help-13

[versed elm]

Hello

[versed elm]

What would it be? I find all the answers similar

[steel stag]

I think it's to do with the units they use

[versed elm]

How do I see what's wrong based on the units

[steel stag]

Notice that all of the examoles have consistent units except one

[versed elm]

70 merchandise?

Oh

Wair

[steel stag]

Well if you evaluated the integral, the integral assumes consistent units for the rate and the bounds of integration

So you would get the number 560 from the integral, but this is not correct for one of the options

[versed elm]

Yea so there isn't units for the rate for merchandise right

Sales option

[steel stag]

Not quite bc the meechandise example is per hour and gives a number of hours

The unit of rate for that one is dollars per hour and time is in hours

[versed elm]

I find all the option right except the last one I just don't understand the wording

[steel stag]

Explain to me how the first option would give a distance of 560 miles

[versed elm]

70x8

But that's wrong no?

[steel stag]

What is time measured in there

[versed elm]

8 is in mins

[steel stag]

Yes, and the speed

[versed elm]

Hts

Hrs

[steel stag]

So you need to convert something

[versed elm]

Yea

[steel stag]

For the calculation to be correct

[versed elm]

Yea

[steel stag]

So it will not give the number 560

[versed elm]

Yea

Not 560

[steel stag]

So imo, that is the only one where the number of the answer is not 560

[versed elm]

Ohh

Since in order to get the right answer we must convert

[steel stag]

Yes, so thendistange would be a different number to 560 so is not representdd by that integral

[versed elm]

Yea ty

Also can i show u one more question

[steel stag]

The integral would have to be adapted so the units are consistent for that example

Ok

[versed elm]

So I know the ans is in between 2 or c

But idk when the abseer should have t in the integral

[steel stag]

What unit is the speed measured in the question as it is cut off

[versed elm]

Cut off?

[steel stag]

In the image

[versed elm]

Mph

[steel stag]

Ok thats fine

So think about it, if you had to calculate this distance without an integral, what would you do?

[versed elm]

Find antiderivative?

[steel stag]

I mean using a reall simple formula that you know

No calculus

[versed elm]

S times t

[steel stag]

Yeah d=st

[versed elm]

Yea

[steel stag]

So there you are multiplying the speed by the time taken. Which integral option will give you an equation like that after you actually integrate?

[versed elm]

C?

Antiderivative right

[steel stag]

Yeah C, why not option 2

[versed elm]

Cuz that would give us uhh like acceleration? Idk

And c will give us speed?

[steel stag]

Yeah sort of, you will end up with a quadratic in time, the coefficient of which, you are right, what you would be an acceleration to keep the units consistent to give distance.

[versed elm]

So 87t is the equation for speed?

And 87t^2/2 is acceleration

[steel stag]

Option 2 has a speed coefficients multiplying time squared after integration

In any case,87t^2/2 is not a valid acceleration, the acceleration is 0 here bc speed is constant

[versed elm]

Hm

In what situation would 87t be the answer?

Option2

[steel stag]

No situation as 87 multiplied by time has inconsistent units with what the integral should give which is distance

[versed elm]

Hmm

[steel stag]

If 87 was an acceleration, then integrating twice to get distance would be valid

[versed elm]

And integrating once would give speed right

[steel stag]

You are right, After one integration you would get v=at+u

After two you would get d=1/2 at^2+ut+c

[versed elm]

I'm still a little confused

How would you know what their asking for?

For the question i posted it only said express the situation as an integral

[steel stag]

They are explicitly asking for distance and you are told 87 is a speed, so it cannot be multiplied by time as v times t already has units of distance before integration

[versed elm]

So distance would be 87t as the answer tho right

[steel stag]

87t is an expression with units of distance, which is then integrated to get a unit of km s not km so this does not have much meaning

87t is the correct expression after integration, not before

[versed elm]

Okay

[steel stag]

,,\int_{0}^{t} 87 dt = 87t

[wraith dagger]

Social Capital Gainer

[steel stag]

Which is consistent with the distance formula

[versed elm]

Okay to summarize 87 is speed and integral of that 87t is distance

[steel stag]

Yes, the integral has the effect of adding a unit of time onto the thing inside it, in this case it multiplies a time unit onto a speed to give a distance

[versed elm]

Okay

Also

For time based if it says 6pm to 7:30pm, is the integral output going to be 6 in the bottom and 7.5 on top?

[steel stag]

Yes, this matters even more when you integral is not a linear function

[versed elm]

Yea

[steel stag]

But you are right from 6pm to 7.30 so 6 hours is the lower limit or whatever number given when timenis measured from

[versed elm]

And 7.5 is the upper

[steel stag]

Yea

[versed elm]

Okay okay

One last question

This one is tricky(for me)

I thought it was a

[steel stag]

Is your new answer D?

[versed elm]

Welllll still Haven't decided

Not sure which unit of time should go where

[steel stag]

The fact you haven't chosen a 25t integral is correct

[versed elm]

Yea

[steel stag]

Not valid for this scenario

So what unit of time is the rate given in?

[versed elm]

Min

[steel stag]

And what unit of time is the specified time in?

[versed elm]

1

Okay I think its a

[steel stag]

1 what

[versed elm]

1 hour

[steel stag]

Not mins

[versed elm]

Yea

[steel stag]

They need to match remember

So what integral has these units matching

[versed elm]

Matching?

