help-0

[harsh ocean]

Oops

Yeah didnt notice

So it would end up not being correct since both integrals of secx would cancel out

Thanks

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[spark latch]

I don't know how to complete this

[lone heart]

@spark latch Has your question been resolved?

[lone heart]

@spark latch Has your question been resolved?

[harsh swallow]

you can split the limit

to see what happens to either

[warm cloud]

e^{2x} just approaches 1, so the limit just depends on what happens in the denominator

[spark latch]

Hmm

[placid zinc]

Subbing in gives 1/0, so you know the limit isn't a real number

[spark latch]

This unit is about using L'Hopitals Rule so wouldn't you do that until you get a real number?

Thats what I did for the questions before but I don't understand this one

[mystic mulch]

You can't use l'Hôpital's here because it's not in the indeterminate form 0/0 or inf/inf

[untold crane]

Well it’s just 1/0 so infinity

You can say that you can minor by 1/5x^3 that tends to +infini when x tends to 0

[spark latch]

Alright thank you

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[lyric night]

depends

do they want you to round

40/8 = 5 but there's 2 leftover in your case

so if they want you to round to the nearest whole number

then 5 is right

but

if they want you to include the remainder

then it'

would be 5 1/4

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[lone heart]

@steep cliff Has your question been resolved?

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[lunar finch]

I cant get the rule help me pls

[lunar finch]

They all must share same rule

Like a+b=c

The teacher didnt give us any solution so i need to trial and error ples help

<@&286206848099549185>

[tiny zenith]

a^2 - b

[lunar finch]

But 10-10 is 0

Not 15

[tiny zenith]

it’s squared

[lunar finch]

Oh

[tiny zenith]

a times a

minus b

[lunar finch]

Omg yes

Ty

[tiny zenith]

Np

[lunar finch]

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[tiny zenith]

This section is on fundamental theorem of calc part 1 idk where to start doing this problem

[glass lichen]

probably linearize f(x) then approximate f(5)

[jagged imp]

If you're allowed a calculator, pretty sure you can use the fact that int_a^b+int_b^c=int_a^c

[tiny zenith]

Yeah i can use calculator

idk if i can use that though bc its from the integral from a to 3 is 4 and its asking a to 5

or am i thinking abt it wrong

[jagged imp]

your calculator can do definite integrals?

[tiny zenith]

yeah

[jagged imp]

int_a^3+int_3^5=int_a^5 right?

[tiny zenith]

yeah

[jagged imp]

you know int_a^3 from the question, and you can find int_3^5 using your calculator

[tiny zenith]

ohh

yeah i understand

ty

[jagged imp]

nwnw

[tiny zenith]

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[tiny smelt]

That is my problem and I need to find The second derivatives of functions ( in the problems my teacher told me to use a=7 )

The second private derivatives of functions sorry ..

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@tiny smelt Has your question been resolved?

[tiny smelt]

<@&286206848099549185>

My other question is about this :

I need to find the relative extrema ( local extrema of the functions)

again a=7

[tiny smelt]

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[novel zenith]

What does A_{n-1} and A_n mean in this context?

[novel zenith]

Here’s an example problem

[glass lichen]

just more indexing

$f(x)=\sum_{i=0}^3 a_ix^i$

[ocean seal]

Mosh

[novel zenith]

:00 I should know what it means oof I learned this last year

rip algebra 2

[novel zenith]

ty!!

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[raven sundial]

Can someone explain this to me, i really don't understand

[glass lichen]

U is union, ie $x\in (A\cup B) \iff x\in A$ or $x\in B$

[ocean seal]

Mosh

[glass lichen]

$B-A=B\cap A^c$

[ocean seal]

Mosh

[raven sundial]

Oh.. ok2 Thanks

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[raven imp]

help plz

[glass lichen]

sure, what have you tried?

[raven imp]

well i dont really know what to do because i got covid and was out of school for like two weeks and we started a new subject but

[glass lichen]

So: Have you talked to your teacher, read the textbook on the section(s), attempted to google resources, asked a friend about what was covered, etc?

[raven imp]

I dont have textbooks, and ive emailed teachers but they havent responded because were on winter break and none of my friends can help because of the same reason, could you show me the first step? Or walk me through the first problem because theres quite a few i need to do once i learn one i can do the rest on my own i just kind of needed an explanation on how to complete it

[glass lichen]

What type of function is the graph?

[raven imp]

i dont know

[glass lichen]

Use your eyes and tell me.

Is it all wobbly and curved, is it a straight line, is it a ghost?

[raven imp]

nah there aint no ghost there ,think its a proportional relationship, but it does have a straight line

[glass lichen]

yes, that black line is a line

what's the general eqn of a line?

[raven imp]

Ax + By = C?

[glass lichen]

yes, though slope-intercept form is more useful.

given you want a proportionality statement, as well as the answer box is in that form.

[raven imp]

What do you mean by that?

