help-13

[grave relic]

so -1, 0 and 3,0

[south tundra]

Yes

That means that x = -1 and x = 3 are the roots of x^2 - 2x - 3 = 0

[grave relic]

SOOO

the answer

is

0?

[south tundra]

No no it's -1 and 3

[grave relic]

ok cool

there’s another one🥲

[south tundra]

Let's start with what's given, "The perimeter of ABCD is 26cm" and "The area of PQRS is 45cm^2", can you turn these statements into equations?

[grave relic]

wait

so

i half it and half it again?

wait

no

😰

Wait

divide by 3

the half one of the thirds

[south tundra]

So, the perimeter of ABCD would be 2(AB + BC), right?

[grave relic]

maybe

[south tundra]

Perimeter is the sum of side lengths, right?

[grave relic]

yes

[south tundra]

So the perimeter of ABCD would be AB + BC + CD + AD but the nice thing about rectangles is that CD = AB and AD = BC meaning that's the same as AB + BC + AB + BC or just 2AB + 2BC and 2(AB + BC)

Here we are given that the perimeter of ABCD is 26, meaning 2(AB + BC) = 26

[grave relic]

jesus okie🤧

sooo

how do i work it out

[south tundra]

Now we can divide both sides by 2 and get AB + BC = 13

Now, what would the area of PQRS be?

[grave relic]

why do we need that if we are only doing a to b

[south tundra]

The only thing we know about AB is that AB + BC = 13, which is not quite useful considering that we don't know the length of BC, so we try to look at the other bits of given information in order to resolve that issue

We are given that the area of PQRS is 45, meaning PQ * QR = 45

But we are also told that QR = 10 and PQ = BC

So that equation turns into 10BC = 45

Meaning BC = ?

[grave relic]

i’m kinda thinking maybe i should give up

[south tundra]

If you want me to slow down/elaborate more, feel free to say so

[grave relic]

no it’s ok i’m sure my teacher won’t mind i’ve already done 2/3rds of the hw😁😁thankyou so much for your time and help!!

[south tundra]

Alright

So, continuing, dividing both sides by 10 gets us that BC = 4.5

And this is great because, like I mentioned earlier, we couldn't solve for AB straight away because we didn't know the length of BC

But that's no longer an issue, we know that BC = 4.5

Meaning AB + BC = 13 turns into AB + 4.5 = 13 and therefore AB = 13 - 4.5 = 8.5

[cedar kiln]

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[mint lily]

Is this true:

[mint lily]

Or is this true:

[south tundra]

Yes

It would be quicker if you just multiplied both sides by -1 though

[cedar kiln]

@mint lily Has your question been resolved?

[mint lily]

But which one?

[cedar kiln]

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[earnest steppe]

would this statement be true if x = -5 even though -5 > 2 is false but (-5)^2 > 4 is true so the implication would be true

Im just a bit confused since the textbook didnt expand on that and just trying to make sure my understanding of implication is correct

[dim tiger]

How is -5>2

-5<0 and 2>0

[spice phoenix]

x^2 maybe

[earnest steppe]

its not, thats why it is a false statement

[dim tiger]

You have to pay attention

That $x>2 \implies x²>4$

[wraith dagger]

calculus is fun

[dim tiger]

Nvm I said something wrong

I'll guide you through this

[dim tiger]

This statement just tells that if x>2 then x²>4

[royal loom]

You can think of it as saying, “if x is greater than 2, then, this implies that…”

[dim tiger]

But It doesn't say $\emph{if and only if}$ $x>2$ then $x²>4$

[wraith dagger]

calculus is fun

[dim tiger]

So it is an implication in one direction only

x²>4 doesn't necessarily imply that x>2

Because any x<-2 also satisfies x²>4

[dim tiger]

But this doesn't contradict this statement

Do you get what I am saying

[earnest steppe]

Hmm okay, I understand, if the implication was both direction it would contradict?

[dim tiger]

Yes so saying $x>2 \leftrightarrow x²>4$ is wrong

Bro why isn't the symbol working

[wraith dagger]

calculus is fun

[dim tiger]

Let's let this pass XD

[earnest steppe]

Okay, thank you, I understand it now

[dim tiger]

This is wrong because you are saying x²>4 means that x is necessarily >2 and x>2 means that x² is necessarily >4

Although the latter is true

But since the former is false then the equivalence fails to be true

[earnest steppe]

alright, thank you

.close

[cedar kiln]

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[strange ingot]

I need help with this Matrix, It's already in row-echelon form, i just want to verify that my solution is correct

[strange ingot]

this is the Matrix

is this solution correct?

This would mean that there are an infinite number of solutions to this system.

