or use sss similarity
#help-19
frigid canopy
short topaz
so all angles r the same
How?
short topaz
Were lines given parallel?
analog void
Were lines given parallel?
the two black triangles
r enlargments
so they musr be parallel
short topaz
Then why you did all that
There theorem that say if 2 line parallel like that of triangle then they similar
Wait a sec
short topaz
This
frigid canopy
well, use the fact that AC is proportional to PR
as they are enlargments of one-another
from that parallelarity follows
short topaz
@frigid canopy will this work in this question?
frigid canopy
<@796939110815629322> will this work in this question?
this is just thales theorm right
short topaz
this is just thales theorm right
Idk exact name but it was In my 10 grade book
frigid canopy
yeah, but we first need to prove that PQR is similar to ABC
frigid canopy
Idk exact name but it was In my 10 grade book
yeah, I know, NCERT, right?
frigid canopy
yes
frigid canopy
I'm starting uni this year
frigid canopy
good luck
short topaz
good luck
Thx
Good luck in uni
Well I think question solved so ima go look at other questions
analog void
could someone explain plz why they did BQ/AP
like i dont get it
even after their comment
analog void
wait, edexel , I thought you were in uni
ye i am, im just tutoring someone and refreshing on this topic
frigid canopy
they are similar
analog void
havent done this in ages 😆
frigid canopy
they are similar
the triangles
frigid canopy
I believe so
frigid canopy
AP and BQ ain't similar
analog void
then why do they divide their respective lengths
clever fjordBOT
very low quality mathematician
analog void
u mean PQR?
clever fjordBOT
very low quality mathematician
frigid canopy
where K is a constant
analog void
yh
frigid canopy
this follows from the definition of similarity
analog void
yh
odd edgeBOT
odd edgeBOT
Available help channel!
mystic saffron
QUESTION
Prove that every circle passing through a fixed point and having its center on a fixed straight line must pass through another fixed point.
mystic saffron
this is my solution. Can anyone check if its correct and if not provide a geometric answer
odd veldt
That seems right to me 🙂
Another option is the point on the fixed line that is closest to the fixed point, though I think your choice is probably easier to justify
odd veldt
Uhhh, basically you took the fixed point P and reflected it on the line l to get the point P'
I'm talking about the point at the intersections between the lines l and PP'
That point must also be in all such circles, though I don't have a real argument for it other than geometric intuition
mystic saffron
so if i took point C1 as close as possible to PP'
it would form a symmetry again
i think that intuition also works
anyways thanks!
odd veldt
No problem!
mystic saffron
.close
odd edgeBOT
signal oar
.close
odd edgeBOT
odd edgeBOT
Available help channel!
exotic granite
I can't follow the rest of the integration where did the sin go??? And from where did my prof pull the cos? 😭
fervent relic
I think that might be a typo
they forgot the sin in the first equation of the second page
fervent relic
That's the most likely scenario because everything would check out
flat mortar
odd edgeBOT
flat mortar
i am not really understanding this
i plugged in a number that is close to 4 which was 3.999
woudlnt the answer be a positive number instead of a negative number?
worn sandal
i plugged in a number that is close to 4 which was 3.999
3.999 should give you -1
flat mortar
what about the absolute value?
worn sandal
The absolute value is only on the numerator
So the numerator would be 0.001, while the denom would be -0.001
worn sandal
odd edgeBOT
@flat mortar Has your question been resolved?
mystic saffron
!help
odd edgeBOT
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
mystic saffron
SO IM REALLY CONFUSED
This teacher solves this problem with the pythagorian method but he rounds the 15 to 20 and he says that it's because there is only 1 significant on the triangle's measures. WHy does this happen I don't understand
<@&286206848099549185>
@dusk warren
<@&286206848099549185>
pls help
worn sandal
Doesn't the hypotenuse literally have 2 sig figs 😵
I also don't see why you would round 15 to 20 in this context
exotic kelp
if not rectanglar triangle, b random.
mystic saffron
Doesn't the hypotenuse literally have 2 sig figs 😵
Only the smaller significant figure is considered in this problem
worn sandal
Only the smaller significant figure is considered in this problem
wdym?
worn sandal
oh sure
mystic saffron
8 has 1 significant figure
worn sandal
Then the side with 8 only has 1 sig fig, so in that case you'd just answer in 1 sig fig
15 in 1 sig fig is 20
mystic saffron
15 in 1 sig fig is 20
why is that
I don't understand why 1 sig fig rounds the number to 20
After solving the problem the teacher said that strange things happen when you have only 1 sig fig
worn sandal
I don't understand why 1 sig fig rounds the number to 20
Because 15 is closer to 20 than 10
lusty hemlock
How do i do this?
