i messed up hold on
#help-17
vagrant cypress
harsh canopy
ok
vagrant cypress
(-inf, 1.5] [1.5 , inf) ?
harsh canopy
yeah and what would that simplify down to?
harsh canopy
yeah
harsh canopy
yep
vagrant cypress
including the 2?
harsh canopy
if you square first then yes
you could also divide by 2 first and then square
both are acceptable
harsh canopy
can you show your work?
vagrant cypress
harsh canopy
you seem to have forgotten about the 2
or at least divided it and didnt change the other side
harsh canopy
yes
vagrant cypress
ok thank you so much
harsh canopy
np π
vagrant cypress
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vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
vocal sleetBOT
vast shale
is there a way to do this like algebraically
without just substituting values
wait
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digital shell
can anyone help me with sat math
vocal sleetBOT
can anyone help me with sat math
digital shell
where the fuck is 0.2 even coming from
they j pullin numbers out of their ass or something ???
vast shale
They are indeed pulling numbers out of their
silk hollow
where the fuck is 0.2 even coming from
5 reposts = 1 follower
1 repost = 1/5 follower = 0.2 follower
vocal sleetBOT
@digital shell Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
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rich rock
So, I have this question
vocal sleetBOT
So, I have this question
rich rock
I've solved it to find x1 = 1 and x2 = 1 (i don't know if i'm correct or not) but how do I leave my answer?
how do i format my conclusion
chrome raptor
First
How can you check if x1=1 and x2=1 is a solution?
How can you verify your solution?
rich rock
subbing it back into each of the equations?
chrome raptor
Yes
rich rock
to see if it equals the y value
chrome raptor
It's important to always check if the system is small as it's this case
So is your solution right or wrong?
rich rock
So this verifies the solutions are correct
chrome raptor
Good
chrome raptor
You can state the answer in different equivalent ways
The solution is x1=1 and x2=1.
The solution is (x1, x2)=(1,1).
The solution is x1=1=x2.
The solution is 1 for both unknowns.
You can write
$$\begin{cases}2x_1-x_2=1, \ x_1+16x_2=17.\end{cases}\Longleftrightarrow x_1=1, \quad x_2=1.$$
rich rock
Okay, so I don't have to form an equation similar to
y = something + something
twin meteorBOT
Categorist
chrome raptor
Okay, so I don't have to form an equation similar to
```
y = something + someth...
That happens when there's infinite solutions. In that case the solution is a line described with an equation.
In this case, though, the answer is a single point, not a line
rich rock
The only reason I ask is because the example provided in notes were relating to three points sitting on a quadratic curve
chrome raptor
Wow, that's way beyond solving system of two linear equations haha
rich rock
aha the question was much simpler than the example provided
which meant i didnt know how to format my conclusion
a tad bit more complicated
but i used this logic to solve the 2x2
Anywho, thanks for confirming I in fact do not need to create some line function as an answer
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river vessel
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river vessel
what does it mean roots of?
silk kindle
what does it mean roots of?
I think they mean the solutions for y in that implicit equation
π€
river minnow
Sometimes 'roots' is synonymous to 'solutions'
river vessel
how do I find the roots
lilac plaza
What's the function?
river vessel
y'=a+(b/(y^2))
vocal sleetBOT
@river vessel Has your question been resolved?
river vessel
what about this
I put it into the same calculator and it could not do it
even with dt^2 on the bottom
.close
pulsar ingot
hi, can anyone check this paper for me please? im not confident in my answers
gritty zenith
My goodness
pulsar ingot
π
im doing ap chem a year early + i joined the class a week late so im a little behind but i think im catching up
karmic imp
especially #s 3, 8, and 9 in the first part
9 is the only question that is wrong in this list
pulsar ingot
ohh i see why
bc when you do the power you need to count all the zeros at the end right
karmic imp
2.0 x 10^-3 does have 2 sig figs but that's scientific notation
gritty zenith
So youβre doing approximation in AP chemistry
gritty zenith
bc when you do the power you need to count all the zeros at the end right
Huh?
karmic imp
You need to convert that to decimal to do the second part
pulsar ingot
yeah
pulsar ingot
yeah yeah mb
karmic imp
Same logic with 6
gritty zenith
karmic imp
And if you are given scientific notation, keep it in scientific notation
pulsar ingot
<@765990158822015016> https://www.calculatorsoup.com/calculators/math/significan...
ohhh thank youu
pulsar ingot
Same logic with 6
π
karmic imp
B2 is wrong
pulsar ingot
wait so 6.023 * 10^23 is basically 6023 with 23 zeros behind it, but bc theres no decimal point the only sig fig that remain are rhe 6023?
karmic imp
wait so 6.023 * 10^23 is basically 6023 with 23 zeros behind it, but bc theres n...
