help-33

[tight furnace]

i would find each displacement vector and add them together

[iron meadow]

you can either think in terms of vectors, add them component-wise then find the overall length of the vector sum, or you could draw a triangle and consider the angles \ lengths and use something like law of sines etc if you're more inclined to geometry

[bold creek]

so far I have

[bold creek]

so adding the x and y componets

?

<@&286206848099549185>

[marsh citrus]

@bold creek Has your question been resolved?

[marsh citrus]

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[quasi knoll]

i need help

[final skiff]

Make an augmented matrix [M|I] where I is identity matrix and row reduce echelon

[quasi knoll]

Could you explain more

[final skiff]

Do you know how to get matrix in row reduced echelon form?

[quasi knoll]

No

[buoyant jetty]

,, A^{-1} = \frac{1}{ad - bc} \begin{pmatrix} d & -b \ -c & a \end{pmatrix}

[elfin berry]

938c2cc0dcc05f2b68c4287040cfcf71

[final skiff]

Yeah then use this ^^

[buoyant jetty]

only if determinant is nonzero

[quasi knoll]

i got the answer to the question now

.close

[marsh citrus]

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[compact crescent]

Hello human

I, as a loyal servant of Mickey Mouse, ask for your help.

Let P(M) be the probability of the event that the question asks for.

Then P(M)= P(teleport at morning)+P(teleport at evening)+P(teleport at both morning and evening)

Agree

Human

[compact crescent]

And that is, numerically, 2 * 1/3 * 1/2 + 1/9

<@&286206848099549185>

[static quarry]

why would you add these probabilities?

generally you don't add probabilities unless the events are disjoint

for events like "X occurs at least once" it's often easiest to compute them as
1 - P(X does not occur)

[compact crescent]

Why

[static quarry]

well to give an example

suppose P(teleport) is 0.5 in the morning and in the evening

then your formula would be:
P(teleport at morning) + P(teleport at evening) + P(teleport at both morning and evening)
= 0.5 + 0.5 + 0.25
= 1.25

which can't be right because probabilities can't exceed 1

[compact crescent]

This means they have no intersection!

You are contradicting yourself

Human

[static quarry]

i disagree

but you do you

[compact crescent]

Your example cannot prove that my approach is false

Bungo left me

I’m so depressed

Is it the consequence of being a loyal servant of Mickey Mouse

[cloud field]

thats not how the formula goes?

P(A∪B) = P(A) + P(B) - P(A∩B)

[compact crescent]

I think it can be explained using Venn diagram

If you draw out the situation using Venn diagram

[cloud field]

i think its easier if you list the sample space tbh

[compact crescent]

That’s treason

In Disneyland

[cloud field]

sure lol

if you explain it using a venn diagram, adding the morning and evening probabilities double count the intersection of morning and evening

so you need to subtract it once to adjust for that

but somehow you added it once again which triple counts it

[marsh citrus]

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[marsh citrus]

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[rain hare]

May ik how to solve this qn?

[dry prawn]

just plug and chug

you have y, so you can take its derivative(s)

[marsh citrus]

@rain hare Has your question been resolved?

[proud ice]

Take second derivative of y and verify

[marsh citrus]

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[frosty oak]

What will be the correct steps for this question,as I have done it the other way and think so it is true but book answer says different

[frosty oak]

My solution

Book solution

And i think I didn't did any mistake will doing my way
So please correct me if anything wrong

<@&286206848099549185>

[runic temple]

you forgot the 2x

[hard gull]

why is there a cosecx? cos2x/sin2x = cot 2x

[runic temple]

its cos(2x)/sin²(2x)

[hard gull]

oh yeah , my bad

[frosty oak]

Ok I min

Is this correct

[runic temple]

dont forget the chain rule

you have a factor of 2 floating around

[frosty oak]

So I should divide whole by 2 make it right

[runic temple]

yes

you can show by trig identites that
2cosecx = tanx + cotx

[frosty oak]

Ohh yes in the final cosec x i forgot to put 2 again

[runic temple]

whoops

2cosec(2x) = tax+cotx

so either answer is correct

[frosty oak]

Thanks man 👍

[runic temple]

would you like a run through of this or youre good?

[frosty oak]

Yes I am good I got everything

[runic temple]

cool

youre welcome

[frosty oak]

Bye

. close

.close

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[tame kindle]

Need help understanding the solution

how did 12min(X,n) - 10n go to 12min(X-n, 0) + 2n

[sweet pawn]

12min(X,n) - 10n is a piecewise function.
If X < n:
= 12X - 10n
If n < X:
= 12n - 10n = 2n

12min(X-n,0) is also a piecewise function.
If X-n < 0:
= 12X - 12n + 2n = 12X - 10n
If 0 < X-n:
= 12(0) + 2n = 2n

they're the same thing

but honestly this solution is overcomplicating things a lot

[tame kindle]

what do you think is better?