odd edgeBOT
How do i do this?
lusty hemlock
I'm stuck at the end of my work (lhs) and i dont know what to do
Plugging it into a math solver says mo solution
lusty hemlock
Which means?
wise pine
arcsin((y-4)/2)/3
lusty hemlock
I'm still lost
lusty hemlock
arcsin((y-4)/2)/3
Is this my answer or do i have to simplify??
wise pine
odd edgeBOT
odd edgeBOT
Available help channel!
plain sun
can someone please help me with this
odd edgeBOT
can someone please help me with this
plain sun
Or do you just want *any* proof?
oops didnt see this
yea its meant to be done with induction, forgot to specify
odd edgeBOT
@plain sun Has your question been resolved?
sterile blaze
whats the base case
plain sun
whats the base case
n = 1?
sterile blaze
yes, do that first
odd edgeBOT
@plain sun Has your question been resolved?
odd edgeBOT
@plain sun Has your question been resolved?
meager juniper
@plain sun ok, you assume it is true for n = 2k - 1, then you show it is true for n + 2 = 2k + 1.
It might be easier going from 2k + 1 to 2k + 3, fewer negatives to worry about
Why not start by expanding the values (2k+1)^4 and (2k+3)^4?
modest field
(2k + 1)⁴ = ||16k⁴ + 32k³ + 24k² + 8k + 1||
odd edgeBOT
@plain sun Has your question been resolved?
plain sun
alr ill try that
plain sun
Why not start by expanding the values (2k+1)^4 and (2k+3)^4?
Question 3
I assume you use the (2k+1) assumption to subtract from the 2k + 3 and get a 16M, and then everything else can be factorised into 16?
faint knot
I assume you use the (2k+1) assumption to subtract from the 2k + 3 and get a 16M...
sounds solid, but itd be easier to handle if
instead of 2k+1 then 2k+3,
you had 2k-1 then 2k+1
dusty bane
i dont know how to read this
odd edgeBOT
i dont know how to read this
dusty bane
its a trapezius formula
odd edgeBOT
@dusty bane Has your question been resolved?
dusty bane
yes
hard rain
Which bit don't you get?
dusty bane
the term in brackets.
not sure what f i+1 is
what i is
and what x is
hard rain
i is the index of summation
hard rain
$f_{i} = f(x_{i})$
clever fjordBOT
ekafeman
hard rain
why has the summation not endvalue ?
because the author is being lazy
he's writing an indefinite integral but it should be definite
the author should've written an integral over an interval [a,b] for example
then you fix some partition x_1, ..., x_n of [a,b]
(where x_1 = a, x_n = b)
then you'd have
clever fjordBOT
ekafeman
odd edgeBOT
@dusty bane Has your question been resolved?
granite lagoon
find 2 sin^2 30 * tan60 -3 cos^2 60 * sec^2 30
odd edgeBOT
find 2 sin^2 30 * tan60 -3 cos^2 60 * sec^2 30
Show your work, and if possible, explain where you are stuck.
paper crag
can someone please help me with this
(2x+1)^4 - 1
languid rain
find 2 sin^2 30 * tan60 -3 cos^2 60 * sec^2 30
do you know the values of sin and cos for 0, 30, 45, 60, 90?
plain sun
(2x+1)^4 - 1
bro I finished the question 💀
odd edgeBOT
@granite lagoon Has your question been resolved?
granite lagoon
Ye
wait i got it
it thought mine was wrong cuz chatgpt was giving wrong answers and i couldnt find anywhere the solution that matches mine
.close
odd edgeBOT
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Available help channel!
urban swallow
Find y'.
$\sqrt {xy} = x - 2y$
odd edgeBOT
Find y'.
$\sqrt {xy} = x - 2y$
urban swallow
How do I deal with the square root
cold sage
you can square both sides
gusty pulsar
Find y'.
