help-13

[dusky pond]

are they right angled?

[halcyon hound]

no

random triangles

[dusky pond]

alr

[dusky pond]

dude

[halcyon hound]

#❓how-to-get-help

[dusky pond]

go away

[halcyon hound]

i got this

[dusky pond]

wow that was mean

sorry

yes

carry on

[halcyon hound]

note that these 2 triangles have one point in common

which is a

[dusky pond]

so are they touching?

at point a?

[halcyon hound]

yes

[dusky pond]

okay

[halcyon hound]

Now, lets say that BC and MN are parallel

[dusky pond]

is it worth drawing these?

[halcyon hound]

not really

[dusky pond]

alr

carry on

[halcyon hound]

the shape that we have described will look like one of these two ways

the first one is from the shape you sent

the second one will look like this

[dusky pond]

ye

[dusky pond]

wait what

how are they

oooh

i see

[halcyon hound]

they both work for thales theorem really

so the law states

in either of these two shapes

you have

ab/am=ac/an=bc/mn

the ratios are the same

[dusky pond]

just to quickly like make sure what is the exact like 'law'

[dusky pond]

ye ok makes sense

[halcyon hound]

if these two lines are parralel then these ratios will happen

[dusky pond]

if bc and mn are parallel?

[halcyon hound]

saying that ab/bm=ac/cn is also the same thing btw

[halcyon hound]

yeah

[halcyon hound]

can you try this in your triangle?

[dusky pond]

wouldnt it be ab/am = ac/an?

[halcyon hound]

yes

but ab/bm=ac/cn also works

[dusky pond]

alr

so

in my triangle specifally

how would i apply the numbers etc

(im a bit stupid)

[halcyon hound]

apply?

just pick up the expression for each length

[dusky pond]

like what would i have to fo

[halcyon hound]

and replace it

[dusky pond]

do*

could u do ONE side for more, like as an example?

[halcyon hound]

ill do the lengths using their names, and we will try to replace them with the given numbers

[dusky pond]

yea thats fine

[halcyon hound]

so we have px/xs=qx/xr

now, what is px?

[dusky pond]

y

[halcyon hound]

and xs?

[dusky pond]

(y+1)

[halcyon hound]

px/xs=y/(y+1)

now rx?

[dusky pond]

(2y-1)

[halcyon hound]

and finally qx?

[dusky pond]

(y+2)

[halcyon hound]

qx/xr=(y+2)/(2y-1)

so now, can you write px/xs=qx/xr using lengths?

[dusky pond]

like that?

[halcyon hound]

yes

do you know what we do next?

[dusky pond]

cross multiply mayber?

[halcyon hound]

yes!

[dusky pond]

cool

[halcyon hound]

make sure to use parens

else everything gets messed up

[dusky pond]

yeye

so it now looks like this

y(2y-1) = (y+2)(y+1)

[halcyon hound]

yeah

[dusky pond]

the second pair

like

(y+2)(y+1)

that equals y^2 + y + 2y + 2 rh?

the next part is giving us overall 2y^2-y = y^2+y+2y+2

[halcyon hound]

whats rh

[dusky pond]

right*

[halcyon hound]

ah

yes

simplify it?

[dusky pond]

2y^2 - y = y^2 +3y + 2

[halcyon hound]

yes

what do we do next tho?

[dusky pond]

set it to 0, i take away y^2 from 2y^2 to give us overall y^2, i then take away 3y from -y to give us -4y and then because you moved the positive two from the right and you need to move it to the left it changes sign so it becomes -2

tada

i showed that y^2 -4y -2 = 0

[halcyon hound]

perfect

do u know how to solve it

[dusky pond]

i use the quadraitc formuala, i alr did it

now this question

its similair to the triangle you drew

[gray condor]

I’m glad I could help

[dusky pond]

da fuck where did u come from

[gray condor]

apologies

which question do you need help with

[zinc pagoda]

?

[dusky pond]

the picture i sent

[gray condor]

which part

[dusky pond]

Q6) a) i)

[gray condor]

area = 0.5 x base x height

what’s the base of the triangke

and height

[dusky pond]

i need to show that x^2 + 5x - 36 = 0

[gray condor]

yeah

[dusky pond]

yea

[gray condor]

that’s your formula

[cunning lance]

use pq formula

oh

[gray condor]

huh

[dusky pond]

pq formula?

[cunning lance]

yes?

x^2 + 5x - 36 = 0

to solve this

[gray condor]

ignore them,

[dusky pond]

@halcyon hound you were good

[cunning lance]

x=-p/2+-sqrt (p/2)^2-q

[gray condor]

no, not what we’re tryna do

brooo

wrong question

[dusky pond]

what

[gray condor]

ignore them

[dusky pond]

i just needa show how to get to x^2+5x-36=0

[cunning lance]

oh sorry my bad

i didnt read teh question

[gray condor]

base = (x+6) +(x+2)

yes?

