help-0

[lone heart]

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[lavish pier]

i got y inter = 6 and gradient 1.5

[wary stream]

Looks good

[lavish pier]

this questions wording is tricky

it wants me to find the length of the ladder right?

[gray ingot]

No

[lavish pier]

the length of the wall??

[lavish pier]

yes that was my initial thought

they should have just said the length of the wall

[gray ingot]

no

[wary stream]

But it's not

[gray ingot]

the wall is taller

I didn't draw the full thing

[lavish pier]

the question mark is the wall though

[wary stream]

Diagram drawn is not accurate

[lavish pier]

why would the wall be taller?

[gray ingot]

this is more accurate

[lavish pier]

how do you know that for sure tho?

it never says that

[wary stream]

It's asking, when you lean the ladder at a 67 degree angle, where on the wall does it fall

[abstract fractal]

There's no reason to think the wall ceases right where the ladder touches it

[lavish pier]

well wouldnt it still be just the length of the wall in this case because thats where the angle of elevation stops

[wary stream]

AKA the vertical position of where the ladder falls on

[wary stream]

Still no

[lavish pier]

it would be a tangent ratio

what does it want me to do then

[wary stream]

Tangent ratio yes, but still not the length of the wall

[abstract fractal]

It's the length from the floor to where the ladder makes contact. The wall itself could still go on past that, so it's not the length of the wall we care about

[lavish pier]

but if we caculate it as the wall length

since the adjacent and hypotenuse are proportional to where the ladder touches it

it wouldnt make a difference i dont think

If we do it how you propose how would you solve this?

[gray ingot]

can you see that the wall is taller than the point where the ladder falls on it?

[wary stream]

Imagine this, you go outside your house with a ladder, and you lean the ladder at a 67 degree angle. The wall of your house is definitely taller than ladder. The question wants you to find the distance from the ground to the ladder, where it falls on the wall

[wary stream]

@lavish pier This is how you solve it

[lavish pier]

i understand that

ok so tell me the caculation you would do to find JUST the point where it touches the wlal

wall*

[gray ingot]

yes and thats what the question wants you to find, there is no way to find the height of the wall with the data given

[wary stream]

Use this

[lavish pier]

EXACTLY

so the wall ceases right at the tip of the ladder

[gray ingot]

?

no?

[wary stream]

No

[gray ingot]

💀

[lavish pier]

you guys are forgetting this a math question not a logic question

[gray ingot]

the question DOES NOT ask you to find the height of the wall

[lavish pier]

ok but how do you know the wall goes on for more than the ladder touches it?

[wary stream]

Finding the height of the wall and where the ladder falls along the wall is two different questions

[lavish pier]

not in this scenario

not in this scenario

[gray ingot]

this clearly implies the wall is taller

[lavish pier]

not really

[wary stream]

Yes it does

[lavish pier]

it could just be crappy wording

[gray ingot]

if not they would have asked the height of the wall

[lavish pier]

ok so let me aks again how would you solve this

[wary stream]

Or it could be you misunderstanding

[lavish pier]

ok solve the question then?

lets see what you propose

[wary stream]

Like that

[lavish pier]

thats not solving it

[wary stream]

What swas showed

[lavish pier]

also didnt u just say the wall is taller than the ladder

the hypotenuse is always the longest side

so how would that work

[frigid hatch]

lol

[gray ingot]

tan67 = x/3.4
x = 3.4tan67

[abstract fractal]

We only care about the part of the wall that goes to the ladder. We couldn't care less about the rest of the wall

[gray ingot]

,w 3.4 * tan(67 deg)

[ocean seal]

Results provided by WolframAlpha

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Requested by Swas.py#7370

[gray ingot]

x=8

[wary stream]

You are getting confused, the hypotenuse is the ladder leaning

[lavish pier]

litreally the same answer i got

[gray ingot]

and that x is the point where the ladder reaches up the wall

[wary stream]

You're find that blue distance

[gray ingot]

not the height of the wall

[lavish pier]

either way it doesnt matter

[wary stream]

Yes it does

[gray ingot]

it does 🗿

[lavish pier]

when u do the caculation YOU DONT TAKE THE REST OF THE WALL INTO ACCOUNT ANYWAYS

[gray ingot]

there is a clear difference between them

yes?

[lavish pier]

MAYBE WHEN U GRAPH IT

[abstract fractal]

The height of the wall is quite different from the height of part of the wall

[lavish pier]

BUT THE ANSWER IS THE SAME

[wary stream]

That question is specifically asking for the blue part, not the entire wall

[lavish pier]

yes

[abstract fractal]

No its not. If it asked for the height of the wall, you wouldn't be able to answer it with the given info

[lavish pier]

how come i did got the same answer as you even though i was opposing your idea?

tell me?

