(i think that's how you say it)
#help-10
fluid plume
modest minnow
it would end up pretty much as a cuadratic equation
n^2 + 2n + (n + 1)
n^2 + 3n + 1
fluid plume
It would be easier to see it as n²+3n+1
yeah
we can see without calculating that neither 1 or 2 are roots of the equation
so we cannot cancel anything
:(
modest minnow
ok thanks for the help
fluid plume
np
proven python
So for this identity can I alter it to be cot^2x = cos^2x/sin^2x
obtuse pebbleBOT
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proven python
So for this identity can I alter it to be cot^2x = cos^2x/sin^2x
obtuse pebbleBOT
So for this identity can I alter it to be cot^2x = cos^2x/sin^2x
proven python
wooden cipher
yes
tranquil depot
So for this identity can I alter it to be cot^2x = cos^2x/sin^2x
Yes, thinking about squaring both sides
obtuse pebbleBOT
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vivid creek
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timid silo
Hi
molten jetty
Hello! Could you guys help me understand why this statement is not valid? Thank you
obtuse pebbleBOT
Hello! Could you guys help me understand why this statement is not valid? Thank ...
brisk matrix
why do you think it is true?
if you believe they multiplied by (x-2), consider what happens when (x-2) < 0
molten jetty
if you believe they multiplied by (x-2), consider what happens when (x-2) < 0
In this case, wouldn't just one side of the inequation be multiplied by -1?
I mean
Ah
that makes sense
forget what I was trying to say
hahaha
thank you very much, @brisk matrix !
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timid silo
Hi how can I find out how Long purple is? Blue and red are given but idk how to find out purple
it is half a cylinder and the purple length is sought
timid silo
<@&286206848099549185>
obtuse pebbleBOT
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@timid silo Has your question been resolved?
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@timid silo Has your question been resolved?
proven python
For question 19 how’d they get the bottom to factor like that at the end
fiery sorrel
For question 19 how’d they get the bottom to factor like that at the end
I believe it’s the line on bottom left?
It was done by treating it as a polynomial
Set U=tan(x), the bottom part of the fraction becomes U^2+3U+2
Which is in our favorite polynomial form and can be factorized into (U+2) (U+1)
Hopefully this explains it?
iron edge
For question 19 how’d they get the bottom to factor like that at the end
!occupied
obtuse pebbleBOT
For question 19 how’d they get the bottom to factor like that at the end
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
iron edge
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obtuse pebbleBOT
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
I have to go soon, so I might not make it till you're back
I'll give you some hints instead
a)EG is on the plane EFGH and plane EFGH is perpendicular to something
b)segment DB is perpendicular to segment AC since it's a cube
c)three perpendicular therom will help
sure
np
I have to go
feel free to ping helpers when you're still confused
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subtle gull
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subtle gull
hello
My problem is here
Have i made a mistake? Cause i dont think theres something in between zero and one
how do i know if its positive or negative here
safe haven
Have i made a mistake? Cause i dont think theres something in between zero and o...
0.1 exists
also it should be 0 < x < 1 not 0 > x > 1
subtle gull
The original function is 6x-2x^3
safe haven
0.1 belongs to R
subtle gull
so i can use numbers that contain points to properly solve it?
Im so scared to apply 0.5 cause they strictly said to not use halves or points
but imma try it
safe haven
!xy
obtuse pebbleBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
safe haven
ok then what are you supposed to do with it
subtle gull
draw it
it just says draw the function
Its supposed to look something like this
Not exactly the same shape i guess
safe haven
did you even do the derivative correctly though
you said f(x) = 6x - 2x³
so shouldnt it be f'(x) = 6 - 6x²?
safe haven
,rccw
warm shaleBOT
subtle gull
Wait i think i didnt remove the x
safe haven
you sure f'(x) = x - 6x²?
subtle gull
yeah its supposed to be 6-6x^2 right?
safe haven
yeah
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edgy needle
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edgy needle
how do i solve this using inverse proportion?
ik how to do it normally
but i get marks for using inverse proportion
obsidian isle
Ñ
edgy needle
or is it impossible?
because when i try and use inverse proportion i get 4.5 minutes
but thats impossible because it takes them 30 minutes to dig 15m
obtuse pebbleBOT
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spare wharf
Hello If 140 glasses need to fit in a box with the dimensions depth 60 width 70 and length 80 what will the diameter be? I just want help knowing the process in solving this
obtuse pebbleBOT
Hello If 140 glasses need to fit in a box with the dimensions depth 60 width 70 ...