<@&286206848099549185>

[cedar kiln]

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@strange ingot Has your question been resolved?

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[twin flax]

Hi, I need with this question

[twin flax]

Integrating it

[buoyant latch]

use your trig identities

[jagged thicket]

notice sin(6x) is sin(2 times 3x) and sin(10x) = sin(2 times 5x)

and sin(30x) = sin(2 times 15x)

and sin(2x) = sin(2 times 1x)

[cedar kiln]

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[untold wigeon]

What is the inverse of the function f(x) = 34 - 4x^2 that exists over a restricted domain?

[untold wigeon]

Ive tried just ignoring the "restricted domain" part because I was told it didnt matter, But there are too many numbers for me to just do it normally. Its really confusing.

[keen bluff]

flip the x and y

x=34-4y^2

now solve for y

sqrt((x-34)/-4) = y

you get sqrt(34-x/4) = y

then u do sqrt(34-x)/2 = y

f^-1(x) = sqrt(34-x)/2

[untold wigeon]

how did the 4 turn into a 2?

oh

cause its squared?

[civic eagle]

you're supposed to help them solve it, not do the work for them.

[keen bluff]

@civic eagle mb

[civic eagle]

yes, 4 is a perfect square.

[keen bluff]

yeah cause you can sqrt(4) so you simplify it

[untold wigeon]

ohhh

okay

so my answer rn is f^-1(x) = square symbol thingy (34-x)/2

is that correct?

im going to take that as a yes

woo

.close.

???

ill just let it do it by its self

[cedar kiln]

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[odd sierra]

What am i doing wron gplz

Like even if its right work shouldnt i be able to cancel stuff out at this point

[paper sleet]

what you got is correct and you can cancel stuff out

[sly abyss]

no its not

i dont know why he got 36

on the top

oh

he has two 6

on the bottom

wait but thats still just wrong

Your very top section is good

but on the second half you

you got an incorrect common demon

@odd sierra

[odd sierra]

Hm

Let me see

[sly abyss]

your 2nd step is incorrect

you do not need to mutiply the top by 6 at all

[odd sierra]

the denominator?

oh

OH

[sly abyss]

you can just have it as

6

lol

[odd sierra]

jomg

Llol

ok

So it should like something like

the bottom part

but the denominator for the second fraction to the right is 6x^2y^2 now

[sly abyss]

not 2y

[odd sierra]

typo sry

6x^2y^2

wth

[sly abyss]

oh

i see

ye

[odd sierra]

Why i keep doing that typo

Ok

[sly abyss]

but u can factor the stuff btw

[odd sierra]

yes then canecl right

[sly abyss]

@odd sierra

what did u end up getting

[odd sierra]

Im stuck

I factored the numerator out on the top left

Like the right fraction wouldnt it just be 6

ya i did something wrong

[sly abyss]

dawg

you dont need that 37

36*

[odd sierra]

ok i got rid of it

I forgot to remove

[sly abyss]

also

its y^2 -x^2

[odd sierra]

ah

Ok

After that stress i got 6xy

i found t hat i can cancel out the y^2-x^2
with otehr

[sly abyss]

rewrite it

and show me your new form

[sly abyss]

you cant cancel

[odd sierra]

OH

its in different order omg

[sly abyss]

ye

[odd sierra]

ahhhhhhhh

Ok

[sly abyss]

you make factor it

into

[odd sierra]

(x-y) (x+y)?

[sly abyss]

well

you want

to make it a lot easier

on the y^2-x^2

[odd sierra]

o

[sly abyss]

you mutiplly it by -1

so it becomes x^2-y^2

and you just have a -1 now

[odd sierra]

AHh

Ok

[sly abyss]

so your answer is right

its just negative

[fallow parrot]

Uhm

@odd sierra

Your orignal answer is right

Without the negative

because if you're just going to cancel out the x^2-y^2 and the y^2-x^2 with (x-y) (X+y) and (x+y) (x-y)

You will be left with 6x^2y^@ all over xy

there fore your answer of 6xy is correct

[odd sierra]

??

Oh

u sure for this one?

[fallow parrot]

100%

[fallow parrot]

See

This is not the case @odd sierra

Take a good read at my explanation @odd sierra

[sly abyss]

no

youre wrong

i am right

[odd sierra]

uh

[sly abyss]

its -6xy

not 6xy

what

[fallow parrot]

It can't be negative

[sly abyss]

dawg it literally is

[fallow parrot]

He factored out

[sly abyss]

i am 100000000000 percent sure

yes but its x^2 -y^2

[fallow parrot]

because if you're just going to cancel out the x^2-y^2 and the y^2-x^2 with (x-y) (X+y) and (x+y) (x-y)

[sly abyss]

this is just wrong

y^2-x^2

[fallow parrot]

You cross them all out

[sly abyss]

goes into

(y+x) (y-x)

so you cancel out y+x and x+y

[fallow parrot]

Ok ...

