help-0

[worn karma]

<@&286206848099549185> Looking for help still on how to find an explicit expression for this

[tacit arch]

Did you calculate T2, T3, T4?

[oak perch]

You can obtain its Generate function though, not sure what to do next cause I don’t study combinatorics
$T_{n}(x)=\sum_{m}a_{n,m}x^m$.then you obtain that $a_{n+2,m+1}=2a_{n+1,m}-a_{n,m+1}$, multiply $x^{n+2}y^{m+1}$ both side you will have the expression of $f(x,y)=\sum_{n,m}a_{n,m}x^{n}y^{m}$

I checked, All you need is $a_{n,0}$ $a_{0,m}$ and $a_{1,m}$ those can be directly calculated

[ocean seal]

Cogwheels of the mind

Cogwheels of the mind

[worn karma]

Not sure I understand hmm..

I also don't know anything about combinatorics, I've studied up to calculus and linear algebra so I assume those are all that is needed to derive the explicit expression

[oak perch]

Anyway I got $f(x,y)=\frac{1-xy}{1-2xy+x^2}$

I am not sure what it’s called, cause I didn’t learn this in English. Generate function? Generating function?

Anyway something in combinatorics

[worn karma]

so apparently this called Chebysshev polynomial:
https://en.wikipedia.org/wiki/Chebyshev_polynomials

and they have an explicit expression there

Not sure how they got to that explicit expression

[ocean seal]

Cogwheels of the mind

[oak perch]

Funny, I almost got the same thing

It says 1-tx but I got 1+t-2xt

I must have calculated it wrong

[worn karma]

I don't get how the generating function is related to the explicit expression though

[oak perch]

But the approach is correct

I only know how to obtain that generating function, not sure what to do next. Maybe you need someone know combinatorics to proceed or you read combinatorics yourself

I got the same thing now

Anyway I got $f(x,y)=\frac{1-xy}{1-2xy+x^2}$

[ocean seal]

Cogwheels of the mind

[oak perch]

My part is done, GL

[worn karma]

I'll probably have to find a different way of doing it, but thank you. It doesn't seem like I'll have to dip into advanced topics unless the professor is being very unfair lol

[oak perch]

You sure you professor asked you to find expression?

Maybe he didn’t ask for that, maybe he only asked to prove some simple things like T_0,T_1,…, is a basis of space of polynomials

[worn karma]

Yeah the question says to
derive an explicit expression for $T_n(x)$

[ocean seal]

Ezra

[oak perch]

😂 I see. He really wants you to learn combinatorics 😂

[worn karma]

Well I'm looking through notes and I found something similar to deriving an expression for fibonacci

using linear algebra

[oak perch]

Different

Fibonacci is linear

[worn karma]

right

[oak perch]

T_n here has a x

xT_n-1

[worn karma]

yes, and that is what is throwing me off! haha

https://mathoverflow.net/questions/286626/is-there-an-explicit-expression-for-chebyshev-polynomials-modulo-xr-1 found something here

not sure what modulo means in this context though

but the matrix representation from one of the answers looks somewhat familiar

[oak perch]

Oh that makes sense

That matrix is diagonalizable , with eigenvalues x+/-sqrt(x^2-1)

Seems like a good approach

[worn karma]

😓

[oak perch]

Good luck with that

[worn karma]

yeah classic "you took a semester of linear algebra so its fair game" type of professor

[oak perch]

When x doesn’t equal 1 then it’s diagonalizable , when x=1 the Jordan normal form is
(1 1
0 1)
Whose power of n =
(1 n
0 1)
I believe your problem will be solved, just very complicated to calculate the final result. And you need to add conjugate parts to obtain a real expression when |x|<1 so when the eigenvalues are complex numbers

[worn karma]

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[alpine sable]

hey, calc newbie here

[alpine sable]

we just started calc 1, and its only the second week and we are already doing derivatives limits and chain rule. I thought a typical calc1 focused primarily on limits and derivatives

if we are already doing this, this early in, whats the rest of the semester usually bound to look like?

i've been doing a large amount of derivative problems to really make sure i can take derivatives easily, but i am wondering what is next, is it worth to keep practicing my derivative skills? or should i move on

[naive valley]

doesn't your course have a syllabus?

[alpine sable]

no it doesn't

im wondering what usually is the next step?

[naive valley]

well it may depend on the course, but usually you do various topics related to derivatives

[alpine sable]

I definitely don't feel like i have 'mastered' taking derivatives yet, but would you say its worth it to just keep doing derivatives?

[naive valley]

sum and product and quotient rules, chain rule

[alpine sable]

or should i try to learn new concepts

[naive valley]

maxima and minima of functions

[alpine sable]

or just get to the point where i can do derivatives in my sleep?