You still need the 10^23 part
B6 is wrong
gritty zenith
0.0000000000000000000000060
pulsar ingot
i thought that if a number didnt have a decimal point then you dont count the zeros (ex, 12,000,000 with no decimal point, its safer to assume 2 sig fig and not 8)
karmic imp
And B7
karmic imp
i thought that if a number didnt have a decimal point then you dont count the ze...
Yes that's true
pulsar ingot
0.0000000000000000000000060
its not 10^-23
karmic imp
But 6.023x10^23 and 6023 are different
pulsar ingot
B2 is wrong
why?
pulsar ingot
But 6.023x10^23 and 6023 are different
ill just ask my teacher about it later today lol
thank you
pulsar ingot
The number of sig figs are wrong
i thought you keep the number of sig figs of the least precise number in your equation
karmic imp
ill just ask my teacher about it later today lol
It's because 6023, you lost the x10^23
pulsar ingot
so how would you round it
karmic imp
so how would you round it
Take 1.23 x 10^4, how mant sig figs is that?
pulsar ingot
Take 1.23 x 10^4, how mant sig figs is that?
3 sig figs followed by 2 zeros?
karmic imp
You need to convert that to decimal to do the second part
No it's just 3, whatever notation you are in keep it... I made a mistake here, my bad
pulsar ingot
oh lol nw
karmic imp
Say I want 1 sig fig for 1.23 x 10^4, what would it be?
pulsar ingot
12300 -> 10,000?
karmic imp
My mistake was telling you to convert it, don't convert it
pulsar ingot
hm alr so it would be 123 rounded to 100?
karmic imp
And B10 is wrong
pulsar ingot
yeah let me redo it
karmic imp
hm alr so it would be 123 rounded to 100?
Not quite, 1.23 x 10^4 rounded to 1 sig fig, would be 1 x 10^4
pulsar ingot
And B10 is wrong
.00151?
karmic imp
Because rounding rules applies to the 1.23
pulsar ingot
Not quite, 1.23 x 10^4 rounded to 1 sig fig, would be 1 x 10^4
ohh ok
pulsar ingot
just 1.51 * 10^-3?
karmic imp
1.152 x 10^-03 is the answer, how many sig figs does that answer need to be?
karmic imp
So what would be the answer?
pulsar ingot
1.5 * 10^-3
karmic imp
Yep
pulsar ingot
ok lol
karmic imp
Can you fix the rest of the callouts I made?
pulsar ingot
thank u so much @gritty zenith and @karmic imp !!
karmic imp
9 is the only question that is wrong in this list
.
karmic imp
Same logic with 6
.
pulsar ingot
oh on the first part
karmic imp
B6 is wrong
.
karmic imp
9 is .002
Keep the notation, don't change from scientific notation if you are given that
karmic imp
6.0 for 6A
Remember the exponent part?
pulsar ingot
Keep the notation, don't change from scientific notation if you are given that
right right so 2 x 10^-3?
pulsar ingot
Remember the exponent part?
6.0 * 10^23?
karmic imp
right right so 2 x 10^-3?
Yes
karmic imp
6.0 * 10^23?
Yes
pulsar ingot
okok i think i got it
karmic imp
b7 is 18.2
Yes
karmic imp
and b3 is 599
Yes
karmic imp
i gtg now lol
Don't forget to close this
north aurora
vocal sleetBOT
north aurora
how would i answer this
karmic imp
You have the vertex and y intercept, you can use that
y = a(x - h)^ + k is vertex form
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crisp raptor
If AB^2 = AD^2 + BD^2
Then AB > BD ???
vocal sleetBOT
If AB^2 = AD^2 + BD^2
Then AB > BD ???
crisp raptor
|AB| >= |BD|
Alr thanks
Wait
It's actually the Pythagoras theorem for a right angle triangle
So the second value cannot be 0
Help pls
vocal sleetBOT
@crisp raptor Has your question been resolved?
crisp raptor
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vast shale
part di
vast shale
I simply did r+0.09=0.64
This gave r as 0.55
I thought that the notation means the entire circle C without the B overlap
vast shale
it means the _conditional_ probability of B' given C
Is that what the straight line seperating B and C means?
yes, it means B | C B given the fact that C happens
Alright thanks
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vocal sleetBOT
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unique spade
<@&286206848099549185> helllp
vocal sleetBOT
<@&286206848099549185> helllp
crisp swan
bro wait 15 mins to get help
unique spade
sorry
unique spade
bro wait 15 mins to get help
heelllllp
crisp swan
nah im too dumb
lilac plaza
!status
vocal sleetBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
!show
vocal sleetBOT
Show your work, and if possible, explain where you are stuck.
