help-23

[long copper]

how do you solve:
$\int \frac{x+4}{x+2}$?
I've tried using standard patterns by letting $y = (x+4)\cdot \ln(x+2)$ but i keep getting the wrong answer

[flat frigate]

I can't believe you've done this

[crisp linden]

poor dx

$\int \frac{x+4}{x+2} \dd x$

[flat frigate]

Remavas

[crisp linden]

Well, I see one immediate route to make this much simpler

I can give you a hint

4 = 2+2

[long copper]

oh

I'm such an idiot

[crisp linden]

I wouldn't say so

I only stated the obvious and you seem to know what to do with it

🙂

[long copper]

Yeah it looks way easier to integrate now

hopefully ill remember dx when i write the calculations out

I think i got it right, is it $x + 2\ln \lvert x+2 \rvert + c$?

[flat frigate]

I can't believe you've done this

[crisp linden]

should be

,w integrate (x+4)/(x+2)

[flat frigate]

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[long copper]

great

thanks so much

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[fathom yew]

I was just asked to convert y=mx+b into a polar equation and solve for r. Anybody have any recommendations? I’m not sure where to start

[broken yew]

Draw a picture.

you mark an arbitrary x, y on that line

and proceed

maybe thats not the best suggestion

I mean converting to polar form is literally just converting to polar coords

look it up if you don't know how

If b = 0, there is an easy visual explanation for the algebra.

Try that and then generalise

[fathom yew]

I think by polar it is meaning anything that includes values like r and including things like sin and cos but excluding x and y

I don’t have to find an actual numerical value of r, just have to modify the equation until it is r= something

My first thought was to use the relationships x=r cos(theta) and y=r sin(theta) and plug them in for x and y

[broken yew]

thats exactly what the q needs you to do?

[fathom yew]

Yes, i just have to make the equation to be in terms of r and theta rather than x and y

And it has to solve for r so my final solution has to be r= something

This is what I’ve done so far, but i need to modify it so that r is alone on one side

<@&286206848099549185>

I think I figured it out but can someone check my algebra?

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@fathom yew Has your question been resolved?

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[ebon jacinth]

how do you perform modulos with large numbers? Is there a formula to it?

[ebon jacinth]

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[lean otter]

Hey guys, my assignment gives me the following statement: Also gives me that signmoid h is a hyperbolic tangent. What does this mean ?

[lean otter]

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[icy hawk]

any help on these 2

[icy hawk]

?

<@&286206848099549185>

[lean otter]

You need a formule to calculate the new price. If it has 30% off the new value will be 70% of the original value of d

Only one of them is not 70% value of the original value

so if the formula equals = d/100 * 70 in any way, it's correct

d/100 * 70 = (d*70)/100 = 0.7d

@icy hawk Did you get it ?

[icy hawk]

sorry

i’m here

lemme re read what you said

which one of the problems is this for btw?

oh the first

ok thanks i get it now

what abt the 2nd problem?

[lean otter]

both of them

there they want the expression that does represent

so find the one that equals

d/100 * whatever percent the new price is

[icy hawk]

wait wdym both of them?

[lean otter]

It's the same trick

but for hte first one you need to find the expression that is not the same as d/100* 70

and in the second one you need to find the expression that is the same as d/100 * 40

The trick is the same, but the question asked is different

The first one they say, which one is not correct among these. And the second one they say, just give me the correct one

[icy hawk]

ok so the same formula?

d/100*40?

[lean otter]

But the calculation you need to do are the same, you need to know the correct ones and then you answer the question

[lean otter]

Yes, since the new price is 40% in the second question

if they said 40% off instead, what do you think it would be then ?

[icy hawk]

0.4?

[lean otter]

no

So thats semantics, if they say 40% off the new price will be 60% of the original

[icy hawk]

oh

ohh

[lean otter]

but they say its 40% from the orignal price. So not 40% off

So you need to be carefull when reading the questions aswell, since depending on how you read it. It will either be 0.6J or 0.4J

[icy hawk]

wait so it would be 60%

which would be 0.6J?

[lean otter]

Yes, if they asked it like that it would be 0.6

but they arent asking that

Just to keep you sharp I asked that lol

They are saying the new price is 40% of the original

[icy hawk]

ok gimme one second

maybe 30

or 60

ok

so

the original price was

100%

correct

[lean otter]

Yes

[icy hawk]

and the sale is taking off 40%

[lean otter]

Nope, thats not what they are saying

If you read carefully, they are saying the new price is 40% of the original. So in a way taking off 60%

Maybe I am reading it wrong now

let me reread

Ah oke, do you perhaps know the asnwer ?

is it. C ?

