help-0

[abstract fractal]

We have r²

We want r

How do we find r?

[ashen scaffold]

square root?

[abstract fractal]

Yes

So what do we have now?

[ashen scaffold]

r = G x m1 x m2 : F

[abstract fractal]

#❓how-to-get-help

[ashen scaffold]

u can create a channel

[abstract fractal]

What happened to the square root?

[ashen scaffold]

.

[ashen scaffold]

idk can you help?

[abstract fractal]

You took the square root of both sides, right?

So why is the RHS unchanged?

[ashen scaffold]

i dont know how to use the sr on m1 and m2 and G and F

so m1 and m2 is 1 kg

[abstract fractal]

No

You're just taking the square root of both sides

r² becomes r

And you just take the square root of the entire RHS

[ashen scaffold]

okay

[abstract fractal]

Then all you need to do is plug in the values to find r

[ashen scaffold]

what was G again

[abstract fractal]

Newton's gravitational constant

,w newtons gravitational constant

[ocean seal]

Results provided by WolframAlpha

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

Requested by Gamer Dio#7663

[abstract fractal]

First number

6.674 x 10^(-11)

[ashen scaffold]

6.674 x 10^(-11) * 1kg * 1kg : 9,81 then?

[abstract fractal]

Where are you getting 1 kg from?

[ashen scaffold]

ahhh

wrong number

[abstract fractal]

And why are you setting F = 9.81 for?

[ashen scaffold]

1kg was nr 1

5kg then

F isnt 9,81

[abstract fractal]

That's one of the masses

[ashen scaffold]

whats F then again

i thought its 9,81

[abstract fractal]

The force

We found it earlier

.

[ashen scaffold]

24 53

?

yes aight

6.674 x 10^(-11) * 5kg * 5kg : 24.53N then?

[abstract fractal]

And don't forget to square root everything

No, only one mass is 5kg

The two masses are the object and the earth respectively

#❓how-to-get-help

[ashen scaffold]

so one is 5kg

and the other one is 9,81

no its not right

[abstract fractal]

What's the mass of the earth?

[ashen scaffold]

one sec

5.97219 × 1024 kilograms

[abstract fractal]

I assume that's 10^24, but yes

That's the second mass

[ashen scaffold]

yes haha

thanks

6.674 x 10^(-11) * 5kg * 5.972*10^24 : 24.53N then?

[abstract fractal]

Don't forget to square root the answer as well

[ashen scaffold]

is the answer 9013412,12

or is the comma wronfg

or something else

[abstract fractal]

,calc 6.674 * 10^(-11) * 5 * 5.972 * 10^(24) / 24.53

[ocean seal]

Result:

8.1241598043212e+13

[abstract fractal]

,calc sqrt(8.12416 * 10^(13))

[ocean seal]

Result:

9.0134122284516e+6

[ashen scaffold]

so thats the distance

[abstract fractal]

Looks right, except it's 9013412.22

That should be the distance, measured from the center of the earth, in meters

[ashen scaffold]

okay thank you, can you help me with another question, thats way easier i guess

[abstract fractal]

Sure

[ashen scaffold]

Calculate the force with which a body with a mass of 1 kg is attracted when it is 20 000 km above the earth

[abstract fractal]

Well, what's r?

[ashen scaffold]

one sec

20 000?

[abstract fractal]

That's the distance from the surface of the earth

We want from the center

[ashen scaffold]

oof

so 20 000 + something, right?

[abstract fractal]

Yep

I gotta go rq, ill try to be back

[ashen scaffold]

okay

20 000km plus 6000km then

also 26 000 km then

i think i goot use F= G * m1 * m2 : r² again

so F= 6,674*10^(-11) x 1kg x 1kg : 26 000²

i thnik#

[abstract fractal]

You're making the same mistake with the masses

The second mass is the earth

Also, you need to convert 26000 km to m

[ashen scaffold]

26000000 then

[abstract fractal]

Yep

[ashen scaffold]

so F= 6,674*10^(-11) x 1kg x 5.972 * 10^(24) : 26000000²

then

[abstract fractal]

Yes

[ashen scaffold]

aight now calculate, correct?

If yes, may you do that in the chat right here, please.

