help-23

[atomic notch]

Right

And will the s scores provide me with enough information to graph this

How do I find the z score

[safe radish]

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[atomic notch]

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<@&286206848099549185>

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[eternal nova]

no idea how the fuck to do this

[eternal nova]

my brain is about to shatter

I don't get what it means

the way they word it is like they're not even speaking english

[granite idol]

What is the cost of making 1 desk

[eternal nova]

110

[granite idol]

Plus the fixed cost

[eternal nova]

27600

what about it

[granite idol]

That is the "cost of doing business". Meaning, if they sell 0 desks, they have still spent $27600 up-front. So that is always factored into the cost, right?

What you need to find is $C(x)$ where $x$ is the number of desks. So it will be $C(x) = 27600 + something$

[flat frigate]

cwatson

[eternal nova]

uh sorry

but how do i find n

number of desks that need to be produced so that the average cost per desk is 170

[granite idol]

Sorry then $C(n)$. So you guessed correctly that each additional desk costs $110 to make, right

So what is the cost formula

[eternal nova]

hey uh sorry but would it be

the total cost over n

and since we have the average

would it be

170 = total cost/n

so do i solve from there?

[granite idol]

Well "total cost" will also have a n in its expression, too. But yes

[eternal nova]

hey sorry but how do i solve from there?

170= 27600 + 110 per desk over n

how do i solve from there?

do i start by moving across the n?

[primal kelp]

Make n the subject

since you're solving for n

[eternal nova]

uh huh

hmmm

wait a sec

@primal kelp

i'm sorry can you help

I literally do not understand

how to solve for it

[primal kelp]

?

[eternal nova]

is 110 per desk different from n

[primal kelp]

move values around

[eternal nova]

I have no idea dude

I am asking for help dawg

[primal kelp]

honeslty i have no idea, i just looked at where you were at and just knew you had to find for n

lemme just have a look at the question

ok

[primal kelp]

170 = 27600 + 110n

correct equation

now you make it so that n is the subject

so

[eternal nova]

oh what

wait

what about

[primal kelp]

-110n = 27600 - 170

[eternal nova]

the over n

what what what

[primal kelp]

?

[eternal nova]

go on

[primal kelp]

if we simplify further

hm

sometings not righ

[eternal nova]

i got it

i skipped a step and found something

it was like

170 = 27600 + 110n over n

=

170n = 27600 + 110n

60n = 27600

n = 460

thank you for trying to help though

.close

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[primal kelp]

wtf

..

did you just do

[eternal nova]

uh

the question

[primal kelp]

how did you get 170n

[eternal nova]

cause it's over n

like i said earlier

you move n to the left

= 170 n = 27600 + 110n

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[primal kelp]

bro u doin sorcery shit i aint ever seen

[primal kelp]

ok so

the original equation was

170 = 27600 + 110n

oh i see

just forgot one more value

sicko mode

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[frozen harbor]

.rotate

I don't understand in my notes here something. It's about series in calculus

[primal kelp]

,rotate

[frozen harbor]

You can rewrite any fraction as a decimal so we wanted to try one

But here i don't understand why we chose .035 as our "a" and not 1

Because the decimal starts with 1 so i thought it's be that

[quasi bison]

the ratio will be a power of ten, here 10^3

if you take 1 as your first term then you will have 1.001001001001...

[frozen harbor]

Do you mean 10^(-3)? I don't get why it's be 10^3

[frozen harbor]

I don't understand what the 1 does then

Or what the "a" does

[quasi bison]

oh yes sorry typo

[frozen harbor]

Np

[quasi bison]

the a is the first term in your geometric series

in terms of decimals it is the first occurrence of the repeating pattern

and there may very well be some other stuff prior to that!

[frozen harbor]

So if i wanna look at a decimal and find a fraction from it, i should first ignore the thing that doesn't repeat and just add that on later right

Then how exactly do you find what the "a" is?

[quasi bison]

i should first ignore the thing that doesn't repeat and just add that on later right
yes

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[knotty viper]

Why did the n start at 1 instead of 0 after he took the derivative of the sum?

