help-17

[spiral inlet]

1-sin^2(x) is a difference of squares

no problem 👍

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✅

[inner osprey]

does E(x) mean e^x

oh

that's cool actually haven't seen that before

one approach here is you can change the limit

like you can replace x with 1/x and evaluate the limit like that

but to be honest that's not actually necessary

this is not true btw

it's very important that you are approaching negative infinity, which means that 1/x approaches 0 from the negative end, not the positive end

you can

since floor(x) is a function that's defined for negative numbers

well what's the floor of a very small negative number

no

recall that the floor function is the "greatest integer function"

which outputs the greatest integer less than or equal to the input

for an easier illustrative example,

consider like what the floor of (-0.01) would be

no

then review it

since 0 is greater than -0.01, not less than

right

now

do you think that the limit of E(1/x) will be undefined as x goes to -infinity

also right

yes though ur reasoning is incorrect

recall that E(-2/x) flips the sign on the negative infinity

no issues

yeah it limits to 0

welcome 🎉

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[brisk moss]

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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).

[brisk moss]

hyzae :3

[vocal sleet]

@earnest flame Has your question been resolved?

[vast shale]

For part 1. Make a perpendicular line to AC (cross it at point G) from centre then you have triangle:
OGC where OG=AD where AD^2= r^2-OD^2
GC=CA-AG
Then AG=OD
Therefor we have
r^2-OG^2=(CA-AG) ^2

Then substitute values:
r^2-(r^2-OD^2)=(CA-OD) ^2
Now let OD=y and CA=x
LHS=y^2
RHS=x^2+y^2-2xy
Therefor LHS=RHS
We have :
x^2=2xy
Therefor y=2x

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@earnest flame Has your question been resolved?

[vast shale]

Part 2 :

Since Op perpendicular to AB then OM 90° to surface from both sides Therefor angles AMO and ANO are equal.
Furthermore OQ=OP=r
Then since both NQC and MBP are right angle triangles Therefor MP=MQ so does angleMPB=angleNQC
Or whatever use this https://www.splashlearn.com/math-vocabulary/rhs

And since triangles are conjurgent sides are the same

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[storm vine]

how do i draw the triangle

[fallen hawk]

What kind of gangster school you go to where bear grylls is part of the curriculum

[hallow plover]

This FELLS like a shitpost

So anyway how would you approach this?

[fallen hawk]

I have no idea

[prime badge]

I'd draw a little reference line off Bear's location representing North, then measure the 25 deg in the west direction.

[storm vine]

i just need to know how to draw the triangle. i know what to do from there

[hallow plover]

Well start by drawing a point for Bear

then follow the instructions with the angles

and you should get something resembling a drawing

[storm vine]

i tried. i dont know what they mean

[prime badge]

The thing about the line to camp is, we don't know how far away camp is, so it's an infinite line.

After Bear moves, the new angle will cross the first line giving you the camp location.

[hallow plover]

Assume a distance

you're not drawing to scale anyway

Just put a point somewhere on the line and work from there

[storm vine]

??

[cyan talon]

looks like a fine start

on the left it's the path bear would take if he were to go directly to the camp

on the right is where he actually goes

[cyan talon]

you're an alt of promiscuous or what

[hallow plover]

Unrelated : This is a prime example of a cursed math diagram

[storm vine]

okay now how do i use the law of sines on that

[cyan talon]

you haven't drawn all the info yet

[storm vine]

what else do i draw?

[vast pivot]

where he went

[prime badge]

Bear's second location. A new North reference line. Angle to camp.

[storm vine]

I dont understand.

if someone could draw the triangle for me i would be eternally grateful

yall fucken suck

.close

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[prime badge]

@storm vine

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[vast shale]

Any1 tryna help me with this

[fallen hawk]

my eyes are tired but seems like 30 to me

[vast shale]

so like 30mm?

[hallow plover]

you reading inch scale or mm?

[vast shale]

mm

[prime badge]

The question says mm

[hallow plover]

Oh right, so what do you think it is?

[vast shale]

if u ask me i think its 0.021 mm

[prime badge]

Look at the whole number before the 0 mark.

[hallow plover]

Look here first

The 0 line denotes the whole amount of mm

[prime badge]

👆

[vast shale]

right between those lines are they like .5 mm?

[hallow plover]

Well that big 10 is 10 mm

and the next line on the top scale is 11

since our 0 line is after the 11 line, but before the 12 line

that means we have 11 mm whole

Now you need to look at the bottom scale for the remainder

[vast shale]

idk if im right but the bottom one would be 2.5 since both lines up perfectly no?

[hallow plover]

yes, but you don't read that as 2.5

you read it as 0.25

[vast shale]

so would be 25 instead

ahh

[hallow plover]

so the solution would be 11 + 0.25

[vast shale]

11.25 is the answer

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[echo plaza]

how would i do this?