[steel stag]

Min in the rate and min in the time

Or hour in the rate and hour in the time

[versed elm]

D

[steel stag]

Yes

[versed elm]

Oh

They have to be matching for every question?

Like hrs to hrs min to min

[steel stag]

Yes

Otherwise the rate doesnt make sense

[versed elm]

I still don't understand in what kind of question there would be a t next to the value

[steel stag]

We could say anything

Ok so let me address two things

First of all, are you ok with units multiplying

[versed elm]

Yea

[steel stag]

So if I have 25 A per B and I multiply this rate by 2 B, then the result is 50 A, where A and B are arbitrary units. A could be miles and B could be hours for example

[versed elm]

Okay

Is this leading to something

[steel stag]

So looking at just the units the rate is miles/hour and time is hours, so miles/hour×hour is miles, the hours cancel

Yes it is

[versed elm]

Yea it cancels

Soo

[steel stag]

So when we integrate

This adds an hours unit (or whatever time unit) onto the expression inside the integral before integration. Therefore whatever is inside, if it has units of volts (V) for example, the units after integrating with respect to time will be volt hours (V h)

So if our expression in side the integral already has units of distance, not of speed, the resulting answer will have units of miles hours not miles

[versed elm]

Hmm okay

[steel stag]

I mean miles hours (mi h) not miles per hour (mi/h)

[versed elm]

Miles hours is speed right

[steel stag]

This is becase it gets one hours unit from the t and another from integration, but speed is just miles/hour, one of the hours cancels and the other is multiplying the distance

No speed is miles per hour

Miles hours is distance multiplied by time, this does not have any meaning

So it goes

,, \frac{miles}{hour}\times hour\times hour

[wraith dagger]

Social Capital Gainer

[versed elm]

Okay I kinda get it

[steel stag]

One hour from the t already in the integral and the other from the integration process itself

Miles hours is not distance which is just miles

We want

,, \frac{miles}{hour}\times hour

[wraith dagger]

Social Capital Gainer

[steel stag]

Where that single hour is from the integration process only

If we had an acceleration however

Then we would need to integrate twice, this puts two hours to cancel with the two on the denominator, so we get a distance

I.e.

,, \frac{miles}{hour^2}\times hour\times hour

[wraith dagger]

Social Capital Gainer

[steel stag]

Where miles per hour^2 is the unit of acceleration

But we are only dealing with speeds so we have only a single per hour to cancel hence integrate only once

[versed elm]

Yea

Okay I think im good now

[steel stag]

Oke, I hope that was useful, be sure to speak to your teacher for more info on handling units

[versed elm]

Yep ty for all the help, surprising since my teacher doesn't cover a fraction of this in class. Ty btw

[steel stag]

Hmm, oke, speak to them anyway though

Bye now

[versed elm]

Bye bye

.close

[cedar kiln]

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[boreal lichen]

Calculator?

[rocky sand]

My calc doesn't give it in exact form

Isn't there a way without using a calculator

@boreal lichen .

[cedar kiln]

@rocky sand Has your question been resolved?

[haughty wyvern]

here is my working out lmk if my handwriting isnt legible ill rewrite it😭

you gotta use ur trig identities for this question

sec^2(x)=1+tan^2(x) and 1+cot^2(x)=cosec^2(x)

[rocky sand]

Thanks a lot but how tf do i know when to do this or what identities to use?

[haughty wyvern]

since it is asking for exact values of ur trig i just assumed it would be an identity question

also if u were to plug that into ur calculator u wouldnt get it in the rational number form

[rocky sand]

What's rational number form?

[haughty wyvern]

so like sqrt(2)

it wouldnt say sqrt(2) on ur calc it would give it as it is

[rocky sand]

For tanA is it negative or positive btw bc it shows it as -2root2 as the answer

[haughty wyvern]

ohh shit

i think i made a mistake somewhere mb

[rocky sand]

Did u do a levels btw

[haughty wyvern]

yh im in yr 13 rn lol

[rocky sand]

Oh lol makes sense I'm doing a gap year rn to do maths and it's longgg I hate trig

[haughty wyvern]

yh icl trig is bare long

its just a matter of sweating questions thats how i got good at trig

[rocky sand]

Yh ig I left it too late tho so I don't really have time to do plenty of questions

[rocky sand]

Did u find ur mistake btw

[haughty wyvern]

nahh actually

i mean my answer for tan a would be +- 2sqrt(2) but i acc dont know why they took the negative value

[rocky sand]

Maybe it's something to do with A being obtuse

[haughty wyvern]

oh

u didnt show that in the image😭😭

[rocky sand]

I showed the whole question lol it says pi/2 < A < pi

[haughty wyvern]

ohh shit yh

omds im on smthn mb

[rocky sand]

😂😂 it's cool lol but why does being obtuse make it the negative one

[haughty wyvern]

when cosine is greater than 90 degrees, ur values become negative so im assuming thats why it is negative

[rocky sand]

Oh

I think I kinda get it

Thanks for your help btw

[haughty wyvern]

np

[haughty wyvern]

it prolly explains why better in the pearsons book but i dont have it on me rn

[rocky sand]

And gl with your exams only couple weeks left but you're probably already ready since u helping others on here lol

Naa the book is ass it barely shows any working out

[haughty wyvern]

icl im sorted for maths and physics im only stressing abt further maths😂

[haughty wyvern]

yh icl the book can be dead sometimes

[rocky sand]

Damn u doing further maths clever guy

I dont like physics either ngl lol I got a C on that shit

[haughty wyvern]

im only tryna get a b so im chilling with physics

icl tho further maths is only cancer ccause revising it is so long

[rocky sand]

Yh I got curious once and I checked some of it and it's long

But it's kinda interesting too yk

[haughty wyvern]

yhh

u should look into some of the topics in the holidays icl its bare interesting

specially if ur gonna do smthn engineering based anyway the first year is basically further maths only

[rocky sand]

Yh I will for sure but for now I just gotta try and cover everything for these exams lol

[haughty wyvern]

yhh gl with them tho

[rocky sand]

I'm doing comp science so won't be too relevant

What u doing tho ? Engineering?