$\sqrt {xy} = x - 2y$
So the task is to express y in terms of x?
urban swallow
oh wait
clever fjordBOT
00x0*97&!3
odd edgeBOT
@urban swallow Has your question been resolved?
odd edgeBOT
@urban swallow Has your question been resolved?
quiet zodiac
i gotta complete the square for this to solve an integral but 2+(2x+1)^2 gives me 4x^2+4x+3 instead
nimble blaze
factor out -1 first
quiet zodiac
factor out where
nimble blaze
of the whole expression at the start
you want a positive leading coefficient when completing the square
quiet zodiac
hm well i solved other questions w no positive coeefficient bcs i let b^2 equal to -b^2
quiet zodiac
is that 9 or 4
where
merry widget
i gotta complete the square for this to solve an integral but 2+(2x+1)^2 gives m...
this
nimble blaze
everywhere
quiet zodiac
4
merry widget
bruh why it look like 9
quiet zodiac
its a 4 man
quiet zodiac
ignore the bottom but heres an example
its a 4 y does it matter can u just help ffs
quiet zodiac
okay and how do i get that
merry widget
ok so first take the negative outside
its an universal rule, the coefficient of the variable u factor has to be always positive
nimble blaze
you messed up your signs here
merry widget
and then you know you have to get -4x
merry widget
you messed up your signs here
no its correct
in order to get -4x u know that if u factor (x-2)^2 u get the -4x for ex. ( (x-2)^2 = x^2-4x +4))
so the squard numerical inside would (x-2)
now you have to get the constant which is -3
remember ur negative sign should be outside the brackets
now u know that when u expand (x-2)^2 u get +4 as ur constant
to get -3 u just subtract 7 from it
and now the negative symbol outside will change the signs of the expression
making it -(x-2)^2+7
= 3+4x-4x^2
nimble blaze
nimble blaze
in your other question you had
a^2 - (bx + c)^2
due to the negative leading coefficient in -16x^2
similarly you should've started with that here too
quiet zodiac
ah
quiet zodiac
that gives u -4x^2+4x+1 though
nimble blaze
a^2 = 2^2 = 4
merry widget
yeah yeah
lone elbow
let $f(x)$ be a function three times differentiable and continuous, such that $|f^{(3)}(x)| \leq \frac{1}{4}, \forall x \in \mathbb{R}$ and let $P(x) = 3(x-1) + 5(x-1)^2$ be the taylor polynomial of degree 2 centered at $x_0 = 1$. Find $Q(x)$, the taylor polynomial of degree 2 of $g(x) = 4x + x^2 + f(7-3x)$ in $x_1 = 2$ and estimate the error of using $Q(2.1)$ instead of $g(2.1)$
clever fjordBOT
studying_calc_real_analysis
odd edgeBOT
@lone elbow Has your question been resolved?
lone elbow
we know P_2(x) is th epoly of degree 2 centered at x_0 = 1
so that means p(1) = f(1)
p'(1) = f'(1)
p''(1) = f''(1)
odd edgeBOT
@lone elbow Has your question been resolved?
upper onyx
do you know how to get the taylor polynomial of degree two for a function h(x)?
lone elbow
,, P_2(x) = h(x) + h'(x)(x-x_0) + \frac{h''(x)}{2!}(x-x_0)^2
clever fjordBOT
studying_calc_real_analysis
upper onyx
so you have a function g(x) use this formula.
lone elbow
,, P_2(x) = \left(4 \cdot 2 + 2^2 + f(7-3\cdot 2)\right) + g'(x)(x-2) + \frac{g''(x)}{2!}(x-2)^2
,, g(x) = 4x + x^2 + f(7-3x)
clever fjordBOT
studying_calc_real_analysis
upper onyx
does it start with g(x_0)?
lone elbow
$x_1 = 2$
upper onyx
well, you now nedd g' and g'', calc them.
upper onyx
by the way: you need to be more precise in using x or x_0.
upper onyx
you have still f in your formulas, you have t get rid of them.
clever fjordBOT
studying_calc_real_analysis
upper onyx
there are still f in your terms, get rid of them. and again: be more precise in using x with or without suscription. you permanently mix them up.
upper onyx
you have given the taylor polynom for f. use it.
clever fjordBOT
studying_calc_real_analysis
lone elbow
p(1) = f(1) somehow
p(1) = 0
f(1) = 0
lol
,w differentiate 3(x-1) + 5(x-1)^2
is it false then?
lone elbow
anyways, f(1) = 0
and if we differentiate p(x)
,w differentiate 3(x-1) + 5(x-1)^2
10x-7 is p'(x)
p'(1) = 10 - 7 = 3
f'(1) = 3
p''(x) = 10
p''(1) = 10
f''(1) = 10
upper onyx
again, youre mixing up usage of x and x with subscriptions. be more precise.
