help-0

[ocean seal]

Simplex

[tacit arch]

Induction

[astral solstice]

Yea

I get stuck at 2n^3

[pale kestrel]

suppose its true

for n (lazy)

i think the n>=10

bit is a hint

[pale kestrel]

for some reason there's something we can't do

unless n >=10

[astral solstice]

I am stuck

[pale kestrel]

$$2^k>k^3$$

[ocean seal]

Shuri2060

[pale kestrel]

$$2^{k+1}>2k^3$$

[ocean seal]

Shuri2060

[pale kestrel]

You want to compare 2k^3 and (k+1)^3 🤔

[glass lichen]

$n^3\geq 6n^2$ when $n\geq 10$

[ocean seal]

Mosh

[astral solstice]

Is this valid?

[hasty elk]

you need to show why that last step is true

[glass lichen]

you made no justification for that step, so no

[pale kestrel]

Let n = 1

[glass lichen]

n=1 is irrelevant

it's for n>=10

[hasty elk]

[astral solstice]

so how do I do that

[glass lichen]

Use the hint I gave.

[astral solstice]

ok

[hasty elk]

maybe to start, write that last step as an inequality on its own and see what you actually need to prove

[pale kestrel]

My point is, it's not obvious why that argument works for n >= 10. Let n = 1, and clearly the argument fails. Indeed - no justification.

[glass lichen]

Yeah but we don't care that it doesn't hold for n=1.

the only issue is no justification, not that it's a false statement

[lone heart]

@astral solstice Has your question been resolved?

[astral solstice]

Is this justification enough?

[pale kestrel]

Scrub this out

otherwise your proof looks backwards

Or wait

maybe I would write that entire double line

the other way round

[astral solstice]

okay

but otherwise it would hold?

[pale kestrel]

looks ok I think

[astral solstice]

.close

[lone heart]

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[bleak latch]

number 42

c(t) = (2cos t, 2sin t)

but how to satisfy condition

[pale kestrel]

shift t?

angle shift?

[ebon condor]

Genius

[bleak latch]

so c(t) = (2cos (t+pi/3), 2sin (t+pi/3))

??

is that riight

[hasty elk]

try subbing in t = 0 and check

[bleak latch]

.close

[lone heart]

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[azure cape]

uhh can I find someone to explain to me a certain topic? I have an exam tmrw and i need to understand a certain topic in statistics

[quartz rapids]

what topic?

[azure cape]

its called hypothesis testing

[quartz rapids]

in stat?

[azure cape]

yessir

[quartz rapids]

ah, I haven't taken stat yet so I can't help you there, im sure someone else here can though

[azure cape]

I hope so

[wary stream]

You can probably look up videos or resources on this

[azure cape]

I did and I got a bit too confused

but ill give it another try

[lone heart]

@azure cape Has your question been resolved?

[lone heart]

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[floral quail]

Cant seem to find what I've fond wrong here

Excessive double integration?

[pale kestrel]

i think partial fractions was the way?

kinda lost whats going on here

you could plug in each line to wolfram and check

oh nvm nvm no partial fractions.

[floral quail]

Yeah couldn't really see anything with Partial fracs

Wait I'll number it out rq

[pale kestrel]

wait you did integration by parts?

[floral quail]

Yeah

[pale kestrel]

You can take this and divide the numerator term by term

[floral quail]

It's on the right

[pale kestrel]

then reverse power rule

[floral quail]

Wait wdym

Isn't it by parts when it's 2 brackets multiplied?

[pale kestrel]

Well you CAN do that

but there was no need.

That aside I don't see how u did parts

[floral quail]

So I'm missing some really simple integration rule here?

uh

[pale kestrel]

i mean i see u did parts

but its kinda hard to follow

[floral quail]

oh ic

[pale kestrel]

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

[ocean seal]

Shuri2060

[floral quail]

1s I'll write it out

Not quite sure how I'd integrate this though

sorry

[pale kestrel]

you have

a constant

times

a power of u

write each term in terms of u^{some power}

[tight locust]

use linearity

[pale kestrel]

And integrate term by term

[tight locust]

(linearity basically means that an operation "distributes" over addition or subtraction)

[pale kestrel]

AH I've found it

This disappeared.

$$\frac{u-1}{2u^3}=\frac{u}{2u^3}-\frac{1}{2u^3}=\frac12u^{-2}-\frac12u^{-3}$$

[ocean seal]

Shuri2060

[pale kestrel]

Anyways, like this

[floral quail]

ahhhh no wonder

silly me

[floral quail]

Would this be a correct way of going through it?

