help-0

[noble sinew]

Another approach is if you know what continuity is. Then our function is continuous in (-infinity,0) and (0, infinity). So to solve |x-3|/(2x)<1 is equivalent to solving
(x-3)/(2x)=1 for (x>3) and
solving (-x+3)/(2x)=1 for (x<3)
then checking a value in each interval we have. (so solving the equation above gives x=1 as only solution.) So now you need to check a value in (-infinity,0) and (0,1) and (1,infinity)
So from that we get easily get the solutions

not valid

[celest void]

I'm confused now

[noble sinew]

ignore that guy it isn't valid

[celest void]

I see

[covert berry]

Just ignore.

[coarse bay]

Omg, thank you, this question bugged me for days , the teacher told me the answer but didn't explain how he got it.

[covert berry]

No problem

[celest void]

I see i get most of it except the part where you were able to infer that the function is continuous from ( -infinity, 0) U 0, infinity)

[noble sinew]

if you know what continuity is this is imo much easier

because you can't divide by 0

so it is continuous everywhere else except when (2x)=0 which it is when x=0

[celest void]

I see so give me a second let me try

[celest void]

Hmm so i solved both those equations

and i got x=-3 and and x=1

I still am not able to wrap my head around uh why you mention x=1 as the only solution

[noble sinew]

how did you get x=-3 as a solution?

[celest void]

Also why is this invalid if we consider a condition of x not equaling to 0

[celest void]

x-3 = 2x

[noble sinew]

because if 2x<0 then we multiply be a negative number so the inequality gets flipped

[noble sinew]

?

its for x>3

[celest void]

wait you gave me two equations right x-3/ 2x = 1 and -x+3/ 2x = 1

[noble sinew]

remember we are solving |x-3|/(2x)=1

I just split it up into when x>=3 and when x<3

so x can't both be greater than 3 and be equal to -3

so it isn't a valid solution

[celest void]

Ohh

so x=1 yeah would be the only solution

now that we have x=1 how do we like check a value between different bounds?

[noble sinew]

So because continuous if there isn't a solution in (-inf,0) for |x-3|/(2x)=1 then it will always be greater/less than 1 for all values in this interval

so pick your favourite number in that interval and check if its above or below 1

[celest void]

-1? and then i plug that into this eq: |x-3|/(2x)=1?

[noble sinew]

just in |x-3|/(2x)

[celest void]

oh sorry

copy pasted the equality by accident

yeah

right so that'd result in 2/-2 or -1

So what does that imply 😭

[noble sinew]

well is -1 greater or less than 1?

[celest void]

less than 1

[noble sinew]

so that implies for every single value in (-inf,0) it is less than 1

[celest void]

ohh

then i have to do that for the remaining bounds?

[noble sinew]

yep

[celest void]

0 to 1 and 1 to infinity

[noble sinew]

we stop at 1 because there was a solution there, so we need to check a value less and greater than 1

[celest void]

so i tried from 0to 1 and i inputted a random value and got -2.5 which is lses than 1 so x<1 again

and from 1 to infinity it's still x<1

[noble sinew]

ah try again

[celest void]

Did i do something wrong? 😭

[noble sinew]

This is a wrong value you got

make sure you calculated correctly

[celest void]

(0.5-3)/2*0.5 = -2.5/1 = -2.5

which is less than 1?

[noble sinew]

remember its |x-3|

[celest void]

ohh

wait so i got x>1 and x<-1

[celest void]

so then i have to consider the mutual points?

[noble sinew]

wdym

[celest void]

Wait there's nothing mutual

[noble sinew]

no matter the value of x you choose in (0,1) you should get its greater than 1

[celest void]

Yes x>1 for 0 to 1

and i got x>1 for 1 to infinity as well

and for -infinity to 1 we got x<1

[noble sinew]

you sure?

[celest void]

oh lol might've made a mistake

let me check again

|2-3|/4 <1

Sry

x<1 for 1 to infinity

[noble sinew]

bad notation saying x<1, we are saying whether |x-3|/(2*x)<1 or not

but yep now you should have all solutions right?

[celest void]

right

|x-3|/(2x)<1 and |x-3|/(2x) >1

[noble sinew]

uh

[celest void]

😭 Did i mess it up again

[noble sinew]

we arrived that if x was in (-infinity,0) then |x-3|/(2x)<1 (which is what we wanted to find solutions for). So x<0 are solutions right?

What were the other solutions?

[celest void]

wait yeah it's x<0

but shouldn't it be x<1

i mean both connote to the same thing in this case

but idk how you got x<0 over x<1

weren't we testing for 1

[noble sinew]

we just said that if x was in (0,1) then |x-3|/(2x)>1

[celest void]

Yes

[noble sinew]

so clearly that isn't a solution

[celest void]

ohh

right now i see we're doing the bound testing to see

which bound is applicable for us

alright so like 1,infinity and -infinity to 0 like we said prior

[noble sinew]

ye or written as x<0 or x>1 if you prefer that

In general you can solve an inequality by solving when they are equal then splitting it up into continuous intervals and checking a value in each continuous interval (need to check a value less and greater than if there is an equality) (while still being in the same continuous interval)

Why this works follows from IVT (Intermediate Value Theorem)

[celest void]

I see that makes sense 😭

so technically what we did is uh try to equate |x-3|/2x = 1

Then we separated it into three bounds (-infinity, 0) , (0 to 1) , and (1, infinity)

then tested in which bounds we get |x-3|/2x <1 as per the question

then just got the conditions from there on out

[noble sinew]

yep so we split it up into 2 continuous intervals but because x=1 was a solution we need to check a value less than 1 (while still being in the interval (0,infinity)) and a value greater than 1

[celest void]

I see so that's where the (0,1) comes from?

