help-19

[brittle beacon]

am I being slow, or aren't those the exact same thing?

Expand out [...](1 + U(t - 1)) = [...] + [...]U(t - 1)

[mystic silo]

oh

the correct answer had a t-1 substituted into the exponent

so in my solution for the second question i got
...+1/2e^(-2t) U(t-1)
while the solution is
...+1/2e^(-2(t-1)) U(t-1)

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@mystic silo Has your question been resolved?

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[dense mirage]

hey :3 stuck on where to go from here, not sure how to get it to completely power series form

[dense mirage]

,rcw

[cold swift]

use this:
$$\sum_{n=0}^{\infty}x^n=\frac{1}{1-x}$$

[clever fjord]

y0shi

[dense mirage]

where?

[cold swift]

for 3/x^2

convert it into that form

via substitution and multiplication

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[ocean hamlet]

Can somebody please explain?

[odd edge]

Please don't occupy multiple help channels.

[ocean hamlet]

How can R^2 x R^3 be isomorphic to R^5 if R^2 x R^3 has dimension = 2 and R^5 has dimension = 5 and two vector spaces are isomorphic if and only if they have the same dimension?

[lavish furnace]

why do you think R² × R³ has dimension 2?

im guessing you thought this way because it has two components, one from R² and one from R³

[ocean hamlet]

This is how the product of vector spaces is defined. For example {((1,0), (5,3)), ((1,1) (2,3) (3,4))} is in R^2 x R^3

[lavish furnace]

but of course that's not what the dimension is, the dimension is the size of a basis

[ocean hamlet]

Where ((1,0), (5,3)) is in R^2 and ((1,1), (2,3), (3,4)) is in R^3

[ocean hamlet]

Yes

[lavish furnace]

so you can check that
((1,0),(0,0,0))
((0,1),(0,0,0))
((0,0),(1,0,0))
((0,0),(0,1,0))
((0,0),(0,0,1))
form a basis, with exactly 5 elements

[ocean hamlet]

There's this theorem though, I'm confused

dim(R^2 x R^3) = dim(R^2) + dim(R^3) = 5

Never mind I'm stupid

[ocean hamlet]

Yeah right

[lavish furnace]

hahah dont worry about it

[ocean hamlet]

Well, I think I got it now. Thanks!

[lavish furnace]

❤️

[ocean hamlet]

Sorry to bother you if you're good in linear algebra can I also ask you another question?

[lavish furnace]

im decent lol but i'll try

[ocean hamlet]

It's in help-32

.close

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[stark lantern]

for (b), can an answer be x = -t, y = 3 + 2t, z = 5 + 7t?

[stark lantern]

Here is what the marks scheme says, but notice at the bottom how it says there can be several answers

now I have no idea how to see if my answer is correct or not

I did get the point of intersection as (0, 3, 7) but from there we differ

I have no idea how they got -4, -2, 0 as a normal vector

Green is my working

[orchid torrent]

Your answer is fine, $-\ell=2t$ in your case

[clever fjord]

Civil Service Pigeon

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@stark lantern Has your question been resolved?

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[sick sigil]

I'm a bit confused here

isn't this matrix multiplication?

Shouldn't we get the matrix

or actually uhh

now im even more confused

i was thinking this

or is he just doing dot multiplication in the first image?

ah yeah its dot producrt

nvm then

.close

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[twin glacier]

Hey, I have a geometry problem i have no clue how to even start on. The problem is as follows:

Seven pine logs are tied together with a wire according to the cross-sectional figure below. How long wire
needed for a turn? Each log has a diameter of 20 cm. Enter the answer in centimeters
accuracy.

[modern gyro]

Hii

[twin glacier]

Hello.

[modern gyro]

Each circle diameter 20

[twin glacier]

Btw if the problem is worded weirdly it's because it's directly translated to from my native language

[modern gyro]

So the dist between two opposite sides of figure is 3 * 20

[modern gyro]

No its okay

[twin glacier]

So from the wire at the top to bottom is 60

as well

[modern gyro]

Yes

Now

See one small circle

[twin glacier]

One small circle?

[modern gyro]

This is a right angle

Onw side length is 20

Other side length is 20+10

So we can get length of one side of the figure

[twin glacier]

ohh

[modern gyro]

@twin glacier We re estimating a rough value okk ?

[twin glacier]

yeah

[modern gyro]

The actual value would be few less

[twin glacier]

yeah

[modern gyro]

So find it and multiply

[twin glacier]

Essentially the side * 5

to get the rough answer

[modern gyro]

Side *6

[twin glacier]

right

xd

[modern gyro]

Six sides we have

[twin glacier]

i forgot that one still exists

[modern gyro]

🙂

[twin glacier]

how do you know it's a right angle?

[modern gyro]

See the circles touch each other

[twin glacier]

ooh rand angle

thingy

[modern gyro]

yeah

[twin glacier]

i forgot the name of it

[modern gyro]

I too dont remeber the theorem

[twin glacier]

so it's just 20^2 + 30^2 = x^2
answer is 6x

[modern gyro]

yeah

Does it matches your answer ?