[icy hawk]

no i don’t know the answer

if i did

and i actually remembered how to solve this

it would be amazing

tbh

[lean otter]

So, I think they are saying this

A new price went up that is 40% of the original price

so a discount of 60%

[icy hawk]

ok

[lean otter]

no hold up

[icy hawk]

there is no f

lol

[lean otter]

ignore that haha

[icy hawk]

that’s e

lol

it’s all good

[lean otter]

I am talking about the second one

with the expressions

[icy hawk]

ok

ik

^

[lean otter]

huh

what are your options then ?

[icy hawk]

A

[lean otter]

I thought you ha to pick one expression

[icy hawk]

B

C

D

E

i have to pick 2

A or B

[lean otter]

oh lol i cant read

[icy hawk]

C or E

B or C

and D or E

[icy hawk]

no, your all good

i just didn’t provide the answers

[lean otter]

No A and D option ?

[lean otter]

its this ojne

I was reading it wrong

I think you are right then, they are saying a discount of 40%

Damn semantics

So, they do want you to find expressions that match (j/100) * 40

[icy hawk]

c just takes away J right?

J-0.4J

if so then yea

[lean otter]

yes exatly

hope I didnt confuse you more lol.

[icy hawk]

you didn’t

your good

[lean otter]

ayy nice

[icy hawk]

big mom for helper

W

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[idle gazelle]

suo

[idle gazelle]

plz help

[steel quail]

I said I hate statistics smh

what

why is this confusing

skip

[worthy hemlock]

You don't need to add pointless comments. If you can't help, don't say anything and let someone else come by

[steel quail]

idk I tried helping

I guess

sorry

I guess

[worthy hemlock]

You tried helping? You didn't say anything that was helpful

[steel quail]

smh you are making me angry and I WILL help

get total number of films watched and divide it by umm

😭

[worthy hemlock]

You just said you hated stats and wanted to skip this. You don't have to help. You just didn't need to add pointless comments

[steel quail]

well it won't be useless after all if I actually helped now

that's my poiny

point

yeah you need to add the y values of the bars to get number of classe

[worthy hemlock]

It would be useless, if you don't really understand stat and could potentially provide wrong info

[steel quail]

and then multiply the x with the y and add them all to get total number of films watched

dividing the latter by the former gives the mean number of films watched per class

[steel quail]

well I am just a bit rusty in it. not that I don't understand it

it takes time for me

now that's the mean

the median is defined as the middle value

you can use the number of classes to get the position of the middle value

that is taking the average of the n/2 and the n/2 +1 if even or the (n+1)/2 if odd

and climb count the number of classes as you take bars from the low x value to the higher

and stop at the desired position and see how many films that is

now you can compare them

here you go hope I helped

sticking tongue emote to dldh06

[idle gazelle]

lads

can u help

instead or being donuts

[steel quail]

I just did just check it out

[idle gazelle]

can u summarize what u said

i dont feel like reading an essay

[steel quail]

umm I actually can't explain it more concisely sorry

[idle gazelle]

so is it C

[steel quail]

I actually haven't done the working but I don't mind you sending your working and I'll check it out

[worthy hemlock]

Or you can read the "essay" and see if you can come up with proper answer

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@idle gazelle Has your question been resolved?

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[quick kestrel]

Abstract algebra: Any theorem that can help me understand how to find all values of k?

[quick kestrel]

All I understand so far is that we have 18=1 mod 25 and 7^k=1 mod 25, but I don't know what else to go from there.

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@quick kestrel Has your question been resolved?

[bronze prism]

18≡1[25] is most certainly false

18 is congruent to, well, 18 mod 25

[quick kestrel]

I'll come back!

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[lean otter]

Hi could someone explain to me why 7 b is 5 and not -5

[lean otter]

This is my work

[pulsar condor]

(-1)^4=1

[lean otter]

It gives me -1 tho

Oh wait never mind I forgot the brackets thanks

.clear

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[neon hedge]

i need help with this

[neon hedge]

i have to find the focus at the origin, directrix, and eccentricity

i divided all of them by 1/4 to get it equal to 1

ep = 3/4

but e = -1 right

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@neon hedge Has your question been resolved?

[neon hedge]

<@&286206848099549185>

helpers check

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@neon hedge Has your question been resolved?

[safe radish]

@neon hedge Has your question been resolved?