[sly abyss]

but you cant cancel out (y-x) (x-y)

[fallow parrot]

Ok even then I am sure the negative will not belong in the answer

[sly abyss]

you can but it would become (x-y)/ - (-y+x)

Bro

it 100 percent does

[fallow parrot]

How so?

[sly abyss]

ok so you think the answer is 6xy?

[fallow parrot]

Exactly

[sly abyss]

?

thats just wrong

[fallow parrot]

You are unable to explain

[sly abyss]

I AM??

I JUST DID

[fallow parrot]

How the negative will be there

Ok how

[sly abyss]

if you want to cancel out

(x-y)/ (y-x)

thats just -1

[fallow parrot]

No where in his work do i see x-y/y-x

[sly abyss]

its factored out

...

[fallow parrot]

What image are you looking at

[sly abyss]

.

you wrote this

but

youre wrong here

OK

so

for right here

[fallow parrot]

Wait a minute

[sly abyss]

(x-y)/ (y-x)

[fallow parrot]

Why did you write (x-y)/ (y-x) then

[sly abyss]

let x=2, and y=1

2-1/1-2

1/-1

= -1

do you see the negative in -1?

@odd sierra

put it into the website

[fallow parrot]

This doesn't look correct at all

[sly abyss]

and i gaurentee you it will say the correct answeer is -6xy

[fallow parrot]

If its a x^2-y^2 on the numerator

What would that turn into then?

[sly abyss]

do you want me to do the entire problem out for you

[sly abyss]

(x+y) (x-y)

[fallow parrot]

OK THEN

[sly abyss]

i agree with you there

[fallow parrot]

See

And then

With y^2-x^2

[sly abyss]

(y+x) (y-x)

[fallow parrot]

OK

There you go

[sly abyss]

you can cancel out (x+y) and (y+x)

but you cannot cancel out (x-y) (y-x)

[fallow parrot]

?

[sly abyss]

it becomes (x-y) / (y-x)

[fallow parrot]

Why?

If x+y got cancled with y+x then the other will

[sly abyss]

x-y is not the same as y-x

[fallow parrot]

OH

[sly abyss]

dawg

[fallow parrot]

OH MY GOD

WTF

Right

[sly abyss]

jesus christ

[fallow parrot]

Now wait a minute.

You will just make a fraction

And put it where exactly

[sly abyss]

(x-y) / (y-x) is -1

[fallow parrot]

Oh

I understand

Now where does this -1 go

[sly abyss]

on the denom

you are left with 6xy on the top

divided by -1

which is -6xy

[fallow parrot]

Right let me try this problem and see what you said is right

[sly abyss]

work it out and then come back

[fallow parrot]

Right

Im at the x-y/y-x part

We have negative on the numerator and a negative on the numerator

= Positive

[sly abyss]

plus in vales

x=6, y=5

6-5 / 5-6

1/-1

-1

[fallow parrot]

Where is the 5 from

[sly abyss]

I just made up random numbers

[fallow parrot]

You are just plug

Oh

[sly abyss]

to prove to you

[fallow parrot]

Let me see here and plug any number

[sly abyss]

chose any two numbers

besies 0

@fallow parrot

u done?

[fallow parrot]

Yup

[sly abyss]

so

[fallow parrot]

It seems like

-6xy

Is correct

[sly abyss]

😭😭

[odd sierra]

uh

dis done

.close thnx for hepl

[cedar kiln]

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[crimson sedge]

Can someone help me with the following problem:
It is given that the four sides of a trapezoid are 1,2,3, and 4. Calculate the area of this trapezoid

[versed fulcrum]

1, 2, 3, 4 in length?

[crimson sedge]

yes

in length

[crimson sedge]

they gave me the length of the sides, how am I supposed to figure out the height

[versed fulcrum]

Pythag

[gray blade]

oh wait nvm

[crimson sedge]

i don't know which ones are bases

I just know the length of sides

hello?

<@&286206848099549185> ??

[cedar kiln]

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[cedar kiln]

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[dreamy zenith]

how did the negative epsilon magically appear on the left

[modern compass]

property of absolute value.
|a| < b if and only if -b < a < b

[dreamy zenith]

ok

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[crimson sedge]

The problem is a factoring the difference of two squares problem

a^2 x b - b^3

My question is :
Am I able to factor out a b?