[twin glacier]

Let me just calculate it one sec

yep

[twin glacier]

tyvm <3

.close

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[twin glacier]

Is it possible to solve this kinds of problems? (Possible for a high schooler)

[mystic saffron]

!original

[odd edge]

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

[twin glacier]

I'll try my best to translate it:

Calle works at a computer game manufacturer and makes a soccer game.
To describe the ball path seen from above for curled shots at goal, Calle chooses one
feature

where meters is the distance from the origin to the destination and meters is the deviation of the ball from the "center line" of the court (see figure).
f(x) = 0.005x^2 + 0.15x

b) How far from the goal is the shooter if the ball goes into the goal at the goalkeeper's right post?
The goal is 7.32 meters wide.

Then this was my thought process, i probably messed up somewhere

And since f(x) = 0.005x^2 + 0.15 I just put that into the pythagorean theorem

and the many zeros above was the result of that

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[twin glacier]

.close

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[pastel pollen]

oh did you figure it out

[twin glacier]

I did not

[pastel pollen]

your picture is a bit misleading! the hypotenuse of that triangle is not equal to f(x)

though it tricked me as well lmao

because if that was true, then yeah, you'd get your quartic equation that's not easily solvable

maybe, with a fresh eye, you wanna look at your triangle again and find out how f(x) actually comes into the picture here

feel free to ping me if you need more hints

[twin glacier]

okay thanks! will do that if i dont manage to do it lol

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[serene mango]

,rotate

[serene mango]

can't tell

what does it say?

1 - sh²x +7ch²x ?

s, c and h variables? sh some function?

[desert vector]

cosh and sinh?

[serene mango]

could be

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@wintry shadow Has your question been resolved?

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[wintry shadow]

Yeah

[wintry shadow]

Yes

[serene mango]

aha

[wintry shadow]

It’s a weird shortcut we do around here

🦅

[serene mango]

Without doubt

[wintry shadow]

I am into something

Nvm

[serene mango]

you can take the first step using cosh²(x) - sinh²(x) = 1 to remove sinh.

[wintry shadow]

Cool

Then

[serene mango]

generally it looks liek subsitution

[wintry shadow]

I don’t think so

[serene mango]

u=cosh(x) or something

[wintry shadow]

Give me a min

Now what

[serene mango]

finish subsitutation

sinh(x) must go

[wintry shadow]

Now what

Now what

[serene mango]

agony

[wintry shadow]

Can I use partial

On square roots?

[serene mango]

highly doubt

let's revisist subsitution

[wintry shadow]

I will try

U=coshx ^2

I got a dum ass idea

Now can I try partial

[serene mango]

it does not look promising at all

partial integration requires that one term gets easier with differnetiation and the other not too much worse.

Let's go about it from different direction.

If we had 1/(6cos²(x)) to integrate

it would be tan(x)/6.

So 1/(6cosh²(x)) is probably tanh(x)/6 (verify this).

Can we modify this function to get a summand?

[odd edge]

@wintry shadow Has your question been resolved?

[serene mango]

Maybe you can susbsitute u = tanh(x) (so cosh²(x) = 1/(1/cosh²(x)) = 1/((cosh²(x) - sinh²(x))/cosh²(x)) = 1/(1-u²))

@wintry shadow

[wintry shadow]

I am confused

[serene mango]

I am going to dinner now

I think it is very promising though

[wintry shadow]

Since when is Cosh^2 = 1/cosh2

[serene mango]

you should try.

[wintry shadow]

Alright

Have good one

[serene mango]

I never said so

[wintry shadow]

=1/coshx^2

[serene mango]

neither

[wintry shadow]

Nvm

I misread it

[serene mango]

happens XD

I believe if you susbirtute

you get some fraction with no square root

[wintry shadow]

Ok but when

[serene mango]

you can then itnegrate

[wintry shadow]

I am still confused

[odd edge]

@wintry shadow Has your question been resolved?

[wintry shadow]

Kys bot

[odd edge]

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[steady musk]

How is #9 C?

[clever fjord]

You must be a bot manager to use this command!

May 9, 2024, 8:01 PM

[sharp oak]

!status

[odd edge]

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

[steady musk]

I just don’t know whrrr to begin

[odd edge]

@steady musk Has your question been resolved?

[tawdry wagon]

U can kinda think of it like a triangle. So like if the x side is 1/sqrt2 and the y side also, the angle between them is pi/4. Same as y=x

Tbh idk why the put sqrt2 on the bottom. You can put any real constant there other than 0.

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[eternal glade]

Hey guys

[eternal glade]

If i have a continous, bijective function between metric spaces, f:X->Y
Is f': X\x -> Y\f(x), x -> f(x) continous as well?

[odd edge]

@eternal glade Has your question been resolved?

[eternal glade]

<@&286206848099549185>

[odd edge]

@eternal glade Has your question been resolved?

