help-10

[snow gull]

thank you both!

i got -(9x^2-10)/(3x^3-x)^2

for my derivative

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[worldly shore]

I know the equation I just forgot how to solve it

I solved it this morning but I forgot..

[timid silo]

As in, you don't know how to plug in the numbers?

[worldly shore]

no I know that part

but when I tried to solve it just wasn't the write answer

[high lily]

show work

[worldly shore]

every way I tried to do it

[high lily]

you can't just remove that root like that

also () are needed aroung the -6

$-6^2$ is not the same as the $\red{(}-6\red{)}^2$ you should've had

[warm shale]

ℝamonov

[worldly shore]

oh

oh I see

[high lily]

anyway, fixing that, you'd have
$$\sqrt{36-16}$$
try simplifying that further

[warm shale]

ℝamonov

[high lily]

oh missed your issue with the 4 + 4 as well

[obtuse pebble]

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[true jungle]

Hey could someone confirm if this would be a correct solution for my limit?

[wise talon]

,w lim x to 2 of (x-2)^(2x-4)

[warm shale]

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Requested by DerpZ#9141

[wise talon]

lets ask wolfie

0^0 is 1 yeah

[true jungle]

ye I tried wolfie alr but they used a diff way than mine

they started using exp instead of ln

[wise talon]

wait did you just

switch the log and the limit

[true jungle]

I added an ln

[wise talon]

yeah in line 2

[true jungle]

and then switched them

[wise talon]

is that valid here

[true jungle]

because ln is continue

[wise talon]

i mean yes it is continuous at x=2

oh ok yeah it should be fine

[true jungle]

great cheers

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[hot dawn]

does this type of graph / equation have a name?

[hot dawn]

for $\sqrt{x^2+b} ;\exists b\in\mathbb{R}$

[warm shale]

normalAtmosphericPa=101,325

[wise talon]

thats not how you write a range

[hot dawn]

oops

I meant to say for some b in R

[wise talon]

oh

idk thats just the graph of sqrt(wtv)

lol

[hot dawn]

basically

[wise talon]

parabola maybe?

[hot dawn]

I don't think that's a parabola lol

if b=0, the graph would resemble a piecewise

[wise talon]

piecewise what

if b =0 the graph is just y=|x|

i suppose you mean that

[hot dawn]

yeah

[obtuse pebble]

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[next reef]

What have you tried?

[cobalt totem]

So like For the table would it be 2π•0.4=

31.416

[high lily]

where's 31.416 coming from

[cobalt totem]

Wydm

I have to round it to three decimal places

So that the answer

[high lily]

you typed

31.416
what's that supposed to be, how did you obtain that value

[cobalt totem]

Check now

[high lily]

2pi * 0.4 isn't 31.416

its not even anywhere close to that

[cobalt totem]

Then

2.51327412287

[high lily]

yeh and round that to 3dp

[cobalt totem]

2.513

[high lily]

yes

[cobalt totem]

do i do that for the next ones

[high lily]

same idea

plug and evaluate

[cobalt totem]

ok

thanks

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[timid silo]

When I plug the equation into desmos I get 0.0143

[timid silo]

Midpoints at pi/8, 3pi/8, 5pi/8, and 7pi/8

[gilded needle]

you must have plugged it in wrong

evaluated using matlab: ```

N=4;
x = (0:(N-1))pi/N + (pi/(2N));
f = 2.x.((sin(x)).^2);
delta = pi/N;
sum(f)*delta
ans =
4.9348

which is reasonably close to the true value:

[obtuse pebble]

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[elfin burrow]

,w midpoint rule 2xsin²(x) 4 intervals x = 0 to pi

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[warm shale]

Results provided by WolframAlpha

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Requested by tushar#0942

[gilded needle]

interestingly, the midpoint method appears to give exactly the same answer as actual integral for any N >= 2

[gilded needle]

that should be possible to confirm analytically but it's 5:25 am here and i'm going to bed haha

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[timid silo]

can someone tell me if the answers are right pls?

[obtuse pebble]

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[timid silo]

<@&268886789983436800> why a tiimeout?

[dreamy forum]

You need to react to the bots prompt

If you dont do it in time, the bot will automatically close the channel.

[timid silo]

I see

[timid silo]

Does anyone here know AI?

[thick oracle]

Do you have a specific question?

[timid silo]

yeah, if the answers on the pic are right

[unreal musk]

it also doesn't mean you're "punished" or anything btw, it just means the bot assumes you've moved on, you can make another channel just fine

[timid silo]

tbh i dont think anyone is able to verify if my answers are correct they are more AI related 😦

[unreal musk]

Looks like discrete math to me, no? [not that I can even claim discrete anymore lol]

If worst comes to worst and nobody can help, maybe try #discrete-math and if not then they'll tell you where would be suitable to go to

[timid silo]

I will try

[obtuse pebble]

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@timid silo Has your question been resolved?