[lean otter]

you can do it but ultimately it would be 0

[mortal sandal]

yeah the n=0 term works out to a constant

[knotty viper]

oh ok n=0 is 0 so theres no point i see

[stray socket]

Yeah

[knotty viper]

.close

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[lean otter]

yeh u got it

[stray socket]

Thank you Walter white

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[stray socket]

Are you shitting me

Great bot

.close

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[wind abyss]

Guys im on the way to my test and i had someone help me with this yesterday and this will definitely be on my exam but i am stuck on this

[wind abyss]

What is the next step for it pls thanks

[fresh jackal]

Divide by 3

[wind abyss]

Ok

i do on paper and show

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[winged willow]

$AB = 4(A+B)$ \
$2B = 8 + 4B$ \
$B = -4$

[quasi bison]

\implies

[flat frigate]

Bunnings

[winged willow]

newline

[quasi bison]

$AB = 4(A+B) \ \implies 2B = 8+4B \ \implies B = -4$

[flat frigate]

Ann

[quasi bison]

was this what you wanted to type?

... this does not appear to have any mistakes.

[winged willow]

yes b = -4

but its not in the solutions.

[quasi bison]

yes, i can see that

[winged willow]

.

[quasi bison]

it is the question's fault

[misty coral]

if the product of the two integers is four times the sum

[quasi bison]

AB = 4(A+B) is the correct equation

[misty coral]

I wouldn't say so

[quasi bison]

why

product = 4 * sum

[misty coral]

its stating that the product of a and b is four times that of a+b

[quasi bison]

??

[winged willow]

yeah so ?

[quasi bison]

i don't follow @misty coral
are you sure you are not talking out of your ass?

how much is at stake for answering this question in particular, btw?

[misty coral]

potentially

I think if you solve it as 4 * ab = a+b you would get some fractional bs anyway

lemme read it again slowly

[winged willow]

im not sure what you are talking about

[quasi bison]

who, me or clarkie?

[winged willow]

clarkie

[winged willow]

i thought my equation was correct

[quasi bison]

it is

[misty coral]

yeah

language skill issue

[winged willow]

oh okay

thanks both of you.

.close

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[manic cliff]

How do I solve this? I’m completely stuck. Can someone solve it and give me a step by step explanation pls thanks

[misty coral]

is that a g or a 9?

[lean otter]

I think that's a nine

[misty coral]

hope so

in the case it is, think about expressing terms with a common base

[lean otter]

I surmised it after looking at that one looking like a tent

[manic cliff]

G

[misty coral]

[lean otter]

oh thaty's a g

damn

[manic cliff]

Can you please solve it and send a step by step type of thing pls

[lean otter]

so are we solving for g in terms of a variable x?

[misty coral]

for g?

[misty coral]

in which case kill me now

[manic cliff]

Ik logarithm is involved

Does anyone know the answer is this that hard? 😂

[misty coral]

what are you solving for

[lean otter]

I misread your problem. I see now that these are steps within the same problem. I thought these were three separate givens.

[manic cliff]

<@&286206848099549185>

[lean otter]

Are you sure that's not a nine? Isn't the red writing on the bottom left (0,96)?

Here you go, I'm rather certain that's a nine.

[manic cliff]

Oh yeah

9

Lol

[manic cliff]

Can you explain the steps pls?

Still can someone explain for me:/

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[ashen badge]

I actually have quite a few problems I'm struggling with involving polynomials. I had covid and missed 6 days of school and I don't understand how to classify them. One example is 9x²y⁴

[final halo]

Yep that's a polynomial

In what way are you meant to be classifying them

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[prime mason]

what did I do wrong here guys?

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[prime mason]

<@&286206848099549185>

[glad pagoda]

thats sorta illegible lol

if possible a better photo might help

[prime mason]

its ight I figured it

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[paper lark]

How would j do this?

[junior smelt]

,rccw

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[wispy nimbus]

what is sine of log6 * log2/son3

[wispy nimbus]

sin3 hehe

i mean

please help someone 🙂

sine 3 is teta of which logarithmic function?

thank you in advance.

[trim swan]

You're looking for $\sin\left(\log(6) \cdot \frac{\log(2)}{\sin(3)}\right)$?

[flat frigate]

tatpoj

[trim swan]

?

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[river rose]

i have a table of values and need to find a function for it

[river rose]

this is what it looks like im just having trouble trying to find a function

i wanted to use y=mx+b

but there is no common difference in the y terms

[plucky elk]

for what purpose to do you want the function for

[river rose]

to relate to the data points either passing through a majority of them or be close

when i graph it in sheets

i get a function

[plucky elk]

my question is what are you going to do with the function

[river rose]

i just dont know how they got it lol

[final halo]

linear regression probably

[river rose]

i need to make one that relates to the data thats all

[plucky elk]

"need" for what purpose

what are you going to do with the function

i've asked 3 times now

[river rose]

its for a question lol

idk what u mean

for my class

[plucky elk]

show the original question

[river rose]

i chose my data

now i need to form a model to predict outcomes

[plucky elk]

Choose better data

[river rose]

lol aight nvm

[plucky elk]

Or accept this will be mediocre

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[heavy glade]

can someone explain this step

[crimson field]

It’s the chain rule for functions of three variables. It’s not a step but the starting point.

