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kindred hornet
what would the limit be, im confused?
cedar kilnBOT
what would the limit be, im confused?
@kindred hornet Has your question been resolved?
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quasi orchid
I had "solved" the problem using the slope formula on the coordinate plane below, but I am still unsure if I was correct so I wanted clarification (For the rate of change/slope)
cedar kilnBOT
I had "solved" the problem using the slope formula on the coordinate plane below...
@quasi orchid Has your question been resolved?
quasi orchid
<@&286206848099549185>
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upper wave
Really do not understand this one
cedar kilnBOT
Really do not understand this one
main needle
for logs you basically view numbers are the product of their factors, like 150 is 2*3*5*5
it would make way more sense if you were asked to find log_2 (150), and there's a property that lets you flip that, 1/log_a(b) = log_b(a)
basically "if 150 to the x power is 2, then 2 is the xth root of 150"
upper wave
ohhh i think i kinda get it
let me give it a shot
well i got log_abd^2 (a) = x, and i think I have to use a property to get rid of the log then solve, but I'm not sure how to do that without using log_a (c) = b --> a^b=c
because if i use that x becomes an exponent so I cant really solve for it
main needle
hmmm yea you'll never need to go from log to exponent here, just use the above thing and log(ab)=log(a)+log(b)
main needle
like you figure out log_2(2*3*5*5), and with that you do 1/ to get the answer
main needle
hmm I get 1/7
upper wave
hmm let me do it again
oh yeah i got that too just made a typo in calcullator
thanks so much for the help!
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quaint totem
i need help with this
cedar kilnBOT
i need help with this
What step are you on?
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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
- i dont know where to begin
cedar kilnBOT
@quaint totem Has your question been resolved?
quaint totem
bruhh
ancient quarry
1. i dont know where to begin
what are ways to prove triangles are congruent?
quaint totem
what are ways to prove triangles are congruent?
i kinda know how to do it now, its just aleks is acting up
ancient quarry
you have AB congr BC, the have that angle A = ang C, you have AD = EC right
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small sinew
can anyone help me with this physics problem?
AM radio signals are broadcast at frequencies between 544.0 kHz and 1605.0 kHz (kilohertz) and travel 3.00 ✕ 108 m/s.
(a) What is the range of wavelengths for these signals? (Enter the wavelengths from shortest to longest.)
(b) FM frequencies range between 88.0 MHz and 108 MHz (megahertz) and travel at the same speed. What is the range of FM wavelengths?
onyx dove
!status
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2. I have begun but got stuck midway.
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6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
you know how to find wavelengths?
cedar kilnBOT
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violet brook
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violet brook
this is a rly simple question
but
for part 3
ik its gonna be
separate grant to everyone else (g, not g is 1/9 and not g, g is 1/9 giving the correct answer of 2/9)
but why doesnt this work
ignore the big cross
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violet brook
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ancient quarry
having a hard time reading your work give me one second
violet brook
sorry i can rewrite it
give me a sec
oh my days i figured it out
i didnt multiply the 4/9 w the 1/8
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cedar kilnBOT
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lime igloo
I need to show that La is in Aut(G), so I'm trying to show that La is an isomorphism, but I have not been able to do that🥲
abstract thicket
lime igloo
I guess it is.
rigid lava
What does your proof look like so far
lime igloo
I need to show La is a homomorphism.
rigid lava
Oh uh
Your La is a typo
Didn't notice since I'm on mobile
It should be La(x) = axa^-1
lime igloo
Yeah, thats what I was thinking.
rigid lava
Yeah, multiplication by a fixed element is not an automorphism lmao
lime igloo
Thanks mate.
rigid lava
this mapping is called conjugation and is a very special automorphism
np lmk if you get stuck
lime igloo
this mapping is called conjugation and is a very special automorphism
Why is that?
I'm really sorry if I sound rude, English is not my mother tongue as you may notice.
rigid lava
Uh
lime igloo
I mean, why it's special?
rigid lava
Many many reasons
it shows up a lot
On phone so lazy but a big one you'll learn about later is something called group actions
you can Google these and read for yourself
rigid lava
Np
lime igloo
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cedar kilnBOT
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ionic finch
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ionic finch
when we find a general solution of matrix using row reduced form
does it mean the the rows below it can zeros, but not written ?
ie, the other equations are 0x1 + 0x2 + 0x3 =0
hollow trail
you could, but it wouldn't be particularly useful
ionic finch
this will immediately mean the system has infinite many solutions right?
hollow trail
as long as it is consistent, yes
ionic finch
if a matrix is an row echlon form, then i should only look whether it have 0=b (b!=0) or not right?