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[warm shale]

donut

[weary delta]

Just use it? 😄

It'll work

[warm shale]

donut

[unreal musk]

Hint: you'll get an integral that you'd need to work on

[unreal musk]

This is btw

[weary delta]

or u if you prefer calling it u, but yes, that's the idea

e^t^2 isn't exactly easily integrable

[unreal musk]

Oh you're trying to do by parts from the jump

Peak

[weary delta]

It's so not easily integrable that we just call it erfi(x) and call it a day 😛

[unreal musk]

Do the substitution they tell you first, as per above

[weary delta]

You first need to do the sub, then the ibp will be trivial

[obtuse pebble]

@sand forum Has your question been resolved?

[warm shale]

donut

donut

[weary delta]

$\int t^3 e^{t^2} , dt = \int u\sqrt{u} e^u \frac{, du}{2\sqrt{u}}$

[warm shale]

Learath2

[weary delta]

x^2 smells wrong to me

I did u = t^2

$u = t^2 \implies , du = 2t , dt = 2\sqrt{u} , dt$

[warm shale]

Learath2

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[next reef]

Find the least natural number n, such that there are no primes n to (n+10).

[next reef]

I tried writing writing out primes under 100, which is a pretty dumb way to solve this problem

How should I approach this problem?

[cold thistle]

I feel like you could just find the first case where the difference between two consecutive primes is over 10

[next reef]

[frank hamlet]

pretty much what he was doing before

[cold thistle]

113 and 127 have more than 10 between

[gleaming ridge]

Notice that (n! + 2), (n! + 3), ... , (n! + n) are all composite numbers that are consecutive

where, n! = n x (n - 1) x (n - 2) x ... x 3 x 2 x 1

[next reef]

Hmm

I'm having a tough time with number system

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[deft forge]

I have done question b4!

I just wanted someone to check my work if I had done it accurately.

[sharp pecan]

thats a lot of writing, but sure

[deft forge]

Thanks!!!

[obtuse pebble]

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[timid silo]

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[languid ocean]

Hey there I have a simple question

[languid ocean]

why can't we solve this problem using the area under the curve

[obtuse pebble]

@languid ocean Has your question been resolved?

[obtuse pebble]

@languid ocean Has your question been resolved?

[somber oasis]

Area under the curve gives you displacement

You need the position

At 1 s, the particle is at 2 m

Find the net displacement from 1 s to 6 s

And add it to the position

[lethal wedge]

No but displacement is the measure of change of position does it have a initial position or something

So you would do area under of curve because your given velocit over time

Yea area under the curve

So you have two triangles that have sides of 2 and 3 so cross those out and its just the change between 2 and 3 which would be -1m

I would write something like dispalcment/position is a measure of speed times time which means we can use area under the curve then just use that

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[jolly bramble]

I made a good plan to learn math. Now i need to find ways to learn them such as online and books. The topics that i need books or online courses are:
Pre-Algebra
Geometry
Algebra 1 & 2
Trigonometry
Statistics & Probability
Pre Calculus
Calculus 1 & 2

[brisk matrix]

khan academy will cover most of this

[jolly bramble]

Btw, this is also my math learning plan

[brisk matrix]

if you’re into reading i’d look into textbooks

you can find free pdfs online most of the time

[jolly bramble]

I would love to get book suggestions

[jolly bramble]

Yes, but will they go Very in-depth?

Problems and stuff i can find

[brisk matrix]

as in depth as you need to id say

when your goal is to go up to calc 1/2

[jolly bramble]

There is discrete math and linear algebra after calc, but its for the future

[brisk matrix]

i’m curious as to what motivated this list, and what your current level of math is

[jolly bramble]

Ill answer the 2nd question first, im in 8th grade

[bold bane]

Geometry should come after Algebra.

[dark stirrup]

And number theory, analysis and topology, it's quite endless

[jolly bramble]

Yes, after prealgebra right?

[jolly bramble]

Noting it

[brisk matrix]

i was asking what your previous experience in math classes has been

that

[jolly bramble]

Till 6th grade, it was good, from 7th it took a huge downhill. We are currently learning algebra and Geometry quite a lot

[solar trellis]

There's nothing to plan, just Google what you want

[jolly bramble]

And the motivation was to start from the basics and learned advanced topics

Cuz my finals are in a few months and i have the entire book for the exam

[dark stirrup]

Sounds like you just need to review what you've learned so far

[jolly bramble]

Yea but i wanna go in a order rather than going all over the place with advanced topics, idk how to say it

[solar trellis]

Pick an order at random

[jolly bramble]

Thats the point for this motivation, if i learn atleast till algebra 1, im very prepared for the exam

[brisk matrix]

i would suggest continuing wherever your curriculum left off, and just asking around if you ever come across something that doesn’t make sense. reviewing all of pre algebra is kind of a lot when you could just be doing algebra and reviewing as concepts come up

[jolly bramble]

Wdym?

