I'm not even sure
#help-28
torn jolt
magic harbor
k well O-C is 2x A->B
đ
now try using that to solve them
and if ur really stuck I can give u the answers
torn jolt
nah, dont
magic harbor
np
torn jolt
I understand the 2(b-a)
magic harbor
nice
magic harbor
ye
magic harbor
oh my bad i must have missed something
i think ur reading the wrong answer
because part C) = -2a + b @torn jolt
torn jolt
oh
i just realized as well xD
I also seem to forget the relationship between different shapes
i didnt know that the top if it was x
the line in the middle is 2x.
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@torn jolt Has your question been resolved?
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@torn jolt Has your question been resolved?
fluid yoke
hi trynna prove a point to my younger sister.
h is directly proportional to g.
when g = 5, h = 8.
if h = 120 find g
fluid yoke
13
lucid sandal
you can either show her that it actually is
kind jay
is she learning proportions or it's just random
fluid yoke
learning proportions
lucid sandal
or tell her to trust the equations over the pictures, although the pictures are a useful tool for understanding
fluid yoke
120 is not even on the graph
so i dont understand how she expects g
to be on the graph as well
the graph goes up to 12
lucid sandal
perhaps draw a bigger graph
fluid yoke
given graph as homework
i told her its unrelated to the graph
ok i proved it to her
by drawing a bigger graph
thx
.close
lucid spear
https://mathworld.wolfram.com/BrachistochroneProblem.html
has the following equation
lucid spear
what happens if y -> 0? I tried to model it in desmos but the integral doesn't exist since y -> 0
it doesn't make sense for it to matter what coordinates you use, so I must be misunderstanding something obvious
lucid spear
I think y is a function of x, that's what my graph is. but I could be misunderstanding something
actually yeah i'm sure its a function of x
the integrand is supposed to give the time it takes for the ball to roll down a tiny line
so i guess it makes sense for it to -> infinity as the curve flattens out...?
but the integral should be bounded
lucid sandal
so if y = f(x)
what is your question?
you are asking about $$\lim_{f(x)\to 0} \text{what?}$$
glossy valveBOT
JamesH
lucid spear
why is the integral unbounded? it should be bounded given the problem (it may not be unbounded and I'm just modeling it wrong)
kinda more of a physics then math question
lucid sandal
you asked about y going to zero. what are you interested in the value of as y goes to zero?
lucid spear
lucid sandal
the integral?
lucid spear
see how the red curve goes to infinity as y -> 0
the red curve is the integrand the green is y
lucid spear
just a random curve I made up such that Y(0) = h and Y(1) = 0 (you can assume P1 = (0,h) and P2 = (0, 1) without loss of generality since you can change coordinates later)
one thing thats weird is the integral is over P1 to P2 instead of x1 to x2, maybe I'm misunderstanding something there. I think this is just notational laziness though
hmm the integral exists if i replace y with (h - y) in the denominator, there's still a singularity but it doesn't mess up the integral anymore. idk why
ok i think the mathworld article was assuming the starting coordinates (0,0) while I was assuming (0,h) & that messed up the derivation
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magic canyon
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magic canyon
echo lance
from binomial expansion, it'd be ${11 \choose 4}$
glossy valveBOT
Doggo
spice orchid
How did you get such a big number lol
echo lance
for our case, n = 11 and the exponent of y is 4 so k = 4
you don't have to write the thing down at all
magic canyon
i got ( 11 4)
echo lance
i got ( 11 4)
you're using a calculator right?
magic canyon
yea desmos
spice orchid
Show us what you did in desmos
magic canyon
i expanded the entire thing
echo lance
i expanded the entire thing
no need for that, as I said above but anyways
11 choose 4 is right
magic canyon
11 x 10 x 9 x 8... x 2 x 1/ 4x 3 x 2 x 1
cancel out
11 x 10 x 9 x 8 ... x 5
echo lance
11 x 10 x 9 x 8... x 2 x 1/ 4x 3 x 2 x 1
cancel out
11 x 10 x 9 x 8 ... x 5
missing the (11 - 4)! part
$${n \choose r} = \frac{n!}{r!(n - r)!}$$
glossy valveBOT
Doggo
magic canyon
so its (11 4(11-4) )?
echo lance
can you write it with latex or send a picture please?
