help-27

[woven radish]

SilverSoldier

[slim rivet]

Yes thats much clearer, thank you so much

.close

[devout snow]

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[slim rivet]

.reopem

.reope

.reopen

[devout snow]

✅

[slim rivet]

But how do you simplify them?

when numbers become larger than 100

such as, 260, or 540

break it down to, root10, root26?

[sick fulcrum]

factorize and find perfect squares

[slim rivet]

Okay

thanks

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[devout snow]

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[left robin]

I have f(x)=(e^(-1/x))/x

[left robin]

I want the limit as x approaches infinity

Only question i have is can i use lambert w somehow?

[pastel pasture]

Sure thing I guess

[left robin]

If not that is fine and i can continue myself

[pastel pasture]

$-(\frac{-1}{x}e^{\frac{-1}{x}})$

[woven radish]

NEONPerseus

[pastel pasture]

Maybe

[left robin]

we^w=z with w=Wk(z)

So w=-1/infinity 🙂

But i dont know how i would get my limit like that

If it doesnr work it is ok, i just want to use it someday haha

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[sly snow]

i need helppp

[stuck field]

What did you try?

[sly snow]

300/180 simplified -> 5/3
5/3 squared multiplied by the area

thats my logic

and its wrong

[winter patrol]

are you squaring and/or entering this into a calc properly?
what are you getting?

[sly snow]

2.7 reccuring

[winter patrol]

is definitely wrong

[sly snow]

yep

💯

[winter patrol]

how are you getting something significantly less than 1692

[sly snow]

oh no i meant the 5/3 squared

im getting 5621.76

that has to be wrong tho

[winter patrol]

um how exactly are you getting that...

[sly snow]

^^ this

[winter patrol]

can you show exactly what you're putting intot he calc or something

[sly snow]

im not that good at maths

[sly snow]

camera broken :/

[winter patrol]

2.7 reccuring
oh no i meant the 5/3 squared
im getting 5621.76
like even with a liberal approximation of 2.7 reccuring
you shouldn't be getting 5621.76

[sly snow]

idk

[winter patrol]

what exactly are you putting into your calc

[sly snow]

my logic is 💩

[winter patrol]

like your theory on the calculations involved is fine,
(properties of similar shapes etc)
but you're messing up the calculation process

[sly snow]

yeppp

[winter patrol]

so tell me

what exactly are you putting into your calc

[sly snow]

so ive done

300/180 then done S->D to get as fraction
then i square it.
then i multiply by 1692

and answe

[winter patrol]

yeh...

[sly snow]

answer*

[winter patrol]

and that should get you the correct answer...

and not 5621.76

[sly snow]

but its not

can you double check the answer

[winter patrol]

like i've pretty much followed the steps you've outlined
and get a very nice number

so either you're not following your own steps or something else is going on

[sly snow]

ngl idk

imma double check rq

[stuck field]

What you're claiming you're doing is what you have to do. But there's probably a mistake in how you're doing it. Probably a calculation mistake. You should check yours. You can use the bot here and tell us exactly what you input.

[sly snow]

what are commands?

[stuck field]

,calc

[woven radish]

Please give me something to evaluate.
See ,help calc for usage details.

Jan 25, 2023, 4:58 PM

[sly snow]

btw i got 4568.4

[stuck field]

And then you essentially write what you want to calc

[winter patrol]

write down exactly what's going into the input of the calc

[stuck field]

Example

,calc 25/2 * 6

[woven radish]

Result:

75

[sly snow]

so id write 5/3 squared * 1692

,calc 5/35/31692

[woven radish]

Result:

4700

[winter patrol]

btw i got 4568.4
is a lot closer but now you're committing another crime

[sly snow]

im getting too

[stuck field]

See this isn't what you said you got earlier.

[winter patrol]

$2.\dot{7}$ is NOT the same as $2.7$

[woven radish]

ℝamonov

[sly snow]

yeh idk

[sly snow]

see i was getting 2.77777777778

[winter patrol]

then i multiply by 1692
saying this you're implying that you're keeping the squared value of 25/9 as 25/9

[sly snow]

ah so i see

i mistook a recurring

[winter patrol]

and not butcher it

[sly snow]

yes

[winter patrol]

like calcs can retain outputs

using the stored output of $2.777...$ would be less ideal but still fine

[woven radish]

ℝamonov

[sly snow]

ah okay

tyty

..clo

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[vital shard]

quick question

[vital shard]

is 1.75 radians

the same as (7xpi)/4 radians

as 1.75 = 7/4

[honest aurora]

no, they are 2 different numbers

[vital shard]

oh alr

[honest aurora]

$\frac{7\pi}{4}=5.49778714....$

[woven radish]

Duh Hello

[vital shard]

ahh ok thanks

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[karmic trout]

find x

will it be 108?

