help-28

[formal swift]

which one do you need help with

[worldly matrix]

we've got it

[tribal marlin]

oh okay

[worldly matrix]

√(ab)=√a√b, but that's multiplication, not addition

[torn jolt]

So did you finally get your mistake

[tribal marlin]

yes and no

[torn jolt]

?

[tribal marlin]

I'm confused

[torn jolt]

with which part

[worldly matrix]

think about it this way: the square root of 9 is 3 and the square root of 4 is 2

the square root of (9+4) is not 5

[tribal marlin]

so after adding √144+36 you get √180 and then I wanna convert that to a radical? I think that's what it's called

cause you got 6√5

[worldly matrix]

it's called simplification, and if you intend to use a calculator it isn't required, but is a good skill to have

6√5 is the same as √180

[tribal marlin]

ohhh I understand

[torn jolt]

and it is required for big calculations like these

root(20) = 2root(5)

because root(20) = root(4 x 5) = root(4) x root(5) = 2root(5)

[tribal marlin]

okay! I got it

[worldly matrix]

🎉

[tribal marlin]

now for volume it's similar steps I assume?

[worldly matrix]

with volume it's similar yeah

you have the formulae for volume; how're you gonna apply them?

you've glued a hemisphere onto a cone to make an ice cream cone shape; how will you evaluate the volume?

[tribal marlin]

so I find the volume of both hemisphere and cone, right?

[worldly matrix]

exactly right

[tribal marlin]

wait what. did I do something wrong or is the volume the same for both?

I got 452.3893 for both

[worldly matrix]

they both happened to be 144π this time

[tribal marlin]

oh okay

I add both right?

[worldly matrix]

yep

so 288π

[tribal marlin]

is there more steps?

[worldly matrix]

what other step would there be? you've got the volume of the entire object; no more and no less

[tribal marlin]

yay! ok thank you so much

[worldly matrix]

very straightforward, right?

[tribal marlin]

mhm, very straight forward

[worldly matrix]

nice; surely example 7 should be much easier, right?

[tribal marlin]

I'd assume so

it's just a cube and a pyramid

wait do I need to find the height or do I just use the slant height?

ohhh nvrm

I see

[worldly matrix]

you calculate height using pythagorean theorem

given slant height

[tribal marlin]

so c²-b²=a²?

yeah

[worldly matrix]

keep in mind that your b is half the width of the base

speaking of, did I read correctly that the dimensions are a 5m cube with a pyramid with a 4 m slant height?

[tribal marlin]

mhm

that's correct

[worldly matrix]

so your h is sqrt(9.75)

[tribal marlin]

so then √9.75=3.1224 then I'd do b×h÷2 right?

[worldly matrix]

it's the base of the pyramid times the height divided by 3

your page says "multiply by a third" but that's the same thing

[tribal marlin]

that'd give us 2.602

[tribal marlin]

so I definitely did something wrong

oh

I see my mistake

[worldly matrix]

by base I mean the area of the square base of the whole pyramid

not the base of the triangle lol

[tribal marlin]

I'ma pack it up as it's 11:51 pm for me, but thank you so much for the help. It means a lot :)

[worldly matrix]

I'm just gonna drop one last tidbit before we depart

[tribal marlin]

okay

[worldly matrix]

the surface area is just adding up squares and triangles

with that I bid you adieu

and good night

[tribal marlin]

thank you once again

should I close this?

[worldly matrix]

If you're ready

[tribal marlin]

I think I am

well thank you, take care

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[glad marten]

How do I find the phase shift for this equation? ( for C )

[wet mirage]

Sine waves have a maximum when theta = pi/2

So just set you sin brackets = to pi/2 and algebra from there

[glad marten]

how do we know that tho

I’m just confused where we got the information

[wet mirage]

If you draw out a sin wave and look at it, a full period (The part after its gone up then down and returned to 0) is 2pi right?

[glad marten]

yea one period

[wet mirage]

So if we look for the maximum, you can see that it is 1/4 of the way through the period

Right?

[glad marten]

Yea

[wet mirage]

So that is pi/2

So pi/2 is the maximum

[glad marten]

But I don’t know where it would be on this graph because we don’t know if it is cos or sin and if it is not a specific one we use the phase shift

I do know that pi/2 is the max on a normal sin equation

[wet mirage]

It can be either

A cos or sin wave

[glad marten]

Yes but I need to know what the graph looks like to write the equation for either one

Because if on the graph it starts at the minimium and I’m writing a sin equation I need to adjust my phase shift so it starts at the midline

And if it was cos I could either reflect over the x axis or shift it to a maximum at the start

so I just don’t know how to figure out the phase shift

And for this one I don’t understand how it is possible because we need a point at 2 at the max but the max is at 1

Like it would make sense if the period was 5 but the period is not 5 it is 6

<@&286206848099549185>

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[lapis glade]

help me pls

[lapis glade]

<@&286206848099549185>

[sturdy valve]

maybe start with expanding it?

