help-28

[silk flame]

Ok

[torn jolt]

do i cross multiply here

[hybrid geyser]

sryy but I don’t understand what ure doing here

[torn jolt]

no you move the 6x to the left

[hybrid geyser]

basically,, multiply x/3 by x and 9/x by 3

then ull get common denominator 3x

[torn jolt]

idk my teacher did this to solve a Rational Equation

he said find the LCD then multiply each fraction by it

to get to the trinomial

or whatever that is binomial

then to solve for x after that

thats the problem he did in class and i have to do these types of problems for homework

sorry i just wrote what my teacher had on the board

i wanted to know how to multiply the fractions

[silk flame]

Thats what everyone's been saying, I don't know any other way to solve than that

[torn jolt]

oh

thank u

how do u get rid of the 3x under the fraction at the second to last step

multiply both sides by 3x?

[silk flame]

Multiply

[torn jolt]

multiply 3x on both sides

yes

oh ok ty

this is clear to me thank u for helping

[silk flame]

Np

[torn jolt]

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[slow gulch]

Bros how do I answer parts ii and iii

[torn jolt]

what have you tried so far?

[slow gulch]

Bro no clue

Got 3 raised to -3q power

[sharp lagoon]

No, that's not right.

Do you have a table of the logarithm rules?

[slow gulch]

Why is it not right

[nocturne creek]

Its right

[slow gulch]

1/27 is 3 raised to -3 power

[nocturne creek]

He just hasn't simplified more yet

[slow gulch]

Yes

That’s where I’m stuck

[sharp lagoon]

Oh, I see. I was looking at the wrong part.

[slow gulch]

Anyone?

[sharp lagoon]

So, you have log₃(p) = q.

[slow gulch]

Uhuh

[sharp lagoon]

So, get rid of the logarithm.

[slow gulch]

Yes

But the questiob requires in terms of p

Damn

I see it bruh

Lmao

3q

3 raised to -p power

How about part iii

[sharp lagoon]

Well, you have log₃(p) = q. Take 3 to the power of each side.

You get p = 3^q.

[slow gulch]

Yes

I managed to get ii answer

[sharp lagoon]

Then, you have 3^(-3q).

[topaz valley]

this doesn't seem right

[sharp lagoon]

Yes, but the answer isn't 3⁻ᵖ.

[slow gulch]

3q is p

-3q is -p

[topaz valley]

have a read of Chai's explanation

[sharp lagoon]

Sorry?

[slow gulch]

BRUH

[topaz valley]

this is not right

[slow gulch]

I’m so done

Read wrongly soz

p = 3^q

[sharp lagoon]

Right, now separate 3^(-3q) into two powers of 3.

Then, you can replace one with p.

[slow gulch]

I make it into (3^q)^-3?

[sharp lagoon]

Yes, that's right.

[slow gulch]

Aight

Final answer is 1/p cubed

How about iii

Nvm i see it

p squared = 5p -6

Amiright

[sharp lagoon]

Right.

[slow gulch]

Thx a bunch bros

[sharp lagoon]

No problem.

[slow gulch]

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[late crown]

Can someone help me get an example for real life situations which involves arithmetic sequence?

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[little helm]

does $\int f(x), d(k - x)$ make any sense?

[glossy valve]

kinglacto

[sharp flame]

💀

I've never seen that in my life

[little helm]

hm ok

[torn jolt]

me neither

in indefinite integrals

[little helm]

what about definite?

[sharp flame]

Is that meant to be $\int f(x), dk - dx$

[torn jolt]

I have seen one case where the dx is written by something else in case of an definite integral I think

[little helm]

no

[glossy valve]

NEONPerseus

[sharp flame]

smh

(k - x) is the variable?

[little helm]

oh

[little helm]

yeah instead of small intervals of x, i.e dx, small intervals of k - x, i.e d(k - x)

hm ig it doesnt make sense yea thank you

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[modern echo]

this is awkward

[kind jay]

can u latex it

[modern echo]

hm

?

wats that?

[spice orchid]

thats an evil request

[kind jay]

true haha

[modern echo]

[spice orchid]

if all your working is correct (havent checked) then you are very close to a nice answer

if the second term in the product in your last line was m/n then we could add exponents

what can we do to the exponent to turn n/m into m/n

[modern echo]

like?

[spice orchid]

$a^b = \left(\frac{1}{a}\right)^?$

[glossy valve]

ΣAC

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[near lance]

Hello

[near lance]

Does anyone know what this would evaluate to?

[torn jolt]

do u have any work?