[slate lintel]

yeah

[versed fulcrum]

Why not

[crimson sedge]

well I was under the impression that everything has to have a b to factor it out in that problem Beacuse when there’s a coefficient

Like for example if the problem is

3x + 6
You can’t factor out the x

Anyways thank you for the help gonna close this up now so the next person can use it

.close

[cedar kiln]

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[feral gust]

would the answer be 4pi^2/g?

[feral gust]

uh

.close

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[crimson sedge]

i dont have paper and tried pretty much everything

i know formulas just need help

[slate lintel]

the trick is finding those side lengths

use the distance formula

[crimson sedge]

thats a lot of non mental math lol i use my head a lot

[slate lintel]

yep sure is

although

you can do some of it in your head

because for the rectangle it's all 45º lines

[crimson sedge]

its sqr(x2-x1)p2 + (y2-y1)p2

right

[slate lintel]

yeah

[crimson sedge]

i dont have paper or a calculator hmmmm

how can i do this

[slate lintel]

you're literally on discord right now?? how do you not have a calculator lol

[crimson sedge]

sqr(20)

[crimson sedge]

phone

[slate lintel]

,calc sqrt(20)

[wraith dagger]

Result:

4.4721359549996

[crimson sedge]

thats the length

i did most in my head

wait is that right?

[slate lintel]

no

[crimson sedge]

😭😭😭

math is not as easy as i assumed

[slate lintel]

you might want to find some paper or something lol

[crimson sedge]

or guess

[slate lintel]

you are not going to guess the square root of 5 to two decimal places

[crimson sedge]

wait

~6.325

right

[slate lintel]

what 😭

i don't think negative numbers really ever make sense in this problem, we're doing area and perimeter here

[crimson sedge]

distand of the triangle side

[slate lintel]

oh discord is silly

squiggle and negative look the same

[crimson sedge]

lol

[royal loom]

no they are very distinct actually

~

[slate lintel]

2 pixels

[crimson sedge]

😭😭😭

wait was i right tho

[slate lintel]

what points are those

[crimson sedge]

i typed it wrong 😭😭😭😭😭😭

2.83

final answer

[slate lintel]

,calc 2*sqrt(2)

[wraith dagger]

Result:

2.8284271247462

[slate lintel]

yeah

[crimson sedge]

im so good

its hard being this amazing

i got the perimeter right

oh god

the area

@slate lintel

[slate lintel]

area is easier than perimeter i think

[crimson sedge]

for the whole shape

[slate lintel]

yeah

[cedar kiln]

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[reef escarp]

How do I prove this?

[cedar kiln]

@reef escarp Has your question been resolved?

[reef escarp]

<@&286206848099549185> can someone help me with this please? I have no idea how to even approach this

[slate lintel]

so the odd characters of the input kind of don't matter, right?

you're going to need to transform the given DFA into the required NFA

[reef escarp]

yeah I get that, but how do I design the transition function

What do I do on odd indexed characters

[slate lintel]

i guess find some way to throw them away

and go back to where you came from

remember you can add extra states and transitions

as many as you want even if it seems silly

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[somber prism]

Can someone explain to me how to use maragin of error like

[cedar kiln]

@somber prism Has your question been resolved?

[somber prism]

No

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[raw wren]

what if they said vovels at first of that word

[crimson sedge]

You could split it into all the different cases a vowel is at the start and do the combinatorics math on the remaining 5 letters

So there's two cases

• you start with E
• you start with I

And so, you can work out the number of combinations for the rest of the letters and add the results

[raw wren]

can i do {EEI} MPR and cosider 4 letter and use permutation 4! * (3!/2!)

but eei can permutate so should i divide by 2?

@crimson sedge

is right?/

[crimson sedge]

I'm not sure of that, I would just say that when it starts with an E, I need to work out the combinations of "MPIRE" and when it starts with an I, I need the combinations of EMPRE

[covert talon]

The word “EMPIRE” has 2 vowels (E, I) and 3 consonants (M, P, R). If the first letter must be a vowel, we have 2 choices for the first position. For the remaining 5 positions, we can arrange the remaining 5 letters in any order.

So, the total number of ways is given by:

2 (choices for the first letter) * 5! (arrangements of the remaining 5 letters)

= 2 * 5 * 4 * 3 * 2 * 1

= 240 ways.

[thorn lotus]

@raw wren If the problem didn't make you do that vowel stuff, how would you calculate it?

[crimson sedge]

Not good practice to just give the solution

[raw wren]

are you answering the question?

[crimson sedge]

!nosols

[cedar kiln]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[raw wren]

its wrong though

[tropic oxide]

is this chatGPT?

[raw wren]

can i do {EEI} MPR and cosider 4 letter and use permutation 4! * (3!/2!) @tropic oxide can you tell this please

[tropic oxide]

that doesn't sound right

you want the 1st letter to be a vowel, no?