[heavy glade]

ahh okay ty, I only knew the old one

.close

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[leaden scaffold]

How do I find last part?

[leaden scaffold]

I have the area when t=10 and t=100, but what's the formula for finding the total area?

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[merry pelican]

What did you do, to find the area for 5 ≤ x ≤ 10 and 5 ≤ x ≤ 100?

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[wheat atlas]

what do we do for the case when x=0?

[wheat atlas]

how do we proceed after lambda=2y^2/5

lagrange multipliers btw

like i know the minimum is at +-sqrt5

but i wanna test when x=0 now

[stray socket]

Uh

What's your constraint and original function

Well I see the original

What's the constraint

It's a bit hard to follow your work

[wheat atlas]

oh ok

sorry about that

btw

is this a valid solution to the problem?

i have multiple ways of doing it

i just wanna know if im doing it right

[stray socket]

Yeah I'm not familiar with the way you're doing it. I usually try to find nil gradients of the lagrangian

[wheat atlas]

wdym

nil?

[stray socket]

0 vector

Like idk where this comes from

[wheat atlas]

wdym

gradient equals 2x, 2y, 2z

gx=2x, gy=-z

[stray socket]

Lemme type it out

[wheat atlas]

gz=-y

[stray socket]

Typically I would let $f(x,y,z) = x^2 + y^2 + z^2$, and then I let the constraint equal to zero, so $g(x,y,z) = x^2 - yz - 5$. I would build the Lagrangian:

$$L(x,y,z,λ) = f(x,y,z) + λ\cdot g(x,y,z)$$

Then I would try to find its nil gradient:

$$\del L(x,y,z, λ) = \vecb{0,0,0,0}$$

[flat frigate]

Umbraleviathan

[wheat atlas]

yeah

whats nil?

[stray socket]

A zero-vector

so a vector where all its components are 0

[wheat atlas]

i always saw it as fx, fy, fz=lambda gx gy gz

[stray socket]

Hm maybe it'll work out the same way

I'm just rather confused as how you got

[stray socket]

This

[wheat atlas]

well its just lambda=fx/gx

well u dont have to do it that way

[wheat atlas]

does this make more sense?

since 2x-2xlambda=0?

[stray socket]

I mean when x = 0, you can just find what the other variables equal

Uh

Sure

[wheat atlas]

how

[stray socket]

Well you have a system:

$$\begin{align*}
2x + 2xλ &= 0 \
2y - zλ &= 0 \
2z - yλ &= 0 \
x^2 - yz - 5 &= 0
\end{align*}$$

Hopefully I did the shit right in my head lol

And you found that x can equal to 0

Ooh yeah that's uh

That implies that lambda can be anything then

Not sure if that'll work

[wheat atlas]

wouldnt it be negative

[stray socket]

No it shouldn't

I also forgot another equation

[wheat atlas]

wat

[flat frigate]

Umbraleviathan
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[stray socket]

Then it should be possible to solve when x = 0

[wheat atlas]

how

could u explain by plugging in x=0

we get -yz-5=0

[stray socket]

LaGrange multipliers state that for a function, $f(A)$ optimized with the constraint of $g(A) = 0$, then:

$$L(A, λ) = f(A) + λ \cdot g(A)$$

[flat frigate]

Umbraleviathan

[stray socket]

Well it's a system of equations so then it boils down to 3 equations with 3 unknown variables

[wheat atlas]

i dont get how u did that

[stray socket]

Get what?

[stray socket]

This?

https://en.m.wikipedia.org/wiki/Lagrange_multiplier

[wheat atlas]

how do u get yz

if x=0

[stray socket]

Oh that's because $\pdv{L}{\lambda} = x^2 - yz - 5$

[flat frigate]

Umbraleviathan

[wheat atlas]

yeah

[stray socket]

Look how I defined L

[wheat atlas]

wat

[wheat atlas]

i dont get that

[stray socket]

I haven't gotten around for all proving the Lagrangian function, like I know it's conceptuals.