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thorny umbra
how can one solve an equation for x when the the variable is to the power of an odd number (f. ex. f(x)=x^5-x^3+8x^2 -8)?
thorny umbra
cause the substitution is only for even ones i think
echo lance
2 variables (x and u)
but one equation
right?
you can only write one in terms of the other if that's the case
thorny umbra
oop sry
thorny umbra
oh i think i remember sth like that- how do you do that? :'
hot herald
depends on what you're given
here you're given something relatively nice
try approach it with factorisation by grouping
torn jolt
how can one solve an equation for x when the the variable is to the power of an ...
x=1 is a root
soft ridge
how can one solve an equation for x when the the variable is to the power of an ...
Is this the function? $f(x) = x^5 - x^3 + 8x^2 - 8$
glossy valveBOT
Science Done Right
thorny umbra
yes
soft ridge
In these cases, this polynomial is called a quintic, an astoundingly hard-to-solve polynomial
99% of the time, there will be a trivial root
like x = 0,1,2,-1,or -2
always
because otherwise it's extremely difficult
x = 1 satisfies the following quintic here. This implies (x-1) is a factor of this polynomial. Divide both
thorny umbra
depends on what you're given
here you're given something relatively nice
try app...
is that f(x)= (x+5)(x+3)(8x-2)-8 then?
hot herald
no
soft ridge
is that f(x)= (x+5)(x+3)(8x-2)-8 then?
Don't do that, in my experience the -8 will create problems
that's not how you do it
thorny umbra
:''''''''''
soft ridge
take x^3 and 8 common
hot herald
your quintic turned into a cubic somehow
consider
$$f(x) = \blue{x^5 - x^3} + \green{8x^2 - 8}$$
glossy valveBOT
âamonov
soft ridge
$x^5 - x^3 + 8x^2 - 8 = x^3(x^2 - 1) + 8(x^2 -1) = (x^3 + 8)(x^2 -1)$
glossy valveBOT
Science Done Right
soft ridge
**âamonov**
exactly
soft ridge
**Science Done Right**
so here, it's quite easy to see that x^3 = -8 which implies x = -2, or x^2 = 1 so x = 1 or -1
so there are 3 roots in total
simple!
soft ridge
**Science Done Right**
@thorny umbra
soft ridge
So, what was your question? Finding roots, right?
If yes, then x = 1, -1 and -2 are all roots
soft ridge
not simple
Always remember why we're doing something
The polynomial given is a quintic, which is very hard to solve
thorny umbra
So, what was your question? Finding roots, right?
"Determine the zeros of the given functions"
soft ridge
so try finding some roots, lie 1, -1, 2, -2, or 0
it will always be one of them, because usually the question is set to be like that
soft ridge
If yes, then x = 1, -1 and -2 are all roots
Yeah then this is the answer
thorny umbra
okayokayokay ill read over this again thanks sm! ||not me struggling w the language barrier (im taught in german)||
soft ridge
okayokayokay ill read over this again thanks sm! ||not me struggling w the langu...
Should I translate my solution to german?
lol
not kidding btw
soft ridge
In diesen Fällen wird dieses Polynom als Quintik bezeichnet, ein erstaunlich schwer zu lÜsendes Polynom
In 99% der Fälle wird es eine triviale Wurzel geben
wie x = 0,1,2,-1 oder -2.
denn sonst ist es extrem schwierig.
x = 1 erfĂźllt hier die folgende Quinte. Dies impliziert, dass (x-1) ein Faktor dieses Polynoms ist. Teilen Sie das Polynom durch x-1.
I used a bit of google translate so sorry if anything is broken and weird
thorny umbra
i get what you saying thanks
oh now i understand that took way too long i am bred thanks yall are holy ppl
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granite linden
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granite linden
i do not understand
how to do this rational approximation thing
i thought it looked like some sort of maclaurin approximation first
but
im not given the expansion for sinhx, and im deffo not working it out for 1 mark
granite linden
how are they using that?
because its arsinh3/4
i get how to do part A btw
part B is my difficulty
echo lance
oh oh
right
according to wolfram alpha it's just maclaurin series
of arcsinh
$$x = sinh(ln 2)$$
we know $x = \frac{3}{4}$ from A,
$$\frac{3}{4} = sinh(ln 2) \implies arcsinh(\frac{3}{4}) = ln(2)$$
glossy valveBOT
Doggo
echo lance
I think this is what they did
echo lance
according to wolfram alpha it's just maclaurin series
only first 2 terms
granite linden
only first 2 terms
how
because
they deffo dont want me to work out maclaurin for 1 mark
thats normally 5 or 6 marks
granite portal
need to get x
f(x)=-0.1x^2 + 5x + 3000
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need to get x
f(x)=-0.1x^2 + 5x + 3000
granite portal
but i got -25 instead of 25 and idk why
grizzled lance
wut
granite portal
i need to find the extremepoint
grizzled lance
oh
granite portal
through derivation
grizzled lance
can u differentiate
granite portal
yes
grizzled lance
ok find derivative and set equal to 0
hot herald
show work
wary nest
If I flip 100 coins and then multiply the number of heads by the number of tails, what is the expected value of that number? Can you give a confidence interval on this number?
fathom saddle
What's E[10]?