[glass lichen]

Look at the answer box.. and you'll see y=[]

[raven imp]

True

[glass lichen]

so... you want your answer.. in that form.

[raven imp]

Okay

[glass lichen]

now since $y\propto x\iff y=mx$, you just need to find m.

[ocean seal]

Mosh

[raven imp]

where did you get the m from?

[glass lichen]

proportionality constant

ie definition of proportionality

[raven imp]

Alright ..

how does that help me?

[glass lichen]

You can use the formula to find m.

[raven imp]

What formula and where did you get m from

[glass lichen]

formula for slope.

and answered already.

[raven imp]

whats the formula?

[glass lichen]

Google it.

[glass lichen]

yes.

[raven imp]

alright

...

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[lone heart]

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[nimble roost]

looking at question 4.

i have an objective function, but no constraint for this optimization problem.

[vale wigeon]

what's your objective function? @nimble roost

[nimble roost]

it would be z (length of crease) = sqrt(x^2+y^2), right?

[vale wigeon]

ok sure

you should probably have the constraint that says the folded corner ends up on the left side

[nimble roost]

right...but am i doing that with some sort of trig function?

what function says that the corner ends up on the left side?

[vale wigeon]

idt this needs trig

i have some ideas in mind but i would probably need to interfere with your choice of notation

[nimble roost]

hmmmmm. that's fine. would you find the x component of the vertical line like a vector?

[vale wigeon]

dunno

actually maybe i WOULD go trigonometric here

try to work something out somewhere

[nimble roost]

sounds good!

[vale wigeon]

maybe my variables would instead be one of your x and y, and the angle between the crease line and one of the sides of the rectangle

[nimble roost]

ohhhhhh i think i see.

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[wary jungle]

do you guys know how im supposed to use a ti-83 to do this

[wary jungle]

what does graph mean

like here

what am i supposed to put in graph

[alpine sable]

is it asking for a derivative?

[wary jungle]

in the y' and y'' columns yes

this slide is the whole question btw no other info available

[alpine sable]

what...

[wary jungle]

what

r u confused cus i am

[raw shard]

they probably don’t know what a derivative is if that confuses them

[alpine sable]

i know what it means

[raw shard]

this question is terrible

[alpine sable]

isn't it just do derivative of the original

solve for intervals

[wary jungle]

yeah but what does "graph" mean

[alpine sable]

that's the part i got confused on

[wary jungle]

ik how to get y' and y''

but all these slides want me to put something in for graph

even tho its just an individual point

idk man

[severe sluice]

how do you graph the derivative at a point?

like

do you graph a horizontal line

[wary jungle]

yes the tangent line

[severe sluice]

oh-

[wary jungle]

r u asking me a question or trying to help me

[severe sluice]

i was just confused-
but can you already calculate a derivative?

[wary jungle]

yes

i just filled the chart in

[severe sluice]

so... you're asking about the graph?

[wary jungle]

yes thats what i said earlier

[severe sluice]

(wait a second do they want the first derivative or the second derivative on the graph?)
(probably the first derivative, right?)

uuuhhhhhh this question is really bad

[wary jungle]

first and second

oh wait

[severe sluice]

so
you have to graph the original function and the first derivative (i mean, as in the function, not the line)

[wary jungle]

i just understood ur question nvm

[severe sluice]

and then draw the lines

[wary jungle]

im supposed to just type something in there

no pics allowed

so idk

[severe sluice]

wait what-

maybe just ask your prof or something

the question's just poorly written

[lone heart]

@wary jungle Has your question been resolved?

[wary jungle]

I’ll just submit it as is but thx guys

[lone heart]

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[knotty wren]

How?

why does he move the K next to A

I don't get it

$Ae^{-Kt}CD(Pt + C)$

[ocean seal]

notSteve

[vale wigeon]

CD?

[knotty wren]

isn't that CD?

[vale wigeon]

are you sure that's not cos? it looks from context like it might be a poorly written cos to me

[knotty wren]

oh fuck you're right

[vale wigeon]

anyway, what's happening here is that we're talking the derivative

and the derivative of e^(-kx) is -k e^(-kx) by the chain rule

[knotty wren]

but isn't the derivative of $e^{x}$ just $e^{x}$

[ocean seal]

notSteve

[vale wigeon]

yes it is

and the derivative of e^(-kx) is -k e^(-kx) by the chain rule

[knotty wren]

can u show me how the chain rule applies here? I have studied the chain rule but I cant' think of how it applies here

[vale wigeon]

it's the composition of e^x with a linear function

d/dx (e^(-kx)) = e^(-kx) * d/dx (-kx)

[knotty wren]

$d/dx (e^{-kx}) = e^{-kx} * d/dx (-kx)$

[ocean seal]

notSteve

[knotty wren]

oh fuck that was simple thank you

[vale wigeon]

$\dv{x} e^{-kx} = e^{-kx} \dv{x} (-kx)$

[ocean seal]

Kanga Gang Annihilator Ann

[knotty wren]

ok so first we differentiate $e^{Kx}$ and then after that we differentiate $kx$ right

[ocean seal]

notSteve

[vale wigeon]

sure...

