help-10

[grand arrow]

write it all in terms of sin to cos

u get

[potent hound]

theres no local max

[grand arrow]

oh

[potent hound]

but anyways

u said to write everything in sin cos?

[grand arrow]

yes

u get

[grand arrow]

now u get sin(x)/cos^2(x) + sin(x) = 0

multiply both sides by cos^2(x)

sin(x)+cos^2(x)sin(x) = 0

factor out sin (x)

sin(x)(1+cos^2(x)) = 0

ur solution set is just when sin(x) = 0

[potent hound]

One sec

[grand arrow]

wait is ur original function sin^2(x) + x

then how is ur derivative sec(x)tan(x) + sin(x)

[potent hound]

That was a different problem

Here's the one we working on

C

[grand arrow]

ur on c?

[potent hound]

Yes

I'm just wondering how to solve when derivative is set to zero

[grand arrow]

then my solution set would be correct

sin(x)(1+cos^2(x)) = 0

ur solution is any N that is an integer * pi

just find the corresponding values within ur interval

[potent hound]

Is my work correct here

[grand arrow]

start from sec(x)tan(x)+sin(x)

1/cos(x) * sin(x)/cos(x)+sin(x)

sin(x)/cos^2(x) + sin(x) = 0

now we do
cos^2(x) * sin(x)/cos^2(x) + sin(x) = 0 * cos^2(x)

sin(x)+cos^2(x)sin(x) = 0

$ \sin x(1+\cos^2 x) = 0 $

[potent hound]

yea i got there

[grand arrow]

yeah see how sin(x) is the coefficient

[potent hound]

sinx +sinx*cos^2x

[grand arrow]

whenever sin(x) = 0 the whole thing = 0

so ur solution would be whenever sin(x) = 0

given ur interval -pi/4 -> pi/4

to thats just 0

[potent hound]

so meaning write it in terms like

Yea?

[grand arrow]

yes

[potent hound]

So all I gotta care for is when sin x is zero

[grand arrow]

yes

exactly

but within the given interval

[potent hound]

Ty....

[potent hound]

I still don't understand how I passed trig....

But this is kinda algebra not so much trig.....

🤔

[grand arrow]

it was problematic to devide -sin(x) = cos^2xsin(x) because we assume sin is not zero

thats why factoring made it work

[potent hound]

yea its confusing because theres multiple steps to try to get to ur answer

and most of the time i have no idea if im even getting closer to my answer

.close

[obtuse pebble]

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[obtuse pebble]

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[reef loom]

hi

[reef loom]

this is some grade 9 enrichment

is this correct?

or do i write 2s+1

for a)

[thorny idol]

if L is $3 and S is $2, if the equation was total = L + S this would mean Ms. Daws only many $5 (3 + 2)

you need to consider the number of large bags and the number of small begs that were sold

[reef loom]

you don't have that information

it says u just gotta write an equation

[thorny idol]

what information?

[reef loom]

how many of however sized bags she sold

[thorny idol]

the algebraic equation depends on how many she sold, or else how would you know how much she gained?

that's what a variable is

[reef loom]

so what would u write

[thorny idol]

first you need to create the variables for the number of large bags and the number of small bags

[reef loom]

i put L as large S as small

[thorny idol]

and in terms of these variables, find the formula for how much she earned based on the prices

[reef loom]

2s + 1?

or am i tripping

[thorny idol]

what happen to L?

[reef loom]

i said let s rep the smaller number then let L rep s+1

so it would be 2s+1 or am i tripping

[thorny idol]

if she sold 3 small bags doesn't necessarily mean she sold 4 large bags

[reef loom]

oh u right

so I just put L+S?

[thorny idol]

they're not both $1

you have to consider the prices

[reef loom]

what???

what about the prices?? cant u just tlel me the formula😭

[thorny idol]

!noans

[obtuse pebble]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[thorny idol]

say she sold 4 small bags and 2 large bags, how would you calculate how much she made?