[sturdy valve]

ur supposed to wait 15 min

[lapis glade]

sr helpers

my bad

[eternal terrace]

You could use !15m

[silk bridge]

-# yes but i thought let's do something else

[eternal terrace]

Valid af

[quick epoch]

!15m

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[quick epoch]

expand that equation

[remote gale]

We dont need 4 people to entertain 1 person of the rules

[quick epoch]

then many things will cancel out

[remote gale]

And yea

[quick epoch]

then use identities

[quick epoch]

Yep

[lapis glade]

ok maybe

[quick epoch]

Hmm then many things will cancel then go for identities

[remote gale]

I would say factorizing would be easier

[lapis glade]

.... i dont find factor

[quick epoch]

Hmm but finding factor will be hard yk

[lapis glade]

.... problems is hard

[topaz valley]

substitute x = a - b, y = b + 1

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[steel vector]

I did my exam and i just want to cry myself to sleep but two question i ddint even try to answer but i kinda want to know how to do them so one was geometric sequence how do i find the 8th term if i only have term 7 and 4

[steel vector]

And then this other word problem i dony know if i can remenber

But it was

Ann was at the top of a 50 m bridge and she saw two boats under

From her angle boat A was at a bearing of 210 and boat B at a bearing of 120

And she estimated that the angle of depression for Boat A was 28 and B i kinda forgot but 30 something 😭

And i have to find the distance from boat a to B

[spice knot]

for this one, remember in a geometric sequence that you * r to get from one term to the next

now usually they say this between term 1 and term 2

(term 1) * r = (term 2)

that happens between any adjacent terms though

(term 2) * r = (term 3)

etc.

so (term 4) * how many r = (term 7)?

[steel vector]

Cuz the formula was like tn=ar^n-1

And we r giving the term and its corresponding number

[steel vector]

I did that

But when i went to check if Ls=Rs it didnt

[spice knot]

that just sounds like a mistake

heres how I would do it

(term 4) * r * r * r = (term 7)

(term 7) * r = (term 8)

that means r * r * r = (term 7) / (term 4)

cube root both sides

I get r

then I (term 7) * r

[steel vector]

Whats r* mean

[spice knot]

the * symbol is how youre supposed to write write multiplying

x is what you learn at first in elementary school before algebra uses that x as a variable

[steel vector]

Oh

[steel vector]

Thats so much less complicated than i was thought

[spice knot]

you know once you see something useful, you dont have to remember a formula to do things with it

thats like having to pull out a textbook to walk a shortcut on the road

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[woven turret]

Every point in a plane is either red, green, or blue. Prove that there exists a rectangle
in the plane such that all of its vertices are the same color.

[outer lotus]

Use the Dirichlet principle

[woven turret]

i dont know what that is

[outer lotus]

Or pigeonhole principle I believe it's called in English

[woven turret]

oh yes

but i dont know how to apply it in this scenario

[outer lotus]

Try to imagine a finite subset of this plane

Such that the existence of only 3 colors necessarily forces something to happen

For example, a column of 4 points

What is guaranteed within this column?

Given that there are only 3 colors available

[woven turret]

one colour will repeat

[outer lotus]

Exactly! At least one color will repeat. Now, how many ways are there to arrange 4 points in a column given 3 colors?

[woven turret]

81

but why are we assuming 4 points

[outer lotus]

Because now, if we look at a 4 by 82 rectangle of points, what are you guaranteed to get?

[woven turret]

wait no i'm lost

[outer lotus]

If there are only 81 unique ways to arrange 4 points in a column, we look at 82 of such columns

What can we infer?

[woven turret]

oh the 82nd column would be the same as one of the columns in the first 81 in terms of arrangement?

[outer lotus]

Exactly

And in those 2 identical columns there is guaranteed to be a repeat

Thus completing the rectangle

[woven turret]

so a rectangle w all 4 vertices same colour can be formed

[outer lotus]

In fact, you only need a 4 by 82 rectangle of points to guarantee it's existence

[woven turret]

okay so i got this but how did you assume a column of 4 points in the beginning like why not say a column of 5 or 6 or ... points or rather a row of some number of points?

[outer lotus]

The pigeonhole principle

If there are only 3 things, I assume 4

[woven turret]

ahhh okay so the 3 colours will be the holes and the 4 points the pigens (in a sense)

[outer lotus]

Yes

if n items are put into m containers with n > m, then at least one container must contain more than one item

You could pick any number greater than m of course, not just m+1. But there is no need

[woven turret]

ah okay got it

thank you so much :))

.close

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[frank tree]

idk if this counts but like my exam is tomorrow and i need some help with reviewing. Is this how im supposed to get help?

[frank tree]

oh there yeah

[neon basin]

Yes

But usually we also need to see what you need help with

[frank tree]

Oh okay I can see if i can get a photo

[neon basin]

Could be useful

[frank tree]

sorry just uploading them

[neon basin]

👍

[frank tree]

hopefully this works

the other files arent loading

Im mainly struggling with word problems like just distance and stuff

ugh it didnt load

[neon basin]

I can see

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@frank tree Has your question been resolved?

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@frank tree Has your question been resolved?