[atomic blade]

Use limit chain

[near lance]

Nope

I was thinking that it would evaluate to 0.

Through Limit Laws and whatnot.

[torn jolt]

well the inside poly approaches some number

move the limit inside the cos

[near lance]

Would that be 3pi/2?

[torn jolt]

yes

[atomic blade]

$\lim_{x\to\infty}\cos\left(\frac{3x^4+3x+1}{2x^4}π\right) \equiv \cos\left(\lim_{x\to\infty} \frac{3πx^4}{2x^4}\right)$$

[modern sentinel]

0?

[atomic blade]

Bruh

[glossy valve]

Umbraleviathan
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[torn jolt]

its jsut cos(3pi/2)

which is 0

[near lance]

Yeah, since cos of 3pi/2 is 0.

Then how did my professor get this?

[atomic blade]

Yeah

[modern sentinel]

it wouldve been 3/2

[near lance]

How?

[near lance]

My question is, where did he get that math from?

[atomic blade]

I mean I have it right here

Hold on

[near lance]

He got 3pi instead of 3pi/2 for the inside.

[atomic blade]

They're literally wrong

[modern sentinel]

(a+b+c)/d=a/d+b/d+c/d he used that

[torn jolt]

he messed up

[torn jolt]

he forgot a/d

[atomic blade]

I mean my work checks out

[modern sentinel]

and yeah it wouldve been 3/2

[torn jolt]

dont worry man professors are also human

[atomic blade]

Your teacher is a fool

Fire him

Take his salary

[near lance]

Ok

So it's just an error on his part then.

Thank you

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[quartz basin]

how would I go about doing this problem, I know that I need to divide everything by x, but I tried it a couple times and I still am not getting it right

[torn jolt]

well i would simplify the x^-5 first

[quartz basin]

so 1/x^5 right

[atomic blade]

Yeah

[quartz basin]

ok

[atomic blade]

And then compare the numerator to the denominator

Or get rid of low order terms

[quartz basin]

and how would I go about getting rid of them

dividing by x right

[atomic blade]

No you literally erase it

[torn jolt]

remember limit properties

[atomic blade]

One of those cases where you grab your eraser and get rid of the fucker

[quartz basin]

yeah so 6/infiniti is essentially 0

[torn jolt]

you can evaluate the limit at only 1/x^5 if you wanted

yes

[quaint pecan]

Yesh

[atomic blade]

$\lim_{x\to\infty} \frac{8\sqrt{x}+x^{-5}}{5x-6} \equiv \lim_{x\to\infty}\frac{8\sqrt{x}}{5x}$

[glossy valve]

Umbraleviathan

[quartz basin]

ok so now what is the square root of infiniti divided by infiniti

[atomic blade]

Well I mean

[quartz basin]

that kinda confuses me

[atomic blade]

Use power rules

[torn jolt]

bottom grows bigger than top

[atomic blade]

Sqrt(x) = x^(1/2)

[quaint pecan]

simplify it to 1/ sq root of infinity

[atomic blade]

But also yeah

Bottom grows bigger than the top

[quartz basin]

oh yeah

so 0

[atomic blade]

Ye

[torn jolt]

just looking at top and bottom growth for most limits works perfect

i would never rely on it tho!

[quartz basin]

ok sounds good I'll put 0 into mathlabs

yeah I don't want to do that all the time

still trying to learn this stuff you know

thanks for your help yall

[atomic blade]

Np

[quaint pecan]

✌️

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[earnest harness]

https://gyazo.com/94b35832d20d3a8e7e01fa1b1a8d83a4

[earnest harness]

really easily but i forgot 😦

[light sonnet]

https://youtube.com/watch?+&v=XsW8HJutIgM&feature=emb_title
See if this helps

[earnest harness]

does it show when there's multiplication added to it too?

[onyx glen]

work out the operations one by one just like you would if the expression didn't have any fractions

first multiply 4/9 * 1/3

then subtract 1/3

then add 4/9

one step at a time

[earnest harness]

i did but got 25/27 somehow

[hot herald]

show work

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[wet vortex]

what number should be written under the sign of the sentence instead of x so that the equality is correct?

idk how to do

[rare dock]

$\frac{\sqrt{75}+\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{75}}{\sqrt{3}}+\frac{\sqrt{3}}{\sqrt{3}}$

[glossy valve]

layla💜

[topaz valley]

"sign of the sentence"?

