help-23

[brave wolf]

the solid looks like this

so the vertical slices arent even disks, you cant use the disk method like you did originally

you could use shell method though, if you know it

[summer lark]

You mean washer or the cylindrical?

[brave wolf]

cylindrical shells

[summer lark]

Yess

[safe radish]

@summer lark Has your question been resolved?

[safe radish]

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[safe radish]

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[lapis seal]

Chat what topics do u think will be on gcse's im going to priortise revising them

[lapis seal]

(I do foundation)

[karmic merlin]

Maybe look at tests from a year or two ago

[lapis seal]

Maybe but its not always accurate

Plus

Its less likely they'll ask more of repeated topics

[summer coral]

ask in #study-discussion or #math-discussion rather than opening a help channel, this is more for specific math problems

[lapis seal]

Oh. Thanks

.close

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[burnt oyster]

I’m really confused on how to get exponential function equations from graphs that have HA

[burnt oyster]

<@&286206848099549185>

[quiet plume]

!15m

[azure harbor]

!15m

[safe radish]

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.

[safe radish]

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.

[plucky elk]

!15m

[safe radish]

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.

[quiet plume]

Oop

[upper forge]

!15m

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[pine wind]

[warm warren]

!15m

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[burnt oyster]

Oop

[iron badger]

!15m

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[burnt oyster]

Omg

[pine wind]

once is okay😭

[upper forge]

got sniped again 🥀

[azure harbor]

Ah yes !15m dogpiling

[burnt oyster]

I’m scared

[quiet plume]

In any case, what are you confused about?

[pine wind]

what do you mean by HA?

[warm warren]

sorry i didnt see it was already done; as a result @burnt oyster let this be a lesson to not repeat it again

[burnt oyster]

Horizontal atmosphere

[pine wind]

u summoned the helpers

[plucky elk]

<@&268886789983436800> troll

[radiant isle]

dont troll in help channels, especially an occupied one

[pine wind]

what's confusing you exactly?

[burnt oyster]

So basically when there’s a horizontal atmosphere that means there’s a transition and im confused on finding b

[brave wolf]

I think you mean asymptote btw

[burnt oyster]

My teacher said you can use any point but when I do that and look at the answers it doesn’t work

[burnt oyster]

Yea

Ok so for example the asymtope is 1 is I add one to the y values of the current values to to get the new value of the transformation right?

Then with those I get the difference for and that will be the value or b in y=ab^x

[burnt oyster]

Answwrddd

[burnt oyster]

Is anyone able to do 6 with me so I can understand better?

I’m not sure how to get b

[brave wolf]

how did you get 2 = a^4 + 1

[brave wolf]

oh wait you have it here

how did you find out its 2^x

[pine wind]

[burnt oyster]

My teacher was helping me and she said the difference of 2 and -2 is 4

So the x value doubles each time?

[brave wolf]

uh i dont quite understand your work, but its not correct

y = ab^x + 1

until here, it is correct

at this point, I'd focus on finding a

try to look at the point where x = 0

[burnt oyster]

I see 0,5 and 1,3

[brave wolf]

okay and what happens when you plug in 0,5?

[burnt oyster]

Add 1 to the y value

[brave wolf]

well, (0, 5) lies on the curve

so you can just plug it in as y = 5 and x = 0

[brave wolf]

. in this

you dont need to add 1 to the y value

just plug it in as x = 0 and y = 5

[burnt oyster]

Y = ab^0 0+1

[brave wolf]

perfect, just plug in y = 5 too

$5 = a \cdot b^0 + 1$

[flat frigate]

MathIsAlwaysRight

[brave wolf]

like this

do you understand why this is true?

[burnt oyster]

No

[brave wolf]

okay so the curve was described by $y = a\cdot b^x + 1$

[flat frigate]

MathIsAlwaysRight

[brave wolf]

and you know that the point (0, 5) lies on it

[burnt oyster]

Yea

[brave wolf]

when a point lies on a curve, it means that it satisfies the equation

so when we plug in x = 0 and y = 5, the equation will be true

i just replaced x with 0 and y with 5 (So i plugged in the point (0,5))

[burnt oyster]

I see

[brave wolf]

now you can simplify this and solve it

as a hint, notice that b^0 = 1 (thats why we plugged in the point with x = 0 first - itll make b disappear)

ill gtg for a min, so you can solve it in the meantime

[burnt oyster]

Ok

5 = a x 1+1

5=2a

Hmmmm

[brave wolf]

careful with pemdas

5 = a * 1 + 1

multiplication is done first

its not a * (1 + 1)

its (a * 1) + 1

[burnt oyster]

Oh

So is it still 2 tho

[brave wolf]

nope, not really

its not 5 = 2a

what is a * 1?

[burnt oyster]

Still a

[brave wolf]

so its 5 = a + 1

[burnt oyster]

Oh

What do we do next then

[brave wolf]

solve it

can you solve 5 = a + 1?

[burnt oyster]

Isolate the a so subtract 1 on both sides 4=a

[brave wolf]

so a is 4

[burnt oyster]

Yay

[brave wolf]

$y = 4 b^x + 1$

[flat frigate]

MathIsAlwaysRight

[brave wolf]

now we just need to find b

for that you can use the other point

[burnt oyster]

1,3?

[brave wolf]

plug it in and solve

[burnt oyster]

3 = 4b^1 + 1

3 = 4b +1

2 = 4b

2 over 4

[brave wolf]

which is 1/2

[burnt oyster]

Omgggg thank you that’s why the answer sheet says

I get it now

[brave wolf]

$y = 4\cdot \left(\frac{1}{2}\right)^x + 1$

[flat frigate]

MathIsAlwaysRight

[brave wolf]

np

[burnt oyster]

So I ca use this formula

[brave wolf]

generally the procedure is to first find the horizontal asymptote

in this case it was 1, so thats why the +1

[burnt oyster]

Can the point be interchangeable or for a should it always be 0 and another number

[brave wolf]

0 is definitely easiest

because it makes b^0 dissappear into 1

if we tried sth else, then b would still be there

and we would have a and b in one equation

which is quite difficult to solve

[burnt oyster]

I see

[brave wolf]

1. find HA
2. find a, by plugging in the 0 point
3. find b, by plugging in any other point

[burnt oyster]

Thanks I’ll definitely use this for my practice

[brave wolf]

np

[burnt oyster]

Wait what’s the normal equation without the numbers

@brave wolf sorryyy

[safe radish]

@burnt oyster Has your question been resolved?