lilac plaza
Show your question
unique spade
1
lilac plaza
What help do you need
unique spade
wh
unique spade
What help do you need
i cant start
lilac plaza
Integrate it
unique spade
Integrate it
what should i do
<@&286206848099549185> oooooo
i am going to sleeeeeeep
byeeeeeeeeeeee
vocal sleetBOT
@unique spade Has your question been resolved?
frigid pivot
This is my problem
vocal sleetBOT
This is my problem
frigid pivot
I know how to start since all I gotta do is move βx+4 besides the 6 and then apply the formula
vast shale
What is the formula
frigid pivot
a2 + b2 - 2ab
in this case
but I always end up applying it wrong which substracts points
civic otter
Show your work
frigid pivot
I'd figure that in this instance it'd be 2x - 1 = 36 - x + 4 - 2 (6 - (x + 4)) think of the parentesis as the square root
civic otter
I'd figure that in this instance it'd be 2x - 1 = 36 - x + 4 - 2 (6 - (x + 4)) t...
Why -x + 4?
civic otter
Yes, but when you square it the minus becomes a plus
civic otter
$${\left(6 - \sqrt{x + 4} \right)}^2 = 6^2 + {\left(- \sqrt{x + 4}\right)}^2 - 2 \cdot 6 \cdot \sqrt{x + 4}$$
twin meteorBOT
Alberto Z.
frigid pivot
And now I just gotta simplify it, which is the easy part
frigid pivot
$${\left(6 - \sqrt{x + 4} \right)}^2 = 6^2 + {\left(- \sqrt{x + 4}\right)}^2 - 2...
How did you do this, though?
.close
vocal sleetBOT
civic otter
.reopen
vocal sleetBOT
β
civic otter
latex you mean?
@frigid pivot
frigid pivot
Yeah, if that's what you call it
signal maple
This is my problem
hi man
frigid pivot
Hi
signal maple
wait a second to upload image
civic otter
Yeah, if that's what you call it
It's a nice formatting language to write pretty looking math stuff but also more in general for make a document good looking, focusing on the content instead on how to do the layout (e.g. have you ever tried MS Word with both text and images? Do you agree that handling images is terrible in word?)
frigid pivot
It's a nice formatting language to write pretty looking math stuff but also more...
I think you got the wrong idea of me
signal maple
I think you got the wrong idea of me
π
frigid pivot
This is the first time I see that language or bother to type math equations
I am really bad at maths and am quite desperate to pass a retake of a retake of a retake maths exam
signal maple
did you understood or what
frigid pivot
I understood I got it wrong
signal maple
what is wrong
frigid pivot
But on the first picture, the 4th line
Where do the last x + 4 cole from?
And they suddenly disappear on the 5th line too
signal maple
And they suddenly disappear on the 5th line too
2x-1 = 36+x+4
to got x-41
frigid pivot
Alright I get this part
frigid pivot
In the 2nd picture, on the 2nd line wouldn't -82x be + 82x? You rose -41 to the power of 2 so you'd think that it'd now be positive and where does the x even come from?
Why is it x2 - 82x instead of x2 + 82x, pretty much
civic otter
What's ${\left(a - b\right)}^2$ equal to?
twin meteorBOT
Alberto Z.
signal maple
**Alberto Z.**
that is the answer
signal maple
What's ${\left(a - b\right)}^2$ equal to?
hey man
i love this language
can you give me resources to learn it
frigid pivot
**Alberto Z.**
a2 and b2
frigid pivot
a - b x a + b
signal maple
this is the basis in math
frigid pivot
Not that one either...?
civic otter
Do you agree that (a-b)Β² = (a-b)β’(a-b)? @frigid pivot
frigid pivot
No
frigid pivot
It'd be positive if that were the case
But I guess you'd know better
Damn, I am worse than I thought...
civic otter
It'd be positive if that were the case
Yes, (a-b)Β² is non negative, but this has nothing to do with my question
frigid pivot
Yes, (a-b)Β² is non negative, but this has nothing to do with my question
What was the question for, though?
civic otter
https://tenor.com/view/dont-forget-gumball-%E6%8F%90%E9%86%92-gif-7544872
You know what? I was right now in my GDrive to look if I have any reference lol
civic otter
What was the question for, though?