Oh, is that literally just a random variable that is a constant 10? Haha
Then yeah E[10] = 10
We're looking at the random variable:
Y = X(100 - X)
Where X is number of heads
That's going to be a pretty messed up distribution, haha
wary nest
We're looking at the random variable:
Y = X(100 - X)
so thats how you find CI?
ivory cairn
That's going to be a pretty messed up distribution, haha
pretty sure there's only 2 ways to get every number except 50^2
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@wary nest Has your question been resolved?
wet agate
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wet agate
so I worked it out as f(1) = 4 and g(1) = 4 => f(1) * g(1) = 4 * 4 = 16
and then I wasn't sure how to tackle b
I guess b might be
h=(1/16)
but what's the function h? I'm not sure what it's asking
random patio
okay so h is the inverse of fg right?
marsh vault
With this context I would feel fairly sure that gf means the composition, such that gf(1) is short for g(f(1)).
wet agate
ok fair enough
random patio
if you have a single function, do you understand how to invert that?
wet agate
so as long as I've done a correctly then I'm golden
ok so I've not done a correctly in that case
as g(f(1)) would be 4/4^2
4/16 = 1/4
isn't that right?
random patio
it is
random patio
bear in mind, you're not trying to find a specific value of h
wet agate
just the input value?
random patio
you want an algebraic expression (i.e. something involving x)
wet agate
would that just be (1/x^n)
random patio
if i said
$$f(x) = 3\left(\frac{4}{x^2}\right) + 1$$
glossy valveBOT
twiceshy
wet agate
well actually since h is fully defined, just (1/x)
random patio
how would you find $f^{-1} (x)$
glossy valveBOT
twiceshy
random patio
oh, erm i think you're getting confused between function inverses and reciprocals
they're different things, though admittedly the notation is very confusing
wet agate
okay, I thought the laws of indices dictate if you have x^-n then it's simply the reciprocal of x to the power of n
i.e. 1/x^n
random patio
function inverses are like,
if $f(x) = 2x$, $f^{-1} (x) = \frac{x}{2}$
random patio
okay, I thought the laws of indices dictate if you have x^-n then it's simply th...
yes, but for functions we have a different concept
glossy valveBOT
twiceshy
random patio
i.e. the inverse function of f reverses the operation that f does
does that make sense?
random patio
**twiceshy**
if you look at this example, you see that $f^{-1} f(x) = x$ for all $x$
glossy valveBOT
twiceshy
random patio
fg is also a function
so i believe function inverse is what the question is looking for
random patio
is this an official past paper?
wet agate
it just looks like it's the inverse of the input value rather than the inverse of the function
it's from 2021 yeah
random patio
maybe i can find the mark scheme to clarify things
wet agate
but i can't find the mark sheet because it's only a year old
teacher says it's not generally available
wet agate
I have another one on here which I'm not sure how to attempt either
random patio
sure
wet agate
I'm just self studying
I'm only doing the foundation syllabus, and I've asked to do the higher exam so I have to do all the material myself, and I can't find in the book some of these topics
so it's fairly difficult for me
random patio
ah, i understand
wet agate
that and the question prior are the two final questions on the 2021 paper
random patio
i am not totally sure what the foundation syllabus covers and doesn't cover
have you learned completing the square method?
wet agate
do you know if there's a mock paper available for this year btw?