[stray socket]

If you read this:

This is how I was taught it

[wheat atlas]

weird

@trim swan

HELP

requesting SOS

[stray socket]

If you plug in x = 0, you're left with 3 equations

Then you can solve for y, z, and lambda

[wheat atlas]

yeah

but i cant solve for y z and lambda

well u can solve it when lambda equals 1

but what about when x=0

like this

@stray socket okay tell me this

if y^2=z^2

then does +-y=+-z?

is that valid?

[stray socket]

Yes

[wheat atlas]

wait

so can i say

y=-z, z

[stray socket]

Yes

[wheat atlas]

and -y=-z, z

so

[stray socket]

Yes

[wheat atlas]

y can equal z positive and z negative?

is that valid

like not even +-y

just y

[stray socket]

Yup

Well

+- y = +-z implies y = +-z for unique solutions

[wheat atlas]

but its valid to say that

y=+-z right?

and that z=+-y

and -y=+-z

right?

if so then im gud

[stray socket]

Yeah

Also I did a bit more reading

[wheat atlas]

yeah

[stray socket]

Doesn't matter if you add or subtract f(A) and λ g(A)

[wheat atlas]

kk

[stray socket]

It'll just change the sign of the multiplier I'm pretty sure

But we don't really care about the value of the multiplier lol

[wheat atlas]

what is the multiplier

[wheat atlas]

wait

jsut want to say again

y=+-z is valid right

[safe radish]

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[stray socket]

.yeah

[stray socket]

.lambda

.you'll find that the algebra is the most painful part of LaGrange multipliers

[wheat atlas]

i have a question

[wheat atlas]

if

lambda = +-2

then why does x=0

oh wait nvm

i got it

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[dreamy finch]

Is this correct?

[dreamy finch]

or does it not exist?

I looked it up...

how

or is this website wrong?

[safe radish]

@dreamy finch Has your question been resolved?

[dreamy finch]

<@&286206848099549185>

I guess my question is if the integer is 0, is a multiplicative inverse always undefined?

and if modulo is negative, is it always undefined as well?

[safe radish]

@dreamy finch Has your question been resolved?

[spiral bane]

What’s wrong about it

0 mod 1 is 0

[dreamy finch]

It just doesn't make sense to me

[spiral bane]

It’s just the remainder no?

[dreamy finch]

no, you're finding the multiplicative inverse

[spiral bane]

But don’t you agree 0 mod 1 = 0

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[lean otter]

I’m not exactly sure how to find the range of x here, I’ve done this before without variables and just whole numbers but the variables are confusing me

[royal kiln]

you are supposed to use the Triangle Inequality and solve for x.

[lean otter]

Yeah but how

[royal kiln]

looks like you were on your way, but I didn't check your work yet. Why did you stop?

[lean otter]

I didn’t know where to go from there

[royal kiln]

looks fine so far

solve for x

[lean otter]

Ok

[royal kiln]

think it's ||18 > x||

oh

and x would have to be bigger than 3, obviously

so 3 < x < 18

[lean otter]

Oh crap you’re right

thank you

wait

I got

13 < x < 18

[royal kiln]

explain this please

why do you think 13 is the lower bound?

[lean otter]

Let me get a pic of my work

10x-30 > 4x+48

That’s the sum of the top two sides are greater than the bottom side

[royal kiln]

where are you getting 10x - 30?

[lean otter]

The sum of the top two sides

oh sorry

left and bottom side

not top two

[royal kiln]

sum of top two is 5x + 45

[lean otter]

i meant x - 3 + 9x - 27

[royal kiln]

ok, so you think the top-right side is the longest side?

hm, maybe it is

[lean otter]

it fits in the chart on the next page

I did the Expanded Pythagorean Theorem wrong

[royal kiln]

this work doesn't explain (to me) how you decided that the upper right side was the longest

I guess it isn't too close though

I am just not sure

I can make a quick spreadsheet

[lean otter]

Process of elimination

I didn’t show it in my work though

[royal kiln]

I mean there's a switchover at x >15 for the longest side

@lean otter why do you think x must be greater than 13?

[lean otter]

That’s what I got when I did this right here

[royal kiln]

that side doesn't need to be the longest side though

oh wait

yes

you are right

after x=13, the sum of any two exceeds the measure of the third

good job!

...

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[lean otter]

thank you!

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[strange plaza]

is this the same logic as

$3\sqrt3=\sqrt{3^2×3}$

[flat frigate]

Jshy <3

[strange plaza]

but since the 3 in this case is on the denominator

$\frac{\sqrt3}{3}=\sqrt{\frac{3}{3^2}}$

[flat frigate]

Jshy <3

[strange plaza]

Am I correct with this?