If you don't know what (a - b)Β² is equal to by heart, at least you have to know how to calculate it in some other way...
frigid pivot
Which is...?
civic otter
Do you agree that (a-b)Β² = (a-b)β’(a-b)? <@787701161016819734>
This one π @frigid pivot
frigid pivot
Oh, alright
But it seems like my teacher was right
I have a huge problem with the basics
Well I'll revisit this problem in a day or 2
Thanks for the help
.close
signal maple
You know what? I was right now in my GDrive to look if I have any reference lol
loook
signal maple
.close
vocal sleetBOT
civic otter
.reopen
vocal sleetBOT
β
civic otter
Look here #latex-help @signal maple
signal maple
Look here <#840667252793802752> <@701755549577904160>
ok
signal maple
Look here <#840667252793802752> <@701755549577904160>
look what f*ck
$$
\begin{tikzpicture}
\draw (0,1) to[bend left=10] (0,6);
\draw (0,1) to[bend right=5] (0,0);
\draw (0,0) to[bend right=10] (2,0);
\draw (2,0) to[bend right=5] (2.25,2);
\draw (2.25,2) to[bend right=10] (3,2);
\draw (1.75,2.125) to[bend right=8] (2.25,2);
\draw (3,2) to[bend right=5] (3,-0.25);
\draw (3,-0.25) to[bend right=10] (5,-0.25);
\draw (5,-0.25) to[bend right=5] (5.25,7.25);
\draw (5.25,7.25) to[bend right=30] (3,10);
\draw (3,10) to[bend right=15] (2,10);
\draw (2,10) to[bend right=30] (0.5,8.28);
\draw (5.25,7.25) to[bend left=5] (6.25,7.15);
\draw (6.25,7.15) to[bend left=5] (6.25,2.5);
\draw (6.25,2.5) to[bend left=20] (5.25,2.25);
\draw (-1,7.08) to[bend right=90] (3.25,7.08);
\draw (-1,7.08) to[bend left=90] (3.25,7.08);
\end{tikzpicture}
$$
twin meteorBOT
α©αͺα°_
civic otter
If you want to train yourself with LaTeX write in #latex-testing
signal maple
If you want to train yourself with LaTeX write in <#844681108473118750>
nice wow i love this lang
civic otter
If you have no more questions, can I close this channel?
signal maple
thanks man for helping about qa
and help me to learn this lang β€β€β€
vocal sleetBOT
vocal sleetBOT
Available help channel!
glacial meadow
how do i solve this?
vocal sleetBOT
how do i solve this?
silent folio
!status
vocal sleetBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
Given you have the dimensions and it's multiple choice, you could just try each one and see which works, but there is a nicer way
Do you know about the relationship between volume, area, and length scale factors?
silent folio
Okay cool let me give an example
If you have a square of side length 1, and then you double it's side lengths, what is the new area?
glacial meadow
4?
glacial meadow
9
silent folio
Yeah great
Do you see a pattern?
Think about the calculation you did each time to get the new area
glacial meadow
side times x then get the area
silent folio
Yes, so the actual area calculation was 2x2 and then 3x3
Or 2 squared and 3 squared
When you multiply the side lengths of a shape by n, the area is multiplied by n^2, does that make sense?
glacial meadow
mhm
silent folio
It sounds like I haven't been very clear, is there a particular bit I'm confusing you with?
glacial meadow
no no im getting it
i just
dont quite understand how to connect it to my problem
silent folio
Ah okay cool sorry
So if I wanted to multiply my shapes area by 16, what would I multiply the sides by?
silent folio
dont quite understand how to connect it to my problem
We are nearly there
glacial meadow
by 16?
silent folio
by 16?
Not quite, remember that the area is multiplied by the square of the side multiplier
glacial meadow
4?
silent folio
Yep!
So a very similar rule applies for volumes
Thinking about a cube with side lengths of 1, can you guess it?
glacial meadow
guess what
silent folio
The rule for the relationship between a side length multiplier and the volume multiplier
Like we have for side lengths and areas
silent folio
No worries
If you multiply the side lengths of a 1 length cube by 2, whats the new volume?
glacial meadow
4
glacial meadow
mhm
silent folio
Do you see the pattern?
For area it's the side length scale factor squared, for volume it's the side length scale factor cubed
So if you want the volume to by multiplied by 4, what would you multiply the sides by?
glacial meadow
4!
silent folio
Not quite, remember you had to square root the 16 in the last example
glacial meadow
ot maybe not
silent folio
That was with areas
glacial meadow
yeah i just tried it
silent folio
With volumes we are cubing
glacial meadow
thats no good
silent folio
Do you get another go at the question?
glacial meadow
no i didnt submit it the answer was bogus
silent folio
Okay cool yeah
Think about what we did for the question I asked with 16
What might you have to do for the 4
glacial meadow
..square root?
silent folio
Nearly!
That was for areas
For volumes you need to cube root
Just like for the other direction you cube
glacial meadow
cube root??
silent folio
Ah have you not come across those before?