[dusk quartz]

Can you highlight what X is referring to?

[devout snow]

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[ruby pebble]

,rotate

[ruby pebble]

My answer seems wrong and I need help in general

I fixed the radius squared but still got a long ass answer

<@&286206848099549185>

I got to this

[devout snow]

@ruby pebble Has your question been resolved?

[devout snow]

@ruby pebble Has your question been resolved?

[long pasture]

looks good to me

[ruby pebble]

And part b?

[long pasture]

use 2 different interpretations for y²

and compare

[ruby pebble]

I tried using that but I got 2 variables

Plus it's only 2 marks

[long pasture]

any pic?

[ruby pebble]

I erased it 😭

I think it was in terms of alpha and theta

[long pasture]

oh okay, lemme try

[ruby pebble]

Ty for your time 🙏🏻

[long pasture]

ohhh

hint: how long is AB

[ruby pebble]

Ab

Um

Do I have to use trigonometry?

Or the answer is in front of my nose?

[long pasture]

right in front of your nose indeed!

[ruby pebble]

Wait u know the circle theorem angle at centre is twice that of circumference it may be unrelated but can I use it here

Also do I have to use kite properties

[long pasture]

AB=3r (why)

[ruby pebble]

Lmaooo

Radius

[ruby pebble]

I still want to know this though

[long pasture]

not likely to be used in this Q

[ruby pebble]

But does theta equal half alpha?

[long pasture]

second hint: what's angle DBA

[ruby pebble]

Or is it the reflex angle

1/2 theta

Sin rule?

[long pasture]

you can use it, but it's a little bit more complicated

[ruby pebble]

Oh no just wanted to make sure

[ruby pebble]

Do I use this

[long pasture]

or simply

equilateral triangle!

[ruby pebble]

3r/sin theta/2 = 2r/sin alpha/2

[long pasture]

wait...

yours better

[ruby pebble]

How would we eliminate theta

[long pasture]

cos(½alpha)=((3r)²+(3r)²-(2r)²)/(2(3r)(3r))

cosine theorem

[ruby pebble]

Mhm

14r^2/ 18r^2

14/18

[long pasture]

would that help?

[ruby pebble]

Should we square both sides and then use sin^2x +cos^2x=1

[long pasture]

wait...

for final answer, we have to check if
alpha=4arcsin⅓

[ruby pebble]

Yees

[long pasture]

that is we need something like
sin(alpha/4)=⅓

[ruby pebble]

I assume so yeah

[long pasture]

so we'd have to use double angle forumla

[ruby pebble]

Uh

Ik the formula but am confused as to where

[long pasture]

cos(alpha/2) = 1-2sin²(alpha/4)

there we go

[ruby pebble]

Wow

And that is equal to 14/18

[long pasture]

yea, and by some calculations, it should be done

[ruby pebble]

Let me try it

Got it !

Omg ty so much for being so patient with me

[long pasture]

no problem at all!

i bet it's easier for (c)

[ruby pebble]

Yeah it's a calc question

I have alpha

And I can use the equation st the start

And maybe I can do something similar to find theta

[long pasture]

yep

[ruby pebble]

Got this

Tysm

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[somber rampart]

Hi. Can someone help me differentiate this function:

ln[x e^(7x)]

I've tried:

(chain rule, product rule) = ( [xe^(7x) ]^-1) * e^7x + 7x^2 * e^7x

= 1/x + 7x^2 * e^7x

But apparently that's wrong..?

[somber rampart]

I really need to learn latex

[upper schooner]

One way to make your life easier is log rules, use them on $\ln(x e^{7x})$

[woven radish]

chartbit

[upper schooner]

That will give you something nicer to work with when you fully simplify

[somber rampart]

So I know ln(x) ' = 1/x

and I tried to use that, but it didn't get me far :c

hence this thing: $\1/(x e^{7x})$

[woven radish]

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

[somber rampart]

i tried

XD

[upper schooner]

Don't do the backslash for it

Just do it without it, like 1/(x e^{7x})

[somber rampart]

ooh

[upper schooner]

[make this a LaTeX lesson at the same time ]

[somber rampart]

clears throat hence, this thing $1/(x e^{7x})$

[woven radish]

rainy

[upper schooner]

Nice!

[somber rampart]

😎 thanks

anyway i still don't know how to proceed s:

[upper schooner]

Anyways, this is right, but how did you differentiate $x e^{7x}$?