to determine consitency
hollow trail
that would indicate it is inconsistent, yes
ionic finch
say a system is consistent
how to determine if it has infinte or unique solution?
what's the idea behind looking at pivots?
hollow trail
we know that a solution will be unique only if there are as many independent equations as there are unknowns
but we can't immediately tell if equations really are independent, or if one equation is really just the sum of scalar multiples of the other equations (what we call a linear combination)
ionic finch
we know that a solution will be unique only if there are as many independent equ...
what if we have more equations that the variables?
hollow trail
when we row reduce, even though the equations look different, we can guarantee they have the same set of solutions
hollow trail
what if we have more equations that the variables?
if there are more equations than variables, then either:
- The system is inconsistent, this is usually the case
- the system is consistent, this must mean that some of the equations are linearly dependent (i.e. they are a linear combination of the other equations), meaning the number of independent equations is the same or less than the number of unknowns
ionic finch
I have this problem, i need to determine if it's consistent and have unique solution
i think it's consistent
hollow trail
assuming the last column is the constants, then that seems correct
ionic finch
dark box is non zero
star can be anything (including zero)
does it have unique solution?
i was just thinking x3 is a free variable
but now i think it's a system of 2 unknowns
so last column is just there for no reason.
hollow trail
but now i think it's a system of 2 unknowns
i agree with that, given the context. i do think that textbooks should more clearly indicate when the matrix is augmented
the last column is there because it is the constants
you need it to know if the system is consistent
ionic finch
my reasoning it's consistent as each pivot column has a non zero pivot
and they are basic variables not free
more like since there are no 0=1 situtation, i can safely back track
hollow trail
consistency is just whether it has any contradictory rows like 0 = something
hollow trail
my reasoning it's consistent as each pivot column has a non zero pivot
this would work to establish if it's unique
cerulean pine
cedar kilnBOT
cerulean pine
please can i get help with b
fringe mauve
well splitting a group of people into two teams of 5 is the same as saying how many ways are there to choose 5 ppl
cause the other 5 are automatically in the other team
cerulean pine
oh but the answer is not the same in a and b
fringe mauve
so its not just 10C5
fringe mauve
i think its cause there are repetitions
because the groups arent defined as like group A or B
so when u do 10C5 u get groups that repeat twice
cause 126 is 10C5/2
cedar kilnBOT
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violet brook
how and why is the derivative of s = ut + (1/2)at^2 equal to u + at
violet brook
i mean
s = ut + (1/2)at^2 is one of the equations of motion
taking ds/dt gives the first equation of motion v = u + at
but how does taking ds/dt give v
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bronze pond
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gusty bison
Hi
bronze pond
Hi
frank carbon
i have 0 idea on angles
Did your teacher teach you the angles?
bronze pond
Did your teacher teach you the angles?
not yet
frank carbon
Ok
bronze pond
im in year 8 rn 😭
scenic brook
bronze pond
idk the answer 😭
west glade
wait which one tho
bronze pond
this 1 is the first page
west glade
number 3?
bronze pond
number 3 and number 4
west glade
ok um
west glade
this is correct so
west glade
angle A would be congruent to 75 degrees
number 3 says to find the values of abcd
vertical angle is a full circle if im explaining this correctly, so a would be 75 degrees, because the opposite side of the angle is always congruent
like up and down and left and right
congruent
bronze pond
west glade
since vertical angle is a circle or smth, you need to subtract 75 degrees with 180 degrees to find the value of C
C and D have the same value as far as i know
B has the same value as A
so just solve
its just subtracting and adding
also i cant clearly see number 4
west glade
👍
west glade
but just remember this tho
cedar kilnBOT
@bronze pond Has your question been resolved?
full forum
cedar kilnBOT
full forum
For b, I get different value from the answer if I use P and Q to get the diameter, and devide that by two to get radius
Why is it??
Better quality
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cedar kilnBOT
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ashen shard
An ellipse has foci at $(9, 20)$ and $(49, 55)$ in the $xy$-plane and is tangent to the $x$-axis. What is the length of its major axis?
wraith daggerBOT
Dork9399
ashen shard
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cedar kilnBOT
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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.
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6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
I'm on step 1
cedar kilnBOT
@ashen shard Has your question been resolved?
ashen shard
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ashen shard
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ashen shard
<@&286206848099549185> please
buoyant latch
An ellipse has foci at $(9, 20)$ and $(49, 55)$ in the $xy$-plane and is tangent...
