yes, so its 53deg north of west
#help-17
vale frigate
half summit
yes, so its 53deg north of west
alr, so the final answer is 15 [W 53 N]?
or N 53 W? 🤔
vale frigate
well im not familiar with this notation u r using..
basically imagine urself facing the west, and then u turn towards the north thru 53deg
half summit
well im not familiar with this notation u r using..
i mean is it 53 degrees from the west or north?
ah
yes I get it now
thank you
.close
vast shale
hello can you help me solve a ratio and proprtian question
vocal sleetBOT
hello can you help me solve a ratio and proprtian question
vale frigate
vast shale
hi
can i ask
Two numbers are in the ratio 9:4 . if 7 is added to each of the numbers.The ratio becomes 5:3 . Find the numbers ?
<@&286206848099549185> Hey im new no one is helping
subtle barn
ok
vast shale
you play roblox
blissful fable
Two numbers are in the ratio 9:4 . if 7 is added to each of the numbers.The rati...
9a = 4a
5(a+7) = 3(a+7)
cursive turret
write it as formulaas.
blissful fable
solve for a
vast shale
i dk algebra
subtle barn
18 and 8
vast shale
im dumb
blissful fable
<@&286206848099549185> Hey im new no one is helping
my guy you posted the message one minute ago have some patience
vast shale
k
blissful fable
i dk algebra
you gotta try
subtle barn
you play roblox
Yeah!
blissful fable
i gave you the simulaneous eq
vast shale
teach me algebra
subtle barn
Two numbers are in the ratio 9:4 . if 7 is added to each of the numbers.The rati...
Let's call the two numbers in the ratio 9:4 as 9x and 4x, where x is a positive constant.
So, we have:
First number = 9x
Second number = 4x
According to the given information, when 7 is added to each of these numbers, the new ratio becomes 5:3. So, we have:
(9x + 7) / (4x + 7) = 5/3
To solve for x, we can cross-multiply:
3(9x + 7) = 5(4x + 7)
Now, distribute the numbers on both sides of the equation:
27x + 21 = 20x + 35
Next, subtract 20x from both sides:
27x - 20x + 21 = 35
Combine like terms:
7x + 21 = 35
Now, subtract 21 from both sides to isolate 7x:
7x = 35 - 21
7x = 14
Now, divide by 7 to find the value of x:
x = 14 / 7
x = 2
So, we've found that x = 2. Now, we can find the two numbers:
First number = 9x = 9 * 2 = 18
Second number = 4x = 4 * 2 = 8
Therefore, the two numbers are 18 and 8.
cursive turret
!nosols
vocal sleetBOT
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.
subtle barn
!nosols\
vocal sleetBOT
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.
subtle barn
!nosols
vocal sleetBOT
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.
subtle barn
!nosols
vocal sleetBOT
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.
river kettle
relax
vocal sleetBOT
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.
river kettle
chill out bro
vocal sleetBOT
@vast shale Has your question been resolved?
main totem
When I complete this problem, Im only subsituting the 2 functions that I circled and Im not exactly sure where Im going wrong
vocal sleetBOT
When I complete this problem, Im only subsituting the 2 functions that I circled...
@main totem Has your question been resolved?
vocal sleetBOT
@main totem Has your question been resolved?
silk kindle
When I complete this problem, Im only subsituting the 2 functions that I circled...
hello, could you show your work? 🤔
silk kindle
When I complete this problem, Im only subsituting the 2 functions that I circled...
the resulting integrand should be
14/(2t^2 + 2t) I think
vocal sleetBOT
@main totem Has your question been resolved?
main totem
the resulting integrand should be
`14/(2t^2 + 2t)` I think
i didnt get that
vocal sleetBOT
i didnt get that
main totem
wait I actually did
it simplifies to 7/t^2+t
right?
the issue is that it still doesnt work
I should subsitute the bounds into the function 7/t^2+t right
silk kindle
I should subsitute the bounds into the function 7/t^2+t right
No, that's not the rule of substitution 🤔
You're given t= tan(x/2)
vocal sleetBOT
@main totem Has your question been resolved?
main totem
No, that's not the rule of substitution 🤔
why arent you allowed to simplify
vocal sleetBOT
@main totem Has your question been resolved?
wide pilot
Can anybody find the pattern?
vocal sleetBOT
Can anybody find the pattern?
cursive turret
without more information i would do a linear interpolation.
cursive turret
300000 sawfly cococons -> 7,5 shrews. 600000 -> 19 you need 500000 which is 2/3 on the way from 300000 to 600000 -> 2/3 from 7,5 to 19 -> ...
wide pilot
300000 sawfly cococons -> 7,5 shrews. 600000 -> 19 you need 500000 which is 2/3 ...
is it 7.67?
cursive turret
plus 7.5 (you start from 7.5)
cursive turret
with a linear interpolation: yes
obtuse needle
How do I get coefficients out of the inside of trigonometric functions?
obtuse needle
I'm in IB Math Y2. We learnt how to change sin(2x) etc, but homework has sin 3x and sin x/2 and like sin sqrt(3)x/3
crisp moat
Im pretty sure it's just formulas
And you have to change what's inside the function to get to a known formula
vocal sleetBOT
@obtuse needle Has your question been resolved?
obtuse needle
oka7y one of us just found more identities int he formula booklet that work 👍
stoic trout
I’m stuck on a basic tangent line question for calculus.