I've done completeing the square many years ago, but not recently no
random patio
there's not a 2022 paper available idt
wet agate
I'm just focusing on paper 1 for now, and then hopefully that won't come up until paper 2 or 3
random patio
completing the square is the best way to solve this problem
wet agate
ah I see
random patio
you can also use the quadratic formula i suppose
wet agate
don't think the quadratic formula will be possible, this is from paper 1
non calculator
no longer familiar with completing the square enough to know whether that's possible without a calc
do you think that's the only method of solving it?
random patio
you can definitely do completing the square without calc
lament flower
This is what I did
wet agate
can I ask, for probability questions, have you studied nCr or are you just using the tree diagram method?
random patio
most probability questions drawing a tree will suffice
random patio
This is what I did
you can also do this method but differentiation is beyond the gcse curriculum
lament flower
ahh
wet agate
cool didn't realise you could apply differentiation to this sort of thing
lament flower
mb man its been a while
yeah but i dont know if marks are given for using calculus in gcse
random patio
i think they are
wet agate
probably fewer as they're expecting you to show knowledge of the GCSE syllabus
perhaps it would be at the examiners discretion
random patio
if you know differentiation that may be easier
im pretty sure any valid method is fully credited
wet agate
I have 3 more evenings to prepare for this, haha I'm not feeling confident
it's actually surprisingly difficult
random patio
good luck my friend
limber forge
struggling to get the right answer to this question
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struggling to get the right answer to this question
candid ice
3-3r=1
subtract 1 to get 2-3r = 0
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wary nest
for lim as x approaches 0 of 1/x its undefined
since the lim as x approaches 0 from the left side is negative inf
lim as x approaches 0 from the right side is positive inf
since both dont equal to each other its undefined right?
light sonnet
You have to wait at least 15 minutes before pinging helpers
wary nest
sorry
glossy valveBOT
wary nest
what's undefined?
since x approaches 0 from left and right dont equal to each other right?
i mean DNE
not undefined sorry
shell flicker
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@shell flicker Has your question been resolved?
celest otter
idk if you still need help but I can try if your here
celest otter
Ight so you got the correct magnitude of xy. Do you know the eqaution to find the unit vector?
Do you need help with the concept of the unit vector of just the steps to get the unit vector?
velvet blaze
Need some help with this one:
$if a, b from Z are coprime, show gcd(2a+b, 2b+a) from {1,3 }$
velvet blaze
$if a, b from Z are coprime, show gcd(2a+b, 2b+a) from {1,3 }$
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@velvet blaze Has your question been resolved?
velvet blaze
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hollow zealot
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@hollow zealot Has your question been resolved?
hollow zealot
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magic parrot
Can anyone tell me if I am correct? Thanks
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Can anyone tell me if I am correct? Thanks
magic parrot
Can anyone tell me if I am correct? Thanks
Nevermind this. I realized my mistake
.close
limpid harness
So I'm trying to get an articulated arm working in a videogame, and I want to find all the angles I can have the joints on the arm while still keeping the end of the arm the same height off the ground
limpid harness
that's my rough diagram of the situation
This feels like a moderately simple trig problem to me, but It's been a whiiillee since I did trig.
my initial approach has been to try and divide the whole thing up into a couple of proper triangles
but I'm struggling to visualise which triangles I should be dividing this whole getup into.
vapid barn
must point X also touch the ground
limpid harness
yup
In the greater context of what I'm doing, imagine x being the hand and I want to scrape it along the ground.
limpid harness
variable
limpid harness
yup
vapid barn
really part of this is up to you and your own limitations
can the arm bend backwards
b > 180?
limpid harness
Nah, it's restricted by the structure that it's attached to
So b must always be less then 180
I think the best way to approach this with the case that I want is to find out 'what value of 'a' do I need for any given of 'b' to keep point 'x' on the ground, as it were'.
vapid barn
and we want x to the left of that right angle
limpid harness
yup
vapid barn
8 + 16sin(b) = 21 sin(x)
wait
i'll have to relabel that
8 + 16sin(B) = 21 sin(y)
that's more accurate
to me it also seems logical to say that b > 90, so B<90
limpid harness
but there are also angles of b that are <90 that would allow an angle of a that keeps point X on the ground, still?
limpid harness
yup
vapid barn
basically the idea is that the total vertical displacement must be 0
limpid harness
yeah
my own thoughts are kinda coming from a different approach
So we can work out 'y' for any given value of 'x' here fairly easily, yeah?
vapid barn
yep
limpid harness
same as 'b'
vapid barn
as soon as x is determined, y and b are also determined here
vapid barn
which z
vapid barn
because?
limpid harness
hm, it makes sense in my head... đ
So the line from 'b' and 'y' should always be 21 units, yeah?
for any given value of x
vapid barn
let me get a better shot
your z1 and z2 won't always be the same
i constructed everything else with the given lengths
limpid harness
hm, okay
still we can calculate it fairly simply, right?
because we can calculate the length of the line between x and y
and we know that z1 = 90-y
so that's one angle and two lengths
sorry, z2 = 90-y
what program did you draw those lines on?
vapid barn
geogebra
limpid harness
Thanks
vapid barn
i still think that setting the vertical displacement = 0 is the easiest way to go
limpid harness
sure, how would we do it that way?
vapid barn
8 + 16sin(B) = 21 sin(y)
Basically what I did up here
limpid harness
So I just rearrange that?