[sweet pawn]

$$E[X] = \sum n \cdot P(X = n)$$

[elfin berry]

Mr. Gamer 🇵🇸

[sweet pawn]

find E[X]

[tame kindle]

but what about the profit

[sweet pawn]

trust. the profit is a function of E[X]

[tame kindle]

so 20.1 + 3*0.4 + 40.5

[sweet pawn]

,w (2,3,4).(0.1,0.4,0.5)

[elfin berry]

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[tame kindle]

ok

[sweet pawn]

the operation i used there is called the dot product. you might recognize from your lin alg or mv calc course

[tame kindle]

yeah

[sweet pawn]

actually the solution is good, i think you should go off of that. you do end up having to use another random variable

is there anything you don't understand about the solution

i showed you how the equation works

[tame kindle]

pls show me

[sweet pawn]

alright so we went over the formula for P_n, does that part make sense?

[tame kindle]

why for X -n <0 12X-12n+2n = 12X - 10n

isn't this when you start losing

actually nevermind

i got it

so how did we get Y_n

[sweet pawn]

we observe that min(X-n,0) is a random variable itself

so far so good?

[tame kindle]

yep

[sweet pawn]

so does the PMF for Y_n make sense?

[tame kindle]

not quite

why does it end at n-2

why not n-3

[sweet pawn]

4-2 = ?

let me see if putting this in plain English helps.

When:
Demand >= Stock, Y_n is 0
Demand = Stock - 1, Y_n is -1
Demand = Stock - 2, Y_n is -2

[tame kindle]

makes sense

but why not when demand = stock - 3

why end when demand = stock - 2

[sweet pawn]

how would X = n - 3 even happen? X and n are both in the range (2,3,4)

[tame kindle]

oh i see,

Makes so much sense

the soluton makes so much sense

wow, this is so ar

[sweet pawn]

yeah it just didn't explain the first step, caught me off guard too for a sec

but glad to see you managed to figure it out

[marsh citrus]

@tame kindle Has your question been resolved?

[marsh citrus]

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[cobalt lance]

Where did they get the 1's and 0's of the W1, W2, and W3?

[cobalt lance]

<@&286206848099549185>

[marsh citrus]

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

[vapid sundial]

im a helper

what do u need?

[cobalt lance]

I would like to ask how they got W1 W2 and W3? I dont get where they got the columns with 1's and 0's

<@&268886789983436800> troll

[lone heart]

The column with (1, 0, 0) is from the W(1, cos(t), sin(t)) matrix

[marsh citrus]

@cobalt lance Has your question been resolved?

[marsh citrus]

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[vivid chasm]

Hello

[vivid chasm]

I was looking at this theorem that stated that every linearly independent set of a finite dimensional vector space can be extended to a basis

I was wondering if there was any algorithm persay to go about this task

this is what i've been given

[whole thorn]

you can write the vectors in a matrix

then row reduce

so you get identity in the top left

reverse the operations to the identity matrix and look at the right columns

[vivid chasm]

sorry what is the identity on the top left

also, is there any intuition as to why this works

i know that we can reduce a spanning set to a basis by making a matrix, row reducing it, and then taking the columns corresponding to leading columns

does the logic of extending a linearly independent subset follow some similarish logic

[whole thorn]

yes

you want the row reduced matrix to be identity

for it to be a basis

[vivid chasm]

okay i am still kinda confused on how we are to set this up

so lets say we have a subset S of the vector space R3, and it consists of three vectors

also, these three vectors are linearly independent and we want to extend S into a basis

we can then construct a matrix A with its columns being the vectors of the subset S

now, i am to believe from what you said that i can create an augmented matrix with the corresponding identity matrix

we then make the left hand side of the matrix into its reduced echelon form

and the right hand side colums will be the basis?

is my logic so far all correct?

[mild perch]

Have you heard of the Gram-Schmidt process

If not I would look it up

[whole thorn]

yeah

but technically that's inverting the matrix

anyway 3 linearly independnant vectors in R^3 already form a basis

[mild perch]

It is algorithmic way of getting an orthonormal basis

[whole thorn]

yh but it's not extending the current basis

i cba to explain more atp sorry

not that i've explained much

[mild perch]

Oops sorry, I misread what was being asked

[vivid chasm]

wait so is this gram-schimdt process something i can use or is just inverting the matrix sufficient

[whole thorn]

basically u want to find vectors st if u row reduce you get identity

like
(1,2,3) and (4,5,6) are lin indep

so

[mild perch]

Gram-schmidt is for a slightly different problem my bad. It is to get an orthonormal basis for the span of a set of vectors

[whole thorn]

1 4
2 5
3 6

row reduces to

1 0
0 1
0 0

you wanna find (v1, v2, v3) such that

1 4 v1
2 5 v2
3 6 v3

row reduces to

1 0 0
0 1 0
0 0 1

[vivid chasm]

wait shouldnt the top right entry be 0 as well?