Can you find the equation of the ellipse
ashen shard
Can you find the equation of the ellipse
how would I do that?
i know that every point has to be the same distance away from both the foci
but i don't know how to make the equation of a rotated ellipse
buoyant latch
How would you construct the equation of a normal ellipse
cedar kilnBOT
@ashen shard Has your question been resolved?
peak lynx
This eclipse is not vertical or horizontal
So list the equation from the definition of eclipse is more intuitive
Eclipse is the orbit of the point whose sum of distance with foci is constant
This constant=the length of major axis=2a
earnest geyser
An ellipse has foci at $(9, 20)$ and $(49, 55)$ in the $xy$-plane and is tangent...
The distance between 2 focii is 2ae
cedar kilnBOT
@ashen shard Has your question been resolved?
ashen shard
The distance between 2 focii is 2ae
and how would I find e?
ashen shard
This eclipse is not vertical or horizontal
So list the equation from the defin...
but how would we find the constant
The distance would be $\sqrt{(x-9)^2 + (y-20)^2} + \sqrt{(x-49)^2 + (y-55)^2}$
wraith daggerBOT
Dork9399
wraith daggerBOT
Dork9399
ashen shard
Then we know that there exists a number such that this equation has only one solution for x
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cedar kilnBOT
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karmic terrace
Hello
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@karmic terrace Has your question been resolved?
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@karmic terrace Has your question been resolved?
solid pivot
hi i need some help with this question, is there a faster way to expand the brackets?
cedar kilnBOT
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topaz saddle
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topaz saddle
for 2 here)
i did this for 1)
but for 2, its asking to prove there exists some graph G with a max of 49 edges
how would i go about that?
im confused
modern compass
Either, find such a graph and give it as an example, or show that constructing such a graph is possible.
that'd be my first guess anyway.
And, for clarity, you aren't showing the graph has 49 edges, your showing the longest path in the graph is 49 edges.
topaz saddle
And, for clarity, you aren't showing the graph has 49 edges, your showing the lo...
oh ok
ive been hinted to try to think about splitting 3000 students into partitions of size 50, and 3000 is divisible by 50.
so i was thinking of maybe using this
to prove the longest path is 49 edges
modern compass
sounds like a good start. If the groups are partitioned into sizes of 50, can you say what sort of graph would be necessary to represent the connections in each group?
topaz saddle
a complete graph of 50 students? so each student (or vertex) is directly connected to every other student in the group i think
tried partioning 3000 into 600 groups, each group is 50
@modern compass thoughts?
modern compass
if you connect the complete graphs, then I can make a path between them to have more than 49 edges.
topaz saddle
if you connect the complete graphs, then I can make a path between them to have ...
ahh and we dont want that?
since were trying to show the longest path in G is 49 edges
modern compass
yes
topaz saddle
how else would we approach this then
modern compass
why are you connecting those groups of 50 friends?
topaz saddle
i thought it'd help prove having at least 49edges
topaz saddle
if you connect the complete graphs, then I can make a path between them to have ...
but like you mentioned, if it exceeds and has more then 49
then i cant take this approach anymore
modern compass
ok, first, are you proving at least 49 edges, or a maximum of 49 edges.
because those are opposite things.
topaz saddle
I completed proving at least 49 edges here , using proof by contradiction ( i think its right, not sure)
as of right now
im trying to provve
topaz saddle
ok, first, are you proving **at least** 49 edges, or a **maximum** of 49 edges. ...
the latter here
maximum
of 49 edges
modern compass
tried partioning 3000 into 600 groups, each group is 50
so then, here you said each group of 50 students has a path of 49 edges.
Then you connected each group with an edge to add "another 49 edges to the path"
why are you trying to add edges to the path of length 49, when that's the maximum length you wanted.
cedar kilnBOT
@topaz saddle Has your question been resolved?
topaz saddle
so then, here you said each group of 50 students has a path of 49 edges.
Then y...
nah you right
i misinterpreted it
topaz saddle
so then, here you said each group of 50 students has a path of 49 edges.
Then y...
so when connecting them, we should ensure that we dont create paths longer then 49
would connecting each group with another with just one edge help
meaning selecting one student from each group and connecting them to one student in another group
modern compass
you shouldn't connect the groups at all.
