ok so in this case, u didn't add the length of other triangle
#help-23
odd nest
X is 18
lean otter
10 + y / y = x / 6
so u added two side on the numerator of left side... right?
RIGHT?!
U APPLY THAT FOR THE RIGHT SIDE
SOOOOO X + 6 / 6
odd nest
X + 6 are NOT connected like y + y + 10
lean otter
X + 6 are NOT connected like y + y + 10
thats fine lol
odd nest
Itâs not?
lean otter
u just have to apply that
lean otter
thats not how it works
if u add two side, u just have to add it
regardless of connectives
lean otter
How is it X / x+6?
it doesnt need to be... but u added two side on the numerator of other side right?
u should apply that for x
lean otter
12 + 8 IS ADDED BECAUSE ITS A SINGLE LINE of the triangle
ok ok so u added it because its a single line right?
lean otter
it doesnt need to be a single line
odd nest
Single side of a BIG triangle
lean otter
Ok Iâm not gonna fight with you
im sry btw
$$\frac{\text{side of small triangle}}{\text{corresponding side of large triangle}} = \text{constant ratio} $$
flat frigateBOT
Da pro
lean otter
@odd nest id calculate it with the small triangle and the large triangle in the first place
odd nest
8x = 120
120:8
15
Somehow chat gpt tells me x = 9
Can Anyone clarify ? <@&286206848099549185>
lean otter
Somehow chat gpt tells me x = 9
so im right?!
odd nest
Now chat got now says itâs 5
austere cypress
chatgpt is dum
summer rover
chatgpt is dum
Whatâs the answer?
lean otter
Whatâs the answer?
15
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granite seal
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glad river
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versed wave
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â
versed wave
just so you know, this problem is called the napkin ring problem
versed wave
theres actually a rather counterintuitive formula for it, but you can derive it yourself
it helps to just consider the cross section of the sphere instead
glad river
the way i think of it is the volume of the sphere minus the hole
i honestly dont understand it at all
i get disk method and washer method but not this
.close
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lean otter
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lean otter
Can someone help me with congruency?
tardy mango
This is mainly just knowing how to interpret the symbols
If two angles are marked with the same (nonzero) number of arcs, then that means that theyâre congruent
tardy mango
Those arent marked with any arcs
lean otter
Wdym arc?
lean otter
If two angles are marked with the same (nonzero) number of arcs, then that means...
So KL and JI?
lean otter
Is K and J not marked with arcs?
tardy mango
There are angles with vertices at those points that are marked if thatâs what you mean
lean otter
Iâm still confused
tardy mango
So angle KLM is congruent to JIH
If these names were supposed to refer to those angles, then the names are wrong
The vertex name goes in the middle
lean otter
The vertex name goes in the middle
Isnt L and I not the vertex
lean otter
These angles are marked if thatâs what youâre saying
Yea thatâs what I was referring to
tardy mango
Isnt L and I not the vertex
??
tardy mango
The vertex is where the two rays that make the angle intersect
In the case of the top circled angle, the vertex is J (as both of the rays that make that angle extend from J)
lean otter
??
Im horrible in math just excuse if I say anything dumb i thought the vertex was the thing that connected things between two lines so like L connections to K and M
tardy mango
i thought the vertex was the thing that connected things between two lines
A better (aka more rigorous) way to frame this is where the two lines/rays/segments that make the angle intersect is the vertex
tardy mango
The vertex is where the two rays that make the angle intersect
Which is what I said here
tardy mango
In the case of the top circled angle, the vertex is J (as both of the rays that ...
Returning back to this example,
See how JH and JI are the sides of the arc
They meet at J
Hence J is the vertex
safe radishBOT
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versed smelt
part b
versed smelt
Could someone check where I went wrong???
brave wolf
here I think
versed smelt
i assumed, but idk what i did wrong there đ¤§
vernal crystal
I'm not sure if a direct u substitution will work with the problem, you could trying multiplying the numerator and denominator with e^-x and then try
brave wolf
it's $\left(1 - \frac{e^t}{u}\right) dt$
flat frigateBOT
MĂŚthIsAlwaysRight
brave wolf
you cant just cancel the e^t and replace dt with du
digital sparrow
what does \left and \right do?
quick crater
make brackets be an appropriate size
digital sparrow
make brackets be an appropriate size
ooh
flat frigateBOT
Skissue ping4response
versed smelt
huh đ
brave wolf
you cant just cancel the e^t and replace dt with du
so yeah, this is the issue with your sub
brave wolf
cause ive made e^t dt = -du
in reality, it looks like this
there are parenthesis
we omit them by convention, but act like if they were there
versed smelt
so its taken as 1 term?
vernal crystal
Also the constant 1 you've integrated should be in terms of t instead of u
vernal crystal
Like when you distribute the dt, you could only covert the e^tdt to du but not with the 1
brave wolf
Also the constant 1 you've integrated should be in terms of t instead of u
wait where?
vernal crystal
The u/u they've cancelled
brave wolf
oh, ic, thats what i was saying
versed smelt
mm
vernal crystal
oh lol
versed smelt
this is the answer btw
photon mentioned smth about multiplying by e^t
just curious
how do i recognise when to multiply by e^t?
vernal crystal
Yeah multiply the denominator and numeraetor by e^-t
vernal crystal
how do i recognise when to multiply by e^t?