[odd edge]

@eternal glade Has your question been resolved?

[fresh ruin]

like taking out a point little x? no

[eternal glade]

Yeah, taking out a little x but also its f(x).

[fresh ruin]

oh I'm wrong https://math.stackexchange.com/questions/2646233/are-functions-still-continuous-even-with-removable-discontinuities

[eternal glade]

Because it certainly seems continous. Look at an easy example like
f: R->R
f(x)=x
and now lets look at f':R\0 -> R\0
f'(x)=f(x)
Now, for every x0 in R\0 and E>0 definitly exists an d s.t. for all x in (x0-d,x0+d) it would still be continous

[fresh ruin]

yea since it's a pointwise definition and it doesn't look like removing something changes things

[eternal glade]

Okay, nice, that really helps with a proof on homeomorphisms.

Either way, thanks for your help with finding that link, i searched for it a while now, but im heavily tired (its 4am over here)

.close

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[frank vortex]

i have 5 minutes to hand this lesson in and i cant figure out this one

please someone help

[idle zephyr]

do you know how to do polynomial long division?

[frank vortex]

yes ive tried

i initially got d

but it wasnt right, i then tried doing it again but it was giving me remainders of 0

for all

[idle zephyr]

Now if one of them is a factor, say 3x - 2 is a factor, then set 3x - 2 = 0, and x = 2/3 is an x intercept of the graph

[torpid owl]

dude you've asked this 3 times

[idle zephyr]

o

lol

[nimble blaze]

its not productive to abandon and repost,
effectively starting from scratch

descriptions of what you did incorrectly

• recommendations

show your updated work and what you now have considering that

and yeh, you can just apply factor theorem instead of approaching this with synth division

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@frank vortex Has your question been resolved?

[odd edge]

@frank vortex Has your question been resolved?

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[mystic saffron]

How can I answer this

[open crown]

Lowkey could plug in any x value

Then u get a y value

So u get a point in term of (x,y)

Repeat until u get the whole graph

[mystic saffron]

How do I plug in any x value tho

Wym by that

[brittle notch]

find 2 points on line and join them?

[open crown]

plug = substitute

[mystic saffron]

But like how do I figure out which points to plot

[open crown]

Any point will work

It doesnt matter

[mystic saffron]

And my graph lowkey weird it skip counts like 2,4,6

[open crown]

Doesnt matter

[mystic saffron]

Okay for example I point 4 and -6 what do I do after

[open crown]

Then mark that point on the graph

[mystic saffron]

And do I make a line?

[open crown]

Choose another point

[brittle notch]

assume x=0 and find y
assume y=0 and find x
u get 2 points

[open crown]

u choose x = 4 and u get y = -6 which mean u got 1 point, now choose another value of x to get another value of y, so u got another point

Then connect them

[open crown]

Thats not a point....

[mystic saffron]

Dawg am I that cooked in this topic🤦🏿

[open crown]

Pay attention to ur teacher

[mystic saffron]

I do a lot but my teacher dosent know how to teach properly

All he does is play around

[open crown]

💀

[mystic saffron]

Na Bro Like fr I ain’t even playing

[astral root]

Use khan academy

[open crown]

U lowkey know another point too, do u know what is a y intersect?

[astral root]

Barring serious health issues, there’s no reason for academic mediocrity except for yourself tbh

[mystic saffron]

U mean intercept? Or am I that dumb to not know what that means

[mystic saffron]

I tried khan academy before it’s still eh

I’m using the chemistry tutor

[astral root]

Intercept is where it crosses an axis

Y-int is where it crosses y-axis

[open crown]

Choose it just mean if x = 0, the function cross the y axis at that value

So whats your next point?

[mystic saffron]

So like I choose any 2 again

-2 and 8

[open crown]

Does it satisfy the function

U should use the point format (x, y)

[mystic saffron]

Lowkey lost rn so I choose -6 and 4 and then what happened after that?

[open crown]

sigh...

Choose another value of x

[mystic saffron]

This is a different approach
convert the equation into this form x/a + y/b =1
and you can easily draw the graph
In this case it's x/2 + y/6 = 1

[mystic saffron]

This lowkey more confusing

[open crown]

Pretty useless method

When he learns quadratic, he would need to learn another method

@mystic saffron

Choose another x value

[mystic saffron]

Okay So x value let’s say 10

[open crown]

Choose something small bruh

[mystic saffron]

2

[open crown]

Now subs x = 2 into the function, whats y = ?

[mystic saffron]

Ohhh wait hold on

So -3(2)+6

[open crown]

....

[mystic saffron]

Forget I said that

[open crown]

which equal?

[mystic saffron]

0

[open crown]

Good

So u got another point

which is....?