The question is:
“Sketch the circle of radius 2 centered at 3,-3 and the Line L with equation y=2x+2. Find the coordinates of all the points on the circle where the tangent line is perpendicular to L.”
I know the slope of the tangent lines that would be perpendicular but I’m stuck trying to find how I could use that to find the specific points on the circle where it is perpendicular to L.
north ruin
if the slope of the tangent at a point is perpendicular to L, then the radius at that point is parallel to L
so intersect the line which passes through the centre of the circle with gradient the same as L, with the circle, to obtain the points
stoic trout
The red line has the same slope since it’s parallel and I figured out the b from the circle’s centre point
Y = 2x-9
But do I then do something like:
-1/2x + b = 2x-9
Wasn’t sure how to progress when I found it was parallel
north ruin
once you have the equation for the red line
you can either equate it to the equation of the circle to get the intersection points
or you can find the points on that line a distance of 2 (the radius) away from the centre of the circle
vocal sleetBOT
@stoic trout Has your question been resolved?
stoic trout
So something like (x-3)^2 + (2x-9+3)^2 = 4?
north ruin
yes
stoic trout
Ok I found one of the answers but how do I find the other one
north ruin
its a quadratic; you should get 2 solutions
stoic trout
Oh I think I messed up at one of the steps but I think I know how to do it now tysm
.closed
north ruin
np
stoic trout
.close
merry cosmos
vocal sleetBOT
@vast shale Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
bitter herald
I need help in geometry, I got a test tomorrow and trying to study, but I’m stuck trying to prove statements. How would I prove angle B is congruent to angle C?
vocal sleetBOT
I need help in geometry, I got a test tomorrow and trying to study, but I’m stuc...
vocal sleetBOT
@bitter herald Has your question been resolved?
forest haven
vocal sleetBOT
forest haven
Does anyone have any idea how to do this question
vocal sleetBOT
@forest haven Has your question been resolved?
lofty spindle
how to solve lim (sin5x)/(3x) as x approaches 0; knowing that sinx/x = 1
pale perch
perhaps let u=5x and do some subbing and factoring
odd pawn
L'hospital brother
grizzled halo
lhopital is so unnecessary here lmao
lofty spindle
lhopital is so unnecessary here lmao
how to solve?
grizzled halo
perhaps let u=5x and do some subbing and factoring
basically this
lofty spindle
kk
undone shell
not sure how they got this answer, but then again, i'm not sure how I got my answer either haha!
vocal sleetBOT
not sure how they got this answer, but then again, i'm not sure how I got my ans...
undone shell
my logic was that we have the initial amount, and its exponentially decaying by 0.6%, but either way, now I'm trying to understand the solution, but it doesn't make much sense to me
<@&286206848099549185>
idle aurora
no
idle aurora
<@&286206848099549185>
sorry im in class
floral pike
oh, I got it
the 207/50000 = 3*69/500
they are accounting for the amount already in the body at the moment t = 0.69s
this way, when t = 0.69, the exponent is 0 and the amount in the body is exactly 0.47 ml
@undone shell
also you shouldn't be exponentiating the rate in your version
undone shell
oh okay, so its the rate (found in first part) to the power of the 0.6% decrease, plus the amount thats already in the body?
floral pike
you would want a form like
f(t) = 0.47(1-0.006)^(t - 0.69)
= 0.47(0.994)^(t-0.69)
and that would be the same
...pretty sure.
floral pike
oh okay, so its the rate (found in first part) to the power of the 0.6% decrease...
no
it's the initial amount, times
undone shell
you would want a form like
f(t) = 0.47(1-0.006)^(t - 0.69)
= 0.47(0.994)^(t-0.69...
Ohhh, okay. are we subtracting it from 1 here because its a percent?
floral pike
this is an equivalent expression
umm, wait
I'm messing it up
when t=0.69 seconds, we need 47 mL, and we need to be losing 0.06% = 0.006 every second
0.006 = 3/500
the formula for decay is P = P_0 e^(-rt)
that's why you see
$Q(t) = \frac{47}{100}e^{-\frac{3}{500}t}$
twin meteorBOT
Disorganized
floral pike
but we also need to make sure that when t=0.69, the exponent is zero
we can do that by just doing 0.006*0.69
which is the same as (3/500)*0.69
and adding it to the existing exponent
which is what they did
undone shell
oh okay, thats where it came from. i see
floral pike
that's 207/50000
undone shell
thank you so much for clearing that up, i really appreciate your time
floral pike
$Q(t) = \frac{47}{100}e^{\left(-\frac{3}{500}t + \frac{207}{50,000}\right)}$
twin meteorBOT
Disorganized
floral pike
you would want a form like
f(t) = 0.47(1-0.006)^(t - 0.69)
= 0.47(0.994)^(t-0.69...
this should still also be true
equivalent
undone shell
okay, thats the form i'm more comfortable with anyways, so thanks for that as well
floral pike
okay, thats the form i'm more comfortable with anyways, so thanks for that as we...
np
vocal sleetBOT
@undone shell Has your question been resolved?
vocal vale
a bit confused on this
vocal sleetBOT
a bit confused on this
vocal sleetBOT
@vocal vale Has your question been resolved?
vocal vale
<@&286206848099549185>
late grove
(f o g)(x) is another way of writing f(g(x))
In this case x=2, so we want to know what f(g(2)) is.