[echo plaza]

is this an invariant quesiton?

[fallen hawk]

hello again

[echo plaza]

hi

[fallen hawk]

a possible move is to add? what

[echo plaza]

yeah im confused about that

how in the world can you get to 0

[solar geyser]

add negative numbers

[echo plaza]

oh

what if you made all the numbers 1

and then subtracted one from each pair

bam

done

but they probably dont want one case

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[vast remnant]

how do I find the average height

[vast remnant]

nvm

got it

.close

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[tardy cove]

Is this solvable? How can I solve this?
i2(0)=0

[tardy cove]

Equations come from here:

[cyan talon]

it's a bit involved, so here's a nice resource explaining how to solve them
https://tutorial.math.lamar.edu/Classes/DE/SystemsIntro.aspx

(I assume you already know how to solve basic ODEs)

and if you're lazy wolfram alpha can certainly solve it for you

@tardy cove

[tardy cove]

I'll try and learn it thanks

.close

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[velvet gulch]

can i get help for these two?

[sharp frost]

The angle OBC is 110

[mild flower]

the first one is an isosceles triangle and the second one is a right triangle

[sharp frost]

So 180= pi
Then 110 = pi/180 x 110

The length of arc is Radius x angle subtended

[mild flower]

let's let her keep going with these hints

[sharp frost]

Oh, wait

[velvet gulch]

uhm

[sharp frost]

U r not the op

[sharp frost]

Did u understand?

[velvet gulch]

i didnt really learn this yet so idk what to do

[sharp frost]

It's a basic formula

Otherwise no other way

[velvet gulch]

what formula

[mild flower]

here's a question, what have you done that seems similar to this

[velvet gulch]

uhh

ik some triangle theorems but i dont think thats similar to this

[sharp frost]

Well, u can only learn then

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[velvet gulch]

.close

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[vast shale]

pls help 😭

[edgy gulch]

you know the formula for area of circle?

[vast shale]

2pi radius^2?

or just pi radius^2

[edgy gulch]

well sorry not area for the entire circle

just for a sector

[vast shale]

one sec

this is the example and i dont really get it

this was the example problem btw

[edgy gulch]

huh ok

have you learnt A = 1/2 r*s before

[vast shale]

arc= 1/2 the angle of the middle point thing

[edgy gulch]

wha

[vast shale]

might be wrong

do you understand the problem?

[edgy gulch]

yeah i do

you have the arc length and radius

and you need to find the area

theres a formula A = 1/2 * radius * arc length

[vast shale]

i think im gonna give up im gonna explode from confusion

[scenic spindle]

whats the formula for the area of a circle?

(im trynna help)

[vast shale]

im happy with the grade ill get so i gave up on that and im doing another assignment

thx for the effort tho yall

[scenic spindle]

its easy

i promise ull understand it

[vast shale]

ok do you mind if i put this on hold to finish another one?

[scenic spindle]

sure

[vast shale]

thanks

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[harsh igloo]

I need help evaluating a piecewise function that is also a limit.

[harsh igloo]

lim f(x)= 2-x if x<0
x^2+2 if 0<x<2 3 x>= 2

evaluate x->0 and x ->2

[lavish sluice]

what is 3x>=2?

[harsh igloo]

couldnt format greater than or equal to lmao

here's the problem

[lavish sluice]

ok so first check x tending to 0- and 0+

if you get same value

then limit is that value itself

[harsh igloo]

So for 0-

2-0 is 0

and for 0+

0^2+2 is 2

so it's 2?

or is that not how you go about it

@lavish sluice is this the correct method?

[lavish sluice]

yea

correct

[harsh igloo]

same applies for 2, but we get different answers. 2- is 4 (2^2+2=4) and 2+ is 3

so does not exist?

[lavish sluice]

yea

[harsh igloo]

one more question

[uneven chasm]

Yes

[harsh igloo]

how can I prove it is an identity

can be rewritten as

1/y+1/x / y/x + y = x/y(1/y)

[inner osprey]

I’d start with the left hand side here

there’s a few ways to continue but one way that i suppose works is ||convert LHS into sine and cosine (this is standard method for dealing with problems with things like tan, cot, sec, csc)||

[inner osprey]

well ig judging by this message it looks like you alrd did that sort of

though it’s not correct

[harsh igloo]

where did I go wrong?

[inner osprey]

when you rewrote Cotx

[harsh igloo]

wait

cot is x/y

yeah just saw

[inner osprey]

nice

now you can just find some way to rewrite that big fraction and you’re good

[harsh igloo]

hmmmm

x/y^2

which is the same as the RHS

thaks

[inner osprey]

yw

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[cobalt plank]

i don’t get how to do 2e

it’s 50 = 4x (6-x) (5 - x)

but how do i figure out x?