[pale kestrel]

The faster way

much faster lol

[floral quail]

yeah haha lol

jus

just running the numbers rq

[pale kestrel]

but the u sub was good

[floral quail]

Alright got the correct answer both ways

Tysm @pale kestrel!! you're a huge lifesaver

enjoy your day

.close

[lone heart]

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[tiny minnow]

It is known that a function $f(x) =x^4+ax^3+bx^2+cx+d$
If f(100) = 102 , f(101) = 103 , f(102) = 104 , f(103) = 106
then determine the value of f(104).

[ocean seal]

IVMCs

[tight locust]

polynomial remainder theorem

[lone heart]

@tiny minnow Has your question been resolved?

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[tiny minnow]

?

.reopen

[lone heart]

✅

[lone heart]

@tiny minnow Has your question been resolved?

[lone heart]

@tiny minnow Has your question been resolved?

[lone heart]

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[sharp widget]

How do I solve this

[ebon condor]

Do you know what domain and range is

[sharp widget]

Yes kind of

[ebon condor]

Okay what is it

[sharp widget]

domain is x value range is y

maybe possible outputs?

[ebon condor]

So yeah, it’s the set of possible X and y values

So the question is really asking what values of X and y are included

[sharp widget]

from the 2 dots?

[ebon condor]

Well in this case yes

But not necessarily between two dots

[sharp widget]

-4,-3 5,5

[ebon condor]

That’s not correct

So you need to look at the graph one at a time

The domain is always more simple than the range

[sharp widget]

So how can I find the domain first

[ebon condor]

So this is a graph of a function

You find the points where X is defined

In this case, it’s all continuous so it’s one big section

But anywhere there’s a line or a dot is part of the domain

[sharp widget]

So what points the highest and the lowest point?

[ebon condor]

In terms of X, yes

[sharp widget]

like 4 terms there would be than?

[ebon condor]

Well there’s two problems with the coordinate pairs you gave

The first is that they’re wrong

And the second is that it doesn’t consider the open circle

[sharp widget]

[-4,-3] (5,5)

[ebon condor]

What notation is that

[sharp widget]

Interval

[ebon condor]

Well (5,5) doesn’t actually exist in interval notation

You probably mean [-4,5) [-3,5)?

For domain and range respectively?

[sharp widget]

That's hard to understand how did you get those two points

[ebon condor]

So if you look at the range, there’s a point lower than the starting point

They’re not points

They’re intervals

[pale kestrel]

you're mistaking

points and intervals

[sharp widget]

I'm sorry I'm slow

[pale kestrel]

(x, y) = (-4, -3) and (5, 5) are points.

[sharp widget]

How did you find intervals

[pale kestrel]

[-4, -3] represents the interval from -4 to -3. This is a set.

don't confuse notation

[sharp widget]

Brain overload, I don't understand how to find the interval

[pale kestrel]

One thing at a time

Domain: All possible inputs

All possible x-values you can input to the function

Tell me in words what x we can put in

@sharp widget Can we put in x = -6

[sharp widget]

No I don't think so

[pale kestrel]

there's no function at x = -6

you cannot.

Can we put in x = -2 ?

[sharp widget]

Yes I think so

[pale kestrel]

x = -2 makes y = 3

Can we put in x = 5 ?

[sharp widget]

Yes

[pale kestrel]

no.

[sharp widget]

Oh

[pale kestrel]

Empty circle means it is not on the graph

[sharp widget]

Than wheres the cutoff at the bottom point at -5?

Or the axis

Idk

[pale kestrel]

what?

[sharp widget]

Don't listen to me

[pale kestrel]

x = 5

this is not on the graph

because it is an empty circle

that's how graph notation works.

x = 4.99, can we put that in?

[sharp widget]

no?

[pale kestrel]

yes.

[sharp widget]

Holy how can i not understand

[pale kestrel]

Everything JUST before 5

is fine

[sharp widget]

Ohhh

[pale kestrel]

The empty circle means JUST 5 is excluded

[sharp widget]

THE Circle?

OH

[pale kestrel]

x = 4.9999999 is good

ok?