[feral linden]

1 I think

[neon hedge]

but how

if its -1 in the formula

the answer is 1 tho

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[scarlet sundial]

Can somebody check if I did this correctly? This is a practice test btw so it isn’t homework, just want to know if I messed up implicit differentiation at all

[scarlet sundial]

My answer is dy/dx = (3y^2 - sin y)/(2x+sec^2x)

[red glen]

,rotate

[scarlet sundial]

Ill rotate it and resend

[scarlet sundial]

Oh nvm

[red glen]

While taking derivative of x^2y^3 use product rule

[scarlet sundial]

That’s what I did

[red glen]

2xy^3 + x^2 3y^2 dy/dx

[red glen]

Where is + sign

When you apply product rule

[scarlet sundial]

Oh wait

Yeah I understood you

I misread it sorry

You meant f(x) = f(x)•g’(x)+f’(x)•g(x) and I was thinking you said power rule for some reason

[red glen]

Use this

[scarlet sundial]

So im 100% confident I did the product rule correctly, but im still getting the hang of implicit differentiation (dy/dx dx/dx, etc) so this made me think of a question

[scarlet sundial]

Why exactly did you put dy/dx at the end right here

[red glen]

Because of derivative of y

[scarlet sundial]

Do you mind explaining a bit further, I am interested I just want to understand it conceptually 100%

[red glen]

The thing is when you take derivative of lets say y^2 what will you get?

Wrt x

[scarlet sundial]

My bad I was moving my stuff to another room, but It would be 2y

[scarlet sundial]

?

[red glen]

Its 2ydy/dx

You varibale is x not y

[scarlet sundial]

So it’s kind of like the bottom or (dx) of dy/dx is saying im taking the derivative of y in respect to x (dx)

[red glen]

Yes

[scarlet sundial]

So if im taking the derivative of something like x^3 would I write it as 3x^2 dx/dx?

[red glen]

Yes

[scarlet sundial]

Correct me if im wrong but is this the right way of how to do it

[worthy hemlock]

You're taking a test?

[scarlet sundial]

No, it's a review sheet that my professor gave me to practice on for tomorrow's test

[worthy hemlock]

But it says test?

[red glen]

Tag me so that i wil get the notification

[scarlet sundial]

I know, but I swear it is a practice sheet that my professor gave me during her office hours

[elfin yew]

but its not a test because they said it wasnt :}

[scarlet sundial]

She did #2 herself, we have distinctly different handwriting

I already know the rules of this discord, I would not be asking for help on a test or posting it

[red glen]

You taking 3y^2dy/dx on other side but why notx^2

Take whole x^2.3y^2 dy/dx on rhs

[scarlet sundial]

I didnt take x^2 because I was thinking that since that is not x^2 dy/dx,, just normal x^2, I moved -3y^2 to the rhs of the = to isolate my numbers which are affected by dy/dx

[red glen]

Its like 2x = 4
So 2 = 4- x. ( This is what you doing)

So be careful

[red glen]

When you taking any part on lhs or rhs take the whole part ( which is in multiplication)

Here its is x^2. 3y^2 dy/dx

[scarlet sundial]

Oh okay I think I understand what you mean

@red glen So on
LHS 2x * y^3 + sec^2x dx/dx
RHS = -siny-x^2 dy/dx(?)

[red glen]

2x.y^3 +sec^2 x =dy/dx( -siny -x^2.3y^2)

[red glen]

Check this

[scarlet sundial]

I mainly got this right except for my placement of dy/dx, and I put a dx/dx meanwhile you didnt

[red glen]

Ita okk dx/dx. Is 1

Not because it get cancelled ( this is by rule)

[red glen]

Check this

[scarlet sundial]

Oh okay, so even though I put dx/dx it doesn't mean im wrong because either way it's multiplying by 1 and gonna stay the same

[red glen]

Yes ,but a good student write 1 ( or just write nothing)insted of dx/dx

[scarlet sundial]

So just wondering does this mean that I shouldnt cancel out my (dx/dx)s and only my (dy/dx)

[red glen]

Yes insted of dx/dx just write nothing

[scarlet sundial]

ok

[red glen]

Simply say 1

[scarlet sundial]

right

[red glen]

Hope you can solve now

[scarlet sundial]

Thank you @red glen , this did help me understand it a bit better, Im going to look over it more or try other problems with this logic

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[winter pivot]

@dim kindle

[dim kindle]

yep

[winter pivot]

Ok

You want to know what 2^(35) mod 7 is

Let us begin.

What is 2^0 mod 7?

[dim kindle]

You can do it.

Cause recently I'm busy

[winter pivot]

This is a help channel haha

If you don't want help then why ask

.close

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[dim kindle]

I do not mean that.

[winter pivot]

?

[dim kindle]

pls help me

[winter pivot]

.reopen

[safe radish]

✅

[winter pivot]

Ok then sure let me help you

Its a really simple problem takes like 2 min haha

2^0 mod 7?

[dim kindle]

I know it.

[winter pivot]

Do you know what mod means?