,calc 6,67410^(-11) x 1kg x 5.972 10^(24) : 26000000²

[ocean seal]

The following error occured while calculating:
Error: Unexpected operator , (char 2)

[ashen scaffold]

oops

6,67410^(-11) x 1kg * 5.972 10^(24) : 26000000²

calc, 6,67410^(-11) * 1kg * 5.972 10^(24) / 26000000²

ycalc 6,67410^(-11) * 1kg * 5.972 10^(24) / 26000000²

,calc 6,67410^(-11) * 1kg * 5.972 10^(24) / 26000000²

[ocean seal]

The following error occured while calculating:
Error: Unexpected operator , (char 2)

[ashen scaffold]

bruh

[abstract fractal]

,calc 6.67410^(-11) * 1 * 5.972 * 10^(24) / (26000000^2)

[ocean seal]

Result:

7.5483720574152

[ashen scaffold]

thank you so much

,calc 6.674 * 10^(-11) * 1 * 5.972 * 10^(24) / (26000000^2)

[ocean seal]

Result:

0.5896024852071

[ashen scaffold]

ain't that right?

you calculated 6.67410^(-11) isnt it 6.674 * 10^(-11)

[abstract fractal]

I fucked up yeah

Yours is right

[ashen scaffold]

no no worries

thank you

i apprechiate you, gotta go to sleep now, tomorrow i have an english exam

its 18 21 for you now, right? for me its 00 21

good night ❤

,close i guess

[lone heart]

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[night mirage]

How to solve without using L’hôpital’s rule

[ornate condor]

yay jam

idk series mayb

[night mirage]

Idk what that is

[ornate condor]

um

taylor expansion

[night mirage]

Just using algebra

[ornate condor]

yes

[night mirage]

Havent learned that

[ornate condor]

taylor series

:c

[snow furnace]

Change tanx to sinx/cosx

Then you can solve the limit

Oh wait

[ornate condor]

wow wrote out all

[snow furnace]

Cot0 is undefined

[night mirage]

Ye

Answer is 1/4

[snow furnace]

You sure?

Graphing it shows 2

[night mirage]

Whoops

Sorry I was looking at the wrong number

Yeah it’s 2

[snow furnace]

Oh, you can just divide the top part by tanx

Should be xcotx+cosx not xcotx+x

Then you find the limit of xcotx

Which you just have to know is 1

And cosx is 1

[night mirage]

There are some ur steps which I don’t get

[snow furnace]

A lot of it is just trig identities

[night mirage]

Why do u divide it by sin again

And why do u add it

[snow furnace]

Top part

Tanx= sinx/cosx

And you divide by the reciprocal

[night mirage]

Oh ok nvm

Thx for the help

.close

[lone heart]

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[snow furnace]

Should be that instead lol

[lone heart]

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[ornate condor]

$z^4=17-12\sqrt2$

[ornate condor]

do ive to show algebraically how to find the roots

seems bit hard to find the 4th root

how wld i do it if i wanted to show algebraically that one of the roots is sqrt2 - 1

and well the rest wld b arg(pi/2, pi, -pi/2)

[slate jolt]

yeah that seems good

[ornate condor]

o well i worked backwards

i just expanded sqrt2 - 1 ^4

lol

[slate jolt]

you write z=re^ic

[ornate condor]

but i think if i wanted to show it the normal way

id first find

[slate jolt]

then r= (......)^1/4

[ornate condor]

some (a+bsqrt2)^2 = 17-12sqrt2

[slate jolt]

and c is in U_4

[ornate condor]

then repeat again

cuz the expansion for (a+bsqrt2)^4 is horrible

i got

[tacit arch]

polar coordinates are fren?

[ornate condor]

a^4+12a^2b^2+4b^4=17

[ornate condor]

yea but

i mean to get exact real val

is hard

unless u guess the ans n work backwards

[slate jolt]

oh you want a neat form

[ornate condor]

yea so this is the 1 bit

the sqrt2 bit will be

4a^3+8ab^3=-12

quite ew

so if i was working nromally id prob find

z^2 first?

[ornate condor]

is there a faster way?

or simpler way

idk

[slate jolt]

my answer would have just been this z=(17-12sqrt(2))^1/4 *e^(i k pi/2)

[ornate condor]

yea but

(17-12sqrt(2))^1/4

[slate jolt]

its ugly yeah

[ornate condor]

i kinda wanna show its <1

which isnt rly straightforward in that form

and when i wanna sub it into later bits i cant exactly use that

[tacit arch]

,calc 12 * 1.4

[ocean seal]

Result:

16.8

[slate jolt]

17-12sqrt(2)<1

[tacit arch]

i beg to differ

[slate jolt]

yeah

[ornate condor]

(17-12sqrt(2))^1/4 = sqrt(2) -1

but is there an easy way to show that without working backwards?

the easiest way i can think of is completing the square twice

[slate jolt]

yeah if i had to i would do this too

[ornate condor]

oki

[tacit arch]

i think this is the only way

[ornate condor]

o well

oki

ty

[tacit arch]

except it's ^4 and not 2

[ornate condor]