Practice
versed smelt
we were taught we either mutliply by "1/1" or "+-1"
when the integration is to complicated
brave wolf
Your approach isnt entirely wrong btw, I think that you could continue with that
vernal crystal
Yeah seems like if you fixed few steps, your method should work fine
versed smelt
oo
versed smelt
and unless you factor out e^t from both terms, you cant cancel it so easily
okok lets get back this then
versed smelt
in reality, it looks like this
separating the term like this isnt wrong right? its just how i move on from there?
vernal crystal
Yeah multiply the denominator and numeraetor by e^-t
The motivation of muliplying the num and den was so we could subsitute e^-x-1 as as u then the integral would turn into a simple 1/u integral
versed smelt
oo
versed smelt
and unless you factor out e^t from both terms, you cant cancel it so easily
how can i do this?
and would that overcomplicate my solution?
versed smelt
we were taught we either mutliply by "1/1" or "+-1"
nvm i think ill try this
.close
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versed smelt
thanks!
brave wolf
and would that overcomplicate my solution?
Idk yet, i was trying it and I got pretty weird results for some reasons. ill try to figure it out
oh wait, nvm, i was looking at the answer key to b
the results i got were correct
basically at this poitn you can split the integral
integral of 1 is gonna be t
and integral of e^t / u dt is gonna be -ln(u) = -ln(1-e^t)
versed smelt
ooo
splitting the integral
never thought of that
so thats where the t came from
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river bolt
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digital sparrow
!status
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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
1
digital sparrow
tell me what a_3 will be
river bolt
(a_1)(a_2)
digital sparrow
ok and what about a_4
river bolt
(a_4) = (a_1)(a_2)(a_3)
digital sparrow
substitue a_3 in this
river bolt
so its just (a_3)(a_3)?
digital sparrow
yup
digital sparrow
now can you think of how to do this?
river bolt
im thinkin 1 sec
since n > 2 lets take 3 for example so a_3 = t which means a_(3+2) is a_5 right?
and sincr we know a_5 = (a1)(a2)(a3)(a4) thats basically (a3)(a3)(a3)(a3) which is (a3)^4
and since a_n = t, then a_5 = t^4?
or does this not work
flat frigateBOT
Wumpus Man
river bolt
but if you used lets say n = 3, that would work? at some point you are getting a_(3-4) which is a_(-1) and how do a2 and a1 come into play here?
digital sparrow
**Wumpus Man**
this is just a generalization
it just means you go from a_n all the way a_1 multiplying all the terms
for a_3 it will just be a_2 * a_1
a_4 = a_3 * a_2 * a_1
river bolt
ok i see makes sense
$a{n+2} = a_(n+1) * a_n * a{n-1} * a{n-2} * a{n-3} ..... a_3 * a_2 * a_1$
flat frigateBOT
Sven
river bolt
damn didnt turn out right
$a{n+1} = a_n * a{n+1} * a{n-1} * a{n-2} * a{n-3} ..... a_3 * a_2 * a_1$
flat frigateBOT
Sven
river bolt
still doesnt work ok idk why its not coming out correctly
safe radishBOT
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zealous jetty
how do you come to that answer??
safe radishBOT
how do you come to that answer??
digital sparrow
$\log({a^b}) = b\log{a}\newline$
$\log({ab}) = \log{a} + \log{b}\newline$
$\log({a/b}) = \log{a} - \log{b}\newline$
flat frigateBOT
Wumpus Man
safe radishBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
verbal token
digital sparrow
**Wumpus Man**
a list of identites that will help you
zealous jetty
**Wumpus Man**
i do know that i just get a different thing
one sec
okay no
am i supposed to solve it like the log isnât there
just w the numbers
or like
make separate logs
fast sierra
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fast sierra
heyo, im just confirming that this wants me to basicly carry out differantiation of "10 x -2^3 + 8 + -2^2 + 5"
fast sierra
could you explain then?
lean otter
heyo, im just confirming that this wants me to basicly carry out differantiation...
differentiating that would give you a 0
you are first supposed to differentiate it wrt x and then input x=-2
lean otter
?
fast sierra
you are first supposed to differentiate it wrt x and then input x=-2
^
ih
oh
you ment with?
lean otter
yep
whhat you are doing here is
finding the slope of the tangent of the curve 10 x^3 + 8x^2 + 5
at x= -2
thin bridge
*to the curve
fast sierra
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pearl sphinx
Can someone please help me understand this and also like if this data has a positive correlation to the 3 variables
I know that (r= .008 , p=.954 ) but which of the both do I base as closer to 1 ? the r or the p ?