[noble sinew]

yep

[celest void]

alright thank you very much

I get it now

[analog locust]

I have a question in regard of linear transformation

is it the same when you apply a rotation and then a shear compared to a shear and then a rotation?

[tacit bay]

Can anyone help me with this question

Q4. One boss decided to increase the salary of an employee by 5%. How much will he get if his salary was $2000?

[granite mountain]

2000*0.05=100
2000+100=2100

[alpine sable]

2000 * 105% = 2100

[tacit bay]

so u converted 5% to decimal then multiplied it by 2000 and then just added the 2 values right

[granite mountain]

Yea

[tacit bay]

ok thx

[granite mountain]

5/100=0.05

[tacit bay]

ye ik thx 👍

[granite mountain]

;)

[mental dune]

I asked this earlier but didnt get a response.

I have graphed one of the possibilities for this region but am not sure what the other one is. any helps pls

[dire spindle]

Can you elaborate on your question

[mental dune]

it asks for 2 different possibilities between x = -1 and 0.

i have sketched one but am not sure the other

[covert berry]

$\text{Prove that:} \newline \newline
( (\frac{1 + \sqrt{5}}{2})^{n + 1} \cdot \frac{1}{\sqrt{5}} - (\frac{1 - \sqrt{5}}{2})^{n + 1} \cdot \frac{1}{\sqrt{5}} - 1 )(( \frac{1 + \sqrt{5}}{2})^{n + 1} \cdot \frac{1}{\sqrt{5}} - (\frac{1 - \sqrt{5}}{2})^{n + 1} \cdot \frac{1}{\sqrt{5}}) \newline \newline
\text{ divides 2017, where n = 2017.}$

[mental dune]

<@&286206848099549185> my question is above

[ocean seal]

rudy

[tacit bay]

What is the percent of change from 80 to 120?
can someone help me with this and tell me the formula too pls

[next sequoia]

120----100%

80-----x

[tacit bay]

?

[next sequoia]

80x100/120=x

[tacit bay]

oh ok

thx

wait thats not right

the ans should be 50%

[next sequoia]

you know how the rule of three works?

[tacit bay]

no

[next sequoia]

look for it

[tacit bay]

ok

[next sequoia]

search for "Rule of three mathematics", if not, anything will pop up

[tacit bay]

ok

[cunning junco]

I’m really confused

[next sequoia]

what confuses you?

[cunning junco]

The table for mass

How am I meant to add that up

[next sequoia]

i believe you only need to use the number after the "="

[cunning junco]

Which is the =

[next sequoia]

there isnt an equal symbol?

[cunning junco]

30<m<40

[next sequoia]

oh

maybe use the 35, like the average of those 2

[cunning junco]

Alright I’ll try that ty

Could someone help?

[lethal stump]

you would want to sub in the values ur given into the equation

so since v = u + at

v = 5 +(10)*(2)

so v would be 25 m/s

[cunning junco]

I somehow ended up with 30

Thank you for clearing that up and explaining it that way

[lethal stump]

no worries

[shut elk]

hi folks

i'm aware the answer is $\frac{a}{b-a}$, i can't see the final step

[ocean seal]

ex

[shut elk]

i don't know how to remedy the fact the numerator contains (b-a) but the denominator does not

[glass lichen]

Well the bottom most line is wrong cause you didnt distribute the a correctly in the numerator

[shut elk]

ah ok let me look over it

thx

[glass lichen]

$\frac{a(b-a)}{(b-a)^2}=\frac{a}{b-a}$

[ocean seal]

Mosh

[shut elk]

sorry for my ignorance, but do we not have negative a^2 in the numerator and positive a^2 in the denominator?

i'll foil this all out to check but

urgh

sorry guys, thanks for @glass lichen

[modest dragon]

never sorry for something you dont know!

[shut elk]

yeah it was obvious idk why i fkd it. thanks as usual ppl.

[viscid harbor]

Is B correct

[shut elk]

...

jesus. good luck.

[glass lichen]

cant read the question.

[viscid harbor]

Um

[twin raft]

Hey i have this equation thats absolutely wrecking me,

[viscid harbor]

open In Original

[twin raft]

someone mind explaining the steps

[glass lichen]

for what?

[twin raft]

to solve x

i tried multiplying both sides by (2*10^-3-x)^2

[glass lichen]

that's correct

[twin raft]

i get

x^2=3.6E-5 - 0.036x + 9x^2

[glass lichen]

also my guess is you're doing chemical equilibrium

[twin raft]

yep

lmao

[glass lichen]

yeah then just move everything to one side then quad formula

[twin raft]

ye but for some reason i cant solve it

so anyway i get 0=10x^2 - 0.036x + 3.6E-5

and then i try to do quadratic

[glass lichen]

should be 8x^2

given 9-1 is 8, not 10

[twin raft]

o shit lmao

[glass lichen]

,w solve 9(2*10^(-3)-x)^2=x^2

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by moshill1#9771

[twin raft]

god damn

that was literally the mistake

also i tried to do it via graph but idk why it wouldnt work

[glass lichen]

im also assuming all your other numbers are correct cause I cba to do it

[twin raft]

i wrote into the graph = (x^2)/(0.002-x)^2

and then find value 9

but it gives me wrong number

it works in desmos

but not in my calculator

i wrote the same in my calc as i did desmos

[lethal stump]

yo can someone help me with the LHS of the inequality in part (e), i got RHS but i've been struggling to show that ln2 >2/3

Here's my working out so far but yea I cant get ln2 >2/3

[ocean seal]

rudy

[covert berry]

<@&286206848099549185>

It's not necessarily 2017, any prime number works.

[small holly]

can i simplify:
4xy+x^2-y^2

[covert berry]

No

If you're uncertain whether ax^2 + bxy + cy^2 can be simplified, check its delta.