🥣

[slate jolt]

yeah this is a way that will yield results for this for sure

[ornate condor]

ye

[tacit arch]

but i think you knew that

[ornate condor]

repeat twice

thats what i meant

[tacit arch]

oh yea

[ornate condor]

completing squ twice

czu the ^4 is horrible

unless thrs a nice shortcut to that

i havent heard of any

[tacit arch]

yea it's not like gonna take you all day hard, just mind numbing algebra

[ornate condor]

ye

.close

[lone heart]

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[calm willow]

hi

[calm willow]

i am reviewing

and this is what i got

the Amp =1 period =2pi and phase shift 3

and when i try to graph it like this

oh wait

i never saw that pi

.close

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[alpine sable]

i got a question about finding the domain of a function where f(x) = x^2/|x+1|
does this just mean find the inverse?

[ornate condor]

#❓how-to-get-help

[ornate condor]

i think it means maximal domain in which f can be defined

or what values of x it can take in

normally it just means watch out for division by 0s

or

[alpine sable]

so find the limit of the inverse function?

[ornate condor]

|x+1|=0

no

[ornate condor]

this

what val of x will the denom be 0

well actually

[alpine sable]

oooooooh

find the limit

ok

[ornate condor]

what val of x itll be defined on

nononoo

ok well

[alpine sable]

what i need to do is find the vertical asymptote so finding the limit would make sense

[ornate condor]

|x+1|=0

is when x=-1

so u just

f is just defined on R\{-1}```

all points except -1

[ornate condor]

only point f is not defined

[ornate condor]

thus this will be the domain

[alpine sable]

i dont really understand what you mean

[ornate condor]

like

the domain of

f(x) = x is

-inf, inf

or R

[alpine sable]

so u mean x is real where x cant be -1

[ornate condor]

yes

[alpine sable]

ok makes sense

[ornate condor]

kinda

R excluding 1

-1

but close

[alpine sable]

what is the difference

[ornate condor]

i mean

i think its the same

idk felt it sounded weird

[alpine sable]

I would just write it as

[ornate condor]

$x \in \real \{-1}$

i cant latex

[alpine sable]

$\left{x\in \mathbb{R},:x\ne :-1\right}$

[ocean seal]

Caleb.

[ornate condor]

ye that works

[alpine sable]

k ty

[ornate condor]

np

🥣

[alpine sable]

.close

[lone heart]

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[stray remnant]

Trying to see which step I went wrong

[ornate condor]

31times lol

[stray remnant]

Yeah nuts right

Lol

[ornate condor]

sad

[stray remnant]

came looking for help

[wary stream]

[stray remnant]

So

[alpine sable]

I can try to help

But not the best fyi

[stray remnant]

Well its better then saying sad so its appreciated

[alpine sable]

Can I c ur work?

Or wut did u do

[stray remnant]

posted it above

[snow furnace]

where did the 12 come from

5^2+3^2 is 34 not 36

[stray remnant]

Word word

[snow furnace]

so it would be 2sqrt(34 on the bottom right?

[alpine sable]

It’s not

12

[stray remnant]

thank you guys

[snow furnace]

was that right?

[stray remnant]

yikes i was losing my mind over something so small

ill check it right now

Yup

Jesus christ cant believe it was just that

[snow furnace]

ah, simple mistake lol

[stray remnant]

preciate you @snow furnace @alpine sable lmaoo much love

you guys should be ranked helpful 😭

[ornate condor]

unlike me

hahaha

[lone heart]

@stray remnant Has your question been resolved?

[lone heart]

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[storm plover]

so I have a FOV of angle x, pointing directly (centered on a point, (p,q))

[storm plover]

is there a way to calculate the height, from the horizontal, of angle X, that would have a FOV length L ?

x, (p,q), L are all given

what i'm thinking is to have the FOV X slide on the line (that points to (p,q)) until we land on FOV length of L

but i don't know the mathematical solution to that

the coordinates of angle X is also always (0,0)

.close

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[hexed cipher]

How would I go about doing these questions. For A. I determined the answer was zero because I plugged zero where t was, but when I was doing B. I tried plugging in infinity, but how would you do e^infinity. I am quite lost, please help

[past bloom]

may i ask what does it mean to uncoupling a coupled equations

[lone heart]

@hexed cipher Has your question been resolved?

[hexed cipher]

<@&286206848099549185>

[lone heart]

@hexed cipher Has your question been resolved?

[tacit arch]

Is this a test!

[lone heart]

@hexed cipher Has your question been resolved?