[robust slate]

.close

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[cerulean rain]

I need help with the characteristic of absolute value functions

Like I get it but I don’t 😭

PLS SOMEONE HELP ME IT DUE TOMMOROW

[stiff musk]

no point shouting

[cerulean rain]

Sorry teach

[stiff musk]

probably you know at least some of these

what's the vertex, for example?

[cerulean rain]

Ye I understand the vertex and the axis symmetry I think

Update TT

[stiff musk]

,rcw

[stiff musk]

y intercept looks wrong, how did you get 3?

[cerulean rain]

TT u want me to be truthful i actually don’t know

It was on the y axis ig

So I picked 3 and since it absolute values I made it positive

[stiff musk]

what's the definition of y intercept?

[cerulean rain]

A point in the y axis

Where the slope pass I think

[thorny bluff]

yeah where does it cross y axis from the graph

[cerulean rain]

It doesn’t really?

[thorny bluff]

where does the red line cross the vertical black line?

[cerulean rain]

Like it doesn’t really hit the point TT

[stiff musk]

it definitely crosses the y axis

but you need to zoom in to estimate the y value

but in any case it's nowhere near 3

[cerulean rain]

So it will be -2?

[thorny bluff]

yeah its not exactly on -2 for some reason but its supposed to be -2

[stiff musk]

i'd say it's a bit below -2 but who knows what value exactly

[thorny bluff]

close enough

[cerulean rain]

😭

[stiff musk]

if the slopes are intended to be 1 then it should cross at -2

oh they're not 1 though, your answer for that was wrong too

[cerulean rain]

I don’t even think my edge slop is correct

[stiff musk]

look at the line connecting the vertex to the point (5,0), what's the slope of that line?

[cerulean rain]

X

[stiff musk]

?

you can give a number

[cerulean rain]

😭 ohh

[stiff musk]

change in y over change in x

[cerulean rain]

-3/4?

[stiff musk]

well is the slope positive or negative?

for that part of the graph

[cerulean rain]

Positive

I think

[stiff musk]

yea it's going upward as you go from left to right, that's a positive slope

so 3/4

how about the slope of the other side?

[cerulean rain]

Wouldn’t it be the same but negative

So negate -3/4?

[stiff musk]

hopefully so, if it's an absolute value type function

you can check using the vertex and the point (-3,0)

[cerulean rain]

So do I change my answer to -3/4 and 3/4?

[stiff musk]

basic idea is taking points that are clearly intended to be at integer coordinates

[stiff musk]

yep!

and now you can use that knowledge to find the y intercept

it's not exactly -2

[cerulean rain]

😭

Ohh

-1?

Y intercept = -1

[stiff musk]

well look at the graph, it's between -2 and -3 right?

so it can't be -1

[cerulean rain]

So it’s a fraction?

[stiff musk]

if you use the slope you can find exactly where it crosses

you have to go to the left by 1 to get to the y axis, how much do you go up when you do that?

remember, change in y over change in x

[cerulean rain]

😭I don’t get it

[stiff musk]

slope = -3/4 for the left side, correct?

[cerulean rain]

Ye

[stiff musk]

so -3/4 = (change in y) / (change in x)

to go to the y axis, (change in x) is -1

so solve for (change in y)

[cerulean rain]

-1/4?

[stiff musk]

oops fixed typo

[stiff musk]

how did you get that

[cerulean rain]

TT idk..

[cerulean rain]

What u mean by this

Like change it to what..

[stiff musk]

that's what slope means

if you take two points, the vertex and the y intercept

(change in y) is the difference in their y coordinates
(change in x) is the difference in their x coordinates

you know the ratio (change in y) / (change in x) is the slope, which is -3/4

you also know (change in x)

because the vertex is at x=1 and the y axis is at x=0

so now you can solve for (change in y) and from that you can get the y coordinate of the y intercept

[cerulean rain]

😭

I feel so dumb

So used the coordinates of. 0,-2 with -3/4?

[stiff musk]

what's 0,-2?

[cerulean rain]

-2 on the axis

[restive geyser]

(I believe that's where she thinks the y-intercept is)

It isn't, for the record; there're other coordinates that are more precise that you could use

[stiff musk]

focus on this segment

in particular, the vertex and the y intercept

you know three coordinates out of 4

you know the vertex is at (1,-3)

and you know the y intercept is at (0, y) where y is what you want to find

and you know the slope is -3/4

so:

-3/4 = (change in y) / (change in x)
= (y - (-3)) / (0 - 1)

does that make sense?

[cerulean rain]

So solve that?

[stiff musk]

yep solve for y

that should give you the exact value instead of having to guesstimate from the graph

(assuming we believe the slopes were intended to be -3/4 and 3/4, which i think they were)

[cerulean rain]

-3y?

😭

[stiff musk]

what is -3y?

you should be able to find y

a number

let me typeset it in case the text is confusing

$$-\frac{3}{4} = \frac{y - (-3)}{0 - 1}$$

[glossy valve]

Bungo

[cerulean rain]

OHHH

-16/3?

Wait..

-9/4??

[eternal terrace]

Yeah

[stiff musk]

are you trying to do it in your head? i recommend writing it down

that way you'll be sure

[cerulean rain]

Ye I’m sure

[stiff musk]

ok good

and yes i agree

-9/4, which is -2.25, just a bit below -2

[cerulean rain]

So y intercept is -9/4

[stiff musk]

yep!