[dim kindle]

Sorry

It was my son

who was

in my laptop

sorry for that

[winter pivot]

Alright

[dim kindle]

😩

[winter pivot]

Did you still need help

[dim kindle]

no

It is really easy for me

it is 4

😋

[winter pivot]

Alright then good job

The pattern is 1 2 4 1 2 4 so you just take the remainder of 35/3 and get 2 so the answer is 4

[dim kindle]

yeeh

tell me how old are you

EndTimes

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[safe radish]

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[cold bane]

you need 1 liter of detergent whose content should be 16%. Unfortunately, there is no undiluted concentrate liquid in the cabinet. There are only two liters of an 8% solution and 0.7 liters of a 20% solution. How much should you mix of these to get the desired solution.

[cold bane]

could someone help with this?🤔

[ember bough]

your work?

[cold bane]

Yes, it's our homework

[ember bough]

i mean, can you show your work?

[cold bane]

I'm pretty lost, don't know where to start

[ember bough]

hmm

try setting up a system of equations

[safe radish]

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[safe radish]

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[crude shoal]

how many ending zeros are in 1x4x7x10x...x697x700

[crude shoal]

i need to work with multiples of 5

correct?

multiples of 2: 117

multiples of 5: 24

multiples of 25: 5

multiples of 125: 1

so is it 30

can someone help to check my work

<@&286206848099549185>

[feral linden]

26 I think

Count how many of those 3k+1 =0 mod 10 then + how many of them =0 mod 100

The first is a periodic sequence with period 10, the second is of period 100

For example the first sequence {3k+1 mod 10} is 4,7,10,13,16,19,22,25,28,31, then repeat, 4,7,… so one for each ten terms, (which is 10) there are 23 terms.

[crude shoal]

but then what about 50 mod 100?

isn't that also multiple of 25

[feral linden]

For those who =0 mod 10, it’s also a periodic sequence {3k+1 mod 100: 3k+1=0 mod 10} 10,40,…,280 then repeat, 10,40,… one of each ten terms. There are 24 terms, so three of them=0 mod 100 (100, 400 ,700)

50 isn’t one of {3k+1}

40 is

And it only contributes one 0

[crude shoal]

but what about 250?

its divisible by 25

50 mod 100

and 3K+1

[feral linden]

It also contributes one 0

[crude shoal]

??

doesn't it contribute 2?

its a multiple of 25

[feral linden]

No

[crude shoal]

(5*5)

it has 2 "5"s

[feral linden]

n=m10^k where 10 doesn’t divide m, then 250n=25m 10^(k+1) , 10 doesn’t divide 25m

[crude shoal]

wait im confused

but then like in 25!

the 25 contributes 2 zeros

[feral linden]

So 250 only contributes one 0

[crude shoal]

ok

thx

i have another question...

[feral linden]

Okay

[crude shoal]

a ten digit number has the product of digits equal to 2^27. how many such numbers are there

[feral linden]

It’s equivalent to x_i=0,1,2,3 find how many combinations such that Σx_i=27 let me calculate that

Replace x_i with 3-x_i It’s equivalent to finding how many combinations such that Σx_i=3

So C(10,3)+10 times 9 +10

=220

[crude shoal]

ok thanks

[feral linden]

Np

[crude shoal]

im just reviewing my mock so i have a lot of questions sry

wait

if

a+b < 7, b+d >7, c+d = 3, c+e = 6, what is the ratio of c+e : b+d?

[feral linden]

What are a,b,…,e?

Positive integers or what?

[crude shoal]

positive integers

[feral linden]

No solution

Cause only two cases c=1 d=2 or c=2 d=1

If it’s the first case, then b>7-d=5 but b<7-a<=6 so it doesn’t work

If it’s the second case then b>7-d=6, b<7-a<=6 also doesn’t work

So no solution

[crude shoal]

ok thx

.close

[safe radish]

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[crude shoal]

the LCM of two numbers, x and y, is less than 98. If x can be a positive integer from 34 to 40 and y can be a positive integer from 57 to 63, find x and y.

[coarse cape]

what are the possible mutliples of y?

[crude shoal]

multiples? can be any integer from 57 to 63

[coarse cape]

yes think about what a multiple of these numbers looks like

[crude shoal]

um... 1?

[coarse cape]

perhaps the smallest is a good way to start

[crude shoal]

so x is a factor of y?

[coarse cape]

is 1 a multiple for 60?