[small holly]

whats delta?

[covert berry]

Discriminant, I think that's what it's called in English.

The b^2 - 4ac

[glass lichen]

,w factor 4xy+x^2-y^2

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by moshill1#9771

[small holly]

i dont even know what half the stuff you're saying are

[glass lichen]

you cant since the y^2 is negative

[small holly]

is that standard form?

[glass lichen]

yes, the result from wolfram is in standard form

[small holly]

alright thank you

[covert berry]

Discriminant = b^2 - 4ac.
Most often, you want integer values for the number in front of your variables, it's "simplifiable" if the discriminant is a square, and otherwise.

[small holly]

i think i know what you mean

i've just never been taught discriminant

or delta, whatever its called

[covert berry]

You should be taught about it soon

Merely a generalized formula to solve quadratic equations.

[small holly]

alright

i might look into it if we dont learn it

ty

[cunning junco]

What is the gradient of a line whose equation is y = -2x+5

[wanton turtle]

it is of the form y = mx + c

where m is the slope and c is the y intercept

compare them both and you should get the value of the gradient/slope (m)

[civic gyro]

I have the coordinates of node 1 ,2, the slope and a width. How can I calculate each point (a,b,c,d)?

node 1 is (2,5) node 2 is (6,3) and the width is 2

i have no clue how I would do this, I was thinking some vectors or sumthing but im kinda new to that

[white siren]

Can someone help me with Trapezoidal rule?

Numerical integration

[alpine sable]

if i have a linear line. (x,y) 10=400 and 20=680. how do i calculate what 18 is??

[alpine sable]

u drew the line?

[civic gyro]

<@&286206848099549185>

[oak chasm]

@white siren @gray dew @alpine sable Sorry, channel is busy.

@civic gyro Is the node exactly halfway between the endpoints? Is the slope the same for both lines?

[alpine sable]

its fine i got it

[oak chasm]

@marsh vector Sorry, channel is still busy.

[civic gyro]

yes the node is in between the points

[oak chasm]

Well, yes, it's in between, but is it exactly halfway between?

[civic gyro]

yeah

[oak chasm]

And the slope is the same for both lines?

[civic gyro]

they are parallel

yea

[tall sage]

does this converge or diverge?

[oak chasm]

@civic gyro OK, what is the slope?

[harsh acorn]

channel is occupied

[civic gyro]

1 sec

[oak chasm]

@night ice Sorry, channel is busy.

[harsh acorn]

channel is occupied

[civic gyro]

-1/2

is the slope

[harsh acorn]

and is it test?

[night ice]

A orksheet

Worksheet

[civic gyro]

-1/2

[kindred pike]

Does a minus cancel out a minus? Like -8 - -2

[oak chasm]

@kindred pike Sorry, channel is busy.

[kindred pike]

K no p

[alpine sable]

yes

[night ice]

No if its 8--2 then yes

[kindred pike]

Then what if its -2 --8

[oak chasm]

@alpine sable @night ice Sorry, channel is busy.

[alpine sable]

im just answering xd

[oak chasm]

Don't.

[alpine sable]

ok

[night ice]

Ok

[kindred pike]

Dont answer a question?nah u lot are fked im outta this bish

[civic gyro]

@oak chasm so the slope is -1/2

and the 1/2 the width is how far the endpoints are from the nodes

[oak chasm]

OK, so the angle here is arctan(-1/2):

Tangent gives the slope of an angle. Arctangent gives the angle of a slope.

Does that make sense?

[civic gyro]

yeah

[oak chasm]

,calc atan(-1/2)

[ocean seal]

Result:

-0.46364760900081

[oak chasm]

So we get that as the radians of the angle.

[civic gyro]

okay

[civic gyro]

atan or arctan?

[oak chasm]

They're the same.

[civic gyro]

o

[oak chasm]

Now, x = r cos(theta), y = r sin(theta)

You use the r as the distance.

[civic gyro]

oh

i see

[oak chasm]

Since the width is 2, it's half that width to the next point and negative half that width to go the other way to the other point.

For one point: x = 1 cos(theta), y = 1 sin(theta).
For the other point: x = -1 cos(theta), y = -1 sin(theta).

Then, you need to add the x and y components of the node.

[civic gyro]

add the x and y components?

[oak chasm]

So, x = 1 cos(theta) + x of node, y = 1 sin(theta) + y of node.
x = -1 cos(theta) + x of node, y = -1 sin(theta) + y of node.

Like that.

[civic gyro]

oh okay

wait so those two points

where would they be?

like can you draw it so i can kinda visualize it better?

[oak chasm]

They would be your A and D for Node 1. They would be your B and C for Node 2.

Yeah, give me a minute.

[civic gyro]

alright

[obtuse crystal]

Hello!

I have very interesting question

[civic gyro]

this channel is occupied rn

[obtuse crystal]

Oh sorry I will wait

[dry vine]

how would I solve for y

[oak chasm]

@dry vine Sorry, channel is busy.

[dry vine]

k

[oak chasm]

Is this image correct?

[civic gyro]

yeah i beleive so

[oak chasm]

And is the line AD perpendicular to the line between the nodes?

[civic gyro]

yeah

[oak chasm]

OK, then the slope of -1/2 has a perpendicular slope of 2.

[civic gyro]

yeah

[ocean seal]

Chai T. Rex

[oak chasm]

@civic gyro Does this make sense ^

[civic gyro]

im writing this down 1 sec

sorry

[oak chasm]

@mellow frigate Sorry, channel is busy.

[mellow frigate]

oh okay

[civic gyro]

oh okay

i get it now

@oak chasm thanks for the help

[oak chasm]

No problem.