[brave wolf]

y = ab^x + c

sorry i was offline

c is the horizontal asymptote

[safe radish]

@burnt oyster Has your question been resolved?

[burnt oyster]

Nope

Now I’m confused with when drawing the inc and Dec graph because inc and Dec goes different ways I know I answered but it’s because I looked at the answer sheet

How can I know which way is it decreasing or increasing

I found this what do they mean by slope?

[safe radish]

Channel closed

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[burnt oyster]

.reopen

[safe radish]

✅ Original question: #help-23 message

[burnt oyster]

I should know these stuff it in elementary school I didn’t put much attention to math until my grade matters like in highschool so I’m tryna be better

[boreal mesa]

Basically, if the base that has the x on the exponent is smaller than 1 and bigger than 0, for example, (1/2)^x, the curve decreases. If it's bigger then 1, the curve increases

[boreal mesa]

For example, 2^x will look like the first function, and (1/2)^x will look like the second one

The reason it's because raising a number between 0 and 1 to an exponent bigger then 1 will make the number smaller as in 0.5^2=0.25

So as x increases the value of f Will keep decreasing

Hope you understood

[burnt oyster]

But like right to left and left to right how do we know

[burnt oyster]

I kinda do thanks

Tbh I don’t lol

I’ll try and find a video I guess

[boreal mesa]

If 0<the base<1, it will look like this:

[burnt oyster]

It’s just like all 4 of those graphs increased and decreased in different ways how do I know which way to start left or right

[boreal mesa]

Is the base is bigger than 1, it will look like this:

[burnt oyster]

I see

But the other graphs did like left to right and right to left

[burnt oyster]

A and c decrease in different ways

[boreal mesa]

In a), the base is 0.5, in b) the base is 4, however, its multiplied by a negative number (which flips it horizontally), in c) the base is 0.5, but it's also multiplied by a negative number, and in d) the base is 4

[boreal mesa]

Because the base in a is 0.5 and in c is 4

[burnt oyster]

Ohh

[boreal mesa]

If you don't understand I request help from someone else lol

[burnt oyster]

I get it now

[boreal mesa]

Nice then

[burnt oyster]

Thanks

[boreal mesa]

No problem

[burnt oyster]

What about the inc one

Same thing

[boreal mesa]

Which one?

[burnt oyster]

The graphs can inc in different ways because the base is neg or positive ?

[burnt oyster]

D and b

[boreal mesa]

If the number that multiplies the base is negative, the function flips

Like this

[burnt oyster]

I see

[burnt oyster]

Can I also have a model for Dec.. hehe I’m sorry

The model is really helpful

[boreal mesa]

Yes

Like this

[burnt oyster]

Thankssss

[boreal mesa]

You're welcome!

[safe radish]

If you are done with this channel, please mark your problem as solved by typing .close

[burnt oyster]

.close

[safe radish]

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[minor meadow]

Any ideas on how to calculate the area?

[broken pewter]

Cutting out parts like if it was cookie dough would work

[worldly lantern]

by calculus or geometry?

[finite igloo]

😭

[worldly lantern]

-# geometry is easier here tbh

[broken pewter]

Ngl I would make this a calc problem yeah

[minor meadow]

Yeah, I tried to divide it on 4 sections. Something like this. (sorry for the perfect drawings lol)

1 is nothing, so I assume is 0.

2 is a circle, so it's pi . r ^2, and I take 1/4 of it.

3 & 4 are kinda confusing for me idk why

[broken pewter]

"Use calculus to find the area)

[finite igloo]

What

There is a big triangle from 3 and 4

[broken pewter]

So, this is the right idea, wrong execution

[worldly lantern]

-# bleh, thatd take too much time

[minor meadow]

Yeah im stupid

[tropic pelican]

I think two sections is all you need

[broken pewter]

See how the right can be just a single triangle

[minor meadow]

?

[broken pewter]

Nah dw, stuff gets easier when u do it once

[tropic pelican]

cookie cut out of the circle and the triangle

[broken pewter]

The entire thing yes. Fill that in mentally, and the circle. You can find those 2 areas you filled in right? So now you have

Mystery shape area - circle/4 - triangle = solution

Now just find the mystery shape by inverting what you just did, "building" it

[minor meadow]

The whole area is b.h = 4x8 = 32

(4x4)/2 = 8

(4x8)/2 = 16

black area = 32-24 = 8

ye? 😭

[broken pewter]

Hm, close

[minor meadow]

well, the whole area of the section 2

[broken pewter]

So if you wanna keep trying urself don't read this spoiler:

||after filling in the big triangle to the right and the quarter circle, you have a rectangle with a triangle on top. That is the mystery shape||

But feel free to cheat by reading it if you are not into learning more than this/are stuck

[tropic pelican]

you only need the base and height of a triangle to find it's area right

but you actually can find the base

and the height is also labeled

[finite igloo]

Why is this wrong

[tropic pelican]

oh wait I didn't even check yeah the calculation is right

[minor meadow]

I forgot to share my 3 possible answers, all of them include pi so that's why i tried using that way

i don't know where the hell i get 4 pi

[broken pewter]

Circle area?

[stoic torrent]

may i suggest an alt method,
instead of dividing right side of the square as 3 and 4, why not treat it as the triangle in upper side of 4, with sides 4,4,4sqrt(2) and the other big triangle in 3 as a triangle with sides 8,4,4sqrt(5)

then its simple subtraction of areas?

[tropic pelican]

so you found the area of the triangle region but now you can find the area of the circle part

[broken pewter]

Uhh I think its 4^2 * pi for that circle, then divide by 4 to get the quarter

[tropic pelican]

||the simplest way is the triangle has base 4 (from the right) and height 4, so (1/2)(4)(4) = 8||

[stoic torrent]

thats what i js said?

