help-13

[cinder saddle]

I will double check

Oh yes it is

So since of theta is (2sqrt2)/3

For sin

What do i do for b c and d❓

[dire geode]

do you know $\tan = \frac{\sin}{\cos}$

[wraith dagger]

riemann

[cinder saddle]

Yes

Is tan 2sqrt 2❓

[dapper forum]

Bro's the type of guy to cancel the d's in dy/dx = y/x

[cinder saddle]

Is sec 3❓

How do i do d❓

[dire geode]

,calc sin(acos(1/3))

[wraith dagger]

Result:

0.94280904158206

[dire geode]

,calc 2 sqrt(2) / 3

[wraith dagger]

Result:

0.94280904158206

[dire geode]

sec = 3 yes

use $\csc = \frac{1}{\sin}$ for d

[wraith dagger]

riemann

[dire geode]

and yes

[cinder saddle]

Csc=(1/2sqrt2)/3

Csc=3/2sqrt2

But how doni do the 90-theta

[dire geode]

$\sin(90 - \th) = \cos(?)$

[wraith dagger]

riemann

[cinder saddle]

I do not know

[twilit escarp]

you can draw it to find

[cinder saddle]

I dont know what to draw

[deep sparrow]

hope this will make you understand the identity

[cinder saddle]

That makes sense i guess

What so i do with that info❓

Do i need to know the value of theta❓

[deep sparrow]

uhhh?

this?

[cinder saddle]

Im confused

[deep sparrow]

if csc = 1/sin, isn't csc(90-x) just 1/sin(90-x)?

[cinder saddle]

Is x theta❓

[deep sparrow]

same thing, i can use whatever i want as long as you understand what that is

so yea, x is theta

[cinder saddle]

What do i do with 1/90-theta now❓

The answrr key says csc(90-theta)=3

.close

[cedar kiln]

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[tawny geode]

Hello guys i need help to understand this, this is integration

[tawny geode]

I don't understand from the 1/3 tranformed into t^-1/3

[restive hedge]

are you asking why $\sqrt[3]{t^2}=t^{2/3}$?

[wraith dagger]

LayneTheAndroid

[tawny geode]

I'm asking why is 1/3 = t^-1/3

[restive hedge]

it isn't

[tawny geode]

And also the circled stuff like how did they become that

[restive hedge]

is it this part

$2\frac{2}{\sqrt[3]{t}}\frac{1}{3}=\frac{4}{3}t^{-\frac{1}{3}}$

[wraith dagger]

LayneTheAndroid

[tawny geode]

Yes

[restive hedge]

okay it's not that the 1/3 =t^(-1/3)

forget about the $\frac{1}{\sqrt[3]{t}}$ for now

[wraith dagger]

LayneTheAndroid

[tawny geode]

Alr

[restive hedge]

To get that 4/3 you just multiplied all the non-t numbers, i.e. $2\cdot{2}\cdot{}\frac{1}{3}=\frac{4}{3}$

[tawny geode]

Yes

[wraith dagger]

LayneTheAndroid

[restive hedge]

Then $\frac{1}{\sqrt[3]{t}}=\frac{1}{t^{1/3}}=t^{-1/3}$

[wraith dagger]

LayneTheAndroid

[restive hedge]

does that make sense?

[tawny geode]

Yeah ik that but where did the 1/3 go

The second one

[restive hedge]

That 1/3 is the 3 on the bottom of 4/3

[restive hedge]

this step

[tawny geode]

That was another 1/3

There is after one another

[restive hedge]

I'm confused.

[restive hedge]

is this part clear?

[tawny geode]

Yes

So we have 22/3√t and after it1/3

[restive hedge]

like the +1/3 at the end?

[tawny geode]

That's+1/9

[restive hedge]

Okay so there are three terms in the integral

The term with the $\frac{1}{\sqrt[3]{t^2}}$

The middle term (which we've been talking about) with the $\frac{1}{\sqrt[3]{t}}$

And the last term that has no $t$ which I now see is +1/9

[wraith dagger]

LayneTheAndroid

[restive hedge]

going between the expanded integral and the simplification of those terms, which are we talking about?

(i.e. the second equals sign)

[tawny geode]

The fourth one

Let me take a pick

Pic

[restive hedge]

okay

[tawny geode]

Right?

[restive hedge]

I'd count 2 and 3 together since everything there is multiplied together

[restive hedge]

and that's what we dealt with here

[tawny geode]

Oh sorry then

Omg I'm so sorry you are right

[restive hedge]

no worries

[tawny geode]

What about the last part

[restive hedge]

the 1/9?

or the green stuff?

[tawny geode]

The green stuff

[restive hedge]

I'm a bit confused what the point of that is but it's not incorrect. Why does it go back and forth between exponent form and surd form?

