help-13

[flat sparrow]

b is just where g is and then minus 1

.close

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[surreal cave]

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[unreal palm]

just confused on how do i get the right side to equal 0?

[digital cliff]

you dont need to?

[surreal cave]

simply take roots :)

[unreal palm]

oh what LOL

my bads

.close

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[lone dune]

your answer isnt wrong

its just not fully simplified

[dusty estuary]

Does anybody know how to do this problem been stuck on it for a while need the answer

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[fiery ermine]

how would I altitude?

[royal loom]

draw a picture

try to identify relevant triangles and label angles and lengths

[fiery ermine]

Then what?

I don't know how to find the altitude part tho

<@&286206848099549185>

[sweet crest]

find another side and then trigonometry for the altitude

there is an equation that uses angles and sides

[cedar kiln]

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[celest otter]

Could someone explain how (2) is derived from (1)?
What steps were taken perhaps?

[foggy merlin]

maybe if you give the whole context

[zenith sail]

try writing out the first few terms of each series

they're almost the same, but the first one starts with a term of -1 which is missing from the second

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[supple niche]

so if i have a a bit pattern with 8 bits 00000000 how many possible ways are there for bit patterns with only 2 and 4, 1's (ex: 10000001, 10100101).

[supple niche]

I was thinking maybe 8! for total number of two's since the first time you have 8 choices and the second time you only have 7 since one spot is already taken and so on???

[zenith sail]

So you have 8 bits, and you need to choose 2 of them to be 1's

[supple niche]

yes

[zenith sail]

you need to choose 2 of them to be 1's

[supple niche]

well that was just how i thought of it but it wants all the combinations

of patterns where there are 2 ones

[zenith sail]

right

all the combinations

[supple niche]

yea

[zenith sail]

There's a specific function for that, I'm choosing my words very carefully here lol

[supple niche]

ok

wdym by function

like an equation?

[zenith sail]

what did you mean by combinations?

like, as opposed to permutations?

[supple niche]

yes permutations

[zenith sail]

well, what do you know about combinations and permutations?

[supple niche]

multiplication principle

my prof does not want us to use equations since this is for discrete math

so there shud be some way to do this without i guess

[zenith sail]

you've learned about nCr and nPr?

[supple niche]

no

[zenith sail]

what about like $\binom{n}{r}$

[wraith dagger]

tatpoj

[zenith sail]

it's another notation for the same thing

or C(n,r)

[supple niche]

no but i think i've seen that in a video about combinatorics i think

but i did not watch it at all

so idk what it is

[zenith sail]

$\binom{n}{r} = \frac{n!}{r!(n-r)!}$

[wraith dagger]

tatpoj

[zenith sail]

it is the number of ways you can choose a group of r objects from a set of n objects

[supple niche]

yea i saw that equation but i dont think i can use it for this class

since we did not cover it

[zenith sail]

well okay

[zenith sail]

you were on the right track here

let's just look at the case for 2 first

Basically you're looking or the number of ways you can choose 2 bits out of all 8

[supple niche]

yea

[zenith sail]

just like choosing two marbles out of a bag of 8

how many options do you have for the first marble? or the first bit to make a 1?

[supple niche]

8 choices

[zenith sail]

and how many for the second?

[supple niche]

7

[zenith sail]

okay, so that's 8*7 choices

but there's a problem

do you see what it is?

[supple niche]

so you need to repick the first marble? but this time u cant pick the same thing u picked b4

?

so is it 8! times 7!?

[zenith sail]

no, that's way too high

[supple niche]

o

[zenith sail]

even if you include all possible combinations of 1's and 0's, there's only 2^8

8! is way bigger than that

[supple niche]

o yea

[zenith sail]

like, if you just pick two marbles out of a bag, there are 8 the first time and 7 the second time

so that would just be 8*7

[supple niche]

yea

[zenith sail]

the problem is that there are two ways to get each combination

if the marbles are labeled ABCDEFGH

you could choose C then F, or you could choose F then C

but that's the same thing

it's the same two bits

so we've counted everything too many times

[supple niche]

yea

[zenith sail]

in fact, we've counted every combination twice

[supple niche]

the order doesnt matter for picking

yea

[zenith sail]

right, but just doing 8*7 doesn't account for that

we need to adjust it

[supple niche]

so divide by 2

so 28

[zenith sail]

right, because for each pair of marbles, there are 2 ways we could have pulled them

[supple niche]

🙀

[zenith sail]

we can do something similar for the case of 4

[supple niche]

so for 4 it is 8 * 7 * 6 * 5 / 2?

[zenith sail]

8*7*6*5

that part's good

[supple niche]

not divide by 2

[zenith sail]

well, if we pull 4 marbles

there are more than two possible orders in which we could have chosen them

[supple niche]

/ 16

[zenith sail]

let's say you pulled marbles ABCD, in how many orders could you have pulled those marbles?

[supple niche]

4!

