help-10

[idle plume]

depending on + or - inf

[median dome]

well, yes

[idle plume]

but i dont understand how we got there

[median dome]

okay

first I will give you an intuitive sense of it and then i'll show you how to prove it

[idle plume]

yes thatd be great

[median dome]

notice that 5^n grows to be much, much bigger than 3^n

as n tends to infinity

do you see why?

[idle plume]

yes i can see that

[median dome]

so in a sense we can "ignore" the 3^n term in the sum

which directly gives you the answer 5

[idle plume]

ohh

what abt -inf

why is it 3

[median dome]

replace n with -n in the limit to make it a limit at +infinity

it will be easier to spot

[idle plume]

oh nvm i see it now

its a fraction

[median dome]

yes

[idle plume]

that clears things up

[median dome]

this isn't super rigorous though, there's a nice way to show why this works

[idle plume]

yes go for it

[median dome]

it's fine for small limits like this but you should still know why it works

[idle plume]

for sure

[median dome]

you can write $\sqrt[n]{5^n+3^n}$ as $5\cdot\sqrt[n]{\frac{5^n+3^n}{5^n}}=5\cdot\sqrt[n]{1+\left(\frac{3}{5}\right)^n}$

[warm shale]

kheerii

[idle plume]

i tried that while solving

[median dome]

now if you take the limit as n tends to infinity we just get 1 for the radical term

[idle plume]

how so

nvm

3/5 goes to zero

this makes sense now

[median dome]

yes

[idle plume]

okay tysm 🙏

this helped alot

.close

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[shell arrow]

Hi, I'm trying to learn parametrized curves. Am I going in the correct direction with this proof?

[shell arrow]

The proposition I want to prove is enclosed in the box. The rest is my reasoning

[obtuse pebble]

@shell arrow Has your question been resolved?

[obtuse pebble]

@shell arrow Has your question been resolved?

[obtuse pebble]

@shell arrow Has your question been resolved?

[obtuse pebble]

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[amber shuttle]

really quick question. this lowk could be a chem question but it was asked in my linear class so imma ask it here. I'm given a chemical reaction without coefficients and I have to balance it. After I solve the system, I come to the conclusion that the coefficients of the reaction will be positive and negative.
The question asks me to argue that although there is a trivial solution to balancing the reaction, the reaction isn't possible. Is this because a chemical reaction can't have negative coefficients? or is it something completely different?

[kind heath]

안녕하세요 기지훈

[amber shuttle]

yo wsg bro

[kind heath]

Korean?

[amber shuttle]

type shi

[kind heath]

So what were u asking

[amber shuttle]

💀

[kind heath]

Oh wait nvm

[amber shuttle]

can a chemical reaction have negative coefficients

[kind heath]

No

[amber shuttle]

damn ok

tf

then why might a chemical reaction not occur

if i found that i could balance it

[median dome]

!xy

[obtuse pebble]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[amber shuttle]

damn aight

made a system to solve for coefficients, now I just stuck on the reasoning for why the reaction cannot occur

[median dome]

looks like you'd have MnO2 + K2CO3 - KNO2 -> K2MnO4 - KNO3 + CO2

the problem with the mathematics part here is that of course the stoichiometric coefficients of a reaction have to be positive

you can "rearrange" the equation to get MnO2 + K2CO3 + KNO3 -> K2MnO4 + KNO2 + CO2

[median dome]

the problem with the chemistry in that reaction is that both MnO2 and KNO2 are being oxidised at the same time (Mn(II) -> Mn(VI) and N(III) -> N(V))

for a redox reaction oxidation and reduction have to occur simultaneously

[amber shuttle]

naw this for my linear class, forget the chem bro 😭

ain't no way he wants us to say that

[amber shuttle]

aight this makes sense

[median dome]

then this is the reason

[amber shuttle]

aight cool

merci beacoup

[median dome]

your method seems a bit long

to find the coefficients

but alright

[amber shuttle]

i mean like yeah, but it's to practice matrix reducing

cuz we need it for other shit

aight thanks

[median dome]

makes sense

[amber shuttle]

.close

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[scenic lake]

I cannot figure out for the life of me how to get the answer in fraction instead of decimal

I tried to S>D button

It Didn’t change anything

[bitter forge]

Your answer looks uncannily like pi, have you considered it may be irrational?

[scenic lake]

I was thinking it’s definitely irrational but my calculator usually includes pi in the fraction. Unless you mean something else by irrational

[bitter forge]

Hm, Dunno if it still can be expressed in terms of pi and a rational number

[scenic lake]

Ahh I see

[worn yoke]

your calculator includes pi in known trig results, but usually they integrate numerically so it won't know a symbolic representation of the answer (especially since it will be in terms of pi)

[scenic lake]

My homework requires an exact answer. Maybe I’m doing the problem wrong?

[kind hawk]

in fact the result is in terms of pi^2 which it will definitely not know

well you could just integrate it by hand

[worn yoke]

a more advanced calculator would be able to do it. but your homework probably expects you to do it by hand

[kind hawk]

its just sin^2. use a trig identity

[obtuse pebble]

@scenic lake Has your question been resolved?

[scenic lake]

.close

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[topaz elk]

Can someone explain to me PDE sub X(x)T(t) part?
For example why X is plugged to the left hand side, wouldnt it be easier to plug T there? Whats the reasoning behind it?