[vocal sleet]

@cobalt plank Has your question been resolved?

[velvet glade]

you would have to expand it and then solve it as a cubic and find the zeros

[cobalt plank]

so 50 = 4x^3 - 44x^2 + 120x

what’s the zeros?

[velvet glade]

have you done factorisation of polynomials?

so youd have the equation $4x^3-44x^2+120x-50=0$

[twin meteor]

FailureToBeGood

[cobalt plank]

okok

[velvet glade]

its impossible to get an integer value for x when you solve it so i think the questions wrong

cause you end up with x = 0.506, 3.56, 6.932

[cobalt plank]

oh so far i’m dividing x-5 by the cubic

and the answers i got for x were 0, 5, 6

could that also be correct

[velvet glade]

when you sub in those solutions the volume goes to zero

[cobalt plank]

so how do i get to this

is it possible with a cas calculator?

[velvet glade]

yea youd need a computer software or like uni level maths

[cobalt plank]

okk thank u

[velvet glade]

sorry i couldnt help

gl tho

[cobalt plank]

nono that question needed a cas calculator which i’m learning rn too

thank u for the help

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[tidal dock]

i have this infinite sum

[tidal dock]

$\sum_{n=1}^{\infty} n(1-p^n)$

[twin meteor]

artemetra

[tidal dock]

where p < 1

p = 5/6 in fact

[tidal dock]

i don't know where to start

[tidal dock]

wait this diverges

[warped nexus]

yes

[tidal dock]

okay then i'll send the full question

i did part a completely

for b) i) i got

E$(X) = \sum_{n=1}^{\infty} n P(X=n)$

[twin meteor]

artemetra

[tidal dock]

and for b) ii) i simplified

$= \sum_{n=1}^{\infty} \left(n\cdot q \cdot \sum_{k=0}^n p^k\right)$

[twin meteor]

artemetra

[tidal dock]

$= \sum_{n=1}^{\infty} \left(n\cdot q \cdot \left(\frac{1-p^n}{1-p}\right)\right)$

[twin meteor]

artemetra

[tidal dock]

$= \sum_{n=1}^{\infty}n (1-p^n)$

[twin meteor]

artemetra

[tidal dock]

since q = 1-p

where is my mistake?

[graceful fox]

what is P(X=n)

[tidal dock]

probability that a die will end up in a 6 after exactly n throws

[graceful fox]

yes so what is it

[tidal dock]

fuck

i realised it

[tidal dock]

q p^n?

[graceful fox]

it is q.p^(n-1)

[tidal dock]

yeah

darn it

thanks tho

i was struggling to see the mistake

.close

[graceful fox]

all good

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[rugged glade]

why does one of the examples have a negative sign for the square root of x²? meanwhile the other exercise doesnt

[outer warren]

definition of absolute value,

depending on the sign of x

for negative x
sqrt(x^2) = |x| = -x → x = -sqrt(x^2)

.
sqrt(x^4) = |x^2| = x^2
sign of x doesn't matter here, x^2 is non-negative

[rugged glade]

so its negative cause of the - infinity?

[outer warren]

yes

[rugged glade]

okay thank you!

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[vast shale]

stuck on learning Linear Functions and their inverse.

[brisk cloak]

these have a pretty clear methodology

now you have an equation of the form y= something

you want to do stuff to end it up on the form x=something

so since we want the x isolated we will move the 15 over to the otherside and have 5x=y+15

and since we want x alone we also divide both sides by 5 to get our answer

[vast shale]

I see

.close

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[mystic frost]

f(x) = (mx-1)(2x-1)^2
m is a paremter
its given that the slope of the tangent in x=1 is 6

find paremeter m

[lusty snow]

am i gay or you just put 1 instead of x and 6 instead of m

[mild flower]

m isn't the slope

[mystic frost]

it isnt the slope

[gritty hemlock]

find f'(x)

[mystic frost]

that is the problem i dont know how to open with paremetrs

[gritty hemlock]

treat m like a constant

[mystic frost]

f'*g g' f

[mystic frost]

ok

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[blissful egret]

I'm need help in simplifying after finding the deriv of the function below,

like after using chain method and quotient I'm left with the two equations but the problems is idk how to simplify at all

I did appreciate if you could go step by step after finding it's derivative of the function, and then telling what to and what not to

[lime gorge]

What have u tried

[blissful egret]

I'm stuck here

After that idk how to simplify at all

[lime gorge]

Ur on the right track

Just evaluate the ‘ parts

Take those derivatives

[blissful egret]

Idk how to evaluate do I multiply the 2x with the inside?

Or do I derive them?

[lime gorge]

Yes the second one

[blissful egret]

Should look like this right?

[lime gorge]

Yes

[blissful egret]

So how do I simplify this with the other one which is 4(2x/x^2 +1)^3?