[crude shoal]

1 is a factor of 60

[coarse cape]

yeah we want the multiples

[crude shoal]

wait im confused

[coarse cape]

alright what im trying to get at is

for the multiple of 57 is 114

which is bigger than 98

[crude shoal]

yes

oh i get it

but 34*2 is more than 63

@coarse cape

[feral linden]

No he means lcm(x,y)=y so x divides y

[crude shoal]

oh ok

but x can't divide y

because 34*2 is more than highest y

[feral linden]

So no solution

[coarse cape]

yes exactly

[crude shoal]

oh ok thanks

but then

um

ok

ill just ask my teacher

@feral linden i realised just now i copied the wrong question

its

[feral linden]

😂

[crude shoal]

a+b < 5, b+d >7, c+d = 3, c+e = 6, what is the ratio of c+e : b+d?

no this one

its a+b <5 not <7

but can you help

i still can't do it

[feral linden]

Still no solution, exactly the same discussion

[crude shoal]

ok lol

thanks!

[feral linden]

Are you sure they are positive integers? It’s a funny coincidence that you asked two questions which have no solutions.

[crude shoal]

yeah...

IDK man

ill talk to my teacher

because

ig

this is uh like olympiad so ig the solution can not exist

[feral linden]

Oh I see

I wonder that. It couldn’t give such simple questions

[crude shoal]

lol

[feral linden]

Questions I met are questions I have no clue when I see them.

[crude shoal]

lol

im just checking there's no solution

when i did, there was no solution

so im just checking

these are the ones i couldn't find a solution

i thought my method wasn't working so i wanted to check

[feral linden]

Oh I see

That explains

[crude shoal]

.close

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[mossy folio]

how do I solve b from part a

I know I can expand it to r squared - r

but how do I use part a to solve part b

[safe radish]

@mossy folio Has your question been resolved?

[mossy folio]

<@&286206848099549185>

<@&286206848099549185>

[coarse cape]

change the equation from (a) so that you can use it in (b)

[mossy folio]

i tried that

what do i do aft that

[coarse cape]

what do you get after you plug it in?

[mossy folio]

wait i sen pic

[coarse cape]

you just multiplied by 1/3

[mossy folio]

yea

?

I multiplied by 1/3 so that it will fit into r(r-1)

[coarse cape]

and know use the equation from (a)

[safe radish]

@mossy folio Has your question been resolved?

[safe radish]

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[strange quest]

Can someone possibly explain what it means for a linear transformation to be onto? I understand what one-to-one means, but I'm still struggling with the definition for onto. I feel like part of the issue is that I'm also struggling to understand codomain vs. range

[broken yew]

I will define it for a general function

f : A -> B

Does this notation make sense

[strange quest]

yeah

where f is the transformation, right

[broken yew]

Function.

Linear transformations are types of functions

:= means 'defined'

im f := f(A) := {f(a) : a in A}

Does this make sense?

This is know as the image of f

Or the range of f

[strange quest]

Ok yeah

[broken yew]

A function f is 'onto' or 'surjective' iff
im f = B

To understand more, you should consider some examples of functions from R to R

[strange quest]

Ok im confused again

give me a sec

ok so if I have a linear transformation T

where

T: R^n -> R^m

The codomain of T is like

is it a basis for R^m?

or is it R^m

or neither of these things

[broken yew]

???

f : A -> B

A is the domain

B is the codomain

Codomain, surjective neither of these terms necessarily relate to linear transformations

These notions are defined for functions in general

[strange quest]

Ok

I've just never had codomain used in a class before this

I get that now

So

The range I also think i get

kind of

If my outputs are all 4 dimensional

Like every output is in R^4

then is the range R^4?

[broken yew]

no???

[strange quest]

or is that

[broken yew]

what

[strange quest]

the codomain

yeah im

[broken yew]

Take what I wrote above

There is nothing that is specific to linear transformations

in what you are trying to understand

f : A -> B

The domain of f is A
The codomain of f is B

The range/image of f -
im f := f(A) := {f(a) : a in A}

[strange quest]

oh

range is image

Thats something I didnt get before lmao

I think I get it now

You can have a range smaller than the codomain

but then it's not onto

right

so if i have a transformation where my codomain is R^4 but my range is a subspace of R^4

then it wouldn't be onto?

[broken yew]

yes

[strange quest]

Ok thanks

[broken yew]

*proper subspace

[strange quest]

wait what

ah isee

never heard that term before either

but makes sense

thanks

.close

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[sage trellis]

help me?

[grizzled fossil]

Do you know what continious means?

[sage trellis]

omg

I just click it I'm sorry

I accidentally clicked it I'm sorry

.close

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[remote sapphire]

Gonna need to know if I did this right

[remote sapphire]

Hello?

[pulsar condor]

Ask your math question in a clear, concise manner.

You must have missed reading that

[remote sapphire]

I got 14.03 for problem

Oh wait wrong one

For problem 16

I was finding XZ

Did I do it correctly?

[pulsar condor]

No clue, post your working.

[remote sapphire]

Tan(41)=12.2/x

14.03

[pulsar condor]

yes.

[remote sapphire]

So hey I need a better understanding

[pulsar condor]

however I asked for your working, and you missed a step.