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@limpid harness Has your question been resolved?
limpid harness
oh, I get what you're saying now
Well that just doesn't work for what I want to do
If you're saying I shouldn't have the arm displaced off the ground that's kinda not really solving my problem đ
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silk solstice
k is a constant
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k is a constant
silk solstice
brave blaze
I don't think the integral converges?
it doesn't obviously
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@silk solstice Has your question been resolved?
brave blaze
integral from -inf to +inf of 1 diverges
sonic void
X^lgx = x^3/100
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X^lgx = x^3/100
teal wigeon
Do log base x on both sides
sonic void
i did that
echo lance
Do log base x on both sides
or you can just say $\log_b(\dots)$ is inverse of $b^{\dots}$
sonic void
lgx¡lgx=lgx3âlg100
glossy valveBOT
Doggo
echo lance
oh wait but the base isn't given
sonic void
ok
teal wigeon
This is the question right?
sonic void
teal wigeon
Oh
echo lance
is lg(x) base 10?
sonic void
its not stated but i think we're only working with bases of 10 right now
sonic void
so i took log of both sides and got log x * log x = log x^3/100
echo lance
assuming base is 10, using quotient rule gets rid of 100
then you get quadratic equation
sonic void
yea - log 100 = -2
echo lance
are the answers 10 and 100?
sonic void
yes
echo lance
yeah that seems to be the solution then
sonic void
how do i go from that to the quadratic formula
teal wigeon
You can sub in logx with a variable like a
echo lance
so i took log of both sides and got log x * log x = log x^3/100
$$\log(x^3 / 100) = 3log(x) - log(100) = 3log(x) - 2$$
glossy valveBOT
Doggo
echo lance
yeah
bronze magnet
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echo lance
how can the remaining distance be negative?
narrow tundra
Iâm having trouble verifying using trig identities. This is just for practice but I want to know how to solve these more complex equations for a test coming up.
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Iâm having trouble verifying using trig identities. This is just for practice bu...
river gate
Iâm having trouble verifying using trig identities. This is just for practice bu...
Try to multiply csc(-x)-1 bottom and top
narrow tundra
ok đ
I got this
oh wait one sec
ik that cot^2(x) would be csc(x) - 1
so then what would happen?
?
torn jolt
You can't multiply it like that when you have to prove
Or you can
But it's just better to pick one side and completely convert it into the other
narrow tundra
Sorry I meant you have to mutiply cot^2x/csc(-x)+1
uhhhh...
narrow tundra
ok take your time đ
I think I figured it out
I split up csc^2(x) - 1 into csc(x) - 1 and csc(x) + 1 and verified from there
river gate
narrow tundra
that works too! but i used a different method
river gate
Ye either way works
torn jolt
thanks for the help <@290592478904582156> and <@456226577798135808> :)))
haha ok i didn't really help though
loud viper
for calculating a functions derivative I calculate innerDeriv*outerDeriv, how would I go about calculating such a functions integral?
loud viper
chainrule for integrals ?
Say I have the function
f(x) = (cos3x)^2 - (sin3x)^2
and wanted to calculate F(x)
what?
candid ice
Say I have the function
f(x) = (cos3x)^2 - (sin3x)^2
and wanted to calculate F(...
double angle identity for cosine
loud viper
double angle identity for cosine
oh
loud viper
double angle identity for cosine
double angle when it's 3 and not 2?
candid ice
double angle when it's 3 and not 2?
cos(3x)^2 - sin(3x)^2 = cos(6x)
loud viper
cos(3x)^2 - sin(3x)^2 = cos(6x)
How would I get the primitive function of cos(6x) then?
candid ice
How would I get the primitive function of cos(6x) then?
sin(6x)/6 + c
loud viper
sin(6x)/6 + c
sin(6x) is the outer prim func but how do you get the other part that you divide it with?
spice orchid
sin(6x)/6 + c
Differentiate this see what you get
candid ice
sin(6x) is the outer prim func but how do you get the other part that you divide...