[reef loom]

6s+2

right?

cuz the large bag is only 1 dollar more

[thorny idol]

why

[reef loom]

wdym why

s=2$ L=3$ i can just say 6s+2

the +2 is from large bag

[thorny idol]

try calculating the actual value

[reef loom]

the actual value is 14$ if its 4 small 2 large

i feel like ur tripping

[thorny idol]

say the number of large bags is L, then the money made from selling large bags is 3L

and if the number of small bags is S, then the money made from small bags is 2S, what would be the total?

[reef loom]

yo ur tripping

did u forget ur let x rep or something

[thorny idol]

huh

[reef loom]

ur tripping dude ur completly wrong

rs

[thorny idol]

lol ok do what you want then

[reef loom]

fuh

i stupid

HELP ME

[obtuse pebble]

@reef loom Has your question been resolved?

[reef loom]

yes king

[obtuse pebble]

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[obtuse pebble]

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[sudden whale]

How to do this problem

[fierce elbow]

write the length in terms of breadth or breadth in terms of length and use the formula for preimeter of a recntangle

[sudden whale]

How to do that?

[fierce elbow]

u can suppose one of the them as x and other one as y

and using the given information try to make an equation out of those 2

[sudden whale]

Can you do it on paper it would be more easier to understand

$Only if you can$

[warm shale]

Prithvi Vasan

[fierce elbow]

what exactly do u not understand?

[sudden whale]

I have made an equation and

Length=3B-6?

Is this equation correct

[fierce elbow]

yeah it is

[sudden whale]

Ok what’s the next step

[fierce elbow]

now use those in the formula of perimeter

[sudden whale]

Perimeter of a rectangle?

[fierce elbow]

yeah

[sudden whale]

Length multiplied by breadth?

[fierce elbow]

no thats the area of a rectangle

[sudden whale]

Then what is the formula?

I got confused.

[fierce elbow]

2* length + 2*breadth = 148

that * is multiplication

[sudden whale]

2 multiplied by length+breadth?

[fierce elbow]

yep

[sudden whale]

But I don’t know how to find the length

[fierce elbow]

yeah u use the quadratic to find L

[timid silo]

l = 34

b = 40

[fierce elbow]

....

[timid silo]

SO

[fierce elbow]

u arent supposed to give the answers directly

[timid silo]

L = B-6 ;

[sudden whale]

I wanna understand it

[fierce elbow]

hold on

[timid silo]

PERIMETER = 2(L+B) = 148

[fierce elbow]

u have the value of l = 3b-6 right

then

use it in the formua

[timid silo]

2(B-6+B) = 148

SOLVE

[fierce elbow]

heck u doing bro

[sudden whale]

Wait what type of formula is that?

[fierce elbow]

who are u asking

[sudden whale]

CR7?

I have never heard of that one formula

[fierce elbow]

idk hes gone prolly

[sudden whale]

Yeah I think so

But why os this problem so hard

[timid silo]

I AM BACK

i will send

the ans

[sudden whale]

@fierce elbow can you show the problem in paper

[gloomy vector]

!nosols

[obtuse pebble]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[fierce elbow]

blud

the length is 6 less than 3 times the breadth

not jsut 6 less than the breadth

[timid silo]

oh

😅

i didnt

read

that

[sudden whale]

Wait I think I got the formula I will try by my one and send the steps can you check the answer?

[fierce elbow]

sure

[timid silo]

well

if u dont understand my handwriting

u can aask me bro

[sudden whale]

Here is the steps

[timid silo]

b= 20

l = 54

[sudden whale]

I got different answers

Oh nvm it is the same

[timid silo]

that's what i also did

that is correct lol

[sudden whale]

Really?

[timid silo]

your approach is correct

[sudden whale]

Thanks so much for help

[timid silo]

yea

so

you are studying 6th grade right

[sudden whale]

7 th grade

[timid silo]

yeah

cbse

right

[sudden whale]

No icse

International syllabus

[timid silo]

ok

[sudden whale]

Why’d you ask?

[timid silo]

i remember this when i was studying 6th grade

i did this sum

[sudden whale]

Kook

Cool

I have another complex one can u help me sole. It

[timid silo]

k

[sudden whale]

Here check it I’ll send it

11th one and 12th one

[timid silo]

ook

wait bro

[sudden whale]

Here u go

[timid silo]

anss is correct

[sudden whale]

It is correct?