[naive valley]

mean value theorem

you'll get plenty more practice with derivatives

[severe sluice]

no. derivatives are not hard, it's just applying chain, product, sum rules over and over

[alpine sable]

so you are suggesting i look into those theorems?

what should i do with my time? I am motivated to get an A in this class

[naive valley]

well they should be covered in the course, if not already then they will be

and with those theorems you'll know how to take derivatives of just about everything

oh and presumably they'll spend some time on particular functions like sin, cos, exp

log

[alpine sable]

and apply derivatives to those right?

[naive valley]

yep

[alpine sable]

im doing practice problems involving sin cos exp log

etc

taking derivatives

do you have any other suggestion for a calc1 class? like what i should do in my free time

is being comfortable in derivatives the single most important thing for calc1?

maybe brush on trig?

[naive valley]

hard to give specific advice without knowing what the course will cover, but more practice problems for anything you're rusty on

sure, trig will be helpful

[alpine sable]

how much more complex do derivatives get?

i solved all of them and got a couple wrong but reviewed em

and im out of problems so im just on google finding many worksheets with answer keys

[naive valley]

you can also buy a calculus book that has answers in the back (maybe for odd numbered problems or whatever) and they usually have tons of problems

if it's not a required textbook you can get older editions for dirt cheap usually

and calculus hasn't changed, so old editions are fine for problems

[alpine sable]

okay, but nonetheless practicing as much as possible with different derivatives problems

is useful right?

for calc1

[naive valley]

sure, as long as you don't do so many that you get bored or burned out

more practice can't hurt

[alpine sable]

okay, no i wont. i promised myself i am getting an A in this class. i got a C and am retaking

playing catchup with math

[naive valley]

fair enough

[alpine sable]

anyways thanks

.close

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[naive valley]

you might discuss these questions with the instructor

[alpine sable]

yeah, i have made sure to understand the ones i got wrong

:)

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[lone heart]

@remote pendant Has your question been resolved?

[lilac orchid]

hi

[proud ibex]

tbh i feel like the question is kinda ambiguous

its not very clear whether they care about the order in which the rides go

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@remote pendant Has your question been resolved?

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@remote pendant Has your question been resolved?

[solemn grove]

5 DIFFERENT horses, 3 IDENTICAL chairs total is 5

if i had 5 cups and you had to pick 3, which 3 would you pick,
5C3 = 10 I think

[solemn grove]

it’s quite vague but I think they meant chairs go on horses,

I thought it had to do with combinations,

permutations would suggest the order matters, combinations suggests the order doesn’t

if the order does matter as suggested by @proud ibex
it would be 5P3 which is 20 if i’m not wrong

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[empty kindle]

which one is larger and how to prove

[loud grove]

the number inside the cbrt is less than 1

so the number with cbrt will also be less than 1

you can prove which is smaller from there

[empty kindle]

how ? 😄

i tried to prove this

first

[pale kestrel]

This is how I would think of it
1 - cbrt 0.999
vs
-1 + cbrt 1.001

Multiplying both expressions by 10 will net you the same comparison needed to do

10 - cbrt 999
vs
-10 + cbrt 1001

notice 10 = cbrt 1000

I think this might be enough of a hint

[empty kindle]

oh

i think i got it ty 😄

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[alpine sable]

"An approximate answer to the right problem is worth a good deal more than an exact answer to an approximate problem or Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise", what does this means? what does approximate problem means ? . I could not understand this

[alpine sable]

I understand that we should try to find the exact answer to a real problem, and if we could not do it for many reasons like time or cost, the best action is to use approximate answer to the real problem, and we should never try to find solution or exact answer to the fake problem or to the wrong question, but I know this is wrong, so I want someone who can understand English to explain this to me please because I found it confusing

[nocturne anchor]

it could be that by approximate problem they are referring to a problem close or similar to the initial problem but simpler than the original problem.

🙂

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@alpine sable Has your question been resolved?

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[autumn lantern]

hi! is there a way to solve this limit without using l'hopital's? thanks!

[oak perch]

Cauchy mean value theorem

2(sin(x)-sin(π/6))/6(x-π/6)

[autumn lantern]

and then? how do i proceed given that it still becomes indeterminate? sorry

[oak perch]

?

You don’t know Cauchy MVT?

Then it equals cos(t)/3 for some t between π/6 and x

Cos is continuous

[autumn lantern]

how do i determine which value of t to use?

[oak perch]

You don’t need to

You don’t know continuous function? Like any ε>0, there exists δ>0,|cos(y)-cos(π/6)|<ε for |y-π/6|<δ

[autumn lantern]

ohhhh yeah i recall that limit definition, but how do i use that to arrive at a limit for the expression? sorry

[oak perch]

By definition

Just do it

I don’t get it why you don’t get it

[autumn lantern]

alright thank you!

[near lagoon]

Nice with Cauchy mean value theorem

[autumn lantern]

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[fossil mason]

Hi

[fossil mason]

Can someone explain (ii)

I get that it’s 12C5

But I don’t get why

[oak perch]

It’s the same

12C7=12C5

Oh

12 terms you choose 5 bx, other 7 are a

For those 12

So C(12,5)

[fossil mason]

Wait nvm I think I get it

Tysm

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[lime hill]

xgiven kcer explain why f(x)=x^4+kx^2+c might not have a solution but (x)=x^3+kx+d must have a solution

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@lime hill Has your question been resolved?