[wet vortex]

im using google translate

sorry

[topaz valley]

i see

if you had

$\sqrt x = b$

[glossy valve]

snowy

[topaz valley]

what would x be

[wet vortex]

how another 3 comes

[wet vortex]

can you explain

how another 3 comes

by this what you said?

[topaz valley]

uh

[topaz valley]

this is because

$\frac {a + b} c = \frac a c + \frac b c$

[glossy valve]

snowy

[wet vortex]

oh

bro u smart

xD

[topaz valley]

if you had

$\sqrt x = b$

what is x?

[glossy valve]

snowy

[wet vortex]

likee

um

sorry im stupid

[topaz valley]

$\sqrt x = 5$

[glossy valve]

snowy

[topaz valley]

what is x

[torn jolt]

x = 25

[wet vortex]

5

[topaz valley]

munt1e is right

$\sqrt {25} = 5$

[glossy valve]

snowy

[wet vortex]

ohh

but

like

[wet vortex]

from this answer is 6

and the right answer for this is 32

how?

could you explain why?

[hot herald]

where's 32 coming from

[wet vortex]

6?

[hot herald]

doesn't answer my question

[wet vortex]

uh

32 is answer from book

[hot herald]

are you sure the book is saying that?

[wet vortex]

yeah

you need to square it or..

[hot herald]

they're asking for the value of $x$ where
$$\sqrt{x} = \frac{\sqrt{75}+ \sqrt{3}}{\sqrt{3}} = 6$$

[glossy valve]

ℝamonov

[wet vortex]

yeah

[hot herald]

x won't be 32

[wet vortex]

so you think book has mistake in answers?

[torn jolt]

square it

[hot herald]

dunno, countless people have looked in the wrong section and/or misread what the book saying

[wet vortex]

but the reason?

[hot herald]

solve sqrt(x) = 6
for x

to find x

[torn jolt]

you can shift the square foot to lhs so basically i mean just square the middle expression

[hot herald]

if the book indeed says x=32, it is wrong

[torn jolt]

in order to find x

yes

[wet vortex]

alright, thank you guys for patience

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[torn jolt]

yes

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[toxic flint]

Ok, we have a function f : Z -> N, could x^2 be surjective? I know it wouldn't be if it was f : Z -> Z because it only maps to the positive integers. So, if it's to natural numbers, it should be surjective, no? or am I missing something?

[humble steppe]

Not really. Image of this function is the set of square number. Since not every integer is a square number, the image does not completely cover N. Hence your function is not surjective on N.

[toxic flint]

oh okay, yeah thats true..

thanks!

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[near lance]

Hello

[near lance]

Does anyone know how to do this?

[livid star]

what's the thing ur tryna achieve?

[near lance]

The first 10 terms

[livid star]

have you tried inserting for each n?

[near lance]

So let's say I have to try to find a2

What would I need to plug in to find it?

[cloud shore]

n=1

[livid star]

well you'd have to find an n such that a_(n+1) = a_(2)

[near lance]

Why is it n=1?

[cloud shore]

1+1=2

[near lance]

Ahhhhh

So if I'm trying to find a3, n =2?

[livid star]

yep

[near lance]

Wow

[livid star]

you got this

[near lance]

I can't believe this.

Lol

And what would I put for an?

Just what I go for the previous one?

[cloud shore]

yes a_n is a_n

[near lance]

Ok

Thank you

I'm assuming I'd have to do the same thing for this one, right?

[livid star]

yep, so if u want to find a_69420, then ud have to solve the mini problem in the bottom for n

so n + 2 = 69420, so n= 69418

thats the general logic for any question of this form

[near lance]

Wait

How'd you get 49418?

[livid star]

mistyped 6 with 4 mb

but you get it now right

[near lance]

Yeah

Wait

[near lance]

For this one

When I tried to find a_8, I got positive 1/64.

Isn't it supposed to be negative?

[livid star]

whats a7 for reference?

[near lance]

Nvm

I got it.

[keen holly]

@near lance I ike your name

[near lance]

Thanks

Sometimes I'm on a lose dosage though.

Lol

[keen holly]

Lol

[near lance]

Ok

So about this.

If I wanted to find a_3, what would I need to do?

@livid star

How would I set it up?

[livid star]

you tell me, what n would you need so that a(n+2) = a(3)

[near lance]

n = 1

[livid star]

now on the rhs, use that n = 1 and ull get an answer 😄

[near lance]

So what? a_3 = a_2 + a_1?

Ahhh

I get it.

So this basically just adds the last through.