[lone heart]

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[slow canopy]

Hey yall, can someone help me figure out the right answers here

and why mine are wrong

and which of mine are right/wrong lol

[slate jolt]

explain how younfound each

[coarse socket]

can’t confirm deny

[slow canopy]

ok

[coarse socket]

looks like test so

[slow canopy]

I updated one (still not all correct)

but

[slow canopy]

homework

not test

it's webwork

[slate jolt]

yeah if they get feedback on whats right/wrong prob not a test

[slow canopy]

So for 1

it's what approaches 2 from the left

[slate jolt]

ok good

[slow canopy]

where it goes up to 2

pretty sure I have 1 correct

[slate jolt]

yes

[slow canopy]

same for 2, it goes to -1 from the right

[slate jolt]

indeed

[slow canopy]

not entirely sure how to do #3

[slate jolt]

a limit has to be unique

[thorn sparrow]

Hey I need help with Rational and Irrational numbers:(

[slow canopy]

please ask in an unoccupied channel

[thorn sparrow]

k

[slate jolt]

do you know about epsilon delta definition of a limit?

[slow canopy]

I do not

[slate jolt]

ok so the rule is

for the general limit to exist

it left and right limit must be the same

so here itd not the case

[slow canopy]

but they aren't the same, so does it not have a general limit

[slate jolt]

yeah

dne

[slow canopy]

ok

same for #4 then

yup

cool thank you

got all of em

.close

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[atomic horizon]

Good day guys, looking to find height in this problem....

[atomic horizon]

I already have all the vertex/distances. I just lack the height since I do not know and I am not familiar with doing it on a parallelogram

[slate jolt]

the heighr?

[atomic horizon]

Yes bro

[slate jolt]

essentially you want the distance of A to the line BC

or C to AB

[slate jolt]

https://en.m.wikipedia.org/wiki/Distance_from_a_point_to_a_line#Line_defined_by_two_points

#❓how-to-get-help

@alpine sable

[alpine sable]

Can someone pls check if 5a) is correct??

[atomic horizon]

How do I know where specifically? because I could just draw a completely straight line and don't know if it's correct

[slate jolt]

the distance is implying the shortest distance

so its the distance to the orthogonal projection

that makes a right angle with the line

[atomic horizon]

So you're saying we can do a straight line from a point downwards?

[slate jolt]

wdym

[lone heart]

@atomic horizon Has your question been resolved?

[atomic horizon]

Is there a formula to draw the line. I am not asking about the formula to measure the line

[slate jolt]

click the link

[slate jolt]

.

and to draw the line just draw the line that goes to two vertices

consecutive vertices

[lone heart]

@atomic horizon Has your question been resolved?

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[vast ingot]

Heyo. I need help.
what is the value of B in x^2 - 49 = 0?

[slate jolt]

0

but here you dont need quadratic formula

just solve for x^2 and take the sqrt

[trim wagon]

wait but what is B

[vast ingot]

so does that mean that I will be using 0 for the b?

[slate jolt]

i assumed as in ax^2+bx+c=0

yeah

[vast ingot]

im trying to find the nature of the roots

oh ok

[trim wagon]

i meant to ask OP but anyways ig it’s clear to them

[vast ingot]

.close

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[green marsh]

i do not understand this explanation.

[green marsh]

this is my problem and i do not know how to solve it

or where to find how to solve it

https://www.youtube.com/watch?v=zMtToQelLN8&list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz&index=17

ive been using this

or this https://www.youtube.com/watch?v=oasIqX74Mhc&list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz&index=15

what type of problem is this called. I know what a resolution is but never did anything with compounds like this

(p V q) and ( NOT p V q ) ---> q V r

thts the resolution formula

[runic trench]

we will take this as the premise , and if we can conclude F from it, then we have proven this =- F

[green marsh]

wait so

[runic trench]

if the compound proposition is equivalent , then the compound position is not satisfiable

??

[green marsh]

srry im confused

[runic trench]

so the steps are

[green marsh]

<@&268886789983436800>

so i have a problem i did before

can i show you

bc i need a reference in terms of wht theyre asking me to do

[runic trench]

1. simplify the premise
2. resolution from ur step 2 to 3
3. use idempotent law in step 4
4. simplify
5. resolution
6. idempotent law
7. conjunction
8. negative law

[green marsh]

ok i didnt do this but

they just want you to bread it down?

[runic trench]

you will come to deny the compound proposition and therefore not satisfiable

i will show u the step

[green marsh]

okay

is it okay if i can look up what a negative and idepotent law is

bc i didnt learn that yet

i was using the videos

[runic trench]

ok

[green marsh]

so i guess she didnt cover it yet

ok srry

wait

.. when they say negative law

does tht just mean the not thing?