[cerulean rain]

How about for the max and minimum

[eternal terrace]

So the graph was correct, a lil below 2 (i got invested)

[stiff musk]

any thoughts about these?

[cerulean rain]

TT

[cerulean rain]

Um I don’t remember but I think the max/min depend on the intercepts

[stiff musk]

can you say in words what they mean?

[cerulean rain]

Maximum the highest point minimum lowest point

Um for this function the highest point is below the graph so..it will be minimum

[stiff musk]

don't confuse vertex with highest point

[cerulean rain]

Since it’s below the graph ?

TT

[stiff musk]

highest point means the maximum y value of the function

in other words, does the graph have an upper limit?

[cerulean rain]

No..

Since the arrows aren’t going down?

💔

So.. it would be maximum?

[stiff musk]

what would be a maximum?

[cerulean rain]

Since the v isn’t upside down

Nvm I believe it’s minimum

Since the v is up

[stiff musk]

i think the answer they want for max and min is either a number or "does not exist"

[cerulean rain]

It would be n/a I think

[stiff musk]

it's not a yes/no type of question

[cerulean rain]

Ye

[stiff musk]

right, there is no maximum, because any y value you can name, like 100, the graph will eventually rise above that

[cerulean rain]

So how do we find out the minimum

[stiff musk]

what does minimum mean?

[cerulean rain]

Lowest point

😭

I don’t know actually can u tell me

[stiff musk]

yea the lowest y value on the graph

what would that be for this graph?

[cerulean rain]

You said it wouldn’t be the vertex right?

Well if it isn’t the vertex it will be 5,0

[stiff musk]

no i didn't say that, but the max and min of a graph aren't always/automatically at a vertex

in this case the min does occur at the vertex

[cerulean rain]

Can I ask why

[stiff musk]

well what's the y value of the vertex

[cerulean rain]

-3

[eternal terrace]

Not necessarily the vertex, bungo was just making sure you don’t mix two things up

[cerulean rain]

Okie

[stiff musk]

ok, and is there any point on the graph with a lower y value than -3?

[cerulean rain]

No

[stiff musk]

correct

so -3 is the minimum

[cerulean rain]

So it would be -3

DUDE.

😭😭😭

[stiff musk]

are those tears of joy

[cerulean rain]

❤️yes

How about the increasing edge and decreasing edge

[stiff musk]

i'm not sure what they want you to say for those tbh

do you have an example where they've filled in answers for those so we can see what they are expecting?

[cerulean rain]

Ye

Yes I know my handwriting is bad..

That’s suppose to be infinities 💔

[eternal terrace]

They do look like infinities for what’s it worth

[stiff musk]

ok so i guess they expect the range (interval) of x values for each edge

[cerulean rain]

Ye

[stiff musk]

so what should those be here?

[cerulean rain]

The increasing edge I think is the left side I think

[stiff musk]

i've seen way way worse, yours is fine

[stiff musk]

the convention here is that increasing means "rising as you move from left to right"

[eternal terrace]

Wouldnt they be asking for the interval where the x values are increasing & the interval where they’re decreasing

[stiff musk]

so which side is increasing here?

[eternal terrace]

Oh ig that’s the same thing

[cerulean rain]

1 , infinite?

[stiff musk]

yea

$[1,+\infty)$

[glossy valve]

Bungo

[cerulean rain]

Then infinite , 3?

[stiff musk]

well we're talking x values right?

so not 3

[cerulean rain]

5

infinite , 5

[stiff musk]

we're talking this edge right?

[cerulean rain]

Ye

Wait..

[stiff musk]

what is the largest x value for that edge

[cerulean rain]

No? Idk

[stiff musk]

that's the decreasing edge

(negative slope)

[cerulean rain]

OH

It will be -3

So infinite , 3

[stiff musk]

you're reading the y value

(i think?)

[cerulean rain]

Infinite, 9/4

[stiff musk]

you want the x coordinate of the vertex

[cerulean rain]

😭

[stiff musk]

because that's where the edge ends, right?

[cerulean rain]

MAN I EVEN CONFUSING THE TEACH

[cerulean rain]

Yes

[eternal terrace]

Do we have the graph of this

[stiff musk]

ok what's that x coordinate?

[cerulean rain]

Ye

0

The x coordinate will be 0?

[eternal terrace]

Girl

[cerulean rain]

😭

[eternal terrace]

At what point does the slope stop decreasing?

[cerulean rain]

Never

[eternal terrace]

😭

[cerulean rain]

💔

[eternal terrace]

The vertex

[cerulean rain]

It doesn’t???

[eternal terrace]

It goes up after that

[cerulean rain]

Oh

[eternal terrace]

Or more like the values do

[cerulean rain]

So would it be 3?

[eternal terrace]

Anyways so, what’s the x coordinate of the vertex?

[cerulean rain]

1

[eternal terrace]

Nice

Thats the end of the decreasing interval

We need to find the start now

[cerulean rain]

💔

Dude I hate to say this I gotta sleep

😭thank u for yall help tho good night

[eternal terrace]

Do we have a start or is the line going left forever?

