help-49

[last slate]

$(r,\theta) = (r,\theta + 2n\pi) = (-r, \theta + (2n +1)\pi$

[grand pond]

What should I do: Physics

[last slate]

https://cdn.discordapp.com/attachments/1018703193473024061/1157110575055241246/image.png?ex=65176ab3&is=65161933&hm=ef37c091a8b34943f1719278c608cc4c1725197e87b617f7874851d4848fc4d9&

[midnight plank]

@last slate Has your question been resolved?

[midnight plank]

@last slate Has your question been resolved?

[last slate]

<@&286206848099549185> where my helpers at

[rare kestrel]

Help

Mfs

[midnight plank]

@last slate Has your question been resolved?

[errant ginkgo]

@rare kestrel don't occupy other's channel
create urs

[errant ginkgo]

watch ur language pal
this isn't the hood u r looking for

[last slate]

.close

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[blissful wren]

hi, im struggling on part c

[blissful wren]

tried to use l'hopital with directional derivatives but that doesnt really help

got to here and now im stuck

[midnight plank]

@blissful wren Has your question been resolved?

[blissful wren]

<@&286206848099549185>

[midnight plank]

@blissful wren Has your question been resolved?

[blissful wren]

<@&286206848099549185>

[midnight plank]

@blissful wren Has your question been resolved?

[blissful wren]

<@&286206848099549185>

[blissful wren]

<@&286206848099549185> any help would be greatly appreciated

[fossil abyss]

I dont have any answers myself but i found that subbing in x=0 into the double partial derivative gave me -1, while subbing in y=0 gave me 1

I dont have any good explanation for this however, i just remember finding myself throwing in substitutions like y=x^2 or y=2x when i needed to find limits like these

[midnight plank]

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[blissful wren]

Gotcha thanks

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[flat spire]

hi is this allowed $\int_{ }^{ }\frac{\sin^{2}x}{\cos^{2}x}dx=\int_{ }^{ }\frac{1-\cos^{2}x}{\cos^{2x}}dx=\int_{ }^{ }\frac{1}{\cos^{2x}}-\frac{\cos^{2}x}{\cos^{2}x}dx=-1\int_{ }^{ }\frac{1}{\cos^{2}x}dx$

[grand pond]

water beam

[lyric charm]

up until the last step (and a ) you are ok

but then you tried to treat the added -1 as a multiplier

which is a no no

[flat spire]

so I should keep the -1

in the integrand

[lyric charm]

well i mean like

$\int \paren{\frac{1}{\cos^2(x)} - 1} \dd{x} = \int \frac{1}{\cos^2(x)} \dd{x} - \int 1 \dd{x}$ is what i would do at that stage

[grand pond]

Ann

[flat spire]

yeah i got it

.close

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[left fable]

i need help solving this

[left fable]

Y cos2x = X sin2y, (pi/4,pi/2)

find y'

or dy/dx

[left fable]

this is a point in the equation, later on you need to put it instead of x and y

i did everything until i reached this

y-2sin2x+y'cos2y=(xy')(2cos2y)+sin2y

i stopped cuz i didnt know what to do with two y primes

i want 1 y prime

what do i do

[midnight plank]

@left fable Has your question been resolved?

[midnight plank]

@left fable Has your question been resolved?

[left fable]

@sonic drum

[fallow scarab]

use algebra and solve for y'

ay + by = (a+b)y

[left fable]

doesnt work

xd

i did it the other way

[fallow scarab]

okay cool

do .close if you're done

[left fable]

i left y'=

the thing/the y' thing

did everything and the final answer is 2

.close

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[wraith flower]

I'm doing exercise 30)c) , so I have to find fg and its domain

[wraith flower]

I have fg

$\sqrt{( - x ^ { 3 }) + \left( 3 \times x ^ { 2 } \right) + x - 3 }$

[grand pond]

ivoturi

[wraith flower]

what I don't know how to find is its domain

I know it's the positive values of the function inside the square root

so I thought I could do this

but I don't know if it's right, and what else can I do

[midnight plank]

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[simple wigeon]

Hello! I’m trying to understand why the -3^2 here becomes a positive rather than a negative. My professor did it like that but I’m having trouble puzzling it out.

[last slate]

It depends on if there is parenthesis

$(-3)^2 = 9$

[grand pond]

Wesley

[last slate]

Because you are mulitplyin the entire -3 by itself: -3 * -3 = 9

$-3^2 = -9$

[grand pond]

Wesley

[last slate]

This can also be thought of as:

$-1 * 3^2 = -9$

[grand pond]

Wesley

[last slate]

Then by pemdas, you would have to do the exponent first

Does that make sense?

$-3^2 = -1 * 3^2 = -9$

[grand pond]

Wesley

[last slate]

It should be minus 9. Check in with your professor about it I guess

$5(2-5) - 3^2 = 5(2-5) - 9$

[grand pond]

Wesley

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[uneven carbon]

how do you solve for y in the table

[dense idol]

with the given equation

[midnight plank]

@uneven carbon Has your question been resolved?