[tropic pelican]

oh you were saying a subtraction of areas?

[stoic torrent]

yeah

[tropic pelican]

the area of the whole triangle is this

[minor meadow]

Yeah, step 2; #help-23 message

pi . r ^2, and I take 1/4 of it. =
pi . 4^2 = pi . 16
pi . 16 / 4 = 4 . pi

none of them has 16 pi

[tropic pelican]

check the radius again

it's not 8

[minor meadow]

[stoic torrent]

-# As in area of big square - quarter circle - quarter sqare - triangle(in part 4)- traingle (in part 3 and 4)

[minor meadow]

wait im stupid^2

yeah its 4

[tropic pelican]

right I'm saying you don't need to do that

[minor meadow]

now 2 of them has 4pi

[tropic pelican]

nw you good

[stoic torrent]

-# its the fastest and most straightforward tho

-# anyways ill not spam js glad op got it resolved

[tropic pelican]

my method is split the whole region down the middle: on the right side the triangle has area 8 because it has base 4, height 4 and the left side is the square - circle as op said. I'm pretty sure that's faster

but whatever works ig it doesn't matter

[minor meadow]

32-8 is 24 - 4pi

[tropic pelican]

yes this is right

[minor meadow]

thanks everyone for the help, i need practice with this lol

.close

[safe radish]

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[cosmic jacinth]

I need help with sketching

[cosmic jacinth]

This is the question

[spiral pewter]

evaluate at 0

evaluate the limits

[cosmic jacinth]

Im genuinely terrible at graphing, do you mind drawing a rough sketch of it all for me?

[spiral pewter]

ok wait 2 mins

[cosmic jacinth]

Thank youu

[spiral pewter]

try to study the variations of f at least

[cosmic jacinth]

Yeah i willl

but do you mind helping me?

[spiral pewter]

there you go

for the variations of f and its graph

dont mind me in the background

basically it's a paranoïa pointing downwards because of the négative coefficient of x²

has 1 max at f(3)=4

[safe radish]

@cosmic jacinth Has your question been resolved?

[safe radish]

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[hoary locust]

kinda weird terminology question. i know there are terms like "dodecahedral" and "tetrahedral" for things related to dodecahedra and tetrahedra. is there a similar term for things to hexagonal tilings?

[plucky elk]

dodecahedra and tetrahedra are polyhedra whereas hexagons are polygons. what are you looking for exactly

[modest ivy]

ur reflection im crine

[modest ivy]

i think having al at the end describes the shape of soemthing else in comparism to the polygon?

[pallid magnet]

i'm not sure i understand ur question

[spiral pewter]

just google it

[hoary locust]

i'm trying to describe something which kinda makes sense if you think of a tiling as a polyhedron with infinite faces, so just saying "hexagonal" wouldn't exactly be what i'm looking for

[hoary locust]

i tried googling it and didn't get anywhere

[modest ivy]

are u talking about inf repeating tiles?

[hoary locust]

yes

[pallid magnet]

there is no regular polyhedral with hexagonal faces

[modest ivy]

hexagonal is the right term then…?

hexagonal tiling…?

Or honeycomb

?

[pallid magnet]

ur talking about a 3d shape made up of regular hexagonal faces?

[modest ivy]

No hes talking about tiles and patterns

p sure the term hes looking for is honeycomb then?

If he doesnt want hexagonal

[hoary locust]

i'm talking about a theoretical infinite volume polyhedron whose faces are hexagonal

[modest ivy]

that doesnt exist dawg

[hoary locust]

yes i know

[modest ivy]

No term then

[spiral pewter]

?

rly

[modest ivy]

That would js be a sphere?

infinitely large

[pallid magnet]

um hexagonal tiling or honeycomb? what it doesn't make sense

this is the name

[modest ivy]

idk

ion do topology

Well sorta

Does geometric topology count

[spiral pewter]

how does that not work

[modest ivy]

yh he wants that but each tile is the face of an infinite polyhedron

[plucky elk]

all polyhedra have finite volume

[modest ivy]

“of inf volume”

[modest ivy]

Fr bro wants an infinitely large sphere atp

[spiral pewter]

okk

so is it tiling .... but in space ?

[pallid magnet]

so um a ball

[hoary locust]

i know it doesn't actually exist

it was a generalization my classmates and i had talked about in my discrete math class years ago and i'm trying to talk to some people about it and saying "hexagonal tiling related" over and over is getting tiring so i was just curious if there was another term that could be used for it

[spiral pewter]

ok

[plucky elk]

if you take out the silly "infinite volume" this could be one polyhedron

[spiral pewter]

hmm cool

[modest ivy]

sphere

[pallid magnet]

basically ball

but um not quite yet

[plucky elk]

stop pinging me thx

[modest ivy]

fah

[spiral pewter]

everyone agreeing it's a ball for some reason

sphere*

[modest ivy]

Yh cus esentially if u have n tiles and u approach infinity u get a sphere

[spiral pewter]

ye ok

you approch it uniformly too

[hoary locust]

.close

[safe radish]

Channel closed

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[safe radish]

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

idk if im just dumb but how do I do 6.25 / 5 without a calculator

[opaque fern]

Plenty of ways

[severe pond]

do you know what 625/5 is

[small sandal]

25^2/5 so 5^4/5 so 5^3 which is 125

[severe pond]

$\frac{6.25}{5} = \frac{625}{5} \cdot \frac{1}{100}$

[warm warren]

multiply numerator and denominator by 2

[flat frigate]

knief

[warm warren]

you can always also do $\frac{6.25}{5} = \frac{6.25\times 2}{5\times 2} = \frac{12.5}{10}$

[flat frigate]

Annie Maqionde

[small sandal]

hmm

i suppose

got another one

[severe pond]

are you asking?

[small sandal]

ye

3456/12

[severe pond]

oh i thought you were asking if we had another method lol

i mean this is both divisible by 4 and 3 so it's divisible by 12

[warm warren]

i mean long division exists, and you can use it?