[mellow frigate]

like there is a question
like how many times are you expected to get tails when you flip a coin n times
is there an equation for it. An easy way to solve these questions

[golden bridge]

Is the channel in use?

Can someone help me with these 2 questions

[glass lichen]

if the numerator and denominator have the same degree, the infinite limit is just the ratio of the leading term co-efficients

[oak chasm]

@mellow frigate See https://en.wikipedia.org/wiki/Binomial_distribution.

[golden bridge]

can you solve question 8 on a paper please if it doesn't bother you ofc

I want to see an example

[glass lichen]

$\lim_{x\to\infty}\frac{2x^{1.5}+1}{-3x^{1.5}+1}=\frac{2}{-3}$

[ocean seal]

Mosh

[golden bridge]

Thanks

[alpine sable]

help

can anyone help me understand how we got to the final result

i understand everything up until there

nvm i understand

[viscid basalt]

s=0.9999999...
10s=9.99999...
10s-s=9s
9s=9
s=9s/9
s=1
if so will s not equal to s

[dire iron]

yo

would someone be able to help me

[viscid basalt]

try not ask to ask, just ask

[dire iron]

ok so

i got this homework sheet

but i dont know how to complete it

lemme send

@viscid basalt

[viscid basalt]

which question

[dire iron]

then vnn diagram one

venn*

[viscid basalt]

bad at math, find another person :)

[dire iron]

...

[alpine sable]

,rotate

[civic gyro]

if the width is 4 would it be x = 2cos(theta), y = 2 sin(theta) ?

[dire iron]

yea so

does anyone know how to do this

[oak chasm]

@civic gyro Right.

[alpine sable]

@dire iron you didnt write the info for the last two points

[dire iron]

wdym

oh

yea

thats the point

u have to find them...

and i have 0 idea on how to...

[alpine sable]

How many students play piano?

[dire iron]

???

[alpine sable]

How many students in total play the piano?

Read the problem text

[viscid basalt]

84

[dire iron]

84

YE

oop

caps

anyway

[alpine sable]

@viscid basalt dont give out answers

@dire iron how many students play piano based on your venn diagram

[dire iron]

uhm if u dont count the only piano ring, (the other 3) its 74

idk if u wanna, but u wanna vc?

[alpine sable]

The "only piano" part will have the rest

I do not

[dire iron]

oaky

so

it says that there are 84 total

so for the only piano ring, do i fill in 10?

[alpine sable]

Yes

[dire iron]

ey

[alpine sable]

Use the same logic for violin

[dire iron]

gimme a sec

is it 6?

@alpine sable

[alpine sable]

Correct

[dire iron]

hol dup, imma get ma calculator, brb

[hexed lintel]

big problem

[dire iron]

oki

i am back

[dire iron]

@alpine sable

can i dm you?

[hexed lintel]

help

[alpine sable]

Sure

[viscid basalt]

wdym

[wanton turtle]

What's the problem?

[hexed lintel]

unable to solve

i don't understand a bit

[viscid basalt]

ok let's try it with 3 and 4

[hexed lintel]

not working

[viscid basalt]

3 is an odd number

then 3 times 3 + 1 = to what

4 is a even, 4/2=?

the sum you get is the return value of the function

[hexed lintel]

ohk

[wind fox]

Can someone please help me out

[viscid basalt]

what's the question?

[storm turret]

The perimeter is the sum of all the sides

So add those

Then isolate n to get your answer

[viscid basalt]

try all solutions a b c d, because KL=n then you can try them all to get the answer

[gaunt fox]

wuts 1+1?

[fierce mortar]

69

[gaunt fox]

oh i thought maybe 11?

[viscid basalt]

1+1 is not yet provable

[fierce mortar]

What

[gaunt fox]

hmm

[viscid basalt]

try time travel to 2000 years later, you might get the answer of 1+1

[gaunt fox]

ok

i will

[viscid basalt]

but someone proved 1+2=3 which is great

[fierce mortar]

That’s good that’s good

Uhhh uhhh

Infinite

https://tenor.com/view/infinity-gif-6038008

[harsh acorn]

If $a,b\in\mathbb{N}$ and $a^2(a-3b)=b^2(b-3a)$ find the number of possible values of $\frac{a}{b}$

[ocean seal]

Hyl1s

[harsh acorn]

Can someone give me a hint?

[gaunt fox]

judging by the values of spanish subtracted from PI i think the answer is 8...

[viscid basalt]

depends on the digestive system

[glacial hedge]

anone know what this question is asking?

[gaunt fox]

uuh

wut

[glacial hedge]

its a multivariable calc questions and i have no idea wtf its saying

[gaunt fox]

neither do i

lol

[sly mantle]

@gaunt fox @cursive tulip stop trolling

[gaunt fox]

sadge

ok

[sly mantle]

unpack definitions. also don't multipost

[shy galleon]

i need help with this plz 😦

[glacial hedge]

@shy galleon domain is all possible inputs

[wary stream]

Do you know the definition of domain, range, and x-intercepts?

[shy galleon]

no im kinda new to this ngl

[glacial hedge]

for domain

you want to find the range of x

so in this image its

[-6, 6]

sorry

im blind

its

[wary stream]

If you are new, watch this https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:introduction-to-the-domain-and-range-of-a-function/v/domain-and-range-from-graphs

[glacial hedge]

[-4,6] but might extend more but just cut off

[glass lichen]

1. dont just give answers
2. saying "domain is range of x" is confusing

[shy galleon]

Ok thanks

[fallen rain]

can someone help me with this question pls?

[alpine sable]

any two or more parallel lines have the same gradient

[wary stream]

If a line that is parallel to another line, it has an attribute that is the same, what is that attribute?

[twin raft]

@fallen rain which one of the values decide the slope of a function?

