help-0

[gray isle]

ok, other places refer to that as vertex form

they use h,k instead of alpha and better

more ideal so you don't mix up a with alpha

you can manipulate your expression to this form with the method of
completing the square

[molten frigate]

can u show me because i did it and im not sure

?

<@&286206848099549185>

@lone heart help me

[gray isle]

show what you did

[molten frigate]

ok

I found a b and c

a= 2

b = (-16)

c= 24

alpha is = -b/2a

= 16/2*2

= 4

beta = - delta/ 4a^2

= (b^2-4ac)/4a^2

= -(16^2 - 4224) / 4*2^2

= -(256-192)/16

= -64/16

= (-4)

finally = a(x- alpha)^2+ beta

= 2(x-4)^2 + (-4)

@gray isle

[gray isle]

1 sec

[molten frigate]

ok

[gray isle]

your formula for beta is wrong

[molten frigate]

how?

[gray isle]

denominator should be just 4a, not 4a^2

[molten frigate]

no it is 4a^2

[gray isle]

where are you reading that?

[molten frigate]

my math book...

[gray isle]

show exactly what your math book is saying

[molten frigate]

ok

[gray isle]

is wrong

[molten frigate]

ok yes u are right

so then i just remove that

so its 8

[gray isle]

-8

[molten frigate]

yes

= 2(x-4)^2 + (-8)

but now

a((alpha-alpha)^2 + delta)

= a(0 + delta)

= 0 - delta

= (-8)

now is this correct?

@gray isle

AAHHHHH

[gray isle]

that's fishy

[molten frigate]

why?

<@&286206848099549185>

[gray isle]

where's that coming from

[molten frigate]

idk man ur supposed to help me

[gray isle]

you're the one that typed it

i'm trying to figure out what property you're trying to apply
and whether the property you have copied down was invalid or you weren't applying it properly

[molten frigate]

one second

the coordonates of the top of the function are alpha and beta

hence alpha is equal to x

f(alpha) = beta

@gray isle

[gray isle]

depending on the sign of the leading coefficient: a,
f(alpha) = beta
will give you the max or min

that doesn't explain where

a((alpha-alpha)^2 + delta)
is coming from

nor anything after that line

[molten frigate]

this is the canonic thing

[gray isle]

its not

[molten frigate]

a(x-alpha)^2 + beta

[gray isle]

yes, and what i'm quoting is very different to what you had been typing

$$a(x-\alpha)^2 + \beta$$
is not the same as
$$a((x-\alpha)^2 + \Delta)$$

[ocean seal]

ℝam()n()v

[molten frigate]

wait no no beta is equal to delta/4ac

$$a((x-\alpha)^2 + \Delta/4ac)$$

[ocean seal]

lune

[gray isle]

no

if you wanted to involve Delta then you'd have

$$a\br{(x-a)^2 - \frac{\Delta}{4a^2}}$$
or
$$a(x-a)^2 - \frac{\Delta}{4a}$$

[ocean seal]

ℝam()n()v

[molten frigate]

yes sorry

you are correct

[gray isle]

but going back to this is unnecssary

you already did the work with this

[molten frigate]

so it is right if we do it that way?

[gray isle]

there are multiple ways to do this,

i wouldn't really recommend using these presestablished shortcuts

as you mess one thing up as you've done multiple times now
and everything falls apart

its important to understand where these come from

but anyway after getting
$$f(x)= 2(x-4)^2 + (-8)$$
you'll get min from $f(4)$

[ocean seal]

ℝam()n()v

[molten frigate]

alright great

but now how can i find this

f(x) > or = to -8

[lone heart]

@molten frigate Has your question been resolved?

[gray isle]

by thinking about the min/max value of 2(x-4)^2

[lone heart]

@molten frigate Has your question been resolved?

[lone heart]

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[river aspen]

hello I need assistance with this problem

[pallid scarab]

Where F is fibonacci?

[river aspen]

Prof didn't say anything so probably yeah?

saw this in google but i dont understand a single thing

[pallid scarab]

Ugh even google can't be rigorous

Anyways, the fibonacci sequence is defined as :
The first two numbers are F0 = 0 and F1= 1, and every next number is the sum of the two previous numbers

So we start with 0, 1

The next number is 0+1 = 1

So 0, 1, 1

The next number is 1+1 = 2

And so on...

[river aspen]

yup...

[pallid scarab]

Ok so

[river aspen]

my intial thought was substituting the numbers greater or equal to 3

and I concluded that the statement was false but now that F is actually Fibonacci

im lost

[pallid scarab]

Substituting for each value one by one?