[woven radish]

chartbit

[somber rampart]

xe^7x = 7x^2 e^7x

or is that wrong?

because i thought d/dx e^xy = ye^xy

o h

oh

[upper schooner]

But it's product rule!

[somber rampart]

well my brain just gained a wrinkle

thanks for the help (and the tex lesson lol)

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[upper schooner]

waaaiittttt

.reopen

[devout snow]

✅

[somber rampart]

D: yes

[upper schooner]

One last point

[upper schooner]

Log rules can also give you $\ln(x e^{7x}) = \ln(x) + \ln(e^{7x}) = \ln(x) + 7x$

[woven radish]

chartbit

[upper schooner]

So also you could have started off by working with that

But that was all!

[somber rampart]

oooh, yeah that would have made it easier

i'll go have a refresher on those, thanks again

[upper schooner]

No worries! catch ya later 🙋‍♀️

[somber rampart]

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[restive river]

Hi how do I reverse calculate the sum of an increasing number?

[topaz beacon]

do you have an example

[supple knot]

show the problem you're working on

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@restive river Has your question been resolved?

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[hybrid snow]

Find a point on that line

Like any random ass point

[restive river]

r(0)=(1, -1, 7)

[hybrid snow]

Okay cool

Create a vector that's from r(0) to (3,3,-4)

Then find the rejection of that vector onto the line's direction vector

[restive river]

do you mean projection?

[hybrid snow]

Well you need to find the projection to get the rejection

The rejection is just $u - \proj{u}{v}$

Where u is the vector between the points

[woven radish]

Umbraleviathan

[hybrid snow]

u is the vector between the points and v is the direction vector

[restive river]

Is v r(0) - (3,3,-4)?

Im having trouble visualizing this

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[gentle ermine]

https://gyazo.com/4c10c8ab4db104422c5f911b2adff542

I'm unsure if there's a (x-d) when finding the equation or if there's only an x.

[gentle ermine]

Y= AsinBx + C

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[devout snow]

@gentle ermine Has your question been resolved?

[gray gust]

what do you mean by your question

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[arctic mirage]

How would I find the domain of the function on the right? The part that is confusing is me is that it has two "inputs"

[gray gust]

an input doesn't have to be a single number

[arctic mirage]

I know that

[gray gust]

The domain of the function is defined for you here

[arctic mirage]

Im mostly torn between answering {1,2,3,4,5,6,7,8,9,10} or {(1,6),(1,7)...}

[gray gust]

well the input is a pair of numbers

so the domain is all the pairs of numbers that you can input

[arctic mirage]

I figured so, but it seems silly to me the question wants me to write every single pair

so I thought I may be wrong

The range, then, would be {6,7,8,9,10} yeah?

[gray gust]

Yeah the question is bad

[arctic mirage]

All I had to hear lmao

[gray gust]

yep that's the range

[arctic mirage]

.close

thx

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[restive river]

im wondering how to proceed, am i supposed to use the triangle?

[restive river]

but how do i know which side(s) are negative?

since im given -8/9

no idea

[sick fulcrum]

do you know that

sin(-x) = -sin(x)

[restive river]

yes

[sick fulcrum]

good

[restive river]

ohhhhh

[sick fulcrum]

(by the way the hypotenuse can't actually be negative)

it's a length

[restive river]

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[restive river]

so as for a square, should i just cut it in half?

[restive river]

as to proceed as i have for circles

or would it be the same. but just with less steps

[sick fulcrum]

well

you're overcomplicating this

that's 1/4 of a circle yeah?

you take the area of the square

and subtract the area of the quadrant

[restive river]

like this just with a square

?

[wild blaze]

what is the area of a sector

[sick fulcrum]

ok let B be the shaded area

and let S be the area of the square

can you compute S - B

the unshaded area

it should follow REALLY fast

[restive river]

yes

thanks.

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[marble quail]

how do i fix the last term?

[marble quail]

does it becomes 5*x^(1/2)

[shy halo]

caculator duh

[pastel pasture]

$f(x) = x^{-2} + \frac{1}{5}x^{-\frac{1}{2}}$

[woven radish]

NEONPerseus

[marble quail]

Why does the 5 stay while the x moves up?

Doesn't the bottom part basically say 1/(5*x^1/2)

[marble quail]

That's not correct

At least it doesn't give me the right answer

[pastel pasture]

You need to find f'(4) I assume?