[topaz elk]

Here is the PDE

.close

[obtuse pebble]

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[acoustic crypt]

Is the use of summation correct here?

I've build a model in excel to estimate the impact on GDP of a certain event.

Shorthand, there are 4 variables: I, S, P, and D

There are 5 different S, P, and D variables.

So when you add them up together, they equal I.

Ex: I = (S1-(S1⋅P1)⋅D1)+(S2-(S2⋅P2)⋅D2)...(S5-(S5⋅P5)⋅D5)

I just want to make sure I've captured this correctly in Eq 3.

Thank you!

[obtuse pebble]

@acoustic crypt Has your question been resolved?

[acoustic crypt]

bump? 🙂

bump please? 😭

[woeful torrent]

you want
$$I_{\mbox{GDP}} = \sum_{i=1}^5 \left( S_i - S_i P_i D_i \right)$$

[warm shale]

Shuba

[woeful torrent]

or even this

$$I_{\mbox{GDP}} = \sum_{i=1}^5 S_i \left( 1 - P_i D_i \right)$$

[acoustic crypt]

Hm, no, that gives me a different result

Ex:
(1000-1000⋅025)⋅1.5 = 1125
(1000-1000⋅025⋅1.5 )= 625

[warm shale]

Shuba

[woeful torrent]

you have this as the formula?
$$I_{\mbox{GDP}} = \left( S_1 - S_1 P_1 D_1 \right) + \left( S_2 - S_2 P_2 D_2 \right) + ... + \left( S_5 - S_5 P_5 D_5 \right)$$

[warm shale]

Shuba

[acoustic crypt]

No, need more parentheses
Its 1000-(250) = 750, than 750*1.5 = 1125

I = (S1-(S1⋅P1)⋅D1)+(S2-(S2⋅P2)⋅D2)...(S5-(S5⋅P5)⋅D5)

S1 = 1001
P1 = 0.25
D1 = 1.5

So I in this case would be 1125

[woeful torrent]

I think you have the parenteses in the wrong place

Do you mean I = (S1 - S1 * P1) * D1 + ...?

[acoustic crypt]

It could be (S1-S1⋅P1)⋅D1

yes!

My question really is focused on the use of summation

[woeful torrent]

(S1 - (S1 · P1) · D1) = (1001 - (1001 · 0.25) · 1.5) = 625.625

[acoustic crypt]

If S1, S2, S3 are different, same with the others, does the use of the summation symbol work here?

[woeful torrent]

(S1 - S1 · P1) · D1 = (1001 - 1001 · 0.25) · 1.5 = 1126.125

[acoustic crypt]

okay fixed that

[woeful torrent]

$$I_{\mbox{GDP}} = \sum_{i=1}^5 S_i \left( 1 - P_i \right) D_i$$

[acoustic crypt]

Awesome, so that would reflect the fact that all the S, P, and D values change?

[woeful torrent]

oops, I've put 1 when it should've been i

[warm shale]

Shuba

[woeful torrent]

that ^

[acoustic crypt]

great thank you

[woeful torrent]

[acoustic crypt]

I tried to help in that other room, it failed lol

[woeful torrent]

I think he's trolling

[acoustic crypt]

I appreciate your time, this was very helpful

ugh I kinda thought that along the way

meh, sad

Anyway, thank you!

[woeful torrent]

np 🙂

[acoustic crypt]

.close

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[deft swan]

How do I do this

I tried but I think I did something wrong

This is what I did

[solar ridge]

looks like you first tried to multiply both sides by 2

which is correct, but you did it incorrectly on the left side

[deft swan]

How

Where exactly did it go wrong

By the b’s?

[solar ridge]

2*(b+b/2) != b+b

sorry i have no idea how to use the bot that makes the math look nice lol

[deft swan]

It’s okay I don’t know how to either I’m barely even getting by in math🥲

Okay so wait what did I do wrong and what was I supposed to do I instead

[solar ridge]

are you familiar with the distributive property of addition?

[deft swan]

I don’t know I study in Swedish so idk the English version of everything

Can u explain what that is

[solar ridge]

this

[deft swan]

Ohhh yes I know that

[solar ridge]

nice, so, what you pretty much did is this

you need to also multiply the first b, by 2

[deft swan]

Which b

And how

I’m so dumb I’m sorry😭

[solar ridge]

dont put yourself down

so this is what you did in the first step right?

times everything by 2

[deft swan]

Yes thats what I did

[solar ridge]

so just make sure you use the distributive property of addition when you are multiplying the 2

[deft swan]

I removed the 2 from b/2 and multiplied the 2 with 9/2

[solar ridge]

but what about the first b?

the arrow is also pointing to it

[deft swan]

Ohhhh wait so where did 2x come from

[solar ridge]

the x is just a multiplication symbol sorry

i should have used a dot

[deft swan]

No no it’s okay I just am too used to seeing x as a letter in algebra rn 🥲

So wait what happens when I do 2 times b/2

[solar ridge]

you did that part correctly, it turns to just b

[deft swan]

So the answer is b=18/2

[solar ridge]

no, you also need to deal with this b

[deft swan]

So b+b is 2b right or is that completely wrong

[solar ridge]

its true that b+b is 2b but you dont have b+b

[deft swan]