[haughty wyvern]

yh prolly not

[haughty wyvern]

yeah hopefully mechanical engineering

[rocky sand]

Thanks imma need it

[rocky sand]

Okay I don't know much about that but sounds hard lol

[haughty wyvern]

you should look at D1 if u do cs its got algorithms u do i think

like bubble and quick sort

[haughty wyvern]

idek either lowkey😭

[rocky sand]

Thanks I'll check it out sometime

[rocky sand]

Lmaooo same with cs for me 😂😂 I'm just doing it cuz of the money

[haughty wyvern]

broo swear im moneyt motivated too😂😂

[rocky sand]

Loool as long as it's stem it sounds good to me 😂😂 fr tho we bouta make bread in the future just gotta endure like 3 years of sleepless nights esp u I hear a lot of engineering horror stories

[haughty wyvern]

yhh just gotta firm uni for 3 years then we're sorted

[rocky sand]

Yessir but thanks for the help tho i appreciate it. can i just dm u if I have another q bc sometimes i don't get an answer in these chats

[haughty wyvern]

yh sure

my applied is lacking lowkey but feel free to ask for pure maths help

[rocky sand]

Thanks g I'll try to keep them to a minimum too

[haughty wyvern]

nahh dw send as much as u need

it doubles back as revision for me too so idm lol

[rocky sand]

Oh shit okay then lol thanks a lot

[haughty wyvern]

np man

[rocky sand]

Ayt I'll close this then

.close

[cedar kiln]

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[fluid pelican]

Hi! I am trying to prove that a Taylor approximation of an even function where n=3 is a binomial. I have tried simplifying the derivatives to their main definitions but that didn't really work since all I get is f(x)-f(0). What can I try? Thanks for the help

[lament elbow]

what does it mean for a function to be even?

[fluid pelican]

when f(x) = f(-x)

so your classic parabolas, 4th degree, and so on

[lament elbow]

great

may i ask what class this is for?

[fluid pelican]

btw, the x0 for this taylor sequence is 0

[lament elbow]

is it calc 2 or advanced calc/analysis

[fluid pelican]

It is school calc but we kinda work on a weird programm

Our topic is exponential functions/taylor/l'hospital

and we continiue integrals

wait, the derivative of an even function at 0 is 0

I think we had something about the derivatives changing their evenness/oddness as the derivatives progress

[steel stag]

So you are looking to show that the approximation up to the f'''(0)/3! term has only two terms

Yes the first and third derivatives will be 0

[fluid pelican]

oddness is when f(-x) = -f(x)

[fluid pelican]

three, $ax^2+bx+c$

[wraith dagger]

Chara_Jay

[lament elbow]

That’s a quadratic

[fluid pelican]

yeah

[lament elbow]

Not a binomial

[fluid pelican]

I am trying to translate german terminology here, it is a hit or miss

[steel stag]

Is that what you mean when you say binomial

[fluid pelican]

I mean the quadratic, sorry for the confusion

[steel stag]

Thats alright

But ye, after cancelling the 0 derivatives you are left with f(0) + f''(0)x^2/2 as the approximation

[fluid pelican]

but even then we cannot shorten the terms if f(x) is a polynomial of 4th degree, am I correct?

So we do not get the quadratic form anyway

[steel stag]

Not without more information about f I think, do you know what it is supposed to look like in the end?

[fluid pelican]

like this, but i have no information on f except that it is an even function

[lament elbow]

try a weirdish example

[steel stag]

Well have we not achieved that

We have a quadratic

[lament elbow]

what is the 3rd taylor polynomial of $$f(x) = cos(x) + sin^2(x) + 1$$

[wraith dagger]

JamesH

[fluid pelican]

lets say that f(0) is a constant, then we do have a quadratic

[steel stag]

Why wouldn't it be a constant? It is evaluated at 0

[fluid pelican]

yeah

[steel stag]

I think that you can take f(0) and f''(0) as constants as they will be numbers dependent on the choice of f

So we have a quadratic of the form a+bx^2

[lament elbow]

i think your binomial interpretation was actually the correct one

[fluid pelican]

no, the formula is there, so i am sure they ask for a 2 degree polynomial

so like there is x^2 and that is the important thing

[steel stag]

a trinomial is a quadratic that looks like ax^2 + bx + c

[lament elbow]

but a stronger claim also holds true

of it being a quadratic binomial

[fluid pelican]

yeah

I am gonna have to ask for context for that one

[steel stag]

I don't really see where else we can reasonably go tbh

[lament elbow]

can you take a screenshot of the question? even if its in german thats fine

[fluid pelican]

yeah, me neither

[fluid pelican]

I have it in paper format

[lament elbow]

a picture is also fine

[fluid pelican]