lone elbow
,, P_2(x) = 12 + f(1) + (8 - 3f'(1))(x-2) + \frac{2 + 9f''(1)}{2!} (x-2)^2
clever fjordBOT
studying_calc_real_analysis
clever fjordBOT
studying_calc_real_analysis
lone elbow
,, P_2(x) = 12 -(x-2) + \frac{92}{2} (x-2)^2
clever fjordBOT
studying_calc_real_analysis
lone elbow
mmm
now they want us to use P_2(x) to calculate P_2(2.1)
I mean Q not P
mb
oh this shit is so confusing
we found Q_2(x)
now for estimating error we can use lagrangian residue formula for finding upper bound of residue
I mean error
upper onyx
sounds like you know what to do.
lone elbow
mmm
here we prolly need to use the fact that $|f^{(3)}| \leq \frac{1}{4} \forall x \in \mathbb{R}$
clever fjordBOT
studying_calc_real_analysis
upper onyx
you do not need to show it to me. if you know what to do its fine for me, and i can leave.
lone elbow
Im still thinking how to do it lol
im just trying to put all the pieces together
all I know is this formula and the fact of |f^(3)| = . ..
x = 2.1
a = 2
n = 2
upper onyx
first you need g^(3) for the lagrange formula. but this wll lead you to f^(3), a = 2, x = 2.1, n = 2, the rest is simple calculation.
clever fjordBOT
studying_calc_real_analysis
lone elbow
,, g''(x) = 2 +9f''(7-3x_1)
clever fjordBOT
studying_calc_real_analysis
clever fjordBOT
studying_calc_real_analysis
upper onyx
you have all you need. do the calc.
lone elbow
mmm
okay
what is Z?
we know f^n+1 means g^(3)
but z?
a = 2
n = 2
z something between 2 and 2?
wtf?
g^(3) (2)
-27f'''(1)
x = 2.1
a = 2
n = 2
$|R_3| \leq \frac{g^{(3)}(2) |2.1-2|^{3}}{6}$
clever fjordBOT
studying_calc_real_analysis
lone elbow
,, g'''(2) = -27f'''(1)
clever fjordBOT
studying_calc_real_analysis
lone elbow
$|R_3| \leq \frac{-27f'''(1) |2.1-2|^{3}}{6} \leq \frac{-\frac{27}{4} |2.1-2|^{3}}{6} \leq -\frac{27}{24} | 0.1|^3$
lone elbow
,calc (0.1)^3
clever fjordBOT
Result:
0.001
,calc 0.001 * 27/4
clever fjordBOT
Result:
0.00675
.close
minor elm
Hello
minor elm
Can smn give me an example of of an equivalence relation that's also an order relation?
Other than the equality, if there exists
tepid pelican
Can smn give me an example of of an equivalence relation that's also an order re...
Ordering must be reflexive, transitive and antisymmetric
Equivalence relation must be reflexive, transitive and symmetric
So let R be an ordering relation on S, that's also an equivalence relation. Then assume aRb, by symmetry bRa, and by antisymmetry a = b. So from this we know that if aRb, then a = b. Hence the relation R must be subset of the equality relation. But since R is reflexive, equality must be subset of R. Hence R is the equality relation
so the equality relation is the only relation thats both ordering relation and equivalence relation
odd edgeBOT
@minor elm Has your question been resolved?
spiral jetty
.close
odd edgeBOT
Available help channel!
minor elm
Ordering must be reflexive, transitive and antisymmetric
Equivalence relation mu...
By this logic wouldn't Rf (xRy--> f(x)=f(y) also be an order rlt if f is injective
minor elm
Order and equivalence*
tepid pelican
By this logic wouldn't Rf (xRy--> f(x)=f(y) also be an order rlt if f is injecti...
What do we know about R
we need some additional information to conclude that it's order / equivalence
in my proof I assumed that it's both
and i got that it must be the equality relation
minor elm
What do we know about R
Nothing it's a hypothetical question
Since I saw smth in my exam that says that for R to be both order and equivalence then it has to be the equality rlt but I wasn't convinced 😔
tepid pelican
By this logic wouldn't Rf (xRy--> f(x)=f(y) also be an order rlt if f is injecti...
This statement alone is not enough to conclude that it's ordering relation
tepid pelican
Since I saw smth in my exam that says that for R to be both order and equivalenc...