2x or -3

[alpine sable]

y = 2x + c where c is a real number

[twin raft]

ok and what does -3 tell us?

[fallen rain]

2x

-3 is the y intercept

[twin raft]

alright

for it to be parallel, does it have to have the same slope?

[fallen rain]

yes

[glacial hedge]

thats a lil overkill, gradient is used for 3d surface curves

[twin raft]

so then you can change -3 to any number as long as you keep the same slope

give me an example for a parallel line to 2x-3

[fallen rain]

y=2x+3

[twin raft]

yep thats right

[fallen rain]

thank you guys

[twin raft]

gl ^^

[dull onyx]

hello!!

my tutor just “taught” me limits but like i feel like i have a huge gap as to what a limit actually is.. if someone has any resources abt limits please link it!’ thank u<3

[wary stream]

Khan academy is very useful

[quartz oxide]

Yea khan academy is very good especially for basic calculus

[native temple]

https://notability.com/n/08VcM2Tx40HQH_2jUZj_LL

At the second to last page what did I do wrong?!

[dull onyx]

oop thank u i totally forgot abt that

[native temple]

youtube

openstax

etc...

[alpine sable]

Your handwriting is illegible for me, sorry. @native temple

[wary stream]

I don't even know what you are referencing to, too many questions on there to determine which one and there's no page breaks so hard to determine what the second to last page is

[native temple]

the last page

wait when sharing there’s no page breaks?

this one

I tried to organize it by having each question be separated by one page

at least

there is a little line that counts as a page break though

...

please look at that question at the bottom of the note

hello

[oak chasm]

@native temple So, use the second equation to get y in terms of x.

Then fill in y in terms of x into the first equation and solve for x.

[native temple]

Oh

Okay

I did it in reverse

You can have x = ay^2 + by + c yes?

[oak chasm]

I don't really see a way to do that with the first equation, but the second equation will have x = by + c, yes.

[native temple]

then why didn’t my solution work after a long process I got

[oak chasm]

Show your work.

[oak chasm]

That doesn't show how you got to there.

[native temple]

https://notability.com/n/08VcM2Tx40HQH_2jUZj_LL

The bottom of the note is my work

[oak chasm]

This is a different question than the one you posed here ^

[alpine sable]

Yo

Can anyone help me out

It really important

[oak chasm]

@alpine sable Sorry, channel is busy.

[native temple]

forgot I could do that

stupid me

oh here’s my work

on this question

I tried to organize it

ignore the equation on the left of the picture

that’s me writing down something from my school’s help video....

anyway

[native temple]

sure find a open question channel

[oak chasm]

@native temple Do you know the order of operations?

[native temple]

Parathesis

uhh exponent

multiplication division addition subtraction

[ocean seal]

Chai T. Rex

[native temple]

oh

oh. o

ni

no

[ocean seal]

Chai T. Rex

[native temple]

Okay

but I acted as if it was otherwise so what else did I do wrong?

[oak chasm]

Otherwise, it looks fine.

[native temple]

what?

.....

Oh

then why is my answer wrong

[autumn socket]

what order would you take to learn up to advance calculus..? if you starting fresh with math thanks

[oak chasm]

@autumn socket Sorry, channel is busy.

[native temple]

Check openstax?

youtube

amazon

?

no

bye

[oak chasm]

@native temple Did you find x from those y values using the second equation?

[native temple]

Yea

[oak chasm]

You need to do it in a way that doesn't confuse you.

[native temple]

it’s not confusing

[oak chasm]

Don't put it like x = 0, -7 and y = 4 - 7, 4 + 0.

What are the y values?

[native temple]

oh

-3

4

[oak chasm]

No.

What are the y values you got from the quadratic formula?

[native temple]

I confused the y valies with the x ones

x is -3

and 4

y is 0

and -7

[oak chasm]

Yes, but you also switched the places of the x values so that they corresponded to the wrong y value.

[native temple]

oh

[oak chasm]

Don't write them together like that.

[native temple]

Was my handwriting hard to read

if so sigh

[oak chasm]

Write y = 0, x = ?. Then write y = -7, x = ?.

[native temple]

I need to draw striaght lines

[oak chasm]

It was a bit.

[native temple]

oh

[oak chasm]

Don't write them all together.

[native temple]

to big right

to big

[oak chasm]

No, the ys looks like xs sometimes, and your 1 in 14 looks like a 2 in a place.

[native temple]

oh

sigh

[main crane]

https://cdn.discordapp.com/attachments/849113494682075158/854037866769940520/10157628c4e1b425c91843b2c5a08662.png

i need help

[ocean seal]

Chai T. Rex

[native temple]

Thanks I see know one needs others to help you learn

Absolutely

[main crane]

@oak chasm

https://cdn.discordapp.com/attachments/849113494682075158/854037866769940520/10157628c4e1b425c91843b2c5a08662.png

can u help me with these questions

[vale wigeon]

@main crane do not multipost, and do not ping individual users at random.

[main crane]

sorry

[wary stream]

Why do you need this so urgently?

[main crane]

because its due today

and i dont understnad the questions

[wary stream]

Perhaps read about the concepts? Do resource. It's about interest

[random pelican]

anyone explain me this please 🥺 im watching some videos but still not understanding nothing

[wary stream]

What's the goal?

[random pelican]

Find the perimeter

[undone dock]

Is M in the middle?

[main crane]

do u think u can check my work?

i just asked someone

and they helped me but idk if its right

https://cdn.discordapp.com/attachments/849840034467414028/854043718029803520/998f30a714c58059bb5e82a233a4b70e.png

[random pelican]

yes

[oak chasm]

@random pelican So, what's the length of MC?

@main crane You got the simple interest problem right (#1). The compound interest problem is wrong, though.