[cerulean rain]

Goes forever

[eternal terrace]

And at that side what’s the value of the x coordinate?

[cerulean rain]

-3

[eternal terrace]

I’ll give answer since i believe it will make it click

-inf

At the far left

x = - inf

Right?

[cerulean rain]

What’s -inf?

[eternal terrace]

Minus infinity

[cerulean rain]

-6?.

[eternal terrace]

Sure if that’s the smallest number you can count to

(The graph stops at -6 sure but it can continue)

It didn’t specify -6 as a starting point

The arrow usually means it will continue

So you can go beyond the numbers you have

[cerulean rain]

-7

[eternal terrace]

It never stops

It goes on forever

[cerulean rain]

Ok so infinity, -6

😭

[eternal terrace]

Girl

Ok

Look

[cerulean rain]

Both ends don’t stop

[eternal terrace]

You have a vertex tho

Your interval for the decreasing values of y

[cerulean rain]

😭the guy said it number was between -2 and -3

[eternal terrace]

Is the x interval going from -inf to +1

Huh

[cerulean rain]

No…

Wel ye it does

[eternal terrace]

Pinky…

[cerulean rain]

☹️

[eternal terrace]

Do you see the interval?

You did the first half perfectly

[1, inf)

[cerulean rain]

1, -3…

[eternal terrace]

Increasing from x= 1 and never stops increasing

So 1 to infinity

If we go the other way

Left to right

We’re decreasing

Till x=1

We started from - infinity tho

Can you see that?

[cerulean rain]

So we have to find y?

[eternal terrace]

The question wants you to find the interval of x where the y values are decreasing

[cerulean rain]

And how do we find that

[eternal terrace]

And the convention is to read the graph from left to right

If you read it left to right

Before meeting the vertex

Do the values of y in that line increase or decrease?

[cerulean rain]

Decrease

[eternal terrace]

Ok

Start from what x point?

[cerulean rain]

1

[eternal terrace]

Actually

It ended there

If you go more right

It increases

[cerulean rain]

So it starts at -3

[eternal terrace]

Why would you think so?

[cerulean rain]

Cause it on the x axis

[eternal terrace]

The start has to be taken from the head of the line

If the line has an arrow

Automatically assume inf

But in this case is it - inf or + inf?

Inf = infinity

[cerulean rain]

-inf..

[eternal terrace]

Yes

[cerulean rain]

Since it going on the left

[eternal terrace]

Write the interval please

[cerulean rain]

Infinite, -3

[eternal terrace]

OH MY DAUS

[cerulean rain]

😭😭

[eternal terrace]

Sorry

[cerulean rain]

I DONT GET IT

[eternal terrace]

-infinity

To 1

You go from -inf on the x

[cerulean rain]

Why TT

[eternal terrace]

Because of the arrow

And you stop at x =1

[cerulean rain]

I been saying x, 1 and yall said no 😭

[eternal terrace]

Because there is the vertex and going further along x the y values will start to increase

[eternal terrace]

That’s correct as the end point not the start…

[cerulean rain]

Ohh TT

[eternal terrace]

You only want the decreasing part so you stop there

You got it finally?

[cerulean rain]

Yes thank u for helping me TT

[eternal terrace]

Anytime

[cerulean rain]

Byeee

[eternal terrace]

The interval for decreasing edge is (-inf, 1]
For increasing edge [1, inf)

[cerulean rain]

Okie

Baii

[eternal terrace]

||i don’t actually know if i can put the sqaure bracket [ or ] on 1 or not you will have to see bungo for that||

[eternal terrace]

Read the spoiler then close the channel and GOODNIGHTTT

Hope you have a good night sleep and sweet dreams, sorry for pushing you past your limits

[cerulean rain]

TT its ok

[eternal terrace]

Youre way over your bedtime i can tell

[cerulean rain]

Sleep well

STOP

TT

[eternal terrace]

Thankss you too

.close

Do this^

and if you have more questions come tmrw and open a new channel

[full forum]

@cerulean rain Has your question been resolved?

[full forum]

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[full forum]

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[azure burrow]

does admit mean contain here?

[azure burrow]

or does it mean like it just doesnt exist at all

if it didnt exist at all then the set couldnt be bounded though right

[brittle sun]

Can mean either depending on what context it's in

[brittle sun]

A maximum element is a unique maximal element

In partial orders, you can have multiple maximal elements

[azure burrow]

heres the full question if that makes it any better

[brittle sun]

Ah okay then it's contains

[azure burrow]

ok thank you

.solved

[full forum]

Channel closed

Closed by @azure burrow

Use .reopen if this was a mistake.

[azure burrow]

oh wait

.reopen

[full forum]

✅ Original question: #help-28 message

[azure burrow]

hmm so are you saying that a unique maximal element doesnt have to exist but the set can be bounded still if it has multiple

hm ok I think I see

so like if we have {1,2,3,a,b,c} where a b c have the same order above the rest

theres no maximum element but its bounded below by 1 and above by a b c?