spare wharf
<@&286206848099549185>
wraith wing
Hello If 140 glasses need to fit in a box with the dimensions depth 60 width 70 ...
what is the shape of the glass
spare wharf
timid silo
ok
wraith wing
0 idea how to calculate that things volume or how itd stack
timid silo
The volume of the box:
Volume of the box = 60 × 70 × 80 = 336000 cm³
Volume of one wine glass (assuming a cylindrical shape):
Volume of one wine glass = (π/4) × Diameter^2 × Height
= (π/4) × Diameter^2 × 15 cm
The total volume of glasses:
Total volume of glasses = Volume of one wine glass × Number of glasses
Diameter:
Diameter = sqrt((Total volume of glasses) / ((π/4) × Height × Number of glasses))
Substitute the values into the formula and calculate the diameter.
spare wharf
This is a way my friend did it but his dimensions are different and I'm not sure what certain steps mean and how he got there:
Thats all the working out for his specific dimensions
@timid silo
timid silo
ok let mne see
ok so besides the area and volume formulas are there any other formulas used here?
spare wharf
I dont think so.
i tried to redo it by trying his way but idk if its correct and i've labelled parts where I'm not sure what it means:
timid silo
bro that name is kind of like the most goofy ass chingchong name
spare wharf
bro that name is kind of like the most goofy ass chingchong name
ik lol first thing that came to my mind when i was changing it
timid silo
oh nice
bro give me sec i'm on something here
i'm trying to solve it
give me 4 minutes
spare wharf
okay ty
timid silo
the padding calculation determines how much extra space is needed around each glass to accommodate the packaging material and provide sufficient cushioning
spare wharf
sorry i forgot to mention that the box will be double layered so instead of having 140 glasses together there will be 70 on the top and 70 on the bottom and in 10 columns 7 rows.
I drew this diagram earlier after trying to copy my friend and it might be helpful for u
timid silo
i cnat understand that writing no offence
spare wharf
sorry lol im getting used to stylus. it reads: We will only have padding vertically because there is more space to be used compared to the number of rows (because its a better ratio)
timid silo
ok thanks
Total Glasses: With 140 glasses in total, and each glass occupying approximately 80 cm², the total area occupied by the glasses is 14080=11200 cm214080=11200cm^2
Arrangement: Given that there are 10 columns and 7 rows on each layer, the total number of columns is 10 and the total number of rows is 7
Padding:
- Since we are only adding padding vertically, we'll calculate the total padding needed for each column.
- Since there are 10 columns, we'll need to add 5 cm of padding between each column, resulting in a total of 9*5=45cm for each column.
Double Layer: With the glasses arranged in two layers, we'll need to account for the spacing between the top and bottom layers. This spacing will depend on the thickness of the glasses and the packaging material.
Total Box Dimensions: To calculate the total dimensions of the box, we'll need to add the dimensions of the glasses, padding, and spacing between layers.
i think that's suppose to be it
spare wharf
dont worry about the spacing between the top and layer box for now, i can do that easily and it involves another way which you dont have enough specific knowledge of this task to do.
because it depends on the height which I get from first getting the diameter of each cup..
spare wharf
after I get my diameter i go to this website which shows the standard height for my wine glass. say the diameter of each wine glass is 7.5cm and on the website it is 7.2cm i just divide 7.5/7.2 then i use that number to multiply it against the standard on the website to get my height. then after I have my height put it into the box then just figuire out how much room there is for spacing.
Note the image above is just an exampler and all of its units are wrong rn
timid silo
Diameter Adjustment: You calculate the diameter of each wine glass as 7.5 cm. Then, you compare it with the standard diameter on a website, which is 7.2 cm. The adjustment factor is then 7.5/7.2
Height Calculation: After obtaining the adjustment factor, you use it to adjust the standard height from the website. This gives you the height of each wine glass.