[uneven carbon]

how but how do you do that

whats the operation

[dense idol]

y=(x+7)/2

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[robust shale]

This looks very similar to this(second picture). Are they the same rule?

[dense idol]

$\frac{v^2}{1-v^2}=-\frac{-v^2}{1-v^2}=-\frac{1-v^2-1}{1-v^2}=-1-(-\frac1{1-v^2})=-1+\frac1{1-v^2}$

awful lot of skipped steps assuming you'd follow

[grand pond]

chlamydia

[robust shale]

oh my

okay so it's not the same

dang

So if I have some integral where it's like:
u^2 / u^2-16, is there anything I can do to make it simpiler

using algebra?

[dense idol]

you could do the above and then partial fractions

but maybe trig sub would work

[robust shale]

ooo

trig sub would work

this looks like arc tan

[slender walrus]

do you mean
$$\frac{u^2}{u^2 -16}$$

[grand pond]

ℝam()n()v

[robust shale]

yes

[slender walrus]

shouldn't really be using trig sub here

tan, arctan would be appropriate if the denominator was
u^2 + 16
which isn't the case here

note that u^2 -16
is a difference of two squares

[robust shale]

oh true

[dense idol]

yeah just do partial

[robust shale]

you mean

ok

yeah yeah

I found an example

ty both

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[fossil cove]

doing some calc 1 review as im going into calc 3 soon

but cannot seem to remember how to do this

[slender walrus]

start with finding
g'(x)

using stuff like quotient rule

[fossil cove]

hmmm

so g(-2)=3/2 right?

or am i going completely in the wrong direction here

[dense idol]

g'(x), not g(x)

[slender walrus]

you'd use g(-2) later,

and that is 3/2,
but not the main part of the problem I was trying to get you to do

[fossil cove]

im not sure how i can apply the quotient rule to this problem

i need severe review of calc 1 💀

[slender walrus]

do you know what the quotient rule states

[fossil cove]

yes

[slender walrus]

can you state that here

[fossil cove]

d/dx(f(x)/g(x) = g(x)f'(x)-f(x)g'(x)/g(x)^2

sorry for the poor formatting

[slender walrus]

missing () , but ok

names of functions were arbitrary,
just like the above you have a quotient of two functions of x

try applying that rule here

[fossil cove]

so I can just replace g(x) with f(x)/x?

or would that be pointless?

[slender walrus]

going to rewrite this to not get names in the rule and your question mixed up

$\dv{x} \frac{p(x)}{q(x)} = \frac{q(x)p'(x) - p(x)q'(x)}{(q(x))^2}$

[grand pond]

ℝam()n()v

[slender walrus]

g(x) = f(x)/x,
yes

apply quotient rule to get it's derivative

[midnight plank]

@fossil cove Has your question been resolved?

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[obtuse void]

I had a question about finding all solutions to x=(fof)(x) for the piecewise fxn f(x)=-x^2+5x+24 if x<0, (x/3)+24 if x=0 or x>0 - I found out you could find the intersection points of f(x)=x and the piecewise fxn to get the answer, but idk how you are supposed to get f(x)=x

[sage helm]

,w solve - x^2 + 5x + 24

[grand pond]

Results provided by WolframAlpha

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Requested by neonperseus

[sage helm]

Maybe it would be easier tol solve for $f(x) = f^{-1}(0)$ for two cases

[grand pond]

NEON

[obtuse void]

im just confused how x=f(f(x)) relates to finding the intersections of the piecewise fxn and x=f(x)

[sage helm]

Oh wait it's x = f(f(x))

nvm then

[obtuse void]

yeah

idk how to do the circle symbol on mobile

[sage helm]

no that wasn't the problem

I thought you were solving f(f(x)) = 0

[obtuse void]

oh

[midnight plank]

@obtuse void Has your question been resolved?

[obtuse void]

<@&286206848099549185>

[brazen palm]

Isn't $f\circ f(x)=f(f(x))$?

[grand pond]

Biscuity

[obtuse void]

yes

[brazen palm]

ahhh, the above convo is confusing to me

consider when's f(x)<0 and f(x)≥0, and then write out the new piecewise function
f(f(x))

[obtuse void]

so x=((3/x)+24))+24 for x>=0

the main thing i need to know is why finding the intersections of the piecewise and f(x)=x give the solutions of x=f(f(x))

[brazen palm]

this feels weird to me, lemme try getting this right in my head...

[brazen palm]

okay, i got some conclusions in my mind:
f(x)=x is an equation, while the piecewise function f(x) is just a function (of course it can be graphed if we put y=f(x).
Why would they have intersection(s)?

[obtuse void]

so x=f(y) by substitution

if x=f(x) then f(x)=f(y) and x=y

if x=/=f(x) then f(x)=/=f(y)

x=f(f(x)) and x=f(y) contradict then

wait

no

[brazen palm]

still feels weird to me...