[abstract fractal]

Because you weren't solving for the height of the wall lol

[gray ingot]

huh? you were saying the question wants us to find the height of the wall

[wary stream]

Because you found the value of the blue part, which is a segment of the wall, not the entire wall itself

[abstract fractal]

Just because you say you're solving for the height of the wall, doesn't mean you actually are mathematically

[lavish pier]

yeah but if it ask u to solve the wall you would have to assume the ladder touches the wall at the tip of its height

Ive done a question like the one i just said before

[gray ingot]

Yes that is the only way to solve it in that case (make huge assumptions as we always do)

[wary stream]

You were saying find the length of the wall, it would be the green plus the blue part
Which the question was not asking

[abstract fractal]

No, if it asks you to solve for the height of the wall, with no other info given, you say "there's not enough info"

[gray ingot]

or this ^

[lavish pier]

thats not even possible in the first place

[abstract fractal]

That's the whole point. That's why we aren't trying to find the height of the wall, because it isn't even possible

[lavish pier]

which is why im saying looking at it from a mathematical stand point in this question screw the rest of the wall

because it doesnt matter in ur caculation anyways

you cant even possibly caculate that

anyways thank you for the help

.close

[lone heart]

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[lavish pier]

.reopen

[lone heart]

✅

[lavish pier]

.close

[lone heart]

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[junior warren]

i am currently solving for the perpendicular

[junior warren]

i have worked all the way through using dot product and now have

k(k-1)=-20

however the answers listed only work when =20

i am trying to figure out where i went wrong'

i think i got it nvm

.close

[lone heart]

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Remember:
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[alpine sable]

whats the bottom text saying?

[alpine sable]

not rly understand what they trying to tell me

[alpine sable]

it's very poorly worded lol

[wanton belfry]

Hey guys my exam is starting could you please help me?

I’ll send here the pictures

[alpine sable]

i'll give you a chance to read the rules and delete that since I don't want to mass ping the mods

[obtuse hatch]

(you have to do the exam yourself) @wanton belfry

its a help channel not a DO IT FOR ME

type beat

[alpine sable]

help channel doesn't apply to marked assesments ^ as dna said

[obtuse hatch]

also @alpine sable you think you can help me in #help-1 ? its aight if you cant

[alpine sable]

help me first haha

.close

[lone heart]

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[lone heart]

Available help channel!

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[lucid hollow]

Hi

[lucid hollow]

Oops

I can’t understand this Q

Part b was quite easy and I solved it, hence I won’t be sending it here.

<@&286206848099549185> pls

[vale wigeon]

do you know in general how to find the intersection point of two lines given their equations?

[willow canopy]

^

at the point of intersection

the y and the x on both equations will be the exact same

so you can just equate them

like for example, say I have a line y = ax + b and a line y = mx + c

I can just solve for ax + b = mx + c

because the y's are the exact same at the intersection point

[lucid hollow]

Which equations are we referring to right now?

[lucid hollow]

Ohhh

[willow canopy]

so what lines are passing through point A?

[lucid hollow]

Ye I forgot bout that rule

2x + 3y = 17 and 4x - y = 6

[willow canopy]

yup

then those 2 are the equations I am talking about

[lucid hollow]

Ye ty but I’m still not sure bout smth

[willow canopy]

what is it?

[lucid hollow]

Oh wait nvm

Tysm sir

[willow canopy]

aye

[lucid hollow]

Lemme solve it rq

Wait so

First do we isolate the y’s?

Like so?

[fallen verge]

Have you ever heard of point slope form?

[lucid hollow]

Nope

[fallen verge]

That comes in real handy

[lucid hollow]

Slope as in gradient?*

[willow canopy]

you can find something like y = ax + b

[fallen verge]

Ah yes

American here

[willow canopy]

then for the equation mx + dy = c

just sub the y straight in

[fallen verge]

Theres an easier way

[lucid hollow]

Oh

[willow canopy]

mx + d(ax+b) = c

[lucid hollow]

Hmm I’m confused

[fallen verge]

Oh wait nvm im stupid nvm

[willow canopy]

i agree, but learning how to do maths isn't a bad thing

[fallen verge]

Ignore me

[lucid hollow]

Is this how I’m supposed to do it?

Before putting the equal in between the 2 equations

[willow canopy]

yea and divide everything by 3

[lucid hollow]

Everything?! Why?

Oh

Ye 3

You scared me for a second ngl

[willow canopy]

you'll get $\y = \frac{-2}{3} x + \frac{17}{3}$

[ocean seal]

Azzurala
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[willow canopy]

then you sub into the equation $4x - y = 6$

[lucid hollow]

I got this

[willow canopy]

and solve for x

[ocean seal]

Azzurala

[willow canopy]

there exists an easier way (computationally) btw but

[lucid hollow]

Gimme a second sir

Can y be negative?