<@&286206848099549185>
or maybe I'm thinking of it wrongly
I'm so lost...
:>
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@pearl sphinx Has your question been resolved?
lilac shale
a) Angle POQ = 1.75 rad
b) Length of PX = 4.7896cm
c) Area of shaded region = ???
safe radishBOT
a) Angle POQ = 1.75 rad
b) Length of PX = 4.7896cm
c) Area of shaded region = ??...
lilac shale
I found area of segment QP
which is 6.128cm
squared
Maybe I can use triangle formula Half * r^2 * sin theta. But idk about theta here
Can you help with 5 (c) please
......
safe radishBOT
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lilac shale
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upbeat current
How do u do this?
safe radishBOT
How do u do this?
upbeat current
<@&286206848099549185>
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@upbeat current Has your question been resolved?
little ibex
How do u do this?
im not familiar with this exact type but
i can try helping
a sinusoidal function would mean f(x) has sin function with some additional things attached
maximum value of a regular sine function is 1 & minimum is -1
so you need to change it in such a way that the maximum is 100 and minimum is 20
so something like f(x) = ksin(x) + c
little ibex
and for a pt to be on the curve
noble frigate
$f(x)=a\sin{(bx)}+c, \text{where a is amplitude, b is frequency, and c is midline}$
whoops
upbeat current
and for a pt to be on the curve
Pt?
little ibex
point (x,y) to be on curve, f(x) = y
upbeat current
Oh
upbeat current
yea ik
flat frigateBOT
UrMom73
upbeat current
Alr
noble frigate
try finding the midline and amplitude first
noble frigate
the equation for period is 2Ď/b
so find a value for b that will result in a period of 30
upbeat current
b?
I use k but it doesn't matter
Period is 30
So 2pi/30
Which is pi/15
@noble frigate
Right?
noble frigate
yup
flat frigateBOT
Donut
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carmine latch
Hey,
A coin is tossed 8 times what is the probability that there are no 3 consecutive head or tails?
i solved it using combinatorics, but i want to solve it using only probability, i am thinking of using binomial distribution, but i am unsure of how to
safe radishBOT
Hey,
A coin is tossed 8 times what is the **probability** that there are no 3 co...
@carmine latch Has your question been resolved?
carmine latch
any helpers 
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unique venture
Hey,
A coin is tossed 8 times what is the **probability** that there are no 3 co...
could you use tree diagrams?
actually, 8 times would be difficult to draw
unique venture
Hey,
A coin is tossed 8 times what is the **probability** that there are no 3 co...
ok so to find the total number of outcomes, you do 2^8 which is 256. youre looking for every probability excluding "HHH" or "TTT"
urban sapphire
Hello please help Iâve been stuck for 2 hours on this
safe radishBOT
Hello please help Iâve been stuck for 2 hours on this
urban sapphire
It looks really easy but for some reason I got stuck
lean otter
I hate geometry
tulip acorn
AC=BC so the big triangle has equal sides so the symetric of A is B where the axis is the perpendeicular line to AB passing by C then you can prove that the symmetric of the point of intersection of the circle of radius AD and the line AB is the the intersection of the cercle of the same radius wich is AD(=BE) and the line AB which is E so the symmetric of D is E so CDE is a triangle of equal sides so the angles are equal
there are other methods but i didnt know what lessons and theorems you can use
so i just wrote down any idea i got
urban sapphire
AC=BC so the big triangle has equal sides so the symetric of A is B where the ax...