[tawny geode]

No idea my teacher does it that way for some reason

[restive hedge]

i.e. $\frac{4}{3}\cdot\frac{1}{\frac{2}{3}}=2$ so it's not wrong

[wraith dagger]

LayneTheAndroid

[restive hedge]

oh, I guess it's to check your solution because you can differentiate it easily to see if you get back what was in the integral

[tawny geode]

Yeah man, ofc I'm a pro too a saw it without a doubt 🤣

[restive hedge]

basically I think your teacherjust wants you to express things in the form a*t^b/b because if you differentiate that it's just a*t^(b-1) which you can compare to what's in the integral

[tawny geode]

So how did we get the last form

[restive hedge]

... well to be honest, the steps almost seem backwards to me

[tawny geode]

Because my teacher does it this way, and everyone online gets confused on my teacher's stuff

[restive hedge]

If you integrate $\frac{4}{3}t^{-\frac{1}{3}}$ then you you get exactly the expression in green

[wraith dagger]

LayneTheAndroid

[restive hedge]

which can be simplified to theone the arrows point to

i.e. just use the usual rule for integrating something of the form at^b and you should see what I mean

[tawny geode]

Yeah man idk what you mean by that

[restive hedge]

do you know how to integrate $\frac{4}{3}t^{-\frac{1}{3}}$

[wraith dagger]

LayneTheAndroid

[tawny geode]

No idea but it is usually something like 1/n+1 times x^n+1?

[restive hedge]

yes. you increase the power by one and then divide by the new power

[tawny geode]

Yeah idk why but mine isn't getting to that

[restive hedge]

could you show me your steps?

[tawny geode]

Like on paper on just write it here?

[restive hedge]

either

I can't point out what went wrong unless I see the working

[tawny geode]

Alright one sec

Oh i think i know what went wrong

Idk what to do with 4/3

Because it has nothing to do with n like in the previous one

[restive hedge]

it just multiplies the term

so like

$\int{}x^n=\frac{x^{n+1}}{n+1}$

$\int{}ax^n=a\frac{x^{n+1}}{n+1}$

[wraith dagger]

LayneTheAndroid

[tawny geode]

Oh right

Yeah it is that

[restive hedge]

(in fact $\int{}af(x)=a\int{}f(x)$)

[wraith dagger]

LayneTheAndroid

[tawny geode]

And it becomes the one that it points to?

[restive hedge]

yes it simplifies to that

and showing that is an exercise in multiplying fractions

[tawny geode]

Sooo how did we get that? 😅

[restive hedge]

so you're asking why

$\frac{4}{3}\cdot{}\frac{t^{\frac{2}{3}}}{\frac{2}{3}}=2\sqrt[3]{t^2}$?

rip

let me try again

[tawny geode]

Ofc

[wraith dagger]

LayneTheAndroid

[tawny geode]

That's right

[restive hedge]

are you happy with why $t^{\frac{2}{3}}=\sqrt[3]{t^2}$?

[wraith dagger]

LayneTheAndroid

[tawny geode]

Happy?

[restive hedge]

like you understand it

[tawny geode]

I accept it as it is yes I understand it

[restive hedge]

okay so the only thing is to show that

$\frac{4}{3}\cdot{}\frac{1}{\frac{2}{3}}=2$

[wraith dagger]

LayneTheAndroid

[tawny geode]

This would be the help?

[restive hedge]

well if you know

a) $t^{\frac{2}{3}}=\sqrt[3]{t^2}$?

and

b) $\frac{4}{3}\cdot{}\frac{1}{\frac{2}{3}}=2$

then is it clear that

$\frac{4}{3}\cdot{}\frac{1}{\frac{2}{3}}t^{\frac{2}{3}}=2\sqrt[3]{t^2}$?

[wraith dagger]

LayneTheAndroid

[tawny geode]

Oh

Now that you put it like that

Yes

[restive hedge]

great

[tawny geode]

How about the one before that?

[restive hedge]

you know what steps do to because we did the middle one

integrate it (you should get the first term on the last line)

then simplify it using rules for simplifying fractions

[tawny geode]

So the t^1/3 will be okay but how about that 12 like not 4/3

[restive hedge]

so $4\frac{1}{3}=\frac{4}{3}$

But that isn't what you have here. You have

$4\frac{1}{\frac{1}{3}}$

[wraith dagger]

LayneTheAndroid

[restive hedge]

i.e. 4 times (1 divided by 1/3)

[tawny geode]

Oh oookay

[restive hedge]

you can use the rule $1/(a/b)=b/a$

[wraith dagger]

LayneTheAndroid

[tawny geode]

Yeah thanks a lot man

You are great

[restive hedge]

no worries. hope this helped.