Space for Spacing: With the dimensions of each wine glass, including the adjusted height, you can now calculate the total space needed for the glasses and padding. Since you're only adding padding vertically, you'll calculate the total space required between rows.
bro if you have anymore doubts my hand will stop working
this is the most i ahve ever typed in one goddamn day
spare wharf
sorry man this is like 1% of my methods assignment I gotta do 💀
I think thats all the help I need anyways thank you very much for your time Kermit
obtuse pebbleBOT
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grim ocean
how to do b
obtuse pebbleBOT
how to do b
tender tusk
one possible way would be to find how many combinations are possible without restrictions then subtract all combinations where those 2 people are on the same team
grim ocean
hmm i did consider that but i'm not sure about how to work out the same team part
o yes and also answer is 210
tender tusk
to work out when they are on the same team you can consider those 2 people as 1 player instead
hoary lotus
grim ocean
ok so wat i did was 315 (number in part a) - (7C2*5C4)/2!
but it was wrong
o wait crap i just realiesd wat i did
nvm sorry
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south kettle
Started learning about convergence tests for infinite series, am stumped on these 2. Tried applying the ratio and the root test
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Started learning about convergence tests for infinite series, am stumped on thes...
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robust raven
Started learning about convergence tests for infinite series, am stumped on thes...
you have to use the ratio test here, have you met any difficulties ?
it only needs precision during calculation of the limit
robust raven
Started learning about convergence tests for infinite series, am stumped on thes...
the second series is an analogous one. that is all
south kettle
you have to use the ratio test here, have you met any difficulties ?
Probably went about it wrong and complicated the issue
robust raven
so far you do ok, but continue simplification
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solemn spindle
need help with this question
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torpid cave
need help with this question
Draw this line. Now the problem is much easier. Try solving it now
The new line is parallel to QR so you can get all the properties you need about it
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whole shell
I am trying to calculate a translation to a region of a circle based on its angle. I have the start and end coordinates along the circumference. below is the first one I did, but I want to use this same rate of change for other regions. I also have the portion of each region in radians if it would be easier to use that.
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 110 110">
<!-- t = 3-->
<path d="M 55 55 L 55 5 A 50 50 0 0 1 105 55 Z" fill="red" transform="translate(3, -3)" />
<path d="M 55 55 L 105 55 A 50 50 0 0 1 55 105 Z" fill="green" />
<path d="M 55 55 L 55 105 A 50 50 0 0 1 19.6447 90.3553" fill="blue" />
<path d="M 55 55 L 19.6447 90.3553 A 50 50 0 0 1 55 5 Z" fill="yellow" />
</svg>
obtuse pebbleBOT
I am trying to calculate a translation to a region of a circle based on its angl...
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whole shell
I may be able to get the sum of the other radians than use cos((a/2)+x), -sin((a/2)+x)
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whole shell
That didnt seem to work
it may have but i need to fix other errors first to be sure
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midnight violet
can someone help
obtuse pebbleBOT
can someone help
midnight violet
with y, 2x+y
glacial wolf
midnight violet
mb
midnight violet
alright
outer needle
!noanswer
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undone plume
hello can someone show me how to solve this?
obtuse pebbleBOT
hello can someone show me how to solve this?
nimble gulch
at 1;1 there must be vertex of parabola i guess
and 1,1 is in parabola means that you can sub in the equation 1 for x and 1 for y
you will get equation for a and b
and then you vertex formula
you can use both vertex formulas to get a and b also
green epoch
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pallid basin
What does del f / del y have to do with uniqueness of a differential equation. I don't get the role it plays
obtuse pebbleBOT
What does del f / del y have to do with uniqueness of a differential equation. I...
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tawdry elbow
What would the bounds in this Double integral be?
obtuse pebbleBOT
What would the bounds in this Double integral be?
gilded needle
the slope of that diagonal line is what?
gilded needle
it's negative though
tawdry elbow
-2y+2
gilded needle
yes
obtuse pebbleBOT
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obsidian lance
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light raft
Might be useful to use the fact that (n+1)! = (n+1)n!
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zinc frost
Can someone show me steps to complete, not sure where to even start.
obtuse pebbleBOT
Can someone show me steps to complete, not sure where to even start.
vague spindle
Can someone show me steps to complete, not sure where to even start.
What do inverse functions do?
zinc frost
Undoes operation of f?
vague spindle
So it takes an output of f and tells you what input gets that output
Now what input gives us an output of 5?
zinc frost
f(4)
vague spindle
So what’s f^-1(5)
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agile girder
Largest interval?
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agile girder
Nope
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vapid leaf
🤓🤓🤓
mint oak
Why would he find the derivative of c = 2pir what is that achieving for a)
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signal yoke
can anyone help with this please?
obtuse pebbleBOT
can anyone help with this please?
signal yoke
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crimson pike
can anyone help with this please?
