help-17

[manic bay]

U can chose any 2 points that are ON the line you need

Just take 30 and 45

Or 30 and 40 idk whichever 2 points work

They need to be ON the line u need tho

[onyx sapphire]

Yes i did that but im not sure whether it matter which i put first in the formula

[manic bay]

Wdym

[onyx sapphire]

So basically

Does it matter if i do 2-4/30-45 or opposite?

Im confused so what would you do and why?

[manic bay]

Take any 2 points you want

30-45/2-4 or 45-30/4-2

Both are correct

[onyx sapphire]

Oh fr?

[manic bay]

Yep

[onyx sapphire]

Alr thank god

[manic bay]

If u take 30-45/2-4 the negative sign will cancel out

[onyx sapphire]

Ahhhhh ok

And will that work for anything?

[manic bay]

Wdym

[onyx sapphire]

Like finding slope cor any other linear line?

[manic bay]

Yep

All linear slopes have the same formula

Y2-Y1/X2-X1

[onyx sapphire]

Alr thats all i needed to know thx

[manic bay]

Don't accidentally chose the points outside the linear line tho

[onyx sapphire]

Oh yeah ik that

[manic bay]

🫡

[onyx sapphire]

Thx

[vocal sleet]

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[wraith basalt]

Task 13 An insurance company employs three telemarketers to sell insurance.
Salesperson 1 handles 20% of the total number of calls, Salesperson 2 handles 35%, and Salesperson 3
accounts for the remaining 45%.
Experience shows that Salesperson 1 is successful in selling insurance in 15% of their calls
calls, and Salesperson 2 is successful in 22% of his calls. Combined, the three salespeople are successful
in selling insurance in 18% of their calls.
a) Create a table with the given information and label the incidents appropriately.
the incidents.
b) Determine the probability that Salesperson 3 is successful in selling insurance
in one of his calls

Translated with DeepL.com (free version)

[wraith basalt]

did I do it right?

[worldly gale]

yeah

it's correct

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[frail dew]

isnt this false?

for n = 2

(-1)^(1) * 4 = -4

[(-1)^(1) * 2(3)] / 2 = -6/2

[scenic oxide]

you forgot the 1^2 on LHS

first term in the sum

[frail dew]

oh i gotcha

ty

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[gusty vessel]

Hello,
I am a bit stuck on this or how I come to this:
s'(x)=(-5/3)t+(2/3)

How is it (-5/3)? I am really stuck on it ^^"

Why isn't the asnwer
s'(x)=(-10/6)t+(2/3)

[quiet echo]

They’re the same thing.

Just one fraction is simplified.

,w is 10/6=5/3

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[gusty vessel]

Ooooh wait I get it!!!
Thank you so much :DD

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[fierce tree]

Hi i would like some help with my statistics

[vocal sleet]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[fierce tree]

I would like to go over some stats that I'm doing lesson 9 through 19

I have a midterm wednesday

.reopen

[rotund shoal]

post ur question

[paper depot]

lesson numbers from an unknown textbook will not tell us anything unfortunately

[fierce tree]

ah okay i see

i was hoping of getting an actual tutor 😭

that would do vc and help me out

[rotund shoal]

50k $ per second for that

[fierce tree]

💀

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[somber dirge]

this is a really new concept to me and i want help
basically, i have to proove that the equation on the left is equal to the one on the right, but im not sure if it has to be always right
also the equal thingy, the minus is attached to the line, not top row

[somber dirge]

Also I get 7x-7y
6(x+2y)

[quick hamlet]

one sec

imma solve n send exp

this is how ive simplified it so far

now what do you mean you have to prove they're equal

[somber dirge]

It quite litteraly says
"Proove they're equal

[regal bane]

So the typical way you'd do this is manipulate the left into the right or vice versa

[atomic jasper]

!nosols

[vocal sleet]

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.

[regal bane]

I see the left is a sum of two rationals. Have you tried adding them together?

[somber dirge]

What do you mean

Btw in the previous exercise I solved the left thing and it became exactly the thing on the right

[somber dirge]

Ohhh nvm yes

Sorry misread that

[somber dirge]

^

[quick hamlet]

so we still havent proved it

did it give values for x and y?

[somber dirge]

Yeah that's why I came here for help

[somber dirge]

No

My only theory is that it might just not be equal?

[quick hamlet]

where did u get the question from

i think something is wrong or im js dumb

[somber dirge]

I'll send the image

Ignore the bottom stuff

[quick hamlet]

where does it say prove

[somber dirge]

It's in a different language, do I show it anyways

[atomic jasper]

!original

[vocal sleet]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[regal bane]

The - is in front of the rational, not on top of it. I think we were making that mistake

It still doesn't work

[somber dirge]

(the exercise is split onto multiple things, were looking at the second exercise)

[regal bane]

If you were asked to prove, you might just have to say "lol no"

[quick hamlet]

yeah theres something wrong

they have to be equal if we were to prove

[atomic jasper]

,w (x-3y)/(2x+4y)+(2x+y)/(3x+6y)=-(x+11y)/(6(x+2y))

[twin meteor]

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[regal bane]

You can disprove with a counter-example, if you'd like. Give an x and y such that the left and right don't evaluate to the same thing.

