help-41

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[rancid dagger]

I know the values of a+b, a*b how do I get a-b?

[cunning palm]

what?

[rancid dagger]

Im trying to get the value of a-b from a+b and a*b is it possible?

[timid vault]

No. You can only build symmetric expressions of a and b

[rancid dagger]

the whole thing was a quadratic equation (3x^2 - 5x + 2 = 0 ) and I need the value of (1/alpha - 1/beta) [alpha and beta here being the solutions]

so I figured the alpha + beta would be 5/3 and alpha * beta would be 2/3 now need help with the rest 😭

[rancid raven]

If you want this , you can use
(a-b)² = (a+b)²-4ab

[rancid dagger]

yes thx

[rancid raven]

Np

[rancid raven]

Why not just find roots that is alpha and beta and then find 1/alpha -1/beta

[rancid dagger]

I tried but eh not the best with fractions

this worked anyways so yeah

[rancid raven]

3x²-3x-2x+2=0 , you can proceed ahead with this

[rancid dagger]

oh shit

didnt realize

I was trying to get it by the b^2 - 4ac thingy

[rancid raven]

Understood

[amber wasp]

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[calm pewter]

someone ehlp

[weak zinc]

any idea of how you'd start?

[calm pewter]

bruh

actually no

this questions r too hard

[quick spoke]

so generally, in chemistry, it's best to think of everything in terms of moles

[calm pewter]

yh

we r given 224

wht do we do with tht

[quick spoke]

so that's the mass of CaO

so we've gotta first convert it into moles

[calm pewter]

56

mr

then

224/56?

[quick spoke]

yep

[calm pewter]

4 moles

[quick spoke]

yep

so moles is just a number - you can think of it as 'dozen'

or like just 4

[quick spoke]

so if we have 4 molecules of CaO

[calm pewter]

yh

[quick spoke]

how many molecules of CaCO_3 must we have started with?

[calm pewter]

wht like the mr?

is 100

[red knot]

1 mole CaCO3 yeilds 1 mole of CaO

How many miles of CaCO3 will yeild 4 moles of CaO

[calm pewter]

is the ans 400?

.close

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[quick spoke]

yep!

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[ashen nebula]

How do I do this question
I tried to make an equation but it led to nothing

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[tough mica]

!status

[amber wasp]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[tough mica]

1

[quick spoke]

what do u think the answer to a is?

[tough mica]

if we recall ftc

we need the function to be continuous

like the original function f

[quick spoke]

as in ignore what thms etc. u know

intuitively, F is the area of f(t) between 0 and x

do u think that's cts?

[tough mica]

its not

but idk how to justify

i need more hand holding

if you can hold my hand that would be great

[quick spoke]

https://www.desmos.com/calculator/xhbpwfke6e

so the red region represents F(x)

if we change x

does the area under the curve change smoothly?

[tough mica]

it does not

how to prove it

i don't have access to wolfram in my exam

@quick spoke

[quick spoke]

what i meant by smoothly was continuously (probs shouldn't do that cus smooth means something different in maths lol)

but the point is that F(x) does change continuously

[tough mica]

im new to math

can you explain with baby steps

[quick spoke]

i think in this case it's easiest just to find a formula for F(x) and G(x)

so if 0 <= x <= 2

F(x) = x

for 2 < x <= 4

F(x) = 2 + 3(x-2)

anyway clearly it's cts from this basically

[tough mica]

polynomial is continuous

or else why you say that

@quick spoke

[quick spoke]

yeah basically

we just need to check that it's cts at 2 as well

[quick spoke]

but basically just plot this and it's quite obvs it's cts

[tough mica]

how would you prove it

[tough mica]

problem is that i cannot access wolfram in the exam

[quick spoke]

basically that's for intuitively why you might think it's cts

[quick spoke]

here we have a piecewise function where both parts are clearly cts

so u just need to check its cts at the 'boundary'

which is easy

[tough mica]

lateral limits

which definition of continuity Are you using

[quick spoke]

the limit one is easier in this case

[tough mica]

can you share the def

so both use the same definition

[quick spoke]

$f$ is cts at $a$ iff
$$\lim_{x\to a} f(x) = f(a)$$

[grizzled pagoda]

LY

[tough mica]

yes perfect

but this is a piecewise

so how would yhe definition of continuity would need to be changed for this one

also a = 2

@quick spoke

[quick spoke]

you just need to check the limit at x=2 exists

[tough mica]

is a piecewise

[quick spoke]

which is easy cus u just show that limit from left = limit from right

[tough mica]