What do I have

[solar ridge]

you have to multiply the first b by 2 as well

so you will have 2b +b

[deft swan]

OHHHHHH

I thought I didn’t have to touch the b on the top

[solar ridge]

distributive property

dont forget about it

[deft swan]

Ohhhhhh

Okay so 3b is 18/2

[solar ridge]

yes

[deft swan]

Then how do I find 1b

[solar ridge]

what does 18/2 equal

[deft swan]

9

OHHHH

[solar ridge]

so you have 3b = 9

[deft swan]

ITS 3

[solar ridge]

yea

[deft swan]

Omgggg theres too many steps in algebra my head is gonna explode

Thank u so much though i definitely wouldn’t have been able to solve this myself 😭

[solar ridge]

lol

you will with some practice

bye now

[kind heath]

Bye

[deft swan]

Bye byeee

.close

[obtuse pebble]

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[gaunt helm]

can i get help verifying this identity

i'll show to where ive gotten

[brazen viper]

As a hint: you have sin^2 a in the denominator, but you want 1 + cos a

If you remember (a - b)(a + b) = a^2 - b^2, and the fact that sin^2 + cos^2 = 1, do you see a path forward?

[gaunt helm]

not really

[brazen viper]

Continue from here

And throw away everything underneath

You have (1 - cos a)^2 / (sin^2 a)

Step 1: rewrite sin^2 a using the identity above

[gaunt helm]

ohhh

[brazen viper]

Now you see!

[gaunt helm]

yes but does that result in what i have to prove

[brazen viper]

It does

You just have one more step you need to make

[gaunt helm]

ohhh

two squares

difference

[brazen viper]

✅

[gaunt helm]

ok that does it

thanks!

.solved

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[timid silo]

<@&286206848099549185>

[timid silo]

How do you use the h definition to find the derivative equation??

My function is f(x)=x^2.

[shut lagoon]

So the definition is
$$f'(x) = \lim_{h\to 0} \frac{f(x+h) - f(x)}{h}. $$
Can you plug you function in there?

[warm shale]

Azyrashacorki

[timid silo]

Yes

[shut lagoon]

And what do you get?

[timid silo]

X^2+ 2xh + h^2 - x^2

Over h sorry

[shut lagoon]

No worries!

And then the x^2's cancel out don't they?

You should be left with
$$f'(x) = \lim_{h\to 0} \frac{2xh + h^2}{h}$$

[warm shale]

Azyrashacorki

[shut lagoon]

Anything you can do now?

[timid silo]

OHHHH

OKAG THẠNK TYPI

You substitute 0 because h approaches 0 after you factor out the h

[shut lagoon]

Yes it cancels out so you should be left with 2x after substituting h=0.

[timid silo]

okay

So the derivative is 2 + 0?

[shut lagoon]

2x

• 0

[timid silo]

Oh shoot right

[shut lagoon]

The derivative will depend on x

[timid silo]

Oh ok

Thank you so much

.close

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[long crown]

This problem is for our homework, I tried to compute it but I can't seem to fully solve the equation. We were given the answer and only provide the solution. Is there something wrong with my solution and how can I improve it?

[civic socket]

looks good to me

unless if you applied the quotient rule

[long crown]

Is it possible to apply quotient rule with increment method?

[obtuse pebble]

@long crown Has your question been resolved?

[obtuse pebble]

@long crown Has your question been resolved?

[obtuse pebble]

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[pearl pine]

i’m not sure how to go about solving this question and was also wondering what type of calc question it’s classified as? (e.g optimisation, rate of change, etc)

[tame python]

find f'(1)
then use the equation for tangent line to find the y = mx + c for the tangent line
since you also know that m = -8 and c = 20, use this to solve for a and b

[pearl pine]

what does this mean 😭

[tame python]

of what does that mean

[pearl pine]

“use the equation got tangent line to fine y=mx + c” part

and solving for a and b

[tame python]

presumably youre doing it step by step

[pearl pine]

mhm

[tame python]

please do it first before asking

did you find f'(1)?

[pearl pine]

i’m assuming that’s the derivative of the function and i got f’(x)=3x^2 + 2ax +b

[tame python]

so you found f'(x) = 3x^2 + 2ax + b

now can you find f'(1) using that information

keep in mind that as a first step, you dont know a and b

so a and b will be variables that you cant get rid of, theyll be in that f'(1)

[pearl pine]

would that be f’(1) = 3 +2a +b

[tame python]

yep

now what's the tangent line equation

[pearl pine]

alright so i did do the workings to get 2a+b = -11

[tame python]

?

[pearl pine]

wdym tangent line equation

i’m a bit slow innit

😭

[tame python]

have you heard of an equation/formula for making a tangent line

[pearl pine]

would that be y-y1 = m(x-x1)

[tame python]

have you seen $y=f'(x_1)(x-x_1)+f(x_1)$ before?

[warm shale]

mtt

[pearl pine]

no ☹️

[tame python]

have you seen the same thing but with a different variable for x1?

[pearl pine]

nope

[tame python]

how did you learn this?

[pearl pine]

it’s a level two new zealand math standard i’m learning in school

it’s from a past paper

[unkempt vault]

do you know the point-slope formula for a line?

[pearl pine]

nope 😭

[unkempt vault]

the line with slope (m) that goes though the origin has equation (y = m x), right?