I can use any edge between groups to make a longer path, because each group already has a path of 49
topaz saddle
tried partioning 3000 into 600 groups, each group is 50
was i on the right track with this
or completely off
modern compass
take what you wrote, and don't connect the groups. There's nothing that says the groups need to be connected.
topaz saddle
take what you wrote, and don't connect the groups. There's nothing that says the...
so groups wont be, but students being connected is valid
im not connecting the groups anymore
modern compass
yes, you're complete graphs on 50 vertices is fine. But each group should be disconnected from eachother.
topaz saddle
yes, you're complete graphs on 50 vertices is fine. But each group should be dis...
hows this
modern compass
that works
cedar kilnBOT
@topaz saddle Has your question been resolved?
sage oracle
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sage oracle
I can't figure this one out
opaque root
Figure out what
sage oracle
I have to simplfiy it to one trig function
opaque root
Have u tried anything?
sage oracle
I have tried to do the math inside of the parentheses
opaque root
Show what u did
sage oracle
I did it on a random page in a notebook it is probably long gone I can quickly try doing it again though
opaque root
Ok do it again
bronze frost
$sin(x)=cos^2(x)-1$ ?
wraith daggerBOT
Br;an
sage oracle
it isn't squared
opaque root
!nosols
cedar kilnBOT
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.
sage oracle
and I don't know how to do the math inside of the parentheses becauwse I am no realizing that I found a found denominator when they already had one
oh you cancled the cos and sec?
bronze frost
and I don't know how to do the math inside of the parentheses becauwse I am no r...
ye you know what sec x is?
opaque root
and I don't know how to do the math inside of the parentheses becauwse I am no r...
Start by rewriting sec(x) as 1/cos(x)
bronze frost
1/cos x hence cos x * sec x = 1
bronze frost
Start by rewriting sec(x) as 1/cos(x)
this
sage oracle
I see how you got that
I just wrote it down
but then how do you mutiple the other things together
sage oracle
probably a long time ago
bronze frost
so your equation is something like this
(a+b)(c+d)(e)
where a = 1, b = -cos, c = 1, etc ... you get the idea
so do the (c+d)(e) part first, find out its (cos x + 1)
now you have
(1 - cos x) ( cos x + 1)
from here you might be able spot this is something called the "difference of two sqaure"
so that is to say its
1 - cos^2 x
then we use the indetity $sin^2 x + cos^ 2x = 1$ to get that this is sin^2 x
sage oracle
yeah I think I see it
if we do that since it is now squared we can do the idenitiy so the answer is sin^2x
that helped a lot thank you
bronze frost
no problem, good luck
sage oracle
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cedar kilnBOT
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dire tundra
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dire tundra
Why do use quotient rule
When finding for the change of V
Why couldn't I just take the derivative of r^3? Since I thought if there coefficient and a single variable that was possible?
stone mountain
Why do use quotient rule
where you got that from
cedar kilnBOT
@dire tundra Has your question been resolved?
livid hound
who's telling you to use quotient rule here?
paper stone
Hey
paper stone
What is Pie
flint plinth
it is like cake
hollow trail
,w pie
wraith daggerBOT
hollow trail
that's a lot of calories
flint plinth
oddly specific for a generic "pie"
exactly 303 mg of sodium
what if it is a salt pie
cedar kilnBOT
@paper stone Has your question been resolved?
dusty raptor
would the correct answer be the first or 2nd photo?
cedar kilnBOT
would the correct answer be the first or 2nd photo?
raven shard
dusty raptor
i shifted the n so that it would = 1
in the first one
but i couldve just been wrong w n in the beginning
2nd photo is before my shift
quaint totem
would the correct answer be the first or 2nd photo?
is that web assign lmao
quaint totem
im only in trig and im 8th so i cant rly help
sry lmao
wasit to practice another and see how webassign do it
dusty raptor
wasit to practice another and see how webassign do it
its a hw quiz and not a just a hw assignment so i cant 😭
im gonna go for the 2nd one
quaint totem
alright gl
cedar kilnBOT
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Available help channel!
slow fiber
How many ways are there to split 20 cookies among 4 friends
so that at least one of them gets at most 2 cookies? - could I have a hint
nimble mulch
How many ways are there to split 20 cookies among 4 friends
so that at least one...
How many ways are there to split 20 cookies among 4 friends?
How many ways are there to split 20 cookies among 4 friends if everyone gets >=3 cookies?
How many ways are there to split 20 cookies among 4 friends with at least one having <=2 cookies
=the first line above minus the second line above
so you can regard the opposite case
if you know the amount of ways for the opposite case, then you also know how many there are for the case itself
is the procedure clear or does something remain vague? :)
slow fiber
so you can regard the opposite case
this part confused me, but what you said above makes sense
nimble mulch
this part confused me, but what you said above makes sense
I referred to it sometimes being easier to calculate the opposite
slow fiber
I see, so if we have n cookies and 4 friends but actually 3 friends, we should have something like
20 + 4 - 1 and from that pick 3
nimble mulch
I see, so if we have n cookies and 4 friends but actually 3 friends, we should h...
but actually 3 friends?