[sharp widget]

Ok

[pale kestrel]

ok, so finally x= -4?

[sharp widget]

Yes?

[pale kestrel]

Colored in circle, so it IS on the graph.

Ok, so now tell me from which x to which x can we input values

[sharp widget]

-4, to 4.999

[pale kestrel]

no

[woven spade]

just think of it as an empty circle having no mass so nothing is on that point

[pale kestrel]

yes and no

I can also put in 4.99999999999999999

[woven spade]

while a filled in circle has mass so it's on the point

[pale kestrel]

The way you say this is

[woven spade]

that's the way i think of it

[pale kestrel]

$-4 \leq x < 5$

[ocean seal]

Shuri2060

[pale kestrel]

Does this make sense?

[woven spade]

that's why we use curved brackets tango

[-4, 5)

[pale kestrel]

x can be equal to 4. But it cannot be equal to 5

[woven spade]

it can get close

but not reach 5

[sharp widget]

You're saying this is a domain?

[woven spade]

yeah

[sharp widget]

-4,-3 5,5

I put this first

Originally

[pale kestrel]

???

no.

[sharp widget]

So remove the Y

[pale kestrel]

That's not the answer

[woven spade]

me or tango

[pale kestrel]

The domain ONLY involves x-values

[sharp widget]

Exactly

Thats what Im saying

Not the Y

but the second number in each pair

[woven spade]

range is y value

[pale kestrel]

This is the domain [-4, 5)

[sharp widget]

so -4, 5

[woven spade]

domain is x

[pale kestrel]

square bracket -4

curved bracket 5

[woven spade]

no, [-4, 5)

[sharp widget]

Because closed circle

[pale kestrel]

Do you understand?

[woven spade]

the brackets matter

[sharp widget]

Open circle

Yes okay domain understood

[woven spade]

ye

[pale kestrel]

Range.

All possible y outputs

[sharp widget]

Soo -3, 5

[pale kestrel]

Is y = 0 a possible output?

[pale kestrel]

no. wrong.

[sharp widget]

Okay

[sharp widget]

Yes?

[pale kestrel]

To check y = 0 is a possible output

I draw the horizontal line

for y = 0

and see if it hits the graph

Yes, it hits it.

[sharp widget]

Okay

[pale kestrel]

Can you see why -3 to 5

is wrong.

[sharp widget]

Why wouldn't if you take it down to -3 it would cross over the closed circle

Or are you talking like -5

If it crosses there

[pale kestrel]

y = -4

Will this hit the graph?

[sharp widget]

Yes

[pale kestrel]

Yes, so y = -4

IS included in the range.

So what should be the full range?

[sharp widget]

Why not y = -5

[pale kestrel]

yes, so what do you think the range is?

[sharp widget]

-5, 2 ?

[pale kestrel]

no.

[woven spade]

brackets

don't forget brackets

they aren't decorational

[pale kestrel]

we can check those after

first we need to get the right range

y = 3, do we cross the graph @sharp widget ?

[sharp widget]

it crosses over

yes

[woven spade]

look man

[pale kestrel]

Yes, so -5 to 2

is not the answer.

[woven spade]

just find the lowest y value on the graph

and the highest

that's your range

[sharp widget]

the 2 dots are X the points like high and low are Y

if theres one dot than there's an infinity?

[pale kestrel]

ok look

[sharp widget]

than why did you say y = -4

[pale kestrel]

I didn't.

I ASKED you

if -4 is in the range

[woven spade]

bro

[sharp widget]

Oh I get you

Okay

[pale kestrel]

because your previous range didnt include it

[pale kestrel]

Ok, take this graph

[woven spade]

lowest y to highest y

[pale kestrel]

Man can you not

???????

[woven spade]

this doesn't count as giving out answers does it?

[pale kestrel]

I'm literally getting there explaining

[sharp widget]

I'm listening to you continue

[woven spade]

ok bye

good luck

[pale kestrel]

You take this graph

and imagine a horizontal line

ok?

[sharp widget]

Ok

[pale kestrel]

This line is going to be our 'scanner'

We move this line up and down

vertically

ok?