I think you should definitely practice this kind of algebraic manipulation outside of the context of integrals. ideally using these rules and making these simplifications should be second nature when you do calculus because otherwise it just slows you down and distracts from learning the calculus itself

but you did understand it fairly quickly, so maybe just a quick refesher

[tawny geode]

Yeah ik , but we just started and i want to get it right, also will definitely practice

[restive hedge]

great, best of luck!

[tawny geode]

Thanks a lot🙏

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[cedar kiln]

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[acoustic hazel]

i need help with financial maths

[cedar kiln]

@acoustic hazel Has your question been resolved?

[flint cape]

(Not entirely sure if I can help here, but) You gotta ask a more specific question than that

[cedar kiln]

@acoustic hazel Has your question been resolved?

[cedar kiln]

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[feral pumice]

I need help with algebra. I'm sorry for not knowing what exactly this is called because i don't know the words in english but basically i could use help with stuff like quadratic equations, factoring, high degree polynomial functions and inequations as i need to learn/improve on all.

[prisma pike]

Sounds like a job for khan academy

https://www.khanacademy.org/

I think they have lessons in other languages as well

If you want you can send come questions here too

[dusky forge]

Yah we can help

[feral pumice]

I'll check it out. thanks.

[cedar kiln]

@feral pumice Has your question been resolved?

[feral pumice]

What course should i do?

[prisma pike]

Algebra 1 or algebra 2

[feral pumice]

I'm doing algebra 1 rn but this seems to be different to what i was doing and way easier

[prisma pike]

I think those have your topics

[prisma pike]

Maybe you're at the start only

[feral pumice]

Yeah i'll see.

[cedar kiln]

@feral pumice Has your question been resolved?

[feral pumice]

Should i say yes for now and ask for help again if i need it?

[cedar kiln]

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[manic kelp]

In a right triangular prism, the sides of the base are
13 cm, 21 cm, and 20 cm. A section is drawn through the lateral edge of the prism and the average height of the base along
the length, the area of ​​which is
63 cm^2. Find the volume of the prism.

[manic kelp]

I found the area of the base triangle (ABC), but I don't know how to find h (the height)

[soft holly]

Are 13, 14, and 15 the sides of the right triangle part

[manic kelp]

13 20 21 sorry

[soft holly]

13, 20, 21 arent valid sides of a right triangle

[manic kelp]

13 20 21 are the sides of the base triangle

[manic kelp]

right triangular prism means the prisms height isnt slanted, does not mean it has to be a right triangle (aka 90 degree angle)

do you get what I mean?

[manic kelp]

basically means it cannot look like this

because the "height" is slanted

therefore it cannot be a right prism

[manic kelp]

im confident I did this correctly I do not know how to find the height from here

[manic kelp]

<@&286206848099549185>

[cedar kiln]

@manic kelp Has your question been resolved?

[cedar kiln]

Channel closed

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[manic kelp]

.reopen

[cedar kiln]

✅

[manic kelp]

<@&286206848099549185>

hello, is this related to my question?)

[earnest idol]

Please open a new channel

[spare kettle]

im trying to understand your question

[manic kelp]

the whole thing or just what I'm having trouble with?

[severe pewter]

Hey sorry, I thought I created a channel but apparently I did not

[manic kelp]

no worries, hopefully you find a solution!

[spare kettle]

actually the whole thing

[manic kelp]

im given a shape (right triangular prism)

[spare kettle]

i dont understand how they cut it actually

[spare kettle]

yes with base dimensions 13 20 21

[manic kelp]

oh yeah i had trouble with that part too

[spare kettle]

you need to find its height

ill look into it

[manic kelp]

i have 13 20 21, it's cut through the base side that is 20

its translated so maybe theres smt off with it

but what I drew is correct and I found the area of the triangle so all I need is heaight

[spare kettle]

uhh i still don't get it

like which of the base it is cutting with

so we can find the dimensions of that rectangle

one of the dimensions of that rectangular cross section is the height which we have to find

other is smth like altitude of one of the base or smth

[manic kelp]

the crossed out part we know it's area does that not help w anything?

[spare kettle]

we have to use that area to find the height

it looks like a rectangle doesn't it?

[manic kelp]

yea

[spare kettle]

and its dimensions looks like to be altitude of one of the base the height of the prism

i got it

@manic kelp

[manic kelp]

yea?

[spare kettle]

got it

you see one of the triangles

with side 20 cm

its height is actually one of the dimensions of the rectangle

and the another dimension is the height of the prism

[manic kelp]

lets assume i can find that side then
ill try what you're saying one sec
ik the answer i need to get is V=630

[spare kettle]

you can find the height of side 20 cm and then substitute that height in area of rectangle formula to find the height

you'll get 5 cm height

height prism

and for base triangle with side 20 you can calculate its height that will be around 12.6

[manic kelp]

wait ill name it so its easier to talk abt sides)

[spare kettle]

yess

[spare kettle]

yeah you you can find AK

[manic kelp]

From AKC?