[still vigil]

kcer?

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@lime hill Has your question been resolved?

[tacit arch]

All cubics cross the x axis because they tend to infinity in one direction and negative infinity in the other direction as x goes to positive and negative infinity. Not all quartics cross the x axis because they tend to positive infinity together or negative infinity together, never opposite.

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[alpine sable]

The diagonals of a rhombus bisect each vertex angle. The diagonals of a rhombus bisect each other at right angles.

[alpine sable]

can someone draw it

to explain what these both statements mean

thank you.

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@alpine sable Has your question been resolved?

[alpine sable]

thanks

what does it mean

when it says

sum of two adjacent angles of a rhombus is always 180 degrees

so lets say angle a is of 58 degrees

so 58-180

122

so thats the angle B?

[floral pawn]

these 2

or any 2 angles that are next to each other

sum to 180 degrees

[alpine sable]

like these 2 right?

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[alpine sable]

.reopen

[alpine sable]

liek these 2 are also adjacent

so

[floral pawn]

yes

also thats not how reopen works

[hidden heart]

this isnt your channel anymore lol

[alpine sable]

ik i forgot

[alpine sable]

thanksss

[alpine sable]

lol

[humble ferry]

Anyone able to help with this? I tried taking slicing in the x direction and using similar triangles i got an expression for the side length of some cross section s as xa/h, i then subbed that into the equation for the area of an equilateral triangle getting that the area of some slice s is given by sqrt(3)/4 x^2a^2/h^2

integrating that gives me that the volume should be a^2h/4sqrt3 but its not, the volume of a regular tetrahedron is a^3/6sqrt2

so im not sure why i have 4sqrt3 when it should be 6sqrt2

my question again since the other guy hijacked the channel

i also tried taking slices in z but im not entirely sure how to relate the length of the side of a slice at some height z to the side of a

<@&286206848099549185>

also the slicing method just refers to finding the volume of a solid by finding a formula for the area of a cross section and integrating it, just if anyones unsure what it is

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@humble ferry Has your question been resolved?

[humble ferry]

<@&286206848099549185>

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@humble ferry Has your question been resolved?

[oak perch]

The area of the bottom multiplied by height then divided by 3

[humble ferry]

Thats entirely unhelpful, i want come up with the formula for its volume as a function of the side legnth a using an integral

i know how to calculate the volume of a tetrahedron

.close

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[carmine harbor]

I’m really struggling with this related rates problem I came up with 30 mph/h but it’s wrong, any help is appreciated

[lone heart]

@carmine harbor Has your question been resolved?

[tacit arch]

not sure if this solves your problem, but

$15 \cdot 2 \cdot \tfrac{1}{\sqrt{2}} \neq 15$

[ocean seal]

riemann

[tacit arch]

,calc -45 + 15 / sqrt(2)

[ocean seal]

Result:

-34.393398282202

[carmine harbor]

Ohhhhhhh

Yeah I forgot about the square root

[tight locust]

$\frac{2}{\sqrt{2}} = \frac{}{\sqrt{ }}$

[ocean seal]

EndTimes

[carmine harbor]

Okay cool cool I got it wrong I thought the process was wrong altogether and I was confused I’ll try part b now thanks 😄

[tight locust]

@carmine harbor that was facetious

don't take what I just posted seriously please.

But you should realize this:
x/sqrt(x) = sqrt(x)
Because:
Sqrt(x) * sqrt(x) = x

[carmine harbor]

Nah you’re goodd man I appreciate the help

I got part b as well I’m all done with it

[tight locust]

👍

[carmine harbor]

thanks @tacit arch and @tight locust 👍

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[dense sleet]

What does ratio like a : b : c actually mean

[dense sleet]

Example :
When we say
a , b , c are in ratio 3 : 4 : 5
does it just mean
a : b = 3 : 4
a : c = 3 : 5
b : c = 4 : 5

Because
a : b : c = 3 : 4 : 5 is false and just makes no sense

This is a yes/no question

Im just goona assume it is

[floral quail]

how is this false

to clarify it means "for every 3 of a, there is 4 of b"

this carries onto "for every 3 of a, there is 5 of c"

and on again: "for every 4 of b, there is 5 of c"

[pale kestrel]

how is it false

a = 60

b = 80

c = 100

a : b : c = 60 : 80 : 100 = 3 : 4 : 5

[lone heart]

@dense sleet Has your question been resolved?

[dense sleet]

I mean sure its "True"
$$\frac{a}{bc} = \frac{3}{20}$$

[ocean seal]

Pluton

[dense sleet]

let a , b ,c = 3x , 4x , 5x
$$3x : 4x : 5x = 3 : 4 : 5$$
$$\frac{3}{20x} = \frac{3}{20}$$

[ocean seal]

Pluton

[dense sleet]

x here needs to be 1 but it can be any number

[dense sleet]

Unfortunatly the way its wrotten

,calc 3/4/5

[ocean seal]

Result:

0.15

[dense sleet]

,calc 60/80/100

[ocean seal]

Result:

0.0075

[pale kestrel]

thats not what it means though

[dense sleet]

Not same

[pale kestrel]

.................