[queen crater]

Yes, but I don't think this question is about partial orders

A in R implies the order we are using is the usual <= total order on real numbers

[brittle sun]

In case of partial orders yeah

[queen crater]

The point of this question is to show you that a subset of R can have an upper bound but no maximum

And if I say any more I'm giving you the solution

[full forum]

@azure burrow Has your question been resolved?

[azure burrow]

I see thank you

[full forum]

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[echo cloak]

hello im trying to learn linear function and slope stuff and anything in between

[echo cloak]

stuff like y= -7/4(x+3) +5

[stiff musk]

what specifically do you want to know about it?

[echo cloak]

well i have exams tmr and i really dont even know where to start

like how would i solve this stuff and how would i plot it on graphs

[stiff musk]

sure

you know about intercepts?

x and y intercepts

[echo cloak]

i think

where they cross the line

[stiff musk]

right

how would you find the x intercept of that line for example?

[echo cloak]

of this one?

[stiff musk]

yep

[echo cloak]

uh

(x+3)

i think?

[stiff musk]

well it should just be a number

the x coordinate where the line crosses the x axis

that gives you a point on the line

similarly for the y coordinate

or, you could just plug in some values for x and get the corresponding y values

those will all be points on the line too

if you have two points then you can draw the line through them

[echo cloak]

ok so the x intercept would be 3?

[stiff musk]

well what's the y coordinate of the x intercept

(always, not just for this line)

[echo cloak]

uh im rlly slow

sorry i dont get it

[stiff musk]

ok let's do this another way then

you want to know how to plot the graph, right?

[echo cloak]

yes

[stiff musk]

and you know it's a line

[echo cloak]

yes

[stiff musk]

so you just need two points on the line

[echo cloak]

yes

[stiff musk]

so you can just plug in two values for x

and get the corresponding y values

then you have two points

plot the points and then draw the line that passes through them

[echo cloak]

wym plug in 2 values for x?

[stiff musk]

for example

if i plug in x=1

then i have y = -(7/4)(x+3) + 5

= -(7/4)(1+3) + 5

= (-7/4)(4) + 5

= -7 + 5

= -2

so if x = 1 then y = -2

this means that (1, -2) is a point on the line

[echo cloak]

ok

[stiff musk]

you can do the same for another choice of x

[echo cloak]

so how do i know what to plug in for x?

[stiff musk]

you can plug in any number you like, but some will give you nicer y values than others

in particular since you have -7/4 out in front, it will help if your x+3 is a multiple of 4

like i chose x = 1 so that 1 + 3 = 4

then -7/4 times 4 gives me a nice integer, -7

you could choose x = 5 for example, then x+3 = 8

which will also work out nicely (no fraction in your y value)

[echo cloak]

ok so i plug in 1 for x i get y= -7/4(1+3) +5

right?

what then?

[stiff musk]

simplify

1+3 = 4

then multiply -7/4 times 4

you get -7

add the 5

result is -2

[echo cloak]

ok so i get -2

then what?

[stiff musk]

so you know that if x = 1 then y = -2

[echo cloak]

yes

[stiff musk]

so the point (1, -2) is on the line

you just need one more point

so pick another x value

i suggest x=5

[echo cloak]

ok

[stiff musk]

the numbers work out nicely then

[echo cloak]

so y= -7/4(8) +5

-7/4 times 8

is -14

+5

is -9

[stiff musk]

yep

[echo cloak]

so y= -9

[stiff musk]

correct

so your second point is what?

[echo cloak]

x=5 y= -9

[stiff musk]

yep!

so now just plot those two points

and then draw the line that goes through them

[echo cloak]

well the question i have on my practice paper says "find the slope and point given by the function y= -7/4(x+3) +5"

[stiff musk]

well what's the slope?

[echo cloak]

-7/4?

[stiff musk]

yep

and they want what, just a point on the line? "find the slope and point"

well you have two points already

so you're good

[echo cloak]

oh i forgot to say its multiple choice

[stiff musk]

oh i see, can you show a screenshot?

[echo cloak]

its on paper

1 sec

[stiff musk]

sure

[halcyon mantle]

U use the formula y-y1= m(x-x1) where (y1, x1) is a point on the graph

[echo cloak]

what

[halcyon mantle]

Wait

I didnt read the question mb

Whats the function

[echo cloak]

y= -7/4(x+3) +5

[halcyon mantle]

Its d

Because

When x = -3, y= 5

And the gradient is the number infront of (x+a)

[echo cloak]

what is gradient?

[halcyon mantle]

m

The form the book uses is y = m(x-a) + b

Or wtv letters you use

A,b is always a point on the graph

And m is the gradient

[echo cloak]

this is extremly confusing lol

[halcyon mantle]

What equations have u learnt

[echo cloak]

wym?

[halcyon mantle]

Like

What method have ur teachers taught you

[echo cloak]

...

idk

[halcyon mantle]

Bro what

How did u solve the above question then

[echo cloak]

6 am math class bro im sleeping

the one above is asking which line is perpendicular and i guessed that

and got it wrong

[halcyon mantle]

Oh.