[spare kettle]

nah

yk the area of triangle

from the area of triangle you can find AK

reverse calculation of 1/2 base height formula

[manic kelp]

126=1/2h

or wait what

[spare kettle]

126 = 1/2 b h

[manic kelp]

126=10h

[spare kettle]

126 = 1/2 20 h

[manic kelp]

yea ok

[spare kettle]

yea

[manic kelp]

h=126:10
?
idk i suck ass w this thing

12,6

[spare kettle]

12.6 yes ur cottect

correct

[manic kelp]

so then 12,6 times 2 cus the two sides thats 25,2

[spare kettle]

now you have one of the dimensions of the rectangle

[manic kelp]

63-25,2

[spare kettle]

bro you finding area

not perimeter

😭

[manic kelp]

huh

ak=a1k1

[spare kettle]

area of region is given

[manic kelp]

oh

[spare kettle]

you can use area of rectangle formula to find height of prism now

[manic kelp]

63=12,6*x

[spare kettle]

yessir

[manic kelp]

x=63:12,6
?

how do ik when to divide or multiply

[spare kettle]

thats 5

[spare kettle]

uhh it depends on problems you'll learn with more practice

[manic kelp]

im in my last year of high school i still haven't learned🥹

but yea i got it we have 5 the height and ik the base area so 126*5 right and thats 630 the volume i was supposed to get

tysm

[spare kettle]

don't worry i was bad at math till my second last year of highschool too

[spare kettle]

yeah thats it

[manic kelp]

i like algebra more i hate rewriting formulas

[spare kettle]

same i like algebra more too

[manic kelp]

another question, could I have found this from akc? @spare kettle

[spare kettle]

yes you could have

but need trigonometry

[manic kelp]

oh so i couldn't assume kc is 10?

[spare kettle]

and its exactly a right angled triangle so

[manic kelp]

or any other number

[spare kettle]

yeah

[manic kelp]

how would i solve it w trigonometry I mean i have a right angle and side can i do anything w that

[spare kettle]

its not a right angle actually

i think

[manic kelp]

nah how else would it be sliced then no..?

[spare kettle]

uhhh well it is right angle but

you can't exactly find the

base lenght

cuz its not cutting at mid point

[manic kelp]

thats not smt i can assume?

[spare kettle]

you can't assume on midpoint

because its not cutting at midpoint

if it was an isosceles triangle then you could have

[manic kelp]

and then ig i cant just assume it to be 12 or smt
how would i solve this w trigonometry though or is that smt you'd rather not get into, i dont need the actual solution just like the general direction of what steps to take in that case

[spare kettle]

you can solve this w trignometry

you do have a right angled triangle

whose 1 side yk

and 1 angle you can find

as well

using the cosine rule

but its rather a longer solution

but its still doable completely

not hard at all

[manic kelp]

which angle is right?)

k?

[spare kettle]

the akc

yeahh

[manic kelp]

yea ok got it

tysm

im somehow really good at looking for harder solutions lol

[spare kettle]

happens.. i got shouted for it 3 times.. in the same class

[manic kelp]

oof

.close

[cedar kiln]

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[cedar kiln]

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[leaden pond]

can someone please help me with these problems?

[hollow totem]

LMNP is a parallelogram, what would turn it into rectangle?

In term of geometry

[leaden pond]

i'm not sure, i'm so confused 😭

[hollow totem]

💀

Whats the definition of parallelogram?

[leaden pond]

a quadrilateral with two different pairs of parallel sides

[hollow totem]

Ok

And for rectangle?

[leaden pond]

also another quadrilateral with two pairs of parallel sides?

[hollow totem]

💀

No

[leaden pond]

oh-

[hollow totem]

Its the same of parallelogram

With 1 key different

1 angle = 90 deg

[leaden pond]

ohh

[hollow totem]

Do u know why is that?

[leaden pond]

because it perpendicular?

[hollow totem]

Not really

[pale dock]

Exponential Functions - Basic I have questions about this can you help me

[solemn elk]

!occupied

[cedar kiln]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[hollow totem]

Go to an empty help channel

[leaden pond]

i'm cooked i don't understand any of this

[hollow totem]

Its basic geometry?

[leaden pond]

the lesson is called Figures in the Coordinate Plane

[hollow totem]

Yes

And it uses geometry

[leaden pond]

yeah

[hollow totem]

Do u know the quadrilateral basis?

[leaden pond]

i'm not sure

[hollow totem]

If a quadrilateral has 1 pair of opposite side parallel, what thats called?