Sometimes it is called the "reverse chain rule" for integration
loud viper
Sometimes it is called the "reverse chain rule" for integration
Yeah I see that you're dividing instead of multiplying but from that I'd think that you'd divide by the prim func of 6x?
candid ice
Yeah I see that you're dividing instead of multiplying but from that I'd think t...
Diffferentiate sin(6x)/6 and see what you get. Differentiate sin(6x)/(3x^2) and see what you get
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zinc cairn
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zinc cairn
$$\text{why is it not }p : \mathbbr{F}^n \rightarrow \mathbbr{F}?$$
glossy valveBOT
1080p
Compile Error! Click the 
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(You may edit your message to recompile.)
spice orchid
why do you think it would be?
nova basin
It's not coefficient to polynomial, it's input to value of the polynomial for that input
zinc cairn
for polynomial to up to the power 3, takes 4 coefficients that is an element of F
spice orchid
right and that defines the polynomial
but like mateo said, the polynomial takes one number, and gives you back another, specifically the result of putting that number into the polynomial
zinc cairn
oh, it's mapping z?
spice orchid
ye
nova basin
Like x -> x^2 + x + 1
zinc cairn
so the coefficients define the function?
spice orchid
coefficients define a polynomial yeah
zinc cairn
cool thanks
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fresh sandal
I have some issues trying to calculate the flux out of a tetrahedron, specifically understanding how the correct answer determines the area element for the integration
fresh sandal
I just dont see the logic of how one comes up with the dot product in the denominator
this is the surface in question, and the vector field is xi + zj
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@fresh sandal Has your question been resolved?
fresh sandal
think I found the reasoning
which was another found in the book 
either way it seems to make sense to me, and then the vector field's dot product with the normal, and with the area element, we end up with which is reasonable
oh well
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sonic void
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sonic void
simplify
how i did it was taking 3 * (1/3)^n+1
then putting in n+1 on both the 1 and 3
then becoming 3 * 1^(n+1)/ 3^(n+1)
then i multiplied in the 3
becoming 3^(n+1)/ 3^(n+1)
= 1
I was wrong đ
idk why
fathom saddle
You just asked this in a different channel, then closed it when someone showed up?
Did you think you had it?
glossy valveBOT
Denascite
sonic void
yea
fathom saddle
So we're at
3(1/3)^(n+1)
sonic void
yes
fathom saddle
I can go a little further with
(1/3)âťÂš (1/3)^(n+1)
sonic void
okay
fast peak
n+1 and not n-1
fathom saddle
Good catch, thank you
fast peak
\begin{align*}
\left(\frac{1}{3}\right)^{n+1} + \left(\frac{1}{3}\right)^{n+1} + \left(\frac{1}{3}\right)^{n+1} = 3\cdot\left(\frac{1}{3}\right)^{n+1} \
= 3\cdot \frac{1^{n+1}}{3^{n+1}}
= \frac{3}{3^{n+1}}
= \frac{1}{3^n}
\end{align*}
glossy valveBOT
Denascite
fast peak
$$3\cdot \frac{1^{n+1}}{3^{n+1}}
= \frac{3}{1}\cdot \frac{1^{n+1}}{3^{n+1}}
= \frac{3}{1}\cdot \frac{1}{3^{n+1}}
= \frac{3\cdot 1}{1\cdot 3^{n+1}}
= \frac{3}{3^{n+1}} $$
glossy valveBOT
Denascite
runic quarry
Anyone know which is congruent and which isn't I'm trying to figure it out but it's getting confusing
runic quarry
brittle herald
The first one
You are just shifting each vertex to the right by 5 units
That equates to just moving the triangle by 5 units
No shape change
Hence it's congruent
However, in the second and third one, you are scaling the vertices by 5x and 0.5x
Meaning it's getting larger(2) and smaller(3)
Not congruent
runic quarry
Ah alright I see thank you very much
brittle herald
In the fourth and fifth cases, you are not scaling any distance, just flipping the triangle around
So the congruent
runic quarry
So the congruent
so last two are congruent right?
brittle herald
Yes
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glacial swift
Iâm confused on how what trig identity I need to use
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Iâm confused on how what trig identity I need to use
glass crystal
tan'=1/cos^2
silent turret
That's sec²x
silent turret
||I think the antiderivative of sec²x is tan x||
silent turret
Sorry could you explain to me the tanâ=1?