[river aspen]

yeah wait ill send my answer

i did it like this cause I thought F was just like function

is the problem different from an counter-example in an inductive reasoning?

[lone heart]

@river aspen Has your question been resolved?

[molten frigate]

no

oh ooh

[lone heart]

@river aspen Has your question been resolved?

[lone heart]

@river aspen Has your question been resolved?

[lone heart]

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[alpine sable]

.open

[sonic harbor]

The bisection method:
Can someone help me understand the question here?

[lone heart]

@sonic harbor Has your question been resolved?

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[alpine sable]

Can someone help me solve this? Its some exercise for arithmetic sequence?

[pale kestrel]

to solve for d, this is a quadratic

expand it out

(hint: factor out 1/2 from each bracket first to make your life easier)

[alpine sable]

From the video i watched,apparently this is solution

And i dont know where did he get 17d?

[pale kestrel]

well show your own work expanding the brackets

because thats what u should get

[pale kestrel]

and the video doesnt, but i would srsly recommend this

[alpine sable]

This is what i got

Just flip your phone xD

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[proud anchor]

Can someone show how to do this?

[wet linden]

i would put each thing under a radical first

[proven leaf]

I would suggest writing 162 and 1250 as a product of their prime factors

[lethal citrus]

$x^{\frac 1n}=\sqrt[n]{x}$

[ocean seal]

deus ex machina

[proud anchor]

what should be the answer?

[lone heart]

@proud anchor Has your question been resolved?

[lone heart]

@proud anchor Has your question been resolved?

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[bold siren]

i dont want helper role

[bold siren]

how to delete the role

[gray isle]

channels and roles top left

[bold siren]

then?

[gray isle]

deselect the i want to help others

[bold siren]

thanks

i got 2k pings

my god

[gray isle]

deselect the really want to help as well

[lone heart]

@bold siren Has your question been resolved?

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[bold siren]

be happy

[lone heart]

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[hearty gulch]

Prove that the following is irrational:

[hearty gulch]

i know there are probably countless proofs for irrationality

but i've tried using some of the techniques

to no avail

[quartz mica]

contradiction might work

[hearty gulch]

yeah but how exactly

cuz taking 3rd power won't be as easy as if it would be with only 1 cube root

[quartz mica]

I think maybe prove cbrt(7) and cbrt(5) to be irrational individually and then blah blah blah maybe

[hearty gulch]

well it won't work tho cuz then i'd still need to prove that difference is irrational

[lone heart]

@hearty gulch Has your question been resolved?

[proud arch]

yoooo

[lone heart]

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[bleak nexus]

Yo

[bleak nexus]

How do i factor this polynomial?

3T^2R^2+13TR+12?

My teacher didnt teach us how to do these types and the HW is due in 2ish hours

[cinder thicket]

Could you write that?

[bleak nexus]

Sure

https://i.imgur.com/n2AZtJu.png

[rancid hazel]

you can subsitute u=TR, so you get 3u²+13u+12

[cinder thicket]

Ok

Yeah

[bleak nexus]

What would i do from there?

Factor normally?

[rancid hazel]

yes

[bleak nexus]

And why is it U specifically?

or does it not matter?

[cinder thicket]

It doesn't matter

[bleak nexus]

Did u mistype as 2 instead of 3?

[rancid hazel]

Hello?

[bleak nexus]

Yea

[rancid hazel]

Is my internet okay?

[cinder thicket]

Yes

[bleak nexus]

So its not just me okay

[rancid hazel]

What happened

[bleak nexus]

im not sure

[cinder thicket]

My discord is also buggin

[rancid hazel]

hello?

can you guys read this message?

[bleak nexus]

I can

[rancid hazel]

Very strange

[bleak nexus]

Yeah

[rancid hazel]

I can read you guys now

[bleak nexus]

So here did u mistype 2 when its supposed to be 3?

[rancid hazel]

yes it was a mistake thank you for noticing it

[bleak nexus]

Okay tyvm

[cinder thicket]

Your answer should be (3tr+4)(tr+3)

[bleak nexus]

https://i.imgur.com/C6J6HLW.png

@rancid hazel@cinder thicket oh so at the end i put in the correct symbols?

[cinder thicket]

Yessir

[rancid hazel]

yes

[bleak nexus]

Thank you so much

.close

[lone heart]

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Closed by @bleak nexus

Use .reopen if this was a mistake.

[rancid hazel]

yo ram

don't say the answer

let them figure it out themselves

[cinder thicket]

He got it so..