[timid silo]

yeah

100% correct

[sudden whale]

I can’t believe

[timid silo]

i too studied this in 7th grade

belive me this is easy

bye'

[obtuse pebble]

@sudden whale Has your question been resolved?

[obtuse pebble]

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[trim frigate]

Triple integral over pyramid (actually a tetrahedron?) bounded by planes

Attempting to solve the following problem:

Find the volume of the pyramid with base in the plane z=-9 and sides formed by the three planes y=0, y-x=2, 2x+y+z=2.

I have arrived at the answer of 40.5 but that was incorrect. I imagine my fault lies somewhere in setting the bounds, but I am struggling to see where I went wrong there.

[obtuse pebble]

@trim frigate Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[frigid burrow]

Can you calculate the avg velocity?

[fresh pebble]

uh i do not think so

so v=d/t

[fiery sorrel]

hope you get the solution…

[fresh pebble]

v=(675(2pi))/24300?

[timid silo]

isn't angular velocity just linearvelocity/radius?

[frigid burrow]

!nosols

[obtuse pebble]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[frigid burrow]

That is correct

[fiery sorrel]

Oh i meant for him to check and ask any queiries…

[frigid burrow]

Now tell me do you know a relation between velocity and angular velocity?

[fresh pebble]

v(2pi) ?

[frigid burrow]

Nope

[fresh pebble]

then i got no clue

[timid silo]

no

[frigid burrow]

v = R omega

[frigid burrow]

But you did just give him the solution right?

[fresh pebble]

we didnt learn all that yet

[timid silo]

well

[frigid burrow]

Hmm

[timid silo]

then how you're getting a question of angular velocity?

[fiery sorrel]

I guess…

[frigid burrow]

Omega is angular velocity

[fiery sorrel]

Sorry haha

[frigid burrow]

@fresh pebble what formulas have you been taught about angular velocity?

[fresh pebble]

v = (distance x 2pi)/time idk im doing that right tho

[timid silo]

What

what is 'v'?

[fresh pebble]

velocity

[timid silo]

Angular?

[fresh pebble]

i hope

[timid silo]

bruh

[fresh pebble]

trigonometry too hard man i miss polynomial things

[frigid burrow]

Bro read your notes once

To make sure you have the right formula

[fresh pebble]

uhh gimme a sec lemme find that

delta theta / delta t?

[frigid burrow]

Yup

But that's instantaneous angular velocity

[knotty dome]

well no

f

[frigid burrow]

We need avg

https://tenor.com/view/i-saw-w-gus-fring-gus-gustavo-deleted-gif-25440636

[knotty dome]

i misread ignore

[fresh pebble]

im doomed

[timid silo]

if you're smart you would find the formula yourself

[frigid burrow]

Total theta / total time lol

[timid silo]

lol

[frigid burrow]

Now do you know total time?

[fresh pebble]

24300 seconds?

[frigid burrow]

,w 6hr 45 mins to seconds

[warm shale]

Results provided by WolframAlpha

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Requested by wum.pus.man

[frigid burrow]

Yup

Total angle?

[fresh pebble]

uhh

yeah idk

[frigid burrow]

Hmm

Do you know about number of rotations?

Like what it means?

[fresh pebble]

i think so

[frigid burrow]

Ok so what will be the number of revolutions to cover the total distance?

[fresh pebble]

uh 675 / (35 x 2 pi)

[frigid burrow]

Correct

[fresh pebble]

finally

[frigid burrow]

But take care of units

Like 675 is km

And 35 is cm

[fresh pebble]

true true

[frigid burrow]

Now how much angle in onle revolutions?

One*

[fresh pebble]

675 / 7000000 pi ?

[fresh pebble]

2pi

[frigid burrow]

Wrong

[fresh pebble]

nah like converting to seconds

[frigid burrow]

What is SI unit for distance?

[fresh pebble]

wdym by si

[frigid burrow]

Still wrong

You are converting to meters right?

[fresh pebble]

waiiit would it be 0.675/3500

[frigid burrow]

Nope

1km is how many m?

[fresh pebble]

yeah no idea anymore

1000

[frigid burrow]

So it would be 675000 / 0.35

[fresh pebble]

oh so i just did it the other way around

[frigid burrow]

And 2 pi too

[fresh pebble]

ohhh i see now

[frigid burrow]

kk

[fresh pebble]

cus 675 km = 675000 m

[frigid burrow]

Can you calculate the total angle now?