[zenith sail]

exactly

[supple niche]

so we are doing 4! times extra counting

[zenith sail]

yes

[supple niche]

so divide by 4!

[zenith sail]

yep 👍

[supple niche]

o

i see

thanks

[zenith sail]

np

btw that formula I showed you does exactly what you just did

if you play around with it a bit, I bet you can convince yourself that it's true and see why it works

[supple niche]

yea maybe seems interesting

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[red whale]

is there a way to get a definitive answer for this without knowing what Alice said? the only thing I can think of is that if Alice told the truth, then her answer would've been understandable, thus Alice is from Truth, but I'm not sure if that's correct

[thorn hollow]

Yeah, you can.

But speaking clearly isn't a requirement for telling the truth or lying. Maybe she just mumbles. The question is, could she have said "I am from Lies"?

In other words, if I am from Truth, I always tell the truth. What island do I say I'm from?

If I am from Lies, I always lie--no exception. What island do I say I'm from?

[red whale]

Truth, since saying you are from lies would be a lie if you really were from there

[thorn hollow]

So, Alice couldn't have said what Bob said she did. So where's Bob from?

[red whale]

ohhhh

so he's from lies

omg that makes so much sense 😭 idk why i didn't consider that

[thorn hollow]

So is Charlie telling the truth?

[red whale]

yes

[thorn hollow]

So you can deduce where Charlie's from!

[red whale]

thank you again, you are the best

[thorn hollow]

[red whale]

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[ornate crescent]

Would this first one not be applied force equal to mgsinx minus the maximum static force?

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[ancient delta]

I don't understand

[rain drift]

what does f'(x) represent/

[astral magnet]

it's asking for what values of x is the slope of the tangent line negative

[rain drift]

?

[ancient delta]

ohh 7 < x < 9?

[astral magnet]

correct

[ancient delta]

thank you

[astral magnet]

np

[ancient delta]

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[lucid path]

how do i solve this question

the height, measured in metres, of 500 people are normally distributed with a standard deviation of 0.080m. Given that the heights of 129 of these people are greater than the mean height, but less than 1.806m, estimate the mean height.

all i know is that X~N( μ, 0.080² )

[cedar kiln]

@lucid path Has your question been resolved?

[lucid path]

<@&286206848099549185>

[buoyant latch]

!status

[cedar kiln]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[inland hound]

Well the Z-score for 1.806 is approximately 3.825. So now you can solve for the mean height (μ) using the Z-score formula: μ = X - (Z*σ)

[buoyant latch]

How do you know the z score for 1.806

[lucid path]

1

[lucid path]

i dont get it

[sinful summit]

Solve CDF equation for $z$:

$$\frac{129}{500} = \Phi(z) - \Phi(0)$$

and use z-score formula

[wraith dagger]

adzetto

[lucid path]

okay ty

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[brave pike]

can you use reduction of order on non-homogenious equations?

[mental trail]

I'm not sure what you mean by that, but you have to account for the constant terms as well in either case

Is reduction of order the technique to reduce the matrix to echelon form?

[brave pike]

Like hop would it differ from just

normal homogenious

[mental trail]

the constant terms are affected

Like if
x + 3y = 5
x - y = 2

you want to reduce it to x+3y = ...

and -...*y = ...

usually all the constant terms on the right are 0 for homogeneous equations

but now that they're non-zero, they're affected by this change

[cedar kiln]

@brave pike Has your question been resolved?

[brave pike]

@mental trail hi hi

sorry im trying problems

ok so my teacher gave us this formula

and im just trying to figure out how to get that to work with a non-homogenious equation

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[cold forge]

Hoee we do i make an ogive graph

[cold forge]

@ me when u see this plz

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[sweet crest]

https://www.statisticshowto.com/ogive-graph/

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[versed patrol]

theres

not enough information?

doesthe 20-8=12 and the 25-8=17 mean something

[vestal tusk]

That's all the information from the question

[vestal tusk]

Yeah, it means 12 (20-8) is the total of students that takes math, and 17 (25-8) is the total of students that takes pancasila

[versed patrol]

yeah but how does the 20-8 and the 25-8 help me

why isnt it like 13-1 or any other number

do you know what the numbers they give you in those mean

[vestal tusk]

So the formula of this subject is A=students who takes math(12)+B=students who takes pancasila(17)+C=students who takes both(8)=37-total students of the class(which there's no information about it, so I have to search it, and been stuck there)=X (students who doesn't takes both of the claesses)

[versed patrol]

does students who don't take both mean students that only take one not 2 or they don't take either

i was thinking about students who dont take either when i first read it, but the more i read it, the more it sounds like how man students only take one or the other since theres no info about the total cohort either

[vestal tusk]

They don't take both

[versed patrol]

but it also feels a bit too simplistic to do a whole ass venn diagram for

so they only take one

[vestal tusk]

No, they don't take both of the classes maths, and pancasila

[versed patrol]

right but doesnt both of the classes means they take both maths and pancasila

[vestal tusk]

Which that's the question, have to search how many students who doesn't take both of the classes

[versed patrol]

or it would be "either" no?

you physically can't find the number of people who don't take either of them cuz theres not enough information

[vestal tusk]

Yeah, either of the claesses

[versed patrol]

do you see where im coming from though

[vestal tusk]

Yes

[versed patrol]

the difference between "how many people don't take BOTH" and "how many people don't take EITHER"

cuz those mean 2 distinctly different things

[vestal tusk]

Either

[versed patrol]

but question says both??