1 ≠ 3

[tough mica]

can you elaborate

i need more handhold

[quick spoke]

that's for f

we're checking it for F

[tough mica]

how do I do that

I am not understanding

[quick spoke]

i think u've probably gotta first understand why F is cts

[quick spoke]

have a look at this again, and play around with it until u've convinced urself that F is cts

[tough mica]

how can u tell if F is cts or no

[quick spoke]

intuitively, a function is cts if 'there are no jumps'

so if u slide k around, does the area suddenly jump up/down?

[tough mica]

however i cannot use geogebra on my exam

what would you recommend in this situation

[quick spoke]

this is more to get familiar and comfortable with like intuitively what the answers should be

(for doing problems)

in the exam you shouldn't need to use anything, u'll have done enough problems to have that intuition

[tough mica]

how do I build that intuition

[quick spoke]

basically i meant like try playing around with the desmos thing i sent

[tough mica]

i did

but looks continuous to me

the integral is the area under the curve right

@quick spoke

[quick spoke]

yh

sorry it's getting late where i live so i'm getting kinda tired so i don't think i can give the best explanation rn lol

maybe see if u can get another helper to help u?

[tough mica]

yes I will go sleep aswell

I think is enough for today

sleep well and dream with integrals

[quick spoke]

fair

[quick spoke]

💤

[tough mica]

gn 💖

.solved

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[ruby stag]

Can someone help me on 9b

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[ruby stag]

<@&286206848099549185>

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[ruby stag]

<@&286206848099549185>

[wanton sentinel]

Can you write A as a function of time?

[ruby stag]

dA/dt

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[regal swift]

a bit confused on how to apply the second condition to the second term

if the first term goes to -inf then that whole term goes to 0

but the second term goes to infinity so I'm not sure

does it just mean that c2 is 0?

got it thanks.

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[storm moth]

an intgral domain neednt have an identity under multiplication?

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[storm moth]

.close

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[proper umbra]

I dont think I understand whats really happening in part b

why did they sub in theta^star for theta in a(theta) + b?

like how did they know that would work

wait wtf im slow

.close

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[neon kettle]

Posting this again, is it possible to make a taylor like series using integrals instead of derivatives and would have a form that is $\sum_{n=0}^{\infty}a_{n}x^{-n}$

[grizzled pagoda]

TimesZeroed

[neon kettle]

@jovial field I know you were about to say something

but the channel go closed

[jovial field]

See I have a test tmrw

Later

[neon kettle]

alright no problem

[torn furnace]

these have problems

but yes

[neon kettle]

alright

could you show me a an example

with like e^x or sin(x)

[torn furnace]

https://en.wikipedia.org/wiki/Laurent_series

some examples here

[neon kettle]

alright thanks

do these use integrals

[torn furnace]

but usually you don't see these in like

[torn furnace]

funny enough, yes

but maybe not in the way you are expecting

[neon kettle]

I have no clue what this is

but I'll get it

thanks for the help

[neon kettle]

I'll make a new channel tomorrow if you have a different way

.close

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[steel kite]

Im solving for where f(x) is increasing using derivatives
I have f'(x) = -3 (x^2 + 3x + 1) / (x^2 - x + 1)^3
I solved for the critical points which are (3 +- rt5)/2 and now im setting the inequality and plugging in points in between. I plugged in x = 0, 1, 3 back into f'(x) to solve for the increasing intervals.

I got f(x) is increasing (-infinity, (3+rt5)/2] but the answer key says its wrong. idk where i went wrong

[steel kite]

<@&286206848099549185>

[patent raptor]

The problem is your denominator

It may be that it gets negative whem multiplying it and the inequality sign flips

You would need to check additionally when x²-x+1 is pos/neg

oh I just realized it's always positive anyway

[steel kite]

apparently the correct answer is increasing on the middle interval

and dec on the left and right intervals

[patent raptor]

Makes sense

-3x²-3x-1

The parabola

Is open downwards

So within the roots it's positive

And outside negative

[steel kite]

do you know where i went wrong in my work?