[leaden pond]

idk a trapezoid?? 😭

[hollow totem]

YEP

And parallelogram is just trapezoid but 2 pairs of opposite side parallel

U can think parallelogram is a stricter version of the trapezoid

[leaden pond]

ok

[hollow totem]

Rectangle is just parallelogram with 1 angle = 90deg

[leaden pond]

ok

[hollow totem]

You might say

Thats not true

Rectangle's all 4 angles all equal 90

Not just 1, right?

[leaden pond]

yeah

[hollow totem]

Because of parallelogram definition, opposite angle = each other

So

if 1 angle = 90 deg, the opposite = 90

The others 2 = each other and the sum = 180. Thus each = 180/2 = 90

So u get a rectangle

A rectangle is just a "stricter" version of the parallelogram

[hollow totem]

So

What the correct answer

[leaden pond]

uhhhh

D?

[hollow totem]

YES!

LP perpendicular to PN would make P = 90deg

Which convert LMNP from parallelogram to rectangle

For this question

It already gave u AB and AC

You need to find BC

You can count...

But u should use the distance formula in case in your test, u encounter something hard

[leaden pond]

is the distance for BC also 10?

[hollow totem]

It is 10 yes

But how?

Did u count it

[leaden pond]

yeah

[hollow totem]

.

[leaden pond]

dw i know the distance formula

so would the answer be D?

[hollow totem]

yep

[leaden pond]

omg tysm, i'm not cooked

[hollow totem]

Use this

[leaden pond]

thankss

how do i close this

[hollow totem]

.close

[cedar kiln]

Channel closed

Closed by @hollow totem

Use .reopen if this was a mistake.

[hollow totem]

Huh?

I can close other....

[plucky owl]

Helpfuls have the ability to close and reopen but don't abuse

[hollow totem]

😈

[cedar kiln]

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• Show your work, and if possible, explain where you are stuck.
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[jolly sail]

One message removed from a suspended account.

[jolly sail]

One message removed from a suspended account.

[sly abyss]

Lock in twin

[jolly sail]

One message removed from a suspended account.

One message removed from a suspended account.

One message removed from a suspended account.

One message removed from a suspended account.

[sly abyss]

Ye

You got this

[jolly sail]

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[sly abyss]

You can do g(-1)

It literally tells you have g is

[jolly sail]

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[cedar lion]

( do you remember what does integration actually means? )

[sly abyss]

no cuh

[jolly sail]

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[sly abyss]

https://tenor.com/view/cat-balloon-shaking-gifdopedrao-gif-18309166828393550457

[cedar lion]

Good, there is another application of integration, think.

[jolly sail]

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[jolly sail]

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[sly abyss]

no but g(x)

[jolly sail]

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[cedar lion]

Area under graph.

[jolly sail]

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[sly abyss]

You gotta flip the thinks tho

Signs

[jolly sail]

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[sly abyss]

• integral from -1 to 0

Because u cant do

Integral from 0 to -1

[cedar lion]

Can you think of how we can find g(-1)?

[sly abyss]

Well you can

But then you’re gonna forget the negative

[jolly sail]

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[sly abyss]

Bro is STILL not locked in

[stoic crystal]

area of a triangle is base times height / 2?

[thick steeple]

Hello

[sly abyss]

😹

[jolly sail]

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[cedar lion]

g(-1) = integration of f(x) with respect to x from -1 to 0.

This means area under graph from x = -1 to x = 0.

Tho, since the upper limit is opposite, the answer might be negative.

[jolly sail]

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[thick steeple]

I can help

[sly abyss]

just always write the lower number of this bottom

And if you swap the places like here

[cedar lion]

Yes sir.

[sly abyss]

Throw a negative outside

[jolly sail]

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[sly abyss]

no bruh

Area

[cedar lion]

No. You didn't integrate.

[sly abyss]

Area of a triangle

[jolly sail]

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[cedar lion]

Integration lowkey means area under graph. ✨

[sly abyss]

Sir are you distrusting college board ap frqs 🤓

[thick steeple]

Focus on one thing at a time.

Find the definite Integral, THEN find g(1).

[cedar lion]

NO. Integration means area under graph.

[jolly sail]

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[cedar lion]

This.

[jolly sail]

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[sly abyss]

Alright they got this

[cedar lion]

👏👍

[sly abyss]

Ima say more one thing just rember on b and c parts to use only the graph f to justify your answers

[jolly sail]

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[thick steeple]

Well, you have to represent that with X

[jolly sail]

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[thick steeple]

Let’s take a pause and start from the beginning. What is f(t)?

[jolly sail]

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[thick steeple]

Yes

[jolly sail]

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[thick steeple]

I believe it involves an absolute value

[jolly sail]

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[thick steeple]

Uh huh

[jolly sail]

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[thick steeple]

You’re on the right track

There’s a constant

The constant is usually f(0) (for single-variable functions)

[jolly sail]

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[thick steeple]

Correct!