[whole thorn]

yes

[vivid chasm]

okay so after finding this other vector, i guess we then augment it with the identity matrix and then everything proceeds as we discussed

[whole thorn]

nah ur done straight away

[vivid chasm]

oh damn

thats crazy

[whole thorn]

(1,2,3)
(4,5,6)
(v1, v2, v3)

is ur basis

[vivid chasm]

yeah cause the basis needs a dimension of three for R3

very cool

if you don't mind, how does this work exactly

[whole thorn]

(i guess this was a lie, idk why i suddenly got energy)

[vivid chasm]

really appreciate it lmao

[whole thorn]

what part

maybe try some examples

like finding v1 v2 v3

[vivid chasm]

i meant like the intuition behind doing something like this

[whole thorn]

ok

so row operations don't change solutions

to a matrix equation

lin indep means a1v1 + ... + anvn = 0 --> a1 = ... = an = 0

u can write a1v1 + ... + anvn = 0 as a matrix equation

where ur solving for a1,...., an

[vivid chasm]

so like a coefficient matrix

[whole thorn]

i think so

[mild perch]

Oh I remember the way we used to do this

There are many ways

But a decent mechanical way is

If your set is vectors v1 v2 for example

And you want to extend to a basis for R^m

You can just put your vectors and the canonical basis for R^m together in a matrix

So [v1 v2 e1 e2 ... em]

Then use guassian elimination on this

The pivot columns tell you which ones you need to keep

This is also quite intuitive

[vivid chasm]

by pivot columns, you are referring to leading columns right

just to make sure

[mild perch]

Like when you get it in row echelon form

[vivid chasm]

okay yeah its the same thing

just did a quick google search

[vivid chasm]

could you go into more depth into this

[mild perch]

This is how you find a rank of a matrix right?

For if your v vectors are linearly independent which are by hypothesis

[vivid chasm]

oh yeah

[mild perch]

Then they are guaranteed to be pivot columns

[vivid chasm]

actually it makes sense, its quite similar to this idea of a subset R explored here

[mild perch]

And then it tells what other columns/vectors you would have needed to keep to get a full rank matrix

[vivid chasm]

like you are filling in whats necessary

[mild perch]

Yes!

[vivid chasm]

thats quite cool

one more thing

the canonical basis vectors for R3 are like (0,0,1), (0,1,0) and (1,0,0) right

its just the standard normal basis vectors

[mild perch]

Yes, but any basis would have work

It's just the easiest

[vivid chasm]

makes sense

you both are goated

thanks for the help

[mild perch]

You're welcome!

[vivid chasm]

.close

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[terse dove]

.

,w integral of 100t/(1+t²)²

[terse dove]

.close

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[elfin berry]

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[marsh citrus]

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[south goblet]

Let n, r, s, i ∈ N. Give a combinatorial proof to show that the number of pairs (A, B)
with A ⊆ Nn, B ⊆ Nn, |A| = r, |B| = s and |A ∩ B| = i equals

[south goblet]

can anyone help me I can't figure this out

I do have the answer

but I don't understand the answer either

anyone can help me

[marsh citrus]

@south goblet Has your question been resolved?

[marsh citrus]

@south goblet Has your question been resolved?

[marsh citrus]

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[golden heath]

Can anyone help me regarding this matter based on the integral by substitution of calculus 2. idk if my answer is correct, if yes or not what are the errors that can be found on my solution.

[marsh citrus]

@golden heath Has your question been resolved?

[marsh citrus]

@golden heath Has your question been resolved?

[marsh citrus]

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[verbal root]

I need help with the 26th one

[verbal root]

,rotate

[lucid zenith]

take the log of both sides

$y\ln x=y-x$

[elfin berry]

kheerii

[lucid zenith]

should be quite easy from here

[verbal root]

okay thx!

.close

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[marsh citrus]

@still temple Has your question been resolved?

[marsh citrus]

@still temple Has your question been resolved?

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[inner grove]

Which one of those is correct

[inner grove]

as a solution to $\sqrt{-16} \cdot \sqrt{-9}$\

[elfin berry]

redve

[zinc tinsel]

-12 is correct

[inner grove]

why first formula is wrong then?

[zinc tinsel]

sqrt(-1) * sqrt (-1) =/ (sqrt(-1* -1))

[inner grove]

isn't it equal in reals, where sqrt(-1) makes no sense?

on the other hand, I used complex numbers in the question

but as reals are subset of complex, they should give the same result tho

[zinc tinsel]

?

[storm crypt]

The equation sqrt(a)sqrt(b)=sqrt(ab) is only true if a and b are non-negative real numbers.

[inner grove]

ah, now I get it

thanks

[storm crypt]

Np

[inner grove]

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[loud flicker]

I'm tryna derive 3/(x+3) using the limits definition of derivatives

[loud flicker]

And my algebra ain't algebraing

I got lim(h->0) ((2/(x+h)+3)-(2/(x+3))/h

And I have no idea how to make the denominators of f(x+h) and f(x) equal

[loud flicker]

Can you walk me through that?

[zinc tinsel]

Sure

just uhh 3/(x+h+3) - 3/ (x+h) , subtract the two fractions

[loud flicker]

That's my issue

I'm simply tryna make the denominators equal and Idk how

[zinc tinsel]

how would you do it if it was 3/ x - 3/y

[vernal forge]

do you know how to add two fractions?

[loud flicker]

Id multiply the denominators together

[zinc tinsel]

and?

[loud flicker]

Yeah, it's just this particular one that I'm struggling with

[zinc tinsel]

write it down

[loud flicker]

Then subtract

[zinc tinsel]

3/x-3/y

=?

[loud flicker]

3-3/xy

Oops

Wait

And the numerator

So 3y-3x/xy

[zinc tinsel]

perfect

[loud flicker]

That's exactly what I tried doing tho but it's not working and the denominators don't equal each other

[zinc tinsel]

now replace y= 3+x, and x with 3+x +h

[zinc tinsel]

here

[raw hawk]

,rotate

[loud flicker]

Just gimme a sec to try it

Yeah I'm still confused

I'm kinda struggling to read that

What did you multiply both denominators by?