[fresh pebble]

675000 / (0.7pi) = 295573 ?

oops i just realized i put a 3 instead of 6

[frigid burrow]

This is?

[fresh pebble]

this

now i just gotta figure out where this goes

295573 / 24300 = 12.16?

total theta / total time

[frigid burrow]

My total theta is something else

Can you show how you found it?

[fresh pebble]

first i did 675000 / 0.7pi

then that divided by total time

295573 / 24300 = 12.16

[frigid burrow]

Wait

You forgot to multiply by 2π

Lol

[fresh pebble]

0.35 x 2 pi

[frigid burrow]

That is total revolutions

Not total angle

[fresh pebble]

uh

[frigid burrow]

This is revolutions

Multiply by 2π to find angle

[fresh pebble]

1857143?

[frigid burrow]

,w (67500 / 0.7 / pi) * 2 pi

[warm shale]

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Upgrade to WolframAlpha Pro!

Requested by wum.pus.man

[frigid burrow]

Nope

[fresh pebble]

now what would we happen to do with this number

[frigid burrow]

Hmmmmm

Bro I have to go now

Good luck

[fresh pebble]

fuck

WAIIIIT

would i divided it by the total time

,w ((67500 / 0.7 / pi) * 2 pi) / 24300

[warm shale]

Results provided by WolframAlpha

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

Requested by guangdongtigersrecruit

[fresh pebble]

i do not think that would be the answer

god damn it

[obtuse pebble]

@fresh pebble Has your question been resolved?

[obtuse pebble]

Channel closed

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[obtuse pebble]

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

If $f(x)= \frac{e^{2x}+1}{e^{x}}$ , then find the critical point and determine whether its Maximum or minimum

[warm shale]

Daddy| |matr!x

[signal idol]

I got its derivative which is $\frac{dy}{dx}=\frac{e^{2x}-1}{e^{x}}$

[warm shale]

Daddy| |matr!x

[signal idol]

by equating it to zero $(e^{x}+1)\times(e^{x}-1)=0$

[warm shale]

Daddy| |matr!x

[signal idol]

so $x = 0$

[warm shale]

Daddy| |matr!x

[signal idol]

now what

the critical point is $(0,2)$

[warm shale]

Daddy| |matr!x

[woeful edge]

analyze the functions behavior

[woeful edge]

u can use table of variations

[signal idol]

I tried

it's positive

on both sides

[woeful edge]

the derivative is positive in ]-inf, 0] ?

[signal idol]

oooooh

[woeful edge]

ur wrong

[signal idol]

it's a minimum

[woeful edge]

yes

gj

[signal idol]

thx man

.close

[obtuse pebble]

Channel closed

Closed by @signal idol

Use .reopen if this was a mistake.

[woeful edge]

or yk

graph the function if ur a mad man

[obtuse pebble]

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[errant galleon]

$y=\frac{36000}{9}15n-n\left(\left(\frac{336+4545+1176+81.25}{36000}\left(36000\right)+\left(9409.95+13929.41+173.79\cdot2+2060\right)\right)-2060\right)-2060$

[warm shale]

I Like Bamboos

[errant galleon]

.close

[obtuse pebble]

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[full musk]

Is a calculator allowed?

I assume not, but just checking.

[fathom kindle]

wellya it is but i need to put them as fractions

[full musk]

What do you mean "put them as fractions?"

[fathom kindle]

for a) i got tantheta = 12/-5

[full musk]

I see

[fathom kindle]

b) sectheta = 13/-5

[full musk]

That seems right

[fathom kindle]

but the answer key says a) is wrong

why is a) 12/13

[full musk]

that makes no sense

hmm

[fathom kindle]

its probs wrong then

and i also dont get c) tho

[full musk]

I'd guess so.