[runic trench]

F

[green marsh]

yeah

false

srry i think ik wht you mean now

i just didnt recall the name

you can continue srry

[green marsh]

oki so i have a couple of questions

so starting from

isnt that resolution

[runic trench]

er i did that didnt i

[green marsh]

wait no no

srry im just trying to udnerstand..

i never did a problem like this tbh

only this

this is the closet

i did tht though

[runic trench]

o lol

[green marsh]

im so sorry but ._. can you take a bigger picture bc i cant see the text as much

your notes

in terms of how you did it

ik the first thing is simplify

[runic trench]

i think ill just write it in this format

[green marsh]

i just want to understand how it was done

and okay

[green marsh]

ohhh

ok i see

so you broke it down into two parts

and then compared the two

[runic trench]

[green marsh]

thank you so much, i see why

may i show you what i did for 24 then

to see if i got the idea right?

[runic trench]

U can send it over

[green marsh]

ty

these are the questions

[runic trench]

for 17

the premise is given so we assume it is true

[green marsh]

yes

but its saying something is wrong with it o.o

[runic trench]

we also know that a person y exists such that H(y) is true
however we do not know if person y is lola as it is possible for person y to not be Lola

So we cannot conclude H(Lola) nor the "lola is happy"

[green marsh]

i dont get it

x is happy

and its saying that lola is x

[runic trench]

So i would say that we do not know that lola is the person for which H(x) is true

[green marsh]

why?

oh wait

H(x) be "x is happy" is the same as H("x is happy")?

not H(x) is happy

?

[runic trench]

ok

[green marsh]

its saying if sometimes x is happy AND lola is happy, THEN lola is happy

youre saying that lola has to be someone

[runic trench]

so we assume h(x), this particular x here is happy, and we have the premise where her existentially each affects what we are given, so we assume this is true

but we dont know if the person y is going to be lola

[green marsh]

y?

where did you get y

[runic trench]

.

[green marsh]

but the question doesnt mention y

[runic trench]

mm ok lemme explain it like this

as per argument, there exists an X for which H(x) is true , which will indicate that x is happy

[green marsh]

yes

[runic trench]

in this case we have arbitrarily selected a person named Lola, and thus H(Lola), for which this statement can be either true or false

[green marsh]

woah.. lol uhh

._. im dumb so

[runic trench]

as per argument, it means that there exists an x and not for all of x

[green marsh]

ok

so its saying x is happy, and lola is happy, therefore lola is happy

i still odont understand

lola would be happy regardless of the situation

seomtimes x is happy

and lola, is happy

so bc someone is happy and lola is happy, lola is happy

..?

[runic trench]

zzzzzzzzzzzzz idk how to make it clearer

we know that this particular x exists, which makes H(x) true,

but we cannot conclude that Lola , in this case H(Lola) satisfies this outcome

[green marsh]

are you saying that lola has to be x for both the first argument and the second argument?

in order to show that lola is happy

?

[runic trench]

yes

we cant know that now

[green marsh]

ohhh

[runic trench]

which goes back to this point

[green marsh]

okay i see

i think

H(lola) isnt the same as Lola is happy?

wait.. no i still dont get it

H(x) is saying that x is happy

H(lola) means that X is lola

?

[runic trench]

yes
But we cannot know that H(Lola) is H(x)

H(x) can be true
But H(Lola) may or may not be true

[green marsh]

.. so H(x) is x is happy.. and H(lola) is just lola.. not lola is happy bc we dont know is lola if x

?

[runic trench]

H(Lola) is either happy or not happy we dont know

[green marsh]

why wouldnt we know is its saying that x is happy

and that lola is x

you plug her name in the saying

(x) is happy

lola is (x)

thts wht H(lola) is

?

[runic trench]

idk how to explain any further than this

its going in circles

bye

[green marsh]

v_v...

[lone heart]

@green marsh Has your question been resolved?

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[sturdy harness]

how to solve (x^2+2x)(x^2+x) = 0

[sturdy harness]

I tried foil and got x^4 + 3x^3 + 2x^2
then i took out an x^2 from it
so it became x^2(x^2+3x+2)
then i tried to use quadratic completion on the function inside the paratensis
x^2 + 3x + 1.5^2 - 1.5^2 + 2
so it became
x^2((x+1.5)^2 + 2 - 1.5^2)

[red kindle]

IIts easier if you keep the parenthesis

[sturdy harness]

How should i solve it?

[red kindle]

The idea is that if you multiply two parenthesis with each other, the only way you could get zero, is if one of them is zero

so, eaither x^2 + 2x = 0

or x^2 + x = 0

Solve these equations, and you have all your solutions!