[obtuse void]

is there any way f(x) and f(y) have to be equal

if they are then that answers everything

[brazen palm]

I'm kinda thinking about this.

[brazen palm]

and I'm totally unsure about this

[obtuse void]

hold on f(x)=f(f(y)

wait no that just leads to f(x)=f(x)

[brazen palm]

XD

[obtuse void]

im tryna figure out why the solutions of x=f(f(x)) and the intersections of the piecewise and y=x are the same

[brazen palm]

yea, i know, and I'll keep working on my f(f(x))

[obtuse void]

alr

#help-15

x=f(f(x)), y=f(x)

[obtuse void]

x=f(y)

[obtuse void]

where did you get -3

[brazen palm]

second line

[obtuse void]

i remember trying to find the solutions by plugging it into itself but the roots of the first equation are all irrational and hard to find

[brazen palm]

,w roots of -x²+5x+24

[grand pond]

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Requested by biscuityxd

[obtuse void]

when you plug that into itself you get a quartic with only irrational roots

[brazen palm]

you mean f(f(x))?

[obtuse void]

yes

[brazen palm]

let's try

,w roots of -(-x²+5x+24)²+5(-x²+5x+24)+24-x

[grand pond]

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Requested by biscuityxd

[brazen palm]

and only 2(1-√7) is needed because x<-3

[obtuse void]

x=f(f(x)), y=f(f(y)), x=f(y), y=f(x)
if x=f(x) then x=y which works
if x=/=f(x) then y=/=x which must not work

f(x)=f(f(f(x))) or f(f(y))

wait no that leads nowhere again

[brazen palm]

oh, typo on the last line, should be x≥0

[obtuse void]

wait both y=f(x) and x=f(y) contradict if theyre different

since it means x is equal to y for a value(y)

ok nvm i finally got it

.close

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[obtuse void]

.reopen

[midnight plank]

✅

[obtuse void]

.close

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[lament wraith]

I dont really get this.
Isnt x = 0 , y = 1?
Since z^3 = -i, therefore z = i

[lyric charm]

is z=i getting rejected?

[lament wraith]

this is the answer key, but i dont get why is it so complicated

[lament wraith]

is this way of thinking wrong?

[lyric charm]

i isn't the only cube root of -i

there are two others

[lament wraith]

what are the other 2? so far in my lecture notes we only know about z=i,z^2=-1,z^3=-i and so on

[lyric charm]

you know about powers of i, is what you were trying to say

[lament wraith]

yea hahahaha

[lyric charm]

but you also know de moivre's ...

anyway the other two are e^(-iπ/6) and e^(7iπ/6)

[lament wraith]

hmm i see thank you, i will look through my notes again 😄

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[last slate]

Need help with basic epsilon delta definiton of a limit. Here is the example I was following everything up until the point where it says "thus we require delta less than or equal to epsilon/17". Why did the inequality change?

[last slate]

I got up to 17|x-8|< epsilon but not sure why the inequality changes here

[plucky mango]

What is your major?

[last slate]

Im studying Maths and Comp sci

[jagged saffron]

If you want 17|x-8| < ε, then you need to have δ <= ε/17.
Since then 17|x-8| < 17δ <= 17ε/17 = ε

[plucky mango]

Icic hold up

[last slate]

wait whered the equal sign come from

[jagged saffron]

Editing

[last slate]

yes but why the <= on the first line

how does it follow from 17|x-8| < ε

[jagged saffron]

Because its what makes the next line work

[last slate]

why not δ < ε/17

[jagged saffron]

Sure you can do that too

Delta is never unique, a smaller delta will always do the job

I'm just following what they did

[last slate]

Im so confused 😭

so it doesnt matter if I choose a stricter delta?

I mean I get that

[jagged saffron]

Smaller delta

And no it doesnt

[last slate]

but why would delta= epsilon /17 be fine

[jagged saffron]

Because then 17|x-8| < 17δ = 17ε/17 = ε

[last slate]

oh you know I think its starting to click a little

I have a strong hunch that Im going to fail Real analysis

thanks for the help

.close

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[queen thistle]

I know how to do the power rule

but not how to do the continuation yet

the method I know how to do is defining the derivative using the lim stuff

but I can't seem to wrap my head around this one

The first time I did it it was easy because it was 4/x^2 when f`(1)

so it was (4/(x^2)-4)/x-1

but this one would be (1/(x^2)-1/25)/x-5

and I'm not sure how to continue off of that

other solution ofc is to figure out how to continue off of -2x^-3

[potent veldt]

difference of squares

[potent veldt]

or for this... Just plug in $5$ for $x$

[grand pond]

992qqoloy

[queen thistle]

Weird

My calculator must be really stingy with the way I type that in

cuz I tried it a few times and it was wrong

but this time I tried it and got it right with that

that method is easier so lemme practice that more

Wow okay that worked

thanks

.close

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[boreal oasis]

Linear functions

[fallen socket]

What?