[dense sleet]

That was the whole question

[pale kestrel]

Are you purposely being thick or what

[pale kestrel]

You make no sense just saying this

It's like saying this makes no sense$$a\leq b\leq c$$

[pale kestrel]

Just because it means a =< b and b =< c

a : b : c just indicates the ratio these numbers are in

[dense sleet]

Ok i agree it was inaccurate of me to say that makes no sense. I was applying that
If a , b , c are in ratio 3 : 4 : 5
a : b : c ≠ 3 : 4 : 5

Unless it is exactly 3 , 4 and 5

[pale kestrel]

no

i just gave you an example

60 : 80 : 100 = 3 : 4 : 5

[dense sleet]

I mean that doesnt mean it litteraly which just makes my head question why its wrotten like that

[pale kestrel]

why not????????/

'a : b : c = x : y : z' is equivalent to 'a : b = x : y and b : c = y : z'

It's just shorthand

and clearer in terms of conveying meaning in a lot of cases

[tight locust]

Ok let me put it this way

: = /

[pale kestrel]

it doesnt

in the 3+ case

another way of thinking about it its just saying

(a b c) and (x y z), the vectors, are parallel

They have the same direction

[mild heath]

Can y’all help me with mine 😅

[pale kestrel]

maybe dont spam other peoples channels

if u are not here to help

[mild heath]

My bad

[dense sleet]

So to end the question using : is basically just a convention that is used to apply a : b : c = d : f : g is shortcut for a : b = d : f , b : c = f : g

[pale kestrel]

yes

just like

a < b < c

means

a < b and b < c

[dense sleet]

Ok thanks

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[wide plaza]

i need to find the area

qt = ts

qr = rs

qt and ts are both root 17

and qr and rs are both root 5

[dense sleet]

I mean just by looking at cubes you can calculate the area

[wide plaza]

hm?

[tacit bison]

the area of a right triangle is half of that of the square

[wide plaza]

there is no right triangle

[tacit bison]

you just need to be creative

[wide plaza]

are you creating a square?

around the figure?

i mean you can certainly do that

[tacit bison]

the figure is drawn in several squares

separate the triangles

[wide plaza]

uh

idk what your talking about

can you explain what i should do to solve this problem??

[dense sleet]

Everything here is a right triangle if you draw it

[tacit bison]

no?

[wide plaza]

bruh wdym

are you scribing a square on the perimeter

[tacit bison]

yes

[wide plaza]

of the figure?

o ok

[tacit bison]

the squares on the perimeter

[wide plaza]

well i mean

even if I find

the area of that

i cant figure out the area of the figure

[tacit bison]

you can

do that first

[wide plaza]

ok well its not even a square

because

[dense sleet]

Best solution at least i think calculate area of 4×4 squares = 16 and remove all other area. All of them are perfect right triangles

[wide plaza]

ok i see that

wdym by remove all the other area?

what is the "other area"

the right triangles that are formed

[tacit bison]

my friend, do you have pen and paper?

[wide plaza]

out of it?

[wide plaza]

yes

i do

i drew it out

[tacit bison]

I suggest you draw this figure on pen and paper

ok

[wide plaza]

and i see how Pluton got 4x4

i understand that

[dense sleet]

Area outside the figure you have but inside 4*4 square

[tacit bison]

now outline the different right triangles that makeup the perimeter

[wide plaza]

there are 4, correct?

so now i basically find the area of all the triangles

[tacit bison]

yes

[wide plaza]

and subtract it

out of 16

ok that makes sense

thx

[tacit bison]

wait what

[wide plaza]

wdym

i thought thats what your saying

[tacit bison]

ah ye my bad

I was thinking of 2x2 then adding the area of the triangles

[dense sleet]

The green outline should be cube

Red area is the one you need to remove from the cube

[tacit bison]

yes

[wide plaza]

ok i understand

ty

@dense sleet

i cant figure out

the top right shaded area

[dense sleet]

Split it in 3 pieces

[wide plaza]

i tried

i keep getting a decimal

it doesnt make sense

[dense sleet]

I see 1 cube and 2 right triangles

[wide plaza]

in that shaded region?

oh wait i think ik what you mean

wait lemme try again

i got the answer @dense sleet !

its 9

thx for your help man

[dense sleet]

Np

[wide plaza]

🙂

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[hardy geyser]

Hi

[dense sleet]

What did you try

[hardy geyser]

I was gonna take the conjugate but idk how to do that with this problem

[dense sleet]

You could maybe use LHopitals rule. But im not sure

[hardy geyser]

What is Lhotpials rule

Actually I’ll search it up

@dense sleet the first one? And khan?