[sturdy harness]

Thank you!

second one is -1 i would guess

[alpine sable]

Iota

[red kindle]

but not only -1?

[alpine sable]

Yea i meant for first

Sorry

Im ded

Leave iy

I read it wrong

[sturdy harness]

i thought it would be x^2 = -x
then divide by -x on both sides

[red kindle]

The easiest way is to put x outside of a parenthesis. That would give you for the second

x(x + 2) = 0

ops thats the first but oki

[sturdy harness]

I see

so it would become x1=0 and x2= -2 on this one

[red kindle]

Again, you multiply 2 things that should be 0. Then x = 0 or x = -2

YEs

[sturdy harness]

second one would be x(x+1) , so that would add so we just add the x3=-1

[red kindle]

perfect

[sturdy harness]

Thank you very much!

[red kindle]

cool!

You can draw it in a digital tool and see whare the function cuts the x-axis

[sturdy harness]

I see

Do you have any tips on where to start when solving such equations?

Actually i got stuck again on another equation

(2x - 4)/(x^2+4x+16) = 0

i took out a two from the upper part so it became 2(x-2)

i tried to do quadratic completion on the lower part so i got (x+2)^2 - 20

[red kindle]

your excercises seem harder than they are!

You have a fraction there

How can a fraction be zero

[sturdy harness]

if the upper part is zero?

[red kindle]

right! So that makes it an easy equation!

And then you have to remember checking just 1 thing.

[sturdy harness]

so the sloution is just x=2?

[red kindle]

Right! And then you should check that 2 is a possible solution.

You are not allowed to get zero under the fraction, so check that 2 is allowed!

If that makes ssense to you?

[sturdy harness]

yeah it does

i actually just checked the answers, it says the answer is two

[red kindle]

all right1

[sturdy harness]

Can i ask as many question as i like here? Because i get stuck on almost every exercise

Now i am stuck on x^2 + x - 1 = 0.
I treid quadratic completion, and the pq method and one another method i learned which i do not know the name of but it is like this x= (-b +- sqrt(b^2-4ac))/2a

I either did wrong somewhere or the solution is none of these methods

[ornate condor]

ye

ask away

or open a new one for a new Q if ud like

[ornate condor]

u want to find x for

x^2 + x - 1 = 0

?

,w solve x^2 + x - 1 = 0

[ocean seal]

Results provided by WolframAlpha

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

Requested by Circle#0025

[sturdy harness]

I actually got this solution

[ornate condor]

then

u good

:spp

🥣

[sturdy harness]

What about 2 + sqrt(x+10) = x ?

[ornate condor]

um

move the 2 over

square the eq

then solve as per normal

[sturdy harness]

How should i square the equation? The only way i can think of is foil

[ornate condor]

um

u multiply the lhs n rhs by themselves?

2 + sqrt(x+10) = x

sqrt(x+10) = x -2

sqrt(x+10)sqrt(x+10) = (x -2)(x -2)

x+10=x^2-4x+4

then u bring all to 1 side n use ur quadratic formula

[sturdy harness]

I got x= 5/2 +- sqrt(59)/2

[ornate condor]

,w solve x+10=x^2-4x+4

[ocean seal]

Results provided by WolframAlpha

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

Requested by Circle#0025

[ornate condor]

welp

[sturdy harness]

Is the pq method appliable to all second grade equation?

[ornate condor]

ive

nvr heard of that

example?

[ornate condor]

that

is exactly the quadratic formula

[sturdy harness]

We call it the pq formula

[ornate condor]

,w what is pq formula

[ocean seal]

Results provided by WolframAlpha

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

Requested by Circle#0025

[ornate condor]

,w what is quadratic formula

[ocean seal]

Results provided by WolframAlpha

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

Requested by Circle#0025

[ornate condor]

wow

im so sad

,w what is the quadratic formula

[ocean seal]

Results provided by WolframAlpha

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

Requested by Circle#0025

[ornate condor]

the

i needed the

wow

anw

thats a name of it ig

[sturdy harness]

So the quadratic fomula is the -b +- sqrt .... formula?

[ornate condor]

well

[ornate condor]

this

[sturdy harness]

Yeah, i have this in my book too, but i do not know when to use pq and when to use quadratic

[ornate condor]

its

[sturdy harness]

since both is applied to second grade equation

[ornate condor]

the same

always use quad

only quad has an a in front

if u div the a u get that p q formula

[tribal oxide]

pq is a special case of the quadratic formula which is used for a=1

[ornate condor]

u can say quad formula generalises pq formula

[sturdy harness]

I see

What about the second grades that are not perfect sequares, can both be used then too?