You've correctly identified that g(2) = 8
but now what value do we plug into f(x)?
vocal vale
1, no?
late grove
Plugging x = 1 into f(x) will give us f(1) = 9
vocal vale
hm
late grove
For f(g(x)), we want to plug x into g(x) and then plug g(x) into f(x)
So for f(g(2)), we want to plug 2 into g(x) and then plug g(x = 2) into f(x)
We have already found g(x = 2) = 8
What value should we then plug into f(x)?
late grove
We don't want to do that. Keep in mind that $$ g(2) = 8 \neq 2$$ and so $$ f(g(2)) \neq f(2) $$
twin meteorBOT
thedude365
late grove
Since $$ g(2) = 8$$, what is $f(g(2))$ equal to? $$ f(g(2)) = f(...) $$
twin meteorBOT
thedude365
vocal vale
3?
late grove
Why 3?
late grove
I think you're reversing the placement of the numbers. The answer's f(g(2)) = f(8) = 3
vocal vale
**thedude365**
i was pretty stuck on tryna figure this out but the second one got it for me
thank you so much
late grove
of course
vocal vale
.close
hushed jetty
vocal sleetBOT
hushed jetty
im not sure why this is wrong
sly sierra
how did you obtain that answer
errant matrix
Help me I'm stupid. I want to add 91% isopropol alcohol to 70%, and then dilute that final mixture with water to a final concentration of 70%. I know about c1v1 = c2v2, but I am having issues actually implementing it
vocal sleetBOT
Help me I'm stupid. I want to add 91% isopropol alcohol to 70%, and then dilute ...
errant matrix
I want the final volume to be 940ml, and I have 320ml of 70%
I just don't know how to procede from here
vast shale
I want the final volume to be 940ml, and I have 320ml of 70%
wut
It is physically impossible to go down to 70% concentraction if you have 0.0000000000000000000000000000000000000000000000000000000000000000000000000001 ml of 91% in it
errant matrix
Sorry, I meant to say add water to dilute it down to 70%
I'll edit the first message
errant matrix
So, I have 320ml of 70% iso, I want to add some volume of 91% and then dilute to a final volume of 940ml
vast shale
So you'll have two equations
One equation for when you add x ml of 91%
and another for when you dillute it with water to reach 940ml
errant matrix
Right, but I feel like I need to solve the two simultaneously...
And I never learned how to solve systems of equations in school 🤷♂️
errant matrix
Hm....
Im trying to think of how tha'd work
Okay maybe I got it
So If I use c1v1 = c2v2, (0.70.32) = (c20.94), that leaves me with a c2 of 0.23....
so that means I need to figure outhow to dilute the 91% to 23%, right?
Did my math do the math things there?
Nope, I screwed that up
Okay let me try this: c1v1 = c2v2. I need 640ml of liquid at 70%, so if I dilute the 91% and find out what v1 is needed, that give me (0.91v1) = (0.70.640), and solving for v1 gives me 0.490ish. Which means I would need to add 490ml and then top off to my final volume with water
I think that's right
athe 640ml of liquid comes from my wanted 940ml, and I already have 320
Which is...wrong...but I think my process and thinking is correct
.close
honest heath
vocal sleetBOT
honest heath
U(8) is the multiplicative group consisting of elements mod 8 such that their greatest common divisor with 8 is 1
hard atlas
can you list the elements of U(8)?
honest heath
1, 3 , 5 , 7
hard atlas
can you list <3>?
honest heath
thats kind of part of my confusion. is it just integer multiples of 3?
hard atlas
no
hard atlas
3^n
honest heath
ohhh duh
hard atlas
the group is under multiplication
honest heath
right
hard atlas
so 3, 3*3, 3*3*3, ...
honest heath
okay
hard atlas
(and inverses)
honest heath
okay so then im lost
hard atlas
which elements do you get if you start at 3 and repeatedly multiply by 3
honest heath
just 3 and 1
honest heath
okay, so then pick an element of U(8) that is not <3>?
hard atlas
yes, for example 5. what is 5*{1,3} ?
hard atlas
yes
honest heath
so <5>={5,7}
hard atlas
so without calculating, what is 7*{1,3} ?
hard atlas
so <5>={5,7}
no
hard atlas
if you want to find <5>, yes
honest heath
so without calculating, what is 7*{1,3} ?
and this is {7,5}
honest heath
oh right okay my bad
hard atlas
ok, so the left cosets of <3> are {1,3} and {5,7}
honest heath
right okay
hard atlas
do we have to calculate the right cosets now or do you know something about the group so that we can skip that?
honest heath
U(n) is abelian right?
hard atlas
yes
honest heath
ok, so the left cosets of <3> are {1,3} and {5,7}
we could predict theres only 2 cosets from lagranges theorem? cuz U(8) has 4 elements and <3> has 2?
am i understanding that correctly?
fathom hedge
vocal sleetBOT
fathom hedge
this is a PRACTICE TEST
how do I figure out f^-1(T)
i just saw that 3 maps to 6 and 6 maps to 6 mod 9
but potentially other things could map to 3 and 6, how can i find them
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
How am i supposed to do this?
vocal sleetBOT
How am i supposed to do this?
vast shale
How do i know where the shape begins and ends?