[livid star]

ye

you got this

[near lance]

Ok, thank you

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[jovial raft]

I am to convert the signed binary 110100 to decimal.
My thinking is that the first "1" signals that the number is negative and then proceed to calculate the remaining bits to:
16+4 = -20
This appears to be incorrect, so what am I missing here? Should I include the value of the sign-bit as well? Giving me:
(-32)+16+4=-12

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[leaden anvil]

Is this inference valid?

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[leaden anvil]

<@&286206848099549185> 🥺

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@leaden anvil Has your question been resolved?

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@leaden anvil Has your question been resolved?

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@leaden anvil Has your question been resolved?

[wild sleet]

It'd saying the same thing twice. It's valid, I'm not sure what's inference.

[leaden anvil]

Thank you!

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[wraith lagoon]

Use the figure (the blue triangle) to geometrically determine the exact values ​​for
cos(π/4) og sin(π/4)

[wraith lagoon]

how do i do?

i know that a=1

because its a unitcircle

do i then have to find arg?

[torn jolt]

Yes so

Lets see

Do you know whats cos π/4?

[wraith lagoon]

isnt it x

or do i have to look at it as a radiant

[torn jolt]

No i mean, what is the value

[wraith lagoon]

nah i dont

[torn jolt]

Its basic trig...

Well

[wraith lagoon]

0,99

[torn jolt]

Cos π\4= √2/2

[wraith lagoon]

.......

[torn jolt]

You dont know this one?

[wraith lagoon]

no

[torn jolt]

Wait

Are you using degree?

[wraith lagoon]

yea

[torn jolt]

Use radian please

We dont really need degrees here lol

Actually, whats cos 45?

[wraith lagoon]

0,7

pi/4

[torn jolt]

Uhh

Dude

We dont use this

0.7

And 0.198394849933 or whatever

We need exact form

Use roots and fractions

This is math not engineering

[wraith lagoon]

(square root 2)/2

[torn jolt]

Good

Now

45 deg = π\4 rad

Got it?

[wraith lagoon]

yeah

[torn jolt]

Theyre the same thing

Now, what about the sin?

[wraith lagoon]

same thing

[torn jolt]

Okay so

We have graph of y=x, the intersection with y axis and axis gives us what kind of triangle?

[wraith lagoon]

complicated triangle

90* triangle

[wraith lagoon]

idk if it correct term in english

[torn jolt]

Its called a right triangle, yes

Okay so

Thats a unit circle right?

[wraith lagoon]

yes

[torn jolt]

Radius?

[wraith lagoon]

1

a=1

[torn jolt]

Now can you tell me whats the length of hypotenuse?

[wraith lagoon]

the hypotenuse

1

[torn jolt]

Now lets call the other two sides A and B

What do you notice about them?

Like, what are they to each other?

[wraith lagoon]

90* to eachother

[torn jolt]

I mean in terms of length

[wraith lagoon]

theyre the same?

[torn jolt]

Exactly

Can you find their lengths using the formula?

[wraith lagoon]

squareroot cos()^2+sin()^2?

[torn jolt]

Use the Pythagorean theorem

[wraith lagoon]

.

[torn jolt]

That is not the Pythagorean theorem is it?

[wraith lagoon]

its what i remember my teacher told us to use

otherwise i rememberede wrong

but a^2+b^2=c^2

[torn jolt]

Yes

That one

We said that a=b right?

[wraith lagoon]

yea

[torn jolt]

And the hypotenuse is 1

We can now solve it to find b

[wraith lagoon]

what is a again??

[torn jolt]

A²+B²=C²

C is the hypotenuse, a and b are opposite and adjacent

[wraith lagoon]

i just found the answer

its (squareroot of 2)/2

[torn jolt]

Okay good

[wraith lagoon]

but ty for the help

[torn jolt]

Okay

You can use cos= adjacent/hypotenuse to prove it

[full forum]

@wraith lagoon Has your question been resolved?

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[jaunty field]

i was studying answers from economic olympiad problems, i tried to understand this, i still dont get how p becomes 100p

[fast peak]

we pull the sum on the left apart and have $\sum_{i=1}^{100} 100i - \sum_{i=1}^{100} p$

[glossy valve]

Denascite

[fast peak]

the second term is just adding p+p+p+p+p... a hundred times

so just 100p

[jaunty field]

ohhh i get itt

[fallow reef]

yes

[jaunty field]

thanks for the help

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[full forum]

@nova osprey Has your question been resolved?

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@nova osprey Has your question been resolved?