26 people take yoga alone 5 of them take yoga and kickboxing how many people take yoga alone ?
signal yoke
i have no clue
crimson pike
i have no clue
come on you can do it
signal yoke
21?
signal yoke
so 15
signal yoke
D?
crimson pike
Yep that’s right
signal yoke
ok thank you!!!!!
crimson pike
any time
signal yoke
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dark cedar
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dark cedar
so i dont see how step 4 makes sense
how do you cancel the x-3
sorry for the sideways picture
gritty vessel
np
dark cedar
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bitter temple
I dont get the thing on the red boxx
obtuse pebbleBOT
I dont get the thing on the red boxx
bitter temple
How did it get 6th root of 3 cube
bitter temple
Howw
fierce elbow
Howw
Its an improper fraction u see
u can write the 3 in terms of raised to
like cube root 3 is 3^1/3
and root 3 is 3^1/2
that makes it much much simpler
bitter temple
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bitter temple
....
Umm can someone ask me questions about multiplying and dividing radicals imma try amd answer it
Nvm
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viscid tulip
p and n are coprime by definition.
I'm not sure how rigourous your proof is expected to be, but maybe elaborate on that? The definition of a prime number p is that it cannot be divided by numbers other than 1 and p, and the definition of gcd(n,p) is the greatest integer that divides both n and p, but the fact that n mod p != 0 implies that gcd(n,p)=1 is not any less trivial than the question itself?
Argument for second question seems to be okay I think
obtuse pebbleBOT
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edgy needle
hi in my test there was this question
obtuse pebbleBOT
hi in my test there was this question
night fox
what's your take
edgy needle
ok so
i solved it
but in like 10 steps
when the question was only 5 marks
so i think i did it wrong
anyways i found the angle in the top left by using tan-1(30/20)
and then i connected the radius to make a triangle like this
so i know diameter is 20 so radius is 10
ok so tan-1(30/20 is 56 degrees
since triangle is isosceles we also know that the remaining angle is 180-(56x2)
which is 68 degrees
and then basically
i used the formula of area of a sector which is theta/360 x pi x r^2
so 68/360 x pi x 10^2
wait is that right
=59cm^2
and then i used area of a triangle formula
a=1/2 x ab x sinC
= 1/2x10x10xsin(68)
=46cm^2
so therefore area of segment is 59-46
=13cm^2
then i did (pi x 10^2/2 -13) - 20x30/2
i mean opposite way round
bc area of triangle is bigger
=155.92cm^2
edgy needle
what's your take
ok thats what i did
rugged mural
Hey can anyone help me by explaining the solution of this question.
edgy needle
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open mountain
Is the restriction of f unique? Is the extension f unique?
obtuse pebbleBOT
Is the restriction of f unique? Is the extension f unique?
open mountain
If anyone can also explain why pls
deep sedge
what is f
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quiet sail
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quiet sail
Hello can anyone help me with this question
obtuse pebbleBOT
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quiet rapids
for implicit differentiation how one here he doesn’t do dx/dy for 5y
obtuse pebbleBOT
for implicit differentiation how one here he doesn’t do dx/dy for 5y
quiet sail
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cunning burrow
<@&286206848099549185>
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quiet sail
Well the answer to this is zero
cunning burrow
for implicit differentiation how one here he doesn’t do dx/dy for 5y
What is being applied is product rule on d/dx (5x)y. d/dx of 5x is 5. So we end up with 5y as the first term.
quiet sail
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cunning burrow
You cannot close because you don't own the channel
Your original channel was closed due to time out
quiet sail
You cannot close because you don't own the channel
Oh ik but I need help now with this again how do I do that?
cunning burrow
Available channels are here
cunning burrow
Oh ik but I need help now with this again how do I do that?
^^
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karmic hedge
obtuse pebbleBOT
https://i.imgur.com/zl2wEcv.png
karmic hedge
I forget how to do these
Cause I know I need to do something with dx right
Like u = 5x+6
x = (u-6)/5
So I can sub in (u-6)/5 for x and u for 5x+6
But what do I do with the dx?