crimson sedge
im doing it manually right now
I hope im not wasting my time lmao and i dont make a mistake
Okay Im done I likely made a mistake somwehere but Ive got it at 60
Ill check to make sure I didnt make any mistakes but lmk if thats correct
sharp frigate
what no??? its literally the task
slow fiber
_but actually 3 friends_?
im sorry, i might of confused myself
could you sort of giive me another hint
sharp frigate
OHHH
slow fiber
can you guys please go to another channel?
sharp frigate
sorry sorry
nimble mulch
could you sort of giive me another hint
Start with the first line
How many ways are there to distribute the 20 cookies among four friends
crimson sedge
Start with the first line
Am i wrong?
nimble mulch
Am i wrong?
didn't calc, but am rather interested in the op understanding it :3
slow fiber
is it not 20 pick 4
nimble mulch
is it not 20 pick 4
careful, we consider the cookies equal
so the friends may end up with the same amounts even if you distributed them in a different order
nimble mulch
20 + 4 - 1 and from that pick 3
you were on the very right track here
because this problem is synonymous to placing 3 bars among 20 objects
which is the same as putting 20 objects into 4 groups
slow fiber
I never learned whatever this bars and stars thing is
nimble mulch
which means for the initial case you have C(20+4-1, 4-1) = C(23, 3)
nimble mulch
I never learned whatever this bars and stars thing is
it's the same as this problem here
distributing objects
slow fiber
kinda what is bars and stars
nimble mulch
e.g. for a smaller sample size, let's look at 5 objects
and 3 groups
then we'd have 5 stars:
*****
and we can place 2 bars
to distribute them into 3 groups
for instance:
**|*|**
now the first group has 2
the second has 1
the third has 2
slow fiber
I understand that makes sense
nimble mulch
kk
and that's just like ordering objects which are equal
since we added 3 objects
slow fiber
which means for the initial case you have C(20+4-1, 4-1) = C(23, 3)
Im sort finding it difficult to correlate that with this though
nimble mulch
Im sort finding it difficult to correlate that with this though
maybe the explanation I just provided makes it clearer
we have a total of 23 objects (20 stars, 3 bars) or equivalently: (20 cookies, 4 groups = 3 group separations)
slow fiber
we have a total of 23 objects (20 stars, 3 bars) or equivalently: (20 cookies, ...
excellent this is great
nimble mulch
neat, and then we just choose three positions
slow fiber
we are on the same page
nimble mulch
which depending on which approach you like more
you can either do via combinations
so we choose three positions from among 23:
C(23, 3)
or via permutations:
we oder 23 objects, of which 20 are the same and 3 are the same:
23! / (20! * 3!)
whichever you feel is more intuitive you can choose :)
nimble mulch
have you not had permutations / combinations yet?
slow fiber
Not in class, just really binomial
but ik the difference
one has order that matters, one doesnt
nimble mulch
kk, we can pick the permutations then, at least I find them easier in most cases
so the quick crashcourse on permutations are two different cases
you either order objects with repeating ones
or you order objects without repeating ones
for instance, take a password consisting of 5 symbols, each from 0-9
then that would be a permutation WITH repetitions
since we can use the same object (number) multiple types
and the amount of ways for that would be 10^5
since we have 10 objects
and 5 positions
so the first position has 10 options
the second position has 10 options
third as well
etc.
so the amount of ways = 10 * 10 * 10 * 10 * 10 = 10^5
slow fiber
for instance, take a password consisting of 5 symbols, each from 0-9
okay cool ive done these sort of questions
nimble mulch
neat, and then come the permutations without repetitions
so for instance let's say we have 10 different letters
and we want to know the amount of ways to arrange them
well then the first position can have 10 different options
but the second position then only has 9, since one option will have been taken by the first position
meaning at the third position we have 8 options
and for the fourth position 7 options
etc.
amount of ways to order 10 objects at 10 positions = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 10!
that principle is crucial
now what if we still have 10 letters, but only 5 positions?
well then again the first position has 10 options
second has 9 options
etc.
and the fifth position has 6 options
amount of ways to order 10 objects at 5 positions = 10 * 9 * 8 * 7 * 6
and the trick to write this in a smaller form is to write 10! / 5!
because the 5! get rid of the * 5 * 4 * 3 * 2 * 1 from the 10!