[vestal tusk]

Miss translated

It was originally from bahasa then i used glens so that will be easier for people who don't know about bahasa

[versed patrol]

can't help u. it's only physically possible if you take it as "both", not "either"

not sure about translation

but it feels like it should be both

[vestal tusk]

It's alr, if that's the help you can give, i would like to see the answer

Cs the deadline is in about 5 hours so i don't really care being right or wrong

[versed patrol]

was gonna just say 12+17

thats teh only thing that makes any sort of sense to me in this goofy lil question

those are the no. people, excluding those who do both

idk about if it's either tho that doesnt make sense 😭

[vestal tusk]

Well that's make sense tho haha, thanks for the help

[versed patrol]

no worries i hope it all goes ok :_)

[vestal tusk]

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[zinc spear]

I have to check if this function is invertible or not with f being defined on Z --> Z

[quaint arch]

Someone help me with this please?

[zinc spear]

I've found it for the first one, but I'm a bit unsure about the last one. If it's surjective it has to give negative numbers too right?

[zinc spear]

Have you tried finding the common denominator?

[quaint arch]

How?

Can you teach me i forgot

[zinc spear]

it's sinx * cosx

[quaint arch]

Then?

[zinc spear]

when you've done that you can sum them together

[quaint arch]

How?

[zinc spear]

like this

now you can sum them together

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@zinc spear Has your question been resolved?

[cedar kiln]

@zinc spear Has your question been resolved?

[cedar kiln]

@zinc spear Has your question been resolved?

[small wigeon]

have you checked whether or not the function is injective and surjective?

i mean, you can disprove its not surjective

by finding an example

or you can write f(x) as y and then equate it for both domains, and then write the equation in the form of x

and if theres multiple answers then its not surjective

and for injective you just take two functions f(x1) and f(x2) and assume they're equal (for both domains)

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[graceful wadi]

hello i need some help to isolate "a" from cos(ax)

[graceful wadi]

same goes to sin(ax)

[jade charm]

What do you mean

[livid hound]

you don't have an equation, nothings isolateable

[small wigeon]

You can't just "separate" a from x

[graceful wadi]

ill show you guys the problem I'm trying to solve

@livid hound @jade charm @small wigeon

[small wigeon]

I would say try to convert 1-sin(ax) into cos terms

i don't remember the identity exactly but you shouldn't need to separate a here

[graceful wadi]

u mean multiply and divide by 1+sin(ax)

so the denominator becomes in terms of cos(ax)

or u mean getting rid of it entirely from the limit

[small wigeon]

Well I was thinking that 1-sin(ax) could be written as (cos(ax/2) - sin(ax/2)) ^2 but that would make it worse

But we also have -1 in the equation

It's the 1/x that's confusing me right now

[graceful wadi]

the entire thing is confusing

i guess it's f(x) bro

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[icy sail]

I’m struggling to find a max cut here can anyone give me some guidance?

[icy sail]

It’s the Same graph on both just different way to represent it

[cedar kiln]

@icy sail Has your question been resolved?

[cedar kiln]

@icy sail Has your question been resolved?

[cedar kiln]

@icy sail Has your question been resolved?

[blazing dune]

What is your question on?
Or what topic is that ?

[icy sail]

reducing a 3SAT to max cut

[cedar kiln]

@icy sail Has your question been resolved?

[wanton sail]

Ooooh algorithms class?

Can you send a picture of the top of the assignment, where the instructions are given? @icy sail

[icy sail]

Yeah

At this point I already turned it In now I just want to know if it was right lol

I pretty much just drew a line down the middle of the first graph for the max cut.

[wanton sail]

ah okay lol

sure I'll look, haven't done this in a while though so might be rusty

[icy sail]

Which idk 🤷🏽‍♂️ I could not find videos online to give me a concept breakdown

If you do know I’d love to know how you come up with the answer since it may come up on a test later on down the semester

[wanton sail]

It looks like you forgot to assign capacities to all the edges

[icy sail]

Edges are 1 except for the a-a b-b

[wanton sail]

ah okay

the first paragraph of this gives a step-by-step instruction for how to reduce 3-NAESAT to Max-Cut btw (had to look it up because I forgot the exact proof)

(it's from this document https://www.cs.cornell.edu/courses/cs4820/2014sp/notes/reduction-maxcut.pdf )

it looks like you constructed the graph correctly

and then an example cut that would work is {abar, b, cbar}, {a, bbar, c} like you have in the second graph, looks good! (I think you forgot to draw the line from abar to bbar in the second graph)