[magic kettle]

what can someone help explain this

is it asking me to find r or explain what r is?

[wary stream]

Find r

Isolate r

[magic kettle]

thats what i thought thank you :)

[random pelican]

idek

[alpine sable]

Please see #help-6

[oak chasm]

@random pelican Well, if M is exactly the middle of the bottom line, the left half and right half of the bottom line are the same length, right?

[magic kettle]

is this technically correct? I am supposed to use a graphing calculator but i couldnt figure it out

[oak chasm]

@magic kettle Your negative sign disappeared.

[magic kettle]

oh yeah i should probably make it plus or minus? like the symbol

[oak chasm]

No.

[ocean seal]

Chai T. Rex

[oak chasm]

The second part has a negative sign, so the third part should have a negative sign.

[magic kettle]

yeah but with context of the question shouldnt it be a positive answer?

[oak chasm]

No, a rate of change can be negative.

[alpine sable]

In the case of the context, the height of the bird above the ground is decreasing.

As T. Rex said, rate of changes can be negative.

[magic kettle]

Thank you! and @alpine sable thank you too

[alpine sable]

👍

[oak chasm]

No problem.

[subtle whale]

where do i need to open parenthesis

[glass lichen]

that's just a false statement..

[oak chasm]

@subtle whale Try them in different places and see which works.

[subtle whale]

i tried

i didn't worked it out

[oak chasm]

Which positions did you try?

[subtle whale]

ill do it like this: 4+3x8=1000

(4+3)x8=1000

[oak chasm]

No, you're doing it a bit wrong.

[subtle whale]

wdym

[oak chasm]

You did the powers.

[subtle whale]

yea

[oak chasm]

Leave the powers as powers.

[subtle whale]

wdym

[glass lichen]

leave them as is is what Chai said

[subtle whale]

ok

so

4+3x8=1000

[glass lichen]

Ok ignore that completely

[undone dock]

If m cuts the line BC in half, What would the ratio between the length of BM and MC be

[ocean seal]

Chai T. Rex

[subtle whale]

bot that didn't helped cuz i already did it

[oak chasm]

What did you try with the exponents still there?

[subtle whale]

i tried the first one

on the (2+3)x2

[ocean seal]

Chai T. Rex

[oak chasm]

The exponents should not disappear.

[subtle whale]

wdym

[subtle whale]

i did it already

[ocean seal]

Chai T. Rex

[subtle whale]

i don't know how to type powers on keyboard

[oak chasm]

Like this: 2^3

(2^3 + 3)*2^3

[subtle whale]

oh ok

so 2^2+3x2^3=1000

the question is

where do i put them

[oak chasm]

Right.

[subtle whale]

for some reason its hard

[oak chasm]

So, try all the places to start them. Try all the places to end them.

[subtle whale]

2^2+(3x2^3)=1000

that can't be

[ocean seal]

Chai T. Rex

You can start them like:
\[(2^3 + 3 \cdot 2^3\]
\[2^{(3} + 3 \cdot 2^3\]
\[2^3 + (3 \cdot 2^3\]
\[2^3 + 3 \cdot (2^3\]
\[2^3 + 3 \cdot 2^(3\]

[subtle whale]

im in grade 6 and im doing tests to try to qualify to an higher class when i get to grade 7

[oak chasm]

Do you see all the start places?

[subtle whale]

yea

i don't think we can put those on Powers yet

[oak chasm]

Oh, OK. One second.

[subtle whale]

we can put numbers with powers but not the powers themselves

[oak chasm]

See all the places you can start and end them?

Wait.

[subtle whale]

yea

[ocean seal]

Chai T. Rex

[oak chasm]

So try all the starts and ends that can work together.

[subtle whale]

i got 5 Questions it will take me HOURS to finish it

i still can't think of it

[oak chasm]

Well, let's try.

Let's use the first start point.

And go through the end points.

[fervent locust]

someone help me on this? please

[oak chasm]

@fervent locust Sorry, channel is busy.

Is this 1000?
(2^3 + 3 * 2^3)

[subtle whale]

no

what

no

its (2^2 + 3 * 2^3)

[oak chasm]

Let's try the next end point.
(2^3 + 3 * 2)^3
Is that 1000?

[subtle whale]

no

[oak chasm]

What is it?

[subtle whale]

30

[oak chasm]

Oh, sorry.

What's (2^2 + 3 * 2)^3?

[subtle whale]

3x2 =6 2x2= 4 4+6=10 10x3 = 30

[oak chasm]

No, the part on the end is an exponent.

It has ^, not *.

[subtle whale]

oh trueeeee

OH YEA

tysm

[oak chasm]

No problem.

[subtle whale]

ur amazing 🙂

[oak chasm]

That's how you do this kind of problem.

You figure out the start points.

You figure out the end points.

Then you go through and try each start with each end.

It can take a while, but that's how you do it.

[subtle whale]

dang it im stuck again

its hard to figure those out

if they aren't wrote down

[oak chasm]

What does : mean?

[subtle whale]

its like /

Deviding

[oak chasm]

Oh, OK.

[ocean seal]

Chai T. Rex

[subtle whale]

btw what grade are you just asking

[oak chasm]

Oh, I'm done with school for now.

[subtle whale]

oh sick

congrats

🙂

[oak chasm]

Thanks.

So, just try the first start point with all the end points. Then, try the next start point with all the end points. And so on.

[subtle whale]

ok

first one with the first end : no

first one with the second end : no

[oak chasm]

What do you get for each?

[subtle whale]

oh yea i need 121

[oak chasm]

Yeah, what did you get for first start with first end?

[subtle whale]

ok so 3^4 is 81 and 3^2 is 9 and 2^2 is 4

[oak chasm]

Right.