Thanks a lot. Do you know how I could write that in a plain theorem sense for the proof?
urban sapphire
I hate geometry
Me tooâŚthe answer is so obvious but then to find a way to prove it lol
Algebra is way better
lean otter
Algebra is way better
FOR REAL
tulip acorn
Thanks a lot. Do you know how I could write that in a plain theorem sense for th...
can you use the symmetry theorems
urban sapphire
can you use the symmetry theorems
Iâm not sureâŚthis module is supposed to just be about congruence I donât think weâve learned any symmetry theorems yet
Unless I just wasnât paying attention
lol
tulip acorn
do you have the theorem that says 2 triangles that has 2 equal sides and equal angle between those side are equal or smthing like that
tulip acorn
i think so i didnt study math in english so i dont know the names
urban sapphire
Oh ok
Yeah like Side angle Side congruency right
I was trying to prove angle A is equal to angle B
But found my figure out how to prove that
Because if those two angles are equal then CPCTC right?
tulip acorn
Because if those two angles are equal then CPCTC right?
didnt understand that
urban sapphire
CPCTCâŚyou know corresponding parts of congruent triangles are congruent
urban sapphire
But how can I prove angle A is equal to angle B?
tulip acorn
you have a triangle ABC where AC=BC
urban sapphire
OHHHHHHHHHHHHHHH
tulip acorn
conclusion its isosceles triangle
tulip acorn
np
tulip acorn
just focus and try to start with small conclusions dont look at the whole picture at one go
urban sapphire
Okay, thanks for the advice
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weary sandal
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weary sandal
Hey can I get some help with this one?
For some reason I feel like none of the answers are correct so I'm kinda stuck
<@&286206848099549185>
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@weary sandal Has your question been resolved?
weary sandal
So my understanding of this is that we have something like this:
v0 ----------- v1
| |
| |
| |
v2 ----------- v3
I don't think the first one is right because the dot product also takes into account the lengths of the vectors ||a|| ||b|| cos(theat) . I don't think the second is correct because it takes into account the size of the paralellogram spanned by the vectors. I don't think the 3rd is right because the diagonals are not always perpendicular and I don't think the last is right due to the same problem as answer 2.
Am I missing something here? <@&286206848099549185>
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@weary sandal Has your question been resolved?
azure delta
For some reason I feel like none of the answers are correct so I'm kinda stuck
Yeah, those all look wrong.
weary sandal
I'm pretty sure the second is the closest but one could be a scalar mult of the other right?
lost cargo
safe radishBOT
lost cargo
vector equation
azure delta
Vector equation, like the one with the parameter?
Or like some cross product equalling zero?
azure delta
Do you know how cross products identify paralellity?
kind forge
wait hold on
lost cargo
yes
kind forge
are we not overthinking this
isn't the vec eqn form of a line just a point plus Îť Ă some vector?
kind forge
oof
azure delta
isn't the vec eqn form of a line just a point plus Îť Ă some vector?
I think that's part 2
kind forge
ah
azure delta
Cause that uses a parameter
In any case, if you don't remember what the cross product does, it will be good for you to review it
lost cargo
so how do i approach these questions in general
when i was given a vector and a point
azure delta
Forget the point for a moment. What vector equation using cross product can you write that describes vectors parallel to the given vector?
azure delta
That's dot product
And oddly enough, we don't really care what the formula for cross product is. We care that the cross product of parallel vectors is zero
azure delta
It is
lost cargo
so if its parallel it would be sin 0?
azure delta
Yes
lost cargo
so for this question it should be a^2 * 2^2 + b^2 * 1^2 + c^2 * 3^2 = 0?
and i solve for a b and c?
lost cargo
oh wait
azure delta
Again, you don't need any formulas for the cross product. You only need to understand that the cross product of parallel vectors is zero.
lost cargo
how can i solve for v
azure delta
why are you trying to solve for v?
lost cargo
don't i need to find the vector equation
azure delta
that is a vector equation
azure delta
v x (2,1,3) = 0 is an equation of vectors
lost cargo
isn't vector equation r = a + lambda b
azure delta
lambda is a parameter, so I think that's a parametric equation
but if you want that, you can write that in one step cause they give you a and b
I guess the parametric equations could be that equation you gave but pulled apart into its components
azure delta
the words are a big ambiguous without the context of your lessons
azure delta
isn't vector equation r = a + lambda b
if you want this, do you know how to find a and b?
azure delta
lambda just lets you go any distance away from point a. b tells you the direction that you need to be going. What direction does the question tell you to go?
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dense wadi
if im not mistaken
safe radishBOT
if im not mistaken
median vigil
we can rewrite $y = mx + b$ as [ \underbrace{\begin{pmatrix} x \ y \end{pmatrix}}{\vb x} = t\underbrace{\begin{pmatrix} 1 \ m \end{pmatrix}}{\vb v} + \underbrace{\begin{pmatrix} 0 \ b \end{pmatrix}}_{\vb x_0} ]
note that this is not the only form that $\vb v$ and $\vb x_0$ have to take
flat frigateBOT
cloud
median vigil
and you are correct that in both cases it shifts the line away from the origin
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dense wadi
are v1 and v2 parallen to x_0?
safe radishBOT
are v1 and v2 parallen to x_0?