[lime gorge]

First simplify numerator here

[blissful egret]

Expand?

[lime gorge]

Whatever

Just simplify

[blissful egret]

Idk how to do that

[lime gorge]

2x^3 + 2 - 6x^3?

[blissful egret]

Do I cancel them out?

What she method I need to use?

Or what is the lesson name I should watch ?

[lime gorge]

It’s just subtraction

[blissful egret]

Subtraction polynomial?

[lime gorge]

Yea ig

[lime gorge]

U can’t do this?

[blissful egret]

I came back from military conscription for 9 month so I forgot every basics and was made to do calculus man

I'm barely holding on the grades

[lime gorge]

Ah man I see

Sorry to hear that

[blissful egret]

So idk where to start

[lime gorge]

Khanacademy is a good resource

And there’s lots of YouTube videos that are helpful

[blissful egret]

Idk where to start and my exam is in wed

I was able to solve the others since they asked to find deriv and the method needed but they didn't taught us how to simplify

So when they asked to simplify idk where to start

[lime gorge]

Yea I understand

Watch some polynomial arithmetic videos I guess

[blissful egret]

Will it have like two fraction and simplifying them?

[lime gorge]

2x^3 + 2 - 6x^3 = 2 - 4x^3

From there u have

[blissful egret]

What did you do?

[lime gorge]

2x^3 - 6x^3

They’re like terms

So we just subtracted

And got

-4x^3

[blissful egret]

And the 2?

Why move it front?

[lime gorge]

Doesn’t rlly matter

2-4x^3 = -4x^3 + 2

Same thing

[blissful egret]

Ah alright so first step subtract like terms that have same power?

[lime gorge]

Yes

[blissful egret]

Term and power are the same? Just wanna confirm

[lime gorge]

Not really

I suggest watching a video, to clarify the basics

A bit tough explaining it like this here

[blissful egret]

It's fine just wanted to confirm not explain

So then now how to simplify the other side we multiply 4 with 2x?

[lime gorge]

$\frac {4 \cdot (2x)^3}{(x^3 + 1)^3} \cdot \frac {2 - 4x^3}{(x^3 + 1)^2}$

This is what we have now

[blissful egret]

There is a 4 on the front

On the left side

[lime gorge]

Oh yes

[blissful egret]

Since we found the derive using chain rule

[blissful egret]

Alright like this

[lime gorge]

So now simplify the left numerator

[blissful egret]

It will be( 8x)^3 right?

[lime gorge]

Not quite

$(ab)^c = a^c b^c$

[lime gorge]

Use that to simplify

[blissful egret]

😭

How do you multiply x with 8? Does it make it into 512x^3???

[lime gorge]

$(2x)^3 = 2^3 x^3$

[lime gorge]

What’s that equal to

[blissful egret]

Oh? 2? I see I see

8x^3

Right? Then we multiply it by 4?

[lime gorge]

Yes

[blissful egret]

32x^3 now what do we do with the power down? Same thing we do the a^c • b^c?

[lime gorge]

No

Now we have

$\frac {32x^3}{(x^3 + 1)^3} \cdot \frac {2 - 4x^3}{(x^3 + 1)^2}$

[lime gorge]

Now how do we multiply 2 fractions

[blissful egret]

Cross? Or num x num and deno x deno?

Then we can subtract 4x with 32 cuz like terms?

[lime gorge]

No u have to multiply

No subtraction

Num num deno deno

[blissful egret]

So it's gonna be -128x^6 + 64x^3

?

[lime gorge]

Correct

And what’s the denominator

Don’t expand it all out

Just combine them

[blissful egret]

It's too long idk TT TT

[lime gorge]

No

[blissful egret]

(X^6 +1)(x^3+1)^2?

[lime gorge]

$a^b \cdot a^c = a^{b+c}$

[lime gorge]

Use that for what we have in deno

[blissful egret]

Oh cuz they are the same right?

So it's (x^3 +1)^5?

[lime gorge]

Yes

So now u have the answer

Actually wait

[blissful egret]

Hm?

[lime gorge]

Yes nvmnd

That’s the answer

[lime gorge]

Numerator

[lime gorge]

Denominator

[blissful egret]

There is a problem tho

They don't match the choice's they given me

[lime gorge]

Show the choices

[blissful egret]

One min

Here they are

The bottom is correct but the top is strange

[lime gorge]

Looks like they just want u to factor out the greatest common factor

[blissful egret]

Is that it?

[lime gorge]

64x^3 - 128x^6

Yea just factor out the gcf

[blissful egret]

How do I do that?

[lime gorge]

For example

Gcf of 15x^2 + 25x^3 is 5x^2

So it becomes

5x^2(3 + 5x)

[blissful egret]

So the gcf here is one of the 32x^3?

[lime gorge]

It’s not 32x^3

[blissful egret]

64?..