[dusky pond]

yes.

[gray condor]

what’s the height ?

[dusky pond]

(x+1)

[gray condor]

and add these please

[halcyon hound]

👍

[dusky pond]

2x + 8?

ty bro ^^^

[gray condor]

what’s half x base x height

[dusky pond]

(x + 8)(x+1)?

[gray condor]

no?

[dusky pond]

fuck

then what

[gray condor]

what’s base x height?

[dusky pond]

2x + 8 = the base rh?

[gray condor]

yep

what’s half of that

[dusky pond]

x + 4

[gray condor]

yep

now that times height

= area

simple as that

[cunning lance]

rylo can i ask you smth real quick?

[dusky pond]

sooo dont i multiply it by (x+1)

[gray condor]

expand the brackets

[gray condor]

yes you do

[dusky pond]

i said that here tho

[gray condor]

sure, maybe dm

[dusky pond]

no

fuck

i didnt

[cunning lance]

ok np

[gray condor]

ye, that’s what you missed

[dusky pond]

ok

now

i did that

i got

x^2 + 5x + 4 = 0

[gray condor]

no

= area

40

[dusky pond]

ah

fuckj

you are right

then i take away 40 from 4

to = -36

then its complete

[gray condor]

yep

[dusky pond]

eyyy tysm bro

[gray condor]

no worries man

happy to help

now factorise to solve

[dusky pond]

yes I will

I love this community sm

[gray condor]

It’s beautiful ey?

[dusky pond]

ye

i got x = 4 and x = -9

so i was looking at the lengths right

and i had to calculate lngth BC

so i did the pyuthagorean theorm

(x+1)^2 + (x+2)^2 = BC^2

[cunning lance]

is it
x^2+5x-36=0
?

[dusky pond]

= 2x^2 +6x +5 = BC^2

now i dont know tf to do

[cunning lance]

divide by 2

so you can have 1 infront of x^2

[dusky pond]

divide it?

[cunning lance]

yeah i think so

or

actuallyu

[dusky pond]

that sounds un logical

[cunning lance]

I don't even know what's going on

tryna find the length of a triangle side?

[dusky pond]

yeye

scroll up to find the paper

[cunning lance]

oki

[dusky pond]

lmk when you know what to do lol

@cunning lance

[cunning lance]

tbh im stumped

[dusky pond]

thats fair

@gray condor

@halcyon hound

@gray condor
@halcyon hound

<@&286206848099549185>

[halcyon hound]

yes?

whats the question

[dusky pond]

this

so basiically

[gray condor]

hello

[dusky pond]

i need to find the side length BC

and i used the pythagoream theorm

but then

i got lost

at the point where it is

2x^2 +6x+5 = BC^2

[gray condor]

yep

x=4

x can’t be negative for the triangle

[dusky pond]

(its a different problem i am talking about)

OH

WAIT

[gray condor]

because it’s a side

[dusky pond]

am i supposed to subsitute

[gray condor]

yeah

[dusky pond]

omfg

dude

sdbfHDSf

ty

[cunning lance]

hahahHHAAH

[dusky pond]

gimme a min imma try it again

[gray condor]

no worries man

[cunning lance]

same same

i feel you

[dusky pond]

holy shit

i feel so dumb

ok one sec

[cunning lance]

waht grade u in?

[dusky pond]

3...rd?

[gray condor]

lmaoo

[dusky pond]

idk im in an english school

[gray condor]

Same lad

[dusky pond]

eyyy lets go bro

[gray condor]

Which year

[cunning lance]

sick

[dusky pond]

10

i sub x in for 15

[gray condor]

15?

[dusky pond]

yea

lookj

no

i sub it for 4

[gray condor]

x = 4, yes

[dusky pond]

i was looking at the wrong page

yes ok

[gray condor]

I finished my math, further maths and stats gcse by the end of y10 lol

[dusky pond]

holy talito

ur a smart dude

wait

so

you ahve done calculus right

im like vaguely into that stuff, would you wanna like gimme some lessons?

[gray condor]

Yeah, I wish. I screwed my MAT so oxford nae naed me

[dusky pond]

just some basic fun stuff

[gray condor]

sure

[dusky pond]

wot?

[dusky pond]

i love you (no homo

wait but first i needa finish this hw lol

[gray condor]

tl maths is a good place for reference

[dusky pond]

mk ill check it out

[gray condor]

yeah, no worries

[dusky pond]

so i got

117 = bc^=2

[cunning lance]

funny i sucked at math and now i can do so much shit im so much better

i have definitely a lot to learn but i am so so much better

[dusky pond]

how old r u

[cunning lance]

im in uhh

idk how it works in other countries but

I'm in year 11?

like

grade 11

[cedar kiln]

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[dim terrace]

i don't really understand what this means exactly

[cedar kiln]

@dim terrace Has your question been resolved?