[warm shale]

Invariance

[pearl pine]

yes

[unkempt vault]

do you know how to do translations? like "translate this graph 3 units up and 2 units to the left" type stuff

[tame python]

its like Im suddenly not here

[pearl pine]

yes

[unkempt vault]

sorry lol

[steady tinsel]

Is this calc 1 lmao? someone was being an ass with hw lmfao

[unkempt vault]

so translate the line (y = mx) so it goes through the point ((x_1, y_1))

[warm shale]

Invariance

[unkempt vault]

i.e. translate it x_1 units right and y_1 units up

[pearl pine]

calc 2 in nz form 😔

[pearl pine]

uh huh

[steady tinsel]

that makes sense i took calc 2 over summer they didnt have enough time to give us stupid questions like this

[unkempt vault]

you end up with (y - y_1 = m (x - x_1)), or rewriting (y = m (x - x_1) + y_1)

[warm shale]

Invariance

[unkempt vault]

and that's the point-slope equation for a line

it goes though the point (x1, y1) and has slope m

[pearl pine]

mhmmmm

[tame python]

now you use this for tangent lines

[pearl pine]

i have seen that equation mb

but what would i sub in

[tame python]

if a tangent line has a slope m and passes through (x1, y1)

that would usually be enough information to pin it down to a tangent line

the slope of the tangent you calculate with f'(x1)

[unkempt vault]

remember, the slope of the tangent line is given by the derivative

[tame python]

do you know why that's the case?

[pearl pine]

nope

[tame python]

do you know how derivatives work?

or something about what a derivative should be like

[pearl pine]

nope

[tame python]

the short idea is that, for a line, theres one number that represents its slope

for example this is slope 1

now for most functions that youll be caring about, you can do the same "idea"

you can think of the derivative as "slope at this point"

so if you figure out that the derivative is 1, that means you can "zoom in" on the function

[tame python]

and see a slope of 1

does that make sense as an idea

[pearl pine]

kind of

[tame python]

heres another example

you can see the slope isnt always the same, right

[pearl pine]

yes

[tame python]

now say you zoom all the way in at (0, 0)

it looks like this

what slope does this function have at x=0?

[pearl pine]

idk 😭

man its okay, go help someone else

[tame python]

can you recognize slopes for lines?

[pearl pine]

ill just skip over this question

[tame python]

skipping over question is how you learn to fail them

lets not let that happen

[pearl pine]

we havent been taught this at school

[tame python]

so its like a diagnostic?

[pearl pine]

no

ig different forms of solving

we dont do graphing

[tame python]

m uh

you realize we're not focusing on the problem right now right

[pearl pine]

yes

[tame python]

we're not doing graphing for the problem either

[pearl pine]

i do

sigh

[tame python]

you know if they give you a question like this, youre expected to be able to answer it

but you first need to know what a derivative is

[pearl pine]

alright

[tame python]

now do you want to choose how its taught?

[pearl pine]

its up to you

[tame python]

then what slope is this line?

[pearl pine]

a positive one?? idk 😭

itd be y=mx+c

[orchid wind]

isnt it the easiest to set their derrivates equal

and then set their regular equations equal

[tame python]

we're going over what a derivative is first

[orchid wind]

oh

[tame python]

you can recognize what slope a line has from how steep it is

do you see here it goes "2" up for every "1" right?

thats the sort of steepness it has

[pearl pine]

yes

[tame python]

this way you read off that the slope of the line is 2

the slope tells you how much y changes when x changes

in this case y is twice as much as x

[pearl pine]

right

[tame python]

a line like this has a slope of 1/2

can you see how that is

[pearl pine]

yes rise/run

[tame python]

nice

now what slope would this be

[pearl pine]

no clue

[tame python]

does y change on this line?

[pearl pine]

oh wait

wait

itll just be the m value would it not?

[tame python]

do you mean that m is slope?

m is slope, yes

[pearl pine]

uh huh

like if that line had an equation itd just be y=mx right?

[tame python]

Im just asking for how steep the line is

[orchid wind]

easiest way to understand

[tame python]

I dont need its equation

the equation would need both a slope and a point

here Im just asking for the slope, or what direction the line is facing

[orchid wind]

and h "approaches 0" you get closer to the actual slope

[tame python]

the slope of this line is 0

do you see that

[pearl pine]

mhm

[tame python]

when I asked you, you couldnt recognize it

are you sure youre seeing what I mean by a slope of 0

[pearl pine]

yes

i think so

[tame python]

so what are you looking for for a slope of 0

(what kind of lines have a slope of 0)

@pearl pine horizontal lines have a slope of 0

if slope = rise/run, then a line that never rises or falls would have a slope of 0

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

what does ㅗ mean in trig? it says AH ㅗ BD

[timid silo]

<@&286206848099549185>

[amber snow]

perpendicular

[river falcon]

perpendicular

[river falcon]

also !15m

[amber snow]

which means its in a 90 degree angle

[river falcon]

!15m

[obtuse pebble]

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[fathom light]

Yes

There is a point H on BD and AH is perpendicular to BD

[obtuse pebble]

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[sullen spruce]

i can do this ez but why is it 0<=k

why not just 0<k<3

[olive dagger]

not mentioned if the given equation is a quadratic equation

[sullen spruce]

wdym

[olive dagger]