[lime gorge]

Yea

64x^3

[blissful egret]

How?

[lime gorge]

64x^3 - 128x^6

64x^3 goes into both of these evenly

32 also works, but it’s not the greatest common factor

It’s just one of the factors

[blissful egret]

So it's the 3 choice?

[lime gorge]

No

[blissful egret]

First?????

[lime gorge]

Yea

[blissful egret]

Damn

Thanks man I have some questions if your okey with it

[lime gorge]

I gtg, just open a new channel and ask

[blissful egret]

Oh alright how do I close?

[lime gorge]

Do .close

[blissful egret]

.close

[vocal sleet]

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[vast shale]

,r

,r

Crazy

Why did they add the time for P onto the time for Q in part B

[tight sonnet]

,rotate

[vast shale]

Thanks

.solved

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[vast shale]

.reopen

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✅

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[unreal sparrow]

Why doesn’t this work?

[lucid crypt]

you can't bring an integral inside a square root

[unreal sparrow]

Ok, how else should i solve this problem?

[lucid crypt]

keep the integral outside and evaluate it normally

[unreal sparrow]

So i take the integral of the distance formula?

[lucid crypt]

formula for distance travelled is $$\int_{t_0}^{t_1} \sqrt{x'(t)^2 + y'(t)^2} \mathrm{dt}$$

[twin meteor]

AlphaNull

[lucid crypt]

yeah basically

[unreal sparrow]

Yep that works thanks, i got 96.726

But i wonder why the integral can’t be inside the radical?

[lucid crypt]

i think the best way to explain this is that the integral is a linear function

you have $\int_a^b f(x) ; \mathrm{dx} + \int_b^c f(x) ; \mathrm{dx} = \int_a^c f(x) ; \mathrm{dx}$

[twin meteor]

AlphaNull

[lucid crypt]

but the square root isn't linear

so bringing it inside then square rooting will not respect linearity

[unreal sparrow]

Ohk i see thanks

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[wind belfry]

Hello
I am a bit confused on what is considered an infinite interval
would a closed interval like [1,2] be an infinite one?

[wind belfry]

Considering there is infinite numbers in it

[brisk cloak]

yup

[mild flower]

i don't think so because then almost all intervals would be infinite

[lucid crypt]

i think a more conventional definition is one where one of the endpoints is infinite

like $(2,\infty)$

[twin meteor]

AlphaNull

[brisk cloak]

okay nevermind

a quick google search led me to this

apparantly "finite and infinite" intervals are just the same as "bounded and unbounded" intervals, and the first way to describe them is far more confusing

[wind belfry]

im confused maybe my terminoligy is wrong
if we take [1,2] there is infinite real numbers in it

same for (1,2) and that does not even have an endpoint right?

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[lean sable]

This is the question

[lean sable]

Is this the right work for 2?

[vocal sleet]

@lean sable Has your question been resolved?

[lean sable]

<@&286206848099549185> it’s been 15 minutes so I think I can @ u? 😭

[vocal sleet]

@lean sable Has your question been resolved?

[vocal sleet]

@lean sable Has your question been resolved?

[lean sable]

I just keep getting ghosted here 💀

[vocal sleet]

@lean sable Has your question been resolved?

[vocal sleet]

@lean sable Has your question been resolved?

[jade cairn]

For part A: it looks like you left out x when you did the ratio test.

[vocal sleet]

@lean sable Has your question been resolved?

[lean sable]

R is still one either way right

[jade cairn]

It's 1/3. The limit of (3xn)/(n+1) as n goes to infinity is 3x. So, x has to be between -1/3 and 1/3.

[lean sable]

What about everything else

Is everything else rigjt

[jade cairn]

For B, the fourth term should be negative. Also, it looks like you forgot to express f' as a rational function, like the question asks.
And for C, when you write a Maclaurin series, you need to evaluate the function at 0. So everywhere you wrote f(x) should actually be f(0).

[lean sable]

Can you also help me with 8

.close

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[shut storm]

last questio of my lesson

i got 206.46 days for 200g of the compound to decay to 65g.

but it isnt any of the multiple choice ?

[vocal sleet]

Show your work, and if possible, explain where you are stuck.

[vast shale]

whats the concept

does it mean that the mass decreases by a half in that time

[peak matrix]

yes

[shut storm]

yes exactly

[peak matrix]

and the decay can be modelled through exponential equation

[peak matrix]

what was the equation you were working with?

Maybe we can trace the mistake from there

[vast shale]

i modelled it using a geometric sequence

[shut storm]

N(t)=N_0​(1/2​)^T/t​

[peak matrix]

okay, cool

what values did you plug in?

[shut storm]

^

[peak matrix]

that's correct

now it just needs to be solved

[shut storm]

yes so isoloate and solve for t

[peak matrix]

mhm

how did you do that?