[knotty wren]

why do u say sure like that?

is my understanding wrong?

how would I solve this?

the last line

[vale wigeon]

chain rule

[knotty wren]

am I going down the right path

[vale wigeon]

missing parentheses in the last line and also you differentiated sqrt(1+x^2) incorrectly

[knotty wren]

i didnt write the full thing but I know what you mean

[lone heart]

@knotty wren Has your question been resolved?

[lone heart]

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[short spear]

If I invest $200 at the beginning of each month, at 2.5% p.a. compounded monthly. Find how long it will take me to save at least $10 000?

[severe sluice]

what's p.a.

like

you mean yearly?

[short spear]

per annum

[severe sluice]

oh ok

find the percentage you gain each month

[short spear]

0.21

[severe sluice]

therefore, in the n-th month, we will have
$200 * (1.0021)^n$ dollars

[ocean seal]

Kanga Gang ¬Sam

[short spear]

how'd you make that

equation

oh

p(1+r)^n

[severe sluice]

yeah

and then it's just a logarithm

[short spear]

so 10000=200(1.0021)^n

then i just go from there

[severe sluice]

yeah

[short spear]

so then 1.0021^n = 50

where do i go from there

[lunar sail]

That's not entirely correct; 200 is being invested each month, not just the first month

[severe sluice]

wait, it's each month?

sorry

didn't read that :C

[lunar sail]

So it's an iterative process, I don't know how to solve that with math haha.

[short spear]

whta would the equation be then

[lunar sail]

You can just calculate it iteratively. So start with 200

[short spear]

before i got upto 10000= (200(1-0.0021^n))/1-0.0021

[lunar sail]

Then multiply by 1.0021, and add 200

Repeat until you get 10000

[short spear]

i don't think my teacher will accept that

[lunar sail]

I don't know how to write it in an equation

[short spear]

i have some formulas that i can use

Sn = a(1-r^n)/1-r

where sn is teh number of terms

a is the first term

r is the common ratio

and n is the number of terms

[lunar sail]

Yeah that's a geometric sum but it doesn't help you here

As far as I know at least

[short spear]

well i'm supposed to use it somehow

guess i'll just leave this one too

[lunar sail]

There is no common ratio: first you get like 205 and add 200, the ratio is approximately 1:1

But later on, you're at like 5000, and you again add 200. Then your ratio is 25:1

[short spear]

.close

[lone heart]

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[twilit quiver]

when I solved quadric equation in the standard form what I actually did was making all the term with x being the opposite of c so together it will reduced to zero right?

[twilit quiver]

say in here:
$$x^2+8x+12 = 0 $$

[ocean seal]

eitiel

[twilit quiver]

I need $x^2+8x$ to be -12

[ocean seal]

eitiel

[lone heart]

@twilit quiver Has your question been resolved?

[twilit quiver]

<@&286206848099549185>

[dusk panther]

What do you mean?

[ocean seal]

Demons

[dusk panther]

Is that what you mean?

Or solve for x @twilit quiver

[tiny minnow]

,w x^2+8x+12=0 ?

[ocean seal]

Results provided by WolframAlpha

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Requested by IVMC Gaming CH#1700

[tiny minnow]

x= -6 and x= -2

use factorize or quadratif formula

[dusk panther]

Yeah factorising is easier.

For this question.

[twilit quiver]

@tiny minnow @dusk panther I'm not looking for the spesific answer but rather asking this:
if that the case case can I solve it also for $ \pm ax^2 \pm bx = \pm c $ instead of 0

?

[tiny minnow]

$\pm ax^2 \pm bx = \pm c$ instead of 0

[ocean seal]

IVMC Gaming CH

[tiny minnow]

u can;t use that

[twilit quiver]

like, is that possible to solve:
$$x^2+8x = -12$$ ?

[ocean seal]

eitiel

[tiny minnow]

first steps make it

$ax^2+bx+c$

[ocean seal]

IVMC Gaming CH

[tiny minnow]

u can't

[dusk panther]

No.

Oh sorry.

Then you can either factorise or use the quadratic formula but in this case factorising is much easier.

[twilit quiver]

so it's possible but not necessarily easier?

[dusk panther]

I mean you could complete the square.

[tiny minnow]

the only way if this is input the x

[tiny minnow]

relly not recommend

[dusk panther]

Not like that.

[tiny minnow]

No

[twilit quiver]

quadric equation is all about completing the square isn't?
I always wondered how they come to that formula we always been told to simply memorize with no explanation

[dusk panther]

Quadratic formula?

It isn't.

You input the values.

[tiny minnow]

[dusk panther]

Oh that yeah.

But I meant using it.