[small sandal]

i only know how to do it for polynomials 😭

[severe pond]

since 56 is divisible by 4 and 18 is divisible by 3 (3 + 4 + 5 + 6 = 18)

[severe pond]

you can do 3600 - 3456 = 144

[warm warren]

https://math.libretexts.org/Bookshelves/Arithmetic_and_Basic_Math/Basic_Math_(Grade_6)/05%3A_Arithmetic_in_Base_Ten/29%3A_Dividing_Decimals/29.02%3A_Using_Long_Division

[severe pond]

3600 is an easy multiple of 12

144 is as well

which makes 3456 easy to find

[small sandal]

yea 12^2 but idk how you know 3456 is div by 3 and 4 tho

[severe pond]

i just told you

[severe pond]

^

[small sandal]

where did the 56 come from?

[severe pond]

you just need to look at the last two digits

if that number is divisible by 4 then the whole number is

[small sandal]

really?

[severe pond]

yes

because the rest of the digits can be split as a multiple of 100 which is divisible by 4

so any 3 digit plus number is just a multiple of 100 plus whatever number the last two digits make

[small sandal]

so like 3040 is div by 4?

[severe pond]

yes

[small sandal]

thats handy to know

idk if im gonna remember the neat stuff like that tho

[severe pond]

if you understand this then it's trivial

you can make a similar statement for multiples of 8

i'm sure you know about multiples of 2

you just look at the ones digit

this is because we can just take the rest of the digits as a multiple of 10 which is a multiple of 2

do you understand what i mean

[small sandal]

more or less yea

[severe pond]

you don't sound convincing

[small sandal]

no it makes sense

[severe pond]

good

so what digits would we look at to test if a number is divisible by 16?

[small sandal]

4

[severe pond]

you mean the last 4

[small sandal]

oh div by 16

i read that wrong

[severe pond]

🤔

[small sandal]

uh see if the last 2 numbers are div by 16 -> 4^2 or just some multiple of 4

oh nvm since we want to know whether or not 16 not a multiple of 16

not multiple but like words....

[severe pond]

how to check if a number is divisible by 8?

[small sandal]

if the last two digits is div by 8 then the whole number is

idk if that applies for 8 as it does 4 tho

[severe pond]

🤔

you haven't been listening

,calc 316/8

[flat frigate]

Result:

39.5

[severe pond]

so you lied...

[small sandal]

not entirely, the div by 4 makes sense but everything else was just a bit to process

i.e. if you gave me a question i wouldn't really know how to begin

[severe pond]

was divisibility by 2 too hard?

if you understood divisibility by 4 then it should make sense for 2, and then for 8, and so on...

[small sandal]

for 4, if last two digits are div by 4 then the whole number is div by 4. So for 2, its just its some even number and 8 i dont really know

[severe pond]

it's great that you can memorize the rule but you clearly didn't listen to my explanation of where the rule comes from and why it works

because if you did you'd be able to extend it to higher powers of 2

[small sandal]

sorry

[severe pond]

i forgive you

now read it again

and ask questions if necessary

[small sandal]

like it makes sense for 4 and 2. But understanding 8 and thus extending it to higher powers of 2 I am struggling with

like reading it over I assume by extend it we look at the next two numbers?

so for 316

31 isnt div by 8 therefore 316 isnt?

[severe pond]

well for 2 i write the number as a multiple of 10 = 2^1 * 5 plus the ones digit

for 4 i write the number as a multiple of 100 = 4 * 25 plus the remaining tens plus ones digit

do you see where i'm going with this

[small sandal]

so for 8,

we write it as 1000 = 8*(something [i assume 125?])? plus the remaining hundred, tens and ones digits?

[severe pond]

yes

[small sandal]

hmm ok that pattern helped alot

ty

[severe pond]

for simplicity we can start writing the other thing as 5^some power

it doesn't really matter

[small sandal]

so with this information, im still confused with how to continue

[severe pond]

with 3456?

[small sandal]

no with like, showing it is or isnt div by 8

[severe pond]

showing what is

[small sandal]

316

[severe pond]

well it's not divisible by 8

[small sandal]

is that bc 316 is less than the thousand we need?

[severe pond]

here there are only 3 digits so you'd just have to know or find a close enough multiple of 8 and see if the difference is a multiple of 8

[severe pond]

yea it's useful for breaking down 4+ digit numbers

[small sandal]

hmm ok, so something like 714 isnt div by 8

[severe pond]

well yea it's not even divisible by 4

[small sandal]

yea since 14 isnt div by 4

[severe pond]

that's another easy thing to do

[small sandal]

hmm ok, that makes much more sense

ty for the help

[severe pond]

you're welcome

[safe radish]

@small sandal Has your question been resolved?

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[pearl field]

What did i do wrong in 5?

[dusk halo]

what is the actual question?

[pearl field]

Nvm i found it out

@junior smelt

[dusk halo]

<@&268886789983436800>

[pearl field]

Mr beast scammer

[junior smelt]

(Do please ping all of the moderators, just in case I happen to be away and unable to act )

[dusk halo]

also addison if you've solved your problem type .close to close this channel

[astral glacier]

!original please, full context would help

[safe radish]

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.

[austere goblet]

think he's done

[astral glacier]

Oh right

[astral glacier]

.close

[safe radish]

Channel closed

Closed by @astral glacier

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hoary seal]

how do we determine the formula?

[upbeat swan]

Well did your teacher teach you a step by step solution to solving these?

[nimble wyvern]

-# that or just R3= R3-4R1

[upbeat swan]

Cuz technically there is no wrong answer, you can solve it any way you like

[hoary seal]

yeah but it was for a diff question

and they are similiar but not the same

[nimble wyvern]

"the solver is never wrong, it's the question that is wrong"

[upbeat swan]

I mean i assume it was still an augmented matrix

[hoary seal]

so how do I do this

[upbeat swan]

Its the same principle

For every matrix

[hoary seal]

augmented matrix is when the vector aka the constants after the = sign, integrated into the matrix

[upbeat swan]

I mean typically you want to bring the matrix into row-echalon form

Ever heard of that?