plucky elk
Doesn't look parallel
plucky elk
Yes these two images look unrelated
mossy lotus
the vectors v1 and v2 are parallel to the plane thru x_0
The vectors v1, v2, x_0 all share the origin as starting point. Ofc they wont be parallel
dense wadi
yeha i realized
mossy lotus
If you draw the parallelogram law of vector addition on x = x_0 + t1v1, youd see the different values of t1 yield different vectors parallel to v1. Similarly for v2
dense wadi
ig the importance is they form a plane thats parallel to each other
mossy lotus
and those vectors span the plane parallel to v1 and v2
mossy lotus
ig the importance is they form a plane thats parallel to each other
yea
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karmic falcon
hello, undergraduate need help for an exam that's after 1 hour calculus derivatives
safe radishBOT
hello, undergraduate need help for an exam that's after 1 hour calculus derivati...
daring crescent
Do you understand what it is asking in part a?
and not know how to do it, or do you not know what it is asking at all?
safe radishBOT
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daring crescent
@karmic falcon !status
karmic falcon
and not know how to do it, or do you not know what it is asking at all?
c isnt clear
didnt see ur massage
This also if you can
daring crescent
hmmm, wording this will be a bit awkward, the slopes can make there own graph and it is asking how that graph behaves (you can assess that with the equation of the slops of 1/a)
daring crescent
Guesstimate the slope and draw a tangent line at the given points on the graph
daring crescent
There is nothing you can do without the function being written out, unless you know how to get the function for those graphs
karmic falcon
daring crescent
All it's asking is for you to draw the tangent line at that point
daring crescent
See in figure 3.3
The only one that has a slope that you can tell accurately is the p2 on 2
karmic falcon
daring crescent
yeah, the red lines are tangent lines
safe radishBOT
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deep imp
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deep imp
i know how to subsitutue it but i want to see how its graphed
young nexus
take an x (e.g. -3), calculate y, draw a point, take the next x ....
wild copper
Ah, yes. The "let's eyeball it" method.
But on a more serious note, a question like graphing is not something that you can ask over internet, because it depends more on your drawing skills. The best we can do is to tell you how to do it.
deep imp
Ah, yes. The "let's eyeball it" method.
But on a more serious note, a question l...
its 2 quadratic equations
how should i set it up to standard form
young nexus
why do you need a standard form?
young nexus
take an x (e.g. -3), calculate y, draw a point, take the next x ....
as i said. do this.
young nexus
easier than typing a tons of questions in a discord channel? during the time i am typing all this messages i would have done this twice.
faint seal
like find aos or vertex
You'll still need at least some reference points to draw the graph accurately
lean otter
I think it'll be more rewarding and better practice if you understand how the shapes of these graphs are affected by translations, stretches, etc. It will take you less time to draw them if you understand how the functions behave in general and are able to apply your knowledge of how these various transformations affect them. @deep imp For example x^2 - 16 is just a translation of the function f(x) = x^2 down by 16 units. If you know the shape of the graph, you should be able to draw it in a few seconds.
lean otter
,w graph f(x) = x^2
flat frigateBOT
lean otter
what can you say about x^2 - 16?
lean otter
correct
lean otter
that's a good question and I'm glad you are no longer trying to find the easy method but the one that'll help you solve these types of problems in the future
so, what do you think?
deep imp
downwards y axis
lean otter
not a bad start
so, in general we say that $f(x - a)$ where $a$ is a constant $\in \mbb{R}$ will translate the graph of $f(x)$ $\emph{horizontally}$ by $a$ units to the right. If we have $f(x) - a$ then it will shift the graph of $f(x)$ to downwards by $a$ units (this is all provided that $a > 0$). So, let's take $f(x) = x^2$ as an example: if we have $h(x) = f(x-1) = (x - 1)^2$ and $g(x) = f(x) - 1 = x^2 - 1$, then which one will result in a horizontal shift and which one will result in a vertical shift?
flat frigateBOT
maxim
lean otter
nah I just realized that I used the same notation twice
deep imp
hx is to the right
lean otter
exactly
deep imp
gx is to down
lean otter
nice
good
and if you want to convince yourself that this is true you can plug in a few values into both functions and play around with them on Desmos, for example
so, back to your question
,w graph f(x) = x^2 for -9 \leq x \leq 9 \land -18 \leq y \leq 18
flat frigateBOT
lean otter
huh
lean otter
yeah, i'll just use desmos to show you
deep imp
i already tried using it earlier
im just confused about the setup
as in how do i show my work via table of values or whatever
lean otter
ah okay, so have you done this type of stuff with linear equations and graphs of them?