[sharp widget]

Ok

[pale kestrel]

Just imagine moving a single line up and down

Now, whenever the line hits the graph

That means that y value is in the range

We need all of the possible y-values that are in the range

That means you need to think of the lowest and highest possible lines

which hit the graph

[sharp widget]

What tool do you use to color

[pale kestrel]

ShareX

[sharp widget]

okay one second

[pale kestrel]

just use paint

[sharp widget]

highest and lowest

[pale kestrel]

its not

you can go higher

[sharp widget]

how so

it's not 3?

y = 3

[pale kestrel]

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

Look, this is what you just gave me

yes?

[sharp widget]

Yes

[pale kestrel]

Can you see that its not the highest

[sharp widget]

But is y=3 the highest

[pale kestrel]

There are bits of the graph you missed on the right side

it isn't.

[sharp widget]

Okay so on the side of the open circle?

[pale kestrel]

What about this stuff here?

You can't forget about that

y = 4 hits the graph, for example

You can go higher for sure.

[sharp widget]

5

[pale kestrel]

right

[sharp widget]

X you said close circle means nothing is there

[pale kestrel]

Yes that's fine

[sharp widget]

but Y you're saying its fine

[pale kestrel]

but the point is

no its not

But step one

Draw TWO horizontal lines

So that the entire graph is sandwitched between them

like this

[sharp widget]

Okay

[pale kestrel]

So we have -5 to 5

[sharp widget]

Correct

[pale kestrel]

THEN decide if we include the end points

So which do we need to include?

[sharp widget]

5

[pale kestrel]

no.

[sharp widget]

the end point for 5

[pale kestrel]

x = 5, y = 5

[sharp widget]

I'm sorry, I'm not trying to be difficult

[pale kestrel]

isn't in the graph

Remember, the empty circle.

So you don't include 5.

I have to draw that line at 5

but I don't actually include it in my range.

y < 5.

Do we include -5?

[sharp widget]

yes

[pale kestrel]

$-5\leq y < 5$

[ocean seal]

Shuri2060

[pale kestrel]

Right, so this is one way of writing the range.

You recognise this notation?

[sharp widget]

Yes inequality

[pale kestrel]

ok

Then you can write the range using interval notation

[sharp widget]

Okay I'm going to rewrite final answer

[pale kestrel]

Oh and your question says you can use either notation

[sharp widget]

Yes

[pale kestrel]

I recommend the inequality notation

It is less confusing

[sharp widget]

Okay so how would you write it ineuqality

the Domain

[ocean seal]

Shuri2060

Shuri2060

[sharp widget]

why with range do you cut off the whole left side

[pale kestrel]

I didn't

[sharp widget]

because its not highest to lowest?

[pale kestrel]

The entire graph is still between my 2 lines

It is still boxed in

[sharp widget]

So you're saying it's -5<=y<5 because it's the highest to lowest interval

[pale kestrel]

yes.

[sharp widget]

That makes a lot more sense

[pale kestrel]

For the Domain

You could also use the same thing

and draw vertical lines

Again, we box the graph in

[sharp widget]

So it would the -4 and 5 because its the widest

I get you I'm going to use the lines

[pale kestrel]

i think close this for now

[sharp widget]

ok

.close

[lone heart]

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[dawn loom]

Can someone please help me I've been at my computer screen for hours

[tight flax]

whats up

[covert agate]

just post it lol

[dawn loom]

Let me screen shot bruh

[buoyant kayak]

• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.

[dawn loom]

I need more than this though

This is just the one I'm on right now

They won't explain how to do it

[covert agate]

ok

do you see how some buildings have blueprints?

they’re apparently not drawn to scale

like the paper is only so big

and we can’t draw 1 km lines

so we use scaling instead

yea?

[dawn loom]

I mean bri that's cool and all but I just needa find how to solve the answer

They use units of length in the actual math

[covert agate]

so here we specify the scale

(length on paper) to (actual length)

[dawn loom]

Yeah

[covert agate]

every 2 millimetre on paper is 1 metre actual length

do you know what this means?

[dawn loom]

So 2:1?

[covert agate]

uhh no

1 metre = 1000 millimetres

lol

so if we wanna represent a 1000 millimetre line irl

[dawn loom]

I just need the answerssssss 😭

[covert agate]

we draw a 2 millimetre line

yea?

[dawn loom]

Alright

[covert agate]

so here, how do we represent a 4 metre line on paper?

[dawn loom]

I got the answer

Hold on

Ima get to a hard one

Ok here we go

[covert agate]

are you good with converting inch, yard and all?