[hoary seal]

but is not part of the system of equations

yeah

[upbeat swan]

Yeah so do that

See if it works

You want to create a sort of staircase

Start by eliminating the x1 term of R2

Ohh wait

[quiet plume]

I mean to get the answer in the question you just need to check which row operation was done between the first and second augmented matrix

[upbeat swan]

They give you the solutoon

Mb

Yeah

Didnt see that

[hoary seal]

wait lets restart

[upbeat swan]

Yes

[hoary seal]

so what do I do again?

[upbeat swan]

This

[hoary seal]

to get the answer in the question?

[quiet plume]

Check which row was changed between the first and second matrix. Then the row operation will be
(that row) = (that row) + (some constant) * (another row)

[hoary seal]

is the first augmented matrix converted to the second? and we're trying to tell what the transformation was?

[quiet plume]

Yes

[hoary seal]

hmm

only the last row was changed

[quiet plume]

Yes, so the row operation should look like R3 = R3 + cR?

[hoary seal]

yes

what row is cR?

the pivot right

[quiet plume]

I just meant c * (some other row)

There are two ways you can get rid of the first entry in R3. Either remove 4R1 or remove 2R2 (from R3)

So just check which of those two gives the row you get in the second matrix.

[hoary seal]

do u mind if i step back a bit an just get my head around the basics of matrices?

as x− 2y = 1 has infinitely many solutions, since once
y is specified, then x is determined and conversely.

how?

[quiet plume]

Well x-2y=1 is the equation of one line, so the points that satisfy the equation are exactly points on the line.

If you have two lines, then the points that satisfy both equations are points that lie on the two lines, i.e. where the intersection of the lines is.

[hoary seal]

how is that a line?

doesnt a line follow

y=mx+b

[quiet plume]

It's the same equation as y = -x/2 -1/2

In general the equation ax + by = c is the equation of a line.

You can solve for y

In terms of x

[hoary seal]

I see

ty

.close

[safe radish]

Channel closed

Closed by @hoary seal

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[glass edge]

A square based pyramid has coordinates A(4,0,2), B(-1,3,2), C(1,-5,2), and D. The apex lies directly above the centre of the base, and the pyramid has surface area 210 units^2.
a)Find the coordinates of D.
b)Find the height of the pyramid, correct to 1 decimal place
c) Hence find the volume of the pyramid

[dusk halo]

what have you done so far?

[glass edge]

theres no working, but i figured out (or think so) that D has the coordinates (4,5,2)

and the apex (0,-1,h), where h is height

From there, i thought that since they gave us the surface area, it would have something to do with the height, but it doesn't

[dusk halo]

i think you can find h if you use the formula for the surface area, A=2bs+b^2

where b is the length of the base

[glass edge]

because this is a pyramid, you take the slanted height, making my hypothesis useless

[dusk halo]

but the slant height is just pythagoras isnt it?

[glass edge]

we've not been taught the surface area formula

we have to find the area of the base, and then the 4 triangular faces, and add them up

[glass edge]

it is?

[dusk halo]

imagine a triangle that is between the midpoint of AB, the apex, and the point on the base directly below the apex

i think thats a right angled triangle

[glass edge]

so ur saying that if i take the midpoint of AC and AD, then the midpoint of AD will be directly below the apex, meaning that the slope of the midpoint AC is a perpendicular bisector of the other midpoint?

so then if i find the distance of the two midpoints, i will have the short leg, and thus will be able to calculate the height?

I dont think so, because to do that, I will need the coordinates of the height itself to figure it out

someone help me please

how do i find the height, it could be literally anything

[glass edge]

what happened man

why you leave me

:(

[dusk halo]

no im trying to figure something out, im not sure your coordinates for D are correct

[glass edge]

oh

huh

why u delete?

[dusk halo]

they were posting mrbeast crypto scam again probably

[glass edge]

oh

[trail lotus]

idk either

[trail lotus]

NOO??

[dusk halo]

idk i saw 4 images and they were the same colour scheme as the scam thats been popping up all day

anyway @glass edge are you sure your coordinates for D are correct?

[glass edge]

i think so yeah

[trail lotus]

IT WASN'T ME, I JS DELETED BC MY PFP WASN'T WORKING

[dusk halo]

plot just the x and y into desmos, you get this https://www.desmos.com/calculator/td57vzgu9d

[glass edge]

thats x and y tho

not x,y, and z

[dusk halo]

all z are 2 though

[trail lotus]

but A(4,0,2) was 2?

[trail lotus]

oh

[errant ravine]

no the pyrmaid base is slightly rotated ibelive so ucannot graph it on 2d

[glass edge]

https://www.desmos.com/3dhere

i did it

https://www.desmos.com/3d/mdlhetsrzo

[errant ravine]

-# i feel like this might be wrong but i am not sure

[trail lotus]

what makes you not sure?

[glass edge]

-# why are you speaking in small text

[errant ravine]

-# because i am not sure

[glass edge]

because there is no evidence to go off off

[trail lotus]

they're soft spoken don't mind it

[glass edge]

you couldve said it in normal, and it would have the same meaning though, right?

[glass edge]

ok

[errant ravine]

(nvm ignore this i just realizei am wrong lol)

[glass edge]

sorry

[trail lotus]

oh so we're js guessing atp okay 💀

[glass edge]

..

[errant ravine]

okay so just to confirm the pyrmaid base has to be asqaure correct?

[trail lotus]

it's still 3d pyramid, i think it's right

[glass edge]

thats why im asking for help here

[errant ravine]

actually u are correc this is a correct plot btw i was wrong ^

[trail lotus]

square bottom, four sides go into one point

[glass edge]

no need to be so rude lmao

[errant ravine]

Oh wait

[trail lotus]

it was a joke chill 😭

[errant ravine]

okay i am sure THat d has a diffrent answer-

okay oaky so look at it this way

u have 3 points! we know thier location

[glass edge]

yes

[errant ravine]

and we know between each angle it must form 90 degrees correct?