C you just plug in arccos(-5/13)

into calculator

[fathom kindle]

this is what i did

sin theta = 12/13
alpha = sin-1(12/13)
alpha = 1.176

theta = pi - alpha

theta = 1.96

but its wrong

[full musk]

hmm

[fathom kindle]

did i do a mistake

[full musk]

It says "possible values"

So there could be another avenue

[fathom kindle]

but why

we know x is negative

[grand arrow]

use pythagoras

[fathom kindle]

omg hi

[grand arrow]

sin^2(x) + cos^2*(x) = 1

u can just plug in the cosine value

[fathom kindle]

bruh he never taught is that

😭

[grand arrow]

lmao

[fathom kindle]

@full musk is there another way

[full musk]

did he just add 2pi to it

2pi to 1.96

or just pi?

[fathom kindle]

whaa

[full musk]

like pi + 1.96 is approximately 5.14, no?

[fathom kindle]

why do u add it tho dont u subtract it

because its in the 2nd quadrent

[full musk]

idfk

[fathom kindle]

since y is positive

oh

um

[full musk]

i'm trying to see how they got it

[fathom kindle]

ah

[full musk]

frankly, you're probably better off asking your teacher

[fathom kindle]

ummm

[full musk]

that answer key is convoluted if not outright unreliable

[grand arrow]

whats the original question

[full musk]

here

[fathom kindle]

this is what i did
sin theta = 12/13
alpha = sin-1(12/13)
alpha = 1.176
theta = pi - alpha
theta = 1.96
but its wrong

[grand arrow]

have u been taught identities yet

[fathom kindle]

am i not allowed to do that???

no.

😭

we have a trig function test on tuesday

[fathom kindle]

well yes in gr 11 obvi but ofc i wont use it now

[grand arrow]

how did u get the value of sin theta

[fathom kindle]

sin = y/r

y = 12 and r = 13

?

[grand arrow]

but u are only given cosine

u usually have to either take an inverse

or u do it using identity

[fathom kindle]

ok

theta = cos-1(5/13)

it equals 1.176

[grand arrow]

but taking an inverse is always iffy

i think hell let u use

pythagorud

since its from last yesr

[fathom kindle]

omg

ok

[grand arrow]

using pythagorud

ensures that ur answer

is within the inequality

[fathom kindle]

ok ill just ask him tmr its ok

thanks anyways

.close

[obtuse pebble]

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Closed by @fathom kindle

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[obtuse pebble]

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[brazen smelt]

Why is there not a moment about point A?

[obtuse pebble]

@brazen smelt Has your question been resolved?

[brazen smelt]

omg there is

.close

[obtuse pebble]

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[obtuse pebble]

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[fathom kindle]

WHY IS THIS THE ANSWER

i said everything exactly the same but i wrote - pi/3

bc ut suppose to go left bruh

[restive gorge]

https://tenor.com/view/cat-cuddle-gif-27222129

[fathom kindle]

do u get what i mean

[restive gorge]

yup

[fathom kindle]

😦

[restive gorge]

you basically answered your own question

[fathom kindle]

but if its + pi/3 then it actually goes left

so shouldnt it be - pi/3 so it goes to the right like i drew

[restive gorge]

without the +pi/3 you would have the green

now you wanna move it to the left so you do +pi/3

[subtle sinew]

It's y = Asin(x - B) + C
If B = -pi/3 and when you plug that in, you get sin( x - -pi/3) or sin(x + pi/3)

[fathom kindle]

wait so in order to do the d value (shift value)

i base it off the original graph?

so like from the original graph i go left so i do +

???

ohh bruhh i did nott realize that

[restive gorge]

😂

[fathom kindle]

wait thats so important

i literally have a test in 1 day

oh well

[restive gorge]

oh

good luck then

[fathom kindle]

LOL

thanks

🥲

.close

[obtuse pebble]

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[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
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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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[prime shadow]

what is a double root

[prime shadow]

roots are just x intercepts, right?

basically all points at which y = 0

yep

So what is a double root

<@&286206848099549185>

[tardy epoch]

https://math.stackexchange.com/questions/2535147/understanding-the-definition-of-a-multiple-double-root

[mossy walrus]

it's just the square root of a square root

[cyan latch]

or something to the power of 1/4

[prime shadow]

what does that have to do with polynomial functions though

[cyan latch]

may give complex answers as well

[mossy walrus]

If we think about roots as fractional powers, then a double root is just (x^(1/2))^1/2

[prime shadow]

I still don't get what it is. Why for example is this one

the 2 i mean

[mossy walrus]

basically x^1/4

[cyan latch]

oh

you mean multiplicity?