[mystic saffron]

0+6

[open crown]

Remember: A point look like this (x, y)

[mystic saffron]

If this is wrong I’m quitting math

(0,6)

[open crown]

U choose x = 2

Then u get y = 0

[mystic saffron]

Yo no one saw that

Okay so (0,6) (2,0)

[open crown]

Its fine, people all make mistake

[open crown]

Its (2, 0)

[mystic saffron]

I hate math bro what

How y’all understand this

[mystic saffron]

True, substitution is good here ig sorry for interrupting

[open crown]

@mystic saffron

Look

Does it make sense now?

[mystic saffron]

Wait for the y=2-3+6=0 how do that work

[open crown]

Its 2 * -3 + 6 = -6 + 6 = 0

[mystic saffron]

Ohhh

[open crown]

Lowkey not trust u understand it, give me another point that lie on the function please

[mystic saffron]

So I chose any 2 other points?

[open crown]

@mystic saffron Use this

[open crown]

x and y alone isnt a point, a point is made up by both x and y, and has a form of (x,y)

[mystic saffron]

Okay let’s say here to choose x, I choose 4 and replace it with the 6? Or am I being dumb

[open crown]

This is ur function

By subs x = something, u replace x with that value, and calculate y

[mystic saffron]

Wait I think I got it

So I js replace x

[open crown]

💀

[mystic saffron]

So -3(4)+6

Which is -6

[open crown]

And u get what point?

[open crown]

😫

[mystic saffron]

(4,-6) ?

[open crown]

YESSS

[mystic saffron]

YOOOOO

FINALLY BRO

[mystic saffron]

finally

[open crown]

Now, mark that point onto the graph

[mystic saffron]

Lmaooo is u js watching

Okay I marked 4 and -6

[open crown]

Picture please

[mystic saffron]

Watch me Mark it wrong😭

[wise dawn]

lol

[open crown]

💀

[mystic saffron]

Na man im cooked Heavy

[open crown]

Here's an example of point (4,-6)

x= 4 and y = -6

[mystic saffron]

So wait did I mark it wrong or right

[open crown]

If u're right, would I send the 💀

💀

[mystic saffron]

I’m weak bro I’m getting flamed by tryna study math

[wise dawn]

(4,-6)
(x, y)

just iamgien it like that u walk along the x axis and then go to the y coordiante

[mystic saffron]

20 mins into this question and I’m still lost am I failing on Sundays test😤

[wise dawn]

nah trust ur gonna ace it

[mystic saffron]

With my slow ahh ion think that’s finna be possible

[wise imp]

yall are overcomplicating it so much for bro 😭 just start with plotting the y -intercept on the y axis and then use rise over run for the slope to plot the rest of the points and connect them at the end

[mystic saffron]

If I were to plot the y intercept on y axsis do I just go to (0,6)

[wise imp]

yes

put a dot on that point first

[open crown]

Bro, learning this way benefit him for other function like quadratic so shut...

[mystic saffron]

Okay did

[mystic saffron]

Wait so who do I listen to now😭

[wise imp]

alr so once you have that point then you know the slope, the slope is just the rise / run. So since your slope is -3, that is basically -3/1 which means you go down 3 and right 1 from your starting point

[mystic saffron]

After the rise over run it went to 2

(This graph goes 2,4,6)

[wise imp]

one sec lemme draw something for you

[open crown]

Here's how to mark any point

[open crown]

Remember u know the function goes through this point

[open crown]

Also this point

Now mark those 2 points on your graph

[mystic saffron]

I marked the (4,-6) and it was wrong tho

[open crown]

Show me

[mystic saffron]

No like u did the 💀

[open crown]

Read this and do it again

[mystic saffron]

OH

Where does 2,0 intersect tho

Hold on I think I got it

Lemme get pic

[open crown]

It may surprise u, but y = 0 is just the x axis itself

So that point lies on the x axis

[mystic saffron]

And from there I js draw a line

[open crown]

The point (4, -6) is correct

However

Check the point (2, 0)

[mystic saffron]

Do I mark it like this one sec lemme pic

[open crown]

YES

Now, connect them and extend the line

[mystic saffron]

Blues:💀

[open crown]

💀 indeed

[mystic saffron]

I’m cooked

[open crown]

Do u own a ruler???

[mystic saffron]

Lmao😭 yes but ion know where it at let me find it rq

[open crown]

That line is as straight as James Charles

💀

[mystic saffron]

We got a ruler🤯🤯

[open crown]

Much better

Now

Its a convention to write the function next to the line

Something like this

[mystic saffron]

Okay okay and what after this

[open crown]

Btw, look what point does your function cross the y axis?

[mystic saffron]

6

Don’t hit me with the 💀

[open crown]

Understand this part?

[mystic saffron]

Yep

[open crown]

Thats what y intercept means

Also, if choose x = 0; y = 6

Also why it calls y intercept

[mystic saffron]

Wait did we finish this question then basically or do we still have more steps

[open crown]

No

Thats it

Btw

[mystic saffron]

But this question a bit more confusing let me show u

[open crown]

Do u know x^2?