[remote sapphire]

oh

Yeah I wrote it

[pulsar condor]

tan(41)=12.2/x
x=12.2/tan(41)
x ~ 14.03

[remote sapphire]

That

Do I have to show it?

[pulsar condor]

You should, yes.

For obvious reasons

[remote sapphire]

Ignore the bottom part

[pulsar condor]

yeah x isn't equal to 14.03

it's approx

[remote sapphire]

w

I thought it was right tho

[pulsar condor]

you wrote x=14.03 in your work

that is wrong

[remote sapphire]

.

[pulsar condor]

as x is only approximately 14.03

[remote sapphire]

So it’s 14.0

[pulsar condor]

No.

[remote sapphire]

wtf

[pulsar condor]

it's 12.2/tan(41)

which is approximately 14.03

[remote sapphire]

🧐

Mk

Is there another step?

Or did I do something wrong

[pulsar condor]

No, you just wrote an equal when there should be an approx sign

As I've said already

[remote sapphire]

Approx sign?

[pulsar condor]

$\approx$

[flat frigate]

Mosh

[remote sapphire]

Oh

Oh lmao

So the =14.03

[pulsar condor]

$x=\frac{12.2}{\tan(41^\circ)}\approx 14.03$

[flat frigate]

Mosh

[remote sapphire]

Oh I didn’t need to include that

😂

So it’s just 14.03

[pulsar condor]

yes.

as I said

[remote sapphire]

God.

Jesus I thought I did something wrong

Lol

Also before you go I have a question to understand this

[pulsar condor]

Given I said yes when you said 14.03 originally...

[remote sapphire]

Whenever the x is on top of bottom of the formula

Like for ex. Sine opp/hyp

[pulsar condor]

"top of bottom"

[remote sapphire]

Opp/x

Top or bottom*

Sorry about that

[pulsar condor]

ok, so when x exists, sure

[remote sapphire]

That’s what I’m trying to find right

That side

[pulsar condor]

yes

[remote sapphire]

Oh

[pulsar condor]

provided you called x what you're looking for

[remote sapphire]

I for some reason I got confused

Wait before you go

Sorry again

I’m doing problem 17 just to make sure I got it right

Cosine(55)=x/100

X=cosine(55)/100

[pulsar condor]

cos(55)

and no

x isn't cos(55)/100

[remote sapphire]

Oof

So what do I do sur

Sir*

Guide me

[pulsar condor]

recall algebra

if you have 3=x/5, how do you solve for x?

[remote sapphire]

Don’t you switch the 3 with x

[pulsar condor]

no...

you isolate for x

get x=(something)

[remote sapphire]

ok

I’m trying to find HI

Which that side is adjacent

I’m trying to find that

Nvm

You their? @pulsar condor

[elfin yew]

i like your profile picture @remote sapphire

[remote sapphire]

Thanks

<@&286206848099549185>

Wya

[safe radish]

@remote sapphire Has your question been resolved?

[safe radish]

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[scenic pivot]

this is the equation for standard deviation. To do this quesiton we find the sum of x squared multiplied by the probability of x and then subtract all of that by the squared mean?

[scenic pivot]

or do we find the sum of (x^2p(x) - mu^2) for each value of x?

[pulsar condor]

$E[X^2]=\sum_{x\in\Omega}x^2p(x)$ by definition

[flat frigate]

Mosh

[pulsar condor]

then you subtract E^2[X]

[scenic pivot]

Which is the mean squared? I am not familiar with that so I am not sure what it is.

[pulsar condor]

yes

[scenic pivot]

ok got it, thank you

[pulsar condor]

Given I already told you $\mu=E[X]$

[flat frigate]

Mosh

[scenic pivot]

yup, i found the mean for the question i am working with

👌

[safe radish]

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[raven kettle]

I am currently doing

[raven kettle]

a chi squared for independent test

this is the first step

and in Activity 5 is the given

do I treat Observed Absences as girl and boys? or do I treat them as another table?

[safe radish]

@raven kettle Has your question been resolved?

[raven kettle]

<@&286206848099549185>

[safe radish]

@raven kettle Has your question been resolved?

[raven kettle]

<@&286206848099549185>

[safe radish]

@raven kettle Has your question been resolved?

[safe radish]

@raven kettle Has your question been resolved?

[safe radish]

@raven kettle Has your question been resolved?

[warped coral]

need help?

@raven kettle

[plucky elk]

.close

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[thorny barn]

Hello, I have answered all parts of this question except the last section which asks for an assumption we have made. Was hoping someone could help explain what the assumption is. Thanks in advance.

[safe radish]

@thorny barn Has your question been resolved?

[thorny barn]

<@&286206848099549185>

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@thorny barn Has your question been resolved?