[modern sentinel]

use similar triangles

it would be easier to tell where you're stuck if u can send ur working

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[torn jolt]

,rotate

[torn jolt]

,rotate

[torn jolt]

So in this task I should calculate the height of that tower. My result was 20.23m

is that correct?

<@&286206848099549185>

<@&286206848099549185>

[full forum]

@torn jolt Has your question been resolved?

[torn jolt]

<@&286206848099549185>

[quaint pecan]

!15m

[full forum]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[slate hemlock]

Only ping helpers once

It's correct though

[torn jolt]

it is??

[slate hemlock]

Yes

[torn jolt]

ok

thanksss very much

[slate hemlock]

yw

[torn jolt]

oh its you again andrea lol

what was it now? the fifth time?

[slate hemlock]

No idea, I don't remember who are all the people I help... I do remember I helped you a couple of times though

[torn jolt]

😄

[slate hemlock]

We already get a lot of pings everyday so hopefully you understand why we have that rule... Be patient and people will come to help eventually

[torn jolt]

I've got more solutions but I wont bother with you that

[torn jolt]

its ok

sometimes tho it takes hours till someone answers

[slate hemlock]

Yeah it's true, but now that school restarted for most people we get a lot more questions and there's not a lot of us

[torn jolt]

yeah, I understand

thanks for the help tho!

[slate hemlock]

If you want to check them yourself try to find another side with the given information (you can find the hypotenuse of the bugger right triangle with the sin rule, for example) and see whether everything checks out (you can either check the sides of the bigger right triangle with Pythagoras theorem or with sin(x)=o/h, in this case)

[torn jolt]

yeah but if I use pythorgoras

and get the hypotenuse

there is nothing to compare it with

[slate hemlock]

No, get the hypotenuse with sin rule

[torn jolt]

my value could still be gibberish and it would match up

[slate hemlock]

Then Pythagoras with hypotenuse and adjacent side to find opposite side

[torn jolt]

I cant, its a triangle with no 90 degrees

just noticed that

[slate hemlock]

This one is 90°

[torn jolt]

I know

but sometimes it isnt

[slate hemlock]

I was talking about this case specifically though

[torn jolt]

ah

[slate hemlock]

Of course if you have something else is not always possible to check it

[torn jolt]

how would I get the hypotenuse with sin if I dont have the value of the kathete

this one

[slate hemlock]

I'm talking about triangle ABC, you can find BC with sin rule

BC is the hypotenuse of BCD

[torn jolt]

um

[slate hemlock]

You already have AC so you can also find AD with cos(x)=adj/hyp

CB²-(AD+AB)²=CD²

[torn jolt]

where do I have AC?

I only calculated CD

[slate hemlock]

You found it before, it's 23.13

AC=23.13

Then you used it to find CD

[torn jolt]

oh

I see

[slate hemlock]

23.13sin(61)=CD

[torn jolt]

my brain is kinda dead right now, too much math

[slate hemlock]

Don't worry

[torn jolt]

ok

if I find AD I can use pythogaras

to check if its correct

and if it isn't a tringular with 90 degrees im basically fucked

[slate hemlock]

Yes, you can do that too

[slate hemlock]

Maybe you can do something with sin rule, but in general it's harder to check if you don't have right triangles

[torn jolt]

maybe split the tringular up

half half

[slate hemlock]

Yeah maybe

[torn jolt]

trinogmetry without 90 degrees is weird

well thanks again for helping me

a ton

[slate hemlock]

Np, you're welcome

[torn jolt]

I can send you my solution to the other problem if you have time

if you dont, no worries

[slate hemlock]

Rn I'm about to have dinner, if you send it rn I might be able to check it real quick though

[torn jolt]

ok

its gonna take like 2 mins

,rotate

[torn jolt]

so basically

I have to calculate the size of the bridge

[slate hemlock]

Did you already try to do something?

[torn jolt]

yes wait

[slate hemlock]

Ok

[torn jolt]

kinda blurry

then I calculated:

371.83 - 104.02 = 267.81 m

[slate hemlock]

Correct

[torn jolt]

THANK YOUUUU

better be on point for that dinner

❤️

thanks a lot

[slate hemlock]

yw

[torn jolt]

ok well

I wont disturb you no more

bon appetit

[slate hemlock]

Thanks, have a good day

[torn jolt]

you too!