[covert raptor]

@dim terrace do you know what row operation is

[dim terrace]

ye

[covert raptor]

ok, so you also know what determinant is?

[dim terrace]

yeah

honestly i think i'm just super tired which is why i'm not getting it

[covert raptor]

hh, I think this sentence is simply saying that when you do row operations to a matrix, the determinant will remains the same

[dim terrace]

alri yeah ty

[cedar kiln]

@dim terrace Has your question been resolved?

[cedar kiln]

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[clear grail]

can someone please help me solve this

[celest ledge]

It told you directly

Separate it

1/(x^2+1/81) dx=1dt

[cedar kiln]

@clear grail Has your question been resolved?

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[real bone]

I can't find any other critical numbers

0 and the end points

But I tried putting in 4 and it doesn't work and 0 isn't in the interval

[river sparrow]

help

[ocean viper]

Is that the derivative?

[real bone]

Yes

[ocean viper]

,w d/dx (x-2)(x-5)^3

[wraith dagger]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by pepper#3419

[real bone]

Hmm

[ocean viper]

Uhhhhhh

[real bone]

Yea that's pretty far off

Surprised the is no + sign

Product rule

[real bone]

Any could you actually walk me through taking that derivative?

[modern compass]

they heavily simplified it

[cedar kiln]

@real bone Has your question been resolved?

[real bone]

Can someone walk me through taking this derivative?

<@&286206848099549185>

[ocean viper]

You can directly use product rule and chain rule.

[real bone]

Hmm

But I did that

[ocean viper]

,w (d/dx) x-2

[wraith dagger]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by pepper#3419

[ocean viper]

Does not look like it

More specifically

I don't think you are applying the formula properly at all

[cedar kiln]

@real bone Has your question been resolved?

[cedar kiln]

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[pastel swift]

how would i do number 2?

[dusty hazel]

You mean b?

[pastel swift]

ya

[dusty hazel]

which quadrant is csc negative in?

[pastel swift]

its the same as sine right?

ik quadrant 2

is negative

and quadrant 1

1 and 2

[dusty hazel]

Nope that's when it's positive.

[pastel swift]

oh

[dusty hazel]

👁️

[pastel swift]

idk which ones its in then

im dog at trig

3 and 4

[dusty hazel]

That would be correct.

So can you write third quadrant as $(\pi + \theta)$ ?

[wraith dagger]

What the hell am I doing here?

[dusty hazel]

Where theta is of course less than or equal to π/2

[pastel swift]

id assusme so

its in 3rd quadrant

[dusty hazel]

Yes it is.

Now when is csc √2

?

[pastel swift]

wha

idk waht that means

[dusty hazel]

I mean

Do you know this,

$csc(x) = \sqrt{2}$

[wraith dagger]

What the hell am I doing here?

[dusty hazel]

0≤x≤π/2

[pastel swift]

soo its in quadrant 1?

[dusty hazel]

This x is, it's an example.

What does x equal to?

[pastel swift]

imma be honest i don't know

we just started trig

only thing we learned is unit circle

[dusty hazel]

I see that's fine,

$sin(\frac{\pi}{4})$

[wraith dagger]

What the hell am I doing here?

[dusty hazel]

Do you know this?

[pastel swift]

sin of 45 degrees?

0.707

[dusty hazel]

You are allowed to use calculator for this question?

[pastel swift]

ya

i got 0.707106

[dusty hazel]

That explains a lot to me now.

Just put

$$csc^{-1}(\sqrt{2})$$

[wraith dagger]

What the hell am I doing here?

[dusty hazel]

On your calculator.

You should be done.

I thought you had to do this, without a calculator lol.

So I was suggesting,

That you do this,

$$csc(\pi + \theta) = -\sqrt{2}$$
$$csc(\frac{3\pi}{2} + \theta) = -\sqrt{2}$$
$$csc(3\pi + \theta) = -\sqrt{2}$$
$$csc(\frac{7\pi}{2} + \theta) = -\sqrt{2}$$

[wraith dagger]

What the hell am I doing here?

[dusty hazel]

But now don't do all this shit. Just use calculator.

[pastel swift]

same i thought you had to do it manually lol

its so much easier now

ty

[dusty hazel]

You can do it manually too.

[pastel swift]

calculator superiority

.close

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[clear chasm]

Help on Number 16

[clear chasm]

I have they are independent because a linear combination of these 3 vectors requires your 3 constants, say a, b, c to all be 0

thus satisfying linear independence by definition

My TA says they are not linearly independent idk whats wrong

[dire geode]

don't make ppl dl files to help you. just screenshot and share

[clear chasm]

sry about that

[celest ledge]

You just check whether det(A)=0 where

[dire geode]

,rotate

[modern compass]

you made it worse lol

[celest ledge]

$A=\begin{pmatrix}1&2&3\1&-1&6\1&1&4\end{pmatrix}$

[wraith dagger]

Cogwheels of the mind

[celest ledge]

Generally you want to check whether some matrices are linear independent, it’s the same as checking whether their corresponding column vectors are linear independent

Where the corresponding column vector of a matrix I mean write all columns as one big column

[clear chasm]

so i can write matrices as vectors?
A(a11, a12)
a21, a22 = [a11, a12, a21, a22]?