[safe radish]

@thorny barn Has your question been resolved?

[thorny barn]

<@&286206848099549185>

[frigid geyser]

this sounds more like a physics question than a math question

suggest asking over the physics server - see #old-network

[thorny barn]

Ah k, asked here cuz this was an AS maths mechanics question, but i can see it would prob make more sense to ask in the physics server. Thanks for the reply xD

.close

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[lean otter]

hello

[lean otter]

what would an answer to an equation like 6(1+1) be

like a number with brackets after it but there is no symbol before the bracket

how do you work it out

wait

i think i got it

so you find the numbers in the brackets, add them together then multiply

ah right thanks

[elfin yew]

dont give people answers

you just did

mk

[safe radish]

@lean otter Has your question been resolved?

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[safe radish]

Please don't occupy multiple help channels.

[elfin yew]

,rotate

[lean otter]

when should I add 180 when trying to find the true direction of a vector for ex:

[lean otter]

for example

i did tan -1(12/8) i got -56

do I just add 180 because its a negative number?

also, what other applications does this apply to

is adding 180 the only rule when it is a negative number?

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

<@&286206848099549185>

[safe radish]

@lean otter Has your question been resolved?

[plucky elk]

your handwriting is illegible. type it out here

[lean otter]

you didnt need to read my handwriting, i already wrote my issue when finding the true direction. the question was to try to find the true direction of (-8,12).
So I did tan-1(12/-8) and i got -56. And then I added 180 to get 123 degrees . my question is do I just add 180 cause its a negative number, and what other rules apply to find the true direction like (adding maybe 90,180,270?)

[plucky elk]

why did you take $\tan^{-1}(12/8)$ instead of your given point (-8,12)

[flat frigate]

riemann

[lean otter]

I miss spelt, I meant -8*

if you type that into your calculator you get -56

[plucky elk]

,calc tan(-56 deg)

[flat frigate]

Result:

-1.4825609685127

[plucky elk]

,calc -12/8

[flat frigate]

Result:

-1.5

[plucky elk]

doesn't look the same

[lean otter]

wdym

[plucky elk]

-1.48... is not the same as -1.5

[lean otter]

ok

[plucky elk]

the question tells you to express the angle between 0 and 360

[plucky elk]

you don't add 90, 180, nor 270 to your angle. those would be different directions

[lean otter]

are you sure?

[plucky elk]

go ahead and plot it

[lean otter]

what is the answer for the question "the direction of D from a standard position (theta) such that 0 < theta 360 degrees rounded to the nearest thousandth using (-8,12)

im pretty sure you add 180

then you will get an answer of 123.69 degrees

@plucky elk

[plucky elk]

did you plot your two angles?

[lean otter]

you dont need to plot using my method

[plucky elk]

your method's wrong. plot it to see

[lean otter]

how is my method wrong lol

i look at my other teachers they use the same method (tan-1 b/a)

[plucky elk]

that tells you something else

[lean otter]

regardless, it isnt my point

[plucky elk]

you're confusing things together

direction of d is different when you add 180 to the angle

[lean otter]

what are you supposed to do then

[plucky elk]

in fact it's the negative direction

[plucky elk]

add 360 for the same direction

,w tan((arctan(-12/8) + 360) deg)

[lean otter]

why

360

not 180

i checked the answers and its 123

@plucky elk

[plucky elk]

the point (-8, 12) is in what quadrant?

oh wait you're right

i thought it was in the 4th quadrant

i read it wrong

[lean otter]

ok

[plucky elk]

it's in the 2nd quadrant

[lean otter]

Ok what are the rules in the 1st 2nd 3rd or 4th quadrant

so i know for 2nd and 3rd you add 180?

what are the rules for the 1st and the 4th quadrant

[plucky elk]

depends what you're calculating

[lean otter]

yeah

how do i know which quadrant my answer is in?

to start off

[plucky elk]

it just depends on the signs of the two values x and y of your point (x, y)

x>0 and y>0 first quadrant

https://www.math.net/quadrant

[lean otter]

OK

caps lock

Point A is in quadrant I since its coordinates are (+, +).

Point B is in quadrant II since its coordinates are (-, +).

Points C is in quadrant III since its coordinates are (-, -).

Point D is in quadrant IV since its coordinates are (+, -).

this essentially

https://gyazo.com/5869ef1458e38ac0832446d450a209f9

@plucky elk so if I know its in quad 1,2,3,4 i use these rules

right

[plucky elk]

looks good

[lean otter]

okay thank you

.close

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[spice linden]

does this just mean that its a maclaurin polynomial

centered at 0 ?