[boreal oasis]

How u do ts

[last slate]

which number are you stuck in

[boreal oasis]

All of them

[last slate]

complete the table

you're graphing a line

[boreal oasis]

How you do 2x + y = 8 you can’t add y and 2

[last slate]

before getting the y values here make y the subject of the formula

can you do that for me

[boreal oasis]

I don’t know what you saying fam

[last slate]

making y the subject of the formula means

y=something

[boreal oasis]

It says y equals 8

[last slate]

y=8?

[boreal oasis]

Yes

[last slate]

from this

[boreal oasis]

Y = 8

[last slate]

2x+y=8
y=?

[last slate]

what happened to the 2x

[boreal oasis]

Oh yuh

But how can y equal something

[last slate]

wdym

[boreal oasis]

It’s the y axis

[last slate]

the values that you get for y will tell you how high the point will be

for example can you show the point x=1 y=2

on a diff sheet of paper

[last slate]

draw a cartesian plane like the one here

lmk if u get stuck @boreal oasis

[last slate]

perfect

[last slate]

so for us to get the y values we need to make 2x+y=8 in the form of y=something

can you tell me what the equation would be

y=..

[boreal oasis]

Does x mean x axis

[last slate]

the x values

[last slate]

do this you'll see what i mean

[boreal oasis]

I still don’t understand how to get what y =

[last slate]

you have an equation

lets say 3x=5+y

if i wanted to make y the subject of the formula (make y stand alone)

id move the 5 to the other side

so i'd be left with

3x-5=y

thats clear to you right

[boreal oasis]

So 2x+8= y

[last slate]

who did you move to the right / left

[boreal oasis]

8 to the left

[last slate]

2x+y=8
2x+y+8=0

so like this?

and what happens to a number when we move it to the right

[boreal oasis]

Uh

[last slate]

x+8=0
make make x the subject for me

(different example)

[boreal oasis]

How do you make “ the subject”

[last slate]

...

"make it standalone"

[boreal oasis]

So make x 0

So 0+ 8= x

[last slate]

who did you move

x?

[boreal oasis]

Yes u said move to other side

[last slate]

ok but what happens to a number/variable when we move it

does it remain the same

[boreal oasis]

No

[last slate]

see my example

[last slate]

so what will happen to x

[boreal oasis]

It becomes the answer

[last slate]

what

[last slate]

it becomes a negative

[boreal oasis]

How

[last slate]

x+8=0
x=-8

where you not taught this

or if i moved x

x+8=0
8=-x

[last slate]

more explicitly

x+8=0
x+8-8=0-8

what we do to one side of the equation we do to the other

i subtracted -8 from both equations

8-8=0

so x+0=-8
x=8

[boreal oasis]

So 8 -8 = 0

[last slate]

lmk if something is unclear

[last slate]

now do for me

2x-3+y=0

make x the subject

or y first since its easier

@boreal oasis you there

[boreal oasis]

Yuh

[last slate]

are you stuck

[boreal oasis]

I think

[last slate]

2x-3+y=0
making y the subject

what are your ideas?

what do we have to move around

to have something like y=....

[boreal oasis]

But there’s already y=

Y=0

[last slate]

uh what about the 2x-3 in front of it

2x-3+y=0

[boreal oasis]

That’s behind it

[last slate]

thats not y=0 tho

its 2x-3+y=0

y=something y is alone

completely

[boreal oasis]

So u can move the y to the 0 and y becomes the 0

[last slate]

can you show me how

always show your work

2x-3+y=0
....?

[boreal oasis]

Ok

[last slate]

what steps are we taking

[last slate]

yes but what did i tell you about what happens to y

or any other variable or constant that gets moved

[boreal oasis]

• y

[last slate]

-y right

[boreal oasis]

Negative

[last slate]

good

you have -y as the subject

but i want y what can you move instead of y to achieve this

[boreal oasis]

X

Wym fam

[last slate]

why do u keep changing your pfp

i thought it was someone else lol

[boreal oasis]

💀

[last slate]

not x what do we have

[last slate]

and your name

[boreal oasis]

My name is the same

[last slate]

w/e what do we have here

we have 2x not just x

[boreal oasis]

Yuh

[last slate]

so move it what do you get

[last slate]

actually faster to type if you can

[boreal oasis]

0-3+y=2x

[last slate]

all steps please

[boreal oasis]

U said move it

[last slate]

2x-3+y=0
0-3+y=2x

this is wrong too

can you tell me why

[last slate]

.

[boreal oasis]

Cause 0 can’t minus 3

[last slate]

0-3 is the same thing as -3

the 2x you moved has a problem

can you tell me what

[boreal oasis]

How it have a problem the 2 is a coefficient

[last slate]

...

[boreal oasis]

So -2x

[last slate]

so what are the full steps

[boreal oasis]

So anytime it moves to equal it has to be negative

[last slate]

yess

[boreal oasis]

Ok

2x-3+0=-y

[last slate]

.