[marsh citrus]

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.

[loud flicker]

I'm just trying to make the denominators of 2/(2+h+3) and 2/(x+3) equal

[zinc tinsel]

how about now?

[loud flicker]

Lemmie try

Sorry, at the start I meant to say 2/x+3 but I did it anyways

When I took the limit I got -2/(x^2+6x+9)

thanks, my algebra is really bad

.close

[marsh citrus]

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[mossy kettle]

omg i hate this site, can someone give tips on what should be corrected?

[frosty jay]

x=-1 looks incorrect?

[mossy kettle]

wdym?

[frosty jay]

What is f(-1)?

[mossy kettle]

0

[frosty jay]

Your graph says f(-1) is undefined

[mossy kettle]

so it should be solid?

[frosty jay]

Yes

Or just a line connecting both parts , no dot required, no idea if your software allows that

[mossy kettle]

but wouldn't that not be correct ragarding the other {}s?\

[frosty jay]

The pieces are completely disjoint, they don't affect each other

[mossy kettle]

okay, ill try changing it

that damned website does not have a an eraser or undo button

I have to erase everything and redo

🥲

welp the solid . did not work

[frosty jay]

No idea, these kinds of software are probably not coded very well to accept all correct answers

[mossy kettle]

very real, I'll try doing a similar problem

oh well

.solved

[marsh citrus]

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[quick orchid]

working on a question i got wrong, this is the solution, im wondering why i couldnt use the function 12w-800w^2, why do i need to simplfy it (this is really messing me up with questions in general, sometimes they simplfy at the last step but some questions dont, would love tips on this)

[quick orchid]

i just used 12w-800/w^2 to find the zeros

[hazy lion]

because its easier to find the 0s of something of the form f/g tbh

you dont need to

you could solve $12w=\frac{800}{w^2}$

[elfin berry]

jan Niku

[hazy lion]

so $w^3 = \frac{800}{12} = \frac{200}{3}$

[quick orchid]

i multiplied both sides by $$w^2$$, then moved the 800 and divided by 12

[elfin berry]

jan Niku

Thyroxine

[quick orchid]

wait i cant do what i did because i would have to also multiply the 12w

ah i think i see what i didnt do

ah i get w^3 , nvm thank you

[hazy lion]

np

[marsh citrus]

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[dreamy hull]

Hello, good afternoon, I need help with this exercise please:
Martina wants to knit a scarf and she has 9 different colors available. If she will use 5 different colored stripes in the scarf, how many different scarves can she knit if they do not have to have blue and black together.

[proud basin]

what colors are there

uh how about this

is like
red blue green yellow black
and
blue red green yellow black
the same or no

like do you could it as a possibility

[marsh citrus]

@dreamy hull Has your question been resolved?

[dreamy hull]

How can I count the chances of two colors being together?

[digital field]

must blue and black be in the scarve

[dreamy hull]

yes..

[digital field]

then number of scarves in total - number in which they are together

[dreamy hull]

That's what I don't understand, how do I calculate the number of ways that two colors are together?

the total number of shapes is 9! / (9-5)!

[digital field]

A = colours together

B = colours are separated

A+B = both colours in scarf

[dreamy hull]

How do I calculate this?

help pls

[digital field]

Literally count

[dreamy hull]

:/

[digital field]

I shit you not

Count

[dreamy hull]

4?

[digital field]

Do you care about the direction she knits in

As in is 12345 the same as 54321

[dreamy hull]

3?

please tell me

I want to move forward with another exercise.

[digital field]

I’m not telling you anything. You’re not even reading my question which is clarifying something

[dreamy hull]

taking that into account, I see that there are 3..

[digital field]

No lol, I want to know how your problem is defined.

And the answer should either be 4 or 8

[dreamy hull]

sorry, I am not English and I thought you were stating something and not asking a question

should be the same

12345 and 54321

[marsh citrus]

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[marsh citrus]

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[polar vector]

I'm doing 17. I get to do it as f(x) - f(a) / x-a . I get to this and I'm stuck but I know it is good

[late geode]

your simplification at the end isn't right

missing the +2

on the numerator

[polar vector]

Ahh thank you

[polar vector]

So it be -3x^2 +12 right still get 0 on denominator

[late geode]

attempting to evaluate at this stage will still give 0/0 so more work is needed

factorise the numerator

[late geode]

factorise more

[marsh citrus]

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[polar vector]

Thank you

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[hollow nexus]

not sure how i shld contiue

[hollow nexus]

tried subbing in h k and solving simul eqn but still got ans wrong not sure if i messed up somewhere idt i messed up my workings tho did it twice

ans was (x-1)^2+(y+1)^2=5

if possible do help might gtg soon not sure where i did wrongly

[brave marsh]

Well as it is your system of equations just doesn't have any solution whatsoever.

You've made a mistake expanding $(-2-k)^2 = 4 + 4k + k^2$, which will yield the equations $-6k + 6h = 12$ and $k + 3h = 2$.

[elfin berry]

Azyrashacorki

[hollow nexus]

oh i did +4k wasant it -4k?

oh wait its +4k..

hmm so if i expaned wrongly

do i sub k=-x and y=-h?

and solve?