[atomic jasper]

theyre only equal for y=-2x

[somber dirge]

Well that's weird

I guess it's a error on their end or it could just not be equal to

[regal bane]

A translator confirms for me that you are only asked to prove as an identity

So this does seem like an error. It happens!

[atomic jasper]

my guess is that they meant this?

then its correct

just a typo

[somber dirge]

Okay yeah that explains it

[regal bane]

Yup that's exactly what it's supposed to be

Oof

[somber dirge]

well.... Atleast I wasn't wrong with my calculations :D

I'll be closing this now, thanks guys (ALOT!!!)

.close

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[rocky pollen]

I have some problems solving the second implication can any one help

[rocky pollen]

this is my attempt with the first one

[flat python]

looks good, do you have to be super rigourous? Or is it just the idea

[rocky pollen]

will i d like to know the idea first so i can try it on my own

[regal bane]

nvs? Normed Vector Space?

[rocky pollen]

yes

[signal pendant]

You can also write an alternate proof for this. Since f is continuous, g: x -> ||f(x)|| is continuous. Note that A_f = g^{-1}({1}) must be closed since {1} is closed

[rocky pollen]

ah yah that is a good one tho my real problem is the other implication i m kind stack on it

[rocky pollen]

yah that is the thing I tried using the continuity general definition (got stack imidiatly ) then I tried to use a contradiction but after suposing that f is not continuous i can't think of any sequence that give as a result and I have no idea how to do it directly I am totally stuck (I m stealing that pic

[signal pendant]

Have you learnt the equivalence of norms?

[rocky pollen]

yes

[signal pendant]

Ok, so try proving this for the sup norm

[rocky pollen]

like useing the sup |f(x)| ?

[signal pendant]

That question doesnt make much sense

[rocky pollen]

oh sorry my bad i meen where do i use the sup norm

[signal pendant]

Maybe you call it the uniform norm, or infinity norm

[rocky pollen]

yah

[cyan talon]

it's never said that E is fin dim anywhere

[rocky pollen]

will so what do you propose we do

[signal pendant]

Can you try getting a contradiction now

Notice the special property about w_k ||(its points are on A_f)||

[twin meteor]

Asteroid

[vocal sleet]

@rocky pollen Has your question been resolved?

[signal pendant]

I think the above argument works without needing any equivalence? Not sure why i thought it was needed

[rocky pollen]

so i need to consider the limit and find it out of the set ?

oh will it doesn't also why using the subordonate norm ?

[signal pendant]

Oh thats just the norm. Sorry for the poor typesetting

[rocky pollen]

oh ok

@signal pendant can you explane the contradiction like i still cannot see it sorry about the trouble

[signal pendant]

Whats the limit of the sequence w_k

[rocky pollen]

it is 0

[signal pendant]

But also note that w_k lies in A_f

[rocky pollen]

so || f(w_k) || = 1

[signal pendant]

Yes

And that is a contradiction because....

[rocky pollen]

lim f(w_k) != f(lim w_k)

like != meen does not equal

oh ty bro

that was really helpfull

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[floral garnet]

Can anyone explain what does this mean

[floral garnet]

here's a sample of the task It is meant to solve

how do you find the gradient of a matrix

or like, the gradient with respect to the model to optimize the output as if it were a variable

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[warped osprey]

Can someone run me through this question, I have no idea how to start

[odd helm]

is this a level

[warped osprey]

um idk what that is i dont think im from that country

[odd helm]

nw

ok

so find vector CD

then, you say CE = lambda CD for some lambda

[warped osprey]

wait CE or DE??

[odd helm]

then you set lambda such that $OE = \mu \vec{b} = OC + \lambda CD$

[odd helm]

CE unless you want your life to be horrible

[warped osprey]

lmao ok

[twin meteor]

Xetrov

[odd helm]

you then see that the $\vec{a}$ component of $\vec{OC} + \lambda \vec{CD}$ is zero

[twin meteor]

Xetrov

[warped osprey]

wait do you mean lambda CE?

[warped osprey]

wait sorry i don't get this bit can you elaborate?

[odd helm]

Ok

so tell me what CD is first

[warped osprey]

2/3 (b-a)

[odd helm]

agreed

Then can you then agree than anything on that line is a multiple of (b-a) from C?

[warped osprey]

Yep

[odd helm]

then add 4a to it

since that's your OA

and that gives you one way to write OE

[warped osprey]

right makes sense

[odd helm]

then you notice that OE has no a component

[warped osprey]

?! wait what about the 4a u just added

[odd helm]

it's compensated for by the lambda

[warped osprey]

wait is this right, OE = 4a + λ(b-a)

[odd helm]

that's the magic

you solve like that

[warped osprey]

OH

[odd helm]

yeah

[warped osprey]

holdup so do i say 4a - λa=0

[odd helm]

yuh

[warped osprey]

wait how did you know to assume that though

like cant lambda be ilke 2

and then it wouldnt be 0

[odd helm]

then you'd have a component of a

[warped osprey]

yea? like wouldnt that disprove the 4a-λa=0

because if λ wasnt 4 then it wouldnt be 0??