[celest ledge]

Yeah

Row/ column it doesn’t matter

[clear chasm]

yeah yeah

i just didnt know i could use the det for linear independence on matrices

kk thx

[celest ledge]

Np

[cedar kiln]

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[ruby quiver]

How to solve this in elimination method

Linear equations

Wait so what is x and y?

Wait so did you use the cross multiplication method?

The answer in the book says x=1 and y=1 but is it what you get

[cedar kiln]

@ruby quiver Has your question been resolved?

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[crimson sedge]

A quadrilateral is drawn into a half circle, one edge is the bottom of the half xircle and the other 2 edges tangent the circles circumference, can you help me find the angle v?

[crimson sedge]

Nvm

!done

!close

.close

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[modern compass]

what have you tried?

[charred sand]

nothing idk how to begin

[modern compass]

take log_5 of both sides

[charred sand]

why 5?

[celest ledge]

Why not 5

[charred sand]

so it could be anything?

[celest ledge]

You question asks you to find log_5(q) so why not 5

[charred sand]

ok

got it 2/p

thx

.close

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[covert aspen]

Are both events exhaustive if they add up to 1?

[exotic furnace]

They must be mutually exclusive too

But yes

[covert aspen]

Thanks

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[quartz vale]

How do I find the range of $\frac{a - b\sqrt{1 - \cos^{2}{\theta}}}{\cos{\theta}}$

[wraith dagger]

kinglacto

[quartz vale]

a > b btw

[exotic furnace]

First, find a way to get rid of that square root

[quartz vale]

umm

it was never there

it was sin(theta)

is that actually easier?

can anyone also, possibly, link a source where I can learn how to find the range of such functions with trig ratios?
so far, from what I've gathered from my textbook (from solved examples):

1. get the whole expression to be expressed in terms of just 1 trig ratio that occurs just once (post which it is easy)
2. or in terms of 2 inverse ratios (which i also kinda understand the reasoning behind from my previous studies on inequalities)

In this case, I am unable to do either

[quartz vale]

<@&286206848099549185> sorry for the second ping

[quartz vale]

ig that changes the graph in any case I still want to find the range of the function in the image

.close

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

aan someone explain me what percentages are?

[misty yew]

yes

how large part out of hundred, per cent

[regal sandal]

I find it hard to cconnnect

[misty yew]

if you have 32%

[regal sandal]

the fraction and decimal part

[merry tulip]

In order to really understand percentages, you'll have to understand normalisation and sampling

[misty yew]

you have 32 out of 100

[merry tulip]

^

But that only applies if you have 100 things

So you have to adjust it first if you're dealing with numbers.

[regal sandal]

ye i know that

its like you ccut it in 100

aand you take a part of it

but like

1/100 = 0.01

[merry tulip]

It's if you took 100 things and found 32 of those things that fit a further description.

[merry tulip]

Yup. That's 1%

[regal sandal]

they say its bot 1 hundreth's

[merry tulip]

That's the same

[regal sandal]

idk i hae the feeling I dont understand a thinng

[merry tulip]

You're comparing a fraction with a decimal number, and they both have the same value in this case

[regal sandal]

but dont know what

decimal number and fraction always do no?

[merry tulip]

Not sure what you're trying to ask

[regal sandal]

they always have the same vvvalue no?

[merry tulip]

You should gain some familiarity with decimals, fractions and ratios though

[regal sandal]

a fraction and its deimal number

[merry tulip]

Well yeah. A better way to organise this in your mind might be as follows:

We name the same numbers using different naming systems.

[regal sandal]

yes

and to get from the one to another we use divvvision?

for example

[merry tulip]

A half of something equals 50% of something, 0.5 times something, 0.5 of something, 1/2 of something...

[regal sandal]

you have 1/3

you want to know its deimal, number

you divide 1 by 3

[merry tulip]

Kinda. You're getting warm.

[regal sandal]

i'm already in college dont know why im asking these question tbh

and why these question ccome up in my head

[merry tulip]

Fractions to percentages can get pretty tricky, especially when you're using a weird base (e.g. prime number base)

[regal sandal]

what do you mean by that?

[merry tulip]

Some fractions have limitlessly-long decimal numbers.

[regal sandal]

that its not as easy as it seems?

[merry tulip]

Yeah. It's difficult.

1/3 = 0.33333333333...

You can't actually write 1/3 in base 10 the normal way!