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[cedar kiln]

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[magic solar]

how do i find the asymptotes of y=xe^x

[upper ruin]

Using the definition of asymptotes

Or better, first think about what types of asymptotes that function can have (among vertical, slanted, horizontal)

[magic solar]

are you referring the the limit as x-> -inf

i dont think it cant slanted since its not really adding

and the domain is all real numbers, so not vertical

what im really asking is how to evaluate the limit as x approaches -infinity

[sleek knoll]

might help to put it in a rational form

like x/e^-x

as x approaches -infinity, the denominator grows in magnitude much faster than the numerator

so it goes to 0

[magic solar]

solving it algebraically preferably

[sleek knoll]

then l'Hopital

[magic solar]

if a limit equals -infinity, can you use lhoptials

i thought it was for limits which are 0/0 or inf/inf

[sleek knoll]

should still work

[magic solar]

okie

ty

.close

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[urban ermine]

how do i prove this with epsilon delta?

[cedar kiln]

@urban ermine Has your question been resolved?

[urban ermine]

<@&286206848099549185>

[jaunty mural]

you could try asking #real-complex-analysis

but i would say writing out the e-d definition of lim

but... i get thats not necessarily helpful advice

[urban ermine]

well if it helps

i'm trying to get sqrt(3-x) to be some multiple of x-3

[jaunty mural]

you write out the definition. Then figure what delta must be for each epsilon

to make that limit 0

!show u need to show for anyone to help you, really

[cedar kiln]

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

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[daring hinge]

i need help with some simple fractions

[daring hinge]

can someone explain that to me? i have dyscalculia

[drowsy mango]

what about it do u not understand

[daring hinge]

how do i figure out the answer

[drowsy mango]

ill assume this is a mixed fraction then

3/4 equals 0.75

do u understand that?

[daring hinge]

yeah

[drowsy mango]

if its a mixed fraction then u just add the 0.75 to the 2

so it becomes 2.75

u follow?

[daring hinge]

yup

[drowsy mango]

now do the same for the second part

[daring hinge]

1.5?

[drowsy mango]

yes ur right

are u allowed calculator?

[daring hinge]

no

[drowsy mango]

ok well ur lucky this is a easy one then

[daring hinge]

okay

[drowsy mango]

how many times does 1.5 fit into 2.75

[daring hinge]

once

[drowsy mango]

yes

then 1.25 is left

[daring hinge]

you are left with 1.25

yeah

[drowsy mango]

now its a bit awkward but u have to divide 1.25 by 1.5

[daring hinge]

uhh

[drowsy mango]

but there is a trick

do u know 1.25 as a fraction?

[daring hinge]

5/4?

or reverse?

[drowsy mango]

yes

ur right

[daring hinge]

oh okay

[drowsy mango]

what is 1.5 as a fraction

[daring hinge]

3/2

[drowsy mango]

yes

now what u do is

u turn the denominator around

so it becomes 2/3

[daring hinge]

mhm

[drowsy mango]

and do 2/3 times 5/4

do u know how to multiply fractions?

[daring hinge]

not really

[drowsy mango]

its really easy

it just becomes 10 over 12

[daring hinge]

so 2x5 and 3x4?

[drowsy mango]

u times the top

[daring hinge]

nvm

[drowsy mango]

and u times the bottom

[dull anvil]

A more better key term to describe this would be the reciprocal

[daring hinge]

yeah

[shrewd blaze]

You not gunna simplify?

[drowsy mango]

no im not gonna simplify it all in one step

bc im trying to explain it step after step

[drowsy mango]

do u know how to simplify this fraction?

[daring hinge]

you mean like 5 over 6?

[drowsy mango]

yep

[daring hinge]

yeah

that i know

[drowsy mango]

good

[daring hinge]

simplifying is easier

[drowsy mango]

now u can put that answer and the initial answer together

[drowsy mango]

so this

[daring hinge]

you mean 1 or 1.25 or 1.5?

[drowsy mango]

1

[daring hinge]

oh okay

[drowsy mango]

so u have 1 5/6

[daring hinge]

1 5 over 6?

[drowsy mango]

yep

[daring hinge]

yeah that

[drowsy mango]

u could also express it as a single fraction but as the question is already in mixed fractions i think the answer should be mixed fractions too

[daring hinge]

i checked my teachers answer and its 1 5/6

[drowsy mango]

yep u got it

gj

[daring hinge]

if anyones up i got another one

different rules though

dont understand with parentheses

[drowsy mango]

do u know what the small two means?

[daring hinge]

yeah

it multiplies 2/3 by 2/3 or something

[drowsy mango]

so u times whatever is in the fraction times itself

yes

[daring hinge]

yeah

[drowsy mango]

do that first

what u get

[shrewd blaze]

Bruh just Do 2/3 x 2/3 then the answer of that you multifly by 1/6

[daring hinge]

4/9

wait thats all?