[lean otter]

@strange plaza yup

[strange plaza]

Thanks!

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[lean otter]

Over reals, cauchy implies convergent and convergent implies cauchy right?

[lean otter]

But under the rationals

it only goes convergent -> caughy right?

ALSO

Differentiality -> Continuity
& also
Continuity -> Integrabilty

all arrows imply one way implications

correct?

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@lean otter Has your question been resolved?

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[prisma epoch]

h

[safe radish]

Please don't occupy multiple help channels.

[prisma epoch]

yeah so my problem is related to sets

wait a sec

posting

I do not understand does does -n[A∩B∪A∩C] converts to n ( A ∩ B ) + n ( A ∩ C ) – n (A ∩ B ∩ C)

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[frosty granite]

For 9b i dont get why u cant equate 3theta-alpha to -90

[frosty granite]

instead u equate to 270 but i dont get why

just because its positive? in part a the only restrictions are on alpha and R

[junior smelt]

Agree with you tbh - they should have e.g. stated the value of theta should be positive or something

[frosty granite]

oh i thought it was just me lol

i got an angle from the -90 and when u sub in it generates the minimum required

but its wrong

[junior smelt]

Which page number is that?

[frosty granite]

195 on digital

[junior smelt]

aight give me a second to see what mine has, and the solution banks too

[frosty granite]

u have this textbook? what

[junior smelt]

Hmmm I thought I did but it's an older copy on my side

Let me search whether the solution banks say anything about it

[frosty granite]

i guess in part c it says theta is positive

but still its a bit poor

[junior smelt]

Hmmm yea the solution banks I found don't match up

[junior smelt]

Yea that personally imo wouldn't count because it's not relevant to part b

[frosty granite]

yeah

its fine ill compare to past paper

[junior smelt]

The fact that they don't say something like "the minimum positive value of theta" or something is bad form and they should have, so it's an issue to the book

[frosty granite]

past papers shud be better

[frosty granite]

ye im not huge fan of our book

[junior smelt]

[because arguably there are infinitely many you could choose from lol]

[frosty granite]

yeah

[frosty granite]

someone made a massive document with all the errors LOL

[junior smelt]

How on earth can they be getting worse from the copy that I had

[frosty granite]

[junior smelt]

They're like evolving, but backwards

[frosty granite]

thanks anyway

.close

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[ionic notch]

How do I solve this, none of the methods I know line up with the answer choices?

[ionic notch]

The answers to the first one are .420, .387, .393

[thin bridge]

what methods are you trying

[ionic notch]

Well like, trying to put the interval through the function, and then use those to find the average rate of of change

[thin bridge]

show work

[ionic notch]

Ugh sorry this isn't going to work

.close

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[dreamy finch]

what's the best way to find 17^6 remainder 7 by hand?

[dreamy finch]

I have:

Is that the best I can work with?

[final halo]

Use the same trick you just got shown in your last channel

[split ether]

Would pick 3

Btw you can just use Euler's theorem/Fermat's little theorem

[final halo]

Oh you are, I'm just illiterate

[dreamy finch]

lol i was a bit confused for a sec

[dreamy finch]

is that little fermat's theorem

whoa

[split ether]

Fermat's little theorem is a special case of Euler's theorem

[dreamy finch]

you literally just edited that as i responded, the timing was so coincidental lol.

[final halo]

Little fermat 🤗

[drowsy moss]

I tend to stick to positive numbers when modding, then just mod as you go

[split ether]

Even if you get the chance to reduce the number to -1? E.g. 8^64 mod 3

[dreamy finch]

so for little fermat's theorem, I do 3^7-1, right?

[split ether]

3^(7-1)?

[dreamy finch]

i guess i forgot the theorem

[drowsy moss]

🤷 it'll get to 1 eventually in that case.
8 mod 3 = 2
2 ^2 = 4 = 1 mod 3
1^32 = 1 mod 3.

[split ether]

It directly implies that this number is congruent to 1 because 6 is 1 less than 7 and 7 is coprime to 17

[split ether]

Ik, but reducing to -1 seems to be the quickest thing

[dreamy finch]

so how do i do little fermat's theorem?

[split ether]

$17^{7-1}=1\mod7$

[flat frigate]

A Lonely Bean

[dreamy finch]

oh damn

that's clean

thank you!