[tiny minnow]

$\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

[ocean seal]

IVMC Gaming CH

[twilit quiver]

yeah but that's the algebraic there is somthing I've heard once about how the Babylonians used this formula by actually completing squares

[tiny minnow]

u can use completing squares to

[twilit quiver]

well I have to go
@tiny minnow @dusk panther thank you both

[tiny minnow]

cya

don't forget to do .close

[twilit quiver]

yes

.close

[lone heart]

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[serene osprey]

what theorems are required for this question?

[rotund steeple]

Just the inscribed angle theorem should be enough

[serene osprey]

whats the inscribed angle theorem?

[rotund steeple]

Let me find a good picture

[serene osprey]

okay

[rotund steeple]

Does this explain it?

[serene osprey]

yeah

i understand

the theorem

i'm just not sure, how to apply it here

like i don't see it

[rotund steeple]

So my hint is that instead of the angle you are asked to find

Try finding its complement, i.e 360-that

[serene osprey]

okay imma try

is that the only theorem necessary to answer this question? Is all other working from geometrical identities?

[rotund steeple]

Yeah

[serene osprey]

hmmmmm okay

is there any other hint i can have please

i can't see any geometric correlation

[rotund steeple]

Yeah so

Look at angles COE and AOE

[serene osprey]

uhhh am i meant to be adding another line?

to the diagram ?

[rotund steeple]

Yeah

[serene osprey]

okay done

COE is obviously 180 right?

[gray isle]

no

[serene osprey]

ohhhhhh

because im assuming the length is straight

okay

so then

okay so i think i finally got something

like the interior angle cOE = 210 ?

[rotund steeple]

Yep

[serene osprey]

ummmm am i meant to do something by proving the triangles are similar?

[rotund steeple]

You got COE, whats AOE

[serene osprey]

i can't seem to find it

[rotund steeple]

Its the exact same logic as COE

[serene osprey]

so its 60?

[rotund steeple]

Yeah

[serene osprey]

i don't understand this

maybe i don't understand the theorem correctly

[rotund steeple]

The theorem just says that if you have two points, say X,Y on the circle. And any other point Z on the circle and the center O. Then the angle XOY is twice the angle XZY

The diagrams give you a visual for this

[serene osprey]

yeah i see the diagram

so in this case

points

x,y are A & E ?

and then O is just obviously the centre?

with

B being Z?

like for this question

[rotund steeple]

Yeah

[serene osprey]

i see

man i never learnt this though

like i only learnt of the first 2 ideas, in that visual proof you gave me

this third idea feels so different

[rotund steeple]

Yeah dw euclidean geo has many random theorems

And it is hard to visualize some of this stuff

[serene osprey]

i see

okay

tysm

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[visual badger]

how can i do this using the binomial therorem

[placid zinc]

Which term is "independent of x"?

Or, which term is the constant term?

[visual badger]

uh 2

do i have to expand the 2 and add it up?

2^9 + 2^8 ...

[vale wigeon]

no

the binomial theorem says $\paren{x^2 + \frac{2}{x}}^9 = \sum_{k=0}^9 \binom{9}{k} (x^2)^k (2/x)^{9-k}$

[ocean seal]

Kanga Gang Annihilator Ann

[vale wigeon]

do you understand this or not?

[visual badger]

well no because this is too advanced

but i think we should use the general term

[vale wigeon]

???

you said "using the binomial theorem"

this is the binomial theorem

but ok, fine, the general term in the expansion is $\binom{9}{k} (x^2)^k (2/x)^{9-k}$, where $k$ ranges from 0 to 9.

[ocean seal]

Kanga Gang Annihilator Ann

[visual badger]

hmm ok thanks

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[sharp minnow]

Can someone help me where am I making mistake? Its Laplace transform of differential equation

[sharp minnow]

<@&286206848099549185>

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@sharp minnow Has your question been resolved?

[sharp minnow]

<@&286206848099549185>

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[fallen frost]

What does the r.[1 1 2] = 10 bit mean here? I know it's the equation of the plane but I haven't seen this notation before

[bleak ridge]

Is it dot product or smthn?

[fallen frost]

I don't think so

[bleak ridge]

I mean [1 1 2] would prob be a vector

And there's a dot

And the question is about perpendicular stuff which dot product is good at

[fallen frost]

that is true

I'm not sure what the r bit is though

is that just an arbitrary point on the plane?

[bleak ridge]

Maybe it's "the line" they talk about in the bottom part?

Seems kinda off though

[fallen frost]

I think this bit is the line referred to in the question

[bleak ridge]

Hmm

Oh I see the text up there

So the r.blah blah is the equation for the plane

[fallen frost]

I think so

[bleak ridge]

Maybe they did define a plane in terms of dot product

But it'd be weird that they didn't give you r

Lemme do some looking around

[fallen frost]

Alright

[sonic fossil]

(1,1,2) is the normal vector of the plane

[fallen frost]

I see

[bleak ridge]

Ok yeah so you were right r is just a point on the plane

[sonic fossil]

So you need to find the direction of the given line and see if it’s a scalar multiple of the normal

[fallen frost]

That makes sense

Thanks for the help!