[patent raptor]

How did you conclude +--

[steel kite]

i plugged in the numbers above the signs to f'(x)
so, f'(0), f'(1), ad f'(3)

[patent raptor]

ahh

Your roots must be off then

,w x^2+3x+1=0

[grizzled pagoda]

Results provided by WolframAlpha

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Requested by adoniszgks

[patent raptor]

I see

Something went wrong with the signs

[patent raptor]

Also its not really a good idea to do this

What if all 3 values give you the same

Something positive

Is it then increasing always?

[steel kite]

i would think so

is there a better way?

[patent raptor]

Figure the roots

And then since there is a minus

It's a parabola open downwards

So in between thos roots it must be positive aka increasing

And outside negative aka decreasing

[steel kite]

you know what

ive been using (x^2 + 3x + 1) instead of (x^2 - 3x + 1)

i got it now

[patent raptor]

Huh

But it is x^2+3x+1?

[steel kite]

supposed to be -3x

[patent raptor]

Ok

[steel kite]

so the roots were originally right, but i had plugged in 0, 1, and 3 into the wrong equation

thanks though

.close

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[shut dust]

hi, I'm struggling to prove those statements, especially 3 and 4. I tried solving 5 and 6 but I don't know if my solution is correct, I'm new to "proving" so I might be doing stuff wrong.

[shut dust]

this is my proof of the 6th statement:

I don't know how to even start with the others

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@shut dust Has your question been resolved?

[shut dust]

I also proved the 1st twos? I think I should prove the other way around (from thesis to hypothesis) but I can't

also tried the 5th one but this isn't working

mmh

gonna try that approach

so my solution is wrong?

aight, I never tried using contradiction tho but I'll try

ok i don't know how to start honestly, I know I should add a new hypothesis that denies the thesis but nothing comes to mind

yeah basically I need to examine the case where there is a element that belongs to B\A and inside the intersection between A and B and this can't exist

I can visualize why this is wrong but I can't write it in mathematical terms

so I can just explain in plain text my reasoning

nice, now I see

I thought I had to somehow "calculate" the result in matehematical terms

[shut dust]

tried here but I think I'm gonna use the contradiction once more time

what do you mean by two cases

ok basically using the axiom of extensionality

i think i've proven the 2nd part, the first part is the hardest one

[shut dust]

here

can't I just write that the difference between B and A added to the intersection between A and B has to be equal to B

in the first part x ∉ A inside (B\A) and x ∈ A in (A ∩ B). after adding those two parts we conclude that only the elements x such that x ∈ A in (A ∩ B) get taken into account

..hence B ⊆ that thing

yeah right lmao

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[split sail]

Hello! Could I please have some help? I am a bit stuck here.

[tough mica]

Sure

[tough mica]

Do u mind

You multiply the second eq by 2 and sum then both

[split sail]

Oh, ok!

[storm moth]

when solving these, you have to try to get rid of one variable

[split sail]

Ohh ok.

[weak zinc]

(there's two general ways you're probably supposed to do these linear simultaneous equations:

either substitution, so rearrange one of the equations for a variable, and then put that into the other equation

or elimination, scale one of the equations such that you have matching coefficients for a term [in this case, you could double the second one], then use that to eliminate a variable)

[vast spade]

there are few methods to slove this ,usually you can do by removing one of the variables

[vast spade]

the other is to slove a matrix

[split sail]

Thank you!!!

[vast spade]

this is correct

[split sail]

I have another question!

[vast spade]

if you have no other questions close it by typing .close

[vast spade]

sure

[storm moth]

new question appears

[vast spade]

[storm moth]

the augmented matrix

[vast spade]

wait its probability off i go!

[storm moth]

its super basic though..

[weak zinc]

Me too

[storm moth]

the probably of picking a green disc is number of green discs/total discs

how many green discs are there?

[vast spade]

my probability skills are even worse than a grade schooler

[split sail]

(B)

Now there are 14 green discs.

How do I find how many pink discs there are now?

Well, the number added.

[storm moth]

u are able to infer the total from the probability given

green/total=2/7

14/total=2/7

solve for total

with that u can figure out how many pink discs were added

[vast spade]

the total number of discs will be 14+7+x

[storm moth]

let snow do it

[vast spade]

[split sail]

Oh, I got it!

Thank youuuuu!!

Now I have more questions, hahahaha.

How could I solve these 2 questions?

[vast spade]

1.do you know what it means to cross the x axis?

[split sail]

Not really.

What does it mean?