[open crown]

Hit me with it

[mystic saffron]

Its prob easy

But it’s js the looks taht are confusing

[open crown]

Repeat the step

[mystic saffron]

What’s this supposed to mean

[open crown]

Dont disappoint me

[open crown]

forget it

[mystic saffron]

Okay so m=1/2 and y intercept is 0 right?

This is js in genral I’m saying

[open crown]

Yep

[mystic saffron]

Okay bet I’ll try not to

[open crown]

Doubt it but continue

[mystic saffron]

Okay I choose 2 for the x and now we do 1/2(2)

Did I disappoint

[open crown]

What point do u get from this

[open crown]

Nope

[open crown]

the answer to this question may

[mystic saffron]

It’s basically .5 x 2 right?

Since it’s half

[open crown]

Yes

[mystic saffron]

Okay 1

[open crown]

I need the point

(x, y) format

[mystic saffron]

(2,1)

[open crown]

Weldone

👍

[mystic saffron]

Yesssisrrr

[open crown]

U need another point

Give me another point

[mystic saffron]

(4,2)

I choose x as 4

.5x4 is 2

[open crown]

Good

Now mark them

[mystic saffron]

YOOO BLUE IM COOKINGGG

[open crown]

.

[open crown]

💀

[mystic saffron]

I don’t trust my self in this

This feels so wrong

[open crown]

Its fine

[mystic saffron]

I got that somehow

💀

[open crown]

Its correct

[mystic saffron]

No way

[open crown]

Good job

[mystic saffron]

Yoooo I got the best teacher in the world

So now I js draw the line

WITH A RULER

That’s crazy with a ruler and it ain’t even hittin the points

[open crown]

[mystic saffron]

🥰

Let me guess, wrong

[open crown]

Its correct

Although

Here's a tip

[mystic saffron]

What’s up

[open crown]

U should choose x value that "far" away to get the graph a bit more correct

[mystic saffron]

So like I should’ve chosen 10 or 8

[open crown]

Like x = 4 for the first point, then the second point should choose x= -4

[mystic saffron]

Okay Blue there’s one question and I’m gonna do it and not disappoint u

This is the question

[open crown]

Here's an example

[mystic saffron]

Wait so like what should I do to get this

[open crown]

Honestly, its fine with whatever x value u choose, but like if u choose x = 5 then the next x should be negative of the first x so x = -5

[mystic saffron]

Wait so like when I choose x can I also make it negative?

[open crown]

Yeah

x can be whatever value

[mystic saffron]

Alr hold on let me answer this and show u now

[open crown]

U should also learn how to present ur work

Step by step to show people how did u get there etc

[mystic saffron]

So far this is the working

But I think I got smth weonb

Wrong*

Like the y is wrong

[open crown]

(6, 7) is correct though

Now another point

[mystic saffron]

And the other one is (-4,-13)

[open crown]

Correct

Now mark them

[mystic saffron]

Now let me mark

Wait question

So it’s -13 and our graph is 10

Do we js add more marks?

Or do I reset

[open crown]

Hmm

U can choose another x term

Something like -2

[mystic saffron]

Alrr let me do it rq

Okay u ready for the answer

[open crown]

💀

[open crown]

Dont disappoint me

[mystic saffron]

I’m not gonna disappoint 😤😤

And I js put the function on the line

[open crown]

BTW @mystic saffron U should present ur work like this, its a standard so people understand what u're doing

[mystic saffron]

Wait do I show working for u to?

[open crown]

You should pay attention to the precision boi

The function should cross the y axis at -5

[mystic saffron]

Is that finna affect the answer ?

It’s js that these graphs are small ykwim

[open crown]

If u dont show ur work then ur teacher can say the graph is off and give u penalty for it

[mystic saffron]

But overall I did it correctly right?

[open crown]

But if u show ur work like this, the teacher cant really do that

[open crown]

Yes, but there's still room to improve

Make me proud is impossible so dont even try

💀

[mystic saffron]

Na Na don’t disrespect me like that😤😤

I ain’t finna disappoint

Okay but last question and then I’ll take a break rq

[open crown]

Is that ur homework?

[mystic saffron]

This one I didint get anyth

[mystic saffron]

Na it’s like a revision packet

[open crown]

Or school work

[mystic saffron]

We got mocks in a few weeks

So Like they give us this to work

[open crown]

5 grade?

Nah 4 grade?

[mystic saffron]

Here I don’t get anyth

[mystic saffron]

Naaaa u wilding dawg😭

This g8 work

[open crown]

💀

[mystic saffron]

Shhhhh

[open crown]

I will show u my 5 grade test

[mystic saffron]

Am I finna feel stupid

[open crown]

Yes, so maybe I will not show it

[mystic saffron]

Ain’t no way

[open crown]

but for grade 5 we study quadratic already

[mystic saffron]

Where u from for it to be that hard dawg

[mystic saffron]

How the hell

[open crown]

💀

[mystic saffron]

How that even possible

[open crown]

Its pretty easy

Do the same

But there's 2 lines on the same graph

[mystic saffron]

Wait so I js change x?