deep imp
yes
lean otter
perfect
so with linear equations
you look at the intersection of the lines
it's the same with this
so you want to look at the points of intersection
so when $x^2 - 16 = -(x + 4)^2$
flat frigateBOT
maxim
lean otter
if you hover over the points of intersection on Desmos, you'll see that (0, -16), is, for example, a point of intersection. Can you find the other pair (x, y)?
deep imp
-4,0
lean otter
yup
so the two solutions are x = -4 and x = 0
and the ordered pair solutions are (0, -16) and (-4, 0)
deep imp
if you hover over the points of intersection on Desmos, you'll see that (0, -16)...
for 0,-16 how do we get that because when i subsitute for x i get -4,0
do i plug -4,0 back into for x
and solvefor y
lean otter
$0^2 - 16 = -(0 - 4)^2$
flat frigateBOT
maxim
lean otter
since $0^2 - 16 = -16$ and $-(-4)^2 = -16$
flat frigateBOT
maxim
lean otter
table of values?
deep imp
my teacher wants 2 to the left and 2 to the right of a given point
perferably the intersections are within the 5
lean otter
can you give me an example of what you need?
lean otter
ah
okay so what you want to do is plug in values into both functions and fill the table up. The harder part is finding the y for each corresponding x. You can pick any value you like for x unless your teacher has specified what they want, but otherwise, it's just a matter of plugging things in
deep imp
yo thank u for ur help @lean otter
u actually took time to bless me up for free
something tutors charge hella for
lean otter
np np happy to help :D
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raw orchid
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https://media.discordapp.net/attachments/903481105888452609/1312998075404521472/...
raw orchid
Continuing with this because it timed out
I have no idea how I'd go about constructing Jordan blocks
Is there some way I can do that
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raw orchid
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raw orchid
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lime apex
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red swan
Can anyone tell me if I did this good?
The image shows two congruent triangles. Calculate the length of x and y.
safe radishBOT
Can anyone tell me if I did this good?
*The image shows two congruent triangles...
digital sparrow
Yes this is correct
red swan
Fr?
red swan
Yes this is correct
Are there two ways possible of calculating x?
digital sparrow
Wdym 2?
You could have also used y/(y+10) but yours is better
Other than that I don't think
red swan
Method 1:
20/8 = x / 6
Method 2:
y+10 = x / 6
digital sparrow
Yup
digital sparrow
That is incorrect lol
digital sparrow
red swan
and also
i put that
into chatgpt
and it told me the SAME answer as the other dude
good that i didnt fix that to theirs method
otherwise i wouldve gotten worse grade
simple gazelle
into chatgpt
don't trust chatgpt with mathematics
simple gazelle
!help
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Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
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digital sparrow
Lmao
@red swan is your doubt still there?
If not then I recommend closing this channel
!done
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hollow reef
Guys help me with solving this
safe radishBOT
Guys help me with solving this
fathom kraken
Guys help me with solving this
Hint: Square - Areas you know
Hint 2: Write equations for square side length
hollow reef
Hint 2: Write equations for square side length
I don't think we can create an equation for the side of square
fathom kraken
Why
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somber cape
were going over hypothesis testing
safe radishBOT
were going over hypothesis testing
somber cape
What is the population here?
I was thinking the population is just all people?
or all people who had their normal diastolic blood pressure measured
oh
wait the population is just the. Mexican American adults in that california town
and the sample is a small portion of them
But how do I test whether there is evidence to suggest that the mean blood pressure of the population differs from 120 without a confidence interval given?
honest perch
is 120 the normal for all people or only mexican americcans
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somber cape
is 120 the normal for all people or only mexican americcans
Iâm not sure
Question doesnât specify any more than that
honest perch
im guessing it's for all people and the population is mexican americans. if the sample mean is different from 120 then that's evidence. that's just my guess tho i haven't studied this stuff
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rain gale
i believe 120 should be for all people (generally speaking), you don't know what blood pressure is average for mexican american adults in small california town (x), do you have reason to believe that (x) is significantly different from 120 given that you took a sample from that population
there should exist some formula out there for calculating significant difference between two means where one of the population sizes is unknown
this is AI generated so be careful, but it sounds reasonable enough:
id suggest confirming this with a reputable source
south lynx
could we not factorise it? how did we think of this substitution?
safe radishBOT
could we not factorise it? how did we think of this substitution?
@south lynx Has your question been resolved?
empty gyro
could we not factorise it? how did we think of this substitution?
Factorizing might work. What did you have in mind?
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south lynx
.reopen
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â
south lynx
Factorizing might work. What did you have in mind?