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[merry burrow]

does anyone have any ideas on what differential equation im supposed to find,, im not sure what the question is referring to exactly

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[terse bane]

so i get that the x intercepts are 7 and 1

bc i expanded it and got

√[(7 - x)(1 - x)]

but idk how to graph it

[rose sage]

ok

so lets assume z=x-3

right

y=sqrt(16-z^2)

[terse bane]

mate

[rose sage]

ya

[terse bane]

i just said here what i did and got

but just not sure how to graph it

idk if i have enough info

[rose sage]

so sqrt of 16- and upside down parabola

[terse bane]

whats 4?

[rose sage]

wdym?

[terse bane]

root 16

[rose sage]

ye

[terse bane]

where does it go

[rose sage]

wdym

[terse bane]

ik its the distance between the x intercepts

[rose sage]

4 is the maximum value of y

[terse bane]

sorry its -1 not 1

[rose sage]

when x=3

[terse bane]

typo

ah ok

that makes sense

thanks mate

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[leaden scaffold]

Could someone tell me if I'm solving these partial fraction problems correctly? I just want to know if I go the process down.

[leaden scaffold]

Problem 1:

problem 2:

Problem 3:

[safe radish]

@leaden scaffold Has your question been resolved?

[leaden scaffold]

<@&286206848099549185>

[safe radish]

@leaden scaffold Has your question been resolved?

[leaden scaffold]

@meager igloo

<@&286206848099549185>

[spiral cave]

which one do you need done the most

[leaden scaffold]

I'm not on any time limit, if you could check all 3 I'd appreciate it. I just want to know if I'm understanding the concept correctly.

[leaden scaffold]

.close

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[radiant apex]

is this the correct way to find local minimums and maximums?

[final halo]

perfect

,w plot x^3+x^2-x+1

[flat frigate]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by iCaird#6258

[radiant apex]

lets fuckin goooooo

what do you do tho if you have higher order functions?

like lets say you ended up with a first derivative with a polynomial of order 5 or somethn

[final halo]

hope that its easy to factor and/or find roots of

theres no general formula for roots of degree 5 or higher polynomials

so if there was no easy trick or roots easy to spot then you'd have to use numerical methods

[radiant apex]

ah, will you generally only be asked at least at a lower level to find stuff like this of polynomials like order 3 or lower?

[final halo]

i would imagine yes

or certain 4th order ones that are 2nd orders in disguise

like x^4 + 5x^2 + 6

[radiant apex]

oh yeah thats epic

this is hype yo

thank you so much 🙏

[final halo]

no worries, keep at it

[radiant apex]

.close

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[lean otter]

when u subbing this, why can't u=x+1?

[lean otter]

yes u can do it by u=x+1

[lean otter]

how

[lean otter]

its simple if u=x+1 then du=dx

yeah

$\int \frac{3}{(u)^2+4} \dd{u}$

[lean otter]

du/u^2+2^2= 1/2 tan^-1(u/2)

can u latex that?

$du/u^2+2^2= 1/2 tan^{-1}(u/2)$

[lean otter]

how does that happen

[lean otter]

now substitute u=x+1 and u will get ur answer

Nope

$\tan^{-1}(x) = \int \frac{1}{1+x^2}$

[lean otter]

here, where does the 3 go?

[lean otter]

what are the steps after this

@lean otter

[lean otter]

3 integration du/u^2+2^2= 3/2 tan^-1(u/2)

latex pls 😭

idk where the 3 went and why u did 2^2

okay i get it

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[dusty talon]

plug in 0?

does the - sign by sin replace the first + sign

[obtuse plover]

Of course

[dusty talon]

oh

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[split cliff]

i need help pls

[faint saffron]

!status

[safe radish]

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

[split cliff]

1

[faint saffron]

okay, first, it says that triangle XYZ and triangle BAC are similar

can you name me similar sides of these triangles?

[split cliff]

triangle XYZ is similar to triangle ABC

[faint saffron]

You occupied two help channels, you have to close one of them!

[split cliff]

how to close

im gonna close the other one

ok done

[faint saffron]

if triangles are similar, it means that its corresponding angles are congruent and corresponding sides are in equal proportion

can you name me their similar sides? [ for example, side XZ is similar to side CB]

[split cliff]

yz similar to ab

[faint saffron]

hmm, actually it is not :/

okaaay, let's try angles then! Can you name me matching angles?

Angles of similar triangles are congruent, so it means that their trigonometric functions are equal!

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@split cliff Has your question been resolved?

[safe radish]

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[wooden oyster]

Is anyone here familiar with numerical method but more specific Euelrs method?