[storm moth]

the x axis can be thought of as the line y=0

you want to find when the line l intersects that line

to do so u can substitute y=0

[split sail]

Hmmm, ok!

[coral wigeon]

hi snow

[split sail]

Hello!

Thank you!

How about the next question?

Hello?

[vast spade]

Hint the product of the two gradiants will be -1

[split sail]

Two gradients?

I don’t understand.

[deep karma]

two slopes

[split sail]

There is only one gradient?

[vast spade]

The gradient of the line l and k

[split sail]

5?

[deep karma]

or you can't just find out the other by

taking the negative reciprocal

[storm moth]

hi layla

[split sail]

5 and k = -1

?

[storm moth]

and hi snow too

[split sail]

Hi!

[deep karma]

take the negative reciprocal, it's the other gradient.

[vast spade]

No 5 x k=-1

[split sail]

-1/5

Is k

[deep karma]

yes!

[split sail]

Is that the answer?

[vast spade]

Yes

[split sail]

Wow.

[deep karma]

yeah snow, you can just remember it like

the gradient of two perpendicular lines always has a product of -1

[split sail]

Okkk thank you!

[storm moth]

given two perpendicular lines
y=mx+c
y=m2x+c2
m*m2=-1

[split sail]

So I have more questions.

[deep karma]

similarly two parallel lines have the same gradient

[split sail]

Thank you!!!

I’m a bit stuck here.

[storm moth]

K being a square number means all powers have to be even

[split sail]

Oh, hmm.

So like.

4

9

16

?

[storm moth]

well those are square numbers yea

but in this case u only need to look at the powers

[split sail]

?

What does that mean?

[storm moth]

we want each to be even and P is an integer

[split sail]

So..

4 and 16?

[storm moth]

so if we write P in terms of its prime factors, it should have 1 term in each odd power

so if N was instead

2*3^2*5```

[split sail]

?

[storm moth]

the powers of 3 is even so we can ignore it

[deep karma]

im not sure about 14, but i can help you with the 15th question

[storm moth]

the power of 2 and 5 are odd

[deep karma]

ill do after pokedance is done with the 14th

[storm moth]

so P would be 2*5

[split sail]

Ok thank you!

[split sail]

What is this?

I don’t get it.

[storm moth]

an example

[deep karma]

^ represents that the term after it is an exponent

[storm moth]

oh yea

[deep karma]

2³ can be written as 2^3

[split sail]

But why is it relevant?

I’m lost.

2 x 3^2 x 5

[storm moth]

yea so

when we multiply that with 2 x 5 we get

2^2 x 3^2 x 5^2

[split sail]

What are we working out?

[storm moth]

so this is a square number as we can rewrite it as

(2 x 3 x 5)^2

[split sail]

???

????????

What are we doing?

[storm moth]

😭

[split sail]

I’m so so so confused.

[storm moth]

can someone else explain better

[split sail]

2, 3, 5????

Random numbers???

I’m so lost.

HAHAHAH.

[storm moth]

2,3,5 are prime numbers

[split sail]

Maybe just move onto (15) first.

[split sail]

Why do we need prime numbers?

P is an integer.

?

????

[storm moth]

yea

so all positive numbers >1 can be written as a product of prime numbers

[deep karma]

15 is quite easy

so you'll have to rearrange the equation in such a way that

the final answer is given as x=

[split sail]

How do I do that?

[storm moth]

easy

[split sail]

If we move 2p

[deep karma]

m = 2p +√(x/y)

[split sail]

To the left

[deep karma]

it becomes -2p

[split sail]

Oh

[deep karma]

m - 2p = √(x/y)

[split sail]

Ok ok..

[deep karma]

now you square the entire equation

[split sail]

If we take off the

[deep karma]

to get rid of the root

[split sail]

Yes ok

[deep karma]

(m - 2p)² = (x/y)

[split sail]

Is this the answer?

[deep karma]

yeah!

[split sail]

Ok!

[deep karma]

or you can expand (m-2p)²

and multiply y inside

but what you've done is perfectly correct

[split sail]

Ok thank you!

[deep karma]

okay now i need help 😭

[storm moth]

u should open your own help channel

[deep karma]

@split sail type .close once you're done

[storm moth]

no she has

problem 14 left

[split sail]

?

HAHAHA

Yeah

Just thinking about it

But I got a question wrong too

And I don’t know why it’s wrong

[storm moth]

do u know what are prime numbers

[storm moth]

which

[split sail]

Non divisible numbers?