[odd helm]

which can't be true because OE has no a component does it

[warped osprey]

:O

oh crap oops

[odd helm]

your pfp is adorable

[warped osprey]

lmao ty i got it off pinterest😂

[odd helm]

fair

[warped osprey]

ok so λ = 4?

[odd helm]

mhm

[warped osprey]

icl im losing track of whats going on

[odd helm]

where did i lose you

[warped osprey]

um so for the λ = 4, like what do i plug that into

[odd helm]

back into OC + CE

[warped osprey]

but didnt we use that to find λ

[odd helm]

we did

but only the a component

we still have the b component

[warped osprey]

so OE = 4b

[odd helm]

mhm

[warped osprey]

oh and then u minus that

from the 2b

[odd helm]

ya

[warped osprey]

ohhhhhh

thank you!

[odd helm]

no worries

[warped osprey]

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[delicate pollen]

Let $S = {1, 2, 3, \ldots, 20}$. Denote $X$ as the set of all subsets of $S$ that do not contain any adjacent integers. That is, if $A \in X$, then for any two distinct elements $x, y$ in $A$, it must be the case that $|x - y| \neq 1$. A subset $A$ is randomly selected from the set $X$ with equal probability, and let the sum of its elements be denoted as $\text{Sum}(A)$. Let the probability that $\text{Sum}(A)$ is divisible by $5$ be $\frac{p}{q}$ (in its simplest fraction form), find the value of $p + q$.

[twin meteor]

Vijendra Kumar

[spiral turtle]

Stars and bars to get |X|.

Not sure what the best way to determine if Sum(A) | 5 though.

Well, a sum over different numbers of bars.

Any way you slice this, this feels ugly. But it looks like an Olympiad question, so this should be doable without a calculator

[ashen remnant]

no, the best way to get |X| is recursion

[spiral turtle]

I could see that

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[somber matrix]

help please

[edgy gulch]

check your indices

the variables should match

[somber matrix]

oh ok

thanks

.close

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[shadow sigil]

can someone solve it and explain it to me

[silk osprey]

damn bro you even pledged your honor to not violate the honor code

[shadow sigil]

wha

[winged tangle]

guyes ineed help plz

-eigen victor and eigen value
-Linear transformation and the standard matrix
-linear combination
-relations and their priorities
-equivalent
kernel, rank, nullity

can any one help me in those i have exam after 4 hours and i dont know thing

[silk osprey]

good luck

[winged tangle]

hell yeah

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[vital loom]

why do they have 5.2 x sin 43

and not 6.2 times sin 43

Hsin theta = 0

Im lost

ping meh pls

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[open spindle]

Is the set of all events in a probability space, where the probabilities are rational numbers, a set algebra? Guys couldn't find counter example for the union property. $P(A \cup B)$ i've tried random probability spaces but I think problem is not within PS

[twin meteor]

konfilik

[vocal sleet]

@open spindle Has your question been resolved?

[visual sequoia]

Hi

[open spindle]

hi

[open spindle]

Any ideas?

<@&286206848099549185>

[sly sierra]

you're asking if given an arbitrary probability space, the subcollection of events with rational probability are an algebra? you should be able to find a simple counterexample using lebesgue measure on [0,1]

[open spindle]

I need to look it up but thanks for the tip

[sly sierra]

food for thought: if A and B are intervals with rational length, does their union necessarily have rational length?

[open spindle]

well if their intersection is irrational the length sould be irrational

If they even have intersection

[sly sierra]

yea, so look for an example like that

they will need to overlap yes

[open spindle]

Gosh

there are tons of counter examples

[sly sierra]

yep you could also cook up an example on a finite space

(one with finitely many outcomes i mean)

[open spindle]

Yes i got it

[sly sierra]

for example suppose you have three elements in the space, a,b,c
let a have irrational probability
and give b and c probabilities such that P{a,b} and P{a,c} are both rational

then {a,b} intersect {a,c} is just {a} and has irrational probability

[open spindle]

I just started thinking not about the subcollections but about their probabilities and got stuck

[sly sierra]

^ oops i guess you would need at least one more element d if the probabilities are going to sum to 1 (which is rational) but you get the idea

[open spindle]

THANK YOU VERY MUCH

[sly sierra]

yw!

[open spindle]

.close

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[open spindle]

.reopen

[vocal sleet]

✅

[open spindle]

@sly sierra wait wait i just read your example one more time you said "let a have irrational probability" but it's stated that a can't have irrational probability since it's a subcollection

well not because it is a subcollection rather any collection can't have irrational value

oh damn i got it sorry

.close

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[sly sierra]

right, {a} itself would not be in the subcollection, but {a,b} and {a,c} would

[open spindle]

it gets harder past 2 o'clock 😂

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[low igloo]

my proffessor did this showed us that he did some actions to prove a iff instead of doign implies from both directions, how can I know that an action I do can work in iff and not only in implies

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[vast shale]

how can i use the method of undetermined coeffs when there is an x term in the LHS of the equation?

[potent anchor]

the homogenous equation is y' + xy =
0

y' = -xy

in other words

[vast shale]

oh okay

i got it

[potent anchor]

dy/dx = -xy

[vast shale]

thanks!!