1a

[lament elbow]

,rotate

[lament elbow]

i see

so what you need to show then is that the 3rd taylor coefficient = 0

[fluid pelican]

and the first one? That is 0 as well though

[lament elbow]

right, but you dont need to show that to prove this

that would be to prove it is a binomial

you only need to show there is no cubic term

[fluid pelican]

okay

[lament elbow]

i.e, that $$f^{(3)}(0) = 0 $$

[wraith dagger]

JamesH

[fluid pelican]

We can assume the laws to prove that, so that should be easy

I think we cannot do anything else here, I will ask my classmates for their solution for context

[lament elbow]

you need the fact that the derivative of an even is odd, and the derivative of an odd is even

[steel stag]

Tou can show this using the same method as for f'(0)=0 just repeat

[lament elbow]

i dont know if you can just use that or if you need to prove it

if you need to prove it, you would need the limit definition of the derivative

[fluid pelican]

exactly, we had the fact that evenness/oddness changes up based on the degree of the derivative

[fluid pelican]

we had that on an exam so we can assume that

[steel stag]

f(x)=f(-x) diffentiate both sides three times, you will need the chain rule on the right

[fluid pelican]

Yeah. Then, I think we are done? Thanks a lot for the help!

[steel stag]

No problem!

[fluid pelican]

.close

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[haughty wyvern]

1 multiplied by b^7 is b^7

[wanton bison]

Why does the b7 replace the 1?

But why does it go there though

[haughty wyvern]

wait ill try and write it maybe it might be easier

[wanton bison]

Thanks

[haughty wyvern]

Lmk what doesn’t make sense

[wanton bison]

Oooh

I get it now

[haughty wyvern]

i miseed a 2 at the bottom on my last line mb

thats better

[wanton bison]

Thank you so much

.close

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[mental ember]

we have a right triangle and lets say the hypotenuse is c and the height against the hypotenuse is h. h/c=2/5
find the ratio between the two cathetus

[cedar kiln]

@mental ember Has your question been resolved?

[mental ember]

<@&286206848099549185>

[cedar kiln]

@mental ember Has your question been resolved?

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@mental ember Has your question been resolved?

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[tawdry shell]

<@&286206848099549185> hii is possible to simplify x/2?

[obsidian coral]

You have to wait at least 15 minutes before pinging helpers

[tight herald]

• After 15 minutes, feel free to ping @Helpers.

[obsidian coral]

And no, it's not

[tight herald]

0.5x is another way of writing, but otherwise no

[cedar kiln]

@tawdry shell Has your question been resolved?

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[tawdry shell]

<@&286206848099549185> hi sorry for asking again, how do you simplify 1/2x^2/3?

[obsidian coral]

You have to wait at least 15 minutes before pinging helpers

So stop prematurely pinging helpers, you did it twice already

[crimson sedge]

what is 4(2x+10)+4(y+10)=?

[crimson sedge]

how did you get 40

4x10?

[latent flame]

simplifyng:

[latent flame]

exactly

distributive

[crimson sedge]

too big of a word

i dont know what that means

[latent flame]

XDD

[obsidian coral]

One, this channel was occupied already, meaning don't clutter it by helping someone who interrupted
Two, don't do the work for people

You teach the person and assist along the way

[latent flame]

https://www.youtube.com/watch?v=AtBUQH8Tkqc Might help

[obsidian coral]

Give hints

[latent flame]

My bad

I'm kinda new here

[obsidian coral]

Then you should read #❓how-to-get-help

[crimson sedge]

i messed up. its 4(2x+10)+4(2y+10)

forgot a 2

[obsidian coral]

And realize that Leon has a channel open, #help-2

[crimson sedge]

@obsidian coral could u help me

[obsidian coral]

I did, in the channel you opened

[crimson sedge]

read

[cedar kiln]

@tawdry shell Has your question been resolved?

[cedar kiln]

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[viscid hearth]

Says it’s wrong

[fair hare]

,w is (a+b)/a=b

[wraith dagger]

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[fair hare]

numbers don't cancel like that

[viscid hearth]

Then how do I solve it?

[fair hare]

,w is (a+b)/a=1 + b/a

[wraith dagger]

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[fair hare]

then it's just a system of equations

[viscid hearth]

??

[fair hare]

yeah

now solve the system

[viscid hearth]

1/2 then?

.close

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[cedar kiln]

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[torpid pier]

For any non-negative k = 0,1,2,3,…. There are exactly 2 coins of value n = 2^k. For a given M, how to calculate the number of different ways that can represent M with the coins?

For example, M = 6 then there are 3 ways {1,1,2,2},{1,1,4}, and {2,4}
I want to solve it in a recursive way in a program and my teacher gave a solution.

If M mod 2 = 0 => Answer = Solve(M/2) + Solve(M/2 - 1)
If M mod 2 != 0 => Answer = Solve((M-1)/2)
But I don't understand the solution.

[upper abyss]

Solution doesn't work for M = 6?

Does Solve() do something weird?