Do you know what I mean when I say to cube a number?
glacial meadow
yes i do, just never heard of cube roots lol
silent folio
Okay cool, so it's like the inverse of cubing
Just like square root is the inverse of squaring
There should be a button on your calculator
If now just type cube root of 4 into google
glacial meadow
1.59!
silent folio
You are very welcome, sorry if it felt like I went on a tangent but I wanted to explain why
silent folio
Im sure you would have got it, remember it's a multiple choice to worse case just try all the options and see which one works
glacial meadow
yeah, I wouldnt have reeeally understood why though
silent folio
Well I'm glad I could help π
vocal sleetBOT
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Available help channel!
cunning saddle
are pascal's triangle and the binomial theorem the same?
vocal sleetBOT
are pascal's triangle and the binomial theorem the same?
rugged orchid
They are very related
cunning saddle
They are very related
who is best?
gaunt pendant
Wdym
rugged orchid
Depends on the context
cunning saddle
do they give the same result?
gaunt pendant
Well if you notice the binomial coefficient (n, k) appears as the kth entry in the nth row of Pascal's triangle (in the binomial theorem)
flat whale
do they give the same result?
for what problem
cunning saddle
any
gaunt pendant
So if you remember some entries itβll prolly be easier to expand than solely relying on the binomial identity
cunning saddle
or if n is too large the theorem is used?
cunning saddle
for what problem
hey you how i can factored a^3-b^3 how i can demostrate that
vocal sleetBOT
Available help channel!
rain linden
vocal sleetBOT
vocal sleetBOT
@rain linden Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
@inland latch Has your question been resolved?
pallid zenith
no
its not
your equation doesnt make sense to me
well for starters
hrm whats the best way to do it
the way youre dividing and multiplying
it doesnt make sense
you could use dimensional analysis to see
yea, exactly
but your equation does not reflect this
how about instead
m/h = (m*h/h + m*h/h)/h
start with each piece of your suggestion here
to find the total distance, we first take the known speed
30 m/h
and multiply by the duration
30 m/h * 2h = 60 mi
now do the same with the mystery speed
V m/h * 2h = 2V mi
yea
wait
no it wasnt
wait
oo
damn i cant read
okay lemme scribble
its correct
sorry about the misreading 
hrm
im not sure if one exists
there are onewheels that can go that fast
i think
well maybe not
well you know
sometimes you do math to find out something is unrealistic
i wanna save up 2000 by the end of august
so far ive saved up 20 dollars
probably not gonna happen
vocal sleetBOT
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bleak crow
Hello! How to prove that the greatest number of a series of integers has to be greater or equal than the mean of those integers?
vocal sleetBOT
Hello! How to prove that the greatest number of a series of integers has to be g...
zinc quail
you can denote the max value of the series as k and each other term as k-x0 to xn if there are n-2 terms
paper depot
multiply that by n
you get the statement "total of your n numbers β€ n times the largest number"
which is obvious
zinc quail
then the mean will be equal to k if x0=x1=...=0
otherwise smaller than k
but I'd also agree it's trivial
paper depot
@zinc quail overcomplicating.
bleak crow
yeah I was thinking it could be trivial but I just wanted to make sure I get a perfect proof for once lol
thank you anyway it was helpful!
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vocal sleetBOT
zinc quail
<@1000186270078750740> overcomplicating.
hm right k*n would be quicker
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sharp ravine
vocal sleetBOT
sharp ravine
I need to find the domain of the following function and write the solution interval notation
twin meteorBOT
A Lonely Bean
river minnow
Can you answer or no?
sharp ravine
No
river minnow
So, the number under the square root needs to be nonnegative, so a >= 0 makes sqrt(a) defined
tired hull
I need to find the domain of the following function and write the solution inter...
try graphing it on desmos
river minnow
Similarly $\sqrt{7 - 14x}$ will be defined if and only if $7 - 14x \ge 0$
twin meteorBOT
A Lonely Bean
river minnow
try graphing it on desmos
They won't learn much by just graphing it
river minnow
**A Lonely Bean**
So, can you solve this inequality here?
sharp ravine
I gotta subtract 7 on both sides ,no?
river minnow
Yes, that would be the first step
And then you divide by -14
Make sure to flip the sign inequality as you do that
So you get $x \le \frac12$, right?
twin meteorBOT
A Lonely Bean
sharp ravine
Oh ok, so it would be -infinty,1/2 ?
paper depot
don't drop the parentheses
you cannot drop the parentheses here because it matters whether you meant (-β, 1/2] (correctl) or (-β, 1/2) (wrong, excludes 1/2 for no good reason)
sharp ravine
Ok, how would I like draw that in a line
river minnow
You would mark 1/2 on the number like and shade everything that's left to it
Make sure you somehow indicate that 1/2 is included as well (typically by making the dot bold at where 1/2 is located)
inner bloom
hi
A is matrix like this:
a b c
m n k
x y z
and B:
a b c
k n m
x y z
in which condition det(A)=det(B)?