So have u learnt the formula y= mx + b or y = m(x-a) + b

[echo cloak]

yes ik y=mx +b

not the second one

[halcyon mantle]

Ok learn this new one

Its faster for this question

So

The function is y= -7/4(x+3)+5

If u compare that to y= m(x-a) + b

A = -3

And b = 5

So the point is (-3,5)

And m is -7/4

[echo cloak]

oh dam thats simple

[halcyon mantle]

Ye

Wait what grade is this

[echo cloak]

10th

[halcyon mantle]

Sometimes teachers mark u doen for using wrong formula

[halcyon mantle]

Ok ur fine

[echo cloak]

1 sec lemme write this down

i got more tho

[halcyon mantle]

More what

[echo cloak]

questions and other things i need to learn

[halcyon mantle]

Its really ez when youve understood it

[echo cloak]

im tryna learn all of linear functions and domain and range all in one night cuz i got my math exam in 8 hours

[halcyon mantle]

..

[echo cloak]

is it over for me?

[halcyon mantle]

How fast of a learner are u

[echo cloak]

https://media.discordapp.net/attachments/948956082431201300/1101800582324428800/blobthing.gif

this sums it up

[halcyon mantle]

Say ggs😭

But anyway

All u really need to knoe

Is

[echo cloak]

https://tenor.com/view/my-mom-is-kinda-homeless-ishowspeed-speeding-please-speed-i-need-this-ishowspeed-trying-not-to-laugh-gif-16620227105127147208

[halcyon mantle]

Domain is the limits for x values

And range is the limits for y values

So if y= 6x+7 for -1<x

-1<x or x>-1 is ur domain

[echo cloak]

what in the world

[halcyon mantle]

And if u plug that in the equation

Ur range would be y> 1

[halcyon mantle]

Its better understood if u draw it

[echo cloak]

uhh

can u hop in a vc and screen share?

im a visual learner

[halcyon mantle]

I cant vc rn but i can send photos

[echo cloak]

yes ty

[halcyon mantle]

Heres an equation

Lets say the domain for x is from 3 to 5

[echo cloak]

1 sec im writing stuff down

[halcyon mantle]

The domain tells you what section of the graph is relevant

So only that section is relevant for this question

The range tells you what y values are possible for the x values in the domain

So because the equation is y=x

The least x value is 3 and the greatest is 5

Y= 3 is the least y value and y=5 is the greatest y value

So the range is 3<y<5

Do u understand this😭

[echo cloak]

absolutely

not

speak english please

[halcyon mantle]

Ok u might have to search yt vids on this

[echo cloak]

ok ill do domain and range later

i have other stuff 1 sec

[halcyon mantle]

Watch the organic chemistry tutor”s video

[echo cloak]

how would you get an equation from a line?

like say i have a line, how do i get the equation

[halcyon mantle]

You have to find 2 points

On the line

And then find the gradient

M = (y1-y2)/(x1-x2)

$M = (y1-y2)/(x1-x2)$

[glossy valve]

wxy

[halcyon mantle]

Wait

.

How do u write fractions

On the boy

Bot

[echo cloak]

idk big dawg

[whole lily]

\frac{y_1 - y_2}{x_1 - x_2}

[halcyon mantle]

$\frac{y_1 - y_2}{x_1 - x_2}$

[glossy valve]

wxy

[halcyon mantle]

Ah

Thx

[echo cloak]

ok hold on

so look

i have a graph and the first plot is at -6,9

the second is at 3,-9

thats the line

[halcyon mantle]

Ok

So

Let x1= -6 and y1= 9

[echo cloak]

well thats to find the slope

[halcyon mantle]

Yes

[echo cloak]

i dont even know the first step to making the equation with these plots

[halcyon mantle]

U use the formula y-y1=m(x-x1)

[echo cloak]

what

i never learnt that

[halcyon mantle]

Well learn it

Its the quickest way

I think

[whole lily]

I think it would be better if you explained the intuition behind slopes and y-intercepts and everything

Then forwarded them on with the respective formula and how they are derived or how they operate

[halcyon mantle]

U can do that bro im ah at teaching ppl😭

[echo cloak]

and im slow in the head

[halcyon mantle]

Ur doing like yr11 stuff in my country besides the parabolas

[echo cloak]

all i know is that i got 2 plots here and i need to make an equation outa them

[echo cloak]

im in canada

[halcyon mantle]

Hm lemme try teach

Do u understand what a gradient is

[echo cloak]

m

the slope

?

[halcyon mantle]

Yeah but what does it mean

[echo cloak]

not a clue

[halcyon mantle]

Its the rate of change of a graph

[echo cloak]

uh

ok

[halcyon mantle]

.

[coral ore]

a graph?

try to be more specific

[halcyon mantle]

So basically its the change in the y coordinates divided by the change in x coordinates

[halcyon mantle]

Alr bro😭

In linear graphs , so on a straight line

[echo cloak]

isnt it usualy a fraction?