[torpid pier]

yeah base case is If M = 0 => return 1

[pulsar skiff]

M = 6 => Solve(3) + Solve(4)

Solve(3) = Solve(1) = 1
{1, 1, 2}
Solve(4) = Solve(2) + Solve(3) = 2 + 1 = 3
{1, 1, 2}, {2, 2}, {4}

M = 6 => 4???

did i interpret right

cuz this is not 3

[torpid pier]

No M = 6 => Solve(2) + Solve (3)

[pulsar skiff]

how is 6/2 = 2

M => Solve(M/2) + Solve(M/2 + 1)

[torpid pier]

Sorry my bad should be Sove(M/2 - 1)

[pulsar skiff]

Solve(M/2) + Solve(M/2 - 1)?

ok

[cedar kiln]

@torpid pier Has your question been resolved?

[simple shale]

wonder how many solutions for j repetition of coins

for j=1 (no repeatitions) binar system dictates only 1 answer

[pulsar skiff]

M = 12 => 1100
1020
1012
0220
0212
5 solutions

so 1000…00 can become 0111…12

but important thing to note is 2^n - 1 = 111111… => 1 sol

so solution is related to number and placement of 0’s in binary form

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[pulsar skiff]

if M mod(4) = 2 then M = xxxx…10 = xxxx…02
solutions of either form, but xxxx…02 is same size as xxxx…01
if xxxx…10 where 1 does not move then this is same size as xxxx…1 which is then same size as xxxx…
thus solve(M) = solve(M/2) + solve(M/2-1) if M mod(4) = 2

[pulsar skiff]

example is M = 10 => 1010 gives solve(5) + solve(4) => 101 + 100
101 => 101, 021
100 => 100, 020, 012
size 5

meanwhile 1010 => 1010, 1002, 0210, 0202, 0122

size 5

so it works

but really weirdly

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[pulsar skiff]

we also see if the number ends in 1 then you can just remove the 1

[pulsar skiff]

so xxxx…y1 -> xxxx…y

thus if M is odd then solve(M) = solve((M-1)/2)

you can then do M mod 8 is 4 so M = xxxx…100 and follow logic of M mod 4 is 2

use this to build up for all evens that aren’t powers of 2

M as a power of 2 seems like it has to be solved explicitly

so solving 1000… gets 0200… 0120… 0112… the two goes through each digit (except 1000… where it’s 1) so a power of 2 is its number of digits in binary

this algorithm’s a little weirder but it works

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[nimble briar]

hi may i get some help on this please?

[cedar kiln]

@nimble briar Has your question been resolved?

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@nimble briar Has your question been resolved?

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@nimble briar Has your question been resolved?

[fair geyser]

no clue, can you link some context, like other similar questions maybe

i guess it's the same length whichever one you do

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[crimson sedge]

can someone help me here

[crimson sedge]

I dont know how to calculate E(X*Y)

this is what I have done so far

I am supposed to get 4/9

so I guess I can't split them up like E(X)E(Y)

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

<@&286206848099549185>

[slow thorn]

pretty sure u do double intergration

limit of y is [0,1] limit of x is [0,1] function u integrate is 8yx

my answer is 2

[crimson sedge]

answer should be 4/9

what formula should I use

[slow thorn]

wait u do use double intergral

i forgot about the extra xy

i got 4/9

8yx * xy

[crimson sedge]

aha

what is the reasoning of doing double integral

as opposed to splitting it up

I am also having trouble with question 4 not sure how to approach P(X+Y<=1/2) couldnt find anything in my book

maybe you could just tell me the property :)?

[slow thorn]

because ur integrating over two dimentions

[crimson sedge]

aha

okay

that kinda makes sense

[slow thorn]

yeah u cant add x and y together

[crimson sedge]

but my reasoning is that since we have f(x) and f(y)

we can just split it up

but I guess not

[slow thorn]

becasue u just get x and just get y splitting it up

[crimson sedge]

yea

isn't that a property tho

E(X*Y)= E(X)*E(Y)

anyway I guess it doesnt apply here since it is two dimensional I will just accept it 😄

is it possible to help me with question 4?

like just throw me a bone or something cos im completely lost

and my book is of no help

;/

[slow thorn]

ill be honest i never learnt that stuff before hahaha

i got no clue

[crimson sedge]

ait

fair

I will create a new help channel then 🙂

thanks for the help

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[cinder brook]

I was wondering if i should write 10 or keep it as 20 divided by 2. Since the question ask me to keep it in exact form

[fervent mason]

You can write it as 10

[cinder brook]

Okay thankyou very much

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[crimson sedge]

This is both a Hamiltonian and Eulerian graph right?

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[crimson sedge]

Okay i figured it out.

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[dusky pewter]

Hello!
I just want to know what’s the name of the material I need to study in question 1

[upper abyss]

Systems of equations

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[dusky pewter]

Thank you Kaynex!!💖✨

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[nova void]

Hi. so here is my question. ( the topic is solving linear EQUATIONS ) i dont get what to do here now.

[idle jay]

what idea do u have to solve this?

[nova void]

wait im trying to solve it one more time if i dont then ill explain

[idle jay]

aight cool

[nova void]

okay yeah i didnt get the answer

im using mathway to see if im getting the right answer or no btw.

[nova void]

Okay so i think that we have to convert -2 3/4 into improper frcation: -11/4 then move it on the right side of = sign making 7y = 1/2 -4/11

[idle jay]

what u did was correct butt the um moving process is wrong

when u move the fraction to the other side, u'll need to change the negative sign to positive

it should be 7y = 1/2 + 11/4

[nova void]

wait but doesn't the sign stay the same tho? cuz in my notes it says sign will remain the same

and we'll do the reciprocal of the f raction

[idle jay]

hmm can i see ur notes?