[last slate]

.

[last slate]

you had the right idea moving the 2x

[last slate]

but its wrong

[boreal oasis]

How

[last slate]

you started with
2x-3+y=0

when you move 2x to the right hand side what happens to it

[boreal oasis]

But u said making y the subject is eaiser

[last slate]

thats where we are getting at

moving the 2x and -3

so y

is alone

lmk if you dont get something

[boreal oasis]

0-3
-3+y=-2x

[last slate]

very good

[last slate]

btw you indicate the 0-3 elsewhere on a side sheet of paper not in the full steps

[boreal oasis]

Yuh

[last slate]

ok you're now left with -3

[boreal oasis]

But there’s no way to do -3+y

[last slate]

-3 is a term
2x is a term
y is a term

they are not linked

[boreal oasis]

But whatever u do to one side u have to do to the other

[last slate]

yes

what can you do to the left hand side

to eliminate 3

what is -5 + 5?

[boreal oasis]

0

-3 -3

[last slate]

good

what

what is -3-3

[boreal oasis]

That’s how u eliminate 3

[last slate]

.

[boreal oasis]

Or is it +

[last slate]

do you not see the difference

[boreal oasis]

Oh yuh

Negative and positive cross out each other

[last slate]

so what are you doing to both sides

[boreal oasis]

• 3

[last slate]

exactly

so write me the full steps

starting from

2x-3+y=0
....
.....
y=....

[last slate]

where did the 3 go to and what did you do to 2x

[boreal oasis]

-2x +3 = -1

And -3 + 3 =0

[last slate]

we started with

2x-3+y=0
you did
-3+y=-2x

[last slate]

idk what that -1 is

[boreal oasis]

Negative 1

[last slate]

?

where did it come from

[boreal oasis]

Cause 3+ negative 2x equals 1x

[last slate]

3 and -2x are not like terms

you only do that for like terms

[boreal oasis]

So it would be y=-2x

[last slate]

2x-3+y=0
-3+y=-2x
y=-2x+3

this are the full steps

[last slate]

and the +3?

[boreal oasis]

But I thought u do negative 3 plus 3 then cross out the 3

[last slate]

2x-3+y=0
2x -2x -3 + y = 0 -2x
-3+y=-2x
-3 +3 + y=-2x +3
0+y=-2x+3

[boreal oasis]

How is the 0 still there tho

If 0 -3

[last slate]

like i told you before the 0 doesnt matter 0+y=y

its for you to understand easily since ur having a problem

[boreal oasis]

So y = 2x+3

[last slate]

-2x

ok i'll give you one last exercise

[boreal oasis]

Ok

[last slate]

2x+y=1

make y the subject of the formula

[last slate]

very wrong
idk what you did to the 1

and we talked about not moving the y since we'll get -y, you can move others

[boreal oasis]

U said make y the subject

[last slate]

not -y

and that -y is wrong even

[last slate]

what is happening with the -1-1 ?

[boreal oasis]

-1 + 1

[last slate]

??

you have
2x+y=1

[boreal oasis]

The subject was 2x

Now the subject is y

So u move the y

To the equal

[last slate]

what?

you had
2x+y=1

[boreal oasis]

U said that in the last problem

[last slate]

you only had to move 2x

to get
y=1-2x

[boreal oasis]

But the subject was y

Oh

[last slate]

another exercise since you're not understanding

x+y=3

make y the subject

[boreal oasis]

Y=3-x

[last slate]

good

[last slate]

ok now back to this

we're gonna do 2 together and i let you do one on your own and i'll leave you with the rest

[last slate]

lets start with no 1

make y the subject

[boreal oasis]

Y=2x-8

[last slate]

look closely

are you sure

[boreal oasis]

Yes

[last slate]

wrong

2x+y=8

[boreal oasis]

How

[last slate]

this is your original equation

[boreal oasis]

Yes

If the subject is y

[last slate]

how did you get this then

[boreal oasis]

It’s y=2x+8

[last slate]

2x remains unchanged?

[boreal oasis]

So y=8+2x

[last slate]

you just typed the same thing

[boreal oasis]

It changed tho

[last slate]

8+2x=8+2x

5+7=7+5

[boreal oasis]

How u get a 5 and a 7

[last slate]

what did i tell you about what happens to a number or variable when we move it

across the =

[boreal oasis]

Y=-2x+8

[last slate]

yes

now that we have y as the subject

[boreal oasis]

But how is this one a plus when the last one was a -

[last slate]

we can use it

[last slate]

which one

x+y=3?

or 2x+y=1?

[boreal oasis]

.

[last slate]

...

[last slate]

what do you not get

[boreal oasis]

But how did it become a -

Instead of a plus

[last slate]

the 2x?