slow fiber
Okay cool sounds good
nimble mulch
ok and the last basic part is having duplicate objects
so for instance what if we want to order 10 letters at 10 positions
but 2 of them are the same
then the principle is to divide by n! where n is the size of the duplicate group
meaning here we have 10! / 2! ways to order them
another example: we want to arrange 10 letters, but 4 of them are the same and another 3 of them are the same
then there are 10! / (4! * 3!) ways to order them
and now you may also see the parallel to our former problem
we had 20 stars
3 bars
(or 20 cookies and 3 group divisions)
meaning we have 23 objects
of which 20 repeat
and 3 repeat
so the amount of ways to arrange them is 23! / (20! * 3!) <<< by permutation
= Amount of ways to distribute 20 cookies among 4 friends
so far clear right
slow fiber
Gotcha
nimble mulch
kk
now we can calculate the opposite case: Amount of ways to distribute 20 cookies among 4 friends where all of them have >=3 cookies
if all of them have at least 3 cookies, well then we can use that as our starting condition for the calculation
meaning each of the friends already has 3 cookies
and we only need to distribute 20 - 4 * 3 = 8 cookies
8 cookies among 4 friends
(8 stars & 3 bars)
just like before, there are 11! / (8! * 3!) ways to arrange them
was I too hasty or is it understandable
slow fiber
okay because 8 cookies to distribute freely, after you do 20 - 4 * 3 right
nimble mulch
yup!
we assume they already have 3 cookies each
so we only need to distribute 8 to know how many ways there are for that case
now you may wonder why we even did the above
it's because now when we have the opposite amount of ways
we can calculate the initial amount: Amount of ways to distribute 20 cookies among 4 friends where at least one of them has <= 2 cookies
I'll denote these three amount with letters so that I don't have to write the full sentences twice: :D
X: Amount of ways to distribute 20 cookies among 4 friends
Y: Amount of ways to distribute 20 cookies among 4 friends where all of them have >=3 cookies
Z: Amount of ways to distribute 20 cookies among 4 friends where at least one of them has <= 2 cookies
and then you may notice that X - Y = Z 🦇
which is the meaning behind the opposite case
because X are all ways to distribute them
Y are all ways IF NOT some condition
Z are all ways IF some condition
meaning Y + Z = X, or rewritten, X - Y = Z
and we're looking for Z!
slow fiber
This is such a good summary, I really appreciate you so. much right now
nimble mulch
np :)
so why did we not just directly calculate Z?
because it's actually a lot harder than calculating X & Y
so I highly recommend remembering this opposite approach
slow fiber
Yeah, that makes a lot of sense
Okay, I get the general idea. Im going to really think about this and then formulate my proof
thank you so so. much
nimble mulch
sure, here the inserted values btw:
X = 23! / (20! * 3!)
Y = 11! / (8! * 3!)
Z = 23! / (20! * 3!) - 11! / (8! * 3!)
and a little piece I just wrote as reward :P
gl!
slow fiber
thank you and nice piano!!!
This was so helpful, really i genuinely appreciate it
.close
lucid lantern
I js need help on how to do these problems like explaining it in details and stuff
winter apex
I js need help on how to do these problems like explaining it in details and stu...
So, you know that the two bottom angles must be equal,
And you know that all 4 angles must add up to 360
So that means 360 - (59*2) = the top angles x2
lucid lantern
Which number is that one?
winter apex
#1
lucid lantern
Oh I got 121 for that
lucid lantern
Not sure if it was correct
Cuz I have a geo test tmrw I was js wondering if we can do one for each section
winter apex
Because 360 - 59*2 is 242,
242/2 = 121
lucid lantern
Can we do 3 for first section?
lucid lantern
Yeah I js wanna know like stepby step
winter apex
It gives you one side angle
lucid lantern
Yeah
winter apex
so 180-130=x
lucid lantern
You can keep talkin ima take notes
winter apex
You're good
#4 I'm not too sure why they're asking you about it, it's a rectangle on that side, so the angle has to be 90.
This is proven in #3, where both side angles must be 180, so if 1 is 90, then the other one is 180-90
lucid lantern
Mmm okay okay
lucid lantern
So, you know that the two bottom angles must be equal,
You can keep explaining 1 then
winter apex
#5 and #6 should be the same across both diagonals I would think
winter apex
So, you know that the two bottom angles must be equal,
#1, it tells us that the two sides are Equal (Indicated by the dashes).