In a quadratic equation we have coefficient of x^2 should not be equal to zero

that's a part of the definition of the quadratic equation

but here it is just mentioned that the given equation is just an equation

[sullen spruce]

oh ok so it should realy be 0<k<3

because if it was 0 then it aint no quadratic anymore

[high lily]

doesn't matter if the resultant equation isn't quadratic

what happens to the equation when k=0, does that equation have any solutions

[sullen spruce]

what i got when solving the equation is 4k(k-3)<0

after is subsituted it into the discriminant and solved

[olive dagger]

that is correct but the discriminant is defined for a quadratic equation

and again the quadratic equation is defined for coefficient of x^2 equal to zero

[sullen spruce]

ig the question was wrong

[high lily]

the question is fine

[sullen spruce]

thanks for the help

[olive dagger]

you need to check it manually

[sullen spruce]

.close

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[rose scroll]

if AP bisects the yellow, it bisects the other one too

[rigid skiff]

pink

[rose scroll]

so showing either one is fine

[obtuse pebble]

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[cerulean sparrow]

Hello everyone! Can you help me find the inverse matrix using the union matrix?

[runic drift]

Idk about Union Matrix But I can find it using Elimination

[obtuse pebble]

@cerulean sparrow Has your question been resolved?

[cerulean sparrow]

Yes, let's do it this way

I think it can help me

[runic drift]

Can you find the row reduced form?

[obtuse pebble]

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[bitter folio]

i need help solving part c for this question. I was able to solve part a and part b of this homework assignment but i am unable to solve part c. can some please guide on how to?

[timid silo]

u solved the integral ?

[tardy epoch]

Show your work for parts a and b

[bitter folio]

ok

[tardy epoch]

!ss

[obtuse pebble]

Please post images (such as PNGs or JPGs) of the question rather than other filetypes such as PDFs which have to be downloaded. Non-image downloads can potentially contain viruses or other security risks.

[bitter folio]

ok ill adjust and send again

its there on chegg but i dont have it

[tardy epoch]

Do you know fundamental theorem of calculus

[bitter folio]

yes

the lim as x -->0

[tardy epoch]

No

That's a limit

,tex .FTC1

[warm shale]

[bitter folio]

oh ok

yea this i get

[tardy epoch]

Use this to find A(t)

[bitter folio]

ok

[tardy epoch]

And I guess A(0)

[bitter folio]

thank you

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[cold brook]

can I please get help with this

[cold brook]

this is what I did

z = 1/2(e^iw + e^-iw) + 1/2i (e^iw - e^-iw)

took e^iw and e^-iw comman

and trying to get rid of i in 1/2 i

but idk how to do that

[tardy epoch]

Maybe try using i=exp(i pi/2)

[cold brook]

so this is what I am getting:

e^iw(1/2 + 1/2i) + e^-iw(1/2-1/2i) = z

should i sub i = e^ipi/2 in place of 1/2 i ?

when i do that

i get

1/2(e^iw + e^w + e^-iw -e^-2ipi/2)

i think i am doing something wrong

[tardy epoch]

This looks fine

Just combine the real parts together into an A

And factor out an i in the exponent form the rest

[obtuse pebble]

@cold brook Has your question been resolved?

[cold brook]

I am having trouble doing that

[tardy epoch]

Only the terms in the exponent that don't have an i are real

[cold brook]

yea so I get something like

R(e^i + 1 -e^-i) - Be^-2i
where R = 1/2 e^w
B = e^pi/2

[tardy epoch]

Why do you have a difference

Oh nevermind I see it now

[tardy epoch]

This isn't the right exponent

e^(iw) + e^w = e^w ( e^(iw-w) +1)

[cold brook]

so this becomes:

1/2(^w ( e^(iw-w) +1) + e^-iw -e^-2ipi/2) but i still have e^-2ipi/2 term

[tardy epoch]

You messed up after this

[cold brook]

oh

[tardy epoch]

The i=exp(ipi/2) should be used in two places

[cold brook]

oh

,rotate

[cold brook]

@tardy epoch i am getting this now

[obtuse pebble]

@cold brook Has your question been resolved?

[tardy epoch]

How did e^w magically appear in the numerator

You really need to be more careful with your basic exponent rules and algebra

[cold brook]

wait you mean here?

.close

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[safe stirrup]

Quick question : What does this Mirrored E means? Can't find where in my notes we have talked about this...

[restive gorge]

there exists at least one

[safe stirrup]

Ehh boy, dunno where I could've covered this in set theory. Thank you.

[restive gorge]

,w there exists

[warm shale]

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[safe stirrup]

Perfect, thank you.

.close

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[bitter gust]

Could someone please assist me with this?

[restive gorge]

Well basically I would take a look at the vector space axioms and briefly explain why it should be a vector space or not

[obtuse pebble]

@bitter gust Has your question been resolved?

[bitter gust]

Is this one not a vector because it doesn't satisfy the 0 vector?

[restive gorge]

react here

[restive gorge]

the null function satisfies the properties of being odd actually.

n(x) = 0
then n(-x) = 0 and -n(x) = -0 = 0

[bitter gust]

Hmm, but the zero polynomial must be in the set for it to be a vector space. However, the zero polynomial is of even degree and it does not satisfy the requirement of being an odd-degree polynomial.