[jolly bramble]

Okay, will do so

[empty sky]

Y do u want to learn math

[dark stirrup]

You can go to your old teachers and ask for old exams because you want to fill in possible gaps

Some teachers would be very happy to see you want to better yourself like that

[jolly bramble]

Lotta random reasons but these are more specific:

1. So that if i learned something such as a bezier curve, i can easily understand the formulas and do it myself
2. I wanna do complex math in minecraft for adventure maps

[jolly bramble]

Okay

Thanks yall

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[timid silo]

I don't even know where to start lol

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[inland schooner]

Topic: "The ratio between trigonometric functions of one argument"

Simplify expressions:​

[dark stirrup]

what have you tried

[inland schooner]

Hmm

nothing, I don't know how to solve this at all._. everyone says it's easy. I hope for your help.

@dark stirrup

[dark stirrup]

Do you know any trig identities?

[inland schooner]

this is algebra, please, this is a school curriculum

[dark stirrup]

Odd that they're giving you trig work in an algebra course

If it was never taught to you, that's something you need to bring up to your instructors

[inland schooner]

2. Right?

@dark stirrup

[dark stirrup]

yeah looks good

Is that tan² you wrote on the right?

Wait what is ctg?

co-tangent?

I'm US, so I assume we use different terminology

[obtuse pebble]

@inland schooner Has your question been resolved?

[inland schooner]

tg² a

[dark stirrup]

what is tg? Tangent?

[inland schooner]

Are you serious?

Yes, tangent

<@&268886789983436800>

Help, pls

[obtuse musk]

dont ping moderators for math help

[dark stirrup]

Yes I'm serious. I'm from the states. We use "tan" for tangent. This is my first time seeing "tg" so I wanted to be sure before I helped you

[inland schooner]

Hmm

[dark stirrup]

anyway

yes

you did problem 2 correctly

[obtuse pebble]

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[timid silo]

I need help with this, I don't understand it.

[timid silo]

I need to write a general linear system of two equations in two unknowns with this Formula

[alpine bison]

the number of equation are the number of row

i.e. m=2

the number of unknowns are the columns

i.e. n=2

[timid silo]

So my answer would be?

[alpine bison]

n is not generic .. n=2

[timid silo]

Okay, I understand

2x2

[alpine bison]

ye

[timid silo]

Thanks

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[timid silo]

is this right ?

[tranquil sonnet]

Yes

[timid silo]

10 * 10 = 100 * 26 = 2600

[tranquil sonnet]

yup

[timid silo]

it said the answer was wrong

and the number on the left has to be between 1 and 10

is it 0.26

[tranquil sonnet]

Oh that’s cause it’s scientific notation

Is 0.26 in between 1 and 10?

[timid silo]

no

its between 0 and 10

[tranquil sonnet]

Which is not allowed

[daring rock]

Where else could you put the decimal, so that it's between 1 and 10?

[timid silo]

2.6

https://tenor.com/view/sad-cat-sunakook-tired-exhausted-gif-24687868

[daring rock]

yep

For scientific notation you always want exactly one digit before the decimal, and it shouldn't be a 0

[timid silo]

it said thats still wrong

[daring rock]

in other words, between 1 and 10 lol

Did you change the exponent too?

[timid silo]

is it still 10^2

[tardy epoch]

,calc 2.6 * 100

[warm shale]

Result:

260

[daring rock]

Does 2.6 * 10^2 = 2600?

[timid silo]

so to the power of 3

[daring rock]

👍 yep

[timid silo]

.close

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[polar aspen]

can it be solved without maclaurin expansion and lhopital

[tight oasis]

What's the point

[daring rock]

I think they mean, at what point are you taking the limit?

[polar aspen]

yup limit x tends to 0

[thick gyro]

Wasn't it limit x tends to 0

Well in any case, I managed to simplify it to just (e^x -1)/(e^x sinx)

[polar aspen]

same here

[warm shale]

Modus

[tight oasis]

Try to factor e^-x

then separate e^-x from the rest

evaluate both limits

oh lol I used Hospital I'm dumb dumb

[thick gyro]

You could remove the e^x at the denominator since that's just 1

And just be left with e^x - 1 / sinx

Does smol angle approximation count as expansion

[polar aspen]

can you tell how you got here

[thick gyro]

factor out e^-x

You're left with

[tight oasis]

Why not use Hospital though

[thick gyro]

e^2x - 2e^x + 1 on the numerator

[polar aspen]

isn't it is whole square though

[thick gyro]

Which is (e^x - 1)^2

Yh

[polar aspen]

after that I am able to solve

[thick gyro]

And then you have xsinx at the bottom

[polar aspen]

thanks

[polar aspen]

to develop algebraic intution, our teacher advises against it.

[thick gyro]

Group out one of the (e^x - 1)/x

This limit is 1. It is kinda trivial.