[boreal oasis]

Instead of. Y=1+2x

Oh I think the 2x is -2x

[last slate]

we started with

2x+y=1

not -2x+y=1

[boreal oasis]

But 2x+y=8 didn’t start with a -2x

[last slate]

i dont get your question

[last slate]

can you make y the subject of the formula for me

[boreal oasis]

For what question

[last slate]

2x+y=8

[boreal oasis]

Y=-2x+8

[last slate]

good

which is the same as
y=8-2x

[boreal oasis]

But it has a t chart

How u do that

[last slate]

8-2x = -2x+8

[boreal oasis]

Oh

[last slate]

what?

[last slate]

like i said

a + b = b + a

[last slate]

so

we had 2x+y=8

you got it as

y=8-2x or y=-2x+8 same thing

now we're gonna find the y values

what is y when x is 2?

[boreal oasis]

2x+y=8
2 x 2=4
4+2=8

[last slate]

?

you use the formula you got

when y is the subject of the formula

so you'll use

y=-2x+8

what is y when x=2

[boreal oasis]

Y=4+8

[last slate]

can you pls show all your working

y=-2x+8
y=-2(?)+8
y=?

[boreal oasis]

Oh yuh it’s a negative

[last slate]

.

[last slate]

.

[boreal oasis]

Y=-2x+8
Y=0+8
Y=8

[last slate]

i gave you a format

[boreal oasis]

Oh

[last slate]

where is x as 2?

[boreal oasis]

Oh it’s •

I thought it was plus

[last slate]

??

[boreal oasis]

So it’s -4+8

4

[last slate]

always full working please dont just give me random numbers

[last slate]

.

type it out tho no need for paper

[boreal oasis]

Fam y=-2x+8
Y=-2(2)+8
Y=4

[last slate]

good

[last slate]

so when x=3 y=4
now do for the rest

fill in the table

[boreal oasis]

There is no 3

Only 2 4 6

And 4 is 0

[last slate]

oh right

[last slate]

good

[boreal oasis]

It’s 4 0 -4

[last slate]

ok

[boreal oasis]

Ok I graphed it

[last slate]

you plotted them right

[boreal oasis]

Yuh

[last slate]

now you can draw a line

that goes through all of those points

[boreal oasis]

Now I don’t know how to do these fractions bruh

I hate fractions

[last slate]

what fractions

[last slate]

have u finished

[boreal oasis]

Yes

[last slate]

ok

[last slate]

you mean for

no 2. 4x-2y=-8

[last slate]

or do you want to do no 3 first

[boreal oasis]

Number 4 and 5

[last slate]

have you finished no 2 and 3?

[boreal oasis]

.

Nah I’ll do those after

[last slate]

ok 5 and 6 then

x-intercept the point where (y=0) solve for x

y intercept the point where (x=0)

solve for y

for example

lets say i had

y=-2x+3

what would be the x intercept

[boreal oasis]

But x is uknown so how u see that

[last slate]

oh no 4 is the same as the others btw

[boreal oasis]

But it has a fraction

[last slate]

thats what you're solving for

[last slate]

x intercept

youre given y=0

find x

[last slate]

are you allowed to use a calculator or you calculate by hand

[boreal oasis]

Desmos

[last slate]

same thing

[dapper crow]

Caculator or count by head head

lol

[last slate]

just treat it the same way you would treat any other number

[boreal oasis]

What about the +2

[last slate]

that was just a random example i gave

with fractions

[boreal oasis]

No for question 5

[last slate]

write for me the equation you get

we have y=1x/2 + 2

we have
$$ y= \frac{1}{2}x + 2$$

[grand pond]

sen

[last slate]

Find the x-intercept (y=0)

[boreal oasis]

I do NOT know fractions

Does y mean (y=?) cause how y = 0

[last slate]

we havent even got to them yet im asking you to give me the equation when y is 0

[last slate]

x intercept is the point where y is equal to 0

[dapper crow]

so is Y= 1 divided 2 times (x)

[last slate]

yes

[dapper crow]

Y= 1 divided 2 times X+ 2

[last slate]

what

[boreal oasis]

Y=1/2 (x)

[dapper crow]

yep

lol

[last slate]

now im asking for the equation when y=0

[dapper crow]

you use X as number plus 2

and you got the answer

[boreal oasis]

0= 1/2(x)

[last slate]

good

[dapper crow]

this one make me remember throw back when I'm in middle school I know all this math but now I am truly remember it

[last slate]

so we have

$$0 = \frac{1}{2}x + 2$$

[last slate]

wait

where's the +2

[grand pond]

sen

$$0 = \frac{1}{2}x + 2$$

[last slate]

like this

have you solved equations like these before @boreal oasis

[boreal oasis]

Yuh

[dapper crow]

and 0 = 1 divided 2 times x plus 2

[boreal oasis]

But I forgot fractions

[last slate]

what ideas do you have

[last slate]

dw

i'll guide you

[dapper crow]

xD

[last slate]

idk what you're on about

[dapper crow]

i meant you have 0 = 1 over 2 and get answer from x and plus that number 2

[boreal oasis]

0= 0.5x+2
0=2.5x

[last slate]

bad

[dapper crow]

lol

[last slate]