Bruh pause this easy asf then (I’m gonna disappoint)

[open crown]

For this, u can choose any x value, but the y value for each function will be different

[mystic saffron]

Wait but look at 49 the other function I don’t get it

[open crown]

U need to modify it

[mystic saffron]

You do a worked example for me right in the beginning 🥰

[open crown]

Please tell me u understand this

[mystic saffron]

Ya I get this

When u bring the x to the other side it become negative

[open crown]

The point is to get the function form of y on the one side

[mystic saffron]

So we put all the other stuff onto one side

[open crown]

Now

[mystic saffron]

And the y onto one side

[open crown]

Give me the form of y = ....... for this

Dont disappoint me

[mystic saffron]

I’m gonna disappoint

We move the 3x to the other side

So -2y=4-3x

💀

[open crown]

Continue

I want the form y = .....

Not -2y=......

How do we get rid of the -2

[mystic saffron]

Y=6-3x

[open crown]

No

[open crown]

.

[mystic saffron]

Ohhhhh

-y=4-3x

That’s wrong

[open crown]

💀

[mystic saffron]

Ahem

[open crown]

How can we get rid of it?

[mystic saffron]

To get rid of the -2 u make it positive

[open crown]

No

U divide both side by -2

[mystic saffron]

Bring it to the other side

Oh

Ahem

[open crown]

A lot of "Ahem" 💀

[mystic saffron]

Wait we also devide the -2 with the 4 right

[open crown]

What do u think?

Should we?

[mystic saffron]

Yes

[open crown]

Then proceed

[open crown]

Final answer?

[mystic saffron]

Y=2x-3x

[open crown]

💀

[mystic saffron]

OKDS

[open crown]

Try again

[mystic saffron]

What did I do wrong

[mystic saffron]

Why did we get 3 over 2

[open crown]

[mystic saffron]

Tbh that’s me rn

[open crown]

@mystic saffron Try this

Dont disappoint me again

[mystic saffron]

Are these supposed to be easy..

[open crown]

it is easy

[mystic saffron]

Should I put the 2 ys together

[open crown]

get the y term on 1 side

and other term on the other side

[mystic saffron]

To let u know in advance I’m disappointing a lot

[open crown]

Are u American?

[mystic saffron]

Ya but moved out

[open crown]

Yeah the American Education system is so cooked

[mystic saffron]

Na but I moved out in g3

[open crown]

Well, I need the answer.....

[mystic saffron]

Im kinda lost..

[open crown]

Hmm

Is it that hard?

[mystic saffron]

Not really I js don’t know where to put stuff correctly

[open crown]

Maybe we should skip it and focus on these assignment

[mystic saffron]

Okay okay but Hold on rq I gotta go to the bathroom

[open crown]

I need to go out for lunch

Cya latter

If neef more help dm or tag me in here

[mystic saffron]

Alr alr bet

.close

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[bright quarry]

can someone help me with this question

[frigid canopy]

,rotate

[brittle notch]

what are intercepts?

[bright quarry]

the a point where the parabola intercepts a value on the y or x value

[brittle notch]

yea so put x=0 for y intercept and y=0 for x-intercept??

whats ur doubt

[bright quarry]

i mean with v)

im not sure how to do the range

[brittle notch]

okay so can y be negative?

[bright quarry]

Not in this case no

[brittle notch]

what is the minimum value of y?

[bright quarry]

would it be 0?

[brittle notch]

nop

if y=0 then x^2 = -4

wait u know differentiation?

[bright quarry]

uh i dont think so

ive heard the term before

[brittle notch]

um fine

ok so by inspection what do you think the minimum value of y is?

[bright quarry]

ohhhh is it 4

[brittle notch]

yep

and what happens to y if u put x = infinity?

or -infinity

[bright quarry]

not sure

[brittle notch]

what is infinity + 4?

[bright quarry]

uh

I have no idea

i jsut started learning parabolas

[brittle notch]

ok fine

so a parabola either has a minimum or a maximum

if it has a minimum it ranges from minimum value to infinity

u drew the graph?

[bright quarry]

yes

[brittle notch]

how did u draw it?

can u show?

[bright quarry]

yeah one second

[brittle notch]

okay

[bright quarry]

,rotate

[bright quarry]

my lines arent that good yet

lol

[brittle notch]

yea so what do see here?

the y goes from 4 to all the way upto infinity

[bright quarry]

yes

thats what the arrows indicate right?

[brittle notch]

yes that is your range

[bright quarry]

ah so

would the range be

y > or equal to 4

[brittle notch]

yep

[bright quarry]

ah i understand now

ty for the help 🙂

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[odd edge]

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• Show your work, and if possible, explain where you are stuck.
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[high field]

How to get sinx, cosx, tanx if tan(x/2) known?

[sullen ferry]

half angle formula :3

well, double angle formula

[high field]

ok, i forgot to specify: tan(x/2) is t, and need to express sinx, cosx, tanx from t ( tan(x/2))

[sullen ferry]

t=tan(x/2)?