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[peak pumice]

What would be the shortest method to find the determinant of matrix on 1008 c)

[severe sluice]

,rotatte

,rotate

[peak pumice]

I tried using cofactor but after 2 sheets of calculations i got a wrong answer

I dont think so

We havent done any matrices using transposition except when its required specifically to transpose a matrix first

[severe sluice]

nvm you're right

seems like you just miscalculated some things...

[peak pumice]

Im trying to figure out how to make all zeros under or over the diagonal

But i cant seem to find a way

[severe sluice]

you can subtract the 2nd, 3rd and 4th rows by the first row

[peak pumice]

I get a couple 1s and some numbers go up some go down

Should i just play with it until i find a way

[severe sluice]

by doing this you should end up with a matrix in RREF

@peak pumice

[peak pumice]

Sorry but what does RREF mean

[severe sluice]

row reduced echelon form

beautiful form

really useful

once you get to a row echelon matrix, to find the determinant, just multiply the diagonal entries

[peak pumice]

I get a 0 in the diagonal this way

[severe sluice]

no? why?

i mean

subtract by the first row, not add

[peak pumice]

I did so

[severe sluice]

and...

[peak pumice]

the last row substracted by the first row i get -5 7 -9 0

Am i doing something wrong

[severe sluice]

wait why? what?

which part are you working on?

[peak pumice]

Im substacting the 3 rows by the first one

After substracting the last one i get a 0 at position 4,4

[severe sluice]

oh
sorry, i thought you were working on A

[peak pumice]

I thought im going crazy for a moment xd

For c) its a bit more complicated

[severe sluice]

for C, well...

[peak pumice]

The cofactor didnt turn out well for me

[severe sluice]

subtract from row 2 (row 1 times 1.5)

[peak pumice]

So r2-r2*1/2

[severe sluice]

typo, sorry

[peak pumice]

Ah ok

[severe sluice]

i mean row 1 times 1.5

[peak pumice]

Ill try that

[severe sluice]

i'm doing this to make the first entry in row 2 zero

[peak pumice]

Wont i get some decimal signs tho

[severe sluice]

you will

[peak pumice]

Step by step they should dissapear right]

[severe sluice]

yeah

and then for the third row

we will make the first element 0 by subtracting it by (row 1 times 2)

and then make the second element 0 by subtracting by row 2 times something

[peak pumice]

Ah i see ok ill try it and reach out if i succees

I get a zero for the third element in row 3

Will it make a problem

[severe sluice]

third element? yes, that's a problem

@peak pumice what did you multiply the second row by before subtracting from the third row

[peak pumice]

It was from multiplying the first row by 2 and substracting

[severe sluice]

can you... show what you did?

[peak pumice]

As u said here i got for the third row first element zero second 1 third also zero and fourth -1

[severe sluice]

ohh

yeah, it's suposed to be that way if you haven't subtracted by (2/7 times the second row) yet.

[peak pumice]

Im so confused doing it this way

Would it be better to stick to cofactor and figure out where my mistake was

Or get additional tips here for the cofactor methid

[severe sluice]

it's only long because i'm explaining it to you step-by-step, and personally, i think that gaussian elimination is still faster when you're actualy using it (although you can use cofactor if you want to)

do you want to switch to cofactor? bc we're almost done here

[peak pumice]

I think i should just leave this problem for the end

Ill just come back to it later

Thanks for the help a lot!

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[ebon slate]

Hi, I wanna ask how to calculate the amount of something I got in second from what I got from minutes? (like If I got 600usd per 4.45 mins how do I know how much I get per second)

[gray isle]

start by converting 4.45 minutes to seconds

[ebon slate]

that's 285 seconds?

[gray isle]

depends on what you meant by 4.45 minutes

as in the decimial valuie 4.45 or 4 minutes and 45 seconds

[raw epoch]

4.45 minutes = 4.45(60) ~ 60 seconds in a minute ~~ Then divide 600/285

If you get 1$ per second, you get 60$ per minute..

If you get 60$ per minute, you get 1$ per second

Per means divide basically

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[ebon slate]

Thanks

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[uncut lava]

My exercise: Find out how many numbers between 0 and 10,000 are divisible by 13 by using a sequence.
I know the basics of sequences and series but I'd have no clue on how to approach this one :3

[indigo jetty]

what is the first number that is divisible by 13?

i'm assuming the question excludes 0 and 10000?

[uncut lava]

13 i suppose, so the sequence would look like that: an = 13*n

probably

[indigo jetty]

now try writing out the first few terms

and see what kind of sequence it is

[uncut lava]

13, 26, 39, ...
It would be an arithmetic sequence if u meant that

[indigo jetty]

yes

basically an AP

so now u can express a_n in terms of the nth term of the AP

[uncut lava]

an = 13*n, am I right?

[indigo jetty]

yup

[uncut lava]

so do I just have to devide 10,000 by 13 to find out how many elements there are?

is that what was meant?