[nova void]

no like with the work ive written
note; when moving fractions, we will do the reciprocal of the fraction and sign will stay the same.

[idle jay]

hmm that happens when u move the fraction when it's times by smtg before

let me show u

[nova void]

okay..

[nova void]

okay so now im getting 7y = 13/4 so do i multiply the 7 with 13/4 ?

[idle jay]

u divide 13/4 by 7

[nova void]

ohh

[nova void]

and can u show that aswell please?

[nova void]

oh yeah forgot about that lol

okay hold on lemme do it

[idle jay]

yeah

can i dm u? i can give u my notes abt this topic

[nova void]

yeah sure

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[muted schooner]

hello

[muted schooner]

i need help

how do i calculate how much btc do i get for 13k if btc price is 33,600.62 per coin

pls help 🙂

<@&286206848099549185>

[scenic mural]

divide the amount of money you have by the price of a coin

[muted schooner]

thanks, i failed school

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[feral crane]

Does anyone have any good links to a site about gaussian elimination for finding determinants

Our lecturer didnt teach us about it at all (like I didnt even know it existed) until i was doing some revision and found some questions in a tutorial on it

whenever i find a site explaining it it's all [.... : ....] so they can rearrange it and change it without it messing up the matrix

[rustic siren]

https://www.youtube.com/watch?v=eDb6iugi6Uk

[feral crane]

thx

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[clear oxide]

so how do you calculate alpha. sin(3/5)?

[clear oxide]

the answer is there, but how do you get 36.869 degrees

[bleak timber]

so you do the inverse of sin^-1(3/5)

can you use a calculator

if you can

[clear oxide]

3/5 is 0.6

sin(0.6) =0,0104717841162457934632253069671

where do i go wrong

[bleak timber]

sin^-1

not juts sin

[clear oxide]

ooohh

ok now i got it

but why do you -1 it?

[bleak timber]

since sin is multiplied by alpha

and it asks for alpha

you take sin and bring it to the other

side

and theres a rule

when you bring

cosine sine and tan

you inverse them

[crystal raptor]

"Sin" is not being multiplied by α, the function sin(x) is being applied to α

[bleak timber]

ohhh

i always thought it was just sine

[crystal raptor]

You apply the inverse function to both sides

[clear oxide]

either one of you use speedcrunch?

[bleak timber]

I've never heard of it, sorry

[clear oxide]

must be finnish thing only then. Cause i got no idea how to solve the problem with the speedcrunch programm.

but ill try to find how to solve it with speed

but thanks alot

[bleak timber]

oh anytime

but did u understand?

[clear oxide]

yes

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[celest ledge]

Correct

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[dusky pollen]

Okay so the question asks to write the answer in fraction form. I already found the quotient and remainder. Is there a equation set-up I should be following?

[dusky pollen]

I’m talking about #12

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@dusky pollen Has your question been resolved?

[upper abyss]

7/2 = 2 + 1/2

You can see the quotient and remainder. Specifically, the remainder is still over the denominator

The answer to 10 is
5x - 28 + 18/(x+1)

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[late drum]

Idk why but I can’t solve this

[late drum]

<@&286206848099549185>

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[cold lodge]

Out of curiosity, without a calculator what is the easiest way to calculate this?

[foggy merlin]

don't tell me you calculate this with a calculator

it can be easily done by simplifying the fraction

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[cold lodge]

Could you point me in the right direction?

Oh wait hmm

Ok I figured it out

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[crimson sedge]

Anyone can help me?

[bold hinge]

Ampere Ohm

[crimson sedge]

? XD

[foggy merlin]

Ampere ohm is just Volt

[crimson sedge]

But what do I have to do, I don't really understand this topic.

[foggy merlin]

write the proper unit

[cold lodge]

Convert to the right metric. As an example, we know that Amps = Watts / Volt. Try to simplify the proper units

[crimson sedge]

So, is 10^6 V

?

[foggy merlin]

yes

[simple shale]

b) 10A

more like a) 10MV

[cold lodge]

Correct. They might also expect you to convert the^6 to the nearest metric

[crimson sedge]

Like, 10M ?

[cold lodge]

Yep! So 10 MV

[crimson sedge]

So, is V because AOmh is V, and for the ^6 is M because 10^6 = 1 millon?

[cold lodge]

Correct!

[crimson sedge]

and for the B?

if i have W/V ?

[cold lodge]

Do you know an equation where you divide watt with volt to calculate something

[crimson sedge]

P/V ?

[cold lodge]

What does that output

[crimson sedge]

Current

[cold lodge]

Yeeh which has the unit A

[crimson sedge]

Aohm?

[cold lodge]

10 A

[crimson sedge]

but, Do you mean exercise A?, 10^6 AOmh= 10MV ?

[cold lodge]

Ah yeah that is correct but I thought you were working on exercise B

My bad 😅

[crimson sedge]

yeah yea, I'm meaning to exercise B, but I don't understand it hahahaha

I have this image, can it help?

[cold lodge]

Sure. Lets look at exercise B.
It has the value 10^-3 kW/V

You told me before that W/V = A (current), right?

[crimson sedge]

yes

because P/V

[cold lodge]

Sure. Then you know that 10^-3 kW/V = 10^-3 kA

[crimson sedge]

I have to replace the k, right?

[cold lodge]

That’s the next step yeah

[crimson sedge]

10^-3 / 10^3

?