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[vast shale]

This seems very simple but for some reason I just cannot make a formula for it to solve it can someone explain to me the formula that they come up with or even how they came up with it

[vast shale]

for future questions

[potent anchor]

half of the total distance at 3 km/h

how long is the time

[vocal sleet]

@vast shale Has your question been resolved?

[vast shale]

we dont know

[hidden turret]

this is quite a cool problem thanks for it (I dont know how to solve it)

[vast shale]

haha

[grim escarp]

gimme a sec

to work it out myself

[peak matrix]

you could try introducing a variable t for total time

then express all the information in equations

[vast shale]

I tried not enough information

[peak matrix]

really? What equations did you get?

[peak matrix]

(you might also want to introduce s for total distance)

[slim birch]

let total time = t and total distance = d

[vast shale]

d = 3km/h x 2
t = 2km/h x 2

d-t = f?

[craggy sentinel]

thats what i am trying rn but the final part where you gotta take S-S1 and T-T1 are messing up by not canceling

[vast shale]

probably doesnt work but just saying

[peak matrix]

t = 2km/h x 2

this one isnt entirely right

[grim escarp]

i got it

[peak matrix]

time = distance / velocity in general

[grim escarp]

you need to form a relationship between the distances

[slim birch]

that doesn't look right

[grim escarp]

and consequently for the times

using simultaneous equations

for ratios

[craggy sentinel]

your time isnt the same in all parts

[grim escarp]

let total time be T and total distance be D, $t_2$ be the time walked at 2km/h, $d_3$ be the distance travelled at 3km/h and so on

[twin meteor]

Sam | TND

[grim escarp]

she walks at 2km/h for T/2

hence we can for an expression for $d_2$

[twin meteor]

Sam | TND

[grim escarp]

which will just simplify to $d_2=2 * T/2 = T$

[twin meteor]

Sam | TND

[grim escarp]

(i cba to use the frac rn)

so we have d2 now

we know d3 is just D/2

we can find t3 with a similar way

and then just say that the rest of the time walking at 4km/h is t4

so the corresponding distance becomes d4 = 4t4

[vast shale]

okay

[vast shale]

not okay, what do you mean

[grim escarp]

speed = distance / time
so distance = speed * time

that's the formula im using for all these expressions

now you can form 2 equations for total T and total D

which should simplify to two 3 variable equations

and you can use those to determine a ratio

can you try doing that?

[hidden turret]

I am incredibly happy that gpt is getting it wrong (I think i got it right)

[grim escarp]

?

can you spoiler your answer

because i got to an answer as well

[hidden turret]

id rather see your process

[grim escarp]

im walking OP thru it

i got ||1/14||

is that what you got too?

[hidden turret]

yeah

[grim escarp]

what'd gpt get

[hidden turret]

1/6 lol

[grim escarp]

out of curiousity did you use the reasoning model or the normal gpt 4 model

[hidden turret]

normal one

[grim escarp]

can you open a different instance (dont use the same chat) and use the reasoning model i believe it's the o1 model iirc, but even on the free version at the bottom if you just enable reasoning it might work

cos last i used chatgpt it was handling problems pretty well

[craggy sentinel]

there are different models of gpt? I thought it had the o4, min and 3.5

[vast shale]

distance = speed * time
time = distance / speed

d1 = 2 * t1
d2 = 3 * t2
d3 = 4 * t3

t1 = d1 / 2
t2 = d2 / 3
t3 = d3 / 4

t1 = 2 * t1 / 2
t2 = 3 * t2 / 3
t3 = 4 * t3 / 4

yall im lost

you have 2 unkown variables how do you solve it??

and either unknown depends on the other

[grim escarp]

okay im gonna clear this out a bit so that it's easier to discern what is what rather than keeping an order 1, 2 and 3

let's start from the top

let total time be T and total distance be D, $t_2$ be the time walked at 2km/h, $d_3$ be the distance travelled at 3km/h and so on

[twin meteor]

Sam | TND

[grim escarp]

so basically d2 and t2 are distance and time travelled at 2km/h
d3 and t3 at 3km/h
d4 and t4 at 4km/h

do you follow this much?

since you're not here im just gonna continue

putting the words of the question into expressions

[vast shale]

im here

[grim escarp]

oh hi

so right the question says

[craggy sentinel]

please @me once yall finish this please

[vast shale]

ok

[grim escarp]

she walked half the total time at 2km/h

so

we can write that as

t2 = T/2

time at 2km/h = half of the total time T

[vast shale]

I understand yes

[grim escarp]

now using the formula speed = distance/time so distance = speed * time

where speed is 2km/h

we can simplify and get an expression for d2

d2 = T

that make sense?