[subtle whale]

81 : 9 is 9 +4 = 13

[oak chasm]

Good.

What do you get for first start with second end?

[subtle whale]

wait nvm

i just calculated it wrong when i did it

how are u typing those options so fast tho

[oak chasm]

Oh, I copy and paste.

Then I just put in a parenthesis in each one.

[subtle whale]

oh

[warm smelt]

1=3^x - 2^x

can i solve for x algebrically?

[glass lichen]

x=1 by inspection

[warm smelt]

yeah but theres no algebric way of doing it?

without inspection

[glass lichen]

I mean there likely is, but inspection is sufficient

[warm smelt]

yeah cause im trying to figure out that way

[subtle whale]

@oak chasm can you type the possible options for me i just can't figure them out

[oak chasm]

Well, let's learn how to figure them out.

You can put one in front of the first 2, right?

[subtle whale]

yea

[oak chasm]

You can put one in front of each nonexponent number, right?

[subtle whale]

yea

[ocean seal]

Chai T. Rex

[oak chasm]

@merry needle Sorry, channel is busy.

@subtle whale See how I put a parenthesis in front of each nonexponent number?

[subtle whale]

yes

[oak chasm]

OK, the end ones are a little different: put a parenthesis after each exponent and after each nonexponent number.

[subtle whale]

that's a lot

[ocean seal]

Chai T. Rex

[subtle whale]

ok

[oak chasm]

That's how I got the ends.

[subtle whale]

can you put them both together?/

so i have the list

[oak chasm]

Well, you can do that. Start with the first start, do all the ends. Go to the next start, do all the ends. And so on.

Some won't make sense because the end comes before the start.

You can leave those ones out.

[subtle whale]

yea ok

first one is just doing the hole Question so it isn't true i checked it

[oak chasm]

Right.

[subtle whale]

first one second end : No

first with Third end : no

first one with forth end : No

first one with fitfh end : No

first one with the six end: No

[oak chasm]

Good so far.

[subtle whale]

can you put them on a list tho its easier to noe scroll up and down

[winter gulch]

I didn't find a very good algebraic way (since you're looking for real values of x, not just integer values of x, otherwise that would be easy.) let f(x) = 3^x-2^x, df/dx = ln(3)3^x - ln(2)2^x. But notice: 2^x>0, 3^x>0 for all real values of x. ln(3)>0 because 3>e, and ln(2)<0 because 2<e, so then -ln(2)>0. Using properties of inequalities we have df/dx=ln(3)3^2 + (-ln(2))2^x > 0 for all values of x, which means f(x) is a strictly increasing function. We know that f(1)=1, then for all x>1, f(x)>1, and for all x<1, f(x)<1. This proves that x=1 is the only solution to 1=3^x-2^x

[subtle whale]

my brain hurts

[winter gulch]

sorry for interrupting but not sure if they wanted a more rigorous solution

[ocean seal]

Chai T. Rex

[oak chasm]

@subtle whale Click on the picture just above and click Open Original

[kind matrix]

are we in the middle of something here? don’t wanna interrupt

[oak chasm]

@kind matrix Sorry, channel is busy.

[kind matrix]

ty

[unique tapir]

angone

anyoen

?

[subtle whale]

oh ok

[oak chasm]

@unique tapir Sorry, channel is busy.

[magic plank]

10/18 i guess

[oak chasm]

@magic plank Sorry, channel is busy.

[unique tapir]

how is it busy

[magic plank]

what is that

[oak chasm]

@unique tapir Someone else is using it.

[magic plank]

idfc

[subtle whale]

(7+3) is 10 +2 is clearly 5 x 3^2 wich is 9 5x9 = 45

[unique tapir]

fine

ok

[oak chasm]

@magic plank @unique tapir See the rules in #❓how-to-get-help.

[subtle whale]

i think @unique tapir

[unique tapir]

oh-

[magic plank]

should we leave the server or the channel ?

[unique tapir]

let me work it our

out

[subtle whale]

ok

[oak chasm]

@magic plank Find a channel that's not in use.

[magic plank]

so someone rented the channel?

[alpine sable]

Just channel, there are 9 other channels. Find one not in use

[oak chasm]

@magic plank I already said to read #❓how-to-get-help, which explains it.

[alpine sable]

Yes, it's reserved

[magic plank]

i cant read all of that duh

[oak chasm]

<@&268886789983436800> Repeated interruptions and refusal to read rules.

[tame falcon]

Muted them

[oak chasm]

@subtle whale Did you find the answer?

[unique tapir]

uh

in used'

?

[oak chasm]

@subtle whale Are you still using this channel?

[subtle whale]

Yea im fine ty

[random pelican]

Dude, i dont know ANYTHING about that

[undone dock]

Okay

Think about a stick

If you cut the stick equally in half

Is one half of the stick longer than the other?

[random pelican]

No

[undone dock]

Yea so BM is the same length as MC

And BM is 1.9cm

[random pelican]

Oh, than it is 1.9 cm?

[undone dock]

Yea

MC is 1.9 cm

[random pelican]

and the perimeter?

[undone dock]

So BC is 1.9cm +1.9cm=3.8cm

You just add AB+BC+CA

2.5cm+3.8+3.5cm=9.8cm

[native temple]

What did I do wrong?

[alpine sable]

What is the a b and c when you set up the quadratic equation?