The degree of 0 as a polynomial is 0?

So it's not a vector space?

[restive gorge]

but the question is if we go by the definition of an odd function

the nullfunction satisfies that

sin(x) is also an odd function

now which degree does sine have

[bitter gust]

Isn't it only talking about it being of odd degree tho?

[restive gorge]

even though it's not a polynomial

oh

you are right

yes

there should be this very subtle but crucial difference

between odd degree polynomial and odd function

then by that it doesn't have a neutral element and it shouldn't be a vector space

[bitter gust]

Yeah that's what I was confused about when you said function lol

[restive gorge]

I just read the degree of the nullfunction is not 0 but -inf wtfffffffffffff

oh a matter of definition

[bitter gust]

Uh

So the conclusion is... It is indeed not a vector space? Lol

[restive gorge]

yes

that would be my take

seems it justs causes trouble

[bitter gust]

Gotcha thanks

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[wary badger]

yes

if you mean something like for all x …

because the negation would be there exists x such that …

if that’s true then the original is false

yea sure

you can consider the negation first

and then conclude that the original is false

yea i wouldn’t

you can though of course

sometimes if it’s a true or false sort of question you might want to start out by saying if it’s true or false

so the grader knows

immediately ya know

it’s personal preference i guess

you’re welcome

[obtuse pebble]

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[surreal quiver]

can somebody verify if this proof is valid?
my friend thought of a math problem and i put it into o1

You have a grid of lattice points that consists of 2 rows and N columns. For each point in the top row, you arbitrarily draw a path to connect to a separate point in the bottom row such that each point in the top row uniquely connects to a point in the bottom row, the path you draw never goes up (so you can draw the path going side to side), and no more than two paths intersect. Now for each point in the top row, retrace its path down to the bottom row, except every time you hit an intersection of two paths, trace the intersecting path. Prove that if you perform this operation on any point in the top row, you'll always end up at the point in the bottom row directly below it in the lattice grid.

[surreal quiver]

i already solved it before with induction

but i cant tell if this works too

also idk if i wrote the problem clearly enough either

[obtuse pebble]

@surreal quiver Has your question been resolved?

[obtuse pebble]

@surreal quiver Has your question been resolved?

[obtuse pebble]

@surreal quiver Has your question been resolved?

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[zenith sentinel]

How to find determinant of matrix 4 x 4?

[worn yoke]

cofactor expansion or row operations

[zenith sentinel]

I don't understand

[worn yoke]

how were you taught to take determinants of 3x3 matrices?

[river falcon]

the same way you do for 3 x 3 matrix

[zenith sentinel]

I know, there should be another way

[obtuse pebble]

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[zenith sentinel]

.close

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[pliant nacelle]

If 2 half of y be able to exceed 3 half of x when x is in its normal variable to cooperate with this equation I'm setting, what leftmost value can you get when the independent value of x keeps going left on a number chart, what prove can we gain from this right equation?

[last pilot]

okay i cannot understand what you've written there.

[obtuse pebble]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

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[autumn knoll]

Hello

[autumn knoll]

I'm trying to understand the proof of an article, but there is one step that I don't understand where it comes from.

It is not clear to me where W comes from, the way it was built.

[brave bramble]

They may not be telling you how W was discovered here. How does the proof continue?

[autumn knoll]

I need to understand the whole test and that W, I don't understand how it was constructed.

<@&286206848099549185>

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[snow patrol]

i know technically chemistry but i swear every time i input this its one decimal off (624.21973)
am i tripping balls or is the sample i was given wrong 😭

[river falcon]

you're right, it should be 624.21973

[obtuse pebble]

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[bright jewel]

Middle is 4cm2

[bright jewel]

So 2 cm is a side

Idk how

[marsh geyser]

You mean you don’t know how is it 2cm?

[obtuse pebble]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[bright jewel]

I gotta calculate the whole area

I don’t know how

[river falcon]

nothing else is given?

[bright jewel]

Yes

[marsh geyser]

You better give more information

[bright jewel]

There’s no

[rose scroll]

Everything is a perfect square?

[bright jewel]

It’s just like this

[bright jewel]

Yes

[marsh geyser]

That is more information

[bright jewel]

There’s not it’s just that middle is 2 by 2 and everything is perfect square

[rose scroll]

knowing all the primitive quadrilaterals are squares is sufficient to solve this.

you can start by naming the sides of all tthe squares

[bright jewel]

Uh…

[bright jewel]

How do I do that

[feral urchin]

idts you can solve it by this much info

[bright jewel]

Wait I think I got it

Idk how to explain it nvm

I think I got it though

[fathom light]

[bright jewel]

.close

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[feral urchin]

how do i begin?

[nova vale]

hi

what class is this

[feral urchin]

12

[nova vale]

gl

i can't solve it

[feral urchin]

hm

[marsh geyser]

I mean, the hint is very powerful and solves the integral immediately

I am not sure how to say without spoiling it

[feral urchin]

i got it now

[marsh geyser]

That is perfect

[feral urchin]

divided everything by cosx

[marsh geyser]

What do you get after that

[feral urchin]

nah wait i didn't get anything lmao

[marsh geyser]

You are in the right way

But cosx is not the right choice

[feral urchin]

cosx.tan^2x in Nr

[marsh geyser]

Cos^6x instead of cosx

[marsh geyser]

I mean this

[feral urchin]

oh but why? for the Dr?