Which one of these is correct?

[fallen verge]

Uh both

[lucid hollow]

But right now which ones usable

Aint no way u could use both

[fallen verge]

But isolating y would mean the bottom one

[lucid hollow]

Aight pog

I got $\frac{-2}{3} x + \frac{17}{3} = 4x - 6$

[ocean seal]

Akashi

[lucid hollow]

Yo I did it it worked

The bot works!!!

@willow canopy

[fallen verge]

I can help too

[lucid hollow]

@fallen verge

Am I correct?

Tagged you so you wouldn’t feel left out

:>

[fallen verge]

Yes

You set the two equations that are y are equal to each other

[willow canopy]

yea

[lucid hollow]

Like so?

[willow canopy]

now there's another method

called eliminaion

it's a lot easier to compute in this case

[lucid hollow]

No no my teacher told me that the elimination method should NOT be relied on

Substitution only, according to him

[willow canopy]

bru

[fallen verge]

Bruh

[willow canopy]

what

use what works best given the situation

[fallen verge]

Eleimination is so much better in like all ways

[lucid hollow]

Okk

Teach me

Pls

He didn’t teach us that method

Are we gonna isolate X?

[fallen verge]

We isolate whichever variable is easier

[willow canopy]

I'd say to watch a video on it

it will explains it better

[fallen verge]

Yeah probably

They will have good demonstrations too

[willow canopy]

but yea, elimination is very useful lol

[lucid hollow]

There’s only 1 variable in this equation tho

Wdym by elimination

Just cut out the thingies

[willow canopy]

oh

you mean when you solve that equation for x?

[lucid hollow]

Ye

[willow canopy]

then yea solve it like usyal

isolate the x and the numbers

[lucid hollow]

Got this $/frac{-14}{3} x = \frac{-35}{3}

Hmm??

Bruh

Got this $\frac{-14}{3} x = \frac{-35}{3}$

[ocean seal]

Akashi

[lucid hollow]

Yup

Got that

Hello??

Brb guys

Help

[fallen verge]

Oh hi

You still here?

[lone heart]

@lucid hollow Has your question been resolved?

[fallen verge]

Ping me pls

[lone heart]

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[silver current]

anyone help? i don’t know what the last part means and how to get it

so far i know the roots are a, b and a+b

[balmy warren]

ok that's a good start

do you know the relationship between the roots and the coefficients of the polynomial?

[silver current]

yep

[balmy warren]

go on

[silver current]

what should I do?

[balmy warren]

tell me

[balmy warren]

avoid labelling your roots a and b becaue a and b are alread defined in the equation

[silver current]

ok i’ll use x, y and x+y

oh wait

t, u and t+u then

[balmy warren]

that works

so can you tell me the relationship between coefficients and roots

[silver current]

t + u + t + u = -a/1

oh shoot

[balmy warren]

i get what you mean

I assume in this case you mean = -a / 1

[silver current]

oh yep

[balmy warren]

$2t + 2u = -a$

[ocean seal]

IntelligentCake

[balmy warren]

so we have one equation

[silver current]

yes

[balmy warren]

what about other coefficients

[fallen verge]

Ah yes vietas

[silver current]

$tu + t^2u + u^2t = b$

[ocean seal]

jacinthaa

[balmy warren]

yup

and 1 more

[silver current]

$t^2u + u^2t = -c$

[ocean seal]

jacinthaa

[balmy warren]

I don't think that's quite right

actually it is

ok so you have 3 equations

[silver current]

yeah

[balmy warren]

try to factor out some terms in these equations

[silver current]

how?

[balmy warren]

look at second equation

what is common in all terms in the left side

[silver current]

tu

[balmy warren]

so try factor that out

what do you get

[silver current]

$tu(1+t+u)$

[ocean seal]

jacinthaa

[balmy warren]

ok good

look at 1st equation

can you factor out something?

[silver current]

2

$2(t+u) = -a$

[ocean seal]

jacinthaa

[balmy warren]

ok can you move the 2 to the other side?

[silver current]

$t+u = -a/2$

[ocean seal]

jacinthaa

[balmy warren]

do you see something that you can do from here?

[silver current]

sub in into the other equation?

[balmy warren]

yup

[silver current]

so from the third equation 2(-a/2)=-a

[balmy warren]

actually I have a better suggestion

[silver current]

oh

[balmy warren]

you don't need to do this

you have a b and c in terms of u and t yes?

[silver current]

yes

[balmy warren]

so you can just sub that in to this equation to show that it = 0

[silver current]

ohh ok

i’ll try that

.close

[lone heart]

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[alpine sable]

How can we use the three angle test to prove similarity here?