[raw wren]

will i need to divide by 2 again so to remove cases when vovels move back?

[raw wren]

no i was asking different doubt

[crimson sedge]

They're not asking you for all the vowels together

[raw wren]

not related to this question

[tropic oxide]

.-.

you confuse us all

[raw wren]

sorry

[raw wren]

this one

[tropic oxide]

you mean all vowels at the beginning?

[raw wren]

ya

[raw wren]

and this approach

[tropic oxide]

in that case {EEI}'s place is fixed.

and you only permute MPR

3! ways

[raw wren]

then i what i said right we consider 4 letters

[tropic oxide]

no

{EEI} has to go first

[raw wren]

ohh

[crimson sedge]

I would think you could also permute EEI itself though, right?

[raw wren]

3! x (3!/2!) this we do?

[raw wren]

ya i did

[tropic oxide]

sure

[raw wren]

but i thought we can negate by dividing by 2

and permute as usuall 4 letters

[raw wren]

its wrong @tropic oxide ?

[tropic oxide]

it looks wrong

[raw wren]

okay understood

[raw wren]

and just one thing in the image question instead of going by each letter and its ways then dividing by 2 any other approach correct or shorter?

35432*(1 /2)

[tropic oxide]

i would count E_____ and I_____ separately. that looks like the least error-prone approach to me.

[raw wren]

okay

.close

[cedar kiln]

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[lost lark]

hello im 13 how can i solve this
If b≠0 and a/2=b/10, what's ab?
a) 2
b) 5
c) 10
d) 20

[crimson sedge]

I would first, to make it a lil simpler, multiply both sides by 10

5a = b

Then I can substitute it into ab, and go from there

[lost lark]

why

[crimson sedge]

it's a way to eliminate one of the variables

[cedar kiln]

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[low niche]

what is the difference between combinations with repetition and stars and bars or are they the same. If so, what situation would each be used for?

[cedar kiln]

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[crude scroll]

So existence of such an element x is easy to show, by definition of supremum. Utm I am not sure how to show that x is the closest element to sup(S)

[idle sonnet]

Because A is finite, what can you tell?

[crude scroll]

There is a maximum?

[idle sonnet]

Yes, there is a maximum of the elements in A

Can you prove that this is s?

[crude scroll]

Hmm I can try

Im not sure..

[idle sonnet]

have you tried using the definitions of upper bound and sup

[idle sonnet]

by the way, what book is this

[crude scroll]

abbott

[idle sonnet]

understanding analysis?

[crude scroll]

yes

[idle sonnet]

I knew it looked familiar

[crude scroll]

lol

anyway

so, s = sup(A) means for all b in A, b <= s

the maximum is in A

[idle sonnet]

yes

[crude scroll]

we wanted to show that max(A) = sup(A)

so now we need to eliminate the case for max(A) < sup(A)?

uh

[idle sonnet]

Yes

[crude scroll]

well,

assume ma(A) > sup(A)

this is not right

right?

[idle sonnet]

prove it

[crude scroll]

Well by definition of max of a set A, it should be an element in set A

But sup(A) can be an element in A or it can not be an element in A.

so sup(A) should be at least as great as max(A)

Is that convincing?

[idle sonnet]

yes

[crude scroll]

Ok thank you

[cedar kiln]

@crude scroll Has your question been resolved?

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[honest garnet]

can someonme just exp[lain how this works please

[fallen moat]

this is about sine law, right?

[honest garnet]

yes

[fallen moat]

oh ok, so for sine law, basically
(one side)/sin(the opposite angle)

[lunar moat]

Sine rule says that ratio of length of side to it's sine of opposite angle is same for all three sides of triangle...

[honest garnet]

so the answer is 12 over sin 63

what would the working out here be

[fallen moat]

= (another side)/sin(the opposite angle)

[lunar moat]

Yes

[honest garnet]

thank you

[lunar moat]

Nothing it's just given and you are writting the answer there's no working

[honest garnet]

ok thank you veyr much for the helkp

.close

[cedar kiln]

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[honest garnet]

.reopen

[cedar kiln]

✅

[honest garnet]

how are you suppoed to use the sine rule here?

i used tan because it had the opposite and adjacent but that was wrong

[fallen moat]

well, there isn't a right angle

[honest garnet]

so you need a right angle for anythigng other then sine

[fallen moat]

the sine rule is just for sine

[honest garnet]

right but

we have the opposite and adjacent

so how r u supposed to use sine to find the opposite

[fallen moat]

well, for SOH those stuff it's for right angled triangle

[honest garnet]

so this isnt a right angle triangle

so the sine rule is soh

so how r u meant to use it

[fallen moat]

that SOH applies when it's right angled triangle

[honest garnet]

ohhh

[fallen moat]

when it's not, it's just plain sine rule

[honest garnet]

how do u do the plain sine rule?