You right tho man

[rancid hazel]

but what if he was stuck

[lone heart]

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[vapid steppe]

is there a way to combine $e^x+e^{2x}$

[ocean seal]

Jash

[vapid steppe]

i’m trying to solve $e^x+e^{2x}=5$

[ocean seal]

Jash

[unkempt robin]

No

You can factor out something however

Thought that isn't necessary in your case

I'd use $a^{mn} = (a^m)^n$

[ocean seal]

USS-Enterprise

[unkempt robin]

Then substitute something for e^x and solve the quadratic equation

[royal latch]

Yeah
You can take the e^x common out of the two terms

[unkempt robin]

Yeah, either way works

[royal latch]

U can then apply log on both sides to find the value of x

[unkempt robin]

Yes

[vapid steppe]

then take ln?

[vapid steppe]

oh

e^x(1+e^x)=5

[royal latch]

Right

[vapid steppe]

x+ln(1+e^x)=ln(5)

[royal latch]

Substitute e^x=t to get a quadratic

[vapid steppe]

ohhh

[royal latch]

This will make it a lil complicated

[vapid steppe]

t(1+t)=5

[royal latch]

Yep

[vapid steppe]

t²+t-5=0

[royal latch]

Find out the roots
Replace it with e^x

[vapid steppe]

ok ye ty

[royal latch]

Wlcm

[vapid steppe]

.close

[lone heart]

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[jaunty sierra]

can someone pls help with this? im not sure how to do parts b and c

[vapid steppe]

multiply the numerator and denominator by 4(4+h)

[thick lynx]

After you've done that, I can show you another, much faster way to compute this limit (assuming you know derivatives, though that might not be the case)

[jaunty sierra]

like this?

oh yeah i got it

thanks

[jaunty sierra]

you can show me now if you'd like

[thick lynx]

Have you done derivatives?

[swift tulip]

l-hospitals!!!!

whatddup folks

how can i help

[jaunty sierra]

yeah

[thick lynx]

Then you can notice that this is the derivative of $f(x) = \frac{1}{x}$ evaluated at $x = 4$.

[jaunty sierra]

ohhhh

that's so much easier

[thick lynx]

Though note that you are using the power rule here, which comes from the limit definition

[jaunty sierra]

got it

thank you

.close

[lone heart]

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[hard marten]

for our homework we were given questions she never covered in class, so im kinda stuck trying to figure out how to use the sec function on my calculator

i'm getting odd answers that i feel aren't right because my classmates are just saying to use a calculator lol

[hard marten]

issue: idk how to do this

i need hints on how to solve this

[cinder thicket]

No calculator?

[kind patio]

Not sure how you would do this without a calculator

however ur final answer is 0.06827

so I assuming 0.1

[hard marten]

how did you get that

all you did was sec 191.3 on your calc

?

[cinder thicket]

Sec inverse=cosinverse(1/x)

Similarly cotinverse(x)=tan inverse(1/x)

[hard marten]

do i just use the values given and put it into cos

or cos^-1

[cinder thicket]

bro

[hard marten]

she literally said nothing

the whole lecture

so i have no idea what im doing

[cinder thicket]

Cos^-1(1/x)=sec^-1(x)

That's it

If you want cotinverse (14.623) just put taninverse(1/14.623) on the calculator

[hard marten]

im getting 89.7

[hard marten]

for

[cinder thicket]

Just saying

[hard marten]

cos^-1(1/191.3)

[cinder thicket]

You need to find x tho

Apply cot on both sides

Cot and cotinverse cancel out

[hard marten]

so im left with cot 191.3

or

[cinder thicket]

X=cot(14.623)

[hard marten]

are we doing the top question or bottom

[cinder thicket]

Bottom yes?

[hard marten]

na im looking at top

i dont even think my input is right at all

[cinder thicket]

You got it right tho

[hard marten]

89.7?

or the one i inputed

[cinder thicket]

2 decimals

[hard marten]

-1.01976

[cinder thicket]

It should be -1.02

[hard marten]

its 89.70

ah

[cinder thicket]

Round off to nearest integer

[hard marten]

so its just 1/cot^-1(14.623)

for the second one

[cinder thicket]

You have cot^-1(x)=14.623

You have to find x

So you apply cot on both sides to get the value of x

Cot(cot^-1(x)=cot(14.623)

Get it?