[lavish pier]

dude idk this question is so vague

[mortal trellis]

what are the three angles of ABE and what are the three angles of ADC

[lavish pier]

it doesnt tell us this

it only has markings to show b is equal to dS

D*

[balmy warren]

yes

so you know ABE = ADC

you have a common angle

do you know the rules for proving similar triangles

[lavish pier]

i wrote that down

AA

SAS

AAA

SSS

?

just having one angle given wont be enough to prove similarity

tho

[mortal trellis]

what about the angle at A

what can we say about it

[lavish pier]

its a common angle

[mortal trellis]

so we have a common angle at A and we know the angles at B and D are the same

[lavish pier]

AA?

[mortal trellis]

yes

[lavish pier]

would an AAA postulate be possible here?

just out of curiosity

[mortal trellis]

sure. if we know two angles of a triangle we know the third, using that they sum to 180°

if the two angles are a and b degrees, then the third is 180-a-b degrees

[lone heart]

@lavish pier Has your question been resolved?

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[lone heart]

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[languid bolt]

it's correct

[lavish pier]

.close

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[languid bolt]

so.. what's the question

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[viral tangle]

The lowest common multiple of the ages of Jack,Sarah and Colm is 36 years. Find their ages.

[languid bolt]

are there any additional informations?

or is that it

[viral tangle]

thats it

[languid bolt]

ok so

what are the common factors of 36

[viral tangle]

9

4

12

2

6

3

oh ye not 13

[languid bolt]

1, 2, 3, 4, 6, 9, 12, 18, and 36.

[viral tangle]

right

[languid bolt]

tbh there are multiple answers idk how to give one answer

[viral tangle]

so i can pick any 3?

[languid bolt]

not rlly

[long iris]

This question is kinda wrong

[languid bolt]

pick one of their age as 36 and yeah

you can pick 2 more

randomly

[vale wigeon]

they could all be 36 lol

[long iris]

Maybe question meant their age is one digit?

[vale wigeon]

or they could be 4, 9 and 1

or they could be 18, 12 and 6

[languid bolt]

yeah exactly

[viral tangle]

on the answer sheet it says 6,9,12 and 18 as possible answers

[vale wigeon]

can you post the answer sheet

[languid bolt]

all of them are possible

[vale wigeon]

as a picture

we want to see the problem EXACTLY as it is stated

[viral tangle]

alright one sec

[stone glen]

They could all be 36

[lone heart]

@viral tangle Has your question been resolved?

[long iris]

why did he left the server

[languid bolt]

idk

did he really left the server?

[lone heart]

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[unborn warren]

Write each of the following in index form:
A. Five factors of 2a
B. Eight factors of m
C. 2x factors of 4y

[lone heart]

@unborn warren Has your question been resolved?

[unborn warren]

<@&286206848099549185>

What does it mean by factors of 2a?

How do you find it

[alpine sable]

what is a?

[unborn warren]

They dont say

They just say find 5 factors of 2a with index law

I can show a pic

Thats it

[vale wigeon]

"five factors of 2a" means "five copies of 2a multiplied together"

[unborn warren]

So does that mean like

2a^5?

Aight thx

.close

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[misty cedar]

I couldn't understand why horizontal velocity would be - sint

[misty cedar]

I mean the position is given by cost, Sint and speed is 1 in this case because cos^2 + sin^2 = 1

I can't figure out where -sint comes in

This is for a ball moving on a unit circle

[lone heart]

@misty cedar Has your question been resolved?

[balmy warren]

what's the question?

[misty cedar]

This

[balmy warren]

so x = cos2t

and y =sin2t

[misty cedar]

Yes those are the x and y valuea

.close

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[frank monolith]

Sorry having a mini crisis but if P(C|B) = 1, does that mean C is a subset of B

[frank monolith]

Convinced theres a typo on this question

[lone heart]

@frank monolith Has your question been resolved?

[placid zinc]

If P(C|B) = 1, that means B is a subset of C

As picking an element in B means with 100% certainty that you've picked an element in C

[frank monolith]

That's what I thought 😅, looks like there must be a typo

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[tawdry whale]

Cos36*cos72

[tawdry whale]

No matter how I turn it around I can't simplify it XD

[balmy warren]

notice how cos72 = cos(36 + 36)

use compound angles

[tawdry whale]

Bro I'm stupid

Thnx

.close

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[slow matrix]

is this

correct?

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[hexed dagger]

Guys??

Matrix help

<@&286206848099549185>

[balmy warren]

what specifically

!15m

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[balmy warren]

this channel will close

use an available one

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[slim mason]

Can someone take me through the step by step of this problem

[languid bolt]

represented by what?

i cant read that

x, y, 4?