[marsh geyser]

Unless i made a mistake…

Let me check

,w ((cos^2xsin^2x)/(cos^6x))

[warm shale]

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[marsh geyser]

,w ((cos^3x+sin^3x)^2/cos^6x)

[warm shale]

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[feral urchin]

def not this

[marsh geyser]

Yes, wait

,w is ((cos^3x+sin^3x)^2/cos^6x)=(tan^3x+1)^2?

[warm shale]

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[marsh geyser]

Yeah i thought so

You can continue from here

[feral urchin]

this is the given sol

idk how

[marsh geyser]

Ok but to reach to that integral u have to do what i just did

Wait u can get that by cosx, but i thought it was easier by cos^6x

I guess is the same

You have to do some identity proofs to work on this

Without that u will have a lot of problems to find out

[feral urchin]

aah

can you tell me which ones
i suck at trigo

[marsh geyser]

Just do the kind of… prove this = that

That helps a lot in this kind of integrals

Also, the proofs try to do from one side or from other side, without using both sides (in general)

[feral urchin]

btw i also did by expanding the square in Dr

[feral urchin]

oh okayy

[marsh geyser]

The sub is faster

[feral urchin]

got 1+2cos^3xsin^3x

[feral urchin]

yeah right

[feral urchin]

idk how to do it from here

[marsh geyser]

,w is (1+tan^3x)^2 = 1+2cos^3xsin^3x?

[warm shale]

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[marsh geyser]

How did u get that?

[feral urchin]

it was in Dr

imma leave it for now

.close

[obtuse pebble]

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[ionic sphinx]

help with 6 and 7

[ionic sphinx]

@junior granite

pls sum help

[shadow dagger]

for 6, sps they are, then square both sides and arrive at a contradiction

7 is a bit...odd

[ionic sphinx]

wait start with 6

[shadow dagger]

so sps for a contradiction that there existed such numbers $x$ and $y$ with $\sqrt{x+y}=\sqrt{x}+\sqrt{y}$

[ionic sphinx]

so we assume they are not posituve real numbers?

[warm shale]

LY

[shadow dagger]

then square both sides to work out what our hypothetical $x$ and $y$ are

[old lily]

absolutely not

[warm shale]

LY

[ionic sphinx]

so we assume the equal sign works'

then we get x+y on both sides right?

[shadow dagger]

what does (a+b)^2 equal?

[ionic sphinx]

a2 +2ab + b2

[shadow dagger]

for 7, i guess we just do by exhaustion?

but that just kinda is true because $\mathbb{R}$ is an integral domain

[warm shale]

LY

[ionic sphinx]

did i do right on 6?

[shadow dagger]

you get x+y+2sqrt(xy) on RHS

[ionic sphinx]

ya i realised forgot the xy term

[old lily]

not even close

[ionic sphinx]

so xy = 0

[old lily]

yes, then appeal to 7

[ionic sphinx]

alright so for 7 we do the same?

[old lily]

what

it's a completely different question

depends how you define R but ig appeal to field axioms

[ionic sphinx]

ok so what we do

but if a and b are two diffrent numbes they cant multiply to get 0 right?

@old lily

[old lily]

don't ping me

[ionic sphinx]

aight

any tips for the question though?

[shadow dagger]

given the context, i think they might just want you to go "if x and y are greater than 0, then xy > 0"

etc.

but it's a bit dumb

[ionic sphinx]

thanks LY, your a lifesaver

ya zuc if x and y is 0 it is ofcourse that xy is 0

if xy=0 there is no two numbers who can get zero yk

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@runic estuary Has your question been resolved?

[red ice]

so for the average speed, first find the total distance travelled

so that's 27.4 * 3

,calc 27.4 * 3

[warm shale]

Result:

82.2

[red ice]

ohokay

well the difference with velocity is it's now displacement/time

displacement = final position - starting position

so just 27.4 m

third base is 27.4 m away from home base

and then the time taken is the same as in part a

orientation is direction, so say northwest

yep!

apologies for the colours

no that's different

it just says the distance between the bases is 27.4 m

the hypotenuse is already 27.4

imagine the green arrow in the picture I sent

for displacement it doesn't matter how they travel

it just matters:

1. where they start
2. where they finish

1. velocity is displacement/time
2. displacement is distance from third base to home base, so 27.4 m
3. time is the same as in part a

that's all the working you need to show for the magnitude of the displacement

then just look at the diagram, northwest

for the orientation

or you could write the bearing, that would be 315 degrees

yes that's wrong

okok

ye

$\Delta (distance)$ doesn't make sense

[warm shale]

south

[red ice]

yeah don't write down something you don't understand

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@runic estuary Has your question been resolved?

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[short compass]

Can someone help me with finding the range of an rational function the numerator and denominator had a both quadratic idk how to find it

[obtuse pebble]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[short compass]

y= 3x²-7x+2/x²-4

[fathom light]

Do you know how to factorize quadratic equation?

[short compass]

Yes but I can't on numerator

I can't solve trinomial

The deno is x+2 and x-2

[fathom light]

3x²-7x+2?