I've read this part of my book three times
and none of those times did the words in the book change to include the information required to solve this
vocal sleetBOT
@vast shale Has your question been resolved?
tacit knot
is there a way to further simplify this?
vocal sleetBOT
is there a way to further simplify this?
languid berry
tacit knot
why is it funny?
languid berry
what forbidden god have you angered to be given this problem
tacit knot
just trying to figure out how to simplify
languid berry
lord have mercy
late grove
vocal sleetBOT
Available help channel!
cyan sky
how do i solve a differential equation with the laplace transform where one of terms is a product of a function of x and y
vocal sleetBOT
how do i solve a differential equation with the laplace transform where one of t...
cyan sky
for example y' = 2x(25-y)
like if i take the Laplace of all terms one of them ends up being 2*L{xy}
how do i evaluate that
worthy citrus
Have you checked the transform table
cyan sky
Have you checked the transform table
for xy?
yes
its not there
unless im missing a property of the transform i can use
i feel like ive checked everything
worthy citrus
30
It looks like you're just gonna get an ODE again though
Your original ODE is separable so don't really need to do laplace
cyan sky
oh wow
cyan sky
Your original ODE is separable so don't really need to do laplace
yea its cause im doing an investigation comparing methods
so i need to show its possible with the laplace transform
cyan sky
It looks like you're just gonna get an ODE again though
would that be solvable
worthy citrus
Don't know I don't know what the resulting ODE is
worthy citrus
Inverse of something involving y?
cyan sky
ok i got something
worthy citrus
Your question didn't make sense as y is a function of x
cyan sky
i got y = Ae^2x - 25x + (25e^2x)/2 - 25/2
cyan sky
Your question didn't make sense as y is a function of x
yea sorry i dont know what i said
i meant product of a function of x AND just y
worthy citrus
,w solve y' = 2x(25-y)
twin meteorBOT
worthy citrus
,w laplace transform of 2t(25-y(t))
twin meteorBOT
cyan sky
what does this mean
cyan sky
That's the laplace transform of the RHS of your ODE
yea but the notation
worthy citrus
The derivative of the laplace transform of y
tough kraken
I want to mention that I just learned the trigonometric functions, and I discovered this thing. I'm sorry if this thing should be explained in school later, but for the moment, I'm still curious.
vale frigate
What have u learned about trigonometric functions so far
vale frigate
U just learned that sin30 = 1/2 etc?
tough kraken
yes, I know the ratios, untill 60*
vale frigate
Okay so u know sin = opp/hyp, cos = adj/hyp rtc
tough kraken
In highschool, in my country, we will learn the trigonometric functions on a circle, and we will prove things, and etc, that's what our professor told us
tough kraken
Okay so u know sin = opp/hyp, cos = adj/hyp rtc
yes
tough kraken
oh, actually, its just proportions, nothing makes sin special
Now I don't even know what I'm asking
vale frigate
Cosine is not the inverse of sine..
tough kraken
Yeah, I'm sorry, Idk what was in my head
Thank you very much for your time, have a great day!
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
brittle canopy
I need help
vocal sleetBOT
I need help
vast shale
Just ask your question
brittle canopy
I need to find slope on a table
vocal sleetBOT
@brittle canopy Has your question been resolved?
solemn cape
I need to find slope on a table
of course your question isn't answered, if you don't put the function/equation or anything related to it how is somebody going to help you. We can't read your mind.
vocal sleetBOT
@brittle canopy Has your question been resolved?
vocal sleetBOT
tawdry wedge
.close
bleak bloom
Your professor has just told you about The Victorian Way (a YouTube channel).1 You
decide to watch two different episodes at random. For this problem, you will need to know
that of the 77 available videos on this channel, 71 feature Mrs. Crocombe and 6 don’t.
What is the probability that only one of the videos you watch will feature Mrs. Crocombe?
vocal sleetBOT
Your professor has just told you about The Victorian Way (a YouTube channel).1 Y...
paper depot
almost but not quite
the probability you calculated is for the event that the first episode you watch features crocombe and the second does not, in that exact order
bleak bloom
So how should I go about fixing it ?
paper depot
multiply by 2
vocal sleetBOT
@bleak bloom Has your question been resolved?
bleak remnant
vocal sleetBOT
bleak remnant
Help pls
paper depot
your handwriting is hard to read
can you write it neater or maybe type it up in LaTeX if you're able
bleak remnant
lim as x->0
sin(3/x) / (3/x)
mb lol
do i have to manipulate this to the sinx/x =1
regal bane
Is it as x approaches 0?
lament linden
do i have to manipulate this to the sinx/x =1
Yes
lament linden
Is it as x approaches 0?
Yes
lament linden
@bleak remnant Recheck if question says infinity or 0 for the value which x approaches
bleak remnant
its 0
lament linden
do i have to manipulate this to the sinx/x =1
This is different from the limit you typed
hard atlas
get rid of the double fraction
bleak remnant
This is different from the limit you typed
no like i remember an examble where we manipulated the function to sinx/x=1
thats why i thought of using that
bleak remnant
wait why are we using u
lament linden
We want to make it look like $$\lim_{x \rightarrow \infty} \frac{\sin x}{x}$$
bleak remnant
twin meteorBOT
Cyrenux
lament linden
Well u= 3/x works too
@bleak remnant Yeah my bad let u=3/x but same result as before
lament linden
What does u approach? @bleak remnant
bleak remnant
0
lament linden
No, thats what x approaches
lament linden
u approaches infinity
Well nah, it can be positive infinity or negative infinity
Depending if you are approaching from left or right
bleak remnant
I don't understand why we changed the it from 0 to infinity
I mean the x approaches
lament linden
You are confusing this limit:
$$\lim_{x \rightarrow 0} \frac{1}{x}$$ this limit does NOT exist
twin meteorBOT
Cyrenux
lament linden
Because if you approach 0 from right, right limit is +infinity
If you approach 0 from left, left limit is -infinity
Since right limit and left limit are not equal, limit doesnt exist
lament linden
You need to understand this limit first
For you to understand next step
Forget your question
Learn this limit correctly first
bleak remnant
Oh ok2
lament linden
You thought it was existed and that it was equal to infinity
Reread what i typed, do you understand
bleak remnant
For infinite limits we check the left and right hand limits first right
I remember it from our discussion
Its dne cuz left is -int and right is +inf
bleak remnant
Yes
lament linden
Now, earlier we were doing a substituion, namely
u=3/x ( where x approaches 0)
But notice u wouldnt be able to approach any value...