[marble quail]

Yes

my options

the last part isn't right i think

[pastel pasture]

,calc -3/40

[woven radish]

Result:

-0.075

[marble quail]

1/x^1/2 becomes x^-1/2

[pastel pasture]

$f'(x) = -2x^{-3} - \frac{1}{10}x^{-\frac{3}{2}}$

[woven radish]

NEONPerseus

[pastel pasture]

Yeah

,calc 1/32

[woven radish]

Result:

0.03125

[pastel pasture]

,calc 1/80

[woven radish]

Result:

0.0125

[pastel pasture]

,calc -0.3125 - 0.125

[woven radish]

Result:

-0.4375

[pastel pasture]

💀 forgor 0

,calc -0.0125 - 0.03125

[woven radish]

Result:

-0.04375

[pastel pasture]

Should be c

[marble quail]

idk

i'm getting -0,34375

[fresh horizon]

,w f(x) = (1/x²) + 1/(5sqrt(x)), evaluate f'(4)

[woven radish]

Results provided by WolframAlpha

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

Requested by biggboy#8536

[marble quail]

How do i do it?

help

[fresh horizon]

,calc -7/160

[woven radish]

Result:

-0.04375

[fresh horizon]

ye

[marble quail]

That might be the answer but i want to learn how to do it

specifically the last term in the f(x)

1/(5rootx)

[fresh horizon]

I see

so

[marble quail]

In my head it'd be 5*x^-1/2

but that isn't corect

[fresh horizon]

take $\frac{1}{5\sqrt{x}}$ as $\frac{1}{5} \cdot \frac{1}{\sqrt{x}}$

do you remember the product rule

[marble quail]

But

That can't be right

because 5x^1/2 is one value

1/5 and 1/rootx like you put it are two different values

[fresh horizon]

1/(5rootx) is just 1/5 and 1/rootx multiplied together

[woven radish]

biggboy

[fresh horizon]

my unicode symbol got lost in the latex I see

[marble quail]

soo it's 0,20x^-0,5

[fresh horizon]

no need to decimalise it

in taking derivatives we have a rule called "the product rule"

it goes as: $\frac{\dd}{\dd x} (f(x)g(x)) = f(x) \frac{\dd g}{\dd x} + g(x) \frac{\dd f}{\dd x}$

[woven radish]

biggboy

[fresh horizon]

can you use that here

[jaunty mantle]

Show me your working

How are you getting this value

[devout snow]

@marble quail Has your question been resolved?

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[vivid ravine]

Are first two correct? I dont get this bruh

[ancient furnace]

Yea those are right

[vivid ravine]

Oh dayumn

Ok

[ancient furnace]

Actually ig the first question is kinda ambiguous tho

[vivid ravine]

For number 3 would 2(3x)-1

F(x) = 2(3x) - 1

[ancient furnace]

Yea

So 6x - 1

[vivid ravine]

Ok

Oh ok

I thought i was doing it wrong

How do i close this help tab

[ancient furnace]

.close

^At least i thought it was that

[vivid ravine]

.close

[devout snow]

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[true nova]

Aight

[true nova]

aight so

I just want the answer dont give me the steps

i want to check my answer

[quasi yoke]

$\frac{1}{\sqrt3}\arctan{(\frac{cosu}{\sqrt3})} + C$

[woven radish]

Polipoli ❤

[quasi yoke]

substitute cosu as sqrt(1-x^2) and I think that’s ur final answer

[true nova]

YES thx my answer is right

.close

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[unkempt holly]

i just want the basics of set builder notation help cause i've tried youtube
and im not getting a clear explanation

[sick marsh]

What exactly is set builder?

Just simple set notation or something more?

[unkempt holly]

just set builder everything else i'll self learn

[unkempt holly]

this is set builder notation for visual representation

with the number line thing

[devout snow]

@unkempt holly Has your question been resolved?

[unkempt holly]

<@&286206848099549185>

[devout snow]

@unkempt holly Has your question been resolved?

[acoustic oxide]

whats ur questoin

cuase ur picture and line graph looks good to me

[devout snow]

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[flint snow]

Hi

[flint snow]

Please

<@&286206848099549185>

[devout snow]

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.

[flint snow]

Ik but ion got 15 minutes

I’m only in here for 20

[fierce heath]

what is this for a test or what

[pseudo notch]

x is 3

i think

oh wiat

am i not supposed to say that

[flint snow]

Assignment

[vale estuary]

do you know about 45-45-90 triangle ratio

[fierce heath]

ur supposed to teach the solution

[pseudo notch]

alr

[flint snow]

I need to show my work

[vale estuary]

do you know special right triangles

[flint snow]

Kinda

Pythagorean

But idk where the legs are

And Baden

[vale estuary]

this is a 45-45-90

do you know the ratio between the sides of a 45-45-90 triangle

[pseudo notch]

i dont believe he does

[flint snow]

Lemme see

Hmm

3

2

One of those

Maybe

[vale estuary]

no

ok so the legs are equal in a 45-45-90

[flint snow]

My notes

[jaunty mantle]

Does this triangle look special to you

[pseudo notch]

yes

it is

[flint snow]

It looks like this to me

[jaunty mantle]

Yep

Do you know some names we would call this kind of triangle?