[regal sandal]

so I dont have to blame mysel I ask these questions

I always learnt to work with it etc.

but nevver thought of it

[merry tulip]

It depends on whether you're expected to know the details or not.

If not, then you shouldn't blame yourself for not learning it.

[regal sandal]

i'm in economics

[merry tulip]

And it's good that you're going out of your way to learn about naming systems

[regal sandal]

1st year college

[merry tulip]

Ah. Then you really need to know these naming systems for numbers!

[regal sandal]

well I need perccentages alot

and I can work with it

like I have good grades etc

what do yoou mean by naming systems

N,Z,Q,R?

[merry tulip]

Okay. Not sure why you wouldn't have learned about these naming systems in any more detail than me given your field of study, but maybe you need a reminder or nobody taught you properly

[merry tulip]

Not those. Those are a different kind of number system

I'm rusty on the nomenclature myself!

[regal sandal]

what do you mean by naming systems

[merry tulip]

I just mean the names that we give to numbers which equal each other

Maybe I should use the term representations

[regal sandal]

ye better

[merry tulip]

e.g. decimal representation, fractional representation

[regal sandal]

ok I get it

[merry tulip]

They all have their different specific uses

Decimal's good for expressing magnitudes relative to a set unit value (1)

[regal sandal]

yes

[merry tulip]

No, wait, I'm thinking of place values

[regal sandal]

you helped me further

ty

[merry tulip]

https://en.wikipedia.org/wiki/Positional_notation

Using positional notation, we call a standard value '1' and then define a bunch of other numbers with special properties and digits which we operate on with certain rules. You know how decimal numbers (base 10) work.

[regal sandal]

ok yes

[merry tulip]

Using percentages, we normalise our calculations so that we're comparing numbers to 100 parts of a unit.

'how many hundredths of a unit does this take...'

[regal sandal]

yes i get this

[merry tulip]

More generally we have ratios. With that, we can split the unit into any real number of parts we want

[regal sandal]

then you talk about fractions right?

[merry tulip]

Yeah. Fractions are very similar to ratios

[regal sandal]

but fractions represent a number

ratios don't?

[merry tulip]

https://en.wikipedia.org/wiki/Ratio

[regal sandal]

ratios just show 'how many from a whole'

[merry tulip]

Great, now I'm confused about the terminology too

[regal sandal]

ow sorry

[merry tulip]

It's not your fault!

[regal sandal]

you see

[merry tulip]

I should know this too!

[regal sandal]

its very easy to ovverthink simple ideas like this

[merry tulip]

And it's also easy to take simple ideas for granted

And it's even easier (at least, for me) to assume that other people use terms the way I do

[regal sandal]

hahahaha

but I apprecciate your help

in what fase are you in your life?

[merry tulip]

20s.

[regal sandal]

also in college?

[merry tulip]

Nope. NEET and proud.

[regal sandal]

NEET?

[merry tulip]

Not in Education, Employment or Training

[regal sandal]

what are you doing then?

[merry tulip]

Sitting in front of my computer screen and writing some very angry walls of text.

[regal sandal]

hahahahaha damn

[merry tulip]

Right. I think I understand the difference between what we call 'fractions' and what we call 'ratios' now.

Fractions are just numbers divided by other numbers.

[regal sandal]

alright I'll listen

yes

[merry tulip]

Ratios are more generally comparisons between the proportions of quantities which may or may not have dimensions

Wait shit no

[regal sandal]

a fraction is like another way of writing a decimal number

[merry tulip]

Fractions can also have dimensions

I get it now

Fractions are proportions of a whole sample

And ratios are comparisons between any two parts of a sample

[regal sandal]

ok i get it

wait

no its ok

I get it

[merry tulip]

https://en.wikipedia.org/wiki/Fraction Thank fuck for Wikipedia sometimes!

When you have a whole number in the denominator, fractions represent a number of equally-sized parts of something which has a unit size

A completely-reduced fraction will have a whole number in its denominator, and you can convert any fraction into a reduced fraction!

[regal sandal]

ok I get it

its just weird

that you can say

no nvm

its ok

[merry tulip]

Ratios on the other hand are just comparisons between the sizes of numbers with which we could describe two or more quantities

e.g. 2:3:5 is a ratio

[regal sandal]

I get it

thank you for the help!

I appreciate it

.cclose

.close

[cedar kiln]

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[thin roost]

Hi again

[thin roost]

So

The question us

*is

Find the equation of a straight line whose portion intercepted is bisected at (2,3)

[paper star]

Is that all the question has?

[thin roost]

Well ye

<@&286206848099549185>

Can someone pls help me

🧐

[misty yew]

ur trying to get a kx+m equation that passes through the coordinates (2,3) or have i misunderstood the question?

how do you bisect a straight line

[thin roost]

No

[thin roost]

I'm tryin' get the x/a + y/b = 1

Equation

[misty yew]

ohh

[thin roost]

I found a solution

But

But

I don't understand

Let me share it

[misty yew]

sure!