So you're left with e^-x (e^x - 1)/sinx

Remove the e^-x since that's just 1

You can then times this by x / x

So you get

(e^x - 1)x/xsinx

Group out an x/sinx

This limit is 1

Then you're left with (e^x - 1)/x

Which is also 1

Q E D i guess

[polar aspen]

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[obtuse pebble]

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[steep holly]

where did the 2x and y come from

[polar aspen]

isn't it is clearly visible

try remultiplying factors to get the idea

[open crown]

it seems they factored out 6x^2y^2

[steep holly]

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[obtuse pebble]

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[compact gate]

Any hints to start this problem?

[wooden cipher]

consider ||assuming n>m, then use euclidean algorithm||

[compact gate]

thanks!

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[timid silo]

Why is this wrong ?

[nocturne minnow]

Because you still have m in there

[timid silo]

so y=4

[nocturne minnow]

No

Equation of a line is y = mx + b

Where m is the slope

And b is the y intercept

[timid silo]

y=1/4 *4+b

1=1/4*4 +b

[nocturne minnow]

What?

You have the graph, use it

What's the y intercept?

[timid silo]

1

[nocturne minnow]

Can you find the slope of that line?

[timid silo]

lol x is the den

so 4 over 1

my b

so y = 4*1 + b ?

[nocturne minnow]

Equation of a line is y = mx + b

The variables x and y don't disappear when you create the equation of a line

[timid silo]

so 4 = 4*1+b

[nocturne minnow]

You are trying to get the equation of a line

[timid silo]

y = 4/1x+b

[nocturne minnow]

And b is?

[timid silo]

1

[nocturne minnow]

And b is the y intercept

[timid silo]

so y = 4x+1

[nocturne minnow]

Nope

[timid silo]

y =4/1x+1

[nocturne minnow]

No

I mentioned before, that /1 is redunant

[timid silo]

y = 4* 1 +1

[nocturne minnow]

Look at the line, is it a positive or negative sloped line?

[timid silo]

postive

[nocturne minnow]

What happened to the x?

[timid silo]

if you gave me the answer i could reverse engineer it in seconds and understand how to do it btw

[nocturne minnow]

Do you know how to tell the difference between a positive and negative sloped line?

[nocturne minnow]

And no, I'm not giving you answers

[timid silo]

the numbers in the slope will be negative

[nocturne minnow]

You want answers, go somewhere else. That's not the purpose of the server

[nocturne minnow]

[timid silo]

ok its a negatively sloped line

[nocturne minnow]

How did you deduce that?

[timid silo]

its going down from left to right

[nocturne minnow]

Then can you formulate the proper equation now?

[obtuse pebble]

Please read #❓how-to-get-help

[inner cedar]

Can anyone teach me how to solve this?

[nocturne minnow]

No

Read #❓how-to-get-help

[timid silo]

you on the wrong street cuh

[nocturne minnow]

You already have a channel #help-3

[timid silo]

y = 4*0+1

[nocturne minnow]

Why is there a 0?

[timid silo]

so the y intercept is (0,4)

[nocturne minnow]

Equation of a line is y = mx + b
The variables x and y don't disappear when you create the equation of a line

[timid silo]

and the x intercept is (0,1)

[nocturne minnow]

Okay and?

Equation of a line is y = mx + b
Where m is the slope
And b is the y intercept

What is the y intercept?

[timid silo]

so
4-1
0-0

[nocturne minnow]

You are overcomplicating

[timid silo]

4

[nocturne minnow]

What?

[timid silo]

1

you keep asking me the same questions over again

we established this ages ago

[nocturne minnow]

And what is m, the slope?

[nocturne minnow]

Yes because you need to stop rushing

[timid silo]

yes we established that ages ago as well

[nocturne minnow]

Then answer that question, what is m?

[timid silo]

4/1

[nocturne minnow]

No

First, as mentioned, that /1 is redundant

[timid silo]

so its just 4

[nocturne minnow]

Second, do you know how to tell if it's a positive or negative sloped line?

[timid silo]

yes we established that

what does the slope being negative mean i need to do ?

i cant read your mind

[nocturne minnow]

It's in the words

[timid silo]

so -4

[nocturne minnow]

Yes

So now form the equation of the line

[timid silo]

y=-4x+1

[nocturne minnow]

Why is there m?

[nocturne minnow]

Yes

[timid silo]

it said that was wrong and i messed up the rise over run for the m intercept

[nocturne minnow]

Well I didn't feel like scrolling back up, so I knew the eh slope had a 4 in it

Since slope is rise over run

What is the rise over run of that line

[timid silo]

1/4

[nocturne minnow]

Here we go again...

do you know how to tell if it's a positive or negative sloped line?

-1/4 and 1/4 are two different slopse

[timid silo]

ok so -1/4

[nocturne minnow]

It is important to know the difference

[timid silo]

ok

[nocturne minnow]

So equation of that line is?

[timid silo]

y =-1x+1

[nocturne minnow]

[nocturne minnow]

If this is the slope

[nocturne minnow]

How are you getting this?