[pseudo notch]

use this to help you

[flint snow]

Um

Isn’t it equilateral

Idk

I think

[jaunty mantle]

No, equilateral triangles have 3 equal sides and 3 equal angles

[pseudo notch]

look so your x in this case is 3 root2 right

[jaunty mantle]

Do you have any other ideas? @flint snow

[pseudo notch]

then just substitute that into the x root 2

[flint snow]

No

[flint snow]

Huh

[pseudo notch]

so 3sqrt2 X sqrt2

[pseudo notch]

look at this

trust

all you need

[jaunty mantle]

What types of triangles do you know?

[flint snow]

It’s a right triangle

But like

Imma need the answer

[jaunty mantle]

What else

Other than it’s a right angled triangle

[flint snow]

That’s the answer ?

[flint snow]

Idk 😭

[jaunty mantle]

Well what triangles do you know of

List them out

[pseudo notch]

no

[flint snow]

Class about to start

😭

[jaunty mantle]

perfect time to ask your teacher then

[pseudo notch]

check dms

[flint snow]

Idk about that

[jaunty mantle]

Please don’t do that

[pseudo notch]

?

[devout snow]

@flint snow Has your question been resolved?

[devout snow]

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[neon aspen]

So from the beginning, let epsilon > 0

In your "for all epsilion" statement let's replace epsilon by epsilon_1

[neon aspen]

How did you get the inequality on the second term?

[fervent jewel]

the last line?

[neon aspen]

Yes

Maybe you meant to multiply the second term by M

Don't think that would work though

[fervent jewel]

hm ok

[neon aspen]

Try bounding each a in the second term by epsilon_1 instead of M

You want to show that for sufficiently large n, |b_n| < epsilon (the same epsilon from the start)

[neon aspen]

Now you can choose epsilon_1 to be anything > 0 (as the statement was for all epsilon_1 > 0...)

And you're already assuming n >= N_1

[fervent jewel]

Meant to multiply that second term by epsilon

why wouldnt that work?

[neon aspen]

epsilon_1*

[neon aspen]

It would, in fact that's what I suggested

I meant using M wouldn't work

[fervent jewel]

ok

oh i see

Now, since we want |bn-1| < epsilon_1

[neon aspen]

Nah

[neon aspen]

^

epsilon is what you're given and trying to achieve

epsilon_1 can be anything you want

[fervent jewel]

oh sorry, I meant to say $|b_n - 0| = |b_n| < \epsilon_1$

[woven radish]

KN

[fervent jewel]

we can just kinda make those two terms to be less than say $\frac{\epsilon_1}{2}$

[woven radish]

KN

[fervent jewel]

does this work?

[devout snow]

@fervent jewel Has your question been resolved?

[fervent jewel]

<@&286206848099549185>

[devout snow]

@fervent jewel Has your question been resolved?

[fervent jewel]

.close

[devout snow]

Channel closed

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[devout snow]

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[crisp silo]

I'm having some issues trying to evaluate this indefinite integral

[crisp silo]

I'm not sure how to proceed replacing the dx for du

[winged rapids]

when you derivate sqrtx = u-1 you have to also add a dx

[devout snow]

@crisp silo Has your question been resolved?

[crisp silo]

ohh

can't believe I missed that

is the rest of the procedure, up to that point, correctly done?

[winged rapids]

ya seems legit

[crisp silo]

I'm still filling in the rest of the dx

but I'm not sure what to add

the du, for certain

dx=2.(u-1)^2.du

is that it?

[winged rapids]

why is it squared tho

[crisp silo]

oh crap

you're right

dx=2u-2.du

[winged rapids]

ye

[devout snow]

Channel closed

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[crisp silo]

.reopen

[devout snow]

✅

[crisp silo]

wait, let me rewrite the integral

my "u"s look like fours sometimes but there are no fours in there

[winged rapids]

you can cancel the 2u-2 with the u-1

[crisp silo]

shouldn't I solve the power first?

[winged rapids]

?

yeah it only reduces one of them

[crisp silo]

oh

right

like that?

ignore the incorrect reduction of sqrt(u).u

[winged rapids]

ya dont forget to pull out the constant

[crisp silo]

after I integrate?