inner bloom
or is there any sort of equality between det(A) and det(B)
like det(A)=-det(B)
vocal sleetBOT
@inner bloom Has your question been resolved?
pallid forge
well what have you tried?
there is a way to make this equality true depending on the values of the elements of the matrix
inner bloom
well what have you tried?
nothing special
just wrote down det and it does not look good
pallid forge
it is quite complicated yes
if you write out det(A)=det(B), there are two terms on either side that cancel each other out
have you done that yet?
inner bloom
actually no I have not becuase I was looking for something else
for example when we switch rows or columns new det = - det
I was looking for this sort of thing
but lemme give it a try
brittle minnow
hi
A is matrix like this:
a b c
m n k
x y z
and B:
a b c
k n m
x y z
in which c...
is that all given in the question?
inner bloom
is that all given in the question?
no no I just saw it somewhere and came to my mind
brittle minnow
hmm... lemme write the matrices properly first
[A = \begin{pmatrix}
a&b&c\m&n&k\x&y&z
\end{pmatrix}
\quad
B = \begin{pmatrix}
a&b&c\k&n&m\x&y&z
\end{pmatrix}
]
inner bloom
second row in B is k n m
twin meteorBOT
numbily
brittle minnow
you just want the determinant to be equal right?
inner bloom
have you done that yet?
I tried it and still nothin
brittle minnow
better to just write down the determinant
inner bloom
you just want the determinant to be equal right?
equal or any type of relation between them
for example det(a)=-det(b)
anything
brittle minnow
you're fixing the two rows and only permuting the elements in the 2nd row so I don't think there'd be relation unless both the entries are same
ofc if the vectors are dependent the det would be zero
But it would be hard to comment anything more
mild flower
\int_{0}^{5}
okay first of all decimals are 
stick to fractions 99% of the time
the integral wasn't done quite right, it should be 25 - 20k
the thing on the left
you got 20 - 20k, it should be 25 - 20k
but i'm confused what you're trying to actually do here
you want to figure out what value of k you need to make that integral equal to 5?
okay... so you want to know whether 25 - 20k = 5, for k > 1?
is that a completely different problem or something? it's not relevant for this one
no, that would only be true if you cared about finding the like unsigned area below and above the curve, or if you had an absolute value somewhere. In this case you're just asked to do the integral
i'm still confused though because like
if you solve the equation 25 - 20k = 5
you get k = 1
yeah neither do i
like
paper depot
,w int[0,5] (3x^2/5 - 4k) dx
twin meteorBOT
paper depot
this sounds like an issue with the problem and/or the copying thereof
but y'all have computed the integral correctly
do you have a picture/screenshot of the problem as stated originally
even if it is in another language
mild flower
is there any context to this problem yeah
paper depot
true or false
okay so then
you didn't need to PROVE this statement, you needed to TELL IF IT'S TRUE OR FALSE.
which is a very different affair.
final olive
vocal sleetBOT
final olive
Can someone please help explain the 16th one
jolly epoch
hi
so it is asking if we draw 3 balls out of 15, at need at least one black
having at least one black is the same as 1 - Pr(all three not black)
in this case 1 is represented by 15C3 because we just want 3 balls
final olive
See, what I did was I did combination for 14C2 and then multiplied by 6 since one black can be selected 6 ways
jolly epoch
and if there are no blacks, that means it must be all red, hence 9C3
final olive
But that way the answer is coming wrong
ruby musk
Im not that good at maths like you can call me a kid or whatever but i really love maths
So like if there is a small number next to a normal number towards the upper right its called as raised to the power of x
But what does it mean when the small number is next to a number towards the lower right??
jolly epoch
See, what I did was I did combination for 14C2 and then multiplied by 6 since on...
your 14 includes black balls as well, so effectively you are drawing from a bag of red AND black balls then considering drawing an additional black ball
jolly epoch
Im not that good at maths like you can call me a kid or whatever but i really lo...
this is not your channel! pls open a ticket separately
ruby musk
this is not your channel! pls open a ticket separately
Oh my bad
final olive
your 14 includes black balls as well, so effectively you are drawing from a bag ...