[vast shale]

yes

[grim escarp]

then the question tells us that half the total distance D is covered at 3km/h

so d3 = D/2

so we can write an expression for t3 now

t3 = d3/3
t3 = D/2 /3 = D/6

finally the rest of the time is travelled at 4km/h

so let's just say that time is t4

and the distance would be

d4 = 4km/h * t4

therefore d4 = 4t4

summarising all this we get

d2 = T
d3 = D/2
d4 = 4t4

and

t2 = T/2
t3 = D/6
t4 = t4

now we can say that D = d2 + d3 + d4 and T = t2 + t3 + t4

can you form expressions?

both in terms of D

like theyre gonna be two 3 variable systems

I want you to write them as D = for both

[polar burrow]

do you have the answer , i wanna cross check

[grim escarp]

||1/14||

is what I got

and another person

just waiting for OP to confirm

[polar burrow]

yeah same

[vast shale]

D = T + D/2 + 4 * t4
T = T/2 + D/6 + t4

D - D/2 = T + 4 * t4
D/6 = T - T/2 - t4

yes?

[grim escarp]

,w solve for D in D - D/2 = T + 4 * t_4

[twin meteor]

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[grim escarp]

,w solve for D in D/6 = T/2 - T + t_4

[twin meteor]

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[grim escarp]

this is flipped fsr wait what

,w solve for D in T = T/2 + D/6 + t_4

[twin meteor]

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[grim escarp]

yeah you made a mistake somewhere

[vast shale]

oh

[grim escarp]

it simplifies to 3T - 6t4

basically then youd just sub the D in both

and get a ratio for t4/T

you'll see it when you work it

[vast shale]

D/6 = T - T/2 - t4

correct?

[grim escarp]

,w solve for D in D/6 = T - T/2 - t_4

[twin meteor]

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[grim escarp]

yep

id reccomend making D the subject

so that you can solve simultaneously

[vast shale]

ok now what

[grim escarp]

solve simultaneously by substituting one D eq into the other

[vast shale]

D = 2(4t4 + T)
D = 3(T - 2t4)

2(4t4 + T) = 3(T - 2t4)
8t4 + 2T = 3T - 6t4
14t4 = T

we still have two unknown variables

[grim escarp]

yes now just make the ratio t4/T

[vast shale]

14t4/T?

[grim escarp]

not quite

[vast shale]

t4/T/14?

[grim escarp]

you had 14 t4 = T right

divide both sides by T first

14 t4/T = 1

now divide by 14

t4/T = 1/14

[vast shale]

shouldnt it be = 0?

[grim escarp]

5/5 = 1

[vast shale]

when you have no variable

[grim escarp]

T/T = 1

[vast shale]

oh

right

[grim escarp]

you're dividing not subtracting

actually

you dont even need to bring T to this side

just write it as

t4 = T/14

t4 is 1/14 of total time

[vast shale]

wow

and im supposed to have 3 minutes to do this question

[grim escarp]

i mean to be fair now that you know how to do similar qsses is it that difficult?

@craggy sentinel

[grim escarp]

for qsses like these id reccomend just taking a second and reading the question and putting the words into expressions

what are you typing 😭

[vast shale]

ok so
T = total time
D = total distance

time = distance / speed
distance = speed * time

A = 2km/h
B = 3km/h
C = 4km/h

Ct = T - At - Bt

At = T/2
Bt = D/2 / 3
Ct = Ct

Ad = T
Bd = D/2
Cd = 4Ct

T = T/2 + D/2 / 3 + Ct

D = 3(T - 2Ct)

D = T + D/2 + 4Ct

D = 2(T + 4Ct)

3(T - 2Ct) = 2(T + 4Ct)
3T - 6Ct = 2T + 8Ct
T = 14Ct
T/14 = Ct

so 14th the total time = the time of 4km/h

yeah bro its not any easier after knowing

thank you very much though

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[craggy sentinel]

thanks!

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@craggy sentinel Has your question been resolved?

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[flint sigil]

help

[flint sigil]

how does

this

1/k(k+1)

get separated into that

[flat whale]

by working backwards

[flint sigil]

I don’t get it

please explain

[flat whale]

working backwards means knowing the answer and doing steps in reverse order to get to the start

[potent anchor]

do you know about partial fraction decomposition

[pearl wadi]

they wrote the numerator as (k+1)-k

[flint sigil]

yes

but I forgot most of it tbh

[potent anchor]

well it's overkill but you could do it here

the trick is to rewrite the numerator

[pearl wadi]

dont really know about those terms but this is a general method so that u get consecutive terms cancelling out

it is usually done when the difference of the denominators is a whole number

[flint sigil]

A/x + b(x+1)

ok but then why is b negative

[pearl wadi]

example if it was k(k+3) they would multiply 3 into the numeraot and write it as k+3 - k

[potent anchor]

im gonna assume you meant to put another /, did you try to solve a and b

[flint sigil]

naur

do I need to

[flint sigil]

ok?

I’m still not quite following

[pearl wadi]

its ok follow what the other guy is saying

[potent anchor]

you should get b = -1 if you do

but liek again this is overkill

[flint sigil]

then how else am I supposed to solve it

😭

[civic otter]

Add and subtract k in the numerator

And then split the fraction properly

[vocal sleet]

@flint sigil Has your question been resolved?

[vocal sleet]

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[plucky token]

Helloooo, currently I am struggling with this sort of graphing, and I will soon have other questions (I guarantee it) but as of right now, how would I find these? I'm thoroughly confused and would appreciate the help!

[oak magnet]

,rccw

[oak magnet]

Vertical asymptote => where denominator is 0 and can't be prolongeable by continuity

[plucky token]

In dummy terms please?