[thin roost]

The question of this solution is

Find the equation of a straight line whose portion intercepted is bisected at (3,-2)

[misty yew]

2x-24 = 3y? then 2/3x - 24/3 = y?

so y = 0.6666x - 8

equation for straight line is y = kx+m, atleast from what ive learned

[thin roost]

Ok ok

Isn't that slope-intercept

[misty yew]

if 2x - 3y = 24, then y = 0.6666x - 8

or what do you mean

[thin roost]

Huh

Bruh

What the

[misty yew]

but to do equation for the line you write the expression for y

and you got this 2x - 3y = 24

[thin roost]

Ye

[misty yew]

then transform this to have Y on left side and X onright side no?

i might be completely lost

i trust ur calculations tho

[thin roost]

Bruh

You're talking about y = mx + c {in ur case kx + m} is a slope-intercept

My books says that

[misty yew]

you did these calculations to find the expression in which the "y = mx + c" intercepted the point you looked for

[thin roost]

I ain't here for slope dude I'm here for the x-intercept and y-intercept

[misty yew]

question states find expression for the straight line

Find the equation of a straight line whose portion intercepted is bisected at (2,3)

[thin roost]

Ye

[misty yew]

"find the equation of a straight line"

[thin roost]

Ye

The question isn't asking "find the equation for slope"

[misty yew]

man i should have paid attention during my english classes lol

[thin roost]

Wtf

How's this related to inglish class

Anyways

Oh

F

I got it

So the formula for midpoint js

Is

$x_1 + x_2 \over 2$

[wraith dagger]

BASU

[thin roost]

Then

$\frac{a}{2} = 2$

[wraith dagger]

BASU

[thin roost]

And do the math and I get it

F

[misty yew]

ez

gj

[thin roost]

Man you made me confused

[misty yew]

man im confused

XD

[thin roost]

Ok

Ye

See ya

Bye

.close

[cedar kiln]

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[cedar kiln]

@crimson sedge Has your question been resolved?

[still barn]

What operator is the langle rangle?

left angled bracket right angled bracket

Those are often called langle rangle

What is the definition

[cedar kiln]

@crimson sedge Has your question been resolved?

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[sour glacier]

This is what I’ve tried to answer for question (a). Is this right or makes sense to anyone? It feels wrong to me

Thank you

[coarse wedge]

Can anyone tell me how many unique solution set does this equation ( 2x^2+2y^2+3z^2=7) has?

[sour glacier]

💀😅

[gleaming jasper]

is this channel already used?

its still on the available section

[stoic quarry]

the bot seems to be broken

[sour glacier]

That’s very weird

[sour glacier]

2 I think

[coarse wedge]

Can you explain?

[sour glacier]

Yes

Subtract 2y^2 and 3z^2 from both sides to isolate x2. You’ll get 2x^2 = 7 blah blah

Then divide by 2 on both sides

Simplify and you get x^2= (7-2y^2 - 3z^2)/2

Solutions are x = square root of what I just told you.

Other one is x = - square root of the equation I just mentioned

Not a math helper but that’s what I was taught idk take it with a grain of salt I guess

[gentle yacht]

Using the PEMDAS rules, and one parathethes, how can you make the following equation So far, I haven't found the answer, and all I am doing so far is literally guessing by placing the parantheses somewhere. Is there a better way of doing this?

The " : " signs are division signs

[livid hound]

i suppose you could try consider the values of
3 * 8
8/2
4 * 5

[cedar kiln]

@gentle yacht Has your question been resolved?

[paper star]

Alright so PEMDAS

You see that Multiplication and Division has higher priority then Addition and Subtraction

You do Multiplication and Division first

[gentle yacht]

Yeah, if you look at the equation and solve it using only PEMDAS, you will get that 40=0, something which is not that cool

[paper star]

So calculate the values of 38, 8/2, 45 first

OH WAIT

I read the question wrong

I gotchu

[gentle yacht]

That's why the question is telling us that we can use only one bracket sign to solve the equation, which is ()

[paper star]

Alright so I got the answer

But I want you to understand the process

[gentle yacht]

Yeah, I would love to hear how you've done it

[paper star]

For something to be equal to zero,

There should be two equal values canceling each other

So as an example

3 - 3 would be 0

So the focus point here is the Subtraction sign

[gentle yacht]

All right,

[paper star]

Now what's 3*8?

[gentle yacht]

24

[paper star]

(We calculate that first since it is in front of the subtraction sign, thus being the positive number in the equation)

So if we look at 3 - 3 = 0

24 would be corresponding to 3

So 24 - X = 0

[gentle yacht]

x = 24

[paper star]

Since we need to use a parenthesis, the only one that would make sense is putting it on (8/2 + 4*5)

So 24 - (4+20)

And that gets you zero

[gentle yacht]

Lovely, you've explained that pretty well, thanks!
I see that this may only apply if the side is 0
However, in what if there's an equation where one of the sides is equal to for example 32?