[jolly sail]

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[thick steeple]

Now you’re going to Integrate that

[jolly sail]

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[sly abyss]

Bro what

Stop

Just do the area under the curve

Don’t find the function

That’s such a waste of time

[jolly sail]

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[sly abyss]

???

[jolly sail]

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[sly abyss]

Ye

But don’t forget the negative

[jolly sail]

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[sly abyss]

Ye but

Its g(x)= integral 0 to x f(t)dt

[jolly sail]

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[sly abyss]

Yes

You can do the rest bro

[jolly sail]

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[sly abyss]

2nd ftc

[jolly sail]

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[cedar lion]

Differentiate both sides, with respect to x.

[jolly sail]

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[jolly sail]

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[cedar lion]

You'll need to know function for this, or there could be another approach.

[jolly sail]

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[cedar lion]

They gave you a graph. You can make function from this.

[jolly sail]

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[sly abyss]

What

Are you talking about

[jolly sail]

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[sly abyss]

Bro

[jolly sail]

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[sly abyss]

g prime = f(x)

….

[cedar lion]

Another approach is to actually make the function, but for parts, piescwise. Since as you can see the graph changes.

[sly abyss]

ye hakken if you do that

You run out of time

[cedar lion]

Yeah.

[sly abyss]

For the other 2 frqs

[jolly sail]

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[sly abyss]

kenzo

[cedar lion]

Do you know @jolly sail what is

Wait

[sly abyss]

you don’t need the function

Look

Bro

[jolly sail]

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[cedar lion]

This,

[jolly sail]

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[sly abyss]

???

[jolly sail]

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[sly abyss]

No

[jolly sail]

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[sly abyss]

g prime (x)= f(x) then

Ask just find f(-1)

And the rest

I know you can do

[jolly sail]

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[sly abyss]

Because we spent like 3 months of derivatives

On

In November

[jolly sail]

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[sly abyss]

And October

And September

[jolly sail]

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[sly abyss]

Everything else is just old super basic stuff

I gotta sleep now

You got it

[jolly sail]

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[sly abyss]

It’s legit just basic knowledge

You took an entire semester of calc

[jolly sail]

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[cedar lion]

It's fine.

Do you know your problem now?

Is it solved?

!status

[cedar kiln]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[jolly sail]

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[sly abyss]

Everything after what just did

Is derivatives

[jolly sail]

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[sly abyss]

not integrals

[cedar lion]

Good.

Find g''(-1) now.

[jolly sail]

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[cedar lion]

yes.

[jolly sail]

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[cedar lion]

Wht is f'(x).

It's the slope, right?

Remember?

[jolly sail]

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[cedar lion]

How? Explain.

[jolly sail]

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[cedar lion]

Good.

Next problem.

[jolly sail]

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[cedar lion]

Yes.

[jolly sail]

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[cedar lion]

It is asking us where g(x) is increasing.

[jolly sail]

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[cedar lion]

And g(x) is integration of f(x).

[jolly sail]

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[cedar lion]

Integration of f(x) means..area under graph.

[jolly sail]

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[cedar lion]

G(x) increases. Integration of f(x) increases. Area under graph increases.

[cedar lion]

Not necessarily. But it should just increase.

You know if a value move from. -100000 to -10 it is still increasing, while still being negative.

[jolly sail]

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[cedar lion]

Not necessarily. Area below x axis is considered negative.

[jolly sail]

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[cedar lion]

"graph"??

[jolly sail]

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[cedar lion]

Area under graph you mean

[jolly sail]

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[cedar lion]

No, the area under graph actually decreases from -1 to 0.

You see, as you move from -1 to 0, you can see the area under graph reducing, can you visualise

[jolly sail]

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[cedar lion]

Yes! It is increasing in that part.

But if you move ahead from 1

The area starts decreasing, as we're getting area from below x axis now!

[jolly sail]

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[cedar lion]

Now let's check what happens in (-2, -1)...

[jolly sail]

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[cedar lion]

You see, when we check the area under graph from (-2,0) it's 0.

Why? Because the area below x axis and above x axis is same.

[jolly sail]

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[cedar lion]

Can you see it?

[jolly sail]

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[cedar lion]

Hmm, let me help you

Let me draw something

One moment

[jolly sail]

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[cedar lion]

@jolly sail

[jolly sail]

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[cedar lion]

The net area is 0

Clear?

Understood?

[jolly sail]

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[cedar lion]

Now, move that dashed line from y = -2 to something more closer to -1

( pic incoming )

@jolly sail

What do you think, is area positive now or negative?