3, 5, 7..

[storm moth]

the only factors are 1 and itself

[storm moth]

2 as well

[split sail]

Why 2? It can be divided by 2 to equal 1.

[storm moth]

yea its cubed

[rancid raven]

Prime number can be divided by 1 and itself only

[storm moth]

height^3 is proportional to volume

[storm moth]

yea so its factors are 1 and 2 or 1 and itself

[split sail]

Hm.. ok.

[storm moth]

1 is a special case and we generally do not take it as a prime number

6 can be written as a product of its primes, 2x3

[split sail]

Okkk

Ok! I get it.

[storm moth]

the reason we first write the number in terms of its prime numbers is to identify any parts which are already squares

eg if we see 9 its actually a square

its easy to identify yea but harder to do if there are a few terms like 6*3

if u write it in terms of prime factors you'll get 2*3^2

from there u can see that 3^2 is a square number while 2 is not

[split sail]

Huuuhhh ok.

[deep karma]

that must be right

[split sail]

Yeah but what are we doing?

[split sail]

It was way wrong.

[deep karma]

unless you made any mistakes in calculation

[storm moth]

explaining how to do 14

[split sail]

Answer was 205.8

[split sail]

Yeah.

N = 806736

[deep karma]

that's not right

[storm moth]

no volume is ~ cube of height

[split sail]

Would I put P x 806736 = k

[deep karma]

this is exactly what snow's done and it is right.

[storm moth]

cube

[storm moth]

no

[split sail]

Oh..

[storm moth]

snow

[split sail]

Yes.

[storm moth]

lets say AB=C
we are given the value of A and we know C is a square number. find the smallest integer of B

so if A is 4 what is B

[split sail]

2

1

[storm moth]

how did u get 2

[split sail]

It’s 1

[storm moth]

yea its 1

and if A is 8, what is B

[split sail]

2

[storm moth]

so in general, when we have a square number B is 1

if A is 2 x square number then B is 2

yea?

[split sail]

?

A is 2 times a square number?

[storm moth]

if A is 2 times a square number

what would B be

[split sail]

Yes

?

[storm moth]

B would have to be 2

[split sail]

Why?

What if it’s 2 x 9?

B would be 2?

[storm moth]

yes

2x2x9 is 4x9

[split sail]

So C would be 36?

[storm moth]

yes

[split sail]

!!!??!?

[storm moth]

TnT

2x2 =4

[split sail]

Yes!

[vast spade]

=T

[storm moth]

yea use that on the 2x2 above

[storm moth]

false

[deep karma]

wrong

[storm moth]

n is defined as the binary operation sending everything to 😭

[rancid raven]

[vast spade]

ah rookie mistake

[split sail]

So what now?

[storm moth]

did u understand this?

[split sail]

Yeah, A is 2 times the square number (9) and B will always equal to 2..

And that means C is the answer of that.

[storm moth]

cool so the reason is that

[split sail]

👍.

[storm moth]

the product of square numbers is always a square number

[split sail]

Ah ok.

[fading wind]

Uo

Yo

@storm moth

[split sail]

So..

[fading wind]

Can u help me

I will give u head

[split sail]

Now what?

[storm moth]

any number^even number is a square number

[fading wind]

Bro please why is no helping me 😭😭😭😭😭😭😭😭

Istg i just want to sleep

Ive been stuck at this assignment for 6 hours

[amber wasp]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[rancid raven]

Did you open your channel @fading wind

[fading wind]

I cant open a channel

[storm moth]

go open your own channel

[fading wind]

Its not letting me

[fading wind]

I opened my a forum tho

Pls help me guys

I beg u

I swear on god i have autism

[storm moth]

what square numbers does N have

[split sail]

4 and 5

That’s the power

?

The little numbers?

[storm moth]

yea

if there is no little number on top its an implicit 1

[deep karma]

mention helpers there

[split sail]

So 4 and 5.

[split sail]

Ah right!

[storm moth]

no

[split sail]

Oh……

[storm moth]

so

[split sail]

So 2?

[storm moth]

2^7

[fading wind]

<@&286206848099549185> i need help pls

[storm moth]

what square numbers are in it

[deep karma]

NOT HERE

[split sail]

Why 2 to the power of 7?

[deep karma]

IN YOUR FORUM

[storm moth]

im just giving an arbitrary example

[split sail]

In what?