I know I need to do something with it
But I dont remember QQ
So right now I have ((u-6)/5) (u)^6 (dx)
pure kelp
is this usub?
karmic hedge
Yep
sage dagger
@karmic hedge
pure kelp
So right now I have ((u-6)/5) (u)^6 (dx)
you can take the derivative of u=5x+6
sage dagger
let u = 5x+6
du/dx = 5 right
pure kelp
let u = 5x+6
du/dx = 5 right
huh
isnt it du=5dx so dx=du/5
ig same thing now that i think abt it
sage dagger
thats the same thing as du/dx = 5
u just rearange it
@karmic hedge do u know what to do next?
pure kelp
I dont see how you got that tho srsy
you know dervs right
sage dagger
I dont see how you got that tho srsy
with u-substitution you are allowed to treat derivative operators like fractions
karmic hedge
you know dervs right
Yep
sage dagger
kinda quirky right
karmic hedge
with u-substitution you are allowed to treat derivative operators like fractions
Can you give an example sry
sage dagger
Can you give an example sry
solve for y in $\frac{y}{x}=5$
warm shaleBOT
water beam
karmic hedge
y=5x
sage dagger
ok then solve for x
karmic hedge
x=y/5
sage dagger
how did you do that
karmic hedge
multiplied 5 by x and divided y by 5
sage dagger
u can do that with the "dx" and "du" here
you can treat the derivative dy/dx like its a fraction
pure kelp
are you confused about the d_ thing or the equation itself
karmic hedge
u can do that with the "dx" and "du" here
What is the equation we have tho sry
sage dagger
$\frac{du}{dx}\cdot dx=5dx=du=5dx$
warm shaleBOT
water beam
sage dagger
$\frac{5dx}{5}=\frac{du}{5}=dx=\frac{du}{5}$
warm shaleBOT
water beam
pure kelp
the basic concept is replacing the dx in the equation with a du
karmic hedge
Im missing the step before all this tho sry
sage dagger
not really quirky but ok
um it is as a new concept
last pilot
no it isn
karmic hedge
Guys pls 😭
pure kelp
stop arguing about the quirkiness about a concept lmao
sage dagger
Im missing the step before all this tho sry
whats the derivative of 5x+6
karmic hedge
whats the derivative of 5x+6
5
last pilot
@sage dagger didn't mean for u to interpret it that way, but okay
can we discuss the question
sage dagger
<@722683408190406667> didn't mean for u to interpret it that way, but okay
can w...
i was literally doing that before u came along
💀
last pilot
okay mb, i'll go ig?
karmic hedge
whats the derivative of 5x+6
Whats the next step sry
sage dagger
you have u = 5x+6 yes?
pure kelp
i think only one person should help them lmao
karmic hedge
you have u = 5x+6 yes?
Yeye
pure kelp
bc the conversation is just jumping back and forth and jsut being complicated
sage dagger
if you take the derivative then you get du/dx = 5 yes?
sage dagger
do you know power rule?
pure kelp
if you take the derivative then you get du/dx = 5 yes?
btw i had a question, how do you get the du/dx form
theres an easier more direct way i think
sage dagger
btw i had a question, how do you get the du/dx form
you differentiate u with respect to x
karmic hedge
btw i had a question, how do you get the du/dx form
Not sure sry
karmic hedge
you differentiate u with respect to x
So u becomes du/dx?
sage dagger
So u becomes du/dx?
yes
sage dagger
ill ask u another question
if you have y = 2x
you want to take the derivative
what is it?
pure kelp
oh youre doing diff eq, nvm then
sage dagger
oh youre doing diff eq, nvm then
huh no diff equations
last pilot
@karmic hedge du/dx is another way of saying u' or the derivative of u
karmic hedge
you want to take the derivative
dy/dx = 2
sage dagger
yes
pure kelp
huh no diff equations
its alr just help odie for now
karmic hedge
<@996564019672535040> du/dx is another way of saying u' or the derivative of u
Ah oke I didnt know this
I think I get it now tho
we have du/dx = 5
pure kelp
theres too many ways to say derv of _
karmic hedge
Which becomes dx = du/5
sage dagger
yes
karmic hedge
So we just sub in du/5 for dx
And then that becomes 1/5
Etc
I think I can solve it now
sage dagger
So we just sub in du/5 for dx
you mean dx
sage dagger
$\int_{ }^{ }x\left(u\right)^{6}\cdot\frac{du}{5}$
karmic hedge
.close
obtuse pebbleBOT
warm shaleBOT
water beam
last pilot
you... also gotta change the x??
obtuse pebbleBOT
Available help channel!