bleak remnant
Yeah
lament linden
So we need to consider two cases
u= 3/x as x approaches 0 from right
And u = 3/x as x approaches 0 from left
For first case, u will approach positive infinity
While on second case, u will approach negative infinity
bleak remnant
Yeah im following
lament linden
Show that both limits have same value
Then our original limit ( which you asked) will exist and have a value
I gtg now
Cya
wary mantle
I don't think so.
alpine saddle
1 / 0.0001 = 10000
1 / -0.0001 = -10000
1 / 0 = Infinity
1 / -0 = -Infinity
But 0 = -0
Hence 1 / 0 is Undefined
wary mantle
1 / 0.0001 = 10000
1 / -0.0001 = -10000
1 / 0 = Infinity
1 / -0 = -Infinity
Bu...
The third and fourth lines are a bit weird to write, but the idea is correct, except that the fourth line should be -infinity, I assume
wary mantle
Though the limit in the question actually exists
wary mantle
$\lim_{x \to 0} \frac{\sin(\frac 3 x)}{\frac 3 x}$ exists and is equal to $L$ iff [\lim_{x \to 0^-} \frac{\sin(\frac 3 x)}{\frac 3 x} = \lim_{x \to 0^+} \frac{\sin(\frac 3 x)}{\frac 3 x} = L.]
So consider these two cases.
bleak remnant
oh is that
squeeze theorem?
cuz if it is then ill have to close this cuz i dont get that yet lol
or yeah
wary mantle
Hm, perhaps not necessarily. Wait a second
Squeeze theorem seems to be the easiest though
paper depot
has it not occurred to anybody here to write $\frac{\sin(3/x)}{3/x}$ as $\frac{1}{3} x \sin(3/x)$
twin meteorBOT
Ann
paper depot
and yes squeeze thm kills this
vocal sleetBOT
vocal sleetBOT
Available help channel!
sonic flame
Man it's hard
vocal sleetBOT
Man it's hard
rugged vortex
crimson sedge
I have done intergrating fractions in the past but i semi rememered how to do it
for example, if i have $\int \frac{1}{x+1} dx$ \ i would do $y = x+1$ \ $\therefore \frac{dy}{dx} = 1 \cdot (x+1)$ \ $\therefore \frac{dy}{dx} = (x+1)$
vocal sleetBOT
I have done intergrating fractions in the past but i semi rememered how to do it...
twin meteorBOT
yomiko
crimson sedge
and then im suppose to compare somewhere
i forgot how to
hard atlas
not sure what you tried to do there
do you mean partial fractions?
the integral of 1/(x+1) is ln|x+1|
crimson sedge
am i meant to do $y = ln(x+1)$?
twin meteorBOT
yomiko
crimson sedge
the integral of 1/(x+1) is ln|x+1|
well yeah but how do you get to that
hard atlas
well you kinda have to know it
crimson sedge
i can't just remeber every integral there is
i did 1/x+1 as an example
i know that its ln|x+1|
i just want to know how i would get to that
hard atlas
well either you take it as the definition of ln
or you differentiate ln and see that this is what you get
hard atlas
i can't just remeber every integral there is
well not every, no. but this is one of those you have to know
1/linear integrates to ln
crimson sedge
or you differentiate ln and see that this is what you get
yh i think thats how i used to do it
$y = ln(x+1)$ \ $\frac{dy}{dx} = \frac{1}{x+1} \cdot 1$ \ compare with integral $\frac{1}{x+1} \rightarrow \frac{1}{x+1}$ \ $\therefore (1)ln(x+1)$
twin meteorBOT
yomiko
crimson sedge
right?
if its $\int\frac{2}{x+1}\frac{dy}{dx}$, $\frac{1}{x+1} \rightarrow \frac{2}{x+1}$ it would be $2$ ln(x+1)
twin meteorBOT
yomiko
crimson sedge
.close
vast shale
Find the volume of the solid above the xy-plane, under the surface z = 1 − x^2-y^2
vocal sleetBOT
Find the volume of the solid above the xy-plane, under the surface z = 1 − x^2-y...
latent jasper
To find volume you use triple integrals
latent jasper
So to find area you have a double integral right?
vast shale
Never seen double integral aswell, area is just normal integral no??