[ornate condor]

um

yes

[sturdy harness]

I do not get where i did wrong in the former equation, i got x^2 -5x -8 = 0

then i proceeded with pq formula, 5/2 +- sqrt((5/2)^2+8)

then i got 5/2 +- sqrt(59)/2

and i could not do anything afterwards

so i do not know where i got it wrong

[ornate condor]

which

x+10=x^2-4x+4

this?

[sturdy harness]

yes

[ornate condor]

well

10

n 4

doesnt get u 8

[sturdy harness]

oh that would become -6

[ornate condor]

yes

yes it wld

[sturdy harness]

Now i got the right answers

[ornate condor]

yay

[sturdy harness]

Am now using the quad formula on -x^2 + 5x + 5

so i got (-5 +- sqrt(45))/-2

[ornate condor]

um

ok?

[sturdy harness]

i do not know where to go from here

[ornate condor]

what

u can just

leave it

its kinda done

[sturdy harness]

I see

It is not telling me to solve x^2 - 2x - 1 = 0 without using the formulas

i tried to use the perfect square method (a-b)^2 = a^2 - 2ab + b^2

But it doesn't really work

[rough crown]

i guess if u want, u can simplify the sqrt45 and fraction, but apart from that questions is done

[rough crown]

u have to solve x^2-2x-1=0 without using the formula?

[sturdy harness]

Yes, without using any formula

[rough crown]

okay so note that (x-y)^2=x^2-2xy+y^2

can you manipulate x^2-2x-1 to have an expression containing the form of (a-b)^2 + smth

pay attention to the -2x to find what a and b would be

[sturdy harness]

Correction: without using any quadratic formula*

[rough crown]

yeah we wont use any quadratic formulas for the solution

think about completing the square

[sturdy harness]

x^2-2x+1-1-1
(x-1)-2 = 0

x-1 = 2

x = 3

[rough crown]

almost correct, but it should be (x-1)^2, not just x-1

[sturdy harness]

(x-1)^2 = 2
x-1 = sqrt(2)
x= sqrt(2)+1

[rough crown]

rmb when taking sqrt, it would become +/- sqrt2

leading to 2 solutions

[sturdy harness]

Indeed,

x1 = 1 + sqrt(2)
x2 = 1- sqrt(2)

[rough crown]

yup u got it

[sturdy harness]

Thank you

.close

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[silk frigate]

guys

[silk frigate]

i have a question

what is x-x

ive always wondered

what is x-x

[trim wagon]

0

or $x_2$

if u are chem guy

[ocean seal]

Deep.

[silk frigate]

the reason why is X's value is 1 and -X value is -1?

[gray isle]

x is x

-x is -x

[trim wagon]

no x can be anything

[silk frigate]

can -x be any integer thats not negative?

[trim wagon]

yes

[silk frigate]

can -x be 0?

[gray isle]

-x can potentially be any integer

[trim wagon]

yea

[gray isle]

x can be pretty much anything you want (within reason)

[trim wagon]

x can be any number you want it to be

[silk frigate]

even absolute infinity?

[trim wagon]

and it will still result in 0

infinity is not a number

[silk frigate]

what is it

[alpine sable]

As long as x has an additive inverse

[silk frigate]

ok i have another question

second thing ive always been thinking

what is the half of zero?

[trim wagon]

0

0/2=0

[silk frigate]

is there

a reason why?

[rough crown]

if u have 0 cake n u divide into 2 parts, each part is still 0 cake

[silk frigate]

mathematically speaking

[rough crown]

0 x n = 0, 0 x 1/2 = 0

[alpine sable]

a*1/2 = a has one solution: a=0

[silk frigate]

ok thanks

third thing that im wondering

because we are having like coordinates or smth

[trim wagon]

https://medium.com/swlh/why-a-0-0-and-other-proofs-of-the-obvious-da52dd0caefb#:~:text=Multiplying by zero produces zero&text=Turns out the distributive law,1 by definition%2C not 0.&text=Any number multiplied by 0,to ditch the distributive law.

[silk frigate]

what is the value of a straight line?

[silk frigate]

.

[rough crown]

what does value mean?

[silk frigate]

like we had a thing about slopes and all that where

it was like

y - y, = m(x-x,)

It says the value of a coordinate

[rough crown]

oh you mean equation of a straight line

[silk frigate]

yes

[rough crown]

it basically states the relationship between the input x and output y

[silk frigate]

smth like this

what is the value of this straight line

[alpine sable]

y = 0×x+0 =0

[rough crown]

find the slope and y-int of the line

[coarse socket]

there is no meaning in your question

[rough crown]

and use y=mx+b

[red kindle]

To draw a line you need a fixed point and how much it rises. The fixed point is where it crosses the y-axis and the slope is the number in front of the x, that tellse you how steep the line is.