[hard marten]

so left cancels out

cuz u cant cot a cot

and u just gotta cot 14.623

[cinder thicket]

Cot and cot^-1() cancels out

[hard marten]

x = cot14.623

[cinder thicket]

So you're left with x=cot14.623

[hard marten]

let me calc

3.83275

[cinder thicket]

Yessir

Now round off to first decimal

[hard marten]

so just 3.8 bc its only

one dec

[cinder thicket]

Yessir

[hard marten]

i feel lost bc there was no clarification on the subject we learning on so the things we learned previously were constantly marked wrong

[cinder thicket]

Like what?

[hard marten]

even though that stuff we learned on our previous course for advanced mathematics didnt cover these simple functions since our course was

like a sped up course

[cinder thicket]

How old are you?

[hard marten]

so right now im confused and afraid to get anything wrong now

21

not math smart

thanks anyways

.close

[lone heart]

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[hard marten]

https://tenor.com/view/big-bird-angry-door-fall-gif-11404358

[hard marten]

ok

uh

maybe a little more help wouldnt hurt

sorry just getting a diagram ready

[ocean seal]

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Requested by .apyx

[hard marten]

what

[lethal citrus]

Pitagorian theorem ?

[hard marten]

i mean i think you're given two

an angle and a measurement idk if theyre both angles are they

ok wait

you can find the sides with three angles?

[lethal citrus]

c is not an angle

[hard marten]

ok thx

c is lower cased

[lethal citrus]

but there's a problem, is c=AC or c=BC ?

[hard marten]

yeah she never clarifies that

thats why im so confused

so i gotta like guess it

or assume

[lethal citrus]

?

ok then b=AC

[hard marten]

whats happening

[lethal citrus]

use Pythagorean theorem to find b

[ocean seal]

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[hard marten]

yeah got that

but she then wants us to find b

which is obviously 90 degrees

[lethal citrus]

b isn't an angle

[cinder thicket]

Use the sin law

[hard marten]

she like

never labelled which one is an angle or a measurement

[lethal citrus]

or just $\cos(A)=\frac cb$

[ocean seal]

deus ex machina

[cinder thicket]

Here's the standard notation

That side opposite to angle A is a

Side opposite to B is b

[cinder thicket]

So obviously B=90

C=90-68.2

=21.8

The ones in capitals are angles

[hard marten]

yeah so the given measurement of c=23.0

how would you find everything else with just one measurement

[lethal citrus]

use this

[cinder thicket]

Or use the sin rule

c÷sinC=b/sinB

[lethal citrus]

this is a retangle triangle

[hard marten]

dawhg what is a sinus theorem

[cinder thicket]

Sine theorem

[hard marten]

i don't know what c is

so how could i even calculate anything with the degrees

of 90 and and 21.8

[cinder thicket]

Dawg just look at this

a/sin(A)=b/sin(B)=c/sin(C)

Find b from that

Then apply Pythagoras

[hard marten]

is this even applicable

or am i using the wrong side

[cinder thicket]

That's right

@hard marten

[hard marten]

the thing i made is right

or am i right that i am using the wrong side

[cinder thicket]

Ayo holdon

Is this the same question?

[hard marten]

she never clarified what c = 23 is

yeah

so if we assume that c is the hypothenuse or sum

its just nothing it dont work

[cinder thicket]

Could you send the entire question?

[hard marten]

sure

[cinder thicket]

It's so confusing

[hard marten]

thats what IM SAYING

[cinder thicket]

With the option too, please.

[cinder thicket]

It's options?

[hard marten]

uh u have to write your options lol

like type it

[cinder thicket]

You have to make your own stuff and submit it?

[hard marten]

no like

whatever you get

for b and C

[cinder thicket]

Why are the variables different in the other picture you should me? Which one are we supposed to refer?

[hard marten]

this one?

i put my answers into a trig calc to calc the missing sides to make sure my answers are right

if u assume the hypothenuse is 23 cm

u cant find anything else

but my TEACHER

didnt clarify which side the only measurement she given is

so im starting to think it may be impossible unless i assume c is another side

which is 50/50

[cinder thicket]

Are These options directly under the question?

[hard marten]

nope

[cinder thicket]

Then?

[hard marten]

u get 21.8 if u subtract the given angle

and 90 degrees

to 180

180 - 90 - 68.2

[cinder thicket]

No like. Is there a seperate site where you submit this?

[hard marten]

its on my school website

[cinder thicket]

And the question?

[hard marten]

the homework she gave us

accessible on the school website

so i may have to assume she might have made an error or sum

[cinder thicket]

Yo are they on the same page or not bruh

Like on the same tab

[hard marten]

uh wym

these two?

[cinder thicket]

Yessir

[hard marten]

theyre both separate

[cinder thicket]

No, right?