[slim mason]

@languid bolt x y and z

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[muted bough]

Shouldn't the negative sign be outside the square root? Otherwise it'd be asking you the square root of -x and not the negative of the result of the square root?

[gray isle]

Otherwise it'd be asking you the square root of -x and not the negative of the result of the square root?
but that is exactly what they're asking...

[muted bough]

oh I'm dumb

I didn't look at the graph closely enough

my bad

.close

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[austere compass]

How do you determine the number of elements in a solution set? (Gauss Algorithm)

[winter tangle]

do you know the types of solutions.

[lone heart]

@austere compass Has your question been resolved?

[austere compass]

uh.. i think?

idk

[winter tangle]

so there are 3 types.

are you able to quote them?

@austere compass

[austere compass]

1 definite solution, no solution, more than 1 solution?

[winter tangle]

great

it's more like 1 unique solution, no solutions and infinite-many solutions

in order

[austere compass]

ahh okay

[winter tangle]

1 unique solution, has identity solution

no solutions, has a row of 0's equaling something.

and infinite-many solutions, has a row of 0's equaling 0

[winter tangle]

@austere compass

[austere compass]

ahhh okay super

thanks

.close

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[wet frigate]

can someone help me prove this

[dry ridge]

Using the definition of union and the definition of subset.

[wet frigate]

so would saying taking the union of subsets of U would yield another subset of U

is that enough?

im new to proof based math idk if thats rigorous enough

[dry ridge]

How do you prove A is a subset of B?

What do you do?

[wet frigate]

show that all elements of A are in B

[dry ridge]

Exactly.

what does it mean an element p is in the union of collection of sets?

[wet frigate]

its all the elements combined

into one set

[dry ridge]

?

Your right there

it’s mean there exist a set in that collection such that p is in it.

[wet frigate]

yes

[dry ridge]

Now use what we just did to prove your question.

That is all you need to do.

[wet frigate]

alright thanks a lot 👍

.close

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[shy bolt]

https://media.discordapp.net/attachments/982848650919149618/988493401722863806/503928755341885450.png

[shy bolt]

Is this equivalent to $log _3 (2) ^2$

[ocean seal]

🔥⃤•AK_ØPᵈᵉᵛ✓

[mortal trellis]

that's probably shorthand for it, yes

[shy bolt]

Oh

[mortal trellis]

but it could also mean $\log_3(\log_3(2))$

[ocean seal]

Denascite

[mortal trellis]

it's ambiguous

[shy bolt]

That's the thing

I am confused

[mortal trellis]

just like sin^2(x) could mean (sin(x))^2 or sin(sin(x))

but that's sadly how it works

I would assume the first in general

[shy bolt]

Like in log i can easily take out the 2 as numerator digit rather than power

[mortal trellis]

oh you are thinking of $\log_3(2^2)$ ?

[ocean seal]

Denascite

[mortal trellis]

that's something else

I thought you meant $(\log_3(2))^2$

[ocean seal]

Denascite

[shy bolt]

The actual question was to simplyfy this

[shy bolt]

Yeah...

[shy bolt]

Ok got it

There isn't any theorem to multiply logs na?

[mortal trellis]

my best guess is that they mean $(\log_3(2))^2$

[ocean seal]

Denascite

[mortal trellis]

no there isn't

[shy bolt]

I got stuck in a situation of $\frac{log_3 12 + log _3^2 2}{log_3^2 6}$

[shy bolt]

So i thought if my assumption of this is wrong

[ocean seal]

🔥⃤•AK_ØPᵈᵉᵛ✓

[shy bolt]

Btw how could I apply the product rule here? Since after the plus there isn't a single term rather than a square of a term .-.

[mortal trellis]

not sure what's the best way to go further

[lone heart]

@shy bolt Has your question been resolved?

[austere compass]

does that mean each row isnt a full row of zeros ?

[winter tangle]

not ur help channel mate

[austere compass]

ok

[lone heart]

@shy bolt Has your question been resolved?

[lone heart]

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[still ibex]

For some brief context, I’ve been trying to learn calculus by myself, and I don’t have a person to ask when I make a mistake, so I’m asking here. This question might sound really stupid.

So I was learning about U-substitution and one of the practise questions was this. I let u=2x^2, since I saw it could cancel with the 8x. The guy in the video let u=40-2x^2, and he got the same answer as me, but just negative. Is there a rule that says you have to take the whole expression in the function when doing u-sub, or am I missing something?

Thank you! :)

[still ibex]

this is what the guy in the video did

[still crest]

You have to take the substitute everything inside the root, if you substitute again just 2x^2 you end up with the same problem but with another variable eg: sqrt(40-u)

[still ibex]

and let's say it was like sin(40 - 2x^2), you'd have to let u = 40 - 2x^2 too?