[dawn loom]

Yeah I already get that

It's just the simplifying

[covert agate]

4 yard = 4 • 36 = 144 inches right?

[dawn loom]

My brain is fried as hell right now I'm just tryna follow

Been on This for 10 hours

[covert agate]

so 9 inch on paper = 144 inch irl

[dawn loom]

Ok

[covert agate]

so 1 inch on paper = 16 inch irl

here we’re figuring out 1 : ??? = paper : irl

(this is the typical way you write scales)

[dawn loom]

Yeah

[covert agate]

i believe you can do the rest

[dawn loom]

Bro I need helping simply find though

It's not conversions it's simplification

[covert agate]

you’re representing scale factors with a ratio

i’ve given you all but the final step lol

you should arrive at the answer if you get what i’ve been sayinf

[hasty elk]

it feels like you're expecting us to just give you the answer - we won't

if you need help simplifying, post what you have difficulty simplifying and we'll guide you on how to simplify

[dawn loom]

I don't expect the answer I just want to know how to simplify it even if you gave a whole different example and simplified it I would've been fine

But more power too you I just came to the wrong place

[covert agate]

i’ve told you how to

lol

[hasty elk]

and if you're still stuck, tell us exactly where you're stuck, and give details, such as the working you have

that's how these help channels work

[covert agate]

(i think he left the server)

[hasty elk]

LOL

[bright hedge]

uh

is that gonna break the bot?

[hasty elk]

didn't we have cases where people came for answers and left when they didn't get them

in the worst case a mod can close the channel

[lone heart]

@dawn loom Has your question been resolved?

[covert agate]

.close

can’t even close

lol

[hasty elk]

we can just wait for timeout

[lone heart]

Channel closed

Closed due to timeout

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[lone heart]

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[strong wedge]

whats the local minima in this graph?

is there more than one point

[covert agate]

alright

there are 3 segments here right
you consider them one by one

do you know the definition of a local minimum point?

[strong wedge]

local minimum point

its the low points in the graph but not the lowest

[covert agate]

do you know the rigorous definition?

with quantifiers?

[strong wedge]

not rlly

im only been taught about graph based questions on this

so visually mainly

[covert agate]

f(x) is a local minimum iff ∃ h > 0 such that ∄ c ∈ (x - h, x) U (x, x + h) such that f(c) ≤ f(x)

do you understand this soup?

[strong wedge]

what is ∃

[covert agate]

‘there exist’

[strong wedge]

idk ∄ c ∈

[covert agate]

like ∃ man ∈ humans s.t. man = your dad

[covert agate]

c is a variable

[covert agate]

this means ‘there exists a man in all humans, such that the man is your dad’

if you don’t understand this don’t worry

[strong wedge]

i kinda undestand now

[covert agate]

basically, if there’s one single number h we find

such that f(x) is smallest in (x - h, x) U (x, x + h)

then f(x) is a local minimum

semantically, f(x) ≤ f(c) for every c near x

so for constant functions, every point is simultaneously minimum and maximum lol

[covert agate]

because we use this definition

[lone heart]

@strong wedge Has your question been resolved?

[lone heart]

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[sly mantle]

this is very unfriendly language

[sly mantle]

.close

[lone heart]

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[sly mantle]

one can (and should) talk about local extrema w/o quantifier soup

[covert agate]

i added a semantic version lol

[sly mantle]

yeah use that language right off the bat (unless theres a question that specifically forces use of quantifiers)

[lone heart]

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[wary dome]

howw do you division with numbers that dont match up i was doing a oroblem and it said 24 divided by 16 and i dont understand how to do this i was not paying attention in class

[lone heart]

@wary dome Has your question been resolved?

[little drum]

Hmm.. the long division method.

[lone heart]

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[rapid gate]

can someone tell me how i can simplify sqrt of 80

[rapid gate]

i got 2 sqrt 20 but then there is a simpler version which is 4 sqrt 5

<@&286206848099549185>

[alpine sable]

√(80) = √(2*2*2*2*5) = 2*2√(5)

[rapid gate]

hm?

[alpine sable]

You can write √20 as √(2*2*5) and now take a 2 out of sqrt.