It indeed does
To prove it, assume that some relation R is both order and equivalence. And then prove that R is the equality relation
minor elm
Transitive: if xRy then f(x)=f(y), if yRz then f(y)=f(z) thus xRz
Reflexive: xRx since f(x)=f(x)
tepid pelican
Transitive: if xRy then f(x)=f(y), if yRz then f(y)=f(z) thus xRz
Reflexive: xRx...
Hmm?
How can you conclude xRz
you assumed xRy and yRz and concluded f(x) = f(y) = f(z)
minor elm
F(x)=F(y)=f(z)
tepid pelican
By this logic wouldn't Rf (xRy--> f(x)=f(y) also be an order rlt if f is injecti...
You'd need to strengthen the implication to equivalence
it would have to be xRy iff f(x) = f(y)
xRy --> f(x) = f(y) doesnt suffice
minor elm
it would have to be xRy iff f(x) = f(y)
Yes that's what I initially meant😭
tepid pelican
Transitive: if xRy then f(x)=f(y), if yRz then f(y)=f(z) thus xRz
Reflexive: xRx...
Alright, then this is good
minor elm
So if it was iff, would that make it both?
minor elm
Wait I think we'll get that x and only x Rx
tepid pelican
x and only x Rx?
minor elm
Would that make a problem?
minor elm
x and only x Rx?
Like no other number but x
tepid pelican
what even is x?
minor elm
A number😔
tepid pelican
huh
minor elm
I mean that the number will have a rlt with itself only
tepid pelican
Correct
minor elm
F(x)=f(y) then x=y
tepid pelican
mhm
minor elm
Since f injective
Would that cause a problem?
tepid pelican
Since f injective
Would that cause a problem?
No it wouldnt cause a problem
f(x) = f(y) iff x = y
minor elm
tepid pelican
assuming f is defined everywhere
minor elm
Okay okay so the argument is still valid
minor elm
Yess
tepid pelican
so R is actually the equality relation
tepid pelican
np
odd edgeBOT
@minor elm Has your question been resolved?
cloud elm
Can someone help me to solve this perms and comb question? How many 4-digit even numbers greater than 5000 can you form using the
digits 0, 1, 2, 3, 5, 6, 8, and 9 without
repetitions?
haughty adder
Can someone help me to solve this perms and comb question? How many 4-digit even...
so
first
you need to find greater than 5000
_ _ _ _
1 2 3 4
at first place
mystic saffron
hint;- observe what causes a number to be even
and what should be done so that no. is greater then 5000
apply these thing
haughty adder
you can put either 5/6/7/8/9
mystic saffron
dont directly give away the solution
haughty adder
and u cannot repeat digits
mystic saffron
@haughty adder
haughty adder
<@795290135356637215>
ok
cloud elm
I did 4x8x8x4
haughty adder
without repetitions
cloud elm
but only 9,8,6,5 are greater than 5 for the given numbers
cloud elm
is not given
cloud elm
can you form using the
digits 0, 1, 2, 3, 5, 6, 8, and 9
the answer is far less from what i got
cloud elm
oh wait
yes
without rep
wait let me try
ok i tried 4x7x6x4???
idk😭
i wrote 7 because the first digit already used one digit
and same as the third digit?
and last digit cause it gotta be even so it can only be 8,6,2,0 so x4
haughty adder
and last digit cause it gotta be even so it can only be 8,6,2,0 so x4
how you choose first digit them?
cloud elm
numbers that are greater than 5
haughty adder
no
you chose 6 there
and then you cannot take that in unit place
if it is 8, you cannot take it in unit place
cloud elm
wdym unit place
haughty adder
4th digit
cloud elm
but how you chose 6 in first digit
haughty adder
i wrote 7 because the first digit already used one digit
it should be 6 i think
haughty adder
can you form using the
digits 0, 1, 2, 3, 5, 6, 8, and 9
both 4 and 7 are not in digits
so
cloud elm
so your formula will be?
haughty adder
2x6x5x4 + 2x6x5x2 = 2x6x5x4 + 1x6x5x4 = 3x6x5x4 = 360
cloud elm
the answer is 420 😮
haughty adder
wait let me check
5689 is for first digit
0268 is for fourth digit
remaining 6 is for second digit
remaining 5 is for third digit
when first digit is odd 5,9 = x2
fourth digit can be 0,2,6,8 = x4
when first digit is even 6,8 = x2
fourth digit can be 0,2,(6/8) = x3
haughty adder
the answer is 420 😮
got my mistake here ^ (read last line)
haughty adder
2x6x5x4 + 2x6x5x2 = 2x6x5x4 + 1x6x5x4 = 3x6x5x4 = 360
2x6x5x4 + 2x6x5x3 = 2x6x5x7 = 420
cloud elm
5689 is for first digit
0268 is for fourth digit
remaining 6 is for second digit...