[indigo jetty]

basically u form an inequality

since u identified it as an AP, it means n will be the number of terms that are divisible by 13

u do not want a_n to exceed 10000

[uncut lava]

13*n < 10,000 and convert it to n<10,000/13 ?

[indigo jetty]

yes

[uncut lava]

so then I get 769 (nice) and can now say that there are 769 elements that fit my criteria, am I right?

[indigo jetty]

yup

[uncut lava]

ahh cool, thx a lot! ^^

[indigo jetty]

👍

[uncut lava]

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[vital wagon]

How to approach this?

[lone heart]

@vital wagon Has your question been resolved?

[raw shard]

this might be the worst question i’ve ever seen in my life

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[amber marsh]

is this equal to p + q by using log rules?

[buoyant kayak]

yea

[amber marsh]

so thats it?

[buoyant kayak]

yep

[amber marsh]

ok ill close this channel thx

.closed

.close

[vital wagon]

it's .close

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[alpine sable]

Tough one

[vital wagon]

Honestly no idea haha

.reopen

[alpine sable]

I have a hunch that its 96

But dont ask why

Is it some sort of iq test?@vital wagon

[vital wagon]

yep it's in the quant section of an entrance exam but seems more on the lr side to me @alpine sable

[amber marsh]

.close

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[vital wagon]

@alpine sable so I somehow guessed it correctly and this is how it was done lmfao

[buoyant kayak]

that's such arbitrary bs

please tell me this is an online iq test or something and not assigned work

[vital wagon]

It's a mock test for an exam similar to gmat haha, would be better if it was an iq test, I got bamboozled at this one

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[wispy wing]

hello, please may can i have some help

[gray isle]

what have you tried?

[wispy wing]

timesing x+ 2 and 5x + 1

[gray isle]

do you have a pic of your work

[alpine sable]

Jeeesus christt

[wispy wing]

I got kinda confused

[gray isle]

can you redo the work

[wispy wing]

yep

[gray isle]

missing components and bad notation is making it extremely hard to read/follow

[wispy wing]

okay sorry

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[wispy wing]

do you want me to rotate it?

[gray isle]

,rotate

[gray isle]

still missing parentheses

[wispy wing]

what is that? i feel like there is a language barrier here between US and UK

[gray isle]

()

[wispy wing]

oh ok

[gray isle]

$a+b(c+d) \neq (a+b)(c+d)$

[ocean seal]

ℝamonov

[gray isle]

ignoring the issue with notation, you have a quadratic equation.

solve it like any other

[wispy wing]

But that’s wrong

I did this part

[gray isle]

you didn't manipulate your equation properly

where's 4x coming from

[wispy wing]

thats 8

i made a little error

[gray isle]

updated values look alright

[wispy wing]

But that is wrong

[gray isle]

but fix the issue with parentheses I mentioned earlier

[wispy wing]

I don’t know how

[gray isle]

don't know how what

[wispy wing]

To fix the parenthesis problem

[gray isle]

recall the order of operations

[wispy wing]

I hate to frustrating but what is that?

I’m 15yrs old and I’ve got this for homework and it’s just all confusing

[gray isle]

bodmas, pedmas, gema or whatever variation your locale uses

[wispy wing]

ok

when did i not use it correctly?

[gray isle]

$a+b(c+d) \neq (a+b)(c+d)$

[ocean seal]

ℝamonov

[gray isle]

5x +1(x+2)
does not represent the product of 5x+1 and x+2

[wispy wing]

so i times them together

[gray isle]

you want an expression that represents their product, what you have written does not achieve that

[wispy wing]

is it 5x^2 + 11x + 2?

[gray isle]

the product of 5x+1 and x+2 is 5x^2 +11x +2

the issue is that you wrote
5x+1(x+2)

[wispy wing]

ok

[gray isle]

e.g if you were asked to simplify
5x+1(x+2)
and followed the order of operations what would you do first and what would you get

[wispy wing]

5x x x

5x^2

[gray isle]

no

[wispy wing]

5(x+2)

[gray isle]

you are doing addition before multiplication for some reason

parentheses are needed to clearly indicate what's being multiplied

5x + 1(x+2)
is the sum of 5x and the product of 1 and (x+2)

which is different from(5x+1)(x+2)

which is the product of 5x+1 and x+2
which is what you actually vwant and should be writing

anyway who's saying
0.48 and -2.08 are wrong

[wispy wing]

oh

the site says its wrong

[gray isle]

what are you entering into the site

[wispy wing]

x = 0.48

x = -2.08

[gray isle]

did you enter any work with it?

[wispy wing]

no

[gray isle]

do you have the exact response the site is giving you

[wispy wing]

no

just says incorrcet and gives me no marks

wow, i put the working in and it gave me the marks

cheers @gray isle

you've been a legend

[gray isle]

the question did tell you to show work

[wispy wing]

it did tbf

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@wispy wing Has your question been resolved?