[shut storm]

^

[peak matrix]

correct

[shut storm]

then

[peak matrix]

what did you do now?

also correct

[shut storm]

now solve for T

[vast shale]

This is what I did

[vast shale]

idk what formulas you get told to use but i think this works quite nicely

[peak matrix]

you probably just wrongly plugged it in calculator

[shut storm]

this is what i plugged in

[peak matrix]

when i plug it in calculator im getting 291

.8

[vast shale]

same

[shut storm]

Weird

alright well appreicate yall

[peak matrix]

ln(13/40) = −1.12393009665

[vast shale]

ln(13/40) is not that

[vast shale]

yeah

[peak matrix]

so yeah, just numerical error basically

[shut storm]

quick question

whats that

on toop

[vast shale]

n

bad hand writing sorry

n is the number of days

[shut storm]

no all good ty

[vast shale]

that 2nd log is looking more like lag lol

[shut storm]

lol

all good thanks so much boys

[vocal sleet]

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[vast shale]

TR = 12 m

XZ = 20 m

UW = 15 m

What is the sum between the shortest distance between S and T and the shortest distance between Z and U.

[plucky trout]

assuming angle SRT = 90, use pythagorean theroem

we have a 5-12-13 triangle so ST = 13 meters

[vast shale]

ST = 13 m

Now we need to find the length of ZU

[plucky trout]

thats easy

[vast shale]

How

[plucky trout]

its 7 meters

we have

XP = 12

[vast shale]

How

[plucky trout]

XP = 12 and SQ = 7

so RT = 12 - 5

wait

RT = 12

but we only want a portion of it

[vast shale]

Have we assumed that TUZZ' is a square ?

Z' is the point on TR where ZX cuts

Just defined it

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@vast shale Has your question been resolved?

[vast shale]

.close

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[upbeat tulip]

Can someone assist me in this problem? I understand I need to reduce to row epsilon form, but I do not know where to go from there

[upbeat spindle]

what does LU stand for , unfamiliar notation

[vocal sleet]

@upbeat tulip Has your question been resolved?

[river minnow]

The LU decomposition means rewriting the matrix as a product of a lower triangular matrix and an upper triangular matrix

[upbeat spindle]

Ty^

In this question the matrix would be equal to a lower triangular matrix * upper triangular matrix

the connection betwwen these matrices would be the diagonals have the same number

in these matrices you fill them with arbitrary constants

multiply each matrix

then the constants will equal the matrix

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[late token]

is the answer B 15

[late token]

I done (2x4)+3 >> 11=2X=1 solve for x so x = 5

for y is was the same 2(3)+3 >> 9 = y-1 solve for y so y = 10

10 +5 =-15

is this prosses correct i havent done this before

[inner osprey]

yes

[late token]

okay thx ❤️

.close'

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[subtle blaze]

What have you tried? Do you know where to start? And what level of maths are you at, there's quite a few ways to solve a cubic

[real barn]

umm wait leme show u

I just know this stuff🦆I can do quadratic but not cubic 🥹

[subtle blaze]

Well for simple cubics like this it's probably easiest to try a few values of x with a small magnitude and see if any work

From there you can compare coefficients with the quadratic that must be the other factor

Looks like -1 works

[real barn]

Can you please teach me.. and use basic words so i can understand

I'm really bad at math

[subtle blaze]

Okay so sub a few small numbers into the function and see if they do in fact equal 0

[real barn]

How?

[subtle blaze]

So i'd start with 0, 1, -1, 2, -2

Replace x with the numbers you're trying

[real barn]

I don't get it 😭

Ok wait

[subtle blaze]

It seems like your notes are following a similar line to what i'm saying

Is there a specific bit you don't get?

[real barn]

Like this?

[real barn]

I'm dumb 😭

[subtle blaze]

Well just sub some x values in

0, 1, -1

See if they work or not

Try that

[real barn]

🥹i still don't get it

[subtle blaze]

Could you maybe try explain which bit you don't get? Your notes show at least a decent understanding so i'm not sure how to explain subbing values in

[real barn]

Synthetic??

[real barn]

Ah it's okay I'm really sorry for wasting your time.. but i think it's better i follow the YouTube i think i get it..

[subtle blaze]

I'm not sure learning synthetic would be the best way forward if you're not sure what I mean by "subbing values in for x"

What method is your teacher teaching you?

[real barn]

I don't know I'm following YouTube no teacher 😭

[subtle blaze]

Also synthetic is gonna rely on you doing the step I was talking about earlier

Finding a small common factor

[real barn]

How to do that

Can you please teach me

[subtle blaze]

What do you understand about what that equation is saying? What does x represent and when a question asks you for a "solution", what does that mean?