[dense sleet]

Ye

[hardy geyser]

Ok

[dense sleet]

Maybe khan would be better

[lone heart]

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[alpine sable]

is this correct and why

this too

[buoyant kayak]

first one is correct, yeah

[alpine sable]

alr

[buoyant kayak]

think about what you're solving for

[alpine sable]

the x intercepts

?

[buoyant kayak]

yeah

[alpine sable]

so i think that one is right too

[buoyant kayak]

yeah second one is right too

[alpine sable]

alr

[lone heart]

@alpine sable Has your question been resolved?

[karmic radish]

For the soccer problem u have to find when the ball hits ground again so after it lands. Ground level in this case is 0. As f(x) is height and x is time u have to find the time (x) when f(x)=0

[lone heart]

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[gaunt finch]

Hey, I'd like some help with geometric progressions

[gaunt finch]

How can I determitate r (what multiplies the numbers, in case you call it different) only having 2 terms (for example a2 and a8)

[glass lichen]

$a_n=ar^n \
a_m=ar^m$

[ocean seal]

Mosh

[gaunt finch]

And then calculate the first term with another one and the r? Like with a8 and r get a1?

[gaunt finch]

Oh I think I'm not understanding that

[glass lichen]

the general term of a geometric sequence (WLOG starting at n=0) is $a_n=ar^n$

[ocean seal]

Mosh

[glass lichen]

$a,ar,ar^2,...$

[ocean seal]

Mosh

[gaunt finch]

I know that part, but I'm not sure how to get the r

This is what I have nos

[merry depot]

What is the ratio of $a_n$ and $a_m$?

[ocean seal]

Zybikron

[gaunt finch]

Now I need to do an equation to get r?

[gaunt finch]

Ok let me try to explain again

I only have 2 terms, a2 = 3 and a4 = 27. With that, I need to get the r

[merry depot]

right.

[glass lichen]

Yeah

[glass lichen]

.

[merry depot]

what is the ratio of a_n and a_m?

[gaunt finch]

What do you mean with ratio?(sorry I'm not very good at english)

[merry depot]

$\frac{a_n}{a_m}$

[ocean seal]

Zybikron

[gaunt finch]

fuck joined here trying to understand more and now I understand even less

Nevermind, thanks for trying to help, I'll try to find a spanish sv or something cause I'm not getting it in english

Thanks tho

[merry depot]

take this, divide a_n by a_m. That's all I'm asking right now. We can go from there

[gaunt finch]

Ah wait wait, i understood

I'm getting 9

[merry depot]

right, and what should 9 be equal to in terms of r?

[gaunt finch]

Idk

Like, the exercise is not giving any information more than an and am

[merry depot]

.

[gaunt finch]

Yeah that is giving me s result of 9

[merry depot]

That's for your particular answers

do it for the image linked. with general m and n

[gaunt finch]

n and m then?

Like, n/m?

Wait no

[merry depot]

Take exactly this. Not your values for a_n and a_m, Exactly these ones. What is a_n/a_m?

[gaunt finch]

I don't know, we've never done something like this with just letters

[merry depot]

ok, let's look at an example. What is x^10/x^7?

[gaunt finch]

x^3?

[merry depot]

yeah, why?

[gaunt finch]

Cause the 7 rests to the 10 as they are both elevating the same coeficient and they are dividing

Not sure if you call the things the same way as I do but I guess you understand it

[merry depot]

I more or less follow

So when dividing, with the same coefficient (or base), what you subtract the exponents

so $\frac{x^{10}}{x^7} = x^{10-7} = x^3$

[ocean seal]

Zybikron

[gaunt finch]

Right

[merry depot]

So if $\frac{a_n}{a_m} = \frac{a\cdot r^n}{a\cdot r^m}$ what should you get?

[ocean seal]

Zybikron

[gaunt finch]

Ah, a•r^n-m

[merry depot]

the 'a' should cancel, but yes!

So in general, $\frac{a_n}{a_m} = r^{n-m}$, and you have $\frac{a_4}{a_2} = 9$. Can you put those together to get r?

[ocean seal]

Zybikron

[gaunt finch]

r^4-2?

[merry depot]

which can be simplified a little

[gaunt finch]

so then I'd get r^2

[merry depot]

and r^2 = 9....

[gaunt finch]

then r is 3

[merry depot]

yep

technically it could also be -3, unless you have more information

[gaunt finch]

Yep we're using only positives

[merry depot]

cool! then yes, r = 3

[gaunt finch]

Is this right then?

[merry depot]

yes

[gaunt finch]

Ok, I think I got it

And then how do I calculate a1 with a2 and r?

[merry depot]

How do you get from a_1 to a_2?

[gaunt finch]

oh i was getting confused with the other progressions

I just need to divide a_m by the r?

[merry depot]

yep

[gaunt finch]

a_2 / 3 in this case?

[merry depot]

yes

[gaunt finch]

ok, ok

I think I got it

Thanks!