[coral ore]

it can be an integer

[halcyon mantle]

U can take over i cant explain stuff to ppl😭

[coral ore]

na you got it

[coral ore]

give a real life example

[halcyon mantle]

😭

Normally i memorise the formulas b4 trying to understand it

[halcyon mantle]

Idk how to do without using the formula😭

[coral ore]

so it is a rate of change of some variable as opposed to another

Lets say a staircase or a hill example

[halcyon mantle]

Thats more confusing.

Ig

[coral ore]

Lets also say that the gradient is 2

so for every meter you go forward, you are going 2 meters upwards

[halcyon mantle]

😭

[coral ore]

how about y = 2x

gradient = 2

[halcyon mantle]

They tried getting me to tutor lil kids but i just couldnt get them to understand anything 😔

[coral ore]

because you are using the formula

[halcyon mantle]

No it was like how to find x if 5+ x = 7

[coral ore]

so what was your approach

[halcyon mantle]

Tried to say you have to get x by itself

[coral ore]

so what did they not get?

[halcyon mantle]

Idk bro😭

[coral ore]

😢

[halcyon mantle]

U think i can survive yr13 maths only memorising the formulas b4 trying to understand them?

[full forum]

@echo cloak Has your question been resolved?

[echo cloak]

so um

where did we leave off?

[full forum]

@echo cloak Has your question been resolved?

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[nimble canyon]

Is the equation for this
911 + 0.80(911) + 0.80(T2) + 0.80(T3)... 0.80(TN-1) + 0.80(TN)

[silk bridge]

every term multiplied by 2 after 911

as it travels both up and down

[nimble canyon]

Oh yeah

[silk bridge]

you can express this as gp

[nimble canyon]

How would one do that?

[silk bridge]

do you know geometric progression ?

[nimble canyon]

Yeah

• /

[turbid badge]

well what are we doing with each next term

[nimble canyon]

a * ar * ar^n-1....

So the first term 99 + 991(0.80)^1 .....

So too account for going down and going up you just multiple the 911 * 2

so 911 + 2(911(0.80)+911(0.80)^2)

[silk bridge]

yh

so what is r here

@nimble canyon

[full forum]

@nimble canyon Has your question been resolved?

[nimble canyon]

0.80?

[silk bridge]

yh

this is an infinite gp

[nimble canyon]

And to find the Sum it would be a / 1- r ?

Yep alright ty

Also I got a question

is this true for when the sum is finite and R < 1 therefore A = A ( 1-rN) / 1 - r

[silk bridge]

the sum converges for R<1

[nimble canyon]

what does that actually mean?

[silk bridge]

,, \sum_{n=0}^{\infty} ar^n = \frac{a}{1-r}, \quad |r| < 1

[glossy valve]

scoob

scoob

scoob

[turbid badge]

to add to this, if i have |r|>1, then as n gets big, r^n also gets big and goes to infinity
for r=1, you have division by zero

[nimble canyon]

Alright but then my textbook states if GP R < then use Sn = a ( 1 - R^n) / 1 - r

What is the difference to this?

[turbid badge]

this is when the sum is infinite

i mean you have infinite terms

[nimble canyon]

but it states to use it when r <

1

[nimble canyon]

Wait so If it is infite and < 1 then u use it??

[turbid badge]

yes

[nimble canyon]

yy

ty

So for this question

Sinfitity = a / 1 - r
-1 < r < 1
5( 1 - r )
CAse 1)
5 ( 1 - 1) = 0
isnt possible)
case 2 )
5/ 1 - ( -1) = 10

so 10 > a > 0

[turbid badge]

yeah i think it's correct

[full forum]

@nimble canyon Has your question been resolved?

[full forum]

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[cold lagoon]

had to crop photo

[cyan mantle]

tf which lvl math is this

[full forum]

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[night socket]

pls someone explain

[sacred yarrow]

Which part are you having problem with?

[whole lily]

They defined $\omega = \alpha$, and note that $\omega^2 = b$ and $\omega^3 = 1$ because these are simply cube roots of unity

[glossy valve]

Roy

[whole lily]

also note that $A\omega^{2}+B\omega+C=\omega\left(A\omega+B+C\omega^{2}\right)=\omega^{2}\left(A+B\omega^{2}+C\omega\right)$

[glossy valve]

Roy

[charred carbon]

They made multiple typos here and there so that's indeed confusing

[whole lily]

yeah there should be an extra equals at the beginning of the 3rd line

no idea why they used a new variable omega instead of alpha

[whole lily]

but this essentially allows them to factor it such that a bunch of stuff happens to cancel out nicely

[full forum]

@night socket Has your question been resolved?

[night socket]

ohh

so then :
1+ w^2 +w = -1 right?

[whole lily]

Not quite

that sum is actually the sum of the cube roots of unity which intuitively should be 0

[night socket]

oh ye mb

[night socket]

basically 9w^3 +7w -7w^2 + .. and he takes out w^3

[night socket]

how.

[whole lily]

If you're stuck on how it's factored, try expanding the factored term so you can see how it came to be

it's the properties of roots of unity

[night socket]

ok then, i got it.
now how do i solve the q.
w^20 is what i have in common and

that 9 thing + 14(w++w^2)

w+w^2 =-1

ok nvm got it.
thx @whole lily @charred carbon

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