[rapid gate]

?

wait

[alpine sable]

Hmm check now

[rapid gate]

huh

if it was

sqrt 20 was sqrt 225

then u can do

4*sqrt20

?

which is incorrect

oh wait

prime factorisatio

wait

like this?

$$\sqrt{80}=2^{4}\cdot 5$$
$$\sqrt{16}\times\sqrt{5}$$
$$=4\sqrt{5}$$

[wary stream]

You forgot a closing set of $$

[rapid gate]

oops thanks

[ocean seal]

Fragzz

[rapid gate]

@alpine sable like this?

finding a perfect square in the number 1st?

how would i simplify something like this then?

[wary stream]

Same process

Find the largest square number that you can factor out

[rapid gate]

from which?

sqrt 18?

or 2

bc 2 is sqrt 4 i know that already

[wary stream]

You can't factor the 2

[rapid gate]

so i do the 18?

oh

wait

dont tell me anything

let me try this

hold on

[wary stream]

It's not under the sqrt root

[rapid gate]

ok

is it

like this

given that $\sqrt{qy}=\sqrt{q}\cdot \sqrt{y}$

[ocean seal]

Fragzz

[wary stream]

Yes that's true

[rapid gate]

yeah

o

k

and then

u do

$$2\sqrt{9\times 2}$$
$$=2\sqrt{9}\times\sqrt{2}$$
$$=2\times 3\times \sqrt{2}$$
$$=6\times\sqrt{2}$$
$$=6\sqrt{2}$$

[wary stream]

Yes, exactly that

[ocean seal]

Fragzz

[rapid gate]

and thne

this one

with fraction

@wary stream

i got stuck on this oner one which was

$\frac{\sqrt{75}}{9}$

[ocean seal]

Fragzz

[rapid gate]

i got $\frac{5\sqrt{3}}{9}$

[ocean seal]

Fragzz

[rapid gate]

but idk if that was most simple

[wary stream]

That's all you can do

[rapid gate]

tthats the most simple?

[rapid gate]

how do i do this one then?

[wary stream]

Same process, find the largest square that you can pull out

[rapid gate]

1,4,9,16,25,36,49,64,72,81,100

ok

,calc 147/49

[ocean seal]

Result:

3

[rapid gate]

O OK

1ST TRY

so

,w calc x/2=2

[ocean seal]

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[rapid gate]

o wat

,calc x/2=2

[ocean seal]

The following error occured while calculating:
Error: Invalid left hand side of assignment operator = (char 4)

[rapid gate]

L

,w 147=3^x

[ocean seal]

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Requested by Fragzz#2969

[rapid gate]

uh

[wary stream]

What are you trying to do?

[rapid gate]

,w 147=x^3

[ocean seal]

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Requested by Fragzz#2969

[rapid gate]

wait

i think

wtf

wait

no

wow

i should have know i could have written sqrt 49* sqrt 3 the entire time

@wary stream ok so i got

$\frac{27\sqrt{3}}{14}$

that

[ocean seal]

Fragzz

[rapid gate]

wait

because it started off as

$\frac{3\sqrt{147}}{14}$

[ocean seal]

Fragzz

[rapid gate]

i did

[wary stream]

How 27?

[rapid gate]

$$\frac{3\sqrt{49}\sqrt{3}}{14}$$

so then

i got

[ocean seal]

Fragzz

[rapid gate]

3*sqrt 49 *sqrt3

which is

3*7 *sqrt 3

whic is

$\frac{27\sqrt{3}}{14}$

[ocean seal]

Fragzz

[rapid gate]

does that make ant sense to you @wary stream ?

[wary stream]

$$3 * 7 \neq 27$$

[ocean seal]

dldh06

[rapid gate]

?

omg

its 21

wow

lord

[wary stream]

FYI you can simplify here $$\frac{3\cdot 7\sqrt{3}}{14}$$

[ocean seal]

dldh06

[rapid gate]

$\frac{21\sqrt{3}}{14}$

[ocean seal]

Fragzz

[rapid gate]

thats the final answer?

but

21 and 14 can be

3/2

which is

$\frac{3\sqrt{3}}{2}$

[ocean seal]

Fragzz

[rapid gate]

is that the most simplified? @wary stream

[wary stream]

Can you simplify it more?

[rapid gate]

hm

allow me to think

i dont I can

can you?

[wary stream]

That's what I'm asking you

You have to clarify with yourself and see if you fully understand this and not have to rely on others to check for you

[rapid gate]

i cant

i dont think its possible

i mean

change the top?

wait

let me try

sqrt 14.5?