[cold lodge]

I would multiply it

[crimson sedge]

1

But, why multiply?

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[simple shale]

here's an input and output

[manic stratus]

What have you tried so far @simple shale

[simple shale]

hold on

I use this as my analogy:

so my equations were:

so this was an answer

but my friend wolfie says it's 4.79

https://www.wolframalpha.com/input?i=tan(pi%2F2+-+arcsin(2%2F5)%2F2)

which means

a i s larger than b

but the unit triangle used here got otherwise convention

which suggest an error

[simple shale]

see anything wrong here?

or perhaps an omitted simpler solution?

[manic stratus]

Hmmm this isn't anything I have done in a while but I'll give it a shot

[simple shale]

<@&286206848099549185>

[manic stratus]

Yeah I haven't done this in a long long time, I think someone else will be able to help you better. Sorry 😦

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@simple shale Has your question been resolved?

[cedar kiln]

@simple shale Has your question been resolved?

[cedar kiln]

@simple shale Has your question been resolved?

[simple shale]

anyone got any idea

just to show a mistake?

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[midnight zealot]

So this is the gamma factor (Lorentz factor) representing time dilation. If you look above the hypotenuse of that little triangle you will see change in time * c (where c is the speed of light). My question is, why is the speed of light being multiplied by the change in time?

What does the speed of light, c, have to do with anything here?
https://www.youtube.com/watch?v=nnVq6gmatHU
This is the video by the way. My question comes up at 15:13.

[crimson sedge]

find the possibility of the case that getting 10 people to sit circling a round table and of them of being selected 3 people sitting side by side?

<@&286206848099549185>

[barren tendon]

consider the 3 ppl as one unit

they can be rearranged within the unit

and this unit can be considered as one of the 8 elements that have to be arranged in the circle

[cedar kiln]

@midnight zealot Has your question been resolved?

[crimson sedge]

Could you give the answer?

[sudden pivot]

No

[midnight zealot]

?

[sudden pivot]

Teddyboy open other channel

[midnight zealot]

So this is the gamma factor (Lorentz factor) representing time dilation. If you look above the hypotenuse of that little triangle you will see change in time * c (where c is the speed of light). My question is, why is the speed of light being multiplied by the change in time?

What does the speed of light, c, have to do with anything here?
https://www.youtube.com/watch?v=nnVq6gmatHU
This is the video by the way. My question comes up at 15:13.

[cedar kiln]

@midnight zealot Has your question been resolved?

[simple shale]

to get length

C has dimension of velocity

[cedar kiln]

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[tall mica]

i got ,$\dfrac{64!}{60!2!}$ as a result

but im really really not sure about it

[wraith dagger]

The

[tall mica]

with the idea that there are 60 identical invisible pieces on the board

times that by the 2 other identical pieces

on the denominator

[celest ledge]

Correct

[cedar kiln]

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[tall mica]

thanks!

[cedar kiln]

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[proper epoch]

This question makes no sense since u don’t know the directrix or focus of the parabola

[fair hare]

u know the equation tho

and width

and bottom / top

[proper epoch]

No u don’t

U only know the circle and ellipse

This the answe

No clue how they got it

[fair hare]

"This opening is 18 cm wide"

start labeling stuff

[proper epoch]

But u don’t want the width

U want the height

Of the trophy

Nvm I got it

!close

.close

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[sinful plank]

how to do this

is this correct

i mean for the 1st step

[fair hare]

$$\frac{4y+4d}{3d-fy}=x$$

[wraith dagger]

Chunkin

[fair hare]

don't skip steps, makes it likely to do a mistake

[sinful plank]

what should i do 1st

[fair hare]

$$4y+4d=x(3d-fy)$$

[wraith dagger]

Chunkin

[fair hare]

cause were getting rid of fraction

and then just distriubte

$$4y+4d=3dx-fyx$$

[wraith dagger]

Chunkin

[fair hare]

yup u got it right

[fair hare]

see how I wrote it out tho

[sinful plank]

yep

[fair hare]

this makes it so ur not thinking of a lot of stuff in ur head so u don't make some goofy mistake

happened so much to me in alg 1 💀

[sinful plank]

$$\frac{3dx-fyx-5d}{4}=y$$

[wraith dagger]

ProfDelta

[sinful plank]

is this right

[cedar kiln]

@sinful plank Has your question been resolved?

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[vernal pike]

Give an example of a linear system of equations that has only the solution x = 1, y = 6. The system of equations must consist of two different equations. Both equations must contain the variables x and y.

[fair hare]

ok

what have you tried lol

[vernal pike]

Nothing yet.

[crystal raptor]

He's trying to write something that's for sure

[celest ledge]

x+y=7
2x+y=8

[crystal raptor]

Why we giving out answers

[vernal pike]

Could you explain why this is the solution?

[vagrant stone]

x = 1

y = 6

1 + 6 = 7

now, 2x

x = 1

2(1) + 6

2 + 6 = 8

[fair hare]

thus
x+y=7
2x+y=8

[vernal pike]

wait, it's that easy?

[vagrant stone]

yeah

[fair hare]

yeah

,w plot x+y=7, 2x+y=8

[wraith dagger]

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[vernal pike]

$\begin{cases}55x-3y=37&\ 34x+2y=46&\end{cases}$

[wraith dagger]

AuHasard

[vernal pike]

Is this a solution too?