[timid silo]

y=-1/4x+1

[nocturne minnow]

Try it

[timid silo]

you couldve posted an image like this and I wouldve got it 10hrs ago

feedback

[nocturne minnow]

You could have googled it yourself

Just like that

[timid silo]

i didnt know what i was looking for they are all different this was the only image that showed this

when googling negative slop intercept

[nocturne minnow]

Well you are finding an equation of a line based on the graph so it's pretty obvious to look up something along the lines of "equation of a line given graph"

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[tame gust]

Help pls im stuck

[timid silo]

okay sure

[tame gust]

i found x but idk how to use it to get angle ANS

x=8 if im right

[timid silo]

So you know that opposite angles of a parallelogram are equal?

[timid silo]

yes.

[tame gust]

yeah

[timid silo]

Do you know that adjacent angles of a parallelogram sum up to $180^\circ$?

[warm shale]

Wither

[timid silo]

@tame gust

[tame gust]

Yeah its in my book TT

[timid silo]

so

[warm shale]

Wither

[timid silo]

@tame gust

[tame gust]

Okay wait let me try to solve it

[warm shale]

Wither

[timid silo]

@tame gust got it?

[tame gust]

somehow i got 85? TT

wait i did smth wrong

[timid silo]

10 x 8 -15 = 65

180 - 65 = 115

[nocturne minnow]

Doing the work and giving out answers isn't really "helping" people

Helping people is leading them in the right direction

[tame gust]

My calcu got it right but i dont know what i got wrong

[nocturne minnow]

Can you post your work?

[nocturne minnow]

On how you got this

[tame gust]

Ok wait a sec i gotta get my phone

Ohh now i know what i did wrong

i did 10 times 8 instead of negative 10

[nocturne minnow]

Yep

[tame gust]

So now that means angle ANS=115

[nocturne minnow]

Yes

[tame gust]

Alr alr thanks

Now i need help with another one

[timid silo]

A rhombus has all 4 sides equal

[tame gust]

Ohhhh omg i feel dumb hehe sorry

[timid silo]

np :)

[tame gust]

thanks and i still got another one

Idk where to start on this one

[warm shale]

Wither

[timid silo]

another is $4x - 2$

[warm shale]

Wither

[tame gust]

okayy

[timid silo]

now make the equation

one side is longer than other by 5

[tame gust]

I dont get it TT

[warm shale]

Wither

[tame gust]

ohhhh

now i get it

[timid silo]

now solve for x

and find perimeter

[tame gust]

the ans to (x+5)+5 is x+10 right?

[timid silo]

yes

[tame gust]

This dont feel right TT

[timid silo]

so you get x = 4

[tame gust]

yeah i got x=4

[timid silo]

so now

X + 5 = 9

4x - 2 = 14

perimeter = 2( a + b )

now find it

[tame gust]

wait but i thought its 5 units longer?

[timid silo]

yes

9 + 5 = 14

[tame gust]

46?

[timid silo]

yes

you got it

[tame gust]

Im still stuck why theres no +5 on this one

[timid silo]

cos it was given for making the eqn

[tame gust]

hmm okay okay thankyouuu!

[timid silo]

no probs man

[tame gust]

Now i have to go because i need to go somewheree

[timid silo]

okay

[tame gust]

il be back later bye bye

.close

[obtuse pebble]

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[uneven otter]

I got arcsin(x/3) + C

[uneven otter]

doe its askin fir me to find the C value so

do i

$y = arcsin(\frac{x}{3}) + C$ and I guess you just plug in the ur y and x?

[warm shale]

Worth

[uneven otter]

$3 = arcsin(\frac{-3}{3}) + C$ ?

[warm shale]

Worth

[obtuse pebble]

@uneven otter Has your question been resolved?

[uneven otter]

.close

[obtuse pebble]

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[obtuse pebble]

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[nimble gulch]

why this is equal to 1 ?

[royal basin]

image on its way?

[olive niche]

I was typing the same thing

[olive niche]

.

[nimble gulch]

oh sry

[royal basin]

hm

26 + 15 sqrt(3) = (a + b sqrt(3))^3

= (a^3 + 9ab^2) + sqrt(3)(3a^2 b + 3b^3)

i suppose we can somehow find a and b from knowing a^3 + 9ab^2 = 26 and 3a^2b + 3b^3 = 15

[gleaming ridge]

$\sqrt[3]{26 + 15 \sqrt{3}}$ should simplify to $2 + \sqrt{3}$

[warm shale]

numbpy

[grizzled shore]

^

That’s my first thought

[royal basin]

god knows that would be hard to come up with a priori though.

[grizzled shore]

Do you know it’s 1 or do you want to find it

Is it a “show” or “evaluate” kind of question

[nimble gulch]

show

[grizzled shore]

Because the approach is very different

[royal basin]

.