[hard marten]

the orange one is me using a trig calculator

https://www.omnicalculator.com/math/right-triangle-side-angle#:~:text=To solve a triangle with,side adjacent to the angle.

[cinder thicket]

😭

Cmon bro

That's what I was asking

[hard marten]

its openbook homework

she dont even mind if u cheat or do anything

but i dont

get it

i want to UNDERSTAND

[cinder thicket]

This is the diagram aight?

[hard marten]

is c always the hypothenuse tho

[cinder thicket]

Nope.

Like I said the convention is this

[hard marten]

so if c is the opp

how do i find everything else with just the opps and some angles

[cinder thicket]

Side opposite to the A is a

Using the sine rule

SinB/b=sinC/c

We already know B,C and c

[hard marten]

yeah

[cinder thicket]

We just need b

[hard marten]

90, 21.8 and 68.2

[cinder thicket]

Nope

c=23

A=68.2

[hard marten]

oh oops

ok i calculate

[cinder thicket]

Sin90/b=sin21.8/23

[hard marten]

is it 0.07614642763

[cinder thicket]

Nope

[hard marten]

what happened to the sin 90

how did you operate this

[cinder thicket]

Sin 90= 1

1/b=sin23.8/23

b=23/sin21.8

[hard marten]

i got 56.99

[cinder thicket]

How come

[hard marten]

idk u uh

[hard marten]

used 23.8

instead of 21.8

so i got a diff answer

[cinder thicket]

Why would you

Look at the picture bruh

[hard marten]

dwag

idk cuz u sent dat

[cinder thicket]

Sorry

[hard marten]

kk

she never covered this which is crazy

ik she expects us to probably know how to do this

but i dont so like

its really weird she doesnt explain HOW to do anything to solve these questions so i gotta look on a discord and youtube lol

.close

[lone heart]

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[lone heart]

Please don't occupy multiple help channels.

[late moss]

where does the y=alpha... eqn comes from

[late moss]

i have 2 different doubts

[lone heart]

@late moss Has your question been resolved?

[late moss]

<@&286206848099549185>

[thorn marsh]

#help-11

[late moss]

helpp

[late moss]

<@&286206848099549185>

[plucky sluice]

what's the doubt?

It's a sine curve, no?

Graph on left, function on right

@late moss

[late moss]

the equation

isnt the eqn of sin graph just sinx

[plucky sluice]

Not if you want to capture EVERY sine shaped graph

The amplitude and the wave length are parameters

[late moss]

so i just need to remember

alpha+sin beta x

?

[plucky sluice]

alpha times

[late moss]

yesss

and also

how to find min value of sin+cos

[plucky sluice]

Don't just remember, think of why that's true

[late moss]

by dy/dx

[late moss]

why is that true tho

[plucky sluice]

What's the max value of sin(x)?

1

[late moss]

yes

[plucky sluice]

What if my amplitude is actually 250 dogs/hr

[late moss]

then?

[plucky sluice]

Obviously I need to scale the graph to fit the actual situation

alpha =250 in that case

[late moss]

yup i understood

in idea

ideal*

sinx graph

alpha is 1

and beta is 1

so for diff scales these parameters will change

[plucky sluice]

Yes, yes

[late moss]

.

[plucky sluice]

Especially if you are representing a physical system

[late moss]

dy/dx is sin=cos

[plucky sluice]

yes

[late moss]

now?

[plucky sluice]

You set the derivative = 0

[late moss]

yes

so theta can be 135

[plucky sluice]

voila, find the solutions

[late moss]

or 45

ahh

for 45 it gives max

for 135 min

?

[plucky sluice]

Are you talking about sin + cos?

[late moss]

yes

[plucky sluice]

I don't know the solutions off the top of my head

[late moss]

for 45 it gives max

[plucky sluice]

But yes, the mins and maxs will be infinite

[late moss]

i cant find min

i have to find min value of sin+cos

not the theta

[plucky sluice]

Both are periodic

[late moss]

cant we just use calculus

[plucky sluice]

Yes

[late moss]

like we did to find max val

[late moss]

how

tho

and also

if we do dy2/dx2

it comes as -(sin+cos)

[plucky sluice]

Find the critical points and classify as min or max

[late moss]

how to we know if its +ve

or -ve

[late moss]

.

[plucky sluice]

You need to know, at some point, the specific theta value you're talking about. Consult the unit circle and do the calculation

[late moss]

ahh

we need to put theta to check

so for 45 its coming negaitve

so it will give max

but for what will it be+ +ve

[plucky sluice]

Do you have a list of critical points?