@vagrant stone

[vagrant stone]

solve it yourself

[vernal pike]

I just took random numbers

[vagrant stone]

x = 1

y = 6

[vernal pike]

55-18 = 37

34+12=46

[vagrant stone]

correct

those two sets are correct

[vernal pike]

okay thanks

.close

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[dusty hazel]

Any clues for yourself?

[visual tusk]

Does anyone know what property this would be

I know it is congruent but cannot tell which property it is

[dusty hazel]

Anything at all?

Do you know the criteria for congruency.

Name them if you do.

[visual tusk]

I'm pretty sure it could be an asa

I can choose from SSS, ASA, AAS, AAA, SSA, SAS

[dusty hazel]

What does SSS mean?

[visual tusk]

Side side side

[dusty hazel]

In the figure do you see three congruent sides?

[visual tusk]

yeah i was thinking it could be sss

[dusty hazel]

Unfortunately it's not SSS.

Do you see that symbol on two of the sides?

[visual tusk]

Yeah I see them

Would it be sas or asa?

[cedar kiln]

@visual tusk Has your question been resolved?

[visual tusk]

.close

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[stark bronze]

Hey

[stark bronze]

Simple algebra question

With a problem like “evaluate log2 128”

Is there anyway to solve without just knowing what number to the second power == 128?

[fair geyser]

it means how many times you can divide by 2, you can count that

"what number to the second power" is not going to give you the answer on the other hand

[wraith dagger]

What the hell am I doing here?

[fair geyser]

you;ll only get sqare root

[dusty hazel]

It could also mean, what number you should raise 2 to, in other to get 128.

[cedar kiln]

@stark bronze Has your question been resolved?

[cedar kiln]

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[lone umbra]

Just wanted to double check - this is a typo, right?

[lone umbra]

This should simplify to 3tan(), not sqrt(3)tan() ?

[open sphinx]

yes it's a typo

[lone umbra]

thanks!!!

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[maiden dagger]

HEllo, could anyone help me with that? I've tried to use Taylor series but it didn't match with the result, (i got ~= -9

[upper abyss]

What strategy did you use to get the Taylor series?

[maiden dagger]

that was my result, i just manipulated the function

for taylor series

[upper abyss]

Smart, centering it around x = -3

Then yeah, the 5th derivative of that, at x = -3, should be what you want

[maiden dagger]

Yeah i did that i guess.... i will try to show you what i did

[upper abyss]

,w Taylor series of (x+8)/(x+1) centered at x = -3

[wraith dagger]

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[upper abyss]

I'm getting a slightly different series

My final answer would then be -7(5!)/64

[maiden dagger]

you right then... i did some mistake....

[simple shale]

Is there a general formula for taylor series of rational functions?

[maiden dagger]

Sorry about my calligraphy

did it so fast

so i just manipulated the function so i can use this formula:

the first one

so i compared to taylor:

[simple shale]

yeah but those are degree 0 and 1 polynomials

thought there is formula for any degree of P and Q

Guess such analyze is performed only by Control Theory

though it has very crude look on a matter

[maiden dagger]

idk, feels like i did some little mistake, cause the only difference is that i put -5 instead of -7 😦

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[upbeat basin]

hey

[upbeat basin]

how can we solve this for x

with middle term splitting

,w
x^2-2sqrt3(x)+2=0

[wraith dagger]

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[upbeat basin]

i solved it with quadratic formula

but how to do with middle term splitting

<@&286206848099549185>

[tranquil bolt]

hi

[crimson sedge]

There are ways but not systematic ways

U have

$a+b=-2\sqrt{3}$

$ab=2$

U will probably depend on a lot of guessing

[upbeat basin]

why cant we just do it directly with mts

[wraith dagger]

Pi Creature

[upbeat basin]

i mean the discriminant is a perfect square

so we can do it with mts

but i cant find factors

how can 2 be factored to get sum or differnce as -2/root3

[crimson sedge]

To do that u will need to solve these system of equations basically

[upbeat basin]

why?

[crimson sedge]

That's literally in the definition of how you do ac factoring

[upbeat basin]

no?

thats now how we are taught here

for us u just factor the product of ax and c so that the product is equal to the terms we split bx into

[crimson sedge]

Same thing ig

If u want to find the factors of

$ax^2+bx+c$

U want two numbers whose product s a*c and sum is b

[wraith dagger]

Pi Creature

[crimson sedge]

Which I represented as a system of equations

[upbeat basin]

yes

[crimson sedge]

So ya to solve those system of equations without quadartic equation u will require guessing

[upbeat basin]

ye so like

what guessing

can u guess the factors for mts

<@&286206848099549185>

[onyx sapphire]

hello friends can you guys help with 2b i could not prove that the function is odd

[upbeat basin]

u in which grade

@onyx sapphire

[onyx sapphire]

im degree level

[upbeat basin]

omg

i m in 10th

lul

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[upbeat basin]

.reopen

[cedar kiln]

✅

[cedar kiln]

@upbeat basin Has your question been resolved?

[cedar kiln]

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[trail hearth]

Help? calc 1 class antiderivatives it is a pretty basic question but im kinda lost.

[trail hearth]

1st antiderivative= t^2/2 -6t
2nd antiderivative= t^3/6-3t^2
(it doesnt tell me to use the constant of integration so i dont use it.)

s(t)=t^3/6-3t^2, v(t)=t^2/2-6t

so thats as far as Ive come

.close

[cedar kiln]

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