Under each graph is the area
latent jasper
To find area between two curves you need to use a double integral
Someone can probably explain it better than I can lol but one sec
vast shale
Alr
latent jasper
So here we have a parabola bounded by y = 3
You can’t find the area with one integral, that would give you the area under the parabola which you don’t want
So we set up a double integral
vast shale
Ohhhh i see
latent jasper
We use the blinds of the function in x and y as the parameters of the integral
So we can see that we want values from x=-1 to x=1
vast shale
I see
latent jasper
And we want y values y = 3x^2 (bottom) to y = 3 (top)
latent jasper
You need to go from top to bottom or else your answer will have a wrong sign
vast shale
Ahhh alright
latent jasper
In 3 space it’s the same thing except now we need an integral for z
vast shale
I understand yea
latent jasper
It’s helpful to sketch out the curve
vast shale
can you show that
latent jasper
set one of the variables equal to zero and sketch out the 2d graph. If we set y = 0, we can graph it in the xz plane as z = 1-x^2
which is a parabola
actually it’s better to draw it in the xy plane so set z = 0 and you just get a circle with radius 1
does that make sense
so the surface is like an upside down bowl
vast shale
Ngl no, since this is all new to me, the triple and double integral i mean
vast shale
maybe can u explain the solution there?
And it might be clear then for me
for example
whats r
latent jasper
Okay uh word of advice you should get familiar with shapes in 3 space before jumping into the calculus but yeah
vast shale
why is r=1, where did theta come from
latent jasper
So they put it into cylindrical coordinates to make it easier to solve
Since we know it’s an upside down bowl shape
vast shale
Alright
latent jasper
We know it’s a circle with radius that goes from 0 to 1
latent jasper
So the radius changes as we go down the graph. It starts at 0 at the top and goes to 1 when it hits z = 0
So we integrate radius as a function
vast shale
ohhh
latent jasper
Next is theta. If we look at the graph from the top down we see a circle and a wedge
We can find the bounds of the circle that the wedge is in terms of theta
And we can integrate in terms of theta
And then finally is z, which is still z
vast shale
alright and how do i know what theta to pick
latent jasper
latent jasper
alright and how do i know what theta to pick
graph the wedge over the circle and use the intercepts
I have to go but you should really go over planes and surfaces in 3 space, it’ll make these problems a lot easier
vast shale
I have to go but you should really go over planes and surfaces in 3 space, it’ll...
just one thing, if it was 25-x^2-y^2 what would the theta interval then be?
is it still pi/4 to pi/3?
<@&286206848099549185>
latent jasper
@vast shale how many degrees are in a circle
Does that change when you make the circle bigger?
vast shale
<@456226577798135808> how many degrees are in a circle
360
vast shale
Does that change when you make the circle bigger?
No
So its still pi/4 to pi/3 if r was 5 instead of 1 right? Because the circle is the same
@latent jasper
can anyone confirm this? <@&286206848099549185>
someone?
vocal sleetBOT
@vast shale Has your question been resolved?
vocal sleetBOT
@vast shale Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
sick loom
Why is a number divided by itself equal to 1? What is the concept of this?
dense stump
If want to evenly share 5 apples to 5 friends, how many do you give each friend?
sick loom
But can we only find a concept for division like this? Or can we see it another way?
vague pewter
sick loom
hmm
sick loom
I mean I don’t see an easier way lol
Yea, what I needed was a more complicated way of looking at this
dense stump
may I ask what this is for?
sick loom
may I ask what this is for?
I just thought about it
I wanted to see mathematics in a way beyond rules
Something I could see
exotic quarry
Yea, what I needed was a more complicated way of looking at this
Sure. An axiom of a field is that every number a other than zero has an inverse. That is $a*a^{-1}=1$. In real numbers we call that division and write $a/a=1$. It is by definition like this.
twin meteorBOT
Gigrise
sick loom
Sure. An axiom of a field is that every number a other than zero has an inverse....
I think I got something out of this, thanks for the reply
sick loom
I wanted to see mathematics in a way beyond rules
I wanted to be able to delve deeper into this way of thinking about mathematics, I don't know exactly where to start
lol
(If there are any errors in my grammar, it's because I'm using a translator)
exotic quarry
I wanted to be able to delve deeper into this way of thinking about mathematics,...
Actually you can even weaken that definition. and say every number $a$ other than $0$ must have SOME inverse b. that means
$a*b=1$. THEN you can proove that this number $b$ is actually unique for every $a$. And we can write $b=a^{-1}$ because it is unique.
So it is a proof in a way to ur questions why the number $b$ must be number $a$ itself.
twin meteorBOT
Gigrise
sick loom
Actually you can even weaken that definition. and say every number $a$ other tha...
I don't think I understood very well how a number having an inverse interferes with division resulting in 1.
exotic quarry
I am trying to not further confuse you.
In a field, there is no such operation as division. But we say DIVISION is a multiplication by an inverse. it is a consequence of having an inverse and multiplication operation.
that means by symbol $1/n$ we really mean the inverse of $n$. and the symbol $n/n:=n*n^{-1}$ means $n$ multiplied by the inverse $n^{-1}$
twin meteorBOT
Gigrise
exotic quarry
and multiplication by the inverse means by definition that its product is =1 .
sick loom
I understand. I still need to see other examples and think more about this but you helped me
🫶
exotic quarry
I suggest you take a look at group theory. atleast the very basics.
you will understand
sick loom
Group theory?
exotic quarry
https://pages.mtu.edu/~kreher/ABOUTME/syllabus/GTN.pdf
this for example
vestal lagoon
vocal sleetBOT
vestal lagoon
I've not got a clue how to do it, because everything I thought was the correct method isn't giving me a working answer
Multiplying the matrix by (x,y) gives
3x-2y = x
4x-6y = y
Which I guess gives me the equations y=x and y= 4/7 x
part b by the way
but neither of those are right
really dont know what im supposed to do
tried substituting y for mx but neither of these are right either
lol im just throwing shots in the dark
blazing yacht
How do I do the chain rule versions?
vocal sleetBOT
How do I do the chain rule versions?