0.5x and 2 are not like terms

[last slate]

if you dont have anything helpful to say can you kindly leave

[last slate]

so we cant exactly add them

[dapper crow]

than do you have any helpful to help Lay

[boreal oasis]

How if 1 divided by 2 is 0.5

[last slate]

What i'd do is move the 2 to get
$$ -2 = \frac{1}{2}x $$

[dapper crow]

or you rather just call video with Lay and help it out is better in voice

[grand pond]

sen

[last slate]

we dont have voice here sorry

[last slate]

1/2x and 0.5x is the same thing correct

but you cant add 0.5x + 2 to get 2.5x

[last slate]

now im gonna ask

do you know how to eliminate fractions

[boreal oasis]

Nah

[last slate]

lets say we had

$$\frac{1}{4}$$

[grand pond]

sen

[last slate]

what do you think we could multiply to eliminate it

if you dont know i'll just tell you

[boreal oasis]

1

[last slate]

that wont eliminate it

you'll just get back 1/4

[boreal oasis]

But eliminating is backwards subtraction

If u add it will just be more

[last slate]

ok back

sorry

[last slate]

by eliminating i mean just making it not a fraction anymore

for example

if we multiplied 1/4 by 4

what would we get

Like so
$$\frac{1}{4} * 4$$

[grand pond]

sen

[last slate]

i hope you're familiar with the term 'cancelling out'

[boreal oasis]

Uh

Let’s see here

So it’s 1

[last slate]

right

the two 4's cancel out

I think he would do a better job at explain these than me, so have a look
https://www.youtube.com/watch?v=GvLIEiqxS6s

[last slate]

my point was we can 'eliminate' the fraction here just by multiplying by...?

[boreal oasis]

2

[last slate]

good

[last slate]

so we multiply both sides by 2 and what do we get

[boreal oasis]

-4=2x

[last slate]

good

so what is x

[boreal oasis]

2

[last slate]

2?

-4=2(2)?

[boreal oasis]

how if nothing times 2 would equal -4

[last slate]

-2

[last slate]

to get x

just divide both sides by 2

like

-4/2 = 2x/2

what is -4/2

[boreal oasis]

But ( means multiply

[last slate]

2x/2 is the same as 2/2*x

i should probably latex this

sorry

[boreal oasis]

Oh yuh

[last slate]

$$-4 = 2x$$

[grand pond]

sen

[last slate]

then

divide both sides by 2 so we just get x
$$\frac{-4}{2} = \frac{2x}{2}$$

[boreal oasis]

2 1

[last slate]

or
$$\frac{4}{2} = \frac{2}{2}x$$

[grand pond]

sen

divide both sides by 2 so we just get x
$$\frac{-4}{2} = \frac{2x}{2}$$

[last slate]

i forgot a minus

[boreal oasis]

-2

1

[last slate]

good

so x=-2

you've solved for x

[boreal oasis]

How does x = -2

I’d 2 divided by 2 is 1

[last slate]

$$-2 = x$$

[grand pond]

sen

[last slate]

yes 2 divided by 2 is 1

[last slate]

the lhs -4 divided by 2

[boreal oasis]

Ok

BRB

[last slate]

oki

[midnight plank]

@boreal oasis Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[boreal oasis]

.reopen

[midnight plank]

✅

[boreal oasis]

Ay

[last slate]

ok

[last slate]

we last ended here

is it clear now

[boreal oasis]

So the x is intercept is -4

[last slate]

yes but its a point so you're gonna have to give coordinates

(-4,0)

meaning x=-4

and y=0

is that clear

[boreal oasis]

Why is y a 0

[last slate]

what did we say about the x intercept

[boreal oasis]

That it’s -4

[last slate]

,

[last slate]

thats the x value yes

[ember sinew]

if you imagine this visually... like a bird flying at a high y-value, and when x = -4, that's when the bird strikes through the ground.

[boreal oasis]

But why is it a 0

[last slate]

the point at the y axis

the point that hits the y axis

[ember sinew]

y is basically how high the bird is. When y is 0, that's the ground basically, that's where you are "touching" or "striking through" the x-axis.

[boreal oasis]

Then wouldn’t it be 0,-4 since 0 is the ground

[last slate]

we do our coordinates like (x,y)

right?

[boreal oasis]

Yes

[last slate]

what is y at the y axis

[boreal oasis]

?

[last slate]

(-4,0)

[last slate]

what is the value of y at the y-axis

its y=0 innit

[boreal oasis]

Yes

[ember sinew]

oop! if you wrote it as (0, -4), you are essentially plotting a point that is on the y-axis, and -4 points under ground.