sonic herald
Can somebody help me through this question
obtuse pebbleBOT
Can somebody help me through this question
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
verbal prawn
prove:\left(1+sin\theta -cos\theta \right)^2+\left(1-sin\theta +cos\theta \right)^2=4\left(1-sin\theta .cos\theta \right)
obtuse pebbleBOT
prove\:\left(1+sin\theta -cos\theta \right)^2+\left(1-sin\theta +cos\theta \righ...
verbal prawn
$$ prove:\left(1+sin\theta -cos\theta \right)^2+\left(1-sin\theta +cos\theta \right)^2=4\left(1-sin\theta .cos\theta \right) $$
warm shaleBOT
Nayan
verbal prawn
help lol
last pilot
okay for future reference
in latex/texit it's \sin and \cos not sin and cos
verbal prawn
huh
sweet pond
how do you find an equation of a line if the points are fractions?
obtuse pebbleBOT
how do you find an equation of a line if the points are fractions?
sweet pond
twilit meteor
use the same formulla
twilit meteor
(y2-y1)/(x2-x1) = (y-y1)/(x-x1)
twilit meteor
over -3/8 - 3/2
twilit meteor
so for 1/2 - 1/4 how would you do that
take lcm
twilit meteor
4
twilit meteor
ye
twilit meteor
yea
twilit meteor
wriite it on paper and u willl be able to do everything rather easily
twilit meteor
so 1/4 over -15/8
shud be
twilit meteor
so you turn 1/4 into 2/8 right
yea ok
sweet pond
but how do you
divide 2 fractions
cross multiplication?
cause i completly forgot how to divide fractions
timid silo
hello everyyan
sweet pond
normal
vivid edge
obtuse pebbleBOT
vivid edge
I just want to make sure that 12a is correct?
last pilot
,rccw
warm shaleBOT
last pilot
yes
vivid edge
Or should o rather say y is greater than or equal to one
vivid edge
Alright thanks for the help
obtuse pebbleBOT
If you are done with this channel, please mark your problem as solved by typing .close
hexed gull
I just gotta know what 2 1/2 is as a improper fraction
you must claim a channel
upbeat fox
oh how do I do that
vivid edge
.close
obtuse pebbleBOT
vivid edge
I just wanna Make sure I did the second part right aswell
obtuse pebbleBOT
Available help channel!
open mountain
when does a sequence of functions converge uniformly?
obtuse pebbleBOT
when does a sequence of functions converge uniformly?
frail wraith
idk
fossil crag
when does a sequence of functions converge uniformly?
when ||f_n - f|| converges to 0
being with respect to the uniform/infinite norm
muted ember
Hello, does anyone know how to simplify this trigonometric expression? The result is 1
obtuse pebbleBOT
Hello, does anyone know how to simplify this trigonometric expression? The resul...
versed stratus
is sen sin?
muted ember
yes
versed stratus
hmm, try multiplying and dividing the first part by $1/\sqrt2$
warm shaleBOT
Why am. I here
pine sail
or divide by cos(alpha/2)
versed stratus
that would probably work better tbh, do that
pine sail
It's going to be the same thing either way, but if you see (1+tan(A))/(1-tan(A)) that's quick
muted ember
or divide by cos(alpha/2)
?
pine sail
yes.
But like when you divide the numerator you get 1 + tan(alpha/2)
Do the same for the denominator.
muted ember
But like when you divide the numerator you get 1 + tan(alpha/2)
hmm, I got to an expression I had at the beginning, I'm going to pass on what I had done
the expression I wanted to simplify is the top left one
pine sail
(1+tan(A))/(1-tan(A)) can be simplified using tan(A+B)
muted ember
(1+tan(A))/(1-tan(A)) can be simplified using tan(A+B)
but that's what I did at the beginning
muted ember
see
pine sail
I can now see.
How else do you want it simplified?