I don't think 45 is actually one of them

[late moss]

it is

sin 45 is 1/ root 2

[plucky sluice]

well, ok, you did the calcs

[late moss]

cos 45 is 1/root 2

[late moss]

the derivative of sin+ cos is cos-sin

so cos=sin at 45 deg and 135 deg

[plucky sluice]

ok, so check the sign of the second derivative at the other critical point

[late moss]

its still -ve

at 135

so it iwll give max

[plucky sluice]

send your work for that?

[late moss]

for what?

[plucky sluice]

Are you sure 135 is a critical point?

[late moss]

ah no

sorry

it isnt

sorry sorry

how to find the next crit point then?

[plucky sluice]

I would check 225

You rotated 90deg, so rotate another 90

[late moss]

kkk lemme check

[plucky sluice]

Or, more intuitively, the min will be in the lower left quadrant of the unit circle

because sin and cos are negative there

[late moss]

yup

it is the

crit point

thnx alot

fro this fxn

how to find min value by calculus

@plucky sluice

dy/dx is bcos theta = a sin theta

nvm got it

can it be a st line between the points too?/

@plucky sluice

.close

[lone heart]

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[uneven wedge]

What's the thing p(A,B) means in the context of something like cartesianb product?

[uneven wedge]

It has to do with it but I've forgotten what it's called

[worn fox]

Do you have an example of it from somewhere

[uneven wedge]

I think it's the set of all subsets?

what would that be called

[worn fox]

Power set but that would be P(A x B)

[uneven wedge]

okey yeah thats what I meant

.close

[lone heart]

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[serene vault]

is this correct?

a top left, b top right

c bottom

[lone heart]

@serene vault Has your question been resolved?

[serene vault]

anyone?

[lone heart]

@serene vault Has your question been resolved?

[lone heart]

@serene vault Has your question been resolved?

[lone heart]

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[heavy coral]

Hey

I’m confused

Teacher said

Do this work sheet

[lone heart]

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[heavy coral]

Hey

[heavy coral]

I’m confused hoe to solve

[naive valley]

which one?

[heavy coral]

18

[maiden glen]

if you've done 16 and 17, it's the same process, just with arccos instead of arcsin/arctan

[heavy coral]

Ok

.close

[lone heart]

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[dreamy root]

On question 45 the answer is p = 4csc(phi)

But i can only simplify it to 4 tan (theta) / sin (phi)

This is my work

Is there something wrong with what i did or am i just missing the next step

And what would the next step be

[lone heart]

@dreamy root Has your question been resolved?

[lone heart]

@dreamy root Has your question been resolved?

[lone heart]

@dreamy root Has your question been resolved?

[lone heart]

@dreamy root Has your question been resolved?

[alpine sable]

does csc(phi) means 1/cos (phi) ?

[dreamy root]

No it’s 1/ sin (phi)

[alpine sable]

im not familiar with what csc is

[alpine sable]

oh cosec

[dreamy root]

Yeah

[alpine sable]

p is perpendicular distance?

whats p? @dreamy root

[dreamy root]

P is the distance between the point in space and the origin

[alpine sable]

ohk

i guess ive got the ans

x^2 + y^2 = 16 is a circle with centre as origin and radius 4]

[dreamy root]

Yeah

I have the answer

It is p = 4 csc (phi)

I just don’t know how to get to there from the original equation

[alpine sable]

i guess there is no need to introduce another variable theta when it is given in phi

[dreamy root]

Theta is needed when translating from rectangular to spherical

[alpine sable]

oh i forgot

[dreamy root]

X = p sin (phi) cos (theta)

[alpine sable]

@dreamy root

i guess you did mistake in dividing

ig you need to divide with sin(theta)

[alpine sable]

it said X = p sin theta cos phi

thats the mistake ig]

[loud ridge]

İ have a question

-(18x-9y) is = -18x+9y or?

[granite grail]

yes -+=- --=+

[loud ridge]

Thanks

[lone heart]

@dreamy root Has your question been resolved?

[lone heart]

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[regal oxide]

guyz i want to know about matrices

[vague coral]

hmm ?

find a course about it

[molten pivot]

Matrices are just grids of numbers

Or lists of vectors

[regal oxide]

ok

any free course like 0 to 100% matrices

[molten pivot]

Khan Academy

Linear Algebra

[regal oxide]

oh ok

[lone heart]

@regal oxide Has your question been resolved?

[lone heart]

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[brazen jewel]

this is mechanics

so, my calculations were that the normal reaction force would be the downward component of the 8N, + mg.

but in the answer, its MG - the downward component of the force

whats going on here? did i misinterpret the question? or am i just wrong

[lone heart]

@brazen jewel Has your question been resolved?