@blazing yacht Has your question been resolved?
grizzled halo
apply chain rule, where u is a function of x
blazing yacht
apply chain rule, where u is a function of x
Could you give me the first 3 answers as an example
Is it just like this on all of them?
grizzled halo
yeah lol
vocal sleetBOT
vocal sleetBOT
Available help channel!
sleek wadi
hello, i'd like to ask a question about prime numbers
vocal sleetBOT
hello, i'd like to ask a question about prime numbers
sleek wadi
alright!
so
i was doing a formula for a card game i'm working on, and this formula kept generating prime numbers
then i wondered about other formulas that generate prime numbers like that
could someone send me some links about it?
or tell me more
grizzled halo
note that this doesn't mean every 6n+-1 is a prime, it doesn't go both ways
sleek wadi
that's very interesting, that's basically what i was doing with some extra steps haha! the formula was xy + x + 1 and it kept generating prime numbers every so often when i inputed y as 1/3 and and x as N
thanks for the help
vocal sleetBOT
@sleek wadi Has your question been resolved?
hearty delta
Hi, can someone explain why we set this equation equal to pi and not 0, as sin of both would give us 0?
vocal sleetBOT
Hi, can someone explain why we set this equation equal to pi and not 0, as sin o...
grizzled halo
they're both possible solutions
because periodic trig functions have infinite solutions
hearty delta
But the 0 does not give us the same ans no?
grizzled halo
oh it gives negative solutions does it
hearty delta
,ask -(1.326/(8sqrt(2))
twin meteorBOT
grizzled halo
which is negative time
hearty delta
so its just invalid
hearty delta
ah
makes sense
so we just have to use trial and error in this case
or is there a way to know?
vocal sleetBOT
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Available help channel!
tacit hill
I'm a little new to probability/combinatorics and I was really curious to find out the number of ways to get > k heads out of n total flips. I found a solution (attached) but it only works for n = 2m + r and k = m + r (where m, r > 0). I sort of understand why it doesn't work for values less than this but I'm not entirely sure how I would go about finding a completely closed form.
vocal sleetBOT
I'm a little new to probability/combinatorics and I was really curious to find o...
@tacit hill Has your question been resolved?
tacit hill
<@&286206848099549185> halp please
lyric verge
<@&286206848099549185> halp please
no
tacit hill
no? never in a million years could I have predicted that one
split wind
hello i bet it's better to post some screenshots than just the file (and I'm weak at probability/combinatorics)
vocal sleetBOT
@tacit hill Has your question been resolved?
tacit hill
hello?
split wind
hello!
split wind
hello?
i just read once and got no clue about how you get the conclusion (as I've said, I'm weak at this).
however one thing I'm really curious is that you didn't say the k heads in the at least k has to be consecutive
tacit hill
well I meant in a row = consecutive
split wind
ohhhh
tacit hill
that's kind of what I did in the first part
you can position that whole n - k + 1 different ways in a series of n flips
split wind
arrgggh, hahaha, I'm brain stuck
tacit hill
uhhhh, okay so you can call that one whole W and the rest of the flips (we don't know what they are yet) X. We can have all the consecutive heads first and then all the other random flips: WXXX..., we could have the heads occur after the first flip XWXX... all the way until W is at the very end XXX...W
there are n - k + 1 different places for W to be in
split wind
im still processing XD
tacit hill
okay okay take your time
split wind
and basic calculation:
https://byjus.com/question-answer/what-will-be-the-next-number-in-the-given-number-sequence-1-3-8-19/
split wind
okay okay take your time
but for "why", I don't know 😔,sorry
vocal sleetBOT
@tacit hill Has your question been resolved?
split wind
@tacit hill how's it going?
trim cedar
vocal sleetBOT
trim cedar
I found t = (s^2 + 1)^(-1)
Just making sure, would I plug that into the unit tangent and curvature equations?
vocal sleetBOT
@trim cedar Has your question been resolved?
trim cedar
😢
agile oasis
dont worry guys i got this
trim cedar
🫡
livid tapir
Hold on I gotta refresh cus I only remember Calc 1 and 2 stuff not Calc 3 
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
How do I find the particular solution of this differential Equation and how do I proceed after that to solve the initial value problem?
vocal sleetBOT
How do I find the particular solution of this differential Equation and how do I...
vale frigate
u can actually treat this as a differential equation of y'
let u = y', then u have u' = 1 - u, which is linear
sonic flame
What's 11-67+98-8÷5000
paper depot
What's 11-67+98-8÷5000
!occupied
vocal sleetBOT
What's 11-67+98-8÷5000
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).
@vast shale Has your question been resolved?
Available help channel!
long flame
vocal sleetBOT
long flame
for this equation f, why can we simply substitute e^x as h, and then work with the derivative of only g after?
this question asks us to find the extreme value of the range, to finally determine the entire range of f
can we assume that if x can be substituted with a function, that means, in the context of ranges, some g(x) = x?
hybrid flicker
if you want the extreme values of f(x) = h(g(x)), you are allowed to compute for the extremes of g(x) when h(x) is increasing
vocal sleetBOT
@long flame Has your question been resolved?
cursive fern
do my drawings look correct?
tacit hill
<@725897882959609906> how's it going?