[oak magnet]

Set denominator = 0

And solve for x

[plucky token]

Alright, bottom number?

[oak magnet]

Yeah

[plucky token]

Alright

[oak magnet]

x intersect are x where y = 0

So here its none

Cuz numerator can't be 0

[plucky token]

Alright so for #7 if I'm right the VA is: X = 0 & X= 1?

[oak magnet]

0?

f(0) is -5 there is no VA

But you right about the x = 1

But its missing another one

Which is not X=0

[plucky token]

Hm?

[oak magnet]

deno = 0

X² - 1 = 0

[tough sphinx]

yo

[plucky token]

Ye

[oak magnet]

(X-1)(X+1) = 0

[plucky token]

OH -2??

[oak magnet]

Absolute cinema

[oak magnet]

No

[plucky token]

Or am I slow

[plucky token]

Ye alr I'm a lil' slow 💔

[oak magnet]

Use zero product rule

a*b = 0 => a = 0 OR b = 0

[plucky token]

I think I either fell asleep during that or my teacher never fully explained it

Cause I recognize it

But its confusing

[oak magnet]

I mean it should be basic from 2 or 3 years before doing VA or anything like this

[plucky token]

Oop

[oak magnet]

So maybe thats why they didn't talk about it recently

[plucky token]

Probably

[oak magnet]

Cuz considered as known

Anyway can you solve it now?

[plucky token]

Lemme see

[plucky token]

Yeah wouldn't this equal 0? 1+(-1) = 0

I'm so confused I'm sorry 😭

[oak magnet]

Which value of X makes it true

[oak magnet]

Use this

[plucky token]

So like for example (ik this isn't the answer probably) but I would replace X on the equation with like 1 to see if its true?

See if it = 0?

[oak magnet]

Yeah but as any equations there is method to solve this

Here its nul product

So if you have (X-1)(X+1) = 0

=> X-1 = 0 or X+1 = 0

Which means X = 1 or X = -1

[plucky token]

WAIT I THINK I FIGURED THAT OUT JUST AS YOU WERE TELLING ME 😭💔

[oak magnet]

Great, thats the important part

[plucky token]

Yeah

Now for X-inter, how would I find that?

[oak magnet]

Set your function = 0

And solve (if possible) for x

If you can't, there is none

[plucky token]

So 5/x²-1=0?

[oak magnet]

Else the solutions are the x intersect

[oak magnet]

Yeah

[plucky token]

Alright

Since the square root of 5 is an irrational number, would I put NA? Or did I do something wrong?

[oak magnet]

??

[plucky token]

I solved for X ig

[oak magnet]

Ok but what did you do?

[plucky token]

Though judging by your reaction I didn't do it right

[plucky token]

I added one, then multiplied by 5 to isolate the variable.

X²=5 could only be solved by square rooting it right

[oak magnet]

But what happen to the x² - 1

[plucky token]

I added one

To get it of it

I swapped it into the 0

[oak magnet]

No but you can't do this

Its not allowed

[plucky token]

Wha

[oak magnet]

5/(x²-1) != 5/(x²) - 1

[plucky token]

Oh....

[oak magnet]

Actually

Know that a fraction = 0 <=> numerator = 0

What is the numerator here

[plucky token]

0?

[oak magnet]

Numerator = top of fraction

[plucky token]

Oh

Yeah

And the denominator is the bottom yea

[oak magnet]

So ?

[plucky token]

I'm not sure

[oak magnet]

5/(x²-1)

Numerator =

[plucky token]

5

[oak magnet]

Ok

Is it 0?

For any x ?

[plucky token]

I'm so sorry but I have no idea what youre getting at

But from what I can tell I was supposed to multiply by 5, and leave the one there

Then solve X²-1=0?

Since 5•0=0

[oak magnet]

5/(x²-1) = 0

See the x² -1 ? You can't manipulate x² and -1 individually, its a group

Its x² - 1

[plucky token]

Yeah

[oak magnet]

So there is a proprety for fraction that say a fraction = 0 if the numerator is 0

So we have a fraction here 5/(x²-1)

We look at the numerator

5

Is it = 0?

[plucky token]

No

[oak magnet]

Is 5 = 0?

Ok

So for all x (where its defined) we have that 5/(x²-1) != 0

[plucky token]

Yeah

[oak magnet]

So there is no x intersect

Since its never 0

,w graph 5/(x² -1)

[twin meteor]

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[oak magnet]

See

[plucky token]

Huh

Weird I'm ngl

But I think I might be able to do this? THANK YOUUUUU

.close

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[spark canopy]

!help

[vocal sleet]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[spark canopy]

i gotta find the value of a and c

in f(x) = a(c)^x

[potent anchor]

well theres two variables and two points, so set up two equations and solve for a & c

[spark canopy]

i did 1.5 = a(c)^2
0.75 = a(c)^3

[potent anchor]

ok, then what did you do

[spark canopy]

now

im stuck

do i keep a on one side

and move c3 and c2

[potent anchor]

what if you divide the equations by each other?

does something interesting happen

[spark canopy]

so 1.5 = a(c)^2 / 0.75 = a(c)^3

[potent anchor]

then

[spark canopy]

it becomes c^-1

2c^-1

[potent anchor]

2?

i think youre missing an equal sign

[spark canopy]

yea

[spark canopy]

oh where

[potent anchor]

2 = c^-1?