It looks pretty simplified when it's the tan(pi/4 + A/2) form
muted ember
you want a simpler way out ?
ok
timid silo
so write 1- sin(x) as -->
cos^2(x/2) + sin^2(x/2) -2sin(x/2)cos(x/2)
complete the squares here
after this its straight forward
ping if need help
muted ember
so write 1- sin(x) as -->
cos^2(x/2) + sin^2(x/2) -2sin(x/2)cos(x/2)
complete ...
what is this identity?
timid silo
you got it how i did it for the 1 ?
cos^2(x) + sin^2(x) = 1
and for sin2x = 2sinxcosx
muted ember
hmm
muted ember
cos^2(x) + sin^2(x) = 1
And how do you get from this to the formula you gave me before?
timid silo
And how do you get from this to the formula you gave me before?
i wrote 1 in terms of sinx and cosx
and then did for sinx
muted ember
i wrote 1 in terms of sinx and cosx
I don't quite understand that you cleared
obtuse pebbleBOT
@muted ember Has your question been resolved?
obtuse pebbleBOT
@muted ember Has your question been resolved?
tired shell
you're close now, just multiply the numerator and denominator and the terms should equal
muted ember
you're close now, just multiply the numerator and denominator and the terms shou...
thanks
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
ember spade
how to find the basis of the intersection of two subspaces?
obtuse pebbleBOT
how to find the basis of the intersection of two subspaces?
fickle turret
ember spade
sec please
warm shaleBOT
nothing
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
ember spade
@fickle turret i think this
and will the matrix(s) be useful in solving the problem?
fickle turret
and will the matrix(s) be useful in solving the problem?
Yes
fickle turret
first i found the bases of L1 and L2
Ok, what are they?
fickle turret
first i found the bases of L1 and L2
Then you shouldn't have a problem with the task...
ember spade
L1 with (1, 2, 3), (4, 3, 1)
L2 with (1, 1, 1), (-3, 2, 0)
but what should I do now?
(to find the basis of the intersection of L1 and L2?)
fickle turret
Look which of these basis vectors of L2 is in L1
ember spade
but idk how
ember spade
but if for example more vectors
not as in this example
matrix is better way
but idk how
there are supposedly millions of linear combinations here, that’s why I’m asking, because I can’t just take it and do it - I don’t know how
hard um
hmm
fickle turret
not as in this example
Do the same. You need to express one basis in terms of the other. Then you can just take the intersection of the two basis
ember spade
can you do this with matrix
fickle turret
You can solve the linear system with a matrix
ember spade
can you draw it
fickle turret
I mean you just have to go through the basis of L2 and look whether each of those basis vectors can be represented as a linear combination of the basis
fickle turret
can you draw it
No
obtuse pebbleBOT
@ember spade Has your question been resolved?
exotic pendant
i need help with calculating optimal percenteges for a game
ember spade
.reopen
tired shell
have you done cross products yet
tired shell
you found that both bases are 2 dimensional, and the intersection will be a line that goes through both
if you cross product the two basis vectors you'll find a line perpendicular to the plane
see if you can use the two perpendicular lines here to get to the intersection
cursive vortex
everyone this is rlly urgent i need help with an integral please
velvet lichen
ember spade
@tired shell i'm a bit abstracted from geometry because higher dimensions can occur yk
ember spade
L1 with (1, 2, 3), (4, 3, 1)
L2 with (1, 1, 1), (-3, 2, 0)
so
tired shell
you can do a whole equation of like a*(1,2,3)+b*(4,3,1) = c*(1,1,1)+d*(-3,2,0) and that works in any dimension but I usually do the other way
ember spade
α(1, 2, 3) + β(4, 3, 1) = γ(1, 1, 1) + δ(-3, 2, 0)
oh you sended same
now i need to do this somehow
i'm interested in the matrix method, but i'm not sure how
tired shell
you'd have to write it as a big 3x4 matrix and row reduce again
ember spade
tired shell
yea then you'd zero out these spots
but I think the last 2 columns are supposed to have a minus sign when you rewrite the equation to =0
ember spade
i’m just not very good at it, i just saw problems with more dimensions and not sure i can solve it like this
tired shell
hmm the other option was [(1, 2, 3) X (4, 3, 1)] X [(1, 1, 1) X (-3, 2, 0)]
ember spade
and
obtuse pebbleBOT
@ember spade Has your question been resolved?
half carbon
Hey, I have this assignment. I believe I'm doing with 1, 2, and 3, but am a bit confused on what to graph on 4. Could I get some guidance?
obtuse pebbleBOT
Hey, I have this assignment. I believe I'm doing with 1, 2, and 3, but am a bit ...
half carbon
If you would like, I can tell you the values I found for 1, 2, and 3.
restive gorge
Hey, I have this assignment. I believe I'm doing with 1, 2, and 3, but am a bit ...