[alpine sable]

show your work

[brazen jewel]

its long and complicated but sure

ignore the red pen

thats me going over it afterwards

basically, i did 0.3g + 8sin(10) and they did - instead

[lone heart]

@brazen jewel Has your question been resolved?

[lone heart]

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No need to ask "Can I ask...?" or "Does anyone know about...?"—it's faster for everyone if you just ask your question! See https://dontasktoask.com/

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[tulip oasis]

hi

[tulip oasis]

So how come in the 2nd mile it is doubled

$6

But in this problem

It is trippled to $9

😭

[lone heart]

@tulip oasis Has your question been resolved?

[tulip oasis]

pls

[lone heart]

@tulip oasis Has your question been resolved?

[lone heart]

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[charred dock]

hey

[charred dock]

do we got a sheet for properties of logs

or like a list

for expanding and simplifying

[alpine sable]

[charred dock]

uh okay I suppose

I'm at my girlfriend's house, I don't have any of my notes unfortunately

[alpine sable]

do you know the propeties of log ?

[charred dock]

no

not off the top of my head I'd really like a reference if there is one

[wary stream]

Google one

[charred dock]

good idea!

.close

[lone heart]

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[alpine sable]

@charred dock

[lone heart]

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[green sable]

This is what I get and I have to proof a=c

[green sable]

It is probably like the most simple solution ever but idk why but my mind is just not finctioning

I have been staring at this problem for way too long already and all I have is nothing

[lucid dawn]

for a+b=c+d, we would subtract b from both sides

which gets us a=c+d-b

[green sable]

I tried that somewhere then I got stuck

[lucid dawn]

now you subsitute a from the second equation and you get a=(a+b)-b

then subtract b from both sides which leads you to: a-b=a-b

then you add c to both sides

a-b+c=a-b+c

[green sable]

Uuuuuh

You lost me

[lucid dawn]

you're basically using subsitution

[green sable]

But

You substitute with something that is from the exact same equation

Which just leads to 0=0

[lucid dawn]

@sour raft could you please help me out here, my explaning is really bad

[sour raft]

Yea sure

Im only in 9th grade but i think i can give this a shot

Lets start from the beginning

and using a different approach

[green sable]

Owki

[sour raft]

Lets assume a=c is true, lets see if we can find any contridictions

first lets start with a+b=c+d

this can be rewritten, as the person above said, to a=c+d-b

since we assume a=c, that means that d-b must equal 0 since otherwise, c wouldnt be the same as a

which meands d=b

[green sable]

Ye but searching for contradictions won't be enough cuz if we don't find contradictions we will still have to prove it

[sour raft]

Yes but this can get you somewhere

again im just a 9th grader trying my best-

sorry

[green sable]

Yes yes I do appriciate. Your help

I found something on google

It is quite confusing ngl

[lucid dawn]

think of it as a rectangle

[green sable]

Wut

A rectangle ?

[lucid dawn]

yes

[sour raft]

now youre getting me confused

[lucid dawn]

im an 8th grader so i wouldn't know much

[green sable]

But we don't know that the sides are similar

But guy guys I found something on google

[lucid dawn]

What

[green sable]

Let me write it out I will show then

[sour raft]

Were trying to do this not through google-

[green sable]

I'm trying to understand

[green sable]

Uuh ok I won't spoil

[lucid dawn]

could you solve this as a proof?

[green sable]

You can figure it out yourself

[green sable]

Wdym?

It is meant to be a proof

[lucid dawn]

oh sorry

my bad

i'm in honors geometry so i wouldn't know because i'm starting to learn proofs

[green sable]

The subject is literally called mathemathical proving and reasoning

Lmao

[green sable]

Ah

[sour raft]

wait hold on

we got the thing that a=c+d-b, we all agree on that right?

[lucid dawn]

Yeah we all do

[green sable]

Yes that's correct logically

[sour raft]

in the other example with multiplication, we can solve for a by dividing by b

so we get a=(c*d)/b

[lucid dawn]

yeah but whatever you do to one side you gotta do to the other

so a/b=(c*d)/b

[sour raft]

no

[lucid dawn]

Why? Doesn't it apply for all equations

[sour raft]

since the original thing is a*b=c*d dividing by b gets us (a*b)/b=(c*d)/b

[green sable]

Ye

He alrzdy divided both sides

That's how he got a on one side

[lucid dawn]