[lone heart]

@gaunt finch Has your question been resolved?

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[vapid steppe]

guys can someone check my work

[teal glen]

1. rectangle - triangle

same thing for the second one really but just different shapes

[vapid steppe]

yea can u check if i got the right answer

[teal glen]

what'

what's your answer? if it's 105 it's wrong

[vapid steppe]

oops i meant 85

[teal glen]

yes you're good now

[vapid steppe]

do u like my drawings of the picture

[teal glen]

good artwork

lol

[vapid steppe]

lol ty

.close

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[fierce prairie]

how do I find the inverse of this matrix?

[fierce prairie]

I have no idea where to begin, the teacher only taught us inverse of 2x2

which was a formula

[naive valley]

do you know how to do gaussian elimination / row reduction?

[solar cliff]

basically do elementary row operations on $\begin{bmatrix}0 & 1 & -3\ 4 & 1 & 0\ 1 & 0 & 5\end{bmatrix} $ to get it to be the identity matrix. apply the same order of row operations you used to the matrix $\begin{bmatrix}1 & 0 & 0\ \0 & 1 & 0\ 0 & 0 & 1\end{bmatrix}$ and the result will be the matrix inverse

[ocean seal]

elemen

[fierce prairie]

yea

[fierce prairie]

ohh that makes sense

alright thanks

.close

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[wheat cloud]

hi i have a hw question!

[lone heart]

Please don't occupy multiple help channels.

[wheat cloud]

Professor Rogers has found that the grades on the nursing final exam are normally distributed with a mean of 75 and standard deviation of 6. Your answer should include (i) a sketch of the normal model that illustrates the question being asked, (ii) a statement of the proportion you are calculating, and (iii) an answer in complete sentences.

A) What proportion of the exam grades are between 72 and 87?
B) What grade are 15% of final exam grades above?

[ebon condor]

Do you know how to calculate a z score?

[wheat cloud]

yes

[ebon condor]

Where are you stuck?

[wheat cloud]

on a and b like how i would solve it. do i use the z score equation or the drawn out normal model?

[ebon condor]

So you need to do 3 things

Is there any part of 1,2,3 that you do not understand

well 3 is kinda a qualifier

so 1,2

[wheat cloud]

lol i guess i wouldnt know what to say for 2

[ebon condor]

Well lets take it one step at a time

can you represent a mathematically?

[wheat cloud]

what do u mean? sorry im really not good at this stuff

[ebon condor]

Yeah so can you just like solve part a) without worrying about the rest of the nonsense

just pure math

[wheat cloud]

im not sure, i dont think so?

[ebon condor]

Well you need to convert it to a z score

[wheat cloud]

so would i do two separate z scores and use those as the observed?

[ebon condor]

Well sure

You need both of them to calculate the range

[wheat cloud]

so i would do 72-75/6 and then 87-75/6 to figure out the range? or am i way off

[ebon condor]

so that would be the z score yeah

for that

So you can use the z-table to calculate the area

[wheat cloud]

what is a z-table

wait is that the same thing as a normal model?

we havent used those yet, just z scores and the normal models!

[lone heart]

@wheat cloud Has your question been resolved?

[wheat cloud]

no

[lone heart]

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[wheat cloud]

.reopen

[lone heart]

✅

[swift shore]

You need a table or something to convert from z-scores to probability

That’s what the question is asking for

[wheat cloud]

i dont know anything about tables, we weren't taught that

[lone heart]

@wheat cloud Has your question been resolved?

[wheat cloud]

nope

[lone heart]

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[steady hinge]

im not sure about c and d, thank u 🙂

the answer is 168 and 342 respectively, but i dont know how to reach the answer

would u guys mind explaining the rationale behind the answers? many thanks

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[lone heart]

@steady hinge Has your question been resolved?

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[dusty zenith]

Find the three consecutive odd integers such that four times the middle is equal to two less than the sum of
the other two.

Representation:

Working Equation:

Solution:

[dusty zenith]

ive already gotten the working equation but i'm not sure how to solve for the odd number thingy

[lone heart]

@dusty zenith Has your question been resolved?

[dusty zenith]

.close

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[spice wasp]

I don't know where to start, videos in youtube doesn't make sense to me.. How do I graph all of these ;-;

[noble sinew]

Start with 1. and then 2. and then 3. …

[spice wasp]

Can you atleast

graph 1?

so I can have a guide or smth?

[noble sinew]

What does 1. mean? Do you know that?

[spice wasp]

like

the number 1

the negative thingy

I think you have to put asymptotes there

since theres infinity

but idk yet

[noble sinew]

Yes

[spice wasp]

wdym yes ;-;

[noble sinew]

You said asymptote there

I said yes

[spice wasp]

yes but where exactly?

left or right?

I mean

vertical

or hori

o and btw

[noble sinew]

What does $\lim_{x\to -\infty}$ mean?

[spice wasp]

wait before that

[ocean seal]

ScapeProf

[spice wasp]

how do I graph g(#)= #?

what are the coordinates?

for example

g(-1)=1

how do I graph that?