[still crest]

Yep

[still ibex]

okay thank you very much :))

.close

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[still crest]

You're welcome

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[carmine bronze]

Don't understand. They're supposed to give me a and x right?

[carmine bronze]

oh

wait a minute

I just plug -4x^2 in?

so it's 1?

what about the next ones though

I think it's undefined?

for the second one

[tacit arch]

The difference quotient is a function of both x and h

[carmine bronze]

let me check my work for that one I think I got 1

(-4x^2+.001)-(-4x^2)/(.001)
I think we're supposed to use a small number close to 0 for h right?

[tacit arch]

h is a variable, not any specific number

[carmine bronze]

oh ok I guess I got confused

well won't any number I put in there equal 1

I'm doing something wrong

[tacit arch]

No

Your f(x+h) is wrong

That notation means wherever you see an x, you replace it with x+h

Use parentheses if you're unsure

[carmine bronze]

whenever I see an x I replace with x+h

[tacit arch]

If f(x) = x^2, then f(x+h) = (x+h)^2

[carmine bronze]

in my case it would be f(x+h)=-4(x+h)^2 ?

I guess that slightly clarifies things

(-4(x+h)^2+h)-(-4x^2)/(h)

woops

you said h is a variable

how do I find this variable

[tacit arch]

You don't. Your answer includes h

[tacit arch]

The +h is unnecessary after the squared term

[tacit arch]

This was correct

[carmine bronze]

huh

f(x+h)-f(x)/h becomes -4(x+h)^2 ?

[tacit arch]

It was correct f(x+h)

[tacit arch]

But for some reason you added h to it here

[carmine bronze]

I don't follow

[tacit arch]

You don't see your +h after the squared term here?

[carmine bronze]

let me write it out again

[carmine bronze]

ah ok

in my head though I thought it would look like this

the added h is wrong? I was following your thing

soo no h

[tacit arch]

This is right

[tacit arch]

This is wrong

[carmine bronze]

ah nice

ok now what

does that replace the whole thing?

??

[lone heart]

@carmine bronze Has your question been resolved?

[carmine bronze]

still solving the problem, Bot

[tacit arch]

No

Plug in your formula for f(x+h) into the difference quotient

[tacit arch]

f(x+h) is correct here

You're given f(x) = 4x^2

Now what's f(x+h)-f(x)?

[carmine bronze]

-4(x+h)^2+4x^2

I think we simplify from here right?

[tacit arch]

Right

[carmine bronze]

how I factor this out

got it

ok how do I do second one

finding that limit

[tacit arch]

This looks wrong

[tacit arch]

Oh nevermind

[tacit arch]

Read your question again

[carmine bronze]

how do I find the limit

I forget

is this one plugging in the 0?

woops

[tacit arch]

You can once you fix your limit

[carmine bronze]

I must be missing something here the limit can't be -8x is it?

nah

[tacit arch]

Why not

[carmine bronze]

shouldn't it be a number

[tacit arch]

No

[carmine bronze]

-8x it is

third one I plug in -2?

[tacit arch]

Right

[carmine bronze]

and the h should be a small number right?

last time I asked that you said it's not a fixed variable

so if I'm understanding correctly it can just be any small number close to 0 as possible?

[carmine bronze]

what variable I choose though to plug in

[tacit arch]

You took the limit already. There's no h

[tacit arch]

.

[carmine bronze]

oh

oh

ohhh

ah

gotchu

16?

do my tangent lines look alright?

[tacit arch]

,calc -8*-2

[ocean seal]

Result:

16

[carmine bronze]

I don't think my slope is right

[tacit arch]

What exactly

[carmine bronze]

f'(-2)

I don't think the slope is 16

[tacit arch]

Why not

[carmine bronze]

the graph doesn't look like the slope is 16

oh wait

blind moment

[tacit arch]

You didn't even draw the tangent line

[carmine bronze]

something wrong with my line?

[tacit arch]

Yes. It's not located at x=-2

Your other two tangent lines look right

[carmine bronze]

well there's only 2 tangent lines

ok using f'(x)=-8x to find the slope, f'(-1) should be -8 right

so it should look like this

f'(1) isn't on the line though

ohh

[carmine bronze]

what isn't

oh my x

f'(1) can't possible be -8 though. that's nowhere near the graph

it would have to be vertical

adjusted graph to have -2

howww

this won't touch man

ok this is how I would draw it

I take it back actuall if they want the tangent there then it's supposed to line up

like right here

how I would draw it

lol he went offline

I wonder if I should ping helpers

they probably busy

I'm the one that needs the help here

you asking the wrong person

the helpers are leaving me here to suffer

It's like the stock market. Keeps getting worse when you hope it will get better

ima do it

ima ping the helpers

<@&286206848099549185> I'm sorry my guys you must be busy just need a quick help on my tangent lines

[carmine bronze]

helpers must be damn busy today

I'm afraid if I ping again I'll get banned

do I smell a helper coming?