but first digit 5,6,8,9 and last digit 0,2,6,8 wouldnt there be repetition?
haughty adder
but first digit 5,6,8,9 and last digit 0,2,6,8 wouldnt there be repetition?
what do you mean?
haughty adder
when first digit is odd 5,9 = x2
fourth digit can be 0,2,6,8 = x4
have you read it
haughty adder
when first digit is even 6,8 = x2
fourth digit can be 0,2,(6/8) = x3
and this
odd edgeBOT
odd edgeBOT
Available help channel!
misty bane
odd edgeBOT
misty bane
someone please help
i have all hte work posted here
where in gods name did the E^-3t come from
like i followed completely till that point
that felt so out of no where
someone please help I posted this question before and no one replied for an hour and half and then said they didnt know how to solve it
brittle beacon
The fact that it's [-3] one of your eigenvalues, or?
misty bane
no like where did the e come from
like how do i form the general solution
not just for this problem but in general
like is it always e^eigenvalue +e^eigenvalue
or is that just this problem
im so freaking confused
ok i found out that is how that works
the person who was helping before told me it wasnt
and confused the hell out of me
god
odd edgeBOT
@misty bane Has your question been resolved?
brittle beacon
like is it always e^eigenvalue +e^eigenvalue
Oh, yea, it is, you create them from linear combinations of e^{eigenvalue} * [eigenvector] basically 
[notice how Ae_i = lambda_i e_i gets you that \lambda_i as a coefficient, as does differentiating e^{lambda_i t} wrt t]
fickle cape
how do i do 11
odd edgeBOT
how do i do 11
sullen ferry
https://tutorial.math.lamar.edu/classes/de/undeterminedcoefficients.aspx useful resource for these sorts of problems :)
odd edgeBOT
Available help channel!
faint hound
Okay bit of help on this one?
odd edgeBOT
Okay bit of help on this one?
faint hound
or the zeros
Idk tbh what it's referring to here's the question as a whole and also answers so far
faint hound
try graphing x^2 - 2x - 4 = x - 4
Do I need to simplify the equation 1st?
proven beacon
yea
proven beacon
ok then look at the two x values which pass through the x axis
odd edgeBOT
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modern cave
i need help in probaillity
odd edgeBOT
i need help in probaillity
modern cave
d
proven beacon
count the number of red sectors
modern cave
no?
proven beacon
simplify 5/10
proven beacon
do you know how to simplify fractions
modern cave
but my teacher multiplys it
proven beacon
do you want it in
modern cave
both numbers
proven beacon
percent form
modern cave
yeah
proven beacon
?
modern cave
percent
modern cave
0.50
proven beacon
multiply it by 100
modern cave
why 100
proven beacon
percent
modern cave
in percent form its 50%\
proven beacon
yes
50%
the problem says you need it in fraction, decimal, and percent form
did you simplify 5/10 yet
modern cave
okay another question
so
question b
is 3/10
how do i do in percent
in percent its 0.30
proven beacon
multiply it by 100
modern cave
but why 100?
proven beacon
in percent its 0.30
this is decimal form btw
proven beacon
but why 100?
per-cent
cent which you might hear from century meaning 100
per 100
modern cave
so 3/10 x 100?
proven beacon
yes
proven beacon
its not certain
modern cave
3x100 is 300
modern cave
yes?
proven beacon
so 3/10 x 100?
.
modern cave
?
proven beacon
ok
you have a probability of 3/10 correct
to convert that to percent you multiply it by 100
because percent means per hundred
3/10 * 100 = 30%
or 30/100
which when simplified becomes 3/10
basically percent means some number divided by 100
ex.