[noble sinew]

x-axis input, y-axis output

[spice wasp]

so x is -1?

then y is 1m

1**?

[noble sinew]

Yes

[spice wasp]

so is this the graph of g(0)=1?

tell me if you can't understand xd

[noble sinew]

If I’m meant to ignore the point at (1,1)

Yes there is also a point at the correct place

[spice wasp]

so its the zero then?

[noble sinew]

Yes

[spice wasp]

so this ones wrong huh

ok I think I'm getting the hang of this

so this is correct?

[noble sinew]

No?

[spice wasp]

what why

its zero and 1

[noble sinew]

You just did g(0)=1 above?

I just told you yes one of the points you made is correct

[spice wasp]

OH

oh wait

I stoll don't get it

[noble sinew]

What is input?

[spice wasp]

0

(0, 1)

right??

[noble sinew]

Yes

[spice wasp]

OH

Y IS

THE VERTICAL

THINGY

HOW COULD I FORGET

there

[noble sinew]

Yes if I’m meant to ignore the other point again

[spice wasp]

what other point

wait so this is

[noble sinew]

There is a point in (0,0)

Is there not?

[spice wasp]

oh so you're not supposed

to put one there?

oh I see

[noble sinew]

A point is a single point

[spice wasp]

cuz it's gonna be (0,0)?

[noble sinew]

So no a point should not be two points

[spice wasp]

Ok I'll try the simple ones and come back to you

brb

pls check, thank you

[noble sinew]

Looks good (ignoring the double points again)

[spice wasp]

I still don't know what I'm doing wrong

in the double points thingu

I believe I sent a single point

without touching rhe zero

[noble sinew]

Oh thats prob just from stuff you erased, but g(-2)=0 has 2 points

[spice wasp]

oh I think it just marks of the marker at. the back

lemme put these coordinates to desmos and show you later on

brb

thoughts?

<@&286206848099549185>

[lone heart]

@spice wasp Has your question been resolved?

[lone heart]

@spice wasp Has your question been resolved?

[spark tulip]

What’s the problem

[spice wasp]

what do I do next

how do I graph

the remaining

especially with the infinite ones

[spark tulip]

You see the first one

I think that’s just a reciprocal function

Except it’s y = 1/x-1

[spice wasp]

wait what

the number 1?

[spark tulip]

The first one

Yes

[spice wasp]

you're referring to?

okok

ok please continue

I'm taking notes xd

[spark tulip]

Because as x approaches infinity, y gets infinitely close to -1

Go g(x) = 1/x - 1

[spice wasp]

so there's an asymptote right?

[spark tulip]

Yes

The -1 is to the whole thing

Not to the x

[spice wasp]

Ok wait lemme put the equation in desmos

[spark tulip]

g(x) should equal this

[spice wasp]

oh its

seperatws

okok wait

ok so this is my aysmptote?

[spark tulip]

That should be right

[spice wasp]

where did you get the

1/x?

[spark tulip]

Because this graph is a reciprocal function

1/x

Let’s say y = 1/x

What does x never equal?

Can get infinity close to

But never equal?

[spice wasp]

wait how did you know it's a reciprocal

it seems that I don't quite get it yet

[spark tulip]

answer my question first

[spice wasp]

oh wait

isnt my x -1?

[spark tulip]

?

What do you mean your x - 1

[spice wasp]

x = -1

I mean

[spark tulip]

No no no

The function means

[spice wasp]

oh.

[spark tulip]

That as x approaches infinity, it’s gets infinitely close to -1

X can never be -1

[spice wasp]

OH I SEE

[spark tulip]

Can get infinitely close to

[spice wasp]

I GET IT NOW

is it where

the 0.00000

thingy

[spark tulip]

That’s what limit functions mean

[spice wasp]

I see..

[spark tulip]

Take the function 1/x for example

X can never be 0

[spice wasp]

so 1 over x since it cannot be undefined

[spark tulip]

Because you cannot ever divide by zero

However x can get infinitely close to zero

Now if you want it to be infinitely close to -1

You just translate the graph down 1 unit

Hence the 1/x and then - 1

To translate it down one unit so it fits the condition of getting infinitely close to - 1

[spice wasp]

wait is this only applicable on infinity?

like

negative

[spark tulip]

You see the “limit”

The notation

Of the first question means

The limit of the function g(x) as x approaches infinity

[spice wasp]

oh

okok I think I can help myself with that later

but

what if it's

the other way around?

like the next example?

there's a raised to negative

so which means

its on the left side

right?

[spark tulip]

Is this precalc?

[spice wasp]

limit of g(x) as x approaches to infinity?

calculus

[spark tulip]

Okay

[spice wasp]

I forgot how to read these lmao

[spark tulip]

Which example you taking baout?