[glass edge]

no..?

why would it

[errant ravine]

well if u have a square

we know that all angels are equal correct?

[glass edge]

yes

[errant ravine]

okay and we know that in total we have 360 degrees

so that must mean that each angle is?

[glass edge]

i havent been taught that

[errant ravine]

okay okay lets visualize it then!

[glass edge]

im told to use solely coordinate geometry to solve it

not trig and stuff

[errant ravine]

no no this doesnt need any trig dw!!

look at this square

[glass edge]

yeah, im pretty bad at visualizing 3d

[errant ravine]

dw we dont need any 3d for now!

[glass edge]

okay

[errant ravine]

how many angels does it have?

[glass edge]

4

each 90 degrees

[errant ravine]

(ignore the fact that i highlighted and extra angle on the bottom right)

[glass edge]

total 360

[errant ravine]

okay makes sense so far

so what is a base of a pyrmaid made of?

[glass edge]

length*width

in our case:AC*AD

[errant ravine]

not the area- i mean the angels in the the base of the pyrmaid

[glass edge]

or BC*BD

[glass edge]

oh

90 degrees again?

[errant ravine]

it is made of rectangle or a square correct?

okay visualze a pyrmaid anypyrmaid and look at it from the bottom

what would u see?

[glass edge]

oh yeah, and then a rectangle would have 90 degrees to

[errant ravine]

YUP!

[glass edge]

a rectangle/square base

[errant ravine]

okay so know lets look at the 3 point u graphed!
we should find one that form 90 degrees with the others correct?

[glass edge]

yes

[errant ravine]

kinda of like this in a square

okay so since right now we are doing the base and only the base-

[glass edge]

yeah, but mine is more of a rectangle, two sides are 8, and the other 5

[errant ravine]

can u now try to find where D coul possible be?

this is a top down prespective from ur graph

(i just removed the D)

look at this

which point here forms 90 degrees with the others?

[glass edge]

u see the distance from the red point to the green point over there

its an x amount of right and y amount of down right

i applied the same thing to the grey one above

thinking i would get D

but this is 3d

so it didnt work

[errant ravine]

okay okay so first things off-

dont worry its not 3d yes we have 3 cordinates bet let me show u something really cool
when i look at it from the side they all have 0 hieght

which means we can go ahead and say that they are all on the same plane-

so for our concerns we only need x and y

does that make sense?

[trail lotus]

grey being C (1,-5,2) right?

[errant ravine]

(think of it as kind of writing on paper? if everything is on paper does ur pen ever need to right in 3d?

[glass edge]

4,5,2

[errant ravine]

yes

[glass edge]

but when i draw it on paper, it looks like this

[errant ravine]

okay so go ahead and move the graph so its from a perfect side perpspective

[glass edge]

giving me impressions of different heights

[errant ravine]

do u see any points having diffrent hieghts?

[errant ravine]

yup yup BUT u need to rotate it around!

[trail lotus]

wait are you talking about your presumed idea of where D is?

[trail lotus]

this seems like a discrepancy oh no

[errant ravine]

now lower it a bit so its perfectly from the side and it will look like ^

[glass edge]

ofc, i have no idea where even the apex is

[errant ravine]

||dw ik where D is its pretty easy to figure out but iam trying to explain it to them||

[errant ravine]

okay if u dont trust me hjere is my proff
notice how every point so far has an ending with 2 (aka its location on the Z axis)
that means that they all have the same hieght

correct?

[trail lotus]

based off this model, the d point is actually blue though?

[glass edge]

well, but the thing is i want to find D consistently. not just this problem, which will be hard

[glass edge]

yes

i found that out, which is why i know for sure that z is 2

[trail lotus]

@dusk halo don't stay mysterious where r u

[errant ravine]

yes i am just trying to first to get you to unerstand diemnsions

[glass edge]

i found x to be 4 because the distance from A to C is 4, and the other points are parallel

[errant ravine]

okay since we know we can ignore the Z axis we can look at this from a 2d prespective

[glass edge]

okay

but im scared of all the times we cant do it

but okay

[errant ravine]

look if you undertand how to do something in 2d first then ucan do it in 3d later on

[trail lotus]

yeah and we already understand that the z coordinate will be 2 because they're on the z plane

[errant ravine]

so first things off we would need to choose a point to translate into the fourth corner

i am going to use this example

assuming we choose point (top right purple)do u have an idea how we could translate it to the point we want?

[glass edge]

,w A square based pyramid has coordinates A(4,0,2), B(-1,3,2), C(1,-5,2), and D. The apex lies directly above the centre of the base, and the pyramid has surface area 210 units^2. Find the coordinates of D.

[flat frigate]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by tan211111

[glass edge]

by using the distance from blue to red

and applying it to purple

[errant ravine]

okay perfect! lets apply that to our example!
but Notice something important we had to use the purple point or red point as our refrence becaue what would happen if we had choosen blue point?

[glass edge]

i chose the blue point.

i dont see whats wrong with using blue

and i applied the same to this question

[errant ravine]

well lets use blue! if i move it downwards one where do i end up?

[glass edge]

red

you end up at red

[errant ravine]

but iwant to be in the corner to form a square..

so this is ocunter intutive right?

[glass edge]

ohh

[errant ravine]

its much easeir to chose pruple or red since they are the "edge" points if that makes sense

[glass edge]

yes

[errant ravine]

but how do we determine in our graph earlier which point is blue(aka the one we cant/shouldnt use)?

[glass edge]

no but i think of it like this: the translation from blue to red is 1, and since blue is parallel to purple, then if i move purple down 1, it will have the same result

[glass edge]

its complementary to point D

[errant ravine]

yes but u will end up 1 to the left too muhc- which means to use blue point u will need to first move 1 down and then 1 to the right to complete the square

does that make sense?

[glass edge]

yes

[errant ravine]

okay so knowing this infomration we can go ahead and look at our 3 points up here in 2d can u try to determine which point we Shouldnt/harder to use?