[paper star]

Alright

Do you know that if you move the number to the other side of the equality sign, it gets a minus sign?

[gentle yacht]

Yeah,

[paper star]

Same thing here

Move 32 to the other side

Calculate every Multiplication and Divisions

And then look at the problem again

[gentle yacht]

you're a genius

[paper star]

Ehhh

[gentle yacht]

I'll give your method a try and inform you about the results

[paper star]

Ping me when you do :)

[gentle yacht]

yeah, it doesn't really require that much common sense to get this, it was perhaps just me who wasn't really noticing this trick

[paper star]

Ehhh

[paper star]

Did you get it?

[gentle yacht]

ehhhhhhhhhhhhhhhhhhhh, yeahhhhhhhhhhh, the problem was perhaps a bit too difficult for me
I've made the equation from the picture I've sent you
to:
3*8 - 8 : 2 + 4 * 5 - 32 = 0

which i've made into

24 - 8 : 2 + 4 * 5 - 32 = 0
Now, I am trying to make the numbers on the right side of the equation equal to 24, but it really doesn't seem like it's easy nor possible, considering that we've added the -32

Have you managed to solve the problem?

[paper star]

Sorry for late reply

So what I meant

Is to make it to this

24 - 4 + 20 - 32 = 0

Now try to work it out with that

[gentle yacht]

i am very unsure on whether that's possible or not...

[cedar kiln]

@gentle yacht Has your question been resolved?

[cedar kiln]

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[vital pier]

hi does any one mind helping me?

[vital pier]

so basically there is a ball going up at 7m/s with a weight of 0.2 kg

i need to find the height of the ball when it has a velocity of 3m/s

how would i do this?

[torn hare]

was the ball thrown or is just gravity acting on the ball?

[vital pier]

ball was thrown

i know i need to use gravitational energy formula but im not sure what is the energy at 3m/s

[balmy apex]

you're better off asking this on a physics server

[vital pier]

oh opps

[cedar kiln]

@vital pier Has your question been resolved?

[sick ruin]

#old-network

[cedar kiln]

@vital pier Has your question been resolved?

[ember python]

Eh I mean it’s mechanics it’s reasonable

Probably physics is a bit more suited thougj

though*

[ember python]

Anyway if you’re still stuck find initial KE, KE at the point you want, and deduce GPE

Not the only method, could also use suvat

[cedar kiln]

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[cedar kiln]

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[buoyant perch]

what uses does this have over a parametrised line r = a + tb

[cedar kiln]

@buoyant perch Has your question been resolved?

[cedar kiln]

@buoyant perch Has your question been resolved?

[cedar kiln]

@buoyant perch Has your question been resolved?

[short magnet]

Is the x a dot product!?

[jaunty mural]

cross product?

[short magnet]

Probably, but then it defined a parallel line ?_?

[short magnet]

I mean, it should define some plane then, no?

[jaunty mural]

There's no way that is a dot product

read the equation.

That 0 is the vector 0 as well.

No one would use a cross to denote the dot product.

[short magnet]

Okay lol I got confused, I never described a line like that

[sick ruin]

Like, what’s the point?

[cedar kiln]

@buoyant perch Has your question been resolved?

[cedar kiln]

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[ruby quiver]

On selling a tea set at 5% loss and a lemon set for 15% gain, a crockery seller gains $7. If he sells the tea at 5% gain and the lemon set at 10% gain, he gains $13. Find the actual price of each tea set and lemon set. HELP ME WITH THIS I AM CONFUSED

[shut panther]

what have you tried

[ruby quiver]

I am confused and have only written all the info given in the notebook

[shut panther]

ok
do you know how to set up a system of equations

[ruby quiver]

no how is it done?

[shut panther]

youve got the net profit/loss percents from each item
and the total profit from both
so you can have the actual prices as variables
since you have two examples, you can solve for both variables using both equations together

[ruby quiver]

can you pls show me a first few steps

we only have percents and how both percents give us the amount gained or loss

so how do we solve for tea set and lemon set?

[shut panther]

$$\begin{cases}
-0.05t+0.15l = 7 \
0.05t+0.1l = 13\
\end{cases}$$

[ruby quiver]

do we equate both equations?

[wraith dagger]

Dogecode

[shut panther]

see if you can do anything with that

[ruby quiver]

wait you converted it into decimal format

the percent right

[shut panther]

yeah

do you understand how that works

[ruby quiver]

now I solve for t and l?

[shut panther]

ye

[ruby quiver]

why does the first equation have a negative sign before -0.05t

is it because it is loss?