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[lost rampart]

Hey,
Given are two invertible (n x n) -matrices A and B. Show that the matrix C = A * B is then also invertible and express C ^ (- 1) by the inverses A and B.

Is then also D = A + B always invertible? Give reasons for your answer.

[shell widget]

What have u tried?

[lost rampart]

I was hoping someone had food for thought, how are you supposed to prove that?

[shell widget]

hint: use determinant

[lost rampart]

Without having a matrix (there isn't one)?

[shell widget]

?

matrix A is given

matrix B is given

i mean, you dont have their entries, but you do know that they are invertible

What does this mean?

@lost rampart

?

yeah kinda on the right track

[lost rampart]

C = A*B
invertible means det(A), det(B) != 0 <=> det(A) * det(B) != 0 <=> det(A * B) != 0 <=> det(C) = det(A * B) != 0.

does it make sense?

[shell widget]

Yea

Yes*

[lost rampart]

Alright

[shell widget]

that works

and ur done

[lost rampart]

Alright

What about the second part?

[shell widget]

give it a thought

det(A+B) =! det(A) + det(B) in general

[lost rampart]

D = A + B
invertible means det(A), det(B) != 0 <=> det(A) + det(B) != 0
Because det(A) + det(B) != det(A + B) = det(C)
=> It depends on the matrix of A + B?

[thorny patio]

If it's not always true you can show that is the case with a counterexample

Find a counter example and you solve part 2

[shell widget]

@lost rampart But what if det(A) is -1, det(B) is 1, then det(A) + det(B) = 0

if two numbers aren't 0, you can't conclude their sum isn't 0

[lost rampart]

@alpine sable @thorny patio Alright, THX a lot guys!

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@runic obsidian Has your question been resolved?

[runic obsidian]

<@&286206848099549185>

im not sure how to go with this one

[runic obsidian]

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[buoyant kayak]

<@&268886789983436800>

thank you rocket man

[sly mantle]

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[untold rain]

how would you solve this ?

I am stuck, and not even sure how to start

any assistance would be appreciated

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@untold rain Has your question been resolved?

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[flint kettle]

How do I calculate the steady state solution of
$\frac{d^3y}{dt^3} + \frac{d^2y}{dt^2} - \frac{dy}{dt} -y = e^{-t}$

[ocean seal]

curious_coder

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[alpine sable]

in proportions, how would you solve for 2 variables in 2 separate fractions that are equal and reciprocals of each other?
Example: 2+x+y/3 = 3/2+x+y
how would you solve for x and y

[raw shard]

x is irrelevant in the example you sent

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[hardy lark]

I tried this, but basically I’m stuck with not knowing how to go about it

I’m almost certain there’s a way to do both questions with minimal effort, so if someone could help me see how to do either (or ideally both) problems, that would just be splendid ✨

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@hardy lark Has your question been resolved?

[hardy lark]

<@&286206848099549185> please if I could just get a guiding hand to start me off, I should be able to do the rest! Thank you!!

(Both questions btw)

[drowsy sorrel]

they wont reply

neither to me did

[hardy lark]

Oof really?

[drowsy sorrel]

yh

[hardy lark]

Darn 😔

[drowsy sorrel]

look #help-10

[hardy lark]

Oof

U in geometry?

I’ll see if I can help you...

[drowsy sorrel]

yeah

[drowsy sorrel]

<@&286206848099549185> really help this guy lol

[hardy lark]

Yeah that would be nice 😅

[harsh swallow]

where did you get stuck?

[hardy lark]

I basically didn’t know how to start

The methods I was using were leading me to dead ends

[harsh swallow]

you figured out p q and r

add them together?

a good piece of info is the fact that p q and r are all real numbers

meaning the b is constrained

and because b is constrained a is too

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[hardy lark]

.close

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[dusky palm]

.close

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[lapis hedge]

@dusky palm you got it?

[dusky palm]

yes

[lapis hedge]

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[lone trout]

hi, confused on how exactly to determine a(t) and b(t)

[lone trout]

would i need to derivate V with respect to S and t or would commenting on the boundary conditions suffice?

[raw shard]

[lone trout]

wut

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<@&286206848099549185>

[hardy lark]

The lack of numbers here is astounding

I truly pity you, my good sir

There are even some nonEnglish letters 😂

[lone trout]

i just dont know what the question wants me to do

should i just explain the payoff diagrams that can occur for european puts and calls via this pde

am i allowed to ping helpers more than once

lol

<@&286206848099549185>

[lone trout]

https://tenor.com/view/cute-cat-crying-tears-sad-emotional-gif-15881815

[rose pumice]

I mean, B-S gives $$0 = a'(t)S + b'(t) + rSa(t) - r(a(t)S - b(t)) = a'(t)S + b'(t) + rb(t)$$

[ocean seal]

∧res

[rose pumice]

so if it says "what can you say" about a and b, maybe you just want a relation like that

perhaps you can simplify/manipulate it further into forms you've seen in class

but at least you can write $a$ in terms of $b$ by $a'(t) = -\frac{b'(t) + rb(t)}{S}$

[ocean seal]

∧res

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[lone trout]

ok thank u!