[coarse socket]

value of line doesn’t mean anything

[silk frigate]

what if theres no slope

[coarse socket]

tf

[red kindle]

Then the numebr infront of the x is 0

[silk frigate]

ok

fourth thing ive been wondering is

what is the highest number

that is not infinity

[rough crown]

there isnt a highest number

say x is the highest number, then what would x+1 be?

[obsidian jacinth]

^

[coarse socket]

there is no bound to real numbers

both lower and upper

5 thing now?

[silk frigate]

Nope

thats it

tanks

a lot

[coarse socket]

oh

[lone heart]

@silk frigate Has your question been resolved?

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[alpine sable]

Can somevody tell me what im doing wrong with 3E in figuring out if its a minimum or a maximum?

[ornate condor]

HUTAO

[alpine sable]

Yess ahhaha

[runic trench]

https://tenor.com/view/shut-up-genshin-impact-kiss-doom-doom-eternal-gif-26144053

[ornate condor]

NO MIKU

[runic trench]

HAHAHAH

[ornate condor]

ok idk how u got so many cancellations

but howd u get that

[alpine sable]

I simplified haha

[alpine sable]

Ajhaha its a pfp suggestion from a friend, trio matching pfp

[ornate condor]

err

from what

[alpine sable]

Oh wait

I factorixed

[ornate condor]

no

miku just

hates me

[alpine sable]

the -4

[ornate condor]

💔

[alpine sable]

To -1 and +4

[ornate condor]

im so confused

thrs no -4 riginally

also if u factorised it shld be

something(somethingelse)

miku is bac

to crash

[runic trench]

1. find first derivative
2. set first derivative to 0
3. factor

[alpine sable]

Oh Okay thanks guys I will redo it

.close

[lone heart]

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[ornate condor]

btw

whats 1st derivative test

isnt it

2nd derivative

for nature of stationary pts

[runic trench]

yeah then find 2nd derivative

[ornate condor]

:o

[ornate condor]

also

whats with

factor

[runic trench]

factorize ?

[ornate condor]

nono

y wld u factorise

oh

factorise to find zeros?

[runic trench]

yeah

[ornate condor]

ig that cld work

idk the factorised is horrible to find derivative of tho

n normally u just quadratic

[runic trench]

ok

[lone heart]

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[woeful wind]

When you are integrating 1/ x*sqrt(5x-2) for example, why would you set u as the whole sqrt(5x-2) and not just the 5x-2 inside? I know one works and the other doesnt but for future questions what makes you want to set u as the whole thing including the sqrt? Because usually with substitution you set only the inside of the sqrt as u

[ornate condor]

well

u set the inside to u

to use chain rule

[woeful wind]

.close

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[left bronze]

i just need help with this

i want to know if it is possible

i need x

[vale lichen]

I think its possible just looks like torture

[left bronze]

yhea

[vale lichen]

First divide everything by 1/3?

Do u know how to do it?

[left bronze]

i don't know how

[vale lichen]

Well you gotta isolate x

So expand out all the terms

[left bronze]

ah yes

[vale lichen]

Can u show ur work and where ur at?

[left bronze]

k

ill get it

i dont know if it is good

[proper stag]

anyone know what I-2I-I-5I is?

[left bronze]

-72

@vale lichen

[lone heart]

@left bronze Has your question been resolved?

[lone heart]

@left bronze Has your question been resolved?

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[remote bone]

I don’t know how to approach this

[golden canyon]

pretty sure it helps that X can be written as (10^k - 1) / 9

for any k in Z

*N

$\frac{10^{k}-1}{9}$

[ocean seal]

Jelle

[golden canyon]

for example if k = 1 then X = 9 / 9 = 1

[remote bone]

Yep makes sense

[trim wagon]

i think you can just take 1,11,111

so p+q+r=1

hmm wait no

guess i misread

sry

[golden canyon]

$p\left(\frac{10^{k}-1}{9}\right)^{2}+q\left(\frac{10^{k}-1}{9}\right)+r=\frac{10^{l}-1}{9}$ and maybe multiply by 81 and do mod 10

[ocean seal]

Jelle

[remote bone]

Yeah ill give it a go, thanks

I just really didnt see how to start it

[golden canyon]

where was this problem from?

[lone heart]

@remote bone Has your question been resolved?

[lone heart]

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[smoky meadow]

how?

to prove it

[trim wagon]

use formula

,tex \trigangles

[ocean seal]

Deep.

[trim wagon]

the last two

[smoky meadow]

is this right?

oh it’s tetha

hahahaha lol

then i’m gonna combine like terms?