ive only been shown sin cos and tan

[fallen moat]

https://www.mathsisfun.com/algebra/trig-sine-law.html

[honest garnet]

thanks lemme look

[honest garnet]

so 9 over sin 57

[fallen moat]

nah

[honest garnet]

oh

ohhh

sin 57 = x over sin 9

i think

[fallen moat]

let's see

lemme draw on your pic

[honest garnet]

soo

ohh

so side A is 9cm and angle a is 40

[fallen moat]

yessss

well

[honest garnet]

so to work out x i need to use 57 right

[fallen moat]

side is a, angle is A

[honest garnet]

oh right my bad

[fallen moat]

angle in cap letter

[lunar moat]

"Opposite side"
Angle opposite to that side.
That is angle made by intersection other two sides.

[honest garnet]

so to calculate x it is

sin 57 = x

[fallen moat]

?

[honest garnet]

damn it

[fallen moat]

9/sin(40°) = x/sin(57°)

[honest garnet]

oh so like in the example they r equal cuz it links with each other

ohhh okay

[lunar moat]

9/sin(40) = x/sin(57)
x = 9*sin(57)/sin(40)

[honest garnet]

why do u have to divide it by sin(40)

[fallen moat]

i bet SillyGuy is just simplifying

[honest garnet]

what is the not simple version

cuz i get now that side a over angle A is the same as side b over angle B

[fallen moat]

but then, if you need to find x

[fallen moat]

that will be good for using calculator

[honest garnet]

and the long working out that i need to write is gonna be

9/sin(40) = x/sin(57)

then x = 9sin57 over sin 40

[lunar moat]

You will defo need log table for doin it manually... who the hell knows value of sin 40 or 57

[honest garnet]

wait this is actually making sense

[rigid otter]

can anyone help me witht his question?

i legit have no idea wots going on

[cedar kiln]

Please read #❓how-to-get-help

[honest garnet]

it's 11.7!

fucking hell u lot r amazing

thank u so much

this acc makes sense now so thank yo

.close

[cedar kiln]

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[cloud furnace]

hi

[cloud furnace]

I need help solving this equation, I don't understand the process for completing the equation and solving it.

It's looking for the average rate of change

[cedar kiln]

@cloud furnace Has your question been resolved?

[cloud furnace]

it has not

.close

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[weary compass]

Hi, need some clarification on a Markov Chains exercise

[weary compass]

This is the exercise

This is the suggested solution

what I'm very confused about is the notation

it says E(....)= P\bar{x}^2

and then represents this as P * [1, 25]

I don't understand how squaring a 2x1 vector can result in a 2x1 vector

that's a notational mistake, right?

[cedar kiln]

@weary compass Has your question been resolved?

[cedar kiln]

@weary compass Has your question been resolved?

[cedar kiln]

@weary compass Has your question been resolved?

[cedar kiln]

@weary compass Has your question been resolved?

[vernal shell]

Hello. I guess they want to simplify the notation and use ^2 to say element-by-element square

[cedar kiln]

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[crimson sedge]

Hey, can someone please help me with this

[crimson sedge]

I'm not sure where to start

I'm pretty sure I'm going to have to use the equation $f(x + \epsilon) \approx f(x) + f'(x) \epsilon$ but how to?

[wraith dagger]

Discipline

[crimson sedge]

Or is it simply $f(x) \approx f(a) + f'(a)(x-a)$

[wraith dagger]

Discipline

[crimson sedge]

I'm not sure

[mighty drift]

You just gave two equivalent formulations of the same property

[crimson sedge]

How do I go about the problem

What are x, a, and epsilon in these equations?

[mighty drift]

I recommend having a look at your notes/lecture, which should come with explanations

Regarding the nature of linear approximations

[slate lintel]

this one will be a more useful form

x and a line up with your problem

and f is g

[crimson sedge]

Does this make sense?

[slate lintel]

not quite

you have a = 0, good, but you need x to be the target point, in this case 0.95

oh

wait hold on

[crimson sedge]

Sure

[slate lintel]

ok the equaation was set up right

but how did you get $1 - \frac{0.05}{3} = -2.05$?

[wraith dagger]

hayley!

[crimson sedge]

Oh nah

This is a mistake

1 - (0.05/3) is approximately equal to 0.98

[slate lintel]

that sounds more reasonable

[crimson sedge]

And similarly

[slate lintel]

yee

[crimson sedge]

I feel like I left out the first part of the question though

"Find the linear approximation of the function g(x) at a = 0"

[slate lintel]

oh well it's just this

put the a in there

and f(a) and f ' (a)

[crimson sedge]

I think I got the hang of it

All good

Can you please help me graph this though?