Can u please elaborate
I'm confused
jolly epoch
See, what I did was I did combination for 14C2 and then multiplied by 6 since on...
ok you have 9 red and 6 black balls
your 14 is coming from 9red + 5 black, when you perform 14C2, you are also factoring the chance of selecting a black ball, this number could be 0, 1, 2
does that make sense
final olive
If we fix a black in one of the selection which would have 6 cases . Then we can apply 14C2 to select other balls so the condition for atleast one black ball will be satisfied
jolly epoch
If we fix a black in one of the selection which would have 6 cases . Then we can...
so you are saying we do 14C2 and 1C1 to guarantee a black ball
we canβt do this because the 15 balls are all together, if we do 14C2 and 1C1, we are making two pools where one has 14 balls and one has 1 ball
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
Let $p$ be the preposition that 121 is a perfect square. Would saying that $\neg p$ is the preposition that the square root of 121 is irrational be the nicest way to put it?
vocal sleetBOT
Let $p$ be the preposition that 121 is a perfect square. Would saying that $\neg...
twin meteorBOT
vast shale
It's just a preposition. Ignore the truth of it
crimson jetty
I don't understand
crimson jetty
> 121 is not a perfect square
not p is exactly this statement
vast shale
Yeah
But is "121 is not a prefect Square" equivalent to "the square root of 121 is irrational"?
crimson jetty
But thats not what you wrote
crimson jetty
But is "121 is not a prefect Square" equivalent to "the square root of 121 is ir...
This is a claim
which requires justification or proof
crimson jetty
not p does not translate to what you wrote, and I wouldnt say its nice at all
river minnow
Yeah you would need to show how you got from "121 is not a perfect square" to "the square root of 121 is irrational" or vice-versa
I think
And "121 is not a perfect square" sounds nicer ye
glad sage
I'm not really sure where to start, with this question or what a power calculation is.
Question 8.3.20
vocal sleetBOT
I'm not really sure where to start, with this question or what a power calculati...
silk comet
,rccw
twin meteorBOT
proven garden
maybe show us example 8.3.10
vocal sleetBOT
@glad sage Has your question been resolved?
rugged orchid
Now Iβm not too sure about this but Iβll go out on a limb, maybe itβll inspire some good thinking for you:
It looks like fβ(x) is N(0,1) and thus the critical values for X at π level would be |X| > z_(1-π/2)
rugged orchid
Theyβve done a bunch of stuff in here regarding Hβ but Iβm not too sure about that stuff
(But I would love to have a read should you decide to send me those notes hehe)
vocal sleetBOT
Bot doesn't like me :(
proven garden
lol the timing
paper depot
Bot doesn't like me :(
putting a . at the start of your message suppresses the channel-opening
you just need to not do that
glad sage
Oh I'm just stupid sorry
glad sage
This was the original question
glad sage
And this is the example they are talking about
vocal sleetBOT
@glad sage Has your question been resolved?
open coral
can anyone explain to me how do you get the pi/3 to the outside
vocal sleetBOT
can anyone explain to me how do you get the pi/3 to the outside
open coral
i don't understand how it becomes 3/pi on the outside
rugged orchid
Could you send a bigger picture
Oh
Itβs just the chain rule in action
The reverse chain rule
rugged orchid
You know how you βmultiply by the derivative of the insideβ in the chain rule
open coral
right
rugged orchid
You have to βcompensateβ for that
open coral
so you divide by the inside
open coral
yes
rugged orchid
Where did 1/3 come from
open coral
the x^3
rugged orchid
It came from βcompensatingβ the power rule
rugged orchid
The 1/2 came from the compensation of the derivative of 2x
open coral
right
so we need to compensate for pi/3
so we divide the thing by pi/3
which becomes multiplying it by 3/pi
ok I see it now
i was trying to fit it into this formula
but i didn't know you had to remove the pi/3
anyways thanks for the help
.close
steel fjord
How can I prove this?
vocal sleetBOT
How can I prove this?
steel fjord
It's discrete mathematics
lofty bridge
How can I prove this?
vann diagram
vast shale
nah
steel fjord
does that count as proof though?
vast shale
find an elemnt x in A union (B intersec C)
prove it belongs to the right side as well
steel fjord
ok
our professor told us that that we should try to prove that the set on the left side is a subset of the right side and vice versa, should I do that here?
vast shale
x is element of A union (B intersec C) means x is elemnt of A or x is element of B intersec C
it means x is element of A union B or x is element of A union C
which means x is element of (A union B) intersec (A union C)
after doing this, follow the same steps but backwards
steel fjord
it means x is element of A union B or x is element of A union C
why is x element of A union B or A union C
ohh
no wait doesnt x have to be in B and C?
vast shale
yes but if x is an element of A or an element of B intersects C
it means x is el of A or B and A or C
steel fjord
yeh
vast shale
do you get it now?
steel fjord
yeh I think so
steel fjord
it means x is element of A union B or x is element of A union C
shouldnt it be "and" instead of "or" here then?
vast shale
yes , sorry
steel fjord
yeh then I get it
vast shale
but this just proves the left side is included on the right side.
No find an element x of the right side , and prove it belongs to the left side
so you can prove equality
and the way you do it , its just follow the same steps but backwards
lilac owl
Hello
Sorry I can't make the image more clear but I'm in class so I have no better options.