99% = 99/100
33% = 33/100
30% = 30/100 = 3/10
modern cave
what if i email my teacher how to do it
proven beacon
go ahead
modern cave
but how do you know what to multiply it by
proven beacon
you convert the fraction into decimal form
then multiply it by 100
to get percent form
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charred yarrow
Is this possible i found it on the internet the problem, is it sovable?
worn sandal
There are infinitely many solutions if x, y, and z are just any real numbers
charred yarrow
how?
so just cause there are no ways to sovle, there are infinitly many solutions?
worn sandal
I didn't say that
charred yarrow
ik asking
worn sandal
but like you basicaly just have 3 real numbers that add to 42
charred yarrow
ok
worn sandal
and there are infinitely many ways to do that
charred yarrow
ohh ok
worn sandal
If x, y, and z are integers that might be a bit harder
forest sky
Is this possible i found it on the internet the problem, is it sovable?
the joke is that this is a diophantine equation, where we look for integer solutions, and the solution was only discovered recently:
https://news.mit.edu/2019/answer-life-universe-and-everything-sum-three-cubes-mathematics-0910
charred yarrow
but does it being cubed affect it?
worn sandal
the joke is that this is a diophantine equation, where we look for integer solut...
ah lol
charred yarrow
the joke is that this is a diophantine equation, where we look for integer solut...
ok thanks
forest sky
42 = (-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3
worn sandal
oh shit
charred yarrow
42 = (-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3
i got the same answer after asking ai. idk if its exact same
odd edgeBOT
charred yarrow
.reopen
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charred yarrow
so its solve but i dont fully get how
forest sky
mathematicians made a computer program to test a whole bunch of integers until it found one
charred yarrow
oh ok
forest sky
the details are in the article
charred yarrow
the joke is that this is a diophantine equation, where we look for integer solut...
this?
ok thx everyone
.close
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peak thunder
How can I solve this? It's in Spanish, but the problem asks which statements can be true. I am struggling since the v_2 should be always 0, and the answer sheet says:
First row: False, false, false
Second row: F, T, T
Third row: F, T, T
peak thunder
$$\text{Given } v_1=\min{c^Tx:Ax\geq b, c^Tx\geq d} \text{ and } v_2=\min{0:Ax\geq b, c^T x\leq d}$$
clever fjordBOT
Acrol
peak thunder
Without justifying, indicate which combinations on the table are feasible
odd edgeBOT
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@peak thunder Has your question been resolved?
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@peak thunder Has your question been resolved?
pastel orbit
odd edgeBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
4
the problem statement is on the left, my proof is on the right
any comments or suggestions are appreciated!
even stuff about typography or notation
odd edgeBOT
@pastel orbit Has your question been resolved?
pastel orbit
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@pastel orbit Has your question been resolved?
runic cypress
Looks pretty much perfect
pulsar elbow
yeah this is fine
pastel orbit
one thing
I felt like
writing U_i = (1/i, 1 + 1/i) is like
bad form or smth
or is that fine too?
pulsar elbow
writing U_i = (1/i, 1 + 1/i) is like
why would it be bad form
it's clear what U_i is for each i
pastel orbit
ig so
but U_i are supposed to be sets, and ig using interval notation felt weird to me
pulsar elbow
they are indeed sets
pulsar elbow
topologists will do shit like "let X = " and then draw the picture of the space
you're good
pulsar elbow
it's just easier to communicate once you know that you can back your shit up
jolly zephyr
odd edgeBOT
jolly zephyr
hi am i doing this right so far
i’m a bit confused
so i wanna make sure im. on the right path
dawn tiger
you can't only apply the log to the 5^x and just bring the 9 out
log(9*5^x) != 9 log(5^x)
jolly zephyr
you can't only apply the log to the 5^x and just bring the 9 out
does this look better?
dawn tiger
same problem
dawn tiger
log(9*5^x) != 9 log(5^x)
sorry if this notation wasn't clear, that says not equal
jolly zephyr
oh
dawn tiger
log(ab) isn't the same as alogb
so you can't just bring the 9 out front
you might be able to make use of log(ab) = loga + logb though
dawn tiger
you were correct in taking the log of both sides
so you would get log(9 * 5^x) = log(8^(x+4)) like you got in the first line
you also correctly simplified log(8^(x+4)) to (x+4) * log8
dawn tiger
you might be able to make use of log(ab) = loga + logb though
can you rewrite log(9 * 5^x) using the rule i mentioned here?
dawn tiger
yes exactly except that should be log(5^x), not log(5x)
so you'd get log9 + log(5^x) = (x+4)*log8
dawn tiger
can you simplify log(5^x)?
jolly zephyr
xlog 5?
dawn tiger
yeah
so you'd have log9 + x * log5 = (x+4) * log8
you'd want to solve for x, how would you go about bringing all the x's to one side?