[storm moth]

2^7

[deep karma]

go to #help-33 and type your question

[split sail]

2 x 3 x 4?

I’m a bit confused.

[storm moth]

no

[split sail]

Oh.

[storm moth]

2^7 is

2x2x2x2x2x2x2

[split sail]

Oh.

OHHHHHH

[storm moth]

there is no 3

[split sail]

OHHOHOHOH

RIGHT

Just to expand it..

[storm moth]

so what square numbers are in 2^7

[split sail]

2 x 2 x 2 x 2 x 2 x 2 x2

So 2

[storm moth]

2 is not a square number

[deep karma]

2 is not the product of two same numbers

[split sail]

.

[storm moth]

a square number is like

[split sail]

Oh my gosh.

[storm moth]

2x2

[split sail]

Ok ok.

[deep karma]

1×1, 2×2, 3×3, 4×4,.. are all square numbers

[split sail]

Ok.

[storm moth]

Ok.

[split sail]

Hmmmmmmm.

I’m not sure.

[deep karma]

that is: 1,4,9,16,25,36 and so on

[deep karma]

Ok.

[split sail]

Ok.

[split sail]

4, 4, 4 and x 2

?

[storm moth]

there is 1, 2^2,2^4,2^6

[deep karma]

oops

pokedance im off 😭

[storm moth]

we are only concerned with the greatest square number here so 2^6

[rancid raven]

Maybe don't consider 1, it's irrelevant

Just from 2, 3,5 etc

[split sail]

Maybe we should just skip this question for today.

🥲.

[storm moth]

yea 2^2 and 2^4 is irrelevant too. im just saying it for completeness

[split sail]

How do I do 16?

It came out as wrong

[storm moth]

what is 16

[rancid raven]

No those are not irrelevant

[split sail]

But Bryan said it was right.

[rancid raven]

No that was wrong

[storm moth]

oh this?

as i said, cube

[split sail]

Cube the heights?

[storm moth]

cube height ~volume

yes

why is it wrong thunder

[split sail]

Do I still square the volume?

[deep karma]

im not sure really, id have done the same thing as you

[storm moth]

no u leave the volume as js

[split sail]

Okkk

[deep karma]

how can conclude that it's a cube?

it's only proportional

[storm moth]

we take it as that of a similar shape

[rancid raven]

Excellent question

[split sail]

Ah yes

Got it right then

[deep karma]

is definitely is 67.2

[storm moth]

there u got it

[deep karma]

oh no i get no wages

[storm moth]

well first assume its a cube, the volume will be proportional to the height cubed right?

[deep karma]

im poor.

[rancid raven]

It was a cuboid

Not cube

[deep karma]

no, we can't assume stuff like that

working out basic proportions gives you 67.2

UNLESS specifically mentioned, it can even be a 19 sided figure

or a doughnut

[storm moth]

then to conclude it works on a general shape, a general 3d shape can be broken down to smaller and smaller cubes that would approximate the volume of that given shape

[split sail]

What do we do for (17)?

[storm moth]

each smaller cube will similarly be proportional to the height cubed

[deep karma]

do you know algebra?

[rancid raven]

@storm moth It can't be a cube, else new volume would have been 7³

[storm moth]

theres probably more details u can put in but thats the idea

[deep karma]

assume his initial wage is x

[split sail]

Kind of?? I hope???

Yes.

[storm moth]

i did not say it is. i said it is proportional to it

[deep karma]

and the pay decrease is 7% of x, that is 0.07x

x - 0.07x = 427.8

solve for x from here

[storm moth]

snow

all the best to u

ive helped a bit and i think im going off now

[split sail]

Ok!

Thank you!

[storm moth]

welcome

https://cdn.discordapp.com/attachments/1286403543267410021/1287677776437973012/trump.gif

[split sail]

I’m thinking and I can’t figure out how I could arrange this.

[deep karma]

is there anything i have explain after this, snow?

okayy so

x - 0.07x = x(1-0.07)

and 1-0.07 = 0.93

0.93x = 427.8

divide by 0.93 on both sides

x = 427.8÷0.93

[split sail]

Ok! Understood.

[deep karma]

and you now take 7% of x and add it to x

[split sail]

460

Ok

[deep karma]

that is, x + 0.07x

is brian's wage

460+(0.07×460)

got it?

[split sail]

Yes

492.2

[deep karma]

great!

[split sail]

Thank you!!