[dull sequoia]

This is all I got if it helps, I’m not too familiar but maybe this helps a bit

[wooden oyster]

Well

if u can answer this u will be of much hlep

is this

the same as this:

[dull sequoia]

That does look familiar let me think

[wooden oyster]

You see the equation are very similar

in the first one its h/2

and times hfxn,yn)

but in the bottom its not h*f only f

so i wonder if it is the same

I've found all of these in my attempt to understand Heun's method

[dull sequoia]

I think we haven’t covered heun’s method

Or I don’t remember what that is

[wooden oyster]

perhaps you can call someone who has already graduated in to assist us

cos i am truly in the same boat

[dull sequoia]

It’s currently 4:20 am 😦

I swear something like that was on this week’s slides but I don’t have it 😦 maybe I can get it on Monday

Unless the lecturer replies on a Sunday which I doubt

[wooden oyster]

I understand

But i mean other people in this discord server

Are perhaps inclined to support us

Is what i mean

[dull sequoia]

Hmm I think they are the same, the h/2 thing has something to do with Taylor series but I can’t remember rn

Ah maybe, This might go into advanced section though

[wooden oyster]

Ｈｅｒｅｌｓ#1420

he helped me last time

he got that adavnced role

mby he is like super smart

and we need someone super smart

[dull sequoia]

Maybe #odes-and-pdes or #computing-software

I do actually know a guy but he’s definitely asleep rn :/

[wooden oyster]

asleep

Do you know his time zone?

[dull sequoia]

Yes he lives same place as me he’s an irl friend

[safe radish]

@wooden oyster Has your question been resolved?

[safe radish]

@wooden oyster Has your question been resolved?

[wooden oyster]

No not rly

[lean otter]

@wooden oyster is this from the projectile motion page?

[wooden oyster]

No

I can lend you the pdf if you would like

[lean otter]

please

[wooden oyster]

This time around it is actually in english

This the equation for solving with heuns method

[lean otter]

Φ is a solution to y' = f(t, y)

meaning, y' = f(t, Φ((t) )

[lean otter]

where did you get this?

[wooden oyster]

this?

[lean otter]

yeah

[wooden oyster]

https://web.archive.org/web/20090212005921/http://calculuslab.deltacollege.edu/ODE/7-C-2/7-C-2-h.html

[lean otter]

it isn't in the pdf they provide:

[wooden oyster]

it isnt made by the same ppl

hence my question

[lean otter]

y with the squiggly line is fully expanded in this one

they're the same

[lean otter]

but you can combine these two to get the same

[wooden oyster]

also

d/dt is same as delta t right

[lean otter]

context?

[wooden oyster]

In the text book d/dt is written as deltaT

[lean otter]

as $dt$ ?

[flat frigate]

hannibal

[lean otter]

$d/dt$ might be operated onto the stuff on the left

[flat frigate]

hannibal

[wooden oyster]

not as dt

[lean otter]

but i've never seen it isolated like that. can you screenshot more of the doc?

[wooden oyster]

but as how i showed in the picture

[wooden oyster]

ok

[lean otter]

$\Delta t$ ?

[wooden oyster]

yes

small t

but yes

[flat frigate]

hannibal

[wooden oyster]

context

using Eulers method to approximate the curve of an object being throw with a field with drag force

seeing how close we can getr

[wooden oyster]

That is what i've written

[lean otter]

it might be a differential?

$dv_{n+1} = -\frac{C_d \rho A v^2}{2m}dt$

where a and b is the stuff in the numerator and denominator

if you differentiate this, you get that

[flat frigate]

hannibal

[lean otter]

sorry, pissing in the wind here

nvm that doesn't make sense

[lean otter]

can't you just ignore this for now?

how do they use it, later

[wooden oyster]

wdym im confused

[lean otter]

this doesn't make sense as is

[wooden oyster]

I've changed it to delta t

i might as well just follow the text book

[lean otter]

the acceleration due to air-resistance is

$a = -\frac{C_d \rho A v^2}{2m}$

[flat frigate]

hannibal

[lean otter]

alr

[wooden oyster]

thank u tho

[lean otter]

no worries

[safe radish]

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[strange plaza]

How could this question be visualised?

I was thinking a tree diagram

but thats a bit much...