Wolfram Alpha and such only give 14 as the answer, but my other solution doesn't seem to be wrong. What's the mystery about sqrt(x) + sqrt(y) = 1?
proven garden
it doesn't work
as x and y have to be less than 1
obviously the original equations would not be satisfied
vocal sleetBOT
@lilac owl Has your question been resolved?
grand frigate
grand frigate
How does the geometric sequence note that 2^2008 + 1 is divisible by 2^8 + 1
grand frigate
Close <#423244559682764800>
But it's a different question 
gritty zenith
Itβs still 2 channels
grand frigate
And the other one is getting ignored
gritty zenith
Close it.?
grand frigate
2008/8 = 51
251*
jolly epoch
yep typo sorry
jolly epoch
ok gimme a sec
grand frigate
I mean like... how do you turn it into a geometric sequence
quick estuary
How does the geometric sequence note that 2^2008 + 1 is divisible by 2^8 + 1
because the division is giving a integer
whats your question
grand frigate
I meant like... how does the 2^2008 + 1 being divisible by 2^8 + 1 become a geometric sequence
grand frigate
I meant like... how do you get the geometric sequence
quick estuary
you want to know how this comes?
grand frigate
yes
jolly epoch
quick estuary
the terms given is a geometric sequence
brother
it does not work
like that
u cant cancel
grand frigate
yeah exactly
jolly epoch
why not
jolly epoch
why can't it? 2008/8 is 51
royal kestrel
twin meteorBOT
help
jolly epoch
hm
grand frigate
wait...
grand frigate
2^251 * 2^8 is not even 2^2008
grand frigate
the terms given is a geometric sequence
no, wait ima post the original question, this was the solution
quick estuary
what exactly do u want to know lol
grand frigate
quick estuary
ok
grand frigate
what exactly do u want to know lol
How to use geometric sequence to prove divisibility
Like... how do I know what sequence to use
quick estuary
257 is 2^8+1
grand frigate
yes.
quick estuary
thats hard to know tbh
i can only explain it to you now because i saw the solution
else i would try some other method
quick estuary
i would take that as 1 mod 2^8
and use properties of modulo
2^8+1
get it closest to 2^2015
go from there
quick estuary
however this approach is good
it has to be divisible by 2^8+1
when can u get this in denominator
grand frigate
im just having a hard time processing on how to get the geometric sequence from the problem
grand frigate
yeah i understand that
quick estuary
ratio is -2^8
so they did 2^8(n) such that its just less than 2^2015
then multiplied by 128
and then said that next few multiples will come after 257
grand frigate
yeah that i get
i was just having trouble processing on how they got the gp
thanks!
.close
finite hatch
hi can someone help me!
vocal sleetBOT
hi can someone help me!
jolly epoch
how am i supposed to do dis?
use the ASTC acronym
jolly epoch
sure
quick estuary
all sin tan cos
finite hatch
wait can u help me to apply it
jolly epoch
sure
finite hatch
one sec
quick estuary
apply graph
quick estuary
more accurate
finite hatch
finite hatch
uhhh wait is it this brb
jolly epoch
because its in quadrant 2, we will measure it against 180*
finite hatch
finite hatch
wait wait
ok
So this is question B and the one under is question E
Why is B wrong?
B its 60 degrees but I got 30
.close
crystal drum
can someone pls help me with this?
vocal sleetBOT
can someone pls help me with this?
twin meteorBOT
sand lodge
!status
vocal sleetBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
- I can work out the shaded area plus the rest white area apart from that quarter circle
sand lodge
sorry I don't really get what u mean by that lol
u can get the area of the square?
@crystal drum
split wind
crystal drum
u can get the area of the square?
yea
I just need to find a way to get the extra bit in the corners
vast shale
find the area of all the things that you can first , the square , the 1/4 of the circle, and the small circle inside the square
crystal drum
find the area of all the things that you can first , the square , the 1/4 of the...
yes and?
vast shale
wait i need to write in a notebook
sand lodge
tee bee aych
well there's lots of ways to do this so I'm not sure which one you'd like but yes finding the areas is a good start
I'd try maybe considering the symmetry of the problem
if we had the square and then cut out the circle what would we then be left with
crystal drum
the four parts in the corners?
sand lodge
yes
crystal drum
then i can divide that by 4 to get 1 of them
sand lodge
yes
crystal drum
and I can subtract it from the area of the 10cm radius quarter circle
but then the small parts in the corners are left
sand lodge
didn't u find the small parts in the corners
crystal drum
no the smaller parts
sand lodge
oh I see
vast shale
ok , so isnt the shaded area just the Suqare are - 1/4 circle area - top corner
if the top corner is 1/4 of square area - inside circle area?
crystal drum
but there are some small parts left in the corner bordering the quarter circle and the shaded area
how am I supposed to find that?
sand lodge
u need it