[deep karma]

is there anything else?

[split sail]

Yes.

Haha.

[deep karma]

lol

[split sail]

A lot, I’m preparing for my exams and I really got to study maths.

Hahaha.

So…

Yeah. 😅

And I’ve been away a lot.

[deep karma]

OKAY

[deep karma]

understandable

do you know the formula for acceleration?

[split sail]

Noooo

[deep karma]

the formula is

change in velocity ÷ time taken

[split sail]

Ok!

[deep karma]

so what's the change in velocity

it's 10

[split sail]

Because of “v + 10”?

[deep karma]

yeah

[split sail]

Ok

[deep karma]

it's gone from v to v+10

[split sail]

So

[deep karma]

so change is given as final - initial

v+10 - v

[split sail]

10 divided by 24?

[deep karma]

=10

[deep karma]

yes!

[split sail]

Ok!

[deep karma]

and don't forget the unit

[split sail]

0.42

[deep karma]

the unit for acceleration is m/s²

[split sail]

yes

Ok, so the first question is done

Now (b)

[deep karma]

okay so for the second question

wait a second lemme read

wait ill write it down and show you

[split sail]

Ok!

[deep karma]

similar to acceleration

the formula for velocity is

displacement ÷ time

and you can rearrange the formula such that

displacement = velocity × time

[split sail]

What’s displacement?

[deep karma]

im sorry distance

[split sail]

Ohhhh

Ok ok

[deep karma]

okay so from the formula

OKAY WAIT

what you have here is called a

velocity time graph

[split sail]

Uh huh!

[deep karma]

finding out the area of the figure gives you the distance covered

do you get the idea?

[split sail]

Yes

I understand the idea

Just how to work it out

[deep karma]

so here, you'll be finding the area

[split sail]

We don’t know the velocity though

[deep karma]

for two figures separately

[split sail]

Nor the distance

So..

[deep karma]

so for that

you find the area of this triangle

[split sail]

16 x v + 10?

Oh..

THAT ONS.

One.

[deep karma]

and subtract it from the area of the rectangle you have there

[split sail]

10 x 24 x 1/2?

[deep karma]

yes

[deep karma]

which is =120

[split sail]

Yes!

[deep karma]

and the area of this rectangle is

24 × (v+10)

got it?

[split sail]

Yes!

[deep karma]

and the actual area we wanted

was this quadrilateral

[split sail]

Yes!

Then how do we work out “v”?

[deep karma]

wait we'll get there eventually

and now we need the area of the remaining triangle

this one

[split sail]

Yeah..

[deep karma]

which is, 1/2 × (40-24) × (v+10)

[split sail]

Yes.

[deep karma]

the sum of the two areas you find here

is exactly equal to the distance

[split sail]

Yes.

So what do we do?

[deep karma]

you solve it out like this

and now since the question gives us the distance

we equate what we found to 1.24

[split sail]

Yess.

[deep karma]

BUT

there's a catch

the distance here is given in kilometres

which means you have to convert it into metres before substituting

[split sail]

Why into metres?

[deep karma]

because the graph says that the velocity is in the unit metres/second

[split sail]

OOhhhhh.

1.24 x 1000

[deep karma]

perfect

solve the equation

and you'll get your velocity in m/s

this is how it goes

[split sail]

Woah thank you!

[deep karma]

you'll get it with more practice

[split sail]

Ok!!!

So, now with (20)?

I think I have an idea

[deep karma]

it's quite simple

[deep karma]

which is?

[split sail]

Rearrange it so that..

8y - 16ay - 6ax + 3x

[deep karma]

yes!

any idea after that?

[split sail]

8y(1-2a) - 3x(2a+1)

[deep karma]

ah

you're on the right track

[split sail]

Wait

-1

[deep karma]

yes, multiply the minus sign inside

[split sail]

Because two negative equal positive

[deep karma]

so you get the same factor

[split sail]

So..

Equals..

(8y-3x)(2a-1)

[deep karma]

NOO

[split sail]

WHAT!?

[deep karma]

what you'll have to do here

[bleak mason]

8y times 1

[deep karma]

is

you need to have the same factor in the parentheses to

factor like that

8y(1-2a) - 3x(2a+1)

multiply the minus sign inside

so that

[bleak mason]

The - belongs to the 2a

[deep karma]

8y(1-2a) + 3x(1-2a)

you can factorize after this step

[split sail]

How..