[native temple]

32 and 0

[alpine sable]

a, b and c

[native temple]

-48 32 0

[alpine sable]

Not good

[native temple]

0 is because 16 -16 = 0

[alpine sable]

32 is with y^2 not -48

[native temple]

see my processes is in the picture

[alpine sable]

I did see your process, the problem is not c

[native temple]

ohhh

[alpine sable]

Rather a and b

[inner sequoia]

why does transposing work
like if i have 2x + 3 = 1x + 6, why can i move 1x to the other side and reverse the operation to get 2x - 1x = 1x, then move 3 to the other side and reverse operation to get 6-3 = 3, so x = 3

ik ur supposed to do it, but WHY does it work

[alpine sable]

2x+3 = 1x + 6
2x+3-1x = 1x+6-1x

[native temple]

@alpine sable How does one detect these things

as O can’t do math alone

sigh

[inner sequoia]

so transposing is just an easier way to see it?

[alpine sable]

I suggest you literally write a= 32, b=-48 and c=0 @native temple

[native temple]

oh go through the process

okay

Make ot explicit

the whole process

[alpine sable]

It'll help you see better. a is always with x^2 or y^2

[native temple]

I was askibg how to properly check your work

I’m bad at it and it slows me down

[inner sequoia]

so its just an easier way to see it, ur not actually moving the number, the reason it's moving is because you're cancelling it out it out, if i'm understanding right @alpine sable

[native temple]

not just this

[alpine sable]

@inner sequoia you subtract something from both sides. On one side it cancels out, but it looks like it's moving from one side to the other and changes signs

[inner sequoia]

oh so it just looks like its moving

[alpine sable]

@native temple how did you know it was wrong?

[inner sequoia]

bruh these mfs online told me it was actually moving

scam

[native temple]

Because....The standard form is ax^2 + bx + c

and I confided a with b

But I always miss something

always and then I need help

sigh

[alpine sable]

Well most view it that way.
If you have 2=x-1
The first step is to add 1 to both sides
2+1=x-1+1
-1+1 is 0

@native temple you can sub the values back to check

[inner sequoia]

thank you
this caused my head to rip apart why it worked

[native temple]

What do you mean

[inner sequoia]

nobody told me that it only looked like it was moving

[native temple]

to check your work

check your steps and sub the values

[alpine sable]

x^2-4y^2=16

Sub back in what you got for x and y

[native temple]

ohhh

I see now I remever

Sigh why do I always need tutors

[alpine sable]

x=0
y=2/3
(0)^2-4(2/3)^2=0-4(4/9)=16/9

Which is not 16, so something is wrong

That helps you see you did something wrong. You still wont know where exactly though

[gleaming warren]

Why do we not cancel the exponents of -8 and 6

[gray isle]

the sqrt root isn't linear

$\fdream$

[ocean seal]

ℝamonov

[alpine sable]

Nice command

[gray isle]

eg sqrt(1^2 + 1^2 + 1^2) isn't 3

[alpine sable]

Dejavu

You just wrote this somewhere

[gleaming warren]

what is linear

[gleaming warren]

why

[gray isle]

follow the order of operations

simplify the stuff inside the parentheses first

[gleaming warren]

i did that

but still after i could have cancelled it

[gray isle]

how so?

[gleaming warren]

on the last fourth line

$\sqrt-8^2 and 6^2$

the two can be cancelled

[ocean seal]

TheGameBot

[gray isle]

youve been on this issue for several days now

[alpine sable]

If you canceled and had -8+6?

[gray isle]

the point is they dont

[gleaming warren]

the what?

[gray isle]

because that would be breaking algebraic laws

if you follow the order of operations, simplifying everything under the root,
then taking the square root, you get 10 which is good

doing something else, and getting something that isn't 10 means you screwed up

[alpine sable]

$\sqrt{x}=x^\frac12$

[ocean seal]

Em

[random pelican]

How do I do this? I need find X

[alpine sable]

X is a point

[gleaming warren]

x is on the diagram circle it

1st grade question

Is the step 2 correct

does the 2nd step come after the 1st one

or did i miss something

[random pelican]

In the figure below, similar marks indicate congruent elements. Furthermore, M and N are midpoints of sides AC and BC, respectively. Identify the X, Y and Z points

Question full, I just sent the pic last time my bad

[gleaming warren]

@helperas

<@&286206848099549185>

[gray isle]

seems upon closer inspection, the point (0,6) was labelled as (is that a B or D).
what's Q supposed to be?

[gleaming warren]

Srry the B is actually Q

Mistake

[gray isle]

there's a small issue with a sign that didn't affect the overall result in this case

[gleaming warren]

can it be like this

or the way i did is wrong or is it also correct

[gray isle]

you're using x_2 = 0 and x_1 = -8
x_2 - x_1 = 0 - (-8) = 8

[alpine sable]

How do I this? I just need the formula : A 4 ft tall child creates a shadow that is 7.5 ft long. What is
the angle of elevation of the sun?

[gray isle]

the most recent pic is better

and addresses the issue I just stated

[gleaming warren]

is mine also correct?

the first pic

[gray isle]

there's a small issue with a sign that didn't affect the overall result in this case

[gleaming warren]

which sign

[gray isle]

x_2 = 0 and x_1 = -8
x_2 - x_1 = 0 - (-8) = 8
however your x_2 - x_1 was 0 - 8

[gleaming warren]

i know but is it ok teway i d

i did

will i get the marks cuz this i what i wrote on my paper today

[gray isle]

depending on how lenient the marker is, they may dock half a mark

[gleaming warren]

oh

[gray isle]

because of that sign error

[gleaming warren]

ok

thx

and one ;last thing

the law u mentioned above what is the law

[gleaming warren]

this one

[gray isle]

the thing you were previosly continually insisting on applying

[gleaming warren]

oh

[gray isle]

don't do freshmans dream

[gleaming warren]

lol

[gray isle]

$\fdream$ \
bad

[ocean seal]

ℝamonov

[gleaming warren]

oh

thx

[opaque oracle]

Prove (or disprove) that this is a tautology without using a truth table:

[p∧(p→q)]→q