[spark canopy]

ioh yeah

[potent anchor]

ok then find a

[spark canopy]

wait is it gonna be 2 = a(c)^-1?

[potent anchor]

ok i guess yo ushould finish solving for c

rewrite c^-1 as a fraction and then solve for c

[spark canopy]

1/c^1

[hidden turret]

dividing the other way around was much easier😭😭

[spark canopy]

wym?

this?

[spark canopy]

^

[hidden turret]

yeah

[spark canopy]

how can i divide this the other way around

like just put a fraction

in the middle

[hidden turret]

0.75/1.5 = a(c)^3 / a(c)^2

[hidden turret]

this

[spark canopy]

ohh

to keep the exponent positive?

[hidden turret]

yeah

and notice how everything cancels to give you c

[spark canopy]

it gives me 0.5 = c

[hidden turret]

yup

[spark canopy]

but why did we remove the a tho

what happend to the a

[hidden turret]

now you have c you can solve for a by substitution

just choose one of of the equations

[spark canopy]

alr so i just use 1 equation?

[hidden turret]

yeah

[spark canopy]

like 1.5 = a (0.5)^2

[hidden turret]

yeah

and easy enough to solve for a here now

[spark canopy]

alr ty

[hidden turret]

👍

[hidden turret]

if ur done do .close

[spark canopy]

.close

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[tender basalt]

• Point M is in the middle od AC
• Point N is in the middle of BM
• a straight line was led through A and N, cutting BC in point P

• Prove that |PC| = ⅔a

[vocal sleet]

@tender basalt Has your question been resolved?

[hidden turret]

iI got it now but its a vector proof bruh

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[tardy lava]

need help

[tardy lava]

i'm getting the answer,
number of pages torn = 2, page number of these torn pages is 50, 51

but the source of the question says the number of torn pages = 3. (page number is not reported)

[lone linden]

Typically, the page numbers go like follows:

• the first sheet is pages 1 and 2
• the second sheet is pages 3 and 4
• the third sheet is pages 5 and 6
  (etc.)

so it doesn't make sense for the odd page number to be more than the even page number on any given sheet

[tardy lava]

so according to this the number of torn pages must be 1 ?

@lone linden

[tardy lava]

this answer is correct if the specified book just assigns one number to a whole page (front and back included), can be the reason why i'm wrong

,cloce

.close

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[upbeat rune]

z^5 = -i bar(z^3)

[upbeat rune]

how to solve this

the exercise also says that it could be helpful to work out the modules of the solutions first but idk how

[fervent wasp]

$$Assume z = k( cos(theta) + i sin(theta) )$$

Find out the value of k first

[twin meteor]

SkyAndNight

[upbeat rune]

uhhh

ye how

i dont see how we can find out whats k nor theta here

[fervent wasp]

Look carefully

[upbeat rune]

is theta just -i?

so 3pi/2

and atp idk k=1?

[fervent wasp]

Because k = 1, we can rewrite the equation as z^8 = -i

Do you agree?

[upbeat rune]

why is k=1 tho

[fervent wasp]

z^5 = z^3 bar
Bar only indicates the direction you rotate( clock-wise/anti)

[upbeat rune]

im not understanding why the -i is enough to determine the module

ok ye makes snese

so if we had -2j

instead of -j

would the module in that case be 2

or something else

[fervent wasp]

It should be something else

[upbeat rune]

wait why is that the case

u mean z^2?

[upbeat rune]

how to calculate

[fervent wasp]

z bar indicates rotate the opposite direction compared to z, do you agree?

[upbeat rune]

ye

[upbeat rune]

so uh what does that have to do with the fact that we can just multiply them

.close

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[upbeat rune]

.reopen

[vocal sleet]

✅

[upbeat rune]

anyone?

so the module is 1 right

but then how do we proceed

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@upbeat rune Has your question been resolved?

[flat whale]

You got the conditions here. What else are you stuck on

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[gilded spire]

Sorry if this problem looks stupid, I may have glossed over something important but I can’t seem to for the life of me get it figured

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@gilded spire Has your question been resolved?

[flat whale]

use complex logarithm

https://math.libretexts.org/Bookshelves/Analysis/Complex_Variables_with_Applications_(Orloff)/01%3A_Complex_Algebra_and_the_Complex_Plane/1.11%3A_The_Function_log(z)

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[subtle seal]

Can i solve this integral like this? Google gives the same answer but different process

[viral copper]

sure

that's called a reduction formula

rather it's derived from one

I believe this is called Walli's formula

[flat whale]

are you supposed to prove the identity or just use it

[vast shale]

it's very easy to prove

int from a to b of f(x) = int from a to b of f(a+b-x)

[subtle seal]

so i can use it for pi, instead of pi/2?

[vast shale]

comes immediately

[flat whale]

yes

[subtle seal]

ok thanks!