Because we know that the top and bottom line are parallel, the angles created must be identical. In this case,
lucid lantern
Mmm okay
winter apex
Sorry for the bad drawing
lucid lantern
Nah you’re good
So how do we get to 121 exactly? Like k know how but I js wanna know how you would do it
winter apex
Because WVY and WXY are identical
We know that 180-59 must solve for WVY
Another way of proving this is
360 - 59+59 must be equal to 2x such that
2x=242
Dividing both sides by 2 gives us x=121
winter apex
180 - 59 = 121
lucid lantern
Ohhh
winter apex
I just stated 2 ways, the 2nd one definitely more complicated for the same answer
lucid lantern
Right
winter apex
So x (?) is 145
lucid lantern
So we have to find x
lucid lantern
Ohhhhh
lucid lantern
For 3 we have to find H right
winter apex
Yeah,
lucid lantern
Would it js be 90?
winter apex
Well on number 3, we have the angle 130
lucid lantern
Yeah
winter apex
So 130 + ? = 180
lucid lantern
50
winter apex
Yeah
lucid lantern
So it would be 50
winter apex
Yeah
lucid lantern
What about 5 or 6 in the next section how would you explain it
winter apex
The diagonal, assuming 2 sides are the same, will always be the same on both
lucid lantern
Right
winter apex
I js need help on how to do these problems like explaining it in details and stu...
So on 5,
WY=VX
15 is your answer
lucid lantern
Oh is it js that?
winter apex
Yeah
lucid lantern
Is XV=YW?
winter apex
Yup
winter apex
I wanna look at 7 and 9
Starting with 7
Resending this so I don't have to scroll up lol
lucid lantern
Yeah np
winter apex
We know that SU and RT are the same
lucid lantern
Yes
winter apex
So 4x-3=13
lucid lantern
Why’s that?
lucid lantern
No worries what if it’s not the same?
winter apex
We see that in 9
lucid lantern
Ohh
lucid lantern
Because 4x-3 is SU
It would be 4 right
winter apex
Yeah
Looking at 9
If we didn't have any equation in the top left
What would the angle have to be?
(Same as question 1)
lucid lantern
180?
winter apex
What about 180?
lucid lantern
Mmm
unkempt tartan
That's not the time for this, bro. We're here to talk about becoming an alpha, not geometry. Stay focused!
winter apex
You're good man
split crane
That's not the time for this, bro. We're here to talk about becoming an alpha, n...
Yo this guys actually trying to figure out a problem please let him work this is very important rn!
lucid lantern
E is also 75 but the inside adds up to 180 righ
split crane
Sorry for inturupting @winter apex
winter apex
Yeah
lucid lantern
Yeah?
winter apex
So, now bringing back the equation
unkempt tartan
Yo this guys actually trying to figure out a problem please let him work this is...
I'm sorry, I accidentally deployed something on this account
lucid lantern
Wait is 105 right
unkempt tartan
I didn't realize it was running on this server
winter apex
24x+9 must equal 105
lucid lantern
Oh ok ok
winter apex
You're good zucc
lucid lantern
But where did 24x comes from?
lucid lantern
24x+9 must equal 105
^
winter apex
Look at question 9
You solved for the top right angle
But the equation on question 9 is 24x+9
lucid lantern
Ohh
winter apex
So 24x+9=105
lucid lantern
You solved for the top right angle
So that’s 105
winter apex
So that’s 105
Yeah, now you have to solve for x
Do you have access to calculators in geometry by chance?
winter apex
It is
lucid lantern
So 24x+9=105
What’s this one then?
winter apex
split crane
24x + 9 +75 = 180?
That how you solve for x
lucid lantern
Ohhh
lucid lantern
so it’s 180 - 84
winter apex
You're good
split crane
Wait so if number 9 is like that does that mean that number 10 would be 10x+21+79=180?
split crane
You're good
^
winter apex
Wait so if number 9 is like that does that mean that number 10 would be 10x+21+7...
Yeah
So 10x+21=101
10x=80
split crane
yea
winter apex
x=8
lucid lantern
But yeah we can use calculator
split crane
Plug in and find the value
winter apex
But yeah we can use calculator
What calculator do they let y'all use?
split crane
I hopped in here because I was also struglling with this topic thanks fcor the help bro I got a geo test
winter apex
You're good man
split crane
I think I get the texas ti 32 or sum
lucid lantern
What calculator do they let y'all use?
Idek tbh I forgot I think like every other hs calculator 😭
winter apex
Idek tbh I forgot I think like every other hs calculator 😭
You're good no worries
lucid lantern
But I think that’s it but idk can we do one more? I’m a lil worry
winter apex
Yeah sure, I can make one up real quick if you'd like
lucid lantern
Fs
Then you can explain it I’ll take notes
Also is it coo if I dm later if ion get a certain part?
winter apex
Also is it coo if I dm later if ion get a certain part?