Oh, my bad

[sour raft]

since the right side of the equation both multiplies and divides by b, you get a=(c*d)/b

anyway

if we solve for c instead, we get c=a+b-d and c=(a*b)/d

so now we have 4 equations
a=c+d-b
a=(c*d)/b
c=a+b-d and
c=(a*b)/d

[lucid dawn]

so we can subsitute now right

or not

[sour raft]

i dont think we need to

[lucid dawn]

Okay

[green sable]

It's still 2 equations cuz they are like the same

But written slightly different

[lucid dawn]

yup

[sour raft]

huh

that didnt take me anywhere did it

wait hold on

[green sable]

Not rlly

[sour raft]

a=c+d-b
a=(c*d)/b
just a pair of these equations we can see that c+d-b=(c*d)/b

[green sable]

Ye

[sour raft]

we can factor out the c in the left lane to get c+d-b=c*(d/b)

[lucid dawn]

oh yea

[sour raft]

since both sides contain c being modified in different ways, we must conclude that they either do nothing or change C by the same amount

in this case, since the operations are different (adding a difference in one case, and multiplying a divison in another) , they have to do nothing

whic means d-b=0 and d/b=1, which is only possible if b=d

now back to the original a+b=c+d, if b=d, then this can be rewritten as a+b=c+b, and since the +b is the same on either side, we can remove it by subtracting b on both side and get a=c

[lucid dawn]

ill take note of that

[sour raft]

idk if that works

[lucid dawn]

i think it would

[sour raft]

@green sable ?

[green sable]

Let me look

I'm unsure if that is enough proof to assume d-b=0

[sour raft]

I didn't assume it tho

I (tried to) reason to it

[green sable]

Ye

But I'm unsure if it is enough reasoning

It's university

They are very strict on that stuff

What was the command to close a ticket

[sour raft]

I think it's. close

.close

[green sable]

.close

[lone heart]

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[ionic cosmos]

I need help figuring this out pls (the answer is -90 but idk hwo to get there)

[jagged zinc]

multiply everything by 15

[alpine sable]

move all the x's to one side and all the constants to the other and divide by x's coefficient

[ionic cosmos]

how do i move all the x's to one side-

[jagged zinc]

multiply everything by 15 to get rid of the fractions

so its easier to understand

[alpine sable]

by subtracting -2/3x

[alpine sable]

no, teach him not to be afraid of fracs

[jagged zinc]

if the operation is a +4, you -4 from that side and subtract it from the other side

every operation you do on both side has to be equal

[ionic cosmos]

so turn it to 2/3x + 4 - 4 = 3/5x - 2 - 4??

[jagged zinc]

he's right you have to isolate x so x = 90

yes but you simplifiy it

so its 2/3x = 3/5x - 6

[ionic cosmos]

ok and then

[jagged zinc]

then what I would do is get rid of teh fractions

you do that by multiplying both sides by 3

because if 3 is on top and bottom they cancel out and the fraction is gone

[jagged zinc]

yes

[alpine sable]

in the last one i just pulled x out and devided by the coeff

[ionic cosmos]

ok ok

i got it

thanks for the help

.close

[lone heart]

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[red drum]

help plss!!

anyone?

.close

[lone heart]

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[floral current]

I need some help.

[lone heart]

Please don't occupy multiple help channels.

[golden onyx]

Write your question

[scarlet oriole]

what do you need help with on this problem

[golden onyx]

^

[floral current]

Sorry wrong matrix

[scarlet oriole]

you need the whole problem solved or what

[floral current]

Is this correct RREF:

| 1 0 -1 | 16 |
| 0 1 2 | -23 |

[golden onyx]

What operations did you do?

[floral current]

First I flipped it.

Then I multipied R1 by -1.

[golden onyx]

OK.

That gives you 1 1 1 | -7

[floral current]

Then I multiplied R2 by -1 as well

[golden onyx]

ok

a lot of these steps seem unnessary but lets go with it

so you have R2 as
-2 -1 0 | -9

[floral current]

Actually, before I did that I did 2R1 + R2

So I have

1 1 1 | -7
0 -1 -2 | 23

Then I multiplied R2 by -1.

1 1 1 | -7
0 1 2 | -23

Then to remove the 1 I did:

R1 + (-1R2) -> R1

1 0 -1 | -16
0 1 2 | -23

[golden onyx]

2R1 + R2 into R2?

[floral current]

Yes

[golden onyx]

Why isn't this already enough?

[floral current]

They want it in RREF

So is this RREF correct:

1 0 -1 | -16
0 1 2 | -23

And how do I solve for x1, x2, x3 in this case?

@golden onyx

Did you die

[golden onyx]

lol sorry abit busy

[floral current]

Solved it

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