[analog flare]

It means thar taylors polynomial will be close to that function at x = 0

[spice linden]

so should I just calculate as if I was calculating a maclaurin polynomial

[analog flare]

https://youtu.be/3d6DsjIBzJ4

[iron tulip]

yes

[spice linden]

I see, thank you 🙏

.close

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[lean otter]

How do i do part c to this

[lean otter]

Did this idk if it is on the right tracks or not

[long copper]

whoops

guess ill have to read sideways

[lean otter]

Is it right?

[long copper]

i think you made a tiny mistake

[warm drum]

Bro

[long copper]

when square rooting 144x^8

[warm drum]

you took the root wrong

💀

[lean otter]

What should i do

[long copper]

well you got $\sqrt{144} = 12$ but you forgot to take the root of $x^8$

[flat frigate]

I can't believe you've done this

[lean otter]

So it would be 12x^7

[warm drum]

nono

like when you’re square rooting a number it’s like multiplying the power of the number by 1/2

[lean otter]

12x^4

[warm drum]

yess

[lean otter]

Alr i’ll put that in the eq

What do i do from this point?

[long copper]

you're aiming to solve the equation though right

[lean otter]

Find x yes

[warm drum]

how’s your progress

[lean otter]

I’m stuck

[warm drum]

a

[long copper]

at the step $\log_a 18x^3 = \log_a 12x^4$ you can get rid of the logs

[flat frigate]

I can't believe you've done this

[warm drum]

yes

[lean otter]

Oh

[warm drum]

just put “a” as base and it’ll cancel wit log

[lean otter]

So it would just be 2x/3 = 0

[warm drum]

NO

[long copper]

no

[warm drum]

X CANNOT BE 0

[lean otter]

What should it be then

[long copper]

remember that the only number that $\log_a x = 0$ is when $x = 1$

[warm drum]

some value greater than 1

[flat frigate]

I can't believe you've done this

[long copper]

for any base, if the log = 0 then x = 1

because any number to the power of 0 = 1

[warm drum]

Oh wait yea…

I forgor

[long copper]

the fact that $\log_a \frac{2x}{3} = 0$ already tells you that $2x$ and 3 are equal, since the stuff inside the brackets must be equal to 1 in $\log_a$

[flat frigate]

I can't believe you've done this

[lean otter]

This

[warm drum]

yess

[long copper]

yes

[warm drum]

👏

[lean otter]

Thanks

[long copper]

technically you could have used the other working which you did to get $\log_a \frac{2x}{3} = 0$, because you can go straight to the fact that $\frac{2x}{3} = 1$ and so $2x = 3$ and therefore $x = \frac{3}{2}$

[flat frigate]

I can't believe you've done this

[lean otter]

Yeah that’s what i thought but idk if that method would work with other questions

[long copper]

It works in this case, because you had a log which was equal to 0. In other cases it's best to use the method you just used, it's just convenient that in your previous attempt you somewhat did half the question already.

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

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[stable mulch]

Oops

What’s

Finally

Alright is my diagram set up correctly?

Figured it out

.close

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[wanton moth]

If a point on the terminal arm of an angle is -3, -4, and is in quadrant 3, how do I find the angle of that?

[wanton moth]

The numbers don't match up to the 30-60-90 or the 45-45 triangles so I'm assuming I should use the unit circle but how?

[queen parcel]

You can't be sure of the angle exactly - but you can get an exact expression for it in terms of inverse trigonometric expressions

[wanton moth]

ohh

omg oh okay thank you so much

.close

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[lean otter]

so the terms are a, a+r, a+2r, a+3r, a+ 4r and the equation 5a + 10r =30 but I'm stuck after

[quiet cypress]

now solve for a

[lean otter]

how

@quiet cypress

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@lean otter Has your question been resolved?

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[lean otter]

does $\frac{d}{ds}\left(\int _0^s:f:''\left(t\right)dt\right)=f''\left(s\right)ds$

[flat frigate]

Riemann Zeta Male

[lean otter]

is the ds at the end necessary

[pulsar condor]

it'd just be f''(s)

by FTC

[lean otter]

ok

.close

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[lean otter]

does $\int _0^s:f:''\left(t\right)dt:=:f'\left(s\right)$

[flat frigate]

Riemann Zeta Male

[ember bough]

call the derivative of f as g

rewrite

[lean otter]

?

why

[ember bough]

you know fundamental thm of calculus?

[lean otter]

The integral of a function is it's anti derivative

$f''(x)$ represents the derivative if derivative

[flat frigate]

CatHashira

[lean otter]

Then what do u think it's antiderivative is gonna be

f'(x)

is it not?

@lean otter

[drowsy moss]

yes but your answer is not generally correct.

What does FTC say?

[lean otter]

F(x) = integral of f(x) dx

[drowsy moss]

that's one part of it

[lean otter]

Ya