[glass edge]

no cuz u start from purple

and then go down

[errant ravine]

if u use purple as the starting point then all is good!

[glass edge]

okay okay lets just move on

[errant ravine]

-# bassicly what i am trying to say is the point opposite the point we want will require double trasnlation

[glass edge]

yea

[errant ravine]

okay so looking at this

[glass edge]

we shouldnt use red

[errant ravine]

Yup! well done!

okay so red is A in your graph!

[glass edge]

..

its C in my graph

i think i labelled it weong

okay

oka

[errant ravine]

anyways know knowing the cordinates we can go ahead and find the diffrent from A to B and apply that To point C so we get point D

does that make sense?

[turbid ore]

what is left to be found

[glass edge]

yes

[errant ravine]

(i meant as in the desmos graph u sent earlier)

[errant ravine]

okay go for it! you got this!

[errant ravine]

point D aka the fourth point in the sqaure / rectangle

[trail lotus]

the d coordinate

[turbid ore]

oh

[errant ravine]

i am just trying to get Tan to solve it i think he got it now!

[glass edge]

distance from a to c for x is 5

so x =5

distance from c to b for y is 8

so AD =8

and y should be 8

and we know that z=2

D(5,8,2)

[errant ravine]

ah soo not quite.. i belive

[glass edge]

3d is just not for me

[errant ravine]

lets look at this example one more time

look at the cordinats here-

what would u need to do to get purple point to its correct location-

[glass edge]

how do u know the distance from purple to unknown

[errant ravine]

-# dw we are working in 2d here

corrected*

-# also asorry about hand writing

[glass edge]

(0,1) and (0,0), delta y = 1

so should be the same for unknwon

(something,1)

(0,1) and (1,1), delta x =1

[turbid ore]

so i got the point D how i am supposed to explain that

[glass edge]

(1,1)

no it isnt

thats the point above

[errant ravine]

uhh nope close but not quite right-

[glass edge]

omg

[errant ravine]

so here is the thing..

[glass edge]

(0,1)

[errant ravine]

yes that is correct!

okay so here is the thing

when u translate something..

we know that lines blue and red are parraler to purple and unknown correct?

[glass edge]

yes

[errant ravine]

okay so we know that distance red to blue lets call that distand D
we know if we apply that to purple we get our forth point correct?

[glass edge]

yes

[errant ravine]

okay so lets try to calulate the distance for this smple example here

how much is point A (blue) displaced by from point B (red)

reember that its displaced on both the (x and y) axis

[glass edge]

sqrt[(3-1)^2+(2-1)^2]

sqrt(4+1)

[glass edge]

sqrt5

[errant ravine]

okay when in graphs when i mean distance i dont mean actualy length ik u just used pythgerous therom-

i mean by how much should u dsiplace the y and then by how much the x

[turbid ore]

can i give my explanation to the forth point ?

[errant ravine]

to get to thesame point-

[errant ravine]

go ahead!

[glass edge]

4 down 2 left

[turbid ore]

so you can see the red point in the pic i sent

so there's a pattern to every point

go three units down from red and 5 units to right you will get blue

same 3 units left from blue and 5 units down you will get green

and for D

[errant ravine]

-# this is correct btw well done and for refrence leftand right is x and up and down is y so u would translate the point by -2 for x and -4 for why

[turbid ore]

Go 3 units up from green and 5 units to left you get D

[errant ravine]

do you undertand tan?

[glass edge]

no

sorr

y

[errant ravine]

ah okay-

have you take point translation before on a graph

[glass edge]

go three units down from red and 5 units to right you will get blue
same 3 units left from blue and 5 units down you will get green

what same 3 units?? you went RIGHT before 5 UNITs, not left 3

[errant ravine]

-# great explination btw i just think tan doesnt understand translation on graphs yet...

[glass edge]

you went 3 down

not left

[turbid ore]

i also havnt studied 3d geometry yet so i see it in 2 d

[glass edge]

and then u went up, left, and anywhere else

[errant ravine]

-# the entire first half of the question is 2d anyways no worries

okay oaky tan

lets focus on one thing at time-

first do u undertand how to move a point in graphs
for example wahat happens if i add 2 to x of a cordinat of (2,4)

[glass edge]

i will skip my dinner for this one question.

(4,4)

[errant ravine]

hey no you houldnt please dont!

its okay to take a break sometime

ik ik sorry- this is just a pre for a folow up question

[glass edge]

sorry

[errant ravine]

okay can u visualize it happening on a graph?

[glass edge]

yes

[errant ravine]

oaky what if it was something more complicated though lets say we want to move it a distance of 5 for x and 2 for y

[trail lotus]

you can eat n do work yk 😭

[errant ravine]

it would move kinda of like in a daignoal correct?

[glass edge]

(7,6)

[errant ravine]

(i want you to visualize it)

[trail lotus]

(without me having to do the diagram)

[errant ravine]

yes most important thing here is visualization becasue i want you to intutively understand this i could jsut give u a formula and go- but these concept will be realyl important later on)

[glass edge]

i imagine a stair going right 5 and up 2

from 2,4

[errant ravine]

okay okay i guess that works butwhat if u made that stair really smooth-

almost like a ramp

can usee it now?

[glass edge]

it becomes a half of a quadratic

i imagine a parabola

[errant ravine]

i -

[glass edge]

exponential graph

increasing

smoothly

[errant ravine]

i it should be straight line...

i tihnk-?

[glass edge]

oh

[errant ravine]

wait lets plot it

[glass edge]

yeah i imagine it

i can visualize

[errant ravine]

it should look like so

[glass edge]

ues

[errant ravine]

okay makes sense right?

[glass edge]

yes

[errant ravine]

okay now take this graph

i want u to imagne applying that line we had from red to grey
onto the green ball

[turbid ore]

you got it

?/

[errant ravine]

||nope i amstil ltrying to explain it i think he is having trouble with graphs and trasnlation||

[errant ravine]

can u vissiliaze it tan?