tan'x is the derivative of tan x
glacial swift
Yeah I understand now ty
candid ice
the given answer is wrong, and it doesn't converge. see wolfram for evidence
glacial swift
-2 would be wrong?
candid ice
-2 would be wrong?
yes
silent turret
,ask tan(3Ď/4) - tan(Ď/4)
glossy valveBOT
silent turret
@candid ice ?
eager violet
There's an asymptote at Ď/2
glacial swift
đľâđŤ
silent turret
Why is it wrong
glossy valveBOT
candid ice
See the above output from Wolfram Alpha
eager violet
Why is it wrong
You're neglecting the asymptote in the bounds. It's an improper integral
silent turret
I see
glacial swift
So my professor got the answer wrong?
candid ice
So my professor got the answer wrong?
yes
glass crystal
and unfortunately around pi/2 1/cos(x)^2 behaves like 1/((pi/2)-x)^2
glacial swift
Gg
eager violet
Happens to the best of us
glass crystal
so the area under the curve is not finite
gritty rose
,w integrate 1/cos^2(x) from pi/4 to pi/2
glossy valveBOT
deft tulip
I think when theres an asymptote in the interval you have to break it up into two integrals right? With that as one bound
glass crystal
theres no use sec^2(x) is equivalent to (x-pi/2)^-2 at pi/2
which is not integrable
deft tulip
Like a one sided integral, your professor failed to do that i guess so didnt notice it doesnt converge there
deft tulip
Theyre human
glass crystal
yeah but sometimes they just want you tonrecognize a formula and apply it
to see if u know the basics
silent turret
Fair enough
deft tulip
This one should be fairly obvious though, youd think they would check when that cos x in the denominator becomes 0
glacial swift
He used this as last years test too
spice orchid
You should definitely tell him he's wrong then
eager violet
Think of it like this. You can flex your intelligence by proving him wrong
candid ice
He used this as last years test too
tell them and score brownie points with them and become their favourite student đľď¸
candid ice
When he asks how I know Iâll tell him 1345631 told me
no, you should tell him you told yourself it in a dream
glacial swift
no, you should tell him you told yourself it in a dream
Thanks for all the help
candid ice
torn jolt
so i need help b, the solution is given, but its going over my head
torn jolt
fast peak
well where are you stuck
torn jolt
everywhere tbh
it says we are summing as k varies from 1 to n, but k is the number of fixed points
if f has less than n number of fixed points, wouldnt there be numbers say f(a), which do not get mapped to itself
then fof != f
fast peak
but we only need f(f(a))=f(a). so only f(a) needs to be a fixed point
not a itself
for example f sends everything to 1
then only 1 is a fixed point
but clearly also f ° f sends everything to 1
glossy valveBOT
Denascite
torn jolt
hmm, yea i got this, so how do i start counting them
fast peak
so we want to count all functions with k fixed points?
torn jolt
yeye got it
fast peak
then for every other of the remaining n-k elements we need to send it to one of the fixed points
so thats k^(n-k) choices
torn jolt
makes sense
just another thing in mind, what if function is defined like
f(x)= x mod N, dont we have infinite number of functions
fast peak
well if N > n, then x mod N is essentially the same as x
the only problem would be for N=n, cause n mod n = 0 which is not allowed
torn jolt
well if N > n, then x mod N is essentially the same as x
so all of them are considered just 1 function?
oh well makes sense
fast peak
it doesn't matter how the "formula" for the function looks
important is just what the function does
torn jolt
i get it now, thank you
i didnt really understand what they meant by fixed points at first
I'll close now
.close
leaden latch
please help
leaden latch
<@&286206848099549185>
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leaden latch
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gritty rose
⢠Ask your math question in a clear, concise manner.
⢠Show your work, and if possible, explain where you are stuck.
leaden latch
> ⢠Ask your math question in a clear, concise manner.
> ⢠Show your work, and i...
sorry I'm replying late I had to go for a bit
hey?
gritty rose
sorry I'm replying late I had to go for a bit
You just reposted the same screenshot
what is your question
gritty rose
How do I solve it
⢠Show your work, and if possible, explain where you are stuck.
Have you attempted anythign?
leaden latch
Have you attempted anythign?