I'm assuming this problem involves a tangent?

[cedar kiln]

@crimson sedge Has your question been resolved?

[dire geode]

yea looks right

[dire geode]

do you know the slope and a point?

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

For a = 0, the slope is g'(0), 1/3 right?

[crimson sedge]

Do I need to find the tangent line at (0, g(0))?

[dire geode]

Yes yes

[dire geode]

Yes?

[crimson sedge]

Think it's looking good

Thank you for your help

[cedar kiln]

@crimson sedge Has your question been resolved?

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[somber wing]

I wanna try doing this but i dont know what commands for inequality in my sci cal

[somber wing]

Help

Fx-991ES Plus

Cant find the inequality button

Cri

[dire geode]

Did you try googling it?

Calculator model and inequality button

[somber wing]

I did

And my calc brand did not have a tutorial

I tried but the commands were differeny

[dire geode]

Yea no idea then

These channels are for math help, not calculators

[somber wing]

Mb

[cedar kiln]

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[odd sierra]

Hi

I will show my work here but i am stuck unfournately

Thank u very much in advance 🙂

[lunar lynx]

,rccw

[lunar lynx]

You didn't open denominator correctly.

$\sqrt[3]{27} \neq 27$

[wraith dagger]

Enemagneto

[odd sierra]

Ohhhhhhhhhhhhhhhhm

i would have to put 3 there right

?

[lunar lynx]

Yes

[odd sierra]

ah man

Ok

so now

is gonna be the same but denominator change to 3x only?

the rest is good?

[fallow parrot]

I will say

U cancel the 3x and the 3x

and this is ur answer

Im not a professional though so submit at your own risk

[odd sierra]

.

Plz don't troll

I got exam coming up for this

[fallow parrot]

what i said is probably right

i wouldn't troll

[odd sierra]

Wow ok thnx i submited it was right

thnx for the reassurance

.close

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[frigid fjord]

Oh whoops

Sorry

I meant to put this in a different channel

looks like we commented at the same time lol

[royal loom]

<@&268886789983436800>

[cedar kiln]

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[whole bloom]

The number of small squares used in the nth shape of a pattern is given by n^2 + 2n - 2.
Show that the difference in the number of small squares used between two consecutive
odd‑numbered shapes is always divisible by 4.

[whole bloom]

can I get some help

[zenith sail]

odd-numbered shapes, meaning odd n, right?

oh yeah, must be

@whole bloom have you tried anything here? or kinda stuck at the beginning

[cedar kiln]

@whole bloom Has your question been resolved?

[whole bloom]

kinda stuck

@zenith sail

don't you go like (2n+1)^2 + 2(2n+1)-2 - (2n+3)^2 + 2(2n+3)-2

[zenith sail]

with some more brackets, yes

[(2x+1)^2 + 2(2x+1)-2] - [(2x+3)^2 + 2(2x+3)-2]

[whole bloom]

you're 100% sure?

[zenith sail]

about the brackets?

of course

you're subtracting one whole shape minus the other whole shape

not just minus a piece of it, plus the other piece of it

[whole bloom]

and with substituting 2x+1 into both n values?

[obsidian coral]

Btw @whole bloom if you're still using the channel react with the x so the channel doesn't timeout and close

[zenith sail]

yeah, well, 2x+1 for one shape and 2x+3 for the other, like here

I shouldn't have used n there, sorry. Since n is the name of the variable they already gave you

[(2x+1)^2 + 2(2x+1)-2] - [(2x+3)^2 + 2(2x+3)-2]

[whole bloom]

ok

and then you just simplify and subtract and then factorise out 4 to show that its divisible by 4 right?

[zenith sail]

yes

you should also specify that x is an integer

since 4 times a non-integer is not a multiple of 4

[whole bloom]

yep

[cedar kiln]

@whole bloom Has your question been resolved?

[cedar kiln]

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[chrome vigil]

I’m stuck on 31 part B, I’m not sure how to calculate the area of a triangle with only the points

[dim tiger]

hii

construct 3 vectors

which form triangle PQR

then try finding if there is a right angle

by getting dot product between each 2 vectors forming an angle of the triangle

[chrome vigil]

I did that for point P and I got a 60degree angle

[dim tiger]

if one of them is 0 then it is right and you get area by hb/2 after getting length of vectors

[chrome vigil]

Should I try the other two

[gusty forum]

well heron’s formula is an easy way out

[chrome vigil]

I’ve heard of that lemme check

[gusty forum]

probably won’t be asking here if that’s in the syllabus tho

[chrome vigil]

Why does calc gotta be in 3 dimensions fr 😩

[dim tiger]

to extend ideas of areas of curves to volumes of surfaces

[chrome vigil]

Yea this ain’t working out I got 76 degrees for angle between PR and RQ

Does the standard formula for a triangle not work?