4 looks like to just visually graph your results in Desmos
half carbon
I'll get what I found for everything, but I'm not entirely sure what parts of it I'm supposed to graph lol
warm shaleBOT
Someone
warm shaleBOT
Someone
half carbon
$\frac{dy}{dx} = \frac{-4x+5y}{-5x+16y}$
$\$
$\$
$\$
When I plug in $-3\sqrt{3}$ and $3\sqrt{3}$ for x and 0 for y:
$\$
$\frac{4}{5}$
$\$
$\$
$\$
When I plug $\frac{-3\sqrt{3}}{2}$and $\frac{3\sqrt{3}}{2}$ in for y and 0 in for x:
$\$
$\frac{5}{16}$
restive gorge
wait bro chilllll
restive gorge
so you're doing 2) rn?
warm shaleBOT
Someone
half carbon
that's number 3
half carbon
**Someone**
restive gorge
So I read somewhere implicit diff. for 2) why?
restive gorge
ah ok makes sense now
half carbon
number 2 was just throwing in 0 for y to get x's and 0 for x to get y's
but yeah those are the three answers i have right now, not sure what to do from here
restive gorge
- seems correct.
half carbon
yeah
warm shaleBOT
Someone
restive gorge
3 is trivial
restive gorge
**Someone**
looks good
restive gorge
basically 4) is easiest also 1pt
plot 2x²-5xy+8y² = 54
and then plot the 4 tangent lines and save that picture
half carbon
circle :D
half carbon
the "4" tangent lines meaning 4/5 and 5/16?
restive gorge
more like a rotated ellipse
half carbon
it would be (4/5, 0) for 4/5, right?
restive gorge
if you look at the graph it makes sense
restive gorge
it would be (4/5, 0) for 4/5, right?
what is that
half carbon
uhhhh
restive gorge
you can determine tangent line with this formula
warm shaleBOT
adonhs
half carbon
4/5 would be a?
restive gorge
**Someone**
here dy/dx
half carbon
Ohhh, I see
warm shaleBOT
adonhs
restive gorge
Basically 4 points
so a is 3sqrt(3) and then -3sqrt(3)
else a = 0
you basically just need to plug in everything
half carbon
So like this, yeah?
restive gorge
$t_1 : y = \frac{4}{5}(x-3\sqrt{3}) + 0$
warm shaleBOT
adonhs
restive gorge
first tangent line for P1(3sqrt(3), 0)
restive gorge
So like this, yeah?
yea that's good, you plotted the points
also been asking in 4)
now plot the first line
restive gorge
**adonhs**
.
restive gorge
🙂
restive gorge
i would've never figured out that slope, wow
you would
slope is always first derivative
that's why you did that long ass implicit differentiation
half carbon
ohhh
restive gorge
now you can do the rest (hopefully) you sicko
half carbon
the rest is just one more tangent line?
half carbon
wot
restive gorge
**adonhs**
here
restive gorge
you can see that here too
warm shaleBOT
Someone
restive gorge
yea for the P1 the +3sqrt(3)
P2 would be the -3sqrt(3)
i just did a shorter notation
restive gorge
try it 🙂
warm shaleBOT
Someone
half carbon
thought i had to flip them xD
restive gorge
and why did you choose the other slope?
they are parallel you can see that on the graph
restive gorge
**Someone**
you are denying your own work LOL
restive gorge
it's 4/5 again
half carbon
so that?
restive gorge
thought i had to flip them xD
why though lol
restive gorge
**adonhs**
tangent formula again
half carbon
warm shaleBOT
adonhs
restive gorge
your other pair because i am nice
half carbon
i thought we had to use $\pm\frac{3\sqrt{3}}{2}$ for the black one?
warm shaleBOT
Someone
warm shaleBOT
adonhs
half carbon
yeah, so these are P1 and P2?
restive gorge
yea
half carbon
okay, i see
restive gorge
this is what i came up with
you substituted wrong
what is a and what is f(a)
nope
half carbon
wot
restive gorge
that is the y-coordinate
this here
delete it
dont confuse things
no
this one
half carbon
restive gorge
😭
half carbon
lmao
restive gorge
we are done with P1 and P2
restive gorge
here what is a
restive gorge
XES
warm shaleBOT
Someone
half carbon
restive gorge
what
restive gorge
**Someone**
.
half carbon
so it's 5/16?
restive gorge
visual studio aint gon solve your problem 💀
half carbon
my god 😂
restive gorge
yea