[shut panther]

I would probably multiply both equations by 100
if you dont want to deal with decimals

you can do that as long as you do it to both sides on each

[shut panther]

yes

[ruby quiver]

ok

now we use the elimination method or the substitution method

[shut panther]

ye
elimination looks like a good candidate here

[ruby quiver]

ok thank you so much

[shut panther]

np

[ruby quiver]

how do I close this

.close

[cedar kiln]

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[little wolf]

How to convert $-1+i$ to $r\times e^{i\theta}$

[wraith dagger]

MoneyMaker

MoneyMaker

[cedar kiln]

@little wolf Has your question been resolved?

[dusty hazel]

$cos(\theta) = -sin(\theta)$

[wraith dagger]

What the hell am I doing here?

[little wolf]

Hmmm?

[dusty hazel]

We have the real part (-1) and imaginary +1.
Their magnitude is same.

So,

[dusty hazel]

...

[little wolf]

Oh

For sin and cos to have the same value

theta should be

[dusty hazel]

?

[little wolf]

sqrt2 / 2

[dusty hazel]

Correct.

But then,

$Cos(\theta)$ should be negative.\
$sin(\theta)$ should be positive.

[little wolf]

pi/4

[wraith dagger]

What the hell am I doing here?

[unique estuary]

2nd and 4th quadrant right

[dusty hazel]

Only second.

In fourth cos is positive.

We need negative cos and positive sin.

[little wolf]

Second quadrant? then...

[dusty hazel]

Yes.

[little wolf]

But what does it have to do with e

[dusty hazel]

$e^{i\theta} = cos(\theta) + isin(\theta)$

[wraith dagger]

What the hell am I doing here?

[dusty hazel]

Have you seen this?

[little wolf]

Since its second quadrant therefore 3/4 pi?

[dusty hazel]

Correct.

[little wolf]

No, never

Is this some kind of formula?

[dusty hazel]

It is.

I suggest.

Watch video proofs for this.

[little wolf]

Oh cool, another formula i need to memorise

[dusty hazel]

Mate,

How old are you?

[little wolf]

The book doesn't have proofing tho

[dusty hazel]

Yes, I told check videos. You could search Euler's formula proofs and all. You'll get something I suppose.

[little wolf]

Ill just watch some vids online

[little wolf]

Noted

[dusty hazel]

Yes.

Besides what grade is this question for?

I thought you knew the formula that is why it's given.

[little wolf]

12

I am cramming the chapters, might've missed it my bad

[dusty hazel]

Not really. I don't really know if it's there or not.

In any case, theta is 3π/4 then you can figure r out I suppose.

$r cos(\theta) = -1$

[wraith dagger]

What the hell am I doing here?

[little wolf]

Hmmm therefore r would be sqrt 2

[dusty hazel]

It would be, correct.

[little wolf]

Interesting, ok then

I will be watching some euler proofs then

Thanks

.close

[cedar kiln]

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[warm vector]

I forgot how to do 9 b)

[cedar kiln]

@warm vector Has your question been resolved?

[tropic oxide]

try to imagine folding up the circular sector into a cone

and think about what part of the sector becomes the cone base

[warm vector]

I imaged it and the 8cm is the slant height of the cone

And the circumference becomes the cone’s base

[quartz vale]

you mean slant length of the cone?

[warm vector]

Yh sorry

So now what do I do?

[quartz vale]

you have the values

[warm vector]

I’m still lost

[unique estuary]

did you get 9a

the answer to 9a is equal to 2πr @warm vector

so solve for r

[warm vector]

Yh

Do I do 2 pi r =8 ?

And solve for r?

[unique estuary]

if the circumference is 8 then ya

[warm vector]

But 8 is the slant height of the cone so no

[tropic oxide]

well then find the circumference

find the length of that arc

[warm vector]

Wait find the circumference or length of arc?

So I found the length of the arc and set it equal to 2 x pi x r

But I don’t understand how that gave us the radius

And why did we set the ‘circumference’ equal to the arc length?

[azure cosmos]

Circumference is arc length

When calculating arc length you use the formula for calculating the circumference

[unique estuary]

@warm vector

[warm vector]

Ok I see

But don’t I find the circumference of this sector and set that value equal to 2 pi r?

[tropic oxide]

you want the perimeter of the entire sector?

or what

@warm vector do i understand correctly that you think the circumference of the base should equal the entire perimeter of the sector, and not just its arc?

[warm vector]

I’m saying that why we set the arc length to the circumference

I get that we can solve for r here

But why did we set it equal to the arc length

[tropic oxide]

the sector that we glue into the cone has three sides

two straight sides equal to the slant height

and one curved side

the straight sides are glued together

the curved side becomes the circumference of the base

what part of this is unclear to you?

[warm vector]

How does setting the arc length which is 30.16 equal to the circumference give us the radius. Like why not the circumference of the circle?

[tropic oxide]

????