The area below x axis just decreased as we moved towards -1, while area above x axis is same as before!

[jolly sail]

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[cedar lion]

Reasoning?

[cedar lion]

Can you see that?

[jolly sail]

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[cedar lion]

Not necessarily.

[cedar lion]

It will increase until its x = -1.

After that, it will decrease until its x = 0

Move that strip and check

Visualise it

[jolly sail]

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[cedar lion]

Yes!

[jolly sail]

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[cedar lion]

As the area forces from above x axis and below x axis were equal 🚓🚨

[jolly sail]

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[cedar lion]

The area from below x axis is decreasing!

[jolly sail]

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[cedar lion]

And when x belongs to (-1, 0)

There is no area from below x axis.

[jolly sail]

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[cedar lion]

Note that we're doing this for an interval, where maximum is 0.

As we are currently not looking at the graph past 0.

[cedar lion]

Because of lower limit in the integral itself.

[jolly sail]

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[cedar lion]

So move the strip, and tell me all the intervals where area is increasing!

[jolly sail]

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[cedar lion]

You know, answer me.

[jolly sail]

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[cedar lion]

For interval, (-2,-1) wht is it.

🤔

[jolly sail]

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[cedar lion]

It really depends

[cedar lion]

No

How is it zero

[jolly sail]

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[cedar lion]

There is clearly some area

[jolly sail]

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[cedar lion]

Yes

[jolly sail]

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[cedar lion]

For x belongs to (-2,-1)

What is it

[cedar lion]

It is decreasing, good!

The area is becoming negative

What about interval (-1,0)?? @jolly sail

[jolly sail]

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[stoic crystal]

are you guys in a)?

[jolly sail]

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[cedar lion]

Look at this

(-1,0)

[jolly sail]

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[cedar lion]

Don't consider that region, just consider the (-1,0)

[jolly sail]

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[cedar lion]

..

(-1,0)

Look at itm

Carefully

Carefully

[jolly sail]

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[cedar lion]

Ues

[jolly sail]

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[cedar lion]

Slowly move from x = -1 to x = 0... @jolly sail

Look at the area..

The triangle becoming BIG

[jolly sail]

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[cedar lion]

no.

The triangle is increasing???

The triangle is getting bigger???

[jolly sail]

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[cedar lion]

Yeah

[jolly sail]

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[cedar lion]

It is getting bigger...?

[jolly sail]

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[cedar lion]

See??

[jolly sail]

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[cedar lion]

And area is bh/2

[jolly sail]

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[cedar lion]

As h increases

[jolly sail]

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[cedar lion]

Bh/2 increases

[jolly sail]

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[cedar lion]

Area increases

our part of anseer

(-1,0)

Area is strictly increasing

https://cdn.discordapp.com/emojis/1335340422142103623.png?v=1

[jolly sail]

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[cedar lion]

Find me the other interval using same concepts.

Where the area is strictly increasing.

[jolly sail]

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[jolly sail]

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[cedar lion]

Good.

[jolly sail]

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[cedar lion]

Yes.

It is like

Unwrapping a triangle

You see

[jolly sail]

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[cedar lion]

Yes!

[cedar lion]

The area starts decreasing

I think you got your answers now.

!done

[cedar kiln]

If you are done with this channel, please mark your problem as solved by typing .close

[jolly sail]

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[cedar lion]

No worries. ^^

[jolly sail]

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[cedar kiln]

Channel closed

Closed by @jolly sail

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

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

given that 3^(1/x)=7^(1/y)=63^(1/z), express z in terms of x and y

[frank spruce]

approach: took logs on both sides but stuck after that

[tropic oxide]

let $a$ be the common value of all three of these quantities

[wraith dagger]

ann.in.a.teacup

[tropic oxide]

then $a^x = 3, a^y = 7, a^z = 63 = 7 \cdot 9...$

[wraith dagger]

ann.in.a.teacup

[frank spruce]

why a^x=3?

wait nvm got it

thanks

.close

[cedar kiln]

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Closed by @frank spruce

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[cedar kiln]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fast forge]

Hey, can someone help me with this dot product? I have A=30, 20º and B=40,120º
I can do the dot product like this AB=30.40Cos(100) and I'm getting -207.37
But I also tried by coordinates, which I think should be (28.190, 10) and (-20, 2sqrt(3)), but I'm getting around -500 here
I don't think there should be a difference, what am i doing wrong??

[fast forge]

oh

[tropic oxide]

A=30, 20º and B=40,120º
what does this notation mean

[fast forge]

nvm

2sqrt3 is incorrect

.close

[cedar kiln]

Channel closed

Closed by @fast forge

Use .reopen if this was a mistake.