[drifting sand]

derivative of f at 1 is -8, so you know the tangent line has slope -8

[carmine bronze]

yeah that should be correct

my tangent lines are wrong

I need help

[drifting sand]

you are close

the tangent line for x=1 should touch at x=1, so (1, -4) is on the graph just like you have

slope is rise / run

[carmine bronze]

it is on 1,-4

oh

-4

[drifting sand]

so where do you need to put the second point if you start at 1,-4 and have rise/run is -8

[carmine bronze]

hm

huh

rise/run is -8

-8

but that look weird bro

wth is this man

that's not it

[drifting sand]

you want to start at 1, -4 which you know is on the line

rise -8, run 1 to get the second point on the line

[carmine bronze]

you don't mean like this do you

that's straight vertical

[drifting sand]

no

[carmine bronze]

you can't get it 1,-8 it look weird

[carmine bronze]

ok on 1,-4

I see what you mean

[drifting sand]

yes

[carmine bronze]

mmmmm

ahrotan

ahrotan

what about f'(-2)

slope is 16

it seems to only be 8 on the tangent line

wait nvm

it's 12?

not right either

from -16 to -4

that's 12 not 16

[drifting sand]

you know for x=-2 that (-2, f(-2)) is one point on the tangent line, since the tangent line has to touch

you have (-1, -4) and (0, 4) for the other line

[carmine bronze]

that's slope of 8

bro it's wrong

[drifting sand]

the two points you have are (-1, 4) and (0, 4)

but you need one of them to have x-coordinate -2

[carmine bronze]

you think it's the f'(0) ?

[drifting sand]

otherwise it's not tangent at x=-2

[carmine bronze]

woopsies

so like this?

[drifting sand]

yes, you know (-2, -16) has to be on your line

for the second point

you know slope is going to be 16

so apply the same rise/run logic as for the other line

[carmine bronze]

1,-8 can't be on the line man

look at this

there's no way you can get that to work

[drifting sand]

start at -2,-16

rise 16, run 1

[carmine bronze]

oh

I think I get you hold up

[drifting sand]

I think you are mixing up points and slopes

to make a line you need at least two points

one comes from the graph since you know the tangent line has to touch the graph at one point

the other comes from starting at the first point and using the slope, which you get from the derivative

[carmine bronze]

slope of -8

[carmine bronze]

Yeah I think that was the problem

[carmine bronze]

should this be correct now?

[drifting sand]

looks good

[carmine bronze]

yep it's good

I might have to come back to this later

[carmine bronze]

@drifting sand how I do this

probably shouldn't have pinged you

mbad

got it wrong I switch it up

,w (3/x)/x

[ocean seal]

Results provided by WolframAlpha

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Requested by liluzibert#2674

[carmine bronze]

hmm

[carmine bronze]

<@&286206848099549185>

[lone heart]

@carmine bronze Has your question been resolved?

[carmine bronze]

.close

[lone heart]

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[glass bay]

.close

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[shrewd lava]

I was wondering in this explanation how after finding a common denominator (Green circle), what determined A (in the equation being pointed by the green arrow) is with X and is being multiplied by X+1. B does the same but it isn't with X so I was confused and I'm also not sure how C is with X to the power of 2 since the last two were being multiplied to X+1? Any help is very appreciated

[lone heart]

@shrewd lava Has your question been resolved?

[shrewd lava]

<@&286206848099549185>

[tacit arch]

Such a weird presentation of partial fractions

[shrewd lava]

😅 I agree

[tacit arch]

B already has x^2 in the denominator so it doesn't need it be multiplied by x to get the common denominator

[shrewd lava]

Oh so the A B and C are like that because that's the way they would get the common denominator?

Like A is an X due to it's denominator so times the X would make it X to the power of 2 and then it becomes just like the common denominator which is why B doesn't need an X because it's already X to the power of 2 and C is just missing the X to the power of 2 to be like the common denominator because it's already as X+1?

[tacit arch]

Right

[shrewd lava]

Okay thank you so much!!!

.close

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[tropic oasis]

should i be fsctoring anything else?