Like (bh)/2

[gusty forum]

it will work but it’s pretty laborious

pick 2 points form line b then project the 3rd onto the line using distance formula to get h

actually if it’s like an introductory to 3D space this is probably the intent of the exercise lmao

[chrome vigil]

Yea this is like the first unit lol

I’ll figure it out thx anyways 🫡

.close

[cedar kiln]

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[odd sierra]

what am i doing wrong i have been stuck here for half an hour plzz 😭

[vestal bear]

start by making it a common denominator

[odd sierra]

x^2-1?

[vestal bear]

yeah

[odd sierra]

so i multiply the whole thing by this one]

[vestal bear]

no

multiply the individual fractions by 1, (x+1)/(x+1) or (x-1)/(x-1)

the one without a denominator needs to be multiplied by (x^2-1)/(x^2-1)

this is so that it doesnt affect the rest of the equation

[odd sierra]

OHhhh

Ok

I try

[cedar kiln]

@odd sierra Has your question been resolved?

[cedar kiln]

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[main herald]

Please I need help with this page someone please explain to me how to do it 🙏

[main herald]

I don’t know how to start on neither of these and I don’t even onow if a. Is correct

Know*

<@&286206848099549185>

Any help would be appreciated 🙏

[idle sonnet]

the biggest expression you wrote is already correct

and not the one you put in a box

[main herald]

So 2x^2+7x+6?

[main herald]

Wait so what am I supposed to do b?

[idle sonnet]

Blue part is correct for part a. Green should go in part c

[main herald]

Ah ok 😂

Could you please help me on what I would need for b

[hearty arch]

if you're trying to find the areas for each smaller rectangle, it may be helpful to label all the other blank sides with what you know

[cedar kiln]

@main herald Has your question been resolved?

[main herald]

Yessir thank you

[main herald]

I understand how to know

[cedar kiln]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[main herald]

For this one am I supposed to add all the x together and go from there?

[slate lintel]

you want area

try splitting it into two rectangles

there's two ways to do this, both of them will work

[main herald]

Like this?

[slate lintel]

great

now that bottom side, you've split the x + 3 side into two different segments

how long are they?

[main herald]

So the square is x+x

[slate lintel]

it looks like a square but it might not be, looks can be deceiving

[main herald]

So am I splitting the x+3

[slate lintel]

teag

yeah

[main herald]

Like this?

[slate lintel]

how do you know the length on the left is x?

[main herald]

I though I would take the x out of the x+3 but now that I thought about it it’s wrong

[slate lintel]

yeah if you want it to be a rectangle (you do) then you can't split it up like that

but, look at the shape on the right

it's a rectangle and the top edge is x

so the bottom edge has to be x as well

[main herald]

Oh yeah they’re parallel

So would the x-1 be on the other side too

[slate lintel]

it would, yeah, but we don't really need to label that

[main herald]

Ok

[slate lintel]

area of a rectangle is base * height

[main herald]

X^2-2?

[slate lintel]

for what, the one on the right?

[main herald]

Yes

[slate lintel]

no

base is x and height is (x - 1)

so x^2 - x

[main herald]

I’m sorry I don’t understand

I did x+3+x-1

[slate lintel]

that doesn't make any sense to me

this is what you have right

[main herald]

So is the -1 being replaced by an x?

[slate lintel]

what -1

[main herald]

From x-1

[slate lintel]

(x-1) is kind of its own thing

[main herald]

What

[slate lintel]

take a look at this

[upper ruin]

(x - 1) is the measure of the length of that vertical side of the rectangle on the right and that's it

[main herald]

Oh ok so the x is distributing

[slate lintel]

yes, it will be distributed

[main herald]

Aaaa ok so yes it equals x^2-x

So now am I supposed to multiply that by 3x?

[slate lintel]

no, these are two separate areas

think of it like two separate rooms in your house

and you have to put carpet in them

[main herald]

So one equals 3x and the other x^2-x

[slate lintel]

so once we know how much carpet goes in the first room (3x) and how much carpet goes in the second room (x^2 - x) we just add them together

[main herald]

Oh ok

So would it be x^2 + 2x

[slate lintel]

yep

[main herald]

Oh ok I understand now

Thank you for being patient with me 🙏

.close

[cedar kiln]

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Closed by @main herald

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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.

[lavish stag]

hello

[lavish stag]

hello maam/sir how can i solve 8ab - 12 (algebra,polynomial) gcf factoring

[lavish stag]

can i ask please