[winged rapids]

well its usually better to pull out constants the moment you see them cuz you're gonna hvae a ton of numbers inside the integral and thats awkward

sorry i wrote the wrong thing before

@crisp silo by the way have you learned partial fractions yet

[crisp silo]

I think so

[winged rapids]

ok yeah cuz or else i dont think you could have done this integral

anyway keep going

[crisp silo]

is this correct?

Thanks for all the help, by the way

[winged rapids]

?? i dont know how you did that

[winged rapids]

np

[crisp silo]

do I have to decompose the fraction?

[winged rapids]

no

you cant actually do anything at this point

you have to perform another substitution

[crisp silo]

oh

so what substitution would you perform?

sqrt(u).u?

[winged rapids]

well usually you want to get terms with ^2 because you have things like the derivative of inverse trig functions that are like 1/1+x^2 or 1/sqrt(1-x^2) and stuff

i would maybe try v = sqrt(u)

[winged rapids]

wait bro

can you rewrite the integral you have

its not even correct anymore

you did some weird stuff during the reduction

[winged rapids]

@crisp silo

[crisp silo]

I just got it

it was really simple

thank you

can't believe I didn't see it before

[winged rapids]

lol

[crisp silo]

smh

[winged rapids]

anyway keep going

you basically cant do anything and the sqrt is annoying

[crisp silo]

should I substitute now?

with v

[winged rapids]

well i dont see how else you would do it

[crisp silo]

yeah same

Did I make any goofy mistakes?

[winged rapids]

nope

[crisp silo]

wait so is this it?

no way

[winged rapids]

BROW HAT 💀

[crisp silo]

I'm about to give up

I'll take a different approach

[winged rapids]

nah bro but you gotta understand fractions

you cant reduce u^2/u^2-1

if it were flipped, like u^2-1/u^2 you could

but now you cant just cancel em like that

try with actual numbers like 1 or 2

broski this is like 9th grade youre finna die if you dont remember this now

[crisp silo]

I don't know nothing about no grades

I'm not American

I'm trying to get into a university

[winged rapids]

lol

oh nice

[crisp silo]

and I have to study math

so I'm learning

or at least trying to...

[winged rapids]

😮

then you dont have to stress about it

just look you cant really cancel the terms

[crisp silo]

yeah, I got that figured out by now

but what CAN I do?

[winged rapids]

u^2-1 can become (u+1)(u-1) and the top does not have a u+1 or a u-1, so nothing cancels

you can do a little trick to make it into a partial fraction quickly

well

in the right form*

[crisp silo]

what is it?

[crisp silo]

it's 2v^2 on the numerator but I'm guessing I can move it over to the left of the integrate

right?

so the whole thing would now be multiplied by 4

[winged rapids]

yep yep

[crisp silo]

is this now integrable?

I forgot the dv on the right

[winged rapids]

man this integral is hard cuz you have to manipulate it a lot to get to the right form

[crisp silo]

I decided to cheat a bit and see from the video it's from how they solve it

[crisp silo]

they make the first substitution as 1+sqrt(x)=u^2

[winged rapids]

that probably makes it easier since then youd only have to do one substitution

[crisp silo]

better than three

[winged rapids]

they basically did both of the substitutions in one go

yeah

[crisp silo]

I might do it that way because I think going deeper this route is not gonna lead me anywhere

I'm too tired for this, anyways

I'll solve it tomorrow

thanks for the help again

.close

[devout snow]

Channel closed

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[winged rapids]

no man you get to the same place anyway

your welcome though, have a nice day

[devout snow]

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[sturdy gate]

struggling to understand why the answer for C is 1/2

[wicked turtle]

C includes two possibilities:

H followed by T

or T followed by H

each one has probability = ?

[sturdy gate]

Ah gotcha, I undestrand now haha

thank you!

.close

[devout snow]

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[bright burrow]

How do i show the position vector of point A is 0i +bj + ck

this is what i had done

[devout snow]

@bright burrow Has your question been resolved?

[bright burrow]

<@&286206848099549185>

[sick fulcrum]

PA is perpendicular to yz and PB is perpendicular to zx?

[pastel pasture]

The irony

[sick fulcrum]

ehh

the question is phrased so weirdly

[bright burrow]

Yes

[bright burrow]

If i can show this properly the question is done

[sick fulcrum]

I'm trying to recall the equation of plane yz

[bright burrow]

x=0

[sick fulcrum]

But the idea is you want to

show pa is parallel to the normal vector of yz

sorry I'll take a closer look in a bit

(assuming no one helps)

[bright burrow]

If x=0 is the equation of plane yz, then the normal vector of yz is i +0j+0k?

[sick fulcrum]

hmm

yea

[bright burrow]

And pa should be some scalar times the normal vector of yz?