[brave marsh]

I mean you just solve this system of equations whichever way you want.
Elimination works fine here

The point is you'll get the center and then you can compute the radius

[hollow nexus]

ohhh alright

so my current method is right just expanding wrongly

[brave marsh]

Yes

[marsh citrus]

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[marsh citrus]

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[novel juniper]

can I have a hint

this is what I've done, but it feels too verbose

I'm trying to set up a proof my contradiction

[devout mauve]

have you heard of paragraphs

and periods

[novel juniper]

I'll work on improving the formatting, sorry

[devout mauve]

the whole thing about the addition part is what you need to show

an example is not enough

[novel juniper]

I realise that, could I have a hint?

[devout mauve]

the sum still need not belong to the union
why

well take some v1 in V1 and v2 in V2 and consider their sum which is supposed to be in V1 union V2

so its in V1 or in V2

work with that

[novel juniper]

okay

thanks

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[tall sun]

how do i use substitution to solve this system of equations?

[late geode]

first isolate one of the variables from one of the equations

[limber hearth]

You take the first line and isolate y for example

[late geode]

doesn't matter which, but do try to pick the route that won't involve unnecessarily generating fractions

[limber hearth]

Then you replace the expression of the variable you isolate into the second equation and you solve for the other variable

[tall sun]

ok so

to start

isolate a variable

im going to choose y

[tall sun]

what does this mean?

can i have an example?

[late geode]

what is the value of
p + 5
when p = 7

[tall sun]

7+5

[late geode]

its pretty much just that

[tall sun]

ok so

with y from 3+2x-y-0

what do i do now

[late geode]

did you isolate y yet?

[tall sun]

i have to add y to both sides right

[late geode]

that would be the most efficient way to isolate y, yes

[tall sun]

sorry that was going to lead in to the thing but you type faster than me lol

3+2x=y+0

or 3+2x=y

[late geode]

now that you have an expression for y,
in your second equation, replace y with that

i.e. replace y with (3 + 2x)
include the () so you don't mess up the order of operations

[tall sun]

that

is the funky text intentioanl

-3-7y=10x

second equation

so

-3-7*( 3+2x) = 10x

[late geode]

yes

[tall sun]

simplifies to

-1

[late geode]

?

[tall sun]

sorry, x=-1

[late geode]

yes

[tall sun]

same as graphical answer

[late geode]

and sub this back in to either equation for the y value

[tall sun]

alright perfect

let me try that for y

y= 2* -1 + 3

y= -2+3

so y=1

[tall sun]

hows that?

[late geode]

yes

[marsh citrus]

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[proud ice]

porque nunca me djiste que hablas espanol

🇲🇽

Let $b$ and $h$ the base and height of the triangle. Use the $\tan\alpha=\frac12$ to find a relation between $b$ and $h$

[elfin berry]

SWR

[buoyant jetty]

elaborate

[proud ice]

do you remember sohcahtoa?

[buoyant jetty]

can u explain

i need more handholding

[proud ice]

Define these variables

[buoyant jetty]

b adjacent

h opo

[proud ice]

yup

[buoyant jetty]

I need more

handhold

[proud ice]

So you have the two relations: $\frac hb=\tan\alpha$ and $\frac12 hb=$ Area of triangle

[buoyant jetty]

what

you jumped to that without a proper explanation

[elfin berry]

SWR

[buoyant jetty]

1/2hb area of triangle?

okay

[proud ice]

yes

[buoyant jetty]

so its a trigonometry issue + reminding the area of triangle formula

[proud ice]

yes

[buoyant jetty]

how to find perimeter

hypothenuse

I dont get it

[proud ice]

What don't you get?

[buoyant jetty]

perimeter

I need handhold

[proud ice]

perimter is the sum of all three sides

[buoyant jetty]

hypothenuse

[proud ice]

Have you found b and h?

[buoyant jetty]

b adj

h oppo

[proud ice]

But have you actually found their values?

[buoyant jetty]

no

I need more help

and handhold

[proud ice]

solve for h and b here. You have two equations and two unknowns.

[buoyant jetty]

how

,, \begin{cases} \frac{h}{b} = \frac{1}{2} \implies 2h = b \\ \frac{1}{2}hb = 16 \implies hb = 32 \end{cases}

[proud ice]

yup

do you know how to solve for two variables in two equations?

[elfin berry]

938c2cc0dcc05f2b68c4287040cfcf71

[buoyant jetty]

b = 4

,w Solve[{2 * h == b , h*b == 32}, {h, b}]

[elfin berry]

Results provided by WolframAlpha

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Requested by 938c2cc0dcc05f2b68c4287040cfcf71

[buoyant jetty]

but it has to be positive

{h = 4, b = 8} = S , is the solution set

anyways, how to proceed

can u help or no

[proud ice]

find hypotenuse

[marsh citrus]

@buoyant jetty Has your question been resolved?

[buoyant jetty]

how

[proud ice]

It's a right triangle

[buoyant jetty]

how do u know that

[proud ice]

The diagram does not show it explicitly (it should). So you just need to assume it's a right triangle

[buoyant jetty]

isnt that too much of a bold assumption

you saying only because it looks like it its a right triangle or

[proud ice]

because otherwise there is no way to get the perimeter

[buoyant jetty]

anyways, how to solve the problem

[proud ice]

Assume that it's a right triangle, and find the hypotenuse

[buoyant jetty]

how

[proud ice]

how would you normally find the hypotenuse of a right triangle?