[crystal raptor]

They're literally working through it right now chill

[dull anvil]

Now multiply that by 1/6

[drowsy mango]

nope

now times that by 1/6

[drowsy mango]

real

[daring hinge]

4

wait

wait

4/54

[shrewd blaze]

Yup just square the parenthesis then the answer you multifly by 1/6

[drowsy mango]

yes but u can simplify this further

[shrewd blaze]

The answer there you simplify then your done

[daring hinge]

wait lemme think about simplifying

2/27?

i dont think it can be simpler

[dull anvil]

Yeah thats your final answer

[drowsy mango]

yes thats finished

[daring hinge]

you guys are super cool thanks

might be back when im stuck again

[shrewd blaze]

https://www.calculatorsoup.com/calculators/math/fractions.php

[drowsy mango]

bro he is not allowed a calculator

ur not helping yk

[cedar kiln]

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[shrewd blaze]

....

Hdjdjdjdj

Heuieie

[cedar kiln]

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[crimson sedge]

Why do my answer differs from the book ?

[crimson sedge]

Exercise:

Book answer:

[cedar kiln]

@crimson sedge Has your question been resolved?

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@crimson sedge Has your question been resolved?

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@crimson sedge Has your question been resolved?

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@crimson sedge Has your question been resolved?

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@crimson sedge Has your question been resolved?

[vernal shell]

This is correct although it could be simplified using the original equation

You're looking for an eq. in the form y = mx+d

Your books finds the line in the form
...x+...y = ...

Try multiplying that last y0 you got by (y0/b²)(b²/y0)

So now you can factor b²/y0 out of that term and the other one next to it

[crimson sedge]

The equations are fundamentally different

Here is a rewriting of my answer

The left side is the same as in the book answer but the right side differs fundamentally

Oh I think I found

We can replace x_0 with x and y_0 with y in the original equation and thus the right side of my equation becomes 1 ?

Yes it's the case I think

Thank you ELeonardo for your answer

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[ionic flower]

How do I solve 17? I’m thinking maybe you could use simultaneous equations but that would take ages… Is there a simpler way to do it? I can’t really figure out what to do with the information “P(3) = 28”

[ionic flower]

Pls ping me

[cedar kiln]

@ionic flower Has your question been resolved?

[ionic flower]

It’s from a chapter about remainder and factor theorem

[neat dune]

Tells u remainder is 28 when u divide by P(x) by (x-3)

oh hold on there's a more useful way to use that

[ionic flower]

Oh ok what is it?

[neat dune]

Well first of all start by writing P(x) in terms of its factors. So like a(x - c1)(x - c2)(x - c3)

U don't know a and one of the roots

But u do know the other 2 roots

[ionic flower]

Yeah

So a(x + 1)(x - 2)(x - c)

[neat dune]

yeee

Now notice a few things.

1. they tell u what the constant term is, which is -8,

2)u can equate the constant term to the constant term you'd get by expanding that product (don't have to expand the whole thing),

and 3) u can plug in 3 into that expression to get another equality

so basically ull have 2 unknowns - a and c, and 2 equations

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[keen nova]

i'm asked to simplify this fraction to have at least 5 > n instances of x. Does it require me to have any knowledge of trig identities ?

[tropic oxide]

"at least 5 > n instances of x"?

[keen nova]

i tried to phrase it formally but probably had the opposite effect hehe 😉 i mean just in general to simplify it, and i suppose fewer terms, so that x shouldn't be mentioned more than 5 times

that's what the feedback said anyways

[tropic oxide]

so you mean "at most 5 instances of x"?

[keen nova]

yep

[tropic oxide]

well ig you could simplify -7x^2 cos(x) - 8 cos(x) into -(7x^2 + 8)cos(x)

and that would bring the number of instances of x down to exactly 5

[keen nova]

indeed that was the correct answer, thank you, but i have another question

can i decompose (right term?) the fraction into left term 14xsin(x) over sin^2x , and right term stays untouched, and then divide left term nom. and denom. by sin(x) and get 14x over sin(x)?

$\frac{14xsin(x)}{sin^2(x)} = \frac{14x}{sin(x)}$ ?

[wraith dagger]

marty

[mental trail]

yes but if you split the fraction into 2 you have to re-use sin^2(x) for the denominator of the other one

[keen nova]

yes, got that part. Okay, so I see now it is correct

I tried doing this along with the simplification Ann said, and got wrong answer, but it was not because of the simplification but rather because i distributed signs wrongly in the factorization process

thank you both for your help

.close

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[eager wyvern]

Why am i getting zero

[tame zodiac]

Any rule of variable X?

[eager wyvern]

Wdym

This

?

[cedar kiln]

@eager wyvern Has your question been resolved?

[eager wyvern]

<@&286206848099549185>

[spice kraken]

show your work

[eager wyvern]

I did

.close

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[little junco]

How do i show this?

[lunar lynx]

Which one?

[little junco]

Let's start with 1 first.

Please help.

[lunar lynx]

Do you know what is the definition of linearly independent vectors?