[high field]

ye

[sullen ferry]

so your goal is basically to write all the trig functions in terms of t?

[high field]

ye

[high field]

based on
$$
\tan(\frac{x}{2}) = \frac{\sin(\frac{x}{2})}{\cos(\frac{x}{2})}
$$
?

[clever fjord]

Glorious Lynx

[sullen ferry]

its based on double angle identities for sine and cos yes

well, also angle addition property mainly for tangent

[high field]

angle addition? tan(a+b)?

[sullen ferry]

but that identity tells you something if you let 2theta=x/2

tan(x)=

[high field]

isnt trig(a+a) = trig(2a), where trig - one of three usual trig functions?

[sullen ferry]

yes

[high field]

why is it needed then if it simplifies to double angle?

[sullen ferry]

that's the cast for all functions

its needed in case angles are different. or if you have a specific angle where double angle can't be applied

[high field]

Am i understanding it right: to express sinx, cosx, tanx from t = tan(x/2) i need to use angle addition? If so - why?

still confused a lot

[odd edge]

@high field Has your question been resolved?

[high field]

i see i better to use forum

[odd edge]

@high field Has your question been resolved?

[cold plover]

depends on what you mean by "need to"

you can just memorize the tan(x/2) formula

or you could derive it from the addition formulas

hint: tan(a+b) where a = b = x/2

does that help?

[high field]

🤔

ok ill consider it

i thought this give same result as half angle formula, maybe i should try

[cold plover]

they should all give equivalent results

[high field]

maybe in different form?

[cold plover]

you cant use correct rules in combination to get something wrong or different from the correct answer

yeah exactly

the thing about trig

is that there is a scary infinite amount of trig expressions that are nothing alike

but are totally equal*

there is no easier way to hide expressions of different forms that are equal

*excluding particular domain shenanigans

[high field]

ok

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[ember lily]

need help with permutations and combinations

[ember lily]

like just a simplified explanation because the internet is not helping 😭

[stiff wind]

Permutation is order

Combination is picking

Permutation is How many different ways i can order 5 kids

Combination is How many different duo's i can pick from 5 kids

[odd edge]

@ember lily Has your question been resolved?

[ember lily]

Ok thanks. How would i solve this question:
In a class of 28 students is a basketballteam made from 8 players; how many teams are possible

[stiff wind]

C(28,8)

Combination

[ember lily]

yes but how does that work

why c(28,8)

[stiff wind]

You have total of 28 player

you want to PICK 8 of them

[ember lily]

yeah but like what does C(28.8) do, like what type of calculation is happening when i enter that in my calculator

[stiff wind]

${n}C{r} = \dfrac{n!}{r!(n - r)!}$

[clever fjord]

Gokadam

[stiff wind]

in this case n is 28

r is 8

[ember lily]

hmm and how does this work

like whats the logic behind it

cuz i wanna understand why this works you know

[stiff wind]

yeah i see but if i say in discord chat it wouldn't be effective. Just type in combination formula proof and there should be a lot of resources

[ember lily]

like in google?

[stiff wind]

youtube

[odd edge]

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[marble pond]

Anybody know steps necessary to solving for r here?

[marble pond]

I tried finding the triangle but I couldnt figure out the 3rd side

Like for this one which is easy

This one is just $(1+r)^2=1+(1-r)^2$

[clever fjord]

AboutCatHelper

[marble pond]

Basically I think I’m not looking in the right area to solving R in the first one so yeah, need help

[odd edge]

@marble pond Has your question been resolved?

[fluid tundra]

are the two smaller circles equally-sized

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[vale compass]

only confused about this part

why is AM defined as OM-OA and not OM+OA

also O is the origin (Located where B is)

[odd edge]

@vale compass Has your question been resolved?

[tacit wasp]

Try to draw the sum of the two vectors, you'll see which one is correct

[vale compass]

ah ok

thanks

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[sick sigil]

ok i am big confused but i think that this might help me understand the majority of my difficulties

[sick sigil]

Let the lines l1, l2, l3 be defined by --- The lines l1 and l2 lies in a plane pi, the plane pi is "hit" by L3 in a point P, find the point p

So;

I know that one solution is to take the crossproduct of l1 and l2's t vectors and then take the values from that and plug it into a(x-x0) + b(y-y0) + c(z-z0) = 0

and I think the idea here is that if we have the normal(?) vector and we get 0 then it must be a 90 degree between them

meaning that that point is in the plane

but what I'm wondering is are there other approaches to solving this?

more specifically, isn't the plane pi also defined by l1+l2 ?

or more specifically

[true garnet]

do you know the vector equation of a plane?