[proud ice]

Pythag

[buoyant jetty]

elaborate

[proud ice]

pythagorean theorem

[buoyant jetty]

i dont get it

[proud ice]

do you know what pythagorean theorem is?

[buoyant jetty]

,w (16 + 64)^1/2

[elfin berry]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by 938c2cc0dcc05f2b68c4287040cfcf71

[buoyant jetty]

can u help or no

[proud ice]

You found all three sides. So find the perimeter now

[buoyant jetty]

how

[marsh citrus]

@buoyant jetty Has your question been resolved?

[marsh citrus]

@buoyant jetty Has your question been resolved?

[buoyant jetty]

<@&286206848099549185>

[idle ridge]

the perimeter is just the sum of the lengths of the three sides

you already have the lengths of the three sides, right?

[buoyant jetty]

H = 4 B = 8

but I need more handholding

i think by pythagorean hypotenus is 4sqrt5

perimeter = 4 + 8 + 4sqrt5 then

but idk

Can someone help my Fat Ass with trig

@fluid mica

can someone help me and my fat ass with trig

[idle ridge]

please don't ping random people

[idle ridge]

yes, that's fine

what else do you want to ask about

[buoyant jetty]

how do i do this?

i got der perimeter

[idle ridge]

you already know all the sides of the triangle, right?

so how would you find cos(beta)

[buoyant jetty]

cos(x) = b/h

b = 8

h=4

[buoyant jetty]

unsure

[idle ridge]

let's go off of this picture, right?

cosine is adjacent divided by hypotenuse

which side is adjacent to beta

[buoyant jetty]

h

[idle ridge]

yea

[buoyant jetty]

cos(x) =1/2

now what

[idle ridge]

how did you get 1/2

which side is the hypotenuse

[buoyant jetty]

my bad

hipo is 4sqrt5

[idle ridge]

yup

[buoyant jetty]

cos = 1/sqrt5

[idle ridge]

yup!

so what's cos^2(beta)

[buoyant jetty]

1/|5|

[idle ridge]

good

now, do you know the double-angle formula for sine?

sen(2 alpha) = 2 sen(alpha) cos(alpha)

[buoyant jetty]

sure

[idle ridge]

can you use that to calculate sen^2(2 alpha)?

[buoyant jetty]

4sin^2(x)cos^2(x)

[idle ridge]

yes, except it should be alpha, not x

and then how do you calculate that

[buoyant jetty]

sin(x) is oppo/hyp

wrt alpha

4/4sqrt5 = sin

sin(x) = 1/sqrt5

[idle ridge]

good!

and then what about cos(alpha)

[buoyant jetty]

8/4sqrt5

2/swrt(5)=cos

4(1/sqrt5)^2 *(2/sqrt5)^2 = 4sin^2(alpha)cos^2(alpha)

4/|5| * 2/|5| = 4sin^2(alpha)cos^2(alpha)

[idle ridge]

why do you still have "cos" in here

other than that it seems good

[buoyant jetty]

now what do i do

[idle ridge]

now simplify

[idle ridge]

there should be cos^2 on the right-hand side

the right-hand side hasn't changed

[buoyant jetty]

fair

4/|5| * 2/|5| = 4sin^2(alpha)cos^2(alpha) = 8/|5|^2

[buoyant jetty]

can someone help or no

[idle ridge]

I'm confused, what do you need help with

aren't you done

you just need to add sen^2(2 alpha) + cos^2(beta), and you already know the values of both of them

[buoyant jetty]

8/25 + 8/25

=16/25

= 4/5

am I done?

can you guys at least point in which part I did a mistake

guys

?

[buoyant pond]

could you please translate the question

[marsh citrus]

@buoyant jetty Has your question been resolved?

[marsh citrus]

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[cedar mulch]

What should I search on internet to learn how does the formula for the slope and intercept is being made for linear regression

[cedar mulch]

Like I want to know how do those 2 formulas come to be

where it come from and the logic behind it

[frail orbit]

simple least squares regression. It basically comes from wanting to minimize this quantity

$\sum_{i=1}^{n}(y_{i}-\hat{y_{i}})^{2}$

[elfin berry]

🫎 Moosey 🫎

[frail orbit]

where $\hat{y_{i}}=a+bx_{i}$

[elfin berry]

🫎 Moosey 🫎

[frail orbit]

so you can think of this as a function of a,b

typically denoted Q(a,b)

a thing you could google that would walk you through this would probably be 'simple linear regression derivation'

[marsh citrus]

@cedar mulch Has your question been resolved?

[cedar mulch]

Thx!

[cloud field]

https://www.khanacademy.org/math/statistics-probability/describing-relationships-quantitative-data/more-on-regression/v/regression-line-example

i used this to help myself derive the formulas

although it does involve partial differentiation in some parts but its just like normal differentiation

[marsh citrus]

@cedar mulch Has your question been resolved?