[wary stream]

Ask yourself two questions, can the value under the square root be simplified anymore?

[rapid gate]

it can not

[wary stream]

And if it's a fraction, can you simplify the fraction?

[rapid gate]

$\sqrt{14.5}$

[ocean seal]

Fragzz

[rapid gate]

$\frac{\sqrt{27}}{2}$

[wary stream]

It more preferred to be in the fractional form

[ocean seal]

Fragzz

[rapid gate]

idk if this counts

as more simplfied

[wary stream]

Well, $\sqrt{27}$ can be simplified

[ocean seal]

dldh06

[rapid gate]

hm

[bright hedge]

Remember that sqrt(27)/2 is NOT equal to sqrt(27/2)

[rapid gate]

what

ok

[bright hedge]

And that 27/2 = 13.5

[rapid gate]

ok

im quitting maths

thats it

2 digit division

[wary stream]

Since $\sqrt{27}$ can simplified, you have to simplify it

[ocean seal]

dldh06

[rapid gate]

hm

3 sqrt 3

is mos t simple

if u ask me

[wary stream]

So then what's the final answer?

[rapid gate]

$\frac{3\sqrt{3}}{2}$

this

[ocean seal]

Fragzz

[wary stream]

And so, is that the most simplified?

[rapid gate]

YES

100%

sure

[bright hedge]

👍

[rapid gate]

wait is it fr

[bright hedge]

it is

And now you understand why after going through it

[rapid gate]

,w simplify (3sqrt 147)/14

[ocean seal]

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[bright hedge]

We don’t like sqrts on the bottom, and we wanna always pull perfect squares out of square roots

[rapid gate]

YESSSSSSSSSSS

[wary stream]

As I said, ask yourself the two questions, can the value under the square root be simplified anymore and if it's a fraction, can you simplify the fraction?

[bright hedge]

also dldh you should join the mobius earth gang

[rapid gate]

#help-0 message

ok

i'll remember this

thanks 🙂

[rapid gate]

?

[bright hedge]

Don’t worry about it

[wary stream]

Don't even know what that means

[bright hedge]

Senku is the leader , MEG Sam is vice leader, and I am a colonel

[rapid gate]

o

[bright hedge]

Of the mobius earth gang (MEG)

[rapid gate]

can i joi

n

is a private server or smth

[bright hedge]

Yeah you can

Nah it’s not

First you gotta be really active and get the active rank

Then you gotta add MEG to ur name

[rapid gate]

wut

how active is active

@bright hedge can u give me a random surd to simplify

[bright hedge]

Very active is active

Also you can prob find some online

[wary stream]

$$\sqrt{180}$$

[ocean seal]

dldh06

[bright hedge]

Search up “fractions with sqrts to simplify)

[rapid gate]

ezpz

ok

so

um

oh no

uh

wait

let me do this in my book

2 sqrt 4?

$180 \divide 2^2=16$

[ocean seal]

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

[wary stream]

No, that's not it

[rapid gate]

o

no

it cant be

it must be 2 sqrt 4

180 div 4 is 16

wait

no

6

,8

what?

wait

i just did

180/4 is 45

assuming that 4=2

omg wtf

no

im still wrong if it was 2

rip

wait

6 sqrt 5

i got it

[wary stream]

Are you sure?

[rapid gate]

so i did

certain

so i did

180/4=45

[wary stream]

Can that be simplified any more?

[rapid gate]

180 = 2^2*45

it cant

then

[wary stream]

,w sqrt(180)

[ocean seal]

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Requested by dldh06#2659

[rapid gate]

2*sqrt{3} * sqrt{15}

i figured that was wrong bc it didnt have a perfect square in it

so i did

2 *sqrt {9} * \sqrt{5}

which is 2*3 *\sqrt5

which is 6\sqrt 5

does that make sens

e

what happens if there is no perfect square though?

[wary stream]

Then it can't be simplified

[rapid gate]

oh

for real?

[bright hedge]

Well what can you pull out of square roots?

[rapid gate]

wdym

[bright hedge]

Like let’s say you have some square root of something

When can we pull part of that something out of the square root?

[rapid gate]

if it has a perfect square in it

or the entire thing is a perfect square?