jolly zephyr
you'd want to solve for x, how would you go about bringing all the x's to one si...
this is where i’m at
dawn tiger
careful, that should be a -4log8 since you brought it to the left side
but yeah
maybe bring anything that doesn't have an x to the right
jolly zephyr
how would you solve for just x?
uh
dawn tiger
since both terms on the left have an x in them, maybe you could factor the x out?
jolly zephyr
since both terms on the left have an x in them, maybe you could factor the x out...
done
dawn tiger
what do you get for x?
jolly zephyr
rn i’m here
jolly zephyr
what do you get for x?
dawn tiger
yeah good
to solve for x just divide the log5 - log8 over
and you'll get x = log(4096/9) / (log5 - log8)
which is a big mess you plug into a calculator
odd edgeBOT
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brittle crag
Griet Gauss born in 1987 is looking for a password. It must consist of 8 different characters (letters or numbers). How many possibilities are there if the password must not begin with her year of birth?
brittle crag
for the first position you pick 1 out of 35 (excluding the first number of her birth year)
static totem
ah okay
brittle crag
Why can’t I do npr(35,1)*npr(35,7)?
So I thought if it doesn’t begin with a 1 this would work but I got the wrong answer
static totem
and then you add it back but exclude the letter you used instead
brittle crag
Yeah
static totem
well this tries to make them all different
so you can't because it could have repeats
oh nvm
i missed that part, must be different
dawn tiger
why isn't this just 35^4 * 36^4?
also how can i make that a spoiler
idk how to use discord lmao
brittle crag
you can’t have repeats
dawn tiger
oh
static totem
it makes sense, it just misses all passwords that start with 1
static totem
yeah
brittle crag
.close
odd edgeBOT
misty bane
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misty bane
can i solve this like any eigen vector problem like find eigen values the egein vector and plug into the general solution
or do i have to do something different
because y'=Ay
like does that part matter?
<@&286206848099549185>
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@misty bane Has your question been resolved?
mortal quarry
shouldn't this be 4C4?
odd edgeBOT
shouldn't this be 4C4?
mortal quarry
because it is stated that "It does not matter in which order the checks are made"
nimble blaze
they mean that ther's no restriction on whether one check has to be done before another
mortal quarry
mhm this is really weird
past mango
If the order matters, such as (1,2) and (2,1)is the same combination, then it’s 4C4
Otherwise you should multiply by 4! Making it 4P4
If I doesn’t misunderstand it
nimble blaze
e.g. checking
a b c d
in that order would be one way to check
a b d c
would be another
mortal quarry
its just that it literally states that order does not matter
in the question
so im quite unsure
nimble blaze
they mean that ther's no restriction on whether one check has to be done before another
mortal quarry
yea i get ur point
nimble blaze
e.g you don't have to fill the requirement that you have to check c before d
odd edgeBOT
mortal quarry
.reopen
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mortal quarry
oh come on how is this 6P2 * 5P2 and not 6C2 * 5C2
nimble blaze
because it matters which person has which role
muted thicket
mhm
odd edgeBOT
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jolly zephyr
hey
jolly zephyr
so i was checking the asymptotes for this equation
on Mathway it says there’s a HA @ y=-1, but on desmos the graph is able to touch y=-1?
jolly zephyr
if you zoom in, its gonna be around -0.9999
normally it does say something like this
but it doesn’t for this equation
is mathway still right?
tepid pelican
np
jolly zephyr
.close
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urban swallow
How would I approach this?
odd edgeBOT
How would I approach this?
urban swallow
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frigid canopy
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undone basin
do you know the formula of centripetal acceleration?
undone basin
yes
urban swallow
sqrt(37.5)?
undone basin
sounds right
urban swallow
that's for b.) right
undone basin
yes
urban swallow
then for a.) i just substitute the answer from b.) to v^2?
undone basin
umm wait, the acceleration isn't angular acceleration, is it?
urban swallow
that's what i'm confused about too
undone basin
what is the direction of a then? is it along vector-a?
urban swallow
i'm not sure how to answer that
undone basin
assuming the acceleration is in the direction of vector-a, we can resolve it into 2 vectors
urban swallow
how would i do that
undone basin
wait a min
urban swallow
okay thank you
undone basin
ok i'm back
the given acceleration is resultant acceleration it seems
so if you want to find tangential acceleration you can resolve vector-a into two components one along the radius and one along the tangent
the component along radius would be acos(theta)
and the component along the tangent would we asin(theta)