[glass edge]

6 right 10 up

from green

[errant ravine]

IOKAY nice nice nice!

okay wait let me get u an SS with the graph poitning in the right ridrection cause its rotated

okay so looking at this point-

can u try to do what u just did with the green point

[glass edge]

6 left 10 down

its as if you reverse the direction but keep the units

[errant ravine]

yup yup

so know do u understand how u can solve it?

A square based pyramid has coordinates A(4,0,2), B(-1,3,2), C(1,-5,2), and D. The apex lies directly above the centre of the base, and the pyramid has surface area 210 units^2.
a)Find the coordinates of D.

lets look at this (4,0) and (-1,3) , and (1,-5)

can u now using this infomration find point D?

[glass edge]

since in my case c is oppposite of d, translate c to a and do the same using b as starting point

[errant ravine]

YUP!

and then calculat the cordinates!

[glass edge]

1 to 4 is left 3, and -5 to 0 is up 5

so i should go right 3 and down 5

starting from b

[trail lotus]

uh huh

[glass edge]

right 3 from b would give us 2

as x value

an

d

8 as y value

D(2,8,2)

nope

its down 5

[errant ravine]

ah- close

YES-

[glass edge]

D(2,-2,2)

[errant ravine]

okay oaky but wait a moment-

[errant ravine]

does 1 to 4 gives us 3 or maybe ?

[glass edge]

3

[errant ravine]

remeber u started from point (4.0) right? and drew the line to point (1,-5)

[glass edge]

ah

[errant ravine]

-# come on you got this!

if i start from the 4th tile and i end up on the first tile how much did i move

consideing the more i go to the right the higher x i have

[glass edge]

3 left

[errant ravine]

okay 3 Left-

how do we represnt lef in graphs-

[glass edge]

negative

[errant ravine]

YES-

soo its?

[glass edge]

D(-2,-2,2)

[errant ravine]

-# why did u chagne the y value?

[turbid ore]

so i made an eq for the point

should i tell how?

[glass edge]

the y value was always negaitve

[errant ravine]

no no let them figure it out

[glass edge]

down 6

5

[errant ravine]

wait wait ur right

i am cofnuised it is -2

sorry i mae a small mistake oops-

[errant ravine]

tan dont look at this spoiler||wait anmol the answer is (-4,-2,2) right?||

oaky regarding the X

the point we used at refrence

[glass edge]

ive come to the realization that i am egregious at understanding math. I think my best option is to stick to memorizing formulas and when to use them

[errant ravine]

at what cordinate did it start tan-

[errant ravine]

NO NO

wait WAIT

UR SO CLOSE-

[glass edge]

that it how i can make real progress

[errant ravine]

wait

[glass edge]

this is too slow

[errant ravine]

UR LITTERLY RIGHT THERE

u just made 1 tiny mistake-

can u remind me of point B cordinates

it was (-1,3,2)

correct

so waht happens wehn u do -1 -3 ?

[glass edge]

but at what cost

ive lost over a hour and half

i couldve spent on memorizing formulas and when to use them

[glass edge]

-4

[errant ravine]

okay well the answer is going to ||(-4,-2,2)|| the reasn its ||-4|| is because B actually start at ||-1|| not ||1|| as u calculatedearlier

[errant ravine]

there you go!

thats the asnwer-

do u understand now where the answer came from-

[trail lotus]

oh well I got a different answer uhh

https://tenor.com/view/annoyed-fake-smile-ok-leave-me-alone-itchy-head-scratch-gif-15111085

[errant ravine]

pleae go eat dinner and take some rest u have done well-

[errant ravine]

wait wha- what did u get?

[glass edge]

nope..
the only thing i can think of is that the point A has x coordinate 4, and D is in the same x line as A

[trail lotus]

||D = (6, -8, 2) ||(tan don't look)

[glass edge]

no point now its 9pm, ill just finish this worksheet ( or try to) and sleep

bye bye

[errant ravine]

sorry- i wish u best of luck..

[trail lotus]

https://www.geogebra.org/3d?lang=en

[glass edge]

its not ur fault its mine

[errant ravine]

||the question says it must be a square this i belive is aparrelrogram||

[glass edge]

.close

[safe radish]

Channel closed

Closed by @glass edge

Use .reopen if this was a mistake.

[glass edge]

personally, i think its a rectangle

[trail lotus]

me too

[glass edge]

but yeah

bye bye

[errant ravine]

point (-4,-2,2) makes it a square i belive..

[trail lotus]

naturally yeah

[errant ravine]

also the q says "A square based pyramid has coordinates"

[glass edge]

ur right

[trail lotus]

its not about it looking exactly like a square though, it won't be a perfect square with a right angle everytime 😭

[errant ravine]

its okay i am tan you should be proud for triying! ihope maybe one day some of this explination can help you somehow for now rest and i wis u best of luck!!

[glass edge]

WAIT SO THEN ALL SIDES ARE SAME HOW DID I GET 8 AS TWO SIDES AND 5 AS THE OTHER

[errant ravine]

count each ttrasnlation from each point its the same number.. therfore its 90 degrees at each corner

[glass edge]

my brain is more fried than kfc

ok

gn

[errant ravine]

gn!

[turbid ore]

umm

can't say

[trail lotus]

but the vector rule is D = A + (C − B)?

[errant ravine]

-# i think iam gonna go rest aswell for a bit thanks for the graph earlier anmol

[turbid ore]

no problem

ask me i am always here

you here to for my help

[errant ravine]

i should mention here that point A is not and Edge point it is at the corner Opposite of where we actually want to be which is why this Q is so confusing

[errant ravine]

because point A is between Point B and C if that makes sense

[trail lotus]

it's not that confusing gng 💔

[errant ravine]

well to some it is..

[trail lotus]

wdym by that

https://tenor.com/view/dexter-james-doakes-erik-king-stare-staring-gif-1343162792415382650

[errant ravine]

but idk i may be wrong anmol opnoins on this?

[errant ravine]

okay so the 3 points here Point A is the red and as u can see it is on the opposite corner of where we want to be-

[errant ravine]

remeber square = 90 Degrees so there is no other possiblity of any other points bieng the corner other than A