[bright hedge]

Yep

Nope perfect square in it

Remember power is distributive over a product

And multiplication is distributive over a sum

So if I had

(a^2b)^(1/2)

I would have

a^(2*1/2)b^(1/2)

And 2 * 1/2 is just 1

So we have

a * b^(1/2)

Or a sqrt(b$

[lone heart]

@rapid gate Has your question been resolved?

[rapid gate]

wait

[lone heart]

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[jade peak]

Is there a way to Square root but to scale 'squaring' to specific range, like from 0 to 10

[vale wigeon]

@hushed tundra please reserve your own channel. read #❓how-to-get-help

@jade peak what do you mean?

[jade peak]

Like if i have values that reach number of 100-1000 but i want these values to scale to between 0 to 4 however, they should still remine distance Proportion between them even at smaller range of 0 to 4

[vale wigeon]

so you want to map the range [100, 1000] to [0,4] so that the distances between values scale proportionally?

[jade peak]

yes\

it can be 1200 or 104 or 94, numbers can change

i have 4 numbers

[vale wigeon]

...

[jade peak]

exactly

[vale wigeon]

then what's that you said about 1200?

that's not in your range.

you're apparently contradicting yourself, or maybe there's more going on

[jade peak]

i have 4 random numbers

wanted to make it simple

[vale wigeon]

maybe you could say what this is for?

in trying to make it simple you've only made it more opaque

[jade peak]

i have 4 moving averages

they move as prices changes

but i want to scale them down

[vale wigeon]

4 moving averages of what

[jade peak]

of price of product that changes over time

[vale wigeon]

and why do you want to scale it down?

[jade peak]

since i have a place with scale of 0 to 4 to display them

i am going to actually plot the lines of the moving averages scaled down

[vale wigeon]

i mean, you could scale them using the formula f(x) = 4*(x-100)/900, but i somehow doubt that this scaling is going to be meaningful in any way

[jade peak]

why divide 900?

[lone heart]

@jade peak Has your question been resolved?

[jade peak]

will try thanks

[lone heart]

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[vale wigeon]

900 is the length of the input range, which you stated as [100,1000]

[lone heart]

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[gloomy portal]

I need help

[gloomy portal]

Please help

Hello

<@&286206848099549185>

Hi is this correct

I used Pythagorean theorem

[echo socket]

No

[gloomy portal]

How?

[echo socket]

If a, b are the sides, and c is the hypotenuse

Then a^2 + b^2 = c^2

So a^2 + 17^2 = 19^2

[alpine sable]

B² + P² = H² where B is base, P is perpendicular, H is hypotenuse.

[gloomy portal]

But we know that side though

We trying to find the unknown side

[echo socket]

We don't

We know only one side

And the hypotenuse

We need the other side

[gloomy portal]

This side

[echo socket]

So it's a^2 + 17^2 = 19^2

[gloomy portal]

.close

[lone heart]

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[analog tree]

What first step should i do?

[jagged imp]

find f'(a) for arbitrary a

[lone heart]

@analog tree Has your question been resolved?

[analog tree]

Oh yaaaa. Tq

.close

[lone heart]

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[alpine sable]

The answer is y=80x+205

not y=41x

and I know I'm a big dummy lol, but I cannot for the life of me figure out how to turn that into y=80x+205

[alpine sable]

you did mistake here
you can't divide 195 by 5 its divide by whole (x+5)

just multiply both sides by (x+5) and then solve

What operation do I use to get the y out? I really need to brush up on all the rules with manipulating rationals.

aha

[alpine sable]

^

wow, duh. Thank you very much.

.close

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[woeful tartan]

100 = 1/2 m(30)^2, I change 100 with the m? Like change their location will I be dividing 100 by (30)^2?? Can anyone tell me this I'm confused

[lone heart]

@woeful tartan Has your question been resolved?

[lone heart]

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[floral pawn]

Please give some tips to solving this

<@&286206848099549185>

[lone heart]

@floral pawn Has your question been resolved?

[wanton junco]

have you tried anything so far?

[floral pawn]

Ive tried expanding it

and then put it in a polynomial

doesnt seem to give me anything useful

[wanton junco]

I think its a bit simpler than that

unless i've got it completely wrong

Okay so once you expand it

you would be able to subtract all squared terms from both sides correct?

[floral pawn]

yes

[wanton junco]

so you'd be left with 2*x_ix_j type of terms

such that i!=j