[buoyant latch]

You can easily find degenerate examples (this will be more useful if you understand the fundamental concepts)

[tough loom]

if u write the vectors as matrix A and solve for Ax and if u get 0 then its linearly dependent

[lunar lynx]

Are you sure?

Read again.

[tough loom]

visually it means that in the 3d space.. all vectors are oriented in a different plane

[lunar lynx]

Firstly, x has to be non zero vector. Secondly, if you get such a x, that means that they are linearly DEPENDENT.

Not independent.

[tough loom]

wait... what?

[tough loom]

oh wait yes..

i said it the other way around didnt i

mb

[lunar lynx]

Yes.

Anyway, so all you have to do is to try to find such a x.

[cedar kiln]

@little junco Has your question been resolved?

[little junco]

Yes

[lunar lynx]

Oh i thought the other person was the OP. Lol

[lunar lynx]

Just use that.

Or if you are having an issue with that, then tell.

[little junco]

Can you tell me how to start it?

[lunar lynx]

Basic idea is- if you can find three scalers a, b, and c such that not all of them are zero, and
a(v-u) + b(w-v) + c(u-w) = 0, then they are linearly dependent.

[little junco]

That is what i am currently doing now but im stucked there. How do i proceed?

[lunar lynx]

Well, you can find such a, b, and c trivially. Just look carefully at your vectors.

[little junco]

What do I do next?

[little junco]

Please help.

[cedar kiln]

@little junco Has your question been resolved?

[little junco]

@lunar lynx

[lunar lynx]

I'm in a class.

A simple hint: Try adding all of your vectors.

[little junco]

It results to 0.

[cedar kiln]

@little junco Has your question been resolved?

[cedar kiln]

@little junco Has your question been resolved?

[cedar kiln]

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[shell kestrel]

Hi. this is the only one right?

[peak minnow]

the 4th one also correct

change tan into sin/cos

[shell kestrel]

ok let me try

[peak minnow]

2cos^3 * sin^2/cos^2 = 2 sin^2 cos

3rd also @shell kestrel

[shell kestrel]

i cant really see it. should i just keep playing with the expression?

[peak minnow]

change tan into sin/cos again
2 sin/cos * sin * cos^2 = 2 sin^2 cos

dont play with expression

[shell kestrel]

i am a bit rusty tbf tho i forgot a lot of identities 😆

[peak minnow]

play with the answers

[shell kestrel]

.close

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[nocturne wharf]

is this correct?

[sweet crest]

!show

[cedar kiln]

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

[broken mist]

What was your work for finding the side lengths here?

[nocturne wharf]

one sec I am type it all out

[primal socket]

It isn't. How did you get b?

[broken mist]

Work for the second problem would also be nice

[nocturne wharf]

Angle A = 11° 32'
Angle A = 11° 32Side C = 213 units
Angle B = 90° - 11° 32' = 78° 28'
sin(11° 32') = 41.59
cos(11° 32') = 208.70
so it would be C?

[broken mist]

Sin(11° 32’) = a/213 where a is side length a

If you solve for a you’ll also be able to get b from pathag

[primal socket]

Or you can use cosine and solve for b

Both are viable

[cedar kiln]

@nocturne wharf Has your question been resolved?

[primal socket]

Okay, do you know how to get either a or b?

[nocturne wharf]

no

[primal socket]

Are you familiar with trigonometric functions?

[nocturne wharf]

50/50

[primal socket]

Okay. So what does sine tell us

[nocturne wharf]

opposite/hypotenuse

[primal socket]

Correct, and if you take the sine of the given angle (A), the ratio of which sides equals sin(A)?

[nocturne wharf]

oh nvm nvm I figured it out thank you I see where u were going

[primal socket]

👍 Which answer did you get now?

[cedar kiln]

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[acoustic plinth]

can someone help me w question b

[acoustic plinth]

like i don’t understand which rules do we use to solve it

[dire geode]

Find an equivalent expression of cos(x) that's equal to cos(27pi/5)

And you need to know the domain of arccos

[acoustic plinth]

what’s that

[dire geode]

$\cos^\inv$ = arccos

[wraith dagger]

riemann

[acoustic plinth]

sry i just started this class last week

[dire geode]

So you don't confuse it with sec(x)

[acoustic plinth]

how do i use this?

[dire geode]

Do this

[dire geode]

I'm just answering your question

[dire geode]

.

[acoustic plinth]

look at the last statement

that’s what u mean right

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@acoustic plinth Has your question been resolved?

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[celest otter]

Is this the average win?

.close

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[vale ginkgo]

Help

[vale ginkgo]

Not sure if this is correct substitution

[long arrow]

but

then sqrt(x+2) isn't sqrt(2)y

that's false

[vale ginkgo]

What should I do?