[deep karma]

or wait

[split sail]

Did you get it into play?

[deep karma]

let's start from the first

[split sail]

Plus

Ok

[deep karma]

3x+8y-6ax-16ay

3x-6ax+8y-16ay

3x(1-2a)+8y(1-2a)

(3x+8y)(1-2a)

[split sail]

Oooh! Ok!

[deep karma]

try to arrange your question in such a way that you get the same factor within the parentheses

[split sail]

Yess ok!

What’s parentheses?

[deep karma]

brackets

() this thing

[split sail]

Ok ok

Thank youuuu!

I’m going to head off to sleep now.

Thank you!!! 🙏

I really appreciate it.

.close

[amber wasp]

Channel closed

Closed by @gray helm

Use .reopen if this was a mistake.

[deep karma]

alrightty goodnight!

[storm moth]

night!

[amber wasp]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[ancient sparrow]

whats going wrong with my method

[amber wasp]

@ancient sparrow Has your question been resolved?

[amber wasp]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[real helm]

How do i solve this

I have been trying for like 30 minutes to solve this

[undone merlin]

! status

[amber wasp]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[real helm]

2

[undone merlin]

what have you tried?

[real helm]

I tried l hospital 🏥

Many different ways

Like i tried to rewrite this as a function f(x)/f(g) among many other ways

[quick spoke]

hint: remember that

$\lim_{n \to \infty} (1+\frac{1}{n})^n = e$

[grizzled pagoda]

LY

[quick spoke]

so whenever we see something like that we wanna try to write it in this form

[real helm]

Yes i know

But the question is how do i do that

[real helm]

Huh

This was unexpected

[undone merlin]

he's trolling

[real helm]

Lol i know

[undone merlin]

@quick spoke has a good hint

[real helm]

That is not enough

I already knew that

Guys?

Thanks for nothing i guess 🙃

[quick spoke]

so firstly we wanna get it in the form (1 + 1/stuff)^stuff

note that i can write the thing there as

(1 - 2/(2n+3))^n

can u manipulate this more?

[real helm]

Yes i can

I got 1/e is that correct @quick spoke

[ancient sparrow]

this is how i would solve it

lol is it wrong

💀

binomial approximation

[real helm]

I have no idea what have you done lol

[ancient sparrow]

what is the answwer

do you know the answer

is it `

1

[real helm]

I think it is 1/e

[ancient sparrow]

i got 1

💀

[real helm]

If i did it right

[quick spoke]

,w limit as n -> infinity ((2n+1)/(2n+3))^n

[grizzled pagoda]

Results provided by WolframAlpha

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

Requested by lyheart

[quick spoke]

yep

[real helm]

Nice

[ancient sparrow]

where did e come from 💀

did you use lh

method

l hospital thing

[real helm]

Yes

[ancient sparrow]

lemme try with that

nvm i learnt all this only yesterday

lemme start with easier problems

lol

[real helm]

Lol

Ok man

.close

[amber wasp]

Channel closed

Closed by @real helm

Use .reopen if this was a mistake.

[amber wasp]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[low trout]

am I tripping or is this guy using the trig identity, because in my opinion hes not

[mint nacelle]

he is

b = v
a = wv

[low trout]

he should have used cos(A)sin(B)

A=v

[mint nacelle]

what does it matter anyways, same thing

you can just swap a and b in your one to get the formula for cos b sin a

[low trout]

not really, you subtract the 2 things together

here hes added them

[mint nacelle]

I don't get your confusion

you use the formula for sin a cos b in your image

with a = wv
and b = v

[low trout]

what im saying is that A=v, b=wv

because its supposed to be formatted as cos(v)sin(wv)

therefore 1/2(sin(wv+v)-sin(wv-v))

[night jacinth]

and -sin(wv-v) = sin(v-wv) so which formula you use doesn't matter, they're all correct

[amber wasp]

@low trout Has your question been resolved?

[low trout]

yeah ur right, thanks i was just jumbling the numbers up so I thought our answers were different

[amber wasp]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[narrow night]

In good conditions, a sailboat can move at 15 km/h relative to the water. (a) What course must this sailboat follow (in other words, what orientation must the bow of the sailboat have) so that its trajectory is oriented at 35° north of east while it is experiencing a tidal current of 5 km/h directed 15° north of east? (b) What will then be the modulus of its speed relative to the earth?