[boreal oasis]

Ok

[last slate]

is it clear now

we do the y intercept

[ember sinew]

(can I get a short overview of the question? This thread is quite long and I'm kinda lazy to scroll all the way up lol)

[last slate]

we've been at this for a few hours teaching him the basics

[last slate]

ok you've done the x-intercept

[ember sinew]

Ooo healthy practice : D

[last slate]

now do the y-intercept

remember y-intercept (x=0)

$$y= \frac{1}{2}x + 2$$

[grand pond]

sen

[last slate]

what would the equation be now

finding the y intercept is much much easier

[boreal oasis]

Y=2x+2

[last slate]

what did you do here

[boreal oasis]

1/2=2

[last slate]

we're finding the y intercept right and the only info we have is that x=0

[last slate]

what

1/2 is not equal to 2

[last slate]

before we get to the solving part can you subsitute for me the value of x

like we did when finding the x intercept

[boreal oasis]

0

[last slate]

here

[last slate]

full equation please

[boreal oasis]

0=1/2x+2

[last slate]

what will be 0?

[last slate]

no thats for the x intercept (y=0), we've done that already

[boreal oasis]

So

[last slate]

we're on the y intercept x=0

[boreal oasis]

Y=1/2 * 0+2

[last slate]

good

so what is y

[boreal oasis]

Hold

[last slate]

24324234*0=?

@boreal oasis everything good?

[ember sinew]

What happens when you multiply a number by 0?
Imagine you have bunch of empty bag with no apples in them... You choose to pick up an empty bag, how many apples are there inside?

0 * 3 is the same thing as 0 + 0 + 0.
That's the magic with multiplying with 0, you always get a 0.

[boreal oasis]

Back

So then it’s 2 to elimante fraction

[last slate]

exactly

[ember sinew]

🥳

[last slate]

so now whats the y intercept in coordinate form

[boreal oasis]

6,0

[last slate]

6?

[boreal oasis]

2*2=4 4+2=6

[last slate]

you get y as 2 right from this

and you know x=0

[boreal oasis]

But u said we have to do this

[boreal oasis]

I mean this

[last slate]

what?

thats a video on fractions

the basics of fractions where he teaches you how to manipulate them

[boreal oasis]

Ok

[last slate]

so

now that we have the x and y values

what is it in coordiante form

[boreal oasis]

So it’s 2,0

[last slate]

we alr know

x intercept is (-4,0)

[last slate]

x,y remeber

[boreal oasis]

Y is 0,2

[last slate]

good

good good

[last slate]

i think you're well equiped to tackle the rest

good job

[boreal oasis]

How I tackle

[last slate]

the same way we just did

[boreal oasis]

Nah I’m trolling

[last slate]

lmao

any other questions before we close?

[boreal oasis]

Yuh

How u do these two

[midnight plank]

@boreal oasis Has your question been resolved?

[midnight plank]

@boreal oasis Has your question been resolved?

[last slate]

zero of a function is basically where y=0

formally f(c)=0

[last slate]

so here you'd just have to do what we did before

make y the subject of the formula and y=0

[boreal oasis]

Ok

[midnight plank]

Channel closed

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Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
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[raw grove]

Idr understand what's happening in this table

[fading egret]

what are you confused about

[raw grove]

I don't get how to read it

Like how many times quarter was head?

[hearty rune]

the first entry '50' is saying that there were 50 times when the quarter was heads and the penny was heads at the same time for example

[fading egret]

the rows represent h/t for the quarter and the columns represent h/t for the penny

[raw grove]

Ah okay so will it be 47+57/50+47+46+57. * 100
= 52

[hearty rune]

104/(104+96)

yeah

[raw grove]

Okay thank uu

.close

[midnight plank]

Channel closed

Closed by @raw grove

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.
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[naive flint]

hi

[naive flint]

how come brackets are not allowed in the part of the question where they want the increasing intervals

Yet in this example video

brackets are used 😭

Whats the difference

Must be a mistake on their end?

or im just dumb

[velvet oar]

What

Did that example video come with the assignment or did you find it somewhere else?

[a,b] is a closed interval. It includes a and b and all the real numbers between.
(a,b) is an open interval. It includes all the real numbers between a and b, but not a and b themselves.

The open interval is correct here. The presenter in the video is wrong. At x=1, for example, the function is neither increasing or decreasing, so we should not include it in either interval.

[glacial slate]

constant functions are simultaneously increasing and decreasing (but neither strictly increasing/decreasing); the flat points, such as x=1, should be included because of this, though this is mostly convention

[midnight plank]

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[warm monolith]

to find the initial velocity when given a position equation, do i substitute 0 in for s(t) in the position equation or do i substitute 0 in for t in the velocity equation? in other words, to find initial velocity is position = 0 or is time = 0?

[nova yoke]

initial velocity is v(0)

i.e. plug t=0 into the equation for v(t)

[warm monolith]

okay thank you 🙂

.close

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[finite cloud]

Discrete Math: Can anyone explain to me what the difference between consistent systems specifications and proporisitional satisfiability is?

[midnight plank]

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[finite cloud]

.

[meager ore]

Did you mean "propositional satisfiability"?

[finite cloud]

yeah sorry

[midnight plank]

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@finite cloud Has your question been resolved?