[long arrow]

I'd just isolate the square root then square both sides

(be careful about set of possible values of "x" - restrictions)

or if you want the sub method then substitute:
sqrt(x+2) = y
x+2 = y^2
x = y^2 - 2

where y >= 0 and x >= -2

[vale ginkgo]

Ok I’ll try it quickly

I’m lost again

[long arrow]

y = 2 and y = -12

is right

[vale ginkgo]

But then the x part is wrong

[long arrow]

we said y >= 0, so we don't even take y = -12 seriously as a solution

[vale ginkgo]

Why is y>0?

[long arrow]

because y = sqrt(x+2), square root of any real number is nonnegative

[vale ginkgo]

Oh yeah imaginary

[long arrow]

in other words it's impossible to get sqrt(x+2) = smth negative

that's just false over reals

and this is why

so y = 2

[vale ginkgo]

So x is 2 is right?

[long arrow]

no

y = 2 and y = sqrt(x+2)

this follows

sqrt(x+2) = 2

solve this

[vale ginkgo]

+-2

[long arrow]

ah

it's actually 2

mb

[vale ginkgo]

I thought it was only 2 lol

Thanks for the help

[long arrow]

yes it's only 2

sorry for the confusion, I thought you were thinking that x is indeed equal to y

without calculations

[cedar kiln]

@vale ginkgo Has your question been resolved?

[vale ginkgo]

.close

[cedar kiln]

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[crimson sedge]

Hey can you tell me if its correct ?

[flint plinth]

c is wrong

[crimson sedge]

There's no reason the intersection between A and B should exclude C

[zenith sail]

also a

[crimson sedge]

A intersect B doesn't mean "the region that is only part of A and B"

[zenith sail]

oh mb that's what labyrinth said

[crimson sedge]

It means "all regions that are part of both A and B"

For the A ?

[crimson sedge]

Yes, I'm talking about question a

OH YES I SEE

Okay thanks

And the C is incorrect ?

Mhm

A intersect B intersect C should only contain regions which are part of all 3

But A dont intersect C ?

For some reason what you drew here is (A union B) intersect C

[crimson sedge]

It does?

Ah

All of them intersect each other

Okay tysm

The others are correct ?

Mhm

Send us your corrected version before you .close

[flint plinth]

c is wronger than before 😆

[crimson sedge]

Ah, uh... c is even wronger now

[crimson sedge]

Pfff you knew I was gonna write that word and decided to copy me

Whaat

[flint plinth]

it's like a quantum phenomenon

[crimson sedge]

Let me say it again: A intersect B intersect C includes only regions that are part of all 3

What you drew here are regions which are part of the intersection of any 2 of A, B, or C

If you must, do it step-by-step

Start by drawing A intersect B

Then draw That intersect C

First step

And then i only have to draw the middle part ?

[crimson sedge]

Mhm

Only the part of that red area that intersects C

YEP

[crimson sedge]

Show me what you got

[crimson sedge]

Only the yellow part

[crimson sedge]

That's correct

You can now .clsoe

Thx bro ❤️

[flint plinth]

.coose

[crimson sedge]

.close

[cedar kiln]

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[oblique prawn]

$\int_0^4 \frac{1}{x^{4/3}}dx$

[wraith dagger]

Jash

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[fresh imp]

these are the answers

the question is d=kt^2

d= metres

t = seconds

k=constant

given that when t=1 the dsistance travelled by the car is 13.2 metres

use model to work out the distance travelled when car reaches 60mph

i did that

but what does "write down a range of values for t which the model is valid"

what does that mean

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[autumn pond]

how do i create a polynomial function with the zeros of -4, 1, 2, and -sqrt(6)? this is what i got

[autumn pond]

in my graphing calculator its correct but it looks really sketchy

[autumn pond]

like it produces the same graph as (x+4)(x-1)(x-2)(x+sqrt(6))

[flint plinth]

what's wrong with this form ^

[autumn pond]

are you implying theres something wrong

or is it right and youre wondering why i think its wrong

[flint plinth]

my point is, (x+4)(x-1)(x-2)(x+sqrt(6)) is such a polynomial function

[autumn pond]

the instructions say to create one that has rational coefficents, a leading coefficient of 1 and has the given 0's

[flint plinth]

oh, so you are required to put it in the form x^4 + ax^3 + bx^2 etc

[autumn pond]

yeah

idk if mine falls under that umbrella

[autumn pond]

this

[flint plinth]

hmm, well the one above doesn't have rational coefficients

[autumn pond]

how would i simplify it to be rational then

[flint plinth]

moreover, that's not gonna be possible while at the same time having a leading coefficient of 1

that constant term is going to be the product of 4, -1, -2, and sqrt(6)

which is not rational

oh wait though

is it allowed to have other roots as well?

or repeated roots

[autumn pond]

this is what the question says

[flint plinth]

,rotate

[autumn pond]

its the first ne

that saying writing polynomial functions

number 29

[flint plinth]

yea you can make the coefficients rational if you also have +sqrt(6) as a root

but not if you don't

[autumn pond]

we have -sqrt(6) tho

not positive

so is there no answer?