A little
I think you are supposed to do |Position vector of B after T hours - Position vector of A fter Thours| = 0
I have the position vector of the motorboat which is A after T hours
but I don't know how to get the position vector of B
leaden latch
Never answered my question but I figured it out myself
kinda sucked I basically got aired tho
I'm leaving
gritty rose
.close
barren iris
I donât think I understand the hint. How does J^2 = J(J-1) + ?
eager violet
It's not. It's j(j-1) + something
barren iris
It's not. It's j(j-1) + something
there
eager violet
Well, what is the something?
barren iris
Iâm not sure. Im not even sure whatâs going on with the hint. I assume the something is just leading me to what I need to write in place of the âsomethingâ
eager violet
What do you need to add to j(j - 1) to make it equal to j²?
barren iris
j(j-1) + (-j) -> j^2 - j + (-j) = j^2
eager violet
-j + (-j) â 0
eager violet
Yes
lime kelp
The width of a rectangle measures (9x-2)(9xâ2) centimeters, and its length measures (4x+6)(4x+6) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
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The width of a rectangle measures (9x-2)(9xâ2) centimeters, and its length measu...
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neat bay
@lime kelp does he know what perimeter is?
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neat bay
@static leaf yes, I mean you just add all the sides together
static leaf
<@803997344613662720> yes, I mean you just add all the sides together
Perimeter moment
empty marlin
hi i am back for a very quick question, what does it mean by upper and lower bounds here ? i have the error after 15 terms as 1/450 but i dont know how to get bounds with that answer
turbid current
how did you calculate that 1/450 error
empty marlin
took the integral of 1/x^3 (which is -1/2x^2 unless i'm clueless) and just plugged 15 into that
should clarify that that 1/450 is the remainder estimate, idk if that is the same as error i just kind of assumed it was
empty marlin
it sounds familiar but idk what it is off the top of my head
turbid current
its this thing
theres a typo in that btw it should be that f(x) is positive, decreasing, and continuous
so like f(x) = 1/x^3 is a positive, continous, and decreasing function which has f(n) = a_n
and u can easily show the sequence is convergent, so that satisfies all the conditions and you can use this inequality to get lower and upper bounds on your error/remainder
turbid current
would the r_n value there would be 1/450 ?
r_n isnt an exact value but rather a range of values
yeah n = 15
the integral on the right is 1/450 so thats your upper bound (u still need a lower bound)
empty marlin
oh wait would that just just be 1/512?
turbid current
thats what i got yea
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torn jolt
and I'm asked to find the trig form of f(z) following the values of $\theta$ ..I get $f(z)=\frac{1}{\sqrt{2}cos(\theta)}e^{i(\pi/4+\theta)}$ assuming that this is correct, i'd say that f(z) isnt defined when $\theta=\pm\pi/2\ or\ \pi/4\ or\ -3\pi/4$
glossy valveBOT
Crep
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torn jolt
<@456226577798135808> Has your question been resolved?
no
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.close
bitter rapids
How can i convert raw scores into T-scores?
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How can i convert raw scores into T-scores?
gritty rose
What's a T score
bitter rapids
What's a T score
bitter rapids
gritty rose
Do you need help calculating the mean? Or variance?
bitter rapids
I took a test and the raw score is 109 and i want to know the t score of it ( if you need more information please ask im really bad at math so i really dont know all the info i need to give you sorry)
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elfin island
Hello all, I had a question, I have to make a graph for: y =-x. I don't how to do this using the method which uses the gradient and intercept. Please help me if anyone knows how to do this using the gradient and intercept method.
elfin island
thanks
young robin
whats the gradient of this equation?
elfin island
there isn't a gradient, so do I take the gradient as 0?
young robin
there is a gradient
so
all straight line graphs are in the format y = mx + b
in this equation, you don't have a value for b, which is 0
m is the coefficient of x
elfin island
ok
young robin
does this help?
elfin island
mostly
young robin
what is the value of m then?
elfin island
-1?
young robin
your intercept is usually the b (or c) of the equation
e.g y = 3x + 2
but you don't have that value
which means that the intercept is 0
and it goes through the origin
does that make sense?
elfin island
yes
young robin
any other questions?
bleak furnace
It tells me that kx^2 +2kx= 4k-6 and I have to find k when the equation has no real roots (b^2-4ac<0)
bleak furnace
Here's what I tried to do but it just doesn't make sense...
hot herald
why do you have k under your root
hot herald
consider doing a rough sketch of a concave up parabola with those roots
bleak furnace
No idea how I would sketch it, would you mind giving me an example, cause the next problem after this has the same thing with the roots
hot herald
do you know what a concave up parabola looks like?
bleak furnace
Like a smiley face
hot herald
just the smile, no face