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[modern sentinel]

is x! possible when

1. x is a decimal
2. x is a negative integer

[fallow reef]

ofc

[modern sentinel]

x! is factorial

[surreal roost]

you need the gamma function for negative integers

[fallow reef]

yes

gamma function

[modern sentinel]

how do u calculate factorial for decimals

[modern sentinel]

okay

[surreal roost]

you do a complex integral

[fallow reef]

like 1.5! = 3/2 *(1/2)*gamma(1/2)

[modern sentinel]

can u link any video on yt where i can learn about gamma function for factorials

[fallow reef]

https://youtu.be/SduCO-r_TOA

you know hindi ryt

this is good

[modern sentinel]

thx

[fallow reef]

https://youtu.be/c7_F4P71E2E

[modern sentinel]

are u also preparing for jee?

[fallow reef]

yes, but I am so low, I wouldn't even pass it

[modern sentinel]

which batch?

2023?

[fallow reef]

I told you right

[modern sentinel]

i forgor

[fallow reef]

I was Chochan, you asked my book publication

that infinite integration problem

[modern sentinel]

oohh that definate integral

[fallow reef]

it was me

[modern sentinel]

lol

i remember now

[fallow reef]

lol

ye

I changed my pfp

[modern sentinel]

lmao the ques whos ans was ab?

[fallow reef]

that's why maybe

[fallow reef]

yes

and 100 etc for other

we did many together

💀

[modern sentinel]

8 and -9

[modern sentinel]

lol

[fallow reef]

yea

today morining

also

log log x

[modern sentinel]

thx ill watch the video

[fallow reef]

range

[modern sentinel]

yes i remember

[fallow reef]

ok bye see ya

[modern sentinel]

bye

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[fringe finch]

I'm stuck on where to start with this question

[nimble whale]

Basically this question is wanting you to understand how transformations affect mean and standard deviation

like whenever you add a value c to every point in a set, the standard deviation does not change

but if u add a value c to every point in a set, the mean changes exactly by +c

and if u have a scaling factor bx, then the standard deviation & mean is also affected in the same fashion, i.e., it would become b*standard deviation

[fringe finch]

what is +c?

[nimble whale]

in this case, c is -20

so new mean would be 1.4 * 60.8 -20, and new Std would be 1.4*6.6

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@fringe finch Has your question been resolved?

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[prime furnace]

This question is on discrete mathematics, or logic math.

[prime furnace]

So because the first line in the red box says -> not p or r

if the left proposition evaluates to not p, the whole compound proposition is false.

so it must evaluation to r to make the original question true?

looking it up, this may be called distribution of implication for those looking for this in the future

.solved

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[quartz tartan]

so i know its 4

and i know when dividing

when subtract exponents

but i cant figure out how to write those exponents to subtract them

is it 6-7? that would equal 1

is it 6 - (-7) ?

the would equal 13

[scenic wren]

6-(-7)

so 13

[quartz tartan]

ohhhh

[scenic wren]

to check, you can also do the following

$\frac{x^6}{x^-7}=x^6 x^7=x^{6+7}=x^{13}$

[glossy valve]

~Martin

[quartz tartan]

how does it turn into a positive here?

[scenic wren]

$x^y=\frac{1}{x^{-y}}$

[glossy valve]

~Martin

[scenic wren]

or the other way around

[quartz tartan]

ohhhh

thanks so much

[scenic wren]

$x^{-y}=\frac{1}{x^y}$

[glossy valve]

~Martin

[quartz tartan]

what type of math is this called?

if i were to look up videos on it on youtube

like this specifically

[scenic wren]

this specifically is exponent rules

[quartz tartan]

perfect

thanks so much bro

i appriciate u both

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[silk tapir]

We did some others kind of like this but not with linear pairs, can someone point me in the right direction? Don't know where to begin

[silk tapir]

on number 57

[full forum]

@silk tapir Has your question been resolved?

[spiral grail]

Linear pair angles add up to 180 solve for x and h @silk tapir

[silk tapir]

Yeah

[spiral grail]

U got it?

[silk tapir]

No

[spiral grail]

What u confused about

[silk tapir]

how do I solve for the variables?

[spiral grail]

So for x

U would set

12x-8 + 6x + 8 = 180

18x + 0 = 180

18x/18 = 180/18

X = 10

[silk tapir]

18x divided by 18?

[spiral grail]

Yeah

To get rid of the 18 and only have X

[silk tapir]

So the angles on the bottom plus one on the top still equals 180?

[spiral grail]

Wdym

[silk tapir]

Does linear mean that any two will equal 180?

Of the four angles

[spiral grail]

Linear pairs add up to = 180

1 sec lemme find something

So vertical are diagonal from each other and are congruent

So 1 and 7 are equal and they are vertical pairs

But 5 and 7 add up to 180

[silk tapir]

Oh I see

it's just different orientation

[spiral grail]

Yeah

Got it?