[nimble gulch]

i will send original photi from book

[gleaming ridge]

$({{2 + \sqrt{3}}^3) = 2^3 + {\sqrt{3}}^3 + 6\sqrt{3}(2 + \sqrt3) = 8 + 3\sqrt3 + 12\sqrt3 + 18 = 26 + 15\sqrt3$

[warm shale]

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

[nimble gulch]

the third one

[grizzled shore]

Very sus @gleaming ridge

[royal basin]

yes, we get that.

[olive niche]

Anyways that was (2 - √3) on their question

[royal basin]

should i repeat my suggestion a hundred more times?

or two hundred?

[gleaming ridge]

I tried

[royal basin]

maybe it's by the 177th time, and no earlier, that my voice will be heard

[nimble gulch]

i will try

[royal basin]

so i need to say it 176 more times, yes?

[nimble gulch]

no i am trying give me some time

[high lily]

wait, is this a "show" question?

[olive niche]

Yeah

[nimble gulch]

show that equation above is true

@royal basin i can not continue

[high lily]

this is why you should always ask the original in a clear, concise manner

because the approach is very different

[nimble gulch]

true

[grizzled shore]

That’s what I said!

[high lily]

considering the difference of two squares,
1 = (2 - sqrt(3))(2 + sqrt(3))
so confirming that (2+sqrt(3))^3 = 26 + 15qsrt(3)
is enough
you don't have to actually go through the tedious work of finding the cube root from scratch

[nimble gulch]

tnx all

.close

[obtuse pebble]

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[obtuse pebble]

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[haughty blaze]

hey i was confused with a mathematical induction question

[haughty blaze]

my working out

i didn't know where to go from

after this stage

[unreal musk]

Gather together those 2^k’s

[haughty blaze]

how do i do that

like i knew it had to somehow equal 2^k+1

[grizzled shore]

Expand and collect like terms

[haughty blaze]

but i wasn't sure how it worked

[unreal musk]

How would you simplify something like, say, (a+42) + a?

[haughty blaze]

2a + 42

[cobalt crescent]

Same way

[haughty blaze]

like

[cobalt crescent]

2*2^k

[haughty blaze]

then it equals 2^k+1

yeysyeyes?

thank you so much

[haughty blaze]

also since you helped me last time i've done 20 or so more questions and i've gotten them right thanks to you 🥹

thank you!!!!

.close

[obtuse pebble]

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[lament atlas]

can someone help me with this

i know first one is true

i think last one is true too

[obtuse pebble]

Channel closed

Closed due to the original message being deleted

[gleaming ridge]

@lament atlas I think the increasing one is false as an are decreasing

[lament atlas]

sorry

i delted it

[gleaming ridge]

nw, I saw it

[lament atlas]

yeah i think it's right

no wait

but it sats it's unbounded

which is fals i guess

it is bounded

[gleaming ridge]

yes, it is bounded

[lament atlas]

yeah

thanks

[obtuse pebble]

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[lament atlas]

can someone explain me why the domain of this is empty

[loud tangle]

sqrt(x²+1)>x, meaning x-sqrt(x²+1) < 0
-2 would still make it <0

if that makes sense

[lament atlas]

what about 2

in the first eq

that you wrote

[loud tangle]

x-sqrt(x²+1)<0 |-2
x-2-sqrt(x²+1) < -2 < 0

[lament atlas]

is this ok so far

[loud tangle]

i would leave 2 out of the square

because it just makes the difference closer to 0 in the end

[lament atlas]

but why

[loud tangle]

just compare x² and x²+1

[lament atlas]

but is this wrong or what

[loud tangle]

yes, i dont see a reason to square the -2 as well

[lament atlas]

but if you move the square root the the right side

you get x-2 > sqrt

so i squared both sides

[loud tangle]

i stand with this

its like 10x easier

[lament atlas]

but i wont to know what i did wrong

is this ok so far x-2 - sqrt(x^2+1) > 0

then x-2 > sqrt

then square both sides

[loud tangle]

exept its not > 0

its < 0

which is why it has no domain

[lament atlas]

why <?

log should have a positive domain right

[loud tangle]

yes, that s why it has no domain

or empty domain

[lament atlas]

but my ineq result sin x<3/4

[grizzled shore]

Sqrt(x^2 +1) is slightly bigger than x

x - 2 - something slightly bigger than x

Is always negative

[lament atlas]

ok

but the inequality method doesn't work so

[loud tangle]

it does

[grizzled shore]

The inequality method is just writing what I said but with math

[loud tangle]

if sqrt(x²) = x, then sqrt(x²+1) > x (ignoring the modulus)

wait no hold on

[lament atlas]

i don't have to deal with complex

[loud tangle]

yeah i presumed

[lament atlas]

so you are left with -2

i get your idea

but i stil don't get what i did wrong

[loud tangle]

sqrt(x²+1)> x => sqrt(x²+1)-x > 0
=> x-sqrt(x²+1) < 0
=> x-sqrt(x²+1)-2 < -2 < 0
rearranging you 'd get x-2-sqrt(x²+1)<0

[grizzled shore]

$\log(x-\sqrt{x^2+1})$

[warm shale]

Frosst

[grizzled shore]

this also has no domain

the -2 doesn't matter

[lament atlas]

i get this

bcs it's 0>1

which doesn't make sens

[grizzled shore]

what 0 > 1

if i say 3 < 5

then i say 3 - 2 < 5

it's correct

[loud tangle]

are you using proof by false assumption

[grizzled shore]

same here

if x-sqrt(x²+1) < 0

then x-sqrt(x²+1) -2 < 0

is also true

[grizzled shore]

in the same way as this

[lament atlas]

i'm sorry i am going so many times over

but what is wrong with my way

[loud tangle]

?