Of course
lucid lantern
Bet bet
winter apex
@split crane Since you're also doing this, could you also solve this out?
split crane
yes ofc
winter apex
Wait 1 second
lucid lantern
Also added u
winter apex
Yeah sure
split crane
alr
winter apex
dollar sign on both sides
split crane
Messed up
winter apex
Here's one more
split crane
$so 4x+4+24=180$
wraith daggerBOT
Donutttt12344
split crane
$4x+28=180$
wraith daggerBOT
Donutttt12344
winter apex
Sorry, may I stop you rq?
split crane
yes ofc
winter apex
They are on the same side.. what can you tell me about those two angles?
split crane
there equal?
winter apex
Yeah
split crane
Wait so would I subtract like 180-4 -24?
winter apex
You don't need 180 here
split crane
omg
lucid lantern
Why tho?
lucid lantern
Ohhhh
split crane
x=5
winter apex
Yeah
lucid lantern
So for that problem it’s x=5
split crane
48?
split crane
wait 24
winter apex
You're solving for x here
winter apex
Yeah
split crane
My b
lucid lantern
That’s it right?
split crane
lets go
winter apex
This is gonna be a bigger number
split crane
so this would use 180 correct?
winter apex
Yeah
split crane
6x-12+60=180
lucid lantern
Why would this one use 180?
split crane
x=22?
split crane
Why would this one use 180?
Because there on oppisite sides and not equal @winter apex right?
winter apex
A+B=180
B=C
A=D
So, we can infer that
A+C=180
Since B and C are the same
A + (B or C) = 180
split crane
My head is actually exploding
lucid lantern
Because there on oppisite sides and not equal <@364537387004461066> right?
Is he right tho?
winter apex
Yeah
lucid lantern
Ohhh
winter apex
I'm sorry if I'm going too fast
lucid lantern
Nah you’re good
split crane
yea you good
split crane
we could like solve one seperate from each other and not put are answer and wait till were both ready?
winter apex
we could like solve one seperate from each other and not put are answer and wait...
That works for me
lucid lantern
Lemme write it gimme a sec
split crane
Bom that good wit you
winter apex
Let me help Bom real quick with this one and I'll send two problems seperate
split crane
yea I gotchu
lucid lantern
we could like solve one seperate from each other and not put are answer and wait...
Ohh cuz I gotta go Ina bit rn to go out
So I’ll js do this and I’ll come back and see the steps by steps y’all did?
split crane
alr
lucid lantern
Y’all can keep goin I gotta change rn
winter apex
@lucid lantern
We know that A+B must be equal to 180 as the angles is turning around
Logically, if you were following the line, if you turn on A and B, you'd be making a 180 turn
lucid lantern
I’ll come back and do the problem Ina bit
winter apex
So 180-60 must equal x
Now, the equation states that 6x-12=B
And since B is 120,
6x-12=120
winter apex
Add 12 from both sides gives you
6x=132
split crane
wait so that mean if you add 12 to 120 it equals 132 then devide by 6 to get 22
split crane
Add 12 from both sides gives you
6x=132
Why you subtracting?
lucid lantern
wait so that mean if you add 12 to 120 it equals 132 then devide by 6 to get 22
Wait can you do the dollar sign thing mb I need visual
winter apex
Yeah I can rq
split crane
$6x-12=120$
wraith daggerBOT
Donutttt12344
lucid lantern
Ohhh
split crane
$120+12=132$
wraith daggerBOT
Donutttt12344
split crane
$6x=132/6=22$
wraith daggerBOT
Donutttt12344
wraith daggerBOT
Unparalleled
split crane
Of course, always here if I can help
sure
I came in here not knowing the slightest bit of how to do this
you tought everything I know about this lol
split crane
Ohh okay tysm
Goodluck on the geo test youll do great I beleive in you!
winter apex
wraith daggerBOT
Donutttt12344
split crane
$4x+39$
wraith daggerBOT
Donutttt12344
wraith daggerBOT
Donutttt12344
winter apex
Sorry, may I ask where 39 came from?
split crane
$4x=101$
wraith daggerBOT
Donutttt12344
split crane
$4x/4=101/4=25.25?$
wraith daggerBOT
Donutttt12344
split crane
decimal
winter apex
Yup :3
winter apex
This is how I've been making them lol
I'm just plugging numbers in and seeing if it works nicely
winter apex
lemme get a pic
?
winter apex
Those suck]
split crane
ikr
winter apex
$5y-1=5x+9$
wraith daggerBOT
Unparalleled
split crane
lemme cook rq
winter apex
$5y=5x+8$
wraith daggerBOT
Unparalleled
split crane
..
split crane
is that a 180 degree realtion
winter apex
I was solving it like a system of equations, my bad dude
split crane
wait so just the setup part is scary
winter apex
The setup isn't that bad
split crane
you know what the Triangle sum therom is?