[sick sigil]

(3+lambda1+lambda2, lambda2, 1 + lambda1)

I think that should be l1+l2 right?

should I not be able to then say

[true garnet]

why are you adding the lines?

i dont think that gives u the plane equation

[sick sigil]

that is what im wondering

to me I feel like well.. it should

[true garnet]

lol

yeh no it doesnt

but you have two vectors within the plane

and you have a point on the plane

[sick sigil]

why is it the case that it doesn't?

aren't those two vectors in the plane?

so if they're linearly independent and we have lambda to take any value, we should be able to access any point in the plane? 🤔

i think this is the main issue I have :/

[true garnet]

yes those two vectors are in the plane. but you are also adding those 2 'anchor points'. the sum of those 2 points probably isnt in the plane

[sick sigil]

because say we have the vectors (1,0) and (0,1), if we add them together with a lambda before each we would get (lambda1, lambda2)

hmm

ok

but

[sick sigil]

if i just chose one of them?

because irrespectively they're both in the plane right?

uhh that is small

[true garnet]

ah yeh sry

[sick sigil]

thanks

uhhh

how do we get 3i - 4j +k ?

or is that given

[true garnet]

this is a random example

[sick sigil]

ah alright

[true garnet]

in our case

[sick sigil]

yeah but then we can say

[true garnet]

we have the direction vectors of l 1and l2

[sick sigil]

(1,0,0)

• lambda1(1,0,1)

• lambda2(1,1,0)

right?

[true garnet]

yess

so we can equate that to the general point on l3

then we have 3 equations and 3 unknowns

[sick sigil]

ok so is that the same as saying that the plane is defined by

plane pi : (1+lambda1+lambda2, lambda2, lambda1)

[true garnet]

yes

its equivalent

just vector addition

[sick sigil]

yeah that's kinda what I was thinking, just forgot about the set coordinate part

and then we know that there's a lambda3 so that

[true garnet]

so you know how t o solve it now ?

[sick sigil]

hang with me

[true garnet]

yeh np

[sick sigil]

(1+lambda1+lambda2, lambda2, lambda1) = (1+lambda3, lambda3, 2+lambda3)

[true garnet]

yep

[sick sigil]

and then we can say that

1+lambda1+lambda2 = 1+lambda3
lambda2 = lambda3
lambda1 = 2+lambda3

?

[true garnet]

exactly

this system is quite easy to solve

[sick sigil]

would you use gaussian elimination for this?

or just manually move around?

i guess we can replace lambda1 and 2 in the upper one

[true garnet]

equation 2 immediately reduces the system to 2 equations

[true garnet]

how do u write equations like this btw?

[sick sigil]

with the square bracket thingy on the left side

[true garnet]

[] ?

[sick sigil]

uhh no

{

[true garnet]

oh

[sick sigil]

equations after that

[true garnet]

{}

ok

[sick sigil]

not the }

[true garnet]

ah

[sick sigil]

example

okok

that works

now

[true garnet]

{1+lambda1 + lambda3 = 1 + lambda 3

[sick sigil]

my last question before I leave you kind sir

yeah exactly

but i have the x coordinates on the first line, the y coordinates on the line below, z on the last

i dont write out x y z

[true garnet]

yeh i know

[sick sigil]

like this

disregard my poor handwriting

[true garnet]

idk how to write on next line in discord

so weird

[sick sigil]

shift enter

[true garnet]

also your handwriting is good

[sick sigil]

test
nice

[true garnet]

bro why do i not know this

[sick sigil]

^^

i can teach you something too

hehe

anyway

is there a way to go from where i am now to expressing the plane in terms of x y z = something?

[true garnet]

as in the vector (x,y,z)?

[sick sigil]

as in

[true garnet]

oh

cartesian form

[sick sigil]

the plane pi is described by x-y-z-1=0

from what I have now without doing the cross product of l1's and l2's t's

can I get this somehow? 🤔

because while this method did give the right answer (and i thank you so much for the help with this i cant tell you how much i love u) i feel like they want me to get the plane

[true garnet]

idk if htere is a quick way

[sick sigil]

well, it doesn't necessarily have to be quick

just wondering if the a(x-x0) + b(y-y0) + c(z-z0) = 0 is the only way

[true garnet]

im surfing google and cant find anything lol

yeh usually i cross product the direction vectors

to find the normal

then use that to get to cartesian form

[sick sigil]

got it

I do remember that method now but yeah

wanted to check since you clearly know

another question if you do want to help is

with matrix multiplication with other matrixes

i know i have to do row from one matrix and column from the other

but does it always have to be row from the left for example?

because I think that is what I generally have seen

like for this one

solve the equation AXB = BA where a = || and b = ||

so what I wanted to do was to just multiply BA and AXB and set up an equation system but that kinda went to shit when I tried, not sure if I did it wrong

maybe you can see where it goes to shit xd

lemme work on it again and send you a screenshot

[true garnet]

so X = (A^)BA(B^)

where A^ represents A inverse

[sick sigil]

yeah that is what they showed in the answer too

[true garnet]

does it make sense?

[sick sigil]

and I do understand that part looking at it now

but I'm not completely caught up with how to get the inverses the right way

or rather I think it's 1/det(A) * adj(A)

[true garnet]

it's just a formula

[sick sigil]

but dont remember what adj was lmao