Yea i think i got it

Cuz then 2t+2-b=0

2t+2=b

And i get c that way too so A (0,b,c)

[sick fulcrum]

awesome

[bright burrow]

The way i thought was that the normal vector would be lamba i + mu k, since the plane is parallel to y axis, and then if i write the equation of the plane using (r - a).n=0, r being pos vector of a general point, a being pv of a point on the plane and n being the normal vector of the plane
The coefficient of y becomes 0
And then i use this

im asking if this is the correct thought process for this

Alright thanks

.close

[devout snow]

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[nocturne cape]

A group of 100 students were tested in French, English and Mathematics.

Of these,
74 passed French,
65 passed English,
77 passed Mathematics,
at most 47 passed French and English,
at most 51 passed French and Mathematics,
at most 57 passed English and Mathematics.

What is the maximum number of students who passed all 3 exams?

[pastel pasture]

Draw a Venn diagram

[nocturne cape]

I think the maximum's 100 cause
n≤100

[nocturne cape]

What is it ?

[pastel pasture]

You know

The overlapping circles

Like you would in sets

[devout snow]

@nocturne cape Has your question been resolved?

[rain karma]

wouldnt it just be 47

[vast rain]

not necessarily

[rain karma]

why not?

[devout snow]

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[foggy crater]

ok so ehhhhhh im having sum hard time with arithmetic progression

[foggy crater]

All info i have is

a6-a4=10

"find the difference of the progression"

idk how you say that in english

[ancient crow]

could you send the question

[foggy crater]

It's in Bulgarian

so uh, all i can do is

[ancient crow]

its fine

[foggy crater]

Google Translate

[ancient crow]

ok

it will translate correctly

[foggy crater]

For arithmetic progression, it is known that a6-a4=10. find the difference of the progression.

[wooden wraith]

Do you know what an arithmetic progression is?

[foggy crater]

yep

d=a2-a1
a2=a1+d
a3=a2+d etc.

[wooden wraith]

Right

so

if a6-a4 = 10

Then what is d?

[foggy crater]

yeah thats why this is hard for me...

i just dont understand what i have to do, I know that i need to find "d" i just dont know how

[ancient crow]

send a4 to right side

a6 = 10+a4

[foggy crater]

oooh

and

[ancient crow]

open them to last form like

[foggy crater]

a6=10+(a5+d)?

wait

pop[s

ops

nope

[ancient crow]

crimeful equations**************

is this true idk

i didnt learn a formula for this

[foggy crater]

I have missed the last 2 weeks from school cuz i was sick, soooo...

[ancient crow]

they should be cancelling and remain will be difference

write a6 and a4 in different form so they can cancel each other

hope you understand

[foggy crater]

ehhhh nope

im sorry

[ancient crow]

ok

ill try something else

[foggy crater]

a5+d=a4+10... ?
idk im experimenting

[ancient crow]

yes

also

a5 equals a4+d

[foggy crater]

a4+d+d=a4+10

d+d=10

...?

[ancient crow]

yep

[foggy crater]

holy

[ancient crow]

i was trying to write this

lmao

[foggy crater]

aaalright

[ancient crow]

other way is simple

[foggy crater]

yup

danken

thanks*

[ancient crow]

they added 10 4th member to become 6th member

since they are arithmetic

difference is equal

this means they added it twice

you can divide 10 to 2 which is 5

and its the difference

i dont recommend using formula it make simple things harder

[foggy crater]

yeah i know

ah last q

if 2d=10

then d can be

5 or -5

right?

[ancient crow]

nope

[foggy crater]

oh

[ancient crow]

if d was -5

-5 times 2 is -10

(-) x (+) is negative

[foggy crater]

ah yes

ok thats all

thank you very much

[ancient crow]

type .close

to close this thread

[foggy crater]

.close

[devout snow]

Channel closed

Closed by @foggy crater

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[ancient crow]

always

[devout snow]

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[topaz zephyr]

How do I even start is there any way to express AB in terms of the radius?

[cloud remnant]

yes

[topaz zephyr]

how?

[cloud remnant]

do you know the property of chords when they are perpendicular to diameter?

[topaz zephyr]

no except that AE = EB

[cloud remnant]

yes we need that only

we now know that AB is perpendicularly bisected by CD

Now if you would join CA and CB

you see that CE is the altitude which divides AB in 2 halves

that means if you take only AEC triangle you can form the equation of AE using trignometric functions

[topaz zephyr]

ah

thanks a ton bro

[cloud remnant]

np

[devout snow]

@topaz zephyr Has your question been resolved?

