the other, given that the x range crosses the vertex of the quadratic function
lavish kelp
the squared term is positive
near garden
yes
so you can just plug in the two ends of the x range into the original function to see which one is higher and that would be the value for the y maximum
near garden
mhm
near garden
and also you can look for which ever end is farther from the vertex
since quadratic graphs are symmetrical around the vertex vertical line and the farther end point from the vertex woulda grown higher
lavish kelp
since quadratic graphs are symmetrical around the vertex vertical line and the f...
ohhh
wait this makes way more sense
near garden
and also you can look for which ever end is farther from the vertex
so like 0 is 3 away from 3, and 5 is 2 away from 3, so 0 would be the bound other than the vertex bound
lavish kelp
wait thats cool
near garden
:)
lavish kelp
thank you for making math math
near garden
XD np
near garden
wait thats cool
it's cooler when u'd be able to see it at calculus level
but thats not to be worried about for now
hf wiht math
lavish kelp
I gotta worry about that next year 💀
near garden
XD
lavish kelp
full IB
near garden
what year are u in
lavish kelp
going into 10
near garden
sameeeee
lavish kelp
nicee
lavish kelp
thats cool
lavish kelp
enjoy the rest of your day :)
near garden
u2 <3
lavish kelp
.close
lone heartBOT
lone heartBOT
Available help channel!
buoyant mirage
Doing practice papers for NSAA and I’m stuck on how to do these two questions. The first one I’m not even sure where to start and the second one I think you have to do the next term in the sequence subtract the current one to get an equation which I did but now I’ve got no idea how it’s going to end up as a/3 or a/sqr3
lone heartBOT
Doing practice papers for NSAA and I’m stuck on how to do these two questions. T...
@buoyant mirage Has your question been resolved?
buoyant mirage
No
full helm
No
hi. what happens if the function starts decreasing within the small interval you’ve given it?
for the second one that is
you’ve said, well, the function increases if f(x+1)-f(x)>0, which is somewhat going in the right direction, but it leaves room for error
if you’re allowed to use calculus, it becomes trivial. Think of the derivative
now for the first one. try to establish a relationship between L and m, and p and M. Then you can try applying the fact that LM is 5 units long
buoyant mirage
Ok thanks!
Thanks I got the second one now
Why is great than or equal though and not just greater than?
full helm
Why is great than or equal though and not just greater than?
probably just their definition of increasing
buoyant mirage
Weird
full helm
funny thing, I once got into a (verbal) fight with a teacher regarding exactly this
buoyant mirage
How?
full helm
in the exam he asked a question which asked for the exact same thing that you’ve been asked (different numbers)
It was a mcq. One of the choices included the endpoints, and the others didn’t. I picked the one that didn’t, and he claimed I was wrong
and I was extremely salty, it was the only question I got wrong. I took it up with him because he never set a definition for increasing properly in class
it doesn’t make sense for something to be increasing when it literally doesn’t increase or decrease at all at that point (f’=0) (to me, as I mention below, different people have different definitions)
but yeah
different book/curriculums/teachers have different definitions
it’s good this mcq you have doesn’t include both the endpoint included/not included though. Doesn’t leave room for questioning
anyways, I digress
Have you thought of a way for the first one
lone heartBOT
@buoyant mirage Has your question been resolved?
proper vine
What are the key features of radical functions
lone heartBOT
What are the key features of radical functions
proper vine
Im not sure what they are
like if there is a domain, range
asymptote
max min
mud please man
you got this
help
celest terrace
Im not sure what they are
a radical function is a function containing an nth root
celest terrace
take the square root of x for example
celest terrace
sure
proper vine
but for quadratic
celest terrace
which isn't a radical function
celest terrace
not really
proper vine
So what would be the awnser for this
celest terrace
what's the radical function?
celest terrace
can you take a picture of the entire question?
celest terrace
ok
proper vine
Task Goal: To demonstrate your knowledge of the functions you have investigated in this course.
Throughout this course, you have looked at the key features of a variety of functions, including quadratic functions, radical functions, reciprocal functions, exponential functions, and sinusoidal functions.
In this task, you will be demonstrating your knowledge of each of these functions by completing this Functions template. Make a copy and once completed, download the files as a PDF.