Other than listing all the possibilities out, I don't know what else to do

[wooden garnet]

Trees are the only way Ik

Or binomial distributions

Which isn’t rlly a visualisation, but another way of representing trees like this

You don’t need to draw the entire tree, just the parts that are relevant for you

For me example, for a b e f id jusy draw a tree with the outcome of 6 and 6’(not 6)

[strange plaza]

oh right I see

okay that makes things easier

[wooden garnet]

Are you stuck on any in particular?

[strange plaza]

Not anymore, using the method you stated I can understand how I can write it out.

Thank you

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[open sleet]

So I got the derivitive and set it equal to 0 to find where the slope = 0

but I cant solve without x and dont know where to find the range of t with that information

for the derivitive I have 0 = x^2 + tx + 1

[thin bridge]

determine when that doesn't have real solutions

considering stuff like the discriminant

[open sleet]

I guess its confusing me cause I have to find a value t for all values of x

[thin bridge]

don't get intimidated by the presence of t in your quadratic equation in x

approach it like you would any other quadratic equation

apply certain properties to get another equation and solve that

[open sleet]

I mean

so you cant factor it as it is

[thin bridge]

there's no nice factorisation for this

[open sleet]

I guess using the discrminant

I get t^2-4

so if t is < 2 or > -2 then the discriminant would be negative so no solutions

[dull sequoia]

Or 0

Oh wait nvm

[open sleet]

yeah

so

but still in that case I have two answers so that dosent really make sense

so Im probably doing something wrong

[dull sequoia]

There is an option for none of these

[open sleet]

hm okay

so that was along the right path with the discriminant?

[thin bridge]

yes

[open sleet]

ah okay

[thin bridge]

well you conclusion was a bit off

t is < 2 or > -2
that should be AND not or

[open sleet]

oh yeah

thats what i meant lol

okay thanks that helped a lot i didnt consider the discriminant

[dull sequoia]

I was gonna ask why discriminant but you said this

Well I guess he gave you that hint

[open sleet]

yeah that helped

ty

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[supple monolith]

Hello great mathematicians. Could someone giving me some hint(or external resource) regarding when we need to go for partial fraction rather u-substitution when integrating fractional equations?
I tried to integrate following integral using u-sub by u = e^x + 1, and (1/e^x)du=dx to let me integral the known 1/u, but it seems I'm wrong, and partial fraction decomposition method should be used.
So is there any rule or trick about that? How to find out when method hsould be used?
Thank you for your time and consideration.

[rigid widget]

that usub works but you did not substitute dx correctly back in

if du = e^x dx then du / e^x = dx
but e^x = u-1
so dx = du / (u-1)

[supple monolith]

Thank you very much indeed.
Oh, wow. yes I see that now, that's something I should practice more probably regarding u-sub, so if e^x becomes u-1, then it will be 1/u^2-u which ultimately lead us to partial fraction I suppose.
So does it mean everytime I use u-sub, I need to check if du could be presented as u and substitute that as well?
Thanks

[rigid widget]

yes, your integral can only have u’s in it after usub (you cannot have both x’s and u’s)

[supple monolith]

Oh, that x is the point, I'm sorry I'm not really smart.
Thank you very much for your time, wonderful.

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[fallow knoll]

I have to optimise a cylinder to have the lowest surface area possible

[fallow knoll]

But it has a fixed volume of 600cm3

I already have the answer I just want to make sure it’s right

[rigid inlet]

We can't confirm or deny if you don't send your work

[rigid inlet]

,rccw

[rigid inlet]

I don't see anything wrong with it

[fallow knoll]

Ok thanks

[thin bridge]

should probs leave values in terms of pi

don't round unless told to do so

[rigid inlet]

Yeah sure

[fallow knoll]

Ok

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[lean otter]

Hello, I was just looking at my sibling's text book he's in grade 6 and his book says that BODMAS stands for "Brackets, Of, Division and Multiplication, and Addition and Subtraction."

[lean otter]

but in my days

when i was in 6th standard

the O in bodmas stood for "order"

[marsh walrus]

order?

there are a lot of different versions of this mnemonic

in my day we used pemdas

[lean otter]

Yes which refers to the operation of raising a number to a power, which takes precedence over both multiplication and division.

[dull sequoia]

Probably exponentials equivalence

[lean otter]

but doesn't of and multiplication mean the same thing?

[dull sequoia]

It kinda does

[marsh walrus]

ive never heard of

[lean otter]

like if we say 1/2 of 4

[marsh walrus]

but i dont hear a lot of things

[dull sequoia]

Not that of

Order as in powers

[marsh walrus]

of makes me think division

[dull sequoia]

Like indices and exponents

[marsh walrus]

like 3 of 2