I think factorisation should work yes but it makes it a little complicated? the substitution makes the problem a lot easier so I wondering how we thought of that
empty gyro
I think factorisation should work yes but it makes it a little complicated? the ...
will respond in a minute, on the phone rn
south lynx
no worries!
empty gyro
@south lynx i think you want to take advantage of difference of cubes. But I'm not sure yet
It can be factored. Every rational function with a limit can be found through factoring. But damn this one is hard
empty gyro
Okay i have an idea. Get rid of square roots on numerator by multiplying by its conjugate
south lynx
i tried that
empty gyro
At the same time, get rid of cube roots on denominator by multiplying by its conjugate
south lynx
but isn't that just rationalization
so you mean we don't simplify it first?
while multiplying by their conjugates?
oh wait lmao
wow
never mind yeah, you're right. i was originally supposed to rationalize it
we're taught that whenever you see 0/0 or infinity/infinity form, you rationalize/factorise/use l'hĂ´pital's rule
i mis-wrote (?) rationalization as factorisation
my original question still stands
why the substitution (more like how)?
toxic stratus
there is no need to make a substitution
south lynx
i get that. i was just wondering about the approach
toxic stratus
x -> 2, if x = 2 + h, then it is equivalent to saying h -> 0
one makes this substitution because early on in calculus, one is taught to take h -> 0
so the substituion is essentially made so that people don't get scared by a limit not going to 0 and not using h for whatever reason
toxic stratus
it shouldnt be necessary
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lean otter
how do u find critical points
safe radishBOT
how do u find critical points
lean otter
pLs help
lean otter
how do u find critical points
Critical points are points where the derivative is 0 or undefined
smoky nacelle
graphically, flat graph or sharp turn.
smoky nacelle
bro i got 5/2root7
what?
lean otter
i thought i had to like derive gx
cuz that is fx and i tried 3 and 5 already
3, 5, 9 too
<@&286206848099549185>
what do i do
safe radishBOT
@lean otter Has your question been resolved?
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@lean otter Has your question been resolved?
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@lean otter Has your question been resolved?
minor socket
@lean otter you were on the right track when you put 3 and 5, I think you just forgot about your end points. 5 is one because g'(x)=0 at x=5, and 3 is one because g'(x) is undefined there. notice that x=7 is in the domain of g(x) but not in the domain of g'(x). just like 3, 7 is a critical number because g'(x) is undefined there
we all forget to check little things like that sometimes, hopefully that helps
ngl no clue where the 9 came from or the 5/2root7 that you mentioned earlier though, I can't figure out how you got there
lean otter
thank u for responding omg that thought process came from g(x)= root f(x)
minor socket
sorry I saw it so much later than you'd sent the question
lean otter
thank u bro u saved my life
minor socket
no problem
lean otter
.close
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azure kayak
how would you plug this equation into a calculator like this? whenever I try I end up with 13.99 when the answer is 0.262
safe radishBOT
how would you plug this equation into a calculator like this? whenever I try I e...
median vigil
you need to add parentheses around the numerator and denominator
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vocal ibex
Are u able to partial fraction decompose this?
safe radishBOT
Are u able to partial fraction decompose this?
tardy mango
Are u able to partial fraction decompose this?
Technically? Yes. Is it disgusting and painful? Also yes.
,w partial fractions 4x^2 /(x*(x^4+16))
flat frigateBOT
tame chasm
(hi im working with the person above) how did wolfram get to this answer? to decompose, dont you have to turn the denominator into at most repeated quadratic factors?
tardy mango
(hi im working with the person above) how did wolfram get to this answer? to dec...
$x^4+16=0 \implies x=2e^{\frac{(2n+1) i \pi}{4}}, n=1,3,5,7$
flat frigateBOT
Civil Service Pigeon
tardy mango
that's the roots of unity nuke
tame chasm
that's the roots of unity nuke
gotcha, makes sense
rapid trellis
$x^4+16=0 \implies x=2e^{\frac{(2n+1) i \pi}{4}}, n=1,3,5,7$
What type of mathematics is that wow?
tardy mango
What type of mathematics is that wow?
complex numbers (specifically, roots of unity.)
tame chasm
seems like high school concepts to me
we haven't learned it in our classes, so i'm saying no for it lol
vocal ibex
seems like high school concepts to me
calc?
tardy mango
we haven't learned it in our classes, so i'm saying no for it lol
đ¤ˇââď¸
rapid trellis
complex numbers (specifically, roots of unity.)