[real barn]

🐥i don't know

[subtle blaze]

To be completely honest I really think you need to revisit the basics of algebra

Cubic division is not an early topic

You need a decent grasp of what we're trying to do here

[real barn]

🌧️🐥yeah I'll do that.. thn 😭

I should go and do it thn thank you for your time..

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[mellow geode]

?

[mellow geode]

a>0

[candid nymph]

What are you supposed to do ?

[mellow geode]

prove that it's somewhat equal to $\frac{r^{a-1}exp(-r)}{\gamma(a)}$ i think

[twin meteor]

lilisworld.

[candid nymph]

Are you sure ?

[mellow geode]

not sure

[candid nymph]

But what is the question ?

The initial one ?

Just evaluate the integral ?

[mellow geode]

no it's about the density function

x follows a gamma distribution

gamma(0,a) and i want to find Pr(X>r)

.close

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[charred pewter]

Hi, can someone help me with this problem ?

x, such as : x - (3/x) = 1

Calculate :

x^2 + (9/x^2)

[finite swallow]

square the given expression

[charred pewter]

Thank you, I didn't think of this ;-;

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[vast shale]

gois

[vast shale]

gooiiiis

why is f(x) = y

[hidden kelp]

convention

[vast shale]

what

[hidden kelp]

it's convention that f(x) = y

[vast shale]

to what

[hidden kelp]

And I guess it makes sense if you think about it like a graph. you have an x axis, and a y axis, but the y axis depends on what value of x you have, therefore y is a "function of x" or f(x)

[vast shale]

oo makes sense xp
but..
how does y depend on x

y is the output

[hidden kelp]

exactly

[vast shale]

and x is the input?😭

ioh okay

[vast shale]

thank youuu

so u insert x and out comes y?

like squeezing jelly into a pipe

oo

[vast shale]

jelly the input and the squashed jelly is the y aka the ouput

aigh tanks gois

.close

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[jagged swallow]

i dont get it

[hardy vector]

One way is to use trig angle addition/subtraction identities

The other is the theorem sin(theta) = sin(180 - theta) for all values of theta

[vocal sleet]

@jagged swallow Has your question been resolved?

[jagged swallow]

i dont get it

ive only done till p2

🙂

[hardy vector]

p2???

[jagged swallow]

pure math 2

[hardy vector]

Do you not get the theorem. Or are unable to do the question?

[jagged swallow]

both

😰

[hardy vector]

So accepting the theorem at face value the question is very easy

Do you want to give it another go

[jagged swallow]

i do

whats the theorem

[hardy vector]

sin(theta) = sin(180 - theta)

[jagged swallow]

hmmmmmm

where do i go from there

[hardy vector]

So we have 2sin(180-alpha)

[jagged swallow]

2sin(alpha)=sin(180-alpha)

like that

OHHHHHHHHHH

SO ITS

2P

[hardy vector]

yes it is 2p

[hardy vector]

The equation is not correct

[jagged swallow]

2sin(alpha)=2sin(180-alpha)

like that

[hardy vector]

yep

For the proof the theorem you can use the unit circle definition of sine and congruency testing

Then make use of the period

[jagged swallow]

never heard of those

[hardy vector]

It is not that important

Just take it at face value for now

[jagged swallow]

is this like sin(a-180)=(sin 180 - a-180)

so then is ijust -p

omg

i love u

3+sin(180+a)=3+(sin180 - 180 + a)

so p+3

wait

how am i wrong

WHAT

do i need to multiply the -

[hardy vector]

sine is an odd function. A function is odd if f(-theta) = -f(theta)

So you can let u = 180 -alpha

So we get sin(alpha -180) = sin(-u) = -sin(u) = -sin(180 -alpha)

So the above is for the first question

[jagged swallow]

uh

[jagged swallow]

where did the u come from please

[hardy vector]

For this question you need to start using trig angle addition/subtraction identities. Quick google search and they should come up. 6 main identities in total

[hardy vector]

Look one line up

let u = 180-alpha

[jagged swallow]

u right

[jagged swallow]

3+sin(180+a)=3+(sin180 - (180 + a))
3+sin(180+a)=3+(sin180 - 180 - a))
3+sin(180+a)=3+(sin- a)
3-p

like this

am i supposed to put brackets

or did use the theory wrong

[hardy vector]

The first line it is not clear what you are trying to do

180 + a != 180-(180 +a)

What you could instead try to do is write 180 + a as 180 - (-a)

[jagged swallow]

but why

[hardy vector]

why what

[jagged swallow]

why would i make it as a negative theta just to make it positive again

[hardy vector]

You want to apply the theorem sin(180 - theta) = sin(theta)

To do that we need a subtraction sign

[jagged swallow]

u right

tysmm i got it

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[split quest]

can i rearrange terms in factoring by grouping a polynomial

[split quest]

im not sure if i can rearrange because my teacher said nothing about it

[willow dragon]

|x^2+x-6|>6 hi I have this inequality with the module, among the results I only get -4 and 3 for the book asks for a result which is
-4 ≤ x ≤-1 V 0 ≤ x ≤ 3 how can I do?