[tropic oasis]

or is that my final answer

🤔

[vale wigeon]

strongly recommend writing t's with a little hook at the bottom so you don't confuse them for plus signs

anyway let's check whether your answer is correct

,w d/dt ((2t^5-t)(t^3-2t+1))

[ocean seal]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by Ann#0413

[vale wigeon]

checks out

[tropic oasis]

tyyy

@vale wigeon

one question

would this be the

difference rule?

i'm not sure what approach to take with the denominators though

since i saw my professor sometimes make the exponent negative?

when he somehow undoes the fraction

for some problems

i just dont know where it derives from

[vale wigeon]

i was going to say ``if the function were instead written as $2x^{-5} - 3x^{-3}$, would you be able to take its derivative?'' but you seem to have beaten me to the punch

[ocean seal]

Ann

[tropic oasis]

i can take the derivitive of that yes

but how exacctly does it check out to be equal?

it would be

[vale wigeon]

i'm not sure if you're asking "why does 2/x^5 equal 2x^-5 in the first place" or "why does this rewriting help us here specifically"

[tropic oasis]

the first question

[vale wigeon]

basic algebra

definition of negative exponents

x^-n = 1/x^n

[tropic oasis]

ohh okay

so the derivitive would be

-10x^-6

[vale wigeon]

for 2/x^5, yes

now do the other term too

[tropic oasis]

minus -9x^-4

[vale wigeon]

yes

[tropic oasis]

okay thank you

and now i can use that basic algebra to tie it into the

difference formula?

[vale wigeon]

wym "difference equation"

the derivative of the whole thing is -10x^-6 - (-9x^-4) as you already said

[tropic oasis]

difference rule*

oh wait

well its technically the same thing ig

it is the difference rule*

nvm i see now

got confused with the steps i was doing lol

.close

[lone heart]

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[mellow fossil]

what is the expected value if I just do one trial for this experiment?

[median oar]

Expected value as in the expected result?

They are all equally likely

[mellow fossil]

.close

[lone heart]

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[tropic oasis]

so if i'm correct it's asking me at which derivitive equation is that point true?

which means i would have to find the derivitive of f(x) and plug in 2 as x?

[median oar]

Find the derivative of f(x) that’s the slope

Now you have a slope and point you can make an equation for a line

Might have multiple lines though

[vale wigeon]

it's derivative, by the way

and yes, you would need to find f'(2) and this would give you the slope of the tangent line (which is necessary for but, isn't the entirety of, the equation of the tangent line at x=2)

[lone heart]

@tropic oasis Has your question been resolved?

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[carmine bronze]

2nd derivatave???

[kindred warren]

just find the derivative of the derivative

[carmine bronze]

ah ok that makes sense thank you

I didn't find the first derivitave correctly either

dammit

[junior vector]

Review polynomial derivatives

x^a -> ax^(a-1)

so

-2x^3 becomes -6x^2

[carmine bronze]

oh

I didn't do it right then

is that something different than the power thing

[carmine bronze]

ax^b=abx^1-b is this something different

[lone heart]

@carmine bronze Has your question been resolved?

[void niche]

That's the power rule yes

You did not apply it correctly in obtaining your first derivative, so you have no shot at the second

Fix the first derivative first

[carmine bronze]

okey dokey

Haven't applied power rule to polynomial yet idk how it's going to work

I have to apply it to the whole thing?

some vaseline helps

[tacit arch]

<@&268886789983436800>

[carmine bronze]

riemannnnn

you help me por favor?

maybe I gotta talk about how my pets are itchy too

am I on the right track

?

[tacit arch]

You exponent is wrong here

[carmine bronze]

is this completely wrong?

mmm ok

[tacit arch]

Also it's confusing to set them equal when you mean the derivative

[carmine bronze]

I very confuse

[tacit arch]

For some reason you changed the function

[carmine bronze]

I start over

[tacit arch]

-2x^3 +8x + 2 does not mean (-2x+8x+2)^3

[carmine bronze]

I see

hmm

so I only apply to -2x^3

like this?

[tacit arch]

You didn't differentiate the other two terms

The derivative of a sum is the sum of derivatives

[carmine bronze]

ok how I differentiate

I found this thing it might help

[tacit arch]

Why is that helpful

Doesn't tell you how to differentiate at all

[tacit arch]

It's just this

Go through this
https://www.khanacademy.org/math/old-ap-calculus-ab/ab-derivative-rules/ab-basic-diff-rules/a/basic-differentiation-review

Or start at the beginning if you can't do the review problems

[lone heart]

@carmine bronze Has your question been resolved?

[carmine bronze]

don't really understand it. He doesn't get into any polynomial type situations that I saw of

.close

.closeeee

.close

bot broke?

.close

.help

bot offline wth

[weak ravine]

Bennett collets stamps and baseball cards.
He has at most 100 stamps and at most 75 cards
Carlo and Danielle can make no more than 50 items, in total each day.
It costs $0.75 to make a taco and $1.25 to make a burrito
Create an optimization model and use it to determine the maximum and minimum cost to produce and
food items.

Someone help me out start of this question

[carmine bronze]

<@&286206848099549185> having issues with differentiating polynomials

[carmine bronze]

😭 😭

I die

[river fossil]

what have you tried

[carmine bronze]

Oo can you help