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[slim rivet]

Can someone help with part b? I always struggle to understand and visualise how to find k

[slim rivet]

part a gave me two roots, one of which is repeated

[sonic smelt]

Generally the graph of f(x - k) is the same as the graph of f(x) except it's shifted to the right by k units

[pastel pasture]

He's back

[sonic smelt]

Meaning that one of the stationary points here got moved to the right by k units and became (1, 0)

[sonic smelt]

Who?

[pastel pasture]

the Queefking

[slim rivet]

Okay

[pastel pasture]

If you think about it, k is what you'd get at x = 0

Basically it's your y intercept

The higher it is, the more up your graph is

And vice versa

[slim rivet]

and if i know what x=0, then i sub it in?

[pastel pasture]

Sorry?

[slim rivet]

i'm trying to understand how to sub it in to be able to solve for k

[sonic smelt]

First, which of the stationary points, do you think, got moved to (1, 0)?

[pastel pasture]

Oh wait k isn't the constant term

[slim rivet]

well, having 6, and -2, as the stationary points, -2 is a repeated root

and that means

the -2 has been shifted?

[sonic smelt]

Yeah shifting the graph to the right by k units resulted in (-2, 0) moving to (1, 0)

[slim rivet]

by three places

[sonic smelt]

Can you see what k is?

[slim rivet]

3?

[sonic smelt]

Right

[slim rivet]

wait how do i know its from -2, and not 6

[sonic smelt]

x = 6 isn't a stationary point

[slim rivet]

no but its a root?

[sonic smelt]

Yes

And we're talking about stationary points

[slim rivet]

oh i see

okay thats much clearer, thanks guys

.close

[devout snow]

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[mild summit]

is this a typo or what does the three dots mean in the bottom right corner

[mild summit]

why are they not horizontal

[crystal rune]

they just represent the diagonal elements

[wooden wraith]

The table extends both down and to the right

[devout snow]

@mild summit Has your question been resolved?

[devout snow]

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[rich grove]

quick explanation of taylor series?

[rich grove]

i can use it to solve the problem above but i dont understand what a is supposed to represent

[wooden veldt]

the a in the taylor series equation is just the point at which you want to expand the function f

[rich grove]

so in the first picture, why should i equate a in the series to a in the x of f(x)?

[wooden veldt]

well just by seeing that you want to end up with an "f(a)" term

so you should expand f about a

[rich grove]

i see

sounds good ty

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[rocky iris]

Can you even find a function that represents this graph?

[knotty bolt]

,rccw

[knotty bolt]

somehow, could be a 3rd degree polynomial

[rocky iris]

I think it's more likely a 4 degree polynomial tho

[knotty bolt]

or that

[rocky iris]

Is there any way to know a function by it’s graph?

[pseudo basin]

what are you instructed to do...?

[rocky iris]

Find the function

[pseudo basin]

is that the exact wording that was used?

i really suspect that you may have omitted something.

[rocky iris]

Find the function according to the graph

[knotty bolt]

well, to 'find the function' you can use some regression calculators that eat all your points and try to spit out a function that hits the best mean

it very much depends on how many tools you are allowed to use

[rocky iris]

Ok

Thx

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[boreal leaf]

Given the position function s(t)=4t3–6t2+10, which of the following is true?

Question 18 options:

a)

s(0) = 0

b)

v(0) = 0

c)

a(0) = 0

d)

none of the above

[boreal leaf]

i got b

.clode

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[vestal loom]

I have stuck at this one I did find its integral but It dose not look over 0 if the n is in Z it does if n is >0

[vestal loom]

here is where I ended up with the integral

did it by parts

[supple knot]

is that supposed to be e

[vestal loom]

yes

the integral is from e to e^2 aswell

[stone stump]

what is Z^* ?

[vestal loom]

integers without 0

there needs to be an easier way rather than integrating the actual thing , I tried to find an expression similar to that to make an inequality and the integral of the inequality I make to be 0

[stone stump]

I mean the integrand is never negative over the domain, is it?

[stone stump]

and also I think this expression should always be positive

[vestal loom]

if I factorize I end up here and it does look that it could go negative

and I keep on looking over it to find where I could have messed up

[stone stump]

does it?

just roughly, if n is negative then e^(n+1) is absolutely tiny, so times that by 2n+1 it's still essentially nothing

and then you are subtracting n (which is negative) so really you are adding something

you could maybe have problems for n=-1, -2, -3 or so but after than e^(n+1) is way too small

[vestal loom]

let me see if I can graph it

you are right

it just touches 0 in x=-1

I guess I can derivate it and prove it is always equal and greater than 0

[devout snow]

@vestal loom Has your question been resolved?

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