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[queen raven]

hi

[queen raven]

i know this is simple

but i cant figure it out after a specific part

ik that you have to flip the second term and times it

to make it equal to (4x((9x^2)-1))/(((3x^2)+5x+2)((18x^2)-6x))

or this

but then do i expand from here or what?

[lime silo]

thts ur answer

hope it helps

if u didnt get my handwriting

[alpine sable]

you factorize these expressions in the numerator and denominator... and u'll get the answer as posted by v forv vendetta

[lime silo]

if u guys are interested in math i made a little website ...
https://thewarpingtesseract.neocities.org/

[queen raven]

ok thanks

.close

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[knotty wren]

am I doing this right?

[knotty wren]

i didnt use the product rule anywhere

and the only problem is that I missed the denominator rifht

quotient rule

yeah

i forgot that

but apart from that

are my steps correct

lmao

but its not wrong is it

the positive sign?

thats what i did

no?

and i differentiated that first

the high

how?

its d-high•low - d-low•high

what I am not getting right

oh okay

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[knotty wren]

i did it again, are all the steps correct

<@&286206848099549185>

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[crimson beacon]

asa?

angle side angle?

or angle angle side

[severe sluice]

NEI

[crimson beacon]

?

[severe sluice]

i mean

common acronym

stands for not enough information

[crimson beacon]

i mean both of them is right triangle

given amb = cmb

angle a is equal to c

[crimson beacon]

there

[severe sluice]

oh

okay

consider triangle ABC

[light ether]

what are you trying to solve

[severe sluice]

which type of triangle is it? @crimson beacon

[crimson beacon]

isoceles?

[severe sluice]

yep

[crimson beacon]

so ab = cb?

[severe sluice]

and if ABC is isosceles, what info do you have about its side?

[severe sluice]

yep

[crimson beacon]

ok so its aas?

[severe sluice]

yeah

[crimson beacon]

Thanks

for the help

:D

.close

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[twilit ibex]

I just calculated the gradient for the following function

f(x,y) = 2x + xy*y^2

At the point (10,20)

I got

(8002,12000)

I then tried subtracting 10 - 80002, 20 - 12000 and inserting that into the function f.

I expected a lower z-value, but instead I got the value in the screenshot.

What went wrong? Isn't the gradient suppossed to be the steepest slope upwards of the 3D function, and then the negative the steepest slope downards?

[twilit ibex]

Please tag me, if you have an answer

[severe sluice]

isn't the gradient a vector?

[twilit ibex]

It is, and so are the input-variables.

They can be represented as

[x,y] - [8002,12000]

[severe sluice]

i mean
80020 is NOT a vector...

[twilit ibex]

The input

x,y are actually vectors [x,y].

The gradient of f is the vector

nabla_f = [delta_f/delta_x1(x,y) , delta_f/delta_x2(x,y)]

Minussing the input vector and the gradient at the point should - according to my understanding - yield a lower Z-value.

-7992 is the first coordinate of nabla minus x
-11980 is the second coordinate of nabla minus y

[severe sluice]

,w grad 2x+xy^3

[ocean seal]

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Requested by it's ¬Sam#6194

[severe sluice]

,w grad 2x+xy^3 at (10,20)

[ocean seal]

Results provided by WolframAlpha

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

Requested by it's ¬Sam#6194

[severe sluice]

u h h

this is useless-

gimme a second to calculate it.

[twilit ibex]

okay

You do realize once again,

That the partial derivative of f with regards to x is the upper coordinate of the vector.

And partial derivative f wrt(y) is the second coordinate of the vector, right...?

[severe sluice]

yes i know that--

ugh

[twilit ibex]

Right, the gradient has been calculated correctly.

MY question is simply; Why does it not decrease when I subtract the gradient from the input vector?

[severe sluice]

well
the gradient vector only points in the direction of maximum increase locally

it doesn't care if after the initial increase, the x-value drops down or something (since it's just the prtial derivatives at that point)

so you can't just subtract the gradient and expect a smaller value

[twilit ibex]

If its negative is the steepest decline locally, then why does it not decrease then?

[severe sluice]

let me just give you a graph with 1 variable

(it's the same in 2 variables)

argh i'm terrible with the mouse

anyways

at point A, let's say that grad f = df/dx = (a large number)

[twilit ibex]

Oh okay, I think I might understand why:

In a veerrryy small interval it does point towards the steepest decrease.

I.e -gradient(x,y) * g, where g is infinitely close to 0, will always decrease.

[severe sluice]

here

although my handwriting is terrible with a mouse

[twilit ibex]

Is my understanding correct?

In the other message I wrote.

If so, I think I understand.

[severe sluice]

yeah

it's kinda correct

[twilit ibex]

Alright, thank you very much for the clarification 🙂

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