Complete the template for each functions using the linear function y=mx+b as a model.
celest terrace
so basically, function, representations, key features, and description?
celest terrace
have you seen what a radical function looks like?
celest terrace
mind showing them?
proper vine
what are the key features
celest terrace
there's always going to be a domain and range for a function
celest terrace
no
proper vine
if it is bigger than zero
celest terrace
for 0?
proper vine
ya
celest terrace
like x^0?
celest terrace
Thats expo
sorry, i misunderstood your previous statement
celest terrace
a zeroth root is not defined
proper vine
yep
celest terrace
the range depends on costant c right?
since it moves the graph up and down
so it's also limited
celest terrace
y
proper vine
yer with the restrcition of y bieng smaller or equal to 1
celest terrace
yes
proper vine
x+d
celest terrace
domain for this?
celest terrace
yes
celest terrace
just one more thing: the domain also depends on the sign of x
so besides domain and range...
proper vine
yep
celest terrace
I just finished writing it down
for even roots
proper vine
?
celest terrace
there's only a domain and range restriction for even numbered roots
celest terrace
more like this
celest terrace
hm
you know how a radical can be rewritten into the radicand and a fractional exponent?
proper vine
ya
proper vine
Btw you wouldn’t write xER for this one
what would i replace it with
wheat isle
just x>=-3 works
celest terrace
^
wheat isle
because xER implies the domain exists for all real numbers of x
celest terrace
oh it isn't
celest terrace
nope
wheat isle
Can it sometimes be xER
Like are you asking what functions would have the domain of all real x?
celest terrace
a radical can't ever be xer
celest terrace
it would
proper vine
so there is no yER
ocean sealBOT
celest terrace
you can see how the domain doesn't exist when x is negative
since the function doesn't exist there
proper vine
alright
I fixed it
Do we have any more key feature or can we move to the reciprocal functions?
celest terrace
i can't think of any more you can put...
celest terrace
alright
celest terrace
which asymptotate are you talking about?
the vertical or the horizontal asymptote
just specify that
celest terrace
yes
wheat isle
Btw just a thing to note that reciprocal functions also have the domain where x cannot be 0
proper vine
Btw just a thing to note that reciprocal functions also have the domain where x ...
ya
celest terrace
Btw just a thing to note that reciprocal functions also have the domain where x ...
depends
for this graph, x could be zero
wheat isle
True
wheat isle
I’m just thinking of the form 1/x where you cannot divide by 0
celest terrace
ah yes
proper vine
Asymptote- A reciprocal function has an asymptote meaning that there is a restriction that the line will never reach a certain number.
Horizontal asymptote - The horizontal asymptote depends on the value of c since the value of c is the horizontal asympotote.
This is what I wrote so far
proper vine
c?
proper vine
ya
celest terrace
which variable shifts the graph left and right?
proper vine
for the vertical one, what variable is that?
oh I didnt read the first half
mb
i thought you said what variable is that
celest terrace
ah
proper vine
the verticle one depend on the d value
proper vine
ya
Vertical asymptote - The vertical asymptote depends on the value of d since the value of d is the vertical asymptote.
celest terrace
the value of x = d
proper vine
ya
celest terrace
basically just say
the vertical asymptote is a line where x = d
and the horizontal asymptote is a line where y = c
just a suggestion though, i'm not sure how your teacher would want it
celest terrace
let's start on domain
the x values
for the domain
x exists everywhere except for one value
proper vine
So xer with a restriction
proper vine
ya
celest terrace
since the only restrictions are the asymptotes
proper vine
yep
celest terrace
same could be said for the range and the horizontal asymptote
proper vine
Cant I just write this
Domain: X can be all real numbers beside the value of the horizontal asymptote.
Range: y can be all real numbers beside the value of the vertical asymptote.
celest terrace
that works
proper vine
Is that all
celest terrace
instead of saying beside, try saying except
celest terrace
Is that all
that should be all
celest terrace
ok
celest terrace
it should be
proper vine
yep so domain
and range will be pretty similiar to the radical one
just vise versa
right
celest terrace
but?
celest terrace
okay
celest terrace
???