[marsh citrus]

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[wheat ledge]

I dont fully understand this form of a vector space

[wheat ledge]

F is axler's way of representing both R and C btw

[spark otter]

well say f,g are in F^S

and a is a scalar (in F)

then you can define f+g right?

and you can define a*f

it's as you would define them, there's no trap

$\forall s\in S, (f+g)(s) = f(s) + g(s)$

[elfin berry]

rafilou2003

[spark otter]

$\forall s\in S, (a\cdot f)(s) = a\cdot (f(s))$

[elfin berry]

rafilou2003

[marsh citrus]

@wheat ledge Has your question been resolved?

[wheat ledge]

how are functions inputs

in the vecotr

i dont get the deifntion

[marsh citrus]

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[glass sigil]

hi how do i simplify this?

[glass sigil]

This is what I got

[slender bobcat]

,rccw

[slender bobcat]

are the squiggly lines on the numbers 2s?

[glass sigil]

what squiggly lines

[slender bobcat]

also you cant cancel like that

[glass sigil]

why not

[slender bobcat]

these squiggle lines

[glass sigil]

thats ^2

[slender bobcat]

youre subtracting them

not multiplying

[glass sigil]

I dont under stand how do i simply it in a different way

[slender bobcat]

id suggest to factor denominators first

to make like easier

[glass sigil]

ok

[slender bobcat]

its .close

[glass sigil]

.close

[marsh citrus]

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[slender bobcat]

if youre wondering

[marsh citrus]

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[warped bane]

is #2 good? and if so how would i do #3 since there’s no indication of what x = to

[late geode]

there are multiple things wrong with #2

[fathom sun]

explain how you got that figure for #2

[marsh citrus]

@warped bane Has your question been resolved?

[marsh citrus]

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[robust skiff]

can any one help to prove that ?

[robust skiff]

i m self-studying logic and i v been wondering if logical proves and logical thinking solving stuff like that would help with calculus and linear algebra?

[next apex]

are there any constaints on a?

[robust skiff]

oh sorry a in ]0,1[

[calm vortex]

it would probably help with your overall problem solving skills

[robust skiff]

a is an element of ]0,1[

[calm vortex]

but if your calculus and linear algebra are engineering based, there may be less proofs you need to do

[robust skiff]

so calculus doesnt have any relation with tht?

[calm vortex]

it does

[robust skiff]

how?

[calm vortex]

epsilon delta definitions and such

[robust skiff]

but not as hard as that

[calm vortex]

id say epsilon delta proofs are harder to come to grasp with

[robust skiff]

or that

[robust skiff]

i think its a wast of time specially that

[calm vortex]

if you know how to do those from the top of your head then yea it could be a waste of time

but if you can't come up with the proof from the top of your head for those then i'd say continue doing them

[robust skiff]

it just takes me 2pages for that exercice

[robust skiff]

can you solve that i cant come up with any idea

ithink im gonna jump to calculus pls can you give some hardest logic exercises to test my abilities?

[calm vortex]

A classic example from calculus would be to prove that $\forall\epsilon > 0, \exists \delta > 0, 0 < |x-2| < \delta \implies |(x^2+x)-6|<\epsilon$

[elfin berry]

Ham

[calm vortex]

something along those lines

[robust skiff]

nice but its to hard to prove btw im still bad

whats its name i wanna see the prove

[calm vortex]

look up "epsilon-delta definition of a limit"

or just "epsilon-delta proofs"

[robust skiff]

am i sutpid or its hard ?

[calm vortex]

it's one of the harder topics in calculus 1

[robust skiff]

some thing like that ?

[calm vortex]

yea

[robust skiff]

hard to prove

im 15 ithink im stupid

[robust skiff]

Diameter DF not DE

[marsh citrus]

@robust skiff Has your question been resolved?

[marsh citrus]

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[marsh citrus]

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[runic temple]

what

[cunning tinsel]

?

[limber hearth]

what is the context of the question ?

[runic temple]

probably trolling

<@&268886789983436800>

[limber hearth]

oh

ok

[marsh citrus]

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[stone dirge]

This is open ended, how am I getting this wrong?

[marsh citrus]

@stone dirge Has your question been resolved?

[marsh citrus]

@stone dirge Has your question been resolved?

[marsh citrus]

@stone dirge Has your question been resolved?

[stone dirge]

.close

[marsh citrus]

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[stone dirge]

How would I go about solving this? I tried y2-y1/x2-x1 but I don't think I know how to di t

[stone dirge]

do it*

[desert dirge]

"y varies directly with x" means y=kx
where k is some constant

[stone dirge]

does that also mean its a direct variation?

[desert dirge]

yes?

[stone dirge]

oh wait

So would I insert 180 and 5

[desert dirge]

elaborate

[stone dirge]

y would become 180 and x would become 5 in y=kx

[desert dirge]

no, theyre in different instances

its not that 180=5k

its that 180=kn and n=5k

[stone dirge]

ah I see

so its 6

I filled in n with 5k and solved for k

[desert dirge]

youre finding n not k

but you can use that

[stone dirge]

oh

Then whats the correct way?

[desert dirge]

just do what you did to find k, but with n instead

or sub your value of k into the equations and find n

also you have neglected a second possible solution set, but its not the one that shows up in the answers

when you square root remember the negative root is also a solution

[stone dirge]

so instead I would do n=5(180/n)

[desert dirge]

yeah

[stone dirge]

I think I am doing smt wrong

so it would now be 30?