[silk tapir]

So if I solved for x

I could put one of the equations for y equal to 180 after subtracting the one across from it?

Say x was 2

24-8

It's 16

so I could theoretically

take 2y-12=180-16?

And get y?

[spiral grail]

Yes

That works

U can also plug x in for the other angle

[silk tapir]

And I could also solve for y the same way I did for x

[spiral grail]

Yes

[silk tapir]

Ok I think that solves it then, thanks

[spiral grail]

Yw good luck with the rest

[silk tapir]

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[orchid loom]

How do I integrate this to find the original function then find C and plug it in to the original function

I know how to find C and do the rest

(please ping me)

[nova island]

So to integrate, you want the variables to match on both sides right?

@orchid loom

[orchid loom]

Nvm I solved it

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[orchid loom]

thanks tho

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[mystic rover]

how do i solve this integral analytically (preferably a closed form solution for the positive real numbers):

[mystic rover]

i was thinking of using numerical approximation methods; but, wanted clarification if this was analytically derivable

<@&286206848099549185>

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@mystic rover Has your question been resolved?

[mystic rover]

<@&286206848099549185>

[torn jolt]

Have you tried anything yet that isnt just "possible routes"?

((holy shit i just checked a "manual" solution to this, involves polylogarithms, partial frac decomp, quite a lot of subs, a bit of hyperbolic functions, plus some by-parts

This is a really long problem to do by hand which would end up with a complex solution))

just sayin^^

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[torn jolt]

in part a to find the area of a trapezium do i just have to use the formula and plug in values of height and sum of parallel lines which in this case is 2 and 6

[full forum]

Please don't occupy multiple help channels.

[torn jolt]

will it become 1/2 * 3 (2 + 6)

as they said in the question the area of a trapezium so it is from a b c and d

does that make sense?

[deft zodiac]

seems right yea

[torn jolt]

okay so i wanted to ask that if i have to find the total surface area of this shape, is it right to say that there are two rectangles, two trapeziums and two squares?

so ill individually find the area and add them altogether to find the total surface areas

i feel like there will be two rhombus or parallelograms but not a square

[deft zodiac]

i dont see squares.. those are rectangles lol

[torn jolt]

but did you see the bigger one

there are two rectangles and two trapeziums

this red one

[deft zodiac]

i mean

thats a rectangle too

hm 4 rectangles i guess

[torn jolt]

this seemed like a square

the total surface area is 344

and im getting is 304

[deft zodiac]

what is your working?

[torn jolt]

i took out the area of the first rectangle that was 40 so added it became 80, for trapezium the area was 12 so added 12 + 12 = 24 and for the bigger rectangle it was 100 so 100 + 100 that gave 200 so i added it 40 + 40 + 100 + 100 + 12 + 12

that gave 304

[deft zodiac]

um

for one

addition u should use +

not *

[torn jolt]

i might have made an error somewhere

oh no that’s my bad

i got confused a bit

ill edit it

[deft zodiac]

sorry, theres only 1 rectangle with area of 100

theres a faster way to do it which is to get 2* the area of a trapezium +

perimeter of trapizium*height

[torn jolt]

oh

[deft zodiac]

as in this case its kinda just a trapezium stretched

if u do the working ull notice a lot of 20 * length of other side

[torn jolt]

so if the area of a trapezium was twelve can you just multiply it with two

[deft zodiac]

i mean as this case its just the trapezium strectched yea

[torn jolt]

i have been thinking there are two big rectangles

but the bigger one is merely one

[deft zodiac]

i dont know the term but i thnk theres a term for stuff where its just 1 shape stretched into 3d

[deft zodiac]

i dont quite know what u are saying

[torn jolt]

okay so for total surface area i have to add all the areas

[deft zodiac]

yea that works

[torn jolt]

the ones i got were 40 + 40 + 12 + 12 + 100

that gives 204

[deft zodiac]

um there are 6 surfaces and only one with 40

[deft zodiac]

thats why i said to just do this

that will be the surface area of the other 4 surfaces

[torn jolt]

im not sure unable to understand

[deft zodiac]

so like

[torn jolt]

i have been using that idea to find the total surface areas so iwas trying to apply the same thing there

if it’s possible can you explain it with my diagram

[deft zodiac]

this is the surface area of the 2 trapeziums

[torn jolt]

so there are two trapeziums

[deft zodiac]

this is the perimeter of the trapezium

[torn jolt]

i got the area of the first one part a that was 12

so do you have to add all the sides of a trapezium?