Thanks, when do people usually learn this?
tardy mango
Thanks, when do people usually learn this?
idk
I think I learned it when I was 15 or smt?
rapid trellis
Wow
rapid trellis
bro ur insane
I love your avatar
vocal ibex
I love your avatar
thx bro
rapid trellis
I love maths. I'm not deep into it
tame chasm
@vocal ibex the people in calc BC at our school learned partial fraction decomposition along with integrals
cursive slate
Math help with similar polygons
safe radishBOT
Math help with similar polygons
cursive slate
stray hinge
Same ratio as corresponding side lengths
cursive slate
???
cursive slate
Same ratio as corresponding side lengths
What
stray hinge
The ratio of their perimeters would be the same as the ratio of corresponding side lengths
cursive slate
And how do I get that
stray hinge
find the ratio of corresponding side lengths
cursive slate
I think itâs 21
tough briar
How did you get 21?
cursive slate
By doing a maths trick my teacher taught me
X/14 = 12/8
Then
8x=12 x 14/ 8
X=168/8
X=21
Wait
Whoops
I read the question wrong
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pale zenith
Iâm stuck on the concept, I know you need to convert them into ax + by = c, but Iâm confused as to how the slope is calculated with this format as I always am used to y= Mx+b. Also, once converted, it gets more confusing as you need to somehow get the p value, which Iâm confused about as well.
safe radishBOT
Iâm stuck on the concept, I know you need to convert them into ax + by = c, but ...
stray hinge
,rotate
flat frigateBOT
stray hinge
ok so first
when does a system of two linear equations have no solution?
in other words, in what case would two lines never intersect?
pale zenith
when they are parrale
parallel*
aka same slope, different y intercept
js confused about how I can notice that in this form, and after that, how I can figure out the P value.
stray hinge
since they didn't really give it in any specific form like standard form, it would be easiest to just manipulate the equation into a form you know
and then like you said same slopes so set the slopes to equal to each other which will create an equation where you solve for p
pale zenith
true, but I wanna understand standard form bc itâs probs gonna be on the SAT
pale zenith
and then like you said same slopes so set the slopes to equal to each other whic...
but what are the slopes in this form? The coefficient of X, like in Mx+b?
flat frigateBOT
Smiley ă
stray hinge
which if you were to convert to slope intercept form
you get
$y = \frac{-A}{B}*x + \frac{C}{B}$
so if you do have standard form the slope would be -A/B
stray hinge
yes
if you have any doubts
there's no harm in just converting to slope intercept form
since it would only be two steps
flat frigateBOT
Smiley ă
pale zenith
and what would I do once in slope intercept?
stray hinge
**Smiley ă**
btw I had a typo here but it doesn't change anything relating to slope
stray hinge
and what would I do once in slope intercept?
you get the slope explicitly stated
pale zenith
hmm
and then you set the slopes equal to eachother and see what number is needed to bring the lower one equivalents higher?
stray hinge
I'm not completely sure what you mean by the 2nd half, but we would set the slopes equal to each other to find the value of p for which the two lines are parallel
stray hinge
ofc, np
karmic stream
can anyone help me with part b onwards?
safe radishBOT
can anyone help me with part b onwards?
lilac crane
The bold 0 means neutral element, so an element such that a+0=a for any a. So you check if (a_1,a_2)+(0,0)=(a_1,a_2)
karmic stream
where should a be added?
safe radishBOT
@karmic stream Has your question been resolved?
opaque fern
where should a be added?
So in vector spaces, the additive identity $\vb v + \vb 0 = \vb v$ should hold
flat frigateBOT
Aero
opaque fern
but you also know [
(u_1, u_2) + (v_1, v_2) = (u_1 + v_1 +1, u_2 + v_2 +1)
]
flat frigateBOT
Aero
opaque fern
try setting $(v_1, v_2) = \vb 0$. How does the above equation become?
flat frigateBOT
Aero
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signal notch
how to solve this problem
safe radishBOT
how to solve this problem
signal notch
<@&286206848099549185>
pine horizon
how to solve this problem
sinx - cosx = t
pine horizon
(cosx + sinx)dx = dt
t^2 = (cosx-sinx)^2 => t^2 = sin^2x - 2sinxcosx + cos^2x => sin2x = 1 - t^2
signal notch
i did that but . i am getting wrong answer
safe radishBOT
Show your work, and if possible, explain where you are stuck.
signal notch
t^2 = (cosx-sinx)^2 => t^2 = sin^2x - 2sinxcosx + cos^2x => sin2x = 1 - t^2
cos^2 x + sin ^2 x - 2sinxcosx => 1 - 2sinxcosx ..... how 2 sinxcox be t^2 ..
pine horizon
cos^2 x + sin ^2 x - 2sinxcosx => 1 - 2sinxcosx ..... how 2 sinxcox be t^2 ..
2sinxcosx = sin2x
so 1 - sin2x = t^2 => sin2x = 1 - t^2
pine horizon
yeah
lean otter
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lean otter
having trouble not sure what to do with absolute value in integral