[desert dirge]

yup

[stone dirge]

How come we don't multiply the n?

[desert dirge]

what do you mean?

[stone dirge]

like n=5(180/n)
n=(900/5n)
n^2=900/5
n^2=180
n=13.4

[desert dirge]

its all fine until the 13.4

wait no

its wrong from the second line on

[stone dirge]

to find the actual answer I did n=5(180/n)
n=900/n
n^2=900
n=30

[desert dirge]

thats just this but done correctly

[stone dirge]

But i dont understand why we dont multiply to n as well in 5(180/n)

[desert dirge]

a(b/c) isnt (ab/ac)

[stone dirge]

is it because we treat it as 5/1

[desert dirge]

yeah

[stone dirge]

oh that too

[desert dirge]

5/5 would be 1 not 5

[stone dirge]

so if I were to use this example

I would do th same equation y=kx

[desert dirge]

indeed

[stone dirge]

But for k instead right

[desert dirge]

yeah this one is solving for k

[stone dirge]

alright ill get back to you in a minute after I try it out

Yeah I am fumbling idk what I am doing wrong
400=kr
r=4k

I should be solving for k

but

[desert dirge]

400=kr r=4k

remember x and y both have given values for each case

[stone dirge]

400=k(4k)
400=4k^2
divide both sides by 4
100=k^2
10

or also -10

ah I see i forgot about those set values

Would 10 be correct for k?

[desert dirge]

seems alright

[stone dirge]

Alright than kyou

.close

[marsh citrus]

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[stone dirge]

.reopen

[marsh citrus]

✅

[stone dirge]

Is my thought process correct for this question?
y=kx
48=6k
8=k
Next problem we have y=2k
y/2=k
so for 8=k
8=y/2
y=16

[desert dirge]

yup

[stone dirge]

Also how would I go about doing these

I've never done these before, so I got 0 knowledge

[desert dirge]

average rate of change would be the slope of the straight line joining the endpoints

[stone dirge]

What does it by over the interval 2,9

its not on the plotted line

[desert dirge]

x goes from 2 to 9 2<=x<=9

[stone dirge]

OHHH

Hold up let me try this first hahaha

(9-4)/(9-2)?

[desert dirge]

kinda, f(2) isnt exactly 4 though

youre probably better off just leaving the y values as f(9) and f(2)

[stone dirge]

I dont think I'm following, Hee's what I'm thinking I thought you mean like x1 was 2 and x2 was 9 so find the y and do y2-y1/x2-x1

[desert dirge]

that is what youre doing

its just that at x=2 y isnt exactly 4

[stone dirge]

ohhh

its slightly above right?

[desert dirge]

yeah

[desert dirge]

since it just asks for an expression, id assume this is alright

[stone dirge]

This is the correct answer

so you're right

But I don't understand what you mean by using f(9) and f(2) like are you saying to do
2,9 and 9,7

[desert dirge]

f(9) means the value of f at x=2
like if f(x)=2x+5 then f(9)=2(9)+5=23

the graph shows y=f(x), so the y values can be written as such

[stone dirge]

imma be honest I still dont get it]

[desert dirge]

hm, the line here is f(x)
so at each point y=f(x)
so lets look at about x=7
the y value there is about 8, this means y=f(7)=8

f(9) is the y value at 9, and f(2) is the y value at 2

[stone dirge]

so f(9) would be 9?

the 9 beside f is x and the 9 outside is y right

depending on the x is the y

[desert dirge]

yeah f(9) is about 9

[desert dirge]

?

[stone dirge]

nvm

wouldn't f(2) be larger than 4 I dont udnerstand how thats 2

[marble viper]

You would start by using that derivative method

lets say 2 is your base value right? as an x value

9 is your final x value

so you would just use the f(x+h) - f(x)/(x+h-x)

where h is by how much you are adding to the smaller x value to get the larger value

so in this case x would be 2 and x +h = 9

h = 7

just as hectic ark said

dw if you dont get a numerical value answer, just put it as that

[stone dirge]

I'm not following

[stone dirge]

are you saying that y=f(x) so basically y=f(2)
so y=2

so it can be 2,2

and 9,9

[desert dirge]

y=f(2) doesnt imply that y=2

it would be true say if f(x)=x

but its not general

f(x) could be e^(x^2+2) or something, then f(2) would be e^(6)

[stone dirge]

You guys are losing me rn

[desert dirge]

do you know what functions are?

,w graph y=x

[elfin berry]

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[desert dirge]

this is the graph of y=x

[stone dirge]

y=mx+b

[desert dirge]

we could say that f(x)=mx+b sure

and then say y=f(x)

so then the graph is of y=f(x) (which is equivalently y=mx+b)

because thats what f(x) is

[stone dirge]

Okay I think I am starting to understand

NVm I dont understand imma just skip this and come back to it

.close

[marsh citrus]

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[marsh citrus]

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[topaz tide]

A population of 500 bacteria doubles every 15minutes. Find an expression for this population growth. Using this expression, find what the population would be in 87 minutes. Use an exponential model

[topaz tide]

I have the expression P(t) = 500 * 2 ^ (t/15) where t is the time in minutes

[latent coral]

is the question if that's correct?

[topaz tide]

therefore P(t) = 500 * 2 ^(87/15) = 27857.6

yeah