[short compass]

Ya

[fathom light]

Well you can try finding roots in lengthy way (-b±√D)/2a

[short compass]

K I will try

[fathom light]

Or if you want to factorize, find 2 numbers whose multiplication will be 3 * 2 and whose addition/subtraction will be -7

[short compass]

It's 2 and 1/3

[fathom light]

Yeah both are positive?

[short compass]

Yes

[fathom light]

So your factorisation will be
(x-2)(x-⅓) in numerator

[short compass]

Ok

[sturdy arch]

Tbh graphing can solve every problem

[fathom light]

Well for range usually numerator doesn't matter, we need to make sure denominator is not 0

[short compass]

Ok so the numerator is the answer to finding the range of an rational function when the two are quadratic?

[fathom light]

Denominator is actually, numerator can become 0 but denominator should not become 0

[short compass]

Ok thanks

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[covert oyster]

H

[obtuse pebble]

Please don't occupy multiple help channels.

[covert oyster]

Hi

idk what to do at all

[last pilot]

please don't DM me

[covert oyster]

No one is it’s ok

[last pilot]

what...?

[covert oyster]

huh

[obtuse pebble]

@covert oyster Has your question been resolved?

[obtuse pebble]

@covert oyster Has your question been resolved?

[covert oyster]

<@&286206848099549185>

[obtuse pebble]

@covert oyster Has your question been resolved?

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[sand python]

I only made it till 6 here is my work for that

I am confused on if I got the bearing correct, and also how I find the y on part 3 for the position

This is my work

<@&286206848099549185>

[obtuse pebble]

@sand python Has your question been resolved?

[sand python]

<@&286206848099549185>

[craggy zephyr]

is that edexcel IAL?

[sand python]

Idk

It is something my professor gave me

the course I'm doing is Pearson myLab

[jolly light]

wsp abhi

hows ur day

[sand python]

It's alright ig

[obtuse pebble]

@sand python Has your question been resolved?

[sand python]

<@&286206848099549185>

[sand python]

<@&286206848099549185>

[tardy epoch]

That's a lot to read. It's better to upload just one problem at a time with your work for that one problem

[sand python]

Alright yeah but I am really only confused on step 3 and 6

which depend on the previous steps

[obtuse pebble]

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[vivid salmon]

It's asking me to prove this is true

[vivid salmon]

But it's literally not provable

But my textbook said it was and it's trying to do

x^2+2 = x(x+2)

Like what. Am I wrong or..?

[worn yoke]

i believe there is a typo, and that it is supposed to be x^2 + 2x

[vivid salmon]

But the equation itself

is wrong

?

That u cant prove it because

the question is wrong

[worn yoke]

it's wrong as written, yes

[vivid salmon]

okay thank you i was just making sure

becuse the textbook gave such a dumb answer

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[winter citrus]

how is this not a polynomial function

[light flume]

it is a polynomial no?

i dont see why it wouldnt be

[surreal oriole]

no

its the same as 5x so I think they would say it's a bionomial

[alpine bison]

xy is a binomial innit?

[waxen night]

it's a polynomial for sure. polynomial have terms>=0 iirc

[alpine bison]

5x is a monomial

[alpine bison]

.

[winter citrus]

hmm yeah thats what i thought too but the answer key says it isnt

ill ask my teacher about it though

answer key might be wrong

[quaint glen]

it is a polynomial 🙂

monomials and binomials are specific types of polynomials

by the vastly used definitions of those terms

i doubt your class is using a different definition, but its possible

talk to your teacher about it

[surreal oriole]

my bad I thought you were asking if it is a trinomail, yeah its a polynomial

[obtuse pebble]

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[echo nest]

Why would this be an infinite limit (therefore DNE) - I get that it's DNE, but isn't sqrt(x^2 +) irrational?

[echo nest]

Looking at #30 here

[quaint glen]

who cares if its irrational

[gilded needle]

moreover, it's not always irrational, depends on the value of x

[quaint glen]

^^

[echo nest]

So how do I know that it's an infinite limit?

[coarse ibex]

sqrt(x^2+1) > sqrt(x^2) = |x|, and |x| certainly goes to infinity as x goes to infinity.

[echo nest]

Where does the +1 go?

?

[obtuse pebble]

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[errant sonnet]

i need help 😦

[restive acorn]

So

Let's say you have log base 2

Log2(x) = 2

An interesting mechanic of logarithms is that you can "cancel them out" by turning them into exponents

Pick a matching base

In this case 2

Then i can say

2^(log2(x)) = 2^(2)

Then the 2^log2 cancels; you get

x = 2^2

x = 4

@errant sonnet let me know if that example offers some clarity

[errant sonnet]

not really

how does the log get cancelled out?

like by what

[restive acorn]

Logarithms are like the opposite of exponents

Doing 2^x is the opposite of log2(x)

The same way adding and subtracting are opposite

If i do

x + 1 - 1

I get x

If I do

log3(3^x) = x

And the opposite

3^(log3(x)) = x

If you pick the same "base" for the exponent as the logarithm you can cancel them out

[errant sonnet]

so in my case ill have to write n^log7=-1/2

?

is that wring

@restive acorn

[restive acorn]

Other way around

7 to the power of log

And do the same to both sides

If

x = 5

Then

7^x = 7^5

That's the argument you make

Make both sides of the equation the exponents