basically the outer sides to find the perimeter and then add them in the areas i guess

[deft zodiac]

these are the 4 surfaces

idk i drew em tgt so it migth be hard to see

[torn jolt]

but isn’t it to find the total surface area you don’t need the perimeter

[deft zodiac]

i used the diff colors tho

yea i dont

[torn jolt]

oh

[deft zodiac]

i just meant for each of the 4 surfaces

[torn jolt]

two rectangles

[deft zodiac]

the length of 1 side will be 20

the other length will be

2 3 5 and 6

so instead of doing

2 * 20 + 3 * 20 + 5 * 20 + 6 * 20

u can do 20 * (2+3+5+6)

makes it less error prone as well

[torn jolt]

i really liked your method

[deft zodiac]

btw did u get the 4 surfaces? (excluding trapeziums)

[deft zodiac]

the using perimeter one?

[torn jolt]

yes ive understood it but like im still trying to make another surface on my diagram

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[stiff oak]

How do you find the orthocenter of a triangle when given all 3 vertices?

[stiff oak]

Tried searching about it but peoples explaination didn't make sense

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[gilded light]

Hi what is the formula for this function？

[gilded light]

should be polynomials…

it goes to infinity when x tends to infinity

[robust slate]

Ignore what I just sent, didn't account for end behavior.

So there's double roots at -1, 0 and 1

Meaning x², (x-1)² and (x+1)² are factors

Meaning y=ax²(x+1)²(x-1)² for some positive a

[gilded light]

ah ha

thanks

like x^6-2x^4+x^2

[robust slate]

,w expand x^2 (x^2 -1)^2

[glossy valve]

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Requested by messy circle creation#1465

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@gilded light Has your question been resolved?

[gilded light]

yez

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[unreal bloom]

I have no idea how to get the answer

[hidden steppe]

Heh

I don't want to spoil it for you because it's a fun question

Did you try sketching it out with a piece of paper?

[unreal bloom]

Idk how to start it

[hidden steppe]

Sketch it first, trust me

[unreal bloom]

okay i did

[proper galleon]

What did you get?

[unreal bloom]

I only drew it, idk what Im supposed to do after

[hidden steppe]

Well

We want to know the ratio between the blue area and the total area

[proper galleon]

Do you have 9 squares

?*

[unreal bloom]

squares? no?

[proper galleon]

Maybe show what you got

[unreal bloom]

I just drew the same image

[proper galleon]

Try to create squares

Who are equal

[unreal bloom]

ooh okay, yes i got 9

[proper galleon]

How many squares are covered in blie

Blue*

[unreal bloom]

4? or do I turn that into a fraction?

[proper galleon]

Do you have this?

[unreal bloom]

yes

[proper galleon]

What fraction is colored

You have indeed 4 with color. But they are only colored for a part

[unreal bloom]

so 1/4? im not sure

[proper galleon]

No

How many squares can you form with the blue parts

[unreal bloom]

2?

[proper galleon]

Yes

So what fraction is colored

[unreal bloom]

1/2 ?

[proper galleon]

You have 9 squares

And 2 are blue

[unreal bloom]

So 2/9?

Do I multiply 2/9 x 100?

[proper galleon]

Yes

[unreal bloom]

Thank you so much for your help & patience, math is not my best subject

.close

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[stiff oak]

Anybody know how to find the orthocenter of a triangle when given the three vertices

[stiff oak]

Searched it up but still a bit confused

[prisma rampart]

I knew but I kinda forgot I will try to find a video if u want

I think its not that hard from what I can remember

[stiff oak]

please

[prisma rampart]

Do you need someone to talk when they explain in video so you can understand or I can search not english types?

[stiff oak]

yeah i dont need them to talk

[prisma rampart]

Cause I think I have some nice tutorials in my language

[prisma rampart]

Nice I will search and come back to you

https://youtu.be/vPncYFCYIg8

Start watching at 3rd minute

Idk if this will help cause she also explains and you don't know the language but yeah try it

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@stiff oak Has your question been resolved?

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[swift fulcrum]

?

[atomic blade]

Those are certainly numbers

[uncut breach]

I took architecture because I liked drawing pretty buildings

Not for the scary math problems;-;

Lol

[swift fulcrum]

Yoooo

When did you become helper

Congratsss

[uncut breach]

I'm not sure where to start, do I distribute the exponents?

[swift fulcrum]

Yes

[uncut breach]

I got 19517.76x^20y^1.68 but it was incorrect

The x^20 was the only correct