[lament atlas]

i am just using the fact that the thing inside log should b e postivie

[loud tangle]

so yes

[lament atlas]

is this ok

[grizzled shore]

well that's just not true

[loud tangle]

well if it is positive, that means
x-2-sqrt(x²+1)>0 |+2
x-sqrt(x²+1) > 2 > 0
so x > sqrt(x²+1)
sqrt(x²) > sqrt(x²+1)
x² > x² + 1
0 > 1 FALSE

therefore its < than 0

[loud tangle]

i think they're using proof by false assumptions

[lament atlas]

what is that +2 on the first line

[loud tangle]

adding 2 to the equation

[lament atlas]

ah ok

[loud tangle]

well inequality

[lament atlas]

where did 2 go to the third line

[loud tangle]

-2+2 cancel out

[lament atlas]

then the other line

[loud tangle]

0+2 = 2

2>0 so its still >0

[grizzled shore]

then you need to set it up

like a proof by assumption

[lament atlas]

bro i got confused can;t you square both sides

[grizzled shore]

no

[lament atlas]

why

[grizzled shore]

-2 < 3

(-2)^2 < 3^2

is wrong

well fuck

[lament atlas]

ok i got it

[grizzled shore]

that's right

[loud tangle]

immediately it would be worthless

adding 2 to get rid of the constant helps a tpn

ton

[grizzled shore]

-3 < 2
(-3)^2 < (2)^2 WRONG
9 < 4 SUPER WRONG

[lament atlas]

ok got it

thank you

[grizzled shore]

also when you multiiply both sides by -1

the sign flips

so -2 < 3,
2 > -3

[lament atlas]

yeah yeah got it

thank you so much

for your time

closing this

.close

[obtuse pebble]

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[mighty swallow]

the length of sides of a triangle are 7 cm, 13 cm, and 12 cm, find the length og the perpendicular from the opposite vertex to the side whose length is 12cm
will it be fine if i get the answer in decimals and not in the root format
like the answer should be 4root3
which in decimals is 6.928...
and i got the answer directly as 6.928
because i got the triangle area as 24root3
and i equated root3 to 1.732
and i multiplied 1.732 with 24
got 41.568
12 * 1/2 * h = 41.568
6h = 41.568
h = 41.568/6
=6.928
will i get full marks for this?

[high lily]

probably not

[obtuse pebble]

@mighty swallow Has your question been resolved?

[high lily]

you may get 1/2 to 1 mark deducted if this was worth around 4 marks

getting/using decimal approximations was unwarrented

you should have pretty much applied the area formula after

because i got the triangle area as 24root3

12 * 1/2 * h = 24sqrt(3)
and solving for h gives 4sqrt(3)

[obtuse pebble]

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[timid silo]

how do i evaluate this?

[vast wren]

because of the 0/0 uncertainty

you need to do one of the following

(1) multiplying with cojugates

(2) substitution

(3) l'hopital

[timid silo]

how can i do 3?

[vast wren]

well, that involves differentiation

[timid silo]

ok nvm then

[vast wren]

try 1

[timid silo]

thanks

[vast wren]

what's the conjugate of the denominator?

[timid silo]

i did and it works

thanks

[vast wren]

🙏

yw

[timid silo]

.close

[obtuse pebble]

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[obtuse pebble]

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[timber island]

Is it impossible to factorise factorise a^2+b^2+c^2+ab+bc+ca?

[timber fox]

I would say so

[ancient jacinth]

hmm

the closest thing i can see is (a+b+c)^2 -a(b+c)-bc

(a+b+c)^2 -ab-ac-bc

[muted delta]

It doesn’t seem possible to factor

[timber island]

Hmm

[warm canopy]

If you have an original question, send it. Looks like vieta stuff

[muted delta]

Yeah

[ancient jacinth]

= 🤓

[timber island]

I actually need to solve this:

[neat pewter]

Can someone help with this please

[muted delta]

Stop

[timber island]

Which took me to:
x^(a^2+b^2+c^2+ab+bc+ca)/x^2(a+b+c)

[obtuse pebble]

Please read #❓how-to-get-help

[timber island]

Bruh this channel is occupied

[neat pewter]

My bad

[ancient jacinth]

the answer is 1

[timber island]

How..?