[flint plinth]

yes i know

[autumn pond]

i dont think theres an answer key for these questions

[flint plinth]

depends on whether you're allowed to have additional roots besides the ones listed

[autumn pond]

photo math didnt know either

[flint plinth]

if not, then many of those will have no answer

i suspect that they want you to include whaever additional roots are needed in order to get rational coefficients

[autumn pond]

it says of the least degree taht has rational

[flint plinth]

so in the case of complex roots, you include their conjugate

[autumn pond]

so i guess they allow you to go up

[flint plinth]

in the case of radical roots, you include their negative

if you include +sqrt(6) as an additional root then you'll have (x-sqrt(6))(x+sqrt(6)) = x^2 - 6

and the other factors will all be rational as well

[autumn pond]

ahh

so whenever i see a negative sqrt

i want to include the positive version

??

i think there some rule around that

[flint plinth]

yea, if you're required to have rational coefficients you'll need to do that

and then "of least degree" means to add only whatever new roots you absolutely must have in order to get rational coeffs

and no other roots

[autumn pond]

,rotate

[flint plinth]

yes

[autumn pond]

does the conjugate one include -sqrt(6) tho

[flint plinth]

that last paragraph

[autumn pond]

there is no a value

[flint plinth]

yea you just have a special case with a=0

[autumn pond]

so it still works?

[flint plinth]

yep

[autumn pond]

it still applies

if a = 0

[flint plinth]

correct

[autumn pond]

why didnt they include that in the text bru

[flint plinth]

because a=0 is a perfectly good a 😁

[autumn pond]

im assming the complex one applies too?

when a is 0 too

like if i have 1 + 6i vs 6i

[flint plinth]

yes right

if one root is 6i then you'll need -6i as well

[autumn pond]

i got

it doesnt match up in my graphing calc tho

idk where i went wrong

nvm i think i multiplied some of the factors wrng

yeah i put a negative instead of a positive

new answer is correct

[cedar kiln]

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[mortal ether]

Can anyone help me finish this problem?

[cedar kiln]

@mortal ether Has your question been resolved?

[cedar kiln]

@mortal ether Has your question been resolved?

[cedar kiln]

@mortal ether Has your question been resolved?

[next timber]

still need help?

[mortal ether]

I could use it yeah

if you have the time

[next timber]

okay lets see

what do you need help with?

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[shut pond]

How do i tackle this question?

[tropic oxide]

do you know how to do limits of rational functions at infinity

bc this is basically asking you to do that in almost the most general form possible

[shut pond]

its asking to solve a limit of rational functions at infinity

but the function is infinitly long?

[foggy merlin]

no

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[broken sleet]

Any help on this lol?

[vital matrix]

use logs?

use logs to find n in the first equation and then substitute n into the second

[broken sleet]

Uh didn’t take logs yet so is there any other solution?

[vital matrix]

oh

uh

not really i dont think

what is the topic you are studying

oh wait

no you dont have to do that

[broken sleet]

Oh okay

Then what do I do xd

[vital matrix]

so you know the exponential rules

3^x * 3^y = 3^(x+y)

yea?

[broken sleet]

Yes

[vital matrix]

and how

if you divide it then its subtracted

[broken sleet]

Yeah

[vital matrix]

find a way to turn 3^-n into 3^4n by multiplying or dividing using 3^-n

[broken sleet]

Can’t I do it

[vital matrix]

actually im complicating this way too much

sorry

[broken sleet]

3^n = 25?

[broken sleet]

Lol

[vital matrix]

yeah

but wait

[broken sleet]

Wait

I think I solved it lol

It’s just 25^4

[vital matrix]

yes it is

BUT

[broken sleet]

And that’s the answer right?

But what

[vital matrix]

are you familiar with this rule

[broken sleet]

Yeah

I am

[vital matrix]

if x =3, y=-n and z=a specific value, then you get 3^4n

what would z be

[broken sleet]

Z is n?

[vital matrix]

?

on god i actually suck at explaining things

what can you multiply -n by to get 4n

[broken sleet]

Idk I’m confused now 💀💀

[vital matrix]

-n * -4=4n right?

[broken sleet]

Ah yeah

[vital matrix]

so 3^-n becomes 3^4n

and what you do on the right you do on the left

[broken sleet]

Ohhhh

[vital matrix]

what you did on the left was raise everything by a power of -4

you do the same for the right

[broken sleet]

Righttt

[vital matrix]

0.04^-4

you can change that to 1/(0.04)^4

or something

but yeah thats the idea

[broken sleet]

Alright

Thanks

Lmao

.close

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[delicate atlas]

am stuck

just to be sure, im supposed to take the derivative and set it to 0 right?

[crimson sedge]

hello, would you like me to help?
how would you like me to help and what depth should i go to?

[delicate atlas]

would like for you to explain where i went astray

[zenith ridge]

Yes

Just find the value of x

Then show its a minimum

[delicate atlas]

so is what i have so far right?

sent my work

[zenith ridge]

Yes

[crimson sedge]

thank you lucass