[alpine kestrel]

I like the substitution notation

[vast shale]

yes the wallis integrals for any trig function between nice ranges

[flat whale]

there's a u sub you can do to prove it. looks like you did it already

[subtle seal]

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[manic flax]

I've no idea how to do this, f kinda seems like the factorial function, except its extended to all positive reals

[manic flax]

I've heard that there's a function called gamma function, which extends it to all number but i don't know anything about it other than its name

[paper depot]

does working out g'(x), g''(x) and eventually the given expression give us anything

[paper depot]

hm.

ugly

ok wait hold on

figure out some 'recurrence relations' for f' and f''

by differentiating the one you are given, ie f(x+1) = xf(x)

[manic flax]

do i find g''(x+1) now

[manic flax]

ok so i got this does it help me?

i guess not, im stuck

help?

[manic flax]

<@&286206848099549185>

[shadow scaffold]

Is this natural log I am assuming

Can you plug in some numbers and see if it helps like you know f(1) =0

Using f(x+1)= xf(x)

[mossy schooner]

Someone please dm me if they are willing to help me with my pre cal hw it’s just 2 questions

[chrome panther]

u cant put x=0, its defined for N

im not sure if this helps but

$log(f(x+1)) = logx + log(f(x)) \ g(x+1) - g(x)= logx \ g''(x+1)-g''(x) = -\frac{1}{x^2}$

[twin meteor]

Spooki

[shadow scaffold]

No I got that

You can telescope the series no?

Using the last part

You are done

[paper depot]

sorry im busy

[shadow scaffold]

@chrome panther u did it

You have the -1/x2

You can just plug in N-1 and 1/2 on the other side you get what you want

[manic flax]

Ah so i can sub x+1/2 as N

[shadow scaffold]

x= N-1

[chrome panther]

oh yeah i see i think i get it now

[manic flax]

Yeah I'm getting(a), I did g(1+1/2)-g(1/2)=-1/(1/2)^2=-4

[shadow scaffold]

Nice

[manic flax]

thanks everyone for your help!

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[sudden herald]

no using coordinates

[paper depot]

a or b?

!status

[vocal sleet]

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

[sudden herald]

b

found out a =5

[paper depot]

ok so it is AX that you want

[sudden herald]

yes

[paper depot]

how did you find the length of EX?

[sudden herald]

phtagerean

[paper depot]

pythagoras

[sudden herald]

pyhtagerous

yeah

[paper depot]

...ok, spelling, but yes.

you're gonna need the same thm here but twice

find FX first

then AX

[sudden herald]

i see

ill try

[sudden herald]

ik 3d pyth but isnt ax to the point in the baseplane

[paper depot]

....did you accidentally a word?

i don't understand what you're asking here, sorry.

[sudden herald]

how does this work?

[paper depot]

as i said: find FX first, then use it to find AX.

[sudden herald]

okay

[paper depot]

if you did part (a), then each of these two steps in (b) is honestly not that different.

[sudden herald]

i got sq root 33

ty

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[gritty lynx]

How do I know if I have to consider the trailer or van separately or the whole system?

[grim escarp]

you should FIRST consider the system as a whole and THEN move on to a free body diagram

i.e. first find out the overall acceleration considering all forces, and then take each body separately

[gritty lynx]

Is this for every question?

And like considering each separately and considering the whole system would still give me the same answers right?

[vast shale]

i love ice creaaaammmmmmmmmmmm

[grim escarp]

it's a good practice yes

[grim escarp]

yep it should, that should tell you that youve done it correct

remember that in an overall system, the tensions on each object cancel out since theyre equal and in opposite directions

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[west halo]

Hey, can someone help me out with this one?

[west halo]

I seem to have got the values x= 2root2, 2+2root3, but I am not sure on how to proceed further

[flat whale]

You just check the inequality for three different intervals between -inf and your lower root, lower root and bigger root, bigger root and +inf

[west halo]

Oh, will try it once more, thanks!

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[vast shale]

Help me guys need to find the DC i gathered that amount of info but i still cannot find it

[peak matrix]

maybe it could be extended into full equilateral triangle

Yep, that works

try it

[vast shale]

Oh thanks damn sometimes I don’t even see that obvious things damn

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[quasi quest]

getting the wrong answer

[quasi quest]

answer should be 3 and -7/3

[grim escarp]

,rccw

[tranquil charm]

,rccw

[flat python]

last quadratic is wrong

its 4 times 3 times -21

not 4 times 1 times -21

[quasi quest]

oh

[grave arrow]

i got 3, -7/3

maybe im doing smth wrong

[quasi quest]

i got it too

thanks

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[coral lintel]

just dont get it

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[edgy kayak]

reopen ur channel

nvm

[coral lintel]

it said the action is irreversible so i opened a new help channel

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[jolly lantern]

Hello

[jolly lantern]

Um

I need help to solve a pythagorean theorem equation thing

[swift bane]

you can post your question so that people can help you

[vocal sleet]

@jolly lantern Has your question been resolved?

[jolly lantern]

Not yet

Can I send a picture

[livid arch]

Yeah for sure man

[livid arch]

Super easy

Do u know Pythagorean equation formula?

[jolly lantern]

Yea kinda

U square everything

And add it tg

[livid arch]

Smth like that lol