[ancient jacinth]

i think

yes it is

[timber island]

Wait u might be right

[ancient jacinth]

ok

i will explain

[timber island]

I think i got it

[ancient jacinth]

oh

ok

[timber island]

yep i got it from the answer 😃

Tysm!

.close

[obtuse pebble]

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[reef elbow]

I transferred the x to the other side then got 2y<x-4

Then divided by two to get y<x-2

[timber fox]

1/2 x ?

[reef elbow]

?

[timber fox]

when you divide by two

[reef elbow]

It’s supposed to be on all three numbers ?

[timber fox]

if you have 2y<x-4

if you multiply both sides by 1/2

then it would affect both x and -4 yes

did you draw the bottom graph?

it looks good just otherway around

[reef elbow]

No it’s from the pdf the teacher sent

[timber fox]

👍

so do you understand how its 1/2 x and not just x?

[reef elbow]

Yes but how do I get the other points

[timber fox]

do you understand the form its in?

[reef elbow]

I put one point one -2 then what ?

[reef elbow]

Y=Mx+b

[timber fox]

nice

so the gradient here is just

[reef elbow]

.

[timber fox]

well you can get the x intercept but if you know the gradient and y intercept you can draw the line

the x intercept is when y=0

[reef elbow]

That’s the y intercept

[timber fox]

I would agree

[reef elbow]

What is the gradient ?

[timber fox]

you tell me

match the form

y<1/2 x - 2

y < mx+b

[reef elbow]

If it’s false it should be the opposite side am I correct ?

[timber fox]

im not quite sure what you did, I would just solve for the x intercept and draw the line between the y and x intercepts ,

then acknowledge that if you have y<mx+b , the shaded area would be under the line that you have just drawn.

[reef elbow]

I took two points ( the origin) and plugged them in to see if it’s true or false

[timber fox]

ohhh I see, nice.

Yeah in that case it would be the opposite side

so under the line

[reef elbow]

Ok thank you 🙏

.close

[obtuse pebble]

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[timber island]

i have been wracking my brain at this question for 30 MINUTES now, even tried googling it. NOTHING. What the hell is this question and how do I solve it? I suspect it to be some identity magic but I cant really find the indentities to use

[unreal musk]

If a + b + c = 0 then c = -(a+b) and similar

[timber island]

...
That is a stupidly simple answer...Not what I expected

[timber island]

That has to be the trick, it gives me the correct answer!

[unreal musk]

It do be like that, for real

[thick oracle]

[timber island]

Well thank you very much! 🙇

.close

[obtuse pebble]

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[late flare]

lim pi- of cotx

[late flare]

whats the answer

i think its postive inf but apparently its negative

[sage geode]

Yeah, negative

[late flare]

how

i keep getting + answers

[sage geode]

Show your work?

[late flare]

i just used calculator

plug in 179.99

cos/sin

[sage geode]

Are you sure your calculator is in the degrees mode?

[late flare]

no

radian

[sage geode]

Turn the degrees mode on then

It will read 179.99 as 179.99 radians

[late flare]

oh

[sage geode]

Not 179.99 degrees

[late flare]

it is now negatives

ty

so confusing

which side do i take

[tardy epoch]

Normally both sides for the limit of x

[obtuse pebble]

@late flare Has your question been resolved?

[obtuse pebble]

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[north dove]

Isnt this the wrong way around?

shouldnt it be

cos(8o) = cos(9o)cos(o) + sin(9o)sin(o)
cos(8o) = cos(7o)cos(o) - sin(7o)sin(o)

[elfin burrow]

the upside down plus or minus sign signifies that the second sign is opposite the first

[north dove]

No I meant the question

Like they are giving cos(9o) and cos(7o) in terms of 8o

but the question asks for 8o

[elfin burrow]

is there more to the explanation?

seems like they will add the equations together

they want you to derive an expression in terms of cosines whereas you have sines

[north dove]

yeah I didnt know you should use all of cos 9o, cos 7o and cos o to get cos 8o

basically they add up cos 7o and cos 9o and the second part of the equation cancels out and divided by 2 cos o on both sides

[elfin burrow]

yes

you don't need to use all of those if you don't need to, but you can only use those

according to the question

[north dove]

yeah the answer says u gotta use all bit confusing

[obtuse pebble]

@north dove Has your question been resolved?

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[finite turret]

Help

[finite turret]

I need help proving a equation

A trigono one

This one

[whole dock]

What have you tried?

[finite turret]

Wait

Tried like this

But cannot remove this 1 + sin

[dapper robin]

try

squaring on both sides

[finite turret]

No we cannot change sides

Means

[dapper robin]

oh yea

[finite turret]

I dunno the name of the wuestion type

[dapper robin]

i think its coming

[finite turret]

Here we cannot change 1 side

Means have to prove the left equals the right by only solvng the left one

[royal basin]

may i suggest: starting from the right hand side and rewriting it in terms of sin and cos

[finite turret]

I can give u an example if u want

[dapper robin]

oh sorry