[spice wasp]

wait

number

3

3 and 4 seems similar somehow

[spark tulip]

So you see the 3-

The negative above the 3

It means the x value approaches from the left

So question 3 means

The limit of the function g(x) as x approaches -3 from the left hand side is infinity

[spice wasp]

oh I see

so 4 is on the right side?

[spark tulip]

Yeah

[spice wasp]

correct?

[spark tulip]

Because it has prositve

[spice wasp]

okok

so how do I graph this

[spark tulip]

The positive and negative sign in the place where the exponents are meant to be indicates from which side

[spark tulip]

Hmm let me think

[spice wasp]

sure take your time

[spark tulip]

I must say my knowledge is restricted

I am learning precalc atm myself

[spice wasp]

oh

[spark tulip]

You might have to ask someone that is well experienced

[spice wasp]

precal is quite easy to me tbh

[spice wasp]

I see

[spark tulip]

Yeah

I’m in a car right

Let me get home and experiment with some functions

And see if I can find a right one

[spice wasp]

I've been stuck in here cause idk what to do

oh thanks

lemme send a friend request

[spark tulip]

You have the find the function that fits the entire expression

[spice wasp]

I'll update you somehow

[spark tulip]

Okay

[spice wasp]

so deriving ...

[spark tulip]

Pretty much

But it’s like hella simpler than finding derivatives of like parabolas or whatever

As in the algebra should be simpler not that it’s actually complicated

I’m just not good at this because I’m dumb

[spice wasp]

I should be the one saying that

[spark tulip]

Nah you probably just don’t study

[spice wasp]

joining a discord server, desperately seeking for answers

[spark tulip]

This is some pre calc stuff

[spice wasp]

no actually

my teacher

didnt

teach this

[spark tulip]

Your meant to be well versed in what this notation at least means and stands for

[spice wasp]

like she only showed us about

finding

the limit

with graphs given

but never explained the opposite

[spice wasp]

I see what I can do

I'm still searching in the internet but I don't think I can apply those to these

the equations are pretty complicated if you ask me..

[spark tulip]

After pre calc you should be extremely comfortable with different functions

Like exponential, reciprocal, logarithmic

Etc etc

And how to translate/dilate functions

Which I’m not good at

[lone heart]

@spice wasp Has your question been resolved?

[spark tulip]

@spice wasp

[spice wasp]

oh

aait

shouldn't it be

[spark tulip]

The same for question 4

[spice wasp]

1/x

plus 3?

[spark tulip]

Yes

It is plus 3

You may think it should move to the right

But that’s common mistake

Basically when you plus a value to the x

[spice wasp]

wait brb

lemme get my notes

ok

oh

wait

so its just

the opposite then?

[spark tulip]

When you add to the x, you move it left

When you take away you move it right

[spice wasp]

lemme resend this

so I have a visual output

[spark tulip]

Ahh yes

I see

The function g(x) = 2^x whole thing - 1

Also works

Oh yeah

I made an error in the first one

If we were to use the reciprocal function as solution

It should be g(x) = -(1/x) - 1

Not g(x) = (1/x) - 1

[spice wasp]

oof I was waiting in our dms

sorry for rhe late reply

oh I think this one makes sense

because I believe you can:t cross

the asymptotes

and somehow

you need to xonnect the dots

based on the videos I've seen..

[spark tulip]

Oh shit

Lol

I thought this was dms

But yes

So for question 1

I think 2 different functions work

[spice wasp]

oh, but still the same concept?

is that what you're sayingm

?

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[alpine sable]

.close

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[viscid reef]

I am lost and cannot figure out this question

[sudden hinge]

Let's look at the second question first

We have
$$y = \frac{\mathrm{constant,of,variation}}{\mathrm{number,of,workers}}= \frac{k}{x}$$

[ocean seal]

Navix

[sudden hinge]

Try to plug in the information we've been given: 4 workers and 60 hrs

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[native brook]

part ii

[zenith sparrow]

Can you retake the pic

[native brook]

.close

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[dull cypress]

can someone help explain this proof to me?

[split oriole]

In which line you have problem?

[dull cypress]

between b) and i)

i don't know how they got the x^2 >= 0 and y^2 >= 0

and why they're saying y<= -2 or y>= 2

[gray isle]

squares of real numbers are non-negative

[dull cypress]

oh

wait then where does the y<= -2 and y >= 2 come from

[gray isle]

they explained it

5y^2 would exceed 20 (which is already greater than 14)

[dull cypress]

oh so they are trying to get the interval in which the equation will be true?

also why did they choose y

and not x

[gray isle]

they're doing casework efficiently

they could have used a similar idea using x

[dull cypress]

ohh so it really doesnt matter which we choose?

we will get the same answer with both?

[gray isle]

you'd reach the same conclusion in the end

[dull cypress]

kk

would this be a direct proof?

since they are proving it directly

[gray isle]

no, it'd be indirect

[dull cypress]

ohh I see now, thanks

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[supple tundra]

Note that the DE just below the black box is similiar to the DE in the red box.

With that said, what similiar substitution would you use for the red box part? pls explain how you come to decision