Sorry I fell asleep am I allowed to reopen (somewhere else of course)
vocal sleetBOT
@cursive fern Has your question been resolved?
cursive fern
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
rose shard
how does $\int x^2 , 2x , dx=\frac{x^4}{2}+c$
vocal sleetBOT
how does $\int x^2 \, 2x \, dx=\frac{x^4}{2}+c$
twin meteorBOT
SimonWin
rose shard
Because I thought I had to do integration by parts haha
but apparently, you can say $\int2x^3dx$
twin meteorBOT
SimonWin
rose shard
but i don't see how that work
river minnow
x^2 * 2x is just 2x^3, apply power rule for integration
You don't see how x^2 * x is x^3?
rose shard
.close
rapid birch
i solved it but i am not sure about my solve. is it correct?
vocal sleetBOT
i solved it but i am not sure about my solve. is it correct?
rapid birch
The question is to prove algebraically that each function is inverse function to the another function
paper depot
is $g(x) = \sqrt[3]{\frac{x+6}{2}}$ or $\frac{\sqrt[3]{x+6}}{2}$?
twin meteorBOT
Ann
rapid birch
it’s the second one
paper depot
are you sure? because then f and g won't be inverses.
paper depot
so it's $\sqrt[3]{\frac{x+6}{2}}$
twin meteorBOT
Ann
rapid birch
ah my bad
the left side that x’s it’s mean my wrong solve
then i tried one more time in the right. under the row i made
amm
paper depot
no
rapid birch
what?
paper depot
it's an advertiser, ignore them
sonic flame
What is 1-567+68-7-8÷5000×8
paper depot
What is 1-567+68-7-8÷5000×8
!occupied
vocal sleetBOT
What is 1-567+68-7-8÷5000×8
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).
sonic flame
what was the point in telling me the wrong info
!occupied
vocal sleetBOT
what was the point in telling me the wrong info
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).
paper depot
i wrote all my corrections in red
rapid birch
the paper i send its literally a litter
i am sorry for that
i will write it again in another paper
@paper depot
it’s clear now
i solved it in another paper. is it correct?
@paper depot ms. is it correct?🤔
paper depot
these arrows are overkill, also you don't need to be this formal with me
but i guess it is correct
rapid birch
i was worried about the number i I delet it with each other
but if you said it’s correct then i can be sure about
rapid birch
thank you for helping. final question. in (2x^3 -6)+6. is it ok to delete it with each other i mean the 6’s because its Polynomial my teachers said if it’s Polynomial and number alse you can’t delete it with each other like this
vocal sleetBOT
@rapid birch Has your question been resolved?
rapid birch
thank you for helping. final question. in (2x^3 -6)+6. is it ok to delete it wi...
🌹😁
i asked many questions i am sorry but that’s important question for me
indigo vault
are the 2 vertical lines parallel?
vale patio
yeah
indigo vault
aight
lemmme help
note that x, 45, 98 degrees are all ina triangle, and it's sum is always 180.
subtle trail
hi i need help
Linda thought of a natural number and then added a 5 to the left and an 8 to the right in the number representation. This increased the number Lina thought of by 518215.
Find the number Lina thought of and explain why it is uniquely determined.
vocal sleetBOT
hi i need help
> Linda thought of a natural number and then added a 5 to the le...
Show your work, and if possible, explain where you are stuck.
@subtle trail Has your question been resolved?
subtle trail
<@&286206848099549185>
vocal sleetBOT
<@&286206848099549185>
Show your work, and if possible, explain where you are stuck.
subtle trail
pleas.!:!:!:
vocal sleetBOT
pleas.!:!:!:
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
1
step 1
please somoeone im beggigngyou
split wind
let the number be ABCD, then
new number is 5ABCD8,
and 5ABCD8-ABCD=518215
use column form to tackle it.
subtle trail
let the number be ABCD, then
new number is 5ABCD8,
and 5ABCD8-ABCD=518215
use co...
i still dont understand
split wind
```
Column Form
5 A B C D 8
- A B C D
________________
5 1 8 2 ...
there @subtle trail
robust spruce
Can someone explain the steps done here?
vocal sleetBOT
Can someone explain the steps done here?
paper depot
they add and subtract all even numbers from 2 to 2n
so that your odd numbers in the original sum can be grouped into the sum of the first 2n natural numbers
robust spruce
I see, so something like 1+2-2+3+4-4+5 ?
hard atlas
yes
paper depot
+6-6 at the end
the way they did it
but yes
and also they group all the subtracted terms on the right
robust spruce
I still don't quite get how it turns into 2n-2(1+...+n). Can you show in a little bit more detail? 😓 How exactly does he group the subtracted terms? It wouldn't be ...+2n-1-2n would it?
vocal sleetBOT
@robust spruce Has your question been resolved?
robust spruce
.close
opal obsidian
In a arbitrary group G, is the number of elements in the group generated by an element ‘a’ is same as it’s order?
vocal sleetBOT
In a arbitrary group G, is the number of elements in the group generated by an e...
hard atlas
yes
opal obsidian
a^n=e means there is upmost n elements in the set right?
how do i see it exactly n elements?
vocal sleetBOT
@opal obsidian Has your question been resolved?
wintry walrus
How do I do part b of this question I don’t know how to do it ?