[autumn stratus]

!occupied

[vocal sleet]

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).

[split quest]

<@&286206848099549185>

hello can someone answer my question

[hardy vector]

!15min

[hardy vector]

So what do you mean by rearrange. What is the exact transformation you are referring. factorisation can help rewrite an expression

28/4 =7, 49/7 = 7. So it seems like you can do something through factorisation

[split quest]

is 28xy - 49x + 4ky - 7k correct

so they can get common factors

[hardy vector]

yes you can rearrange it like that

[split quest]

common factors of 28xy - 49x is 7x and 4ky - 7k is k

[split quest]

oh okay thank you

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[gray grove]

this is the solutuon to this problem. why is the max of the 4th deriv e^1?

[gray grove]

wouldn't the max be plugging in x --> so e^cos(1)

[crystal gazelle]

What's the maximum value of cos(x)?

[gray grove]

it would be 1

but why do we take the max value of cos andnot the whole thing?

[crystal gazelle]

Well the max value of cos is going to give you the max value of the whole thing

If you imagine e^x, as x gets smaller, so does the value of e^x

So the max value of e^(cosx) is going to coincide with the maximum value of cosx because e is a constant

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@gray grove Has your question been resolved?

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[finite hatch]

how to calculate phase shift

[scenic ravine]

first , what is the amplitude ?

that will give you a

[finite hatch]

5

[merry python]

bum chicken

[finite hatch]

hello friend

[scenic ravine]

after that input an appropriate value of x and solve

$y=5sin(x+ \phi)$

[twin meteor]

ƒ(Why am. I here)=I don't Know

[finite hatch]

guess a value for x!??!

[scenic ravine]

so input x say π

or chose a better value

say an x where it attains a maxima

[finite hatch]

im confused why we subbing a random value

[scenic ravine]

not random

chose a value carefully

[finite hatch]

UM

whats a maxima

[scenic ravine]

maximum value

of the function

[finite hatch]

[scenic ravine]

tell me at what x is y=5

the first time

[finite hatch]

\i found a diff way

that i thinbk is easier

since its + its telling us the graph got shifted to the left

[scenic ravine]

yes

[finite hatch]

so i just did this

[scenic ravine]

that's smart

[finite hatch]

thank u

it took me 1 hour to figure out

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[waxen hawk]

y=x^4 is not a parabola?

[waxen hawk]

How

Someone

Help

[tight sonnet]

its not

[waxen hawk]

Then what it is

[scenic ravine]

just a bi-quadratic equation

[waxen hawk]

Wut

But it looks like a parabola

My mind fucked knowing the truth that it is not a parabola

[tight sonnet]

lmao

[waxen hawk]

How you describe the graph then

Biparabola?

[scenic ravine]

no

just bi-qudratic

[waxen hawk]

But it has symmetric axis

[scenic ravine]

define a parabola for me please

[waxen hawk]

Curve has symmetric axis

[scenic ravine]

no

[river minnow]

If by parabola you mean any curve with an axis of symmetry, then y = x^4 indeed gives a parabola, but conventionally parabolas are the graphs of y = ax^2 + bx + c with a, b, c constants

[scenic ravine]

more specifically a parabola is a the locus of points whos distance from a line and fixed point are the same

[waxen hawk]

What a genius, expert of parabola

Intelligent

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@waxen hawk Has your question been resolved?

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[wary moon]

Just a question that popped up in my head

[wary moon]

say

x+3=y+4

do we subtract or add the constants

[outer warren]

depends on what your goal is, what you're doing

what you plan to do to both sides of the equation

with no clear goal or direction, you do nothing

[wary moon]

oh so only if given a goal, then this can be answered?

[outer warren]

you can make up a goal yourself

its just that as is, each side individually can't be simplified

but you can
do pretty much do the same thing (whatever you want) to both sides of the equation

[wary moon]

Alright next is if there is like a rule that can change the sides of different variables? Like
x=y can turn to x-y=0?

or smth similar to that-

[outer warren]

yes,

[wary moon]

or only the constants can be moved

oh

[outer warren]

that's the result of subtracting y from both sides of the equation

you can add/subtract the same amount to/from both sides of the equation

[wary moon]

Oh ok so say
3x+4=2y, it is just
3x-2y+4=0?

[outer warren]

yes

that would be valid

[wary moon]

alright ty, i can finally sleep

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[vast shale]

I dont know what method i should be using to solve this?

Im stuck at the beginning

I dont know how to solve this at all

[hushed pewter]

please don't occupy multiple channels

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[waxen breach]

Hello, how would I go with solving this for x