[fast forge]

.reopen

[cedar kiln]

✅

[fast forge]

that would be the magnitude and angle

I had somewhere else that for B the y coordinate was 2sqrt 3 but that was incorrect haha

I was just assuming what I had before was correct

but nope

should be around 34, probably that will fix it

but thanks!!

.close

[cedar kiln]

Channel closed

Closed by @fast forge

Use .reopen if this was a mistake.

[cedar kiln]

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Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hollow kiln]

please can someone help me construct this in geogebra?

[hollow kiln]

answer is 4 and the triangle is not rigid, meaning the answer is independent but not completely

ping if help thanks

[soft owl]

Sigma sigma boys

[cedar kiln]

@hollow kiln Has your question been resolved?

[hollow kiln]

? is 9-5 no matter the values

example.. if it was 10 instead of 9 and 4 instead of 5, ? would be 6

[cedar kiln]

@hollow kiln Has your question been resolved?

[cedar kiln]

@hollow kiln Has your question been resolved?

[cedar kiln]

@hollow kiln Has your question been resolved?

[hexed parrot]

yo

@hollow kiln

what are you tryna find

exactly

dotted line?

[hollow kiln]

not trying to find anything

just trying to construct the image in geogebra

[hexed parrot]

<@&286206848099549185> jse this btw when ppl dont eeapond

oh

and why?

[hollow kiln]

to work with it

[hexed parrot]

icl

no clue

havent used geogebra in a minute

[hollow kiln]

its alright

[hexed parrot]

u could ask chatgpt

[hollow kiln]

its pretty bad at those kind of things

[hexed parrot]

helps me sometimes

ight cya

[buoyant latch]

<@&268886789983436800>

[cedar kiln]

@hollow kiln Has your question been resolved?

[steel crest]

how did you prove that?

[steel crest]

i have some ideas, firstly we know that there are 4 degrees of freedom

this means we know 2 points, or a circle and a point on the circle

i feel we should assume the two weirest points, but that leaves one degree of freedom

bo actually it takes 4 degs if freedom

do we know the dashed blue distance?

[hollow kiln]

constructed the problem on any triangle and checked the results

[hollow kiln]

nope

i feel like i dont use geogebra to its fullest ability

this must be constructable

[steel crest]

it is

the locus of G given D is a conic

A is a random point

B is a random point at ditance 9 from A

C is a random point at ditsnace 4 from A

now D is a point at distance 5 from C, E is where DC intersect externagle angle bisector of ABC, DG is the line tangent to the the circle centered at C, and EG is the angle bisector of BEG

Since you know the locus of G, intersect it with the internal angle bisector of ABC

[steel crest]

you can find the conic using any random 5 points, and using conic through 5 points

[steel crest]

that is the incenter

from here you can eaduly find the remaining points

[steel crest]

there probly are better methods, but this is the most obvious one

@hollow kiln

also this is beside the point, but i have seen you post many nice geometry qns, where do you get them?

[hollow kiln]

i was binge solving a lot of geometry problems from wherever i could find them this summer

there was some problems i couldnt solve and i saved them

cant know the exact source but most of them were from small twitter accounts or blog posts

[steel crest]

oh

[hollow kiln]

im pretty sure some of them were from the same source

like these two

maybe you can reverse search and find

9 8 5 problem and its solution is absolutely insane tho

[steel crest]

i liked thr proof type qns more

[steel crest]

hat is it?

[hollow kiln]

lemme send the solution

[steel crest]

actully dont

id want hints

[hollow kiln]

requires a lot of complex

[steel crest]

complex bash?

no synthetic sol?

[hollow kiln]

its in turkish anyways

uses polar lines and harmonics

[steel crest]

oh

[hollow kiln]

9 8 5 makes it special in some way tho

[steel crest]

that is inversion stuff, right?

[steel crest]

hm

[hollow kiln]

yeah

[hollow kiln]

in any case, the red length will be equal to upper tangent length

but when its 9 8 5, B, I and E are colinear

[hollow kiln]

AF=KL

[steel crest]

Oh

[hollow kiln]

solution to this also requires complex analysis

solutions are not by me btw

[steel crest]

Complex analysis as in difficult synth or as in complex bash?

[hollow kiln]

2nd

[steel crest]

Hm

[cedar kiln]

@hollow kiln Has your question been resolved?

[cedar kiln]

Channel closed

Closed by @hollow kiln

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[restive oriole]

https://tenor.com/view/nervous-shy-kermit-terrified-scared-gif-3186014724530266078

hold up a minute 🤨

wait, I'm even more confused

https://tenor.com/view/long-tears-gif-11087877242190144149

[dreamy gale]

What’s wrong

[restive oriole]

Nah, I just have no idea how to start on this, sorry for the spam

[sharp pike]

If I had to guess right off the spot I'd say 0

try to show the rows are linearly dependent

or wait