[prime shadow]

i think so

[cyan latch]

ok

so like (x+1)^2 then

x = -1 has a multiplicity of two

which i guess is what you originally meant by double sqrt?

[prime shadow]

multiplicity means

?

[cyan latch]

tbh idrk how to explain it

it's like

(x+1)^1 has a multiplicity of 1

but (x+1)^2 has a multiplicity of 2

(x+1)^3 has a multiplicity of 3

[hidden compass]

How many times a factor appears in the factorization of a polynomial

[cyan latch]

each multiplicity changes the behavior of the graph at that point

[cyan latch]

thanks for putting it into words 😭

[prime shadow]

and how does one tell the multiplicity?

[cyan latch]

the degree

[prime shadow]

I mean that looks like a normal x intercept to me

[hidden compass]

By looking at the factorization of the polynomial

[cyan latch]

if it's to the power of one it passes through

if it's to an even power it "bounces"

if it's to an odd power it "flexes"

[prime shadow]

oh no, I'm just doing it backward. I'm supposed to construct the function from the graph

[cyan latch]

exactly

[hidden compass]

If the graph is tangent to the x-axis at that root, it means that multiplicity ≥ 2

You can prove it with derivatives

[cyan latch]

x>= 2 + 2n for any integer n

[prime shadow]

oh wait

so like

[cyan latch]

alright go for it!

[prime shadow]

so it bounces, meaning it is an even power, but what does that mena for constructing the function?

[hidden compass]

Why can't it be odd?

[prime shadow]

the guy in the video just made it into (x-2) (x plus 2)

[cyan latch]

it means you make a factor to an even power

[cyan latch]

it'll flex instead

[hidden compass]

Like x³ has 0 as a root with multiplicity 3

[cyan latch]

oh u said tangent

he needs to determine flex vs. pass vs. bounce

[cyan latch]

yeah b/c

[prime shadow]

what does flex and pass mean for you

[cyan latch]

well no

he did it wrong then

[prime shadow]

oh hold up

he made it

[cyan latch]

a pass is multiplicty of one

[prime shadow]

(x-2)^2

[cyan latch]

the graph simply passes through

yup

look at the behavior of the graph at x=2

[prime shadow]

and a flex?

[cyan latch]

lemme show you

[prime shadow]

so at -1

it is considered passing?

[cyan latch]

yes

exactly

[prime shadow]

I see

[cyan latch]

THAT is a flex

[prime shadow]

oh

[cyan latch]

higher the odd degree the more pronounced it'll look

[prime shadow]

that means even power

nvm

odd

[cyan latch]

except one, one is just a pass

[cyan latch]

mhm

[prime shadow]

I see, I see

[cyan latch]

same with evens watch

looks almost like it turns into a line

but it's just a lame "bounce"

[prime shadow]

thank you

that makes a lot of sense now

[cyan latch]

alright let's go back to your problem now

[prime shadow]

next

how does he tell

that it is a 2

and not 4 6 8 10

[cyan latch]

he guesses

for now

also the bounce isn't that flat

like how x^14 was super "flat"/stretched like I showed you

[prime shadow]

yep

[prime shadow]

how is this different from flexing

[prime shadow]

does flexing need to change direction?

as in

from positive to negative?

[cyan latch]

flex needs to pass the x axis

[prime shadow]

I see

[cyan latch]

yeah flexes pass

so what's going on at each intercept?

[prime shadow]

from left to right

passes

[cyan latch]

tell me what the values are too

[prime shadow]

passes

and

bouncce

[cyan latch]

alright

[prime shadow]

-3

[cyan latch]

ok ok I see you

[prime shadow]

-1

2

right?

[cyan latch]

yup!

now

[prime shadow]

so

[cyan latch]

what polynomial factors would give us those?

[prime shadow]

(x plus 1) (xplus 3)

[cyan latch]

e.g. to get a root of -3 we need a factor of (x+3) 🤔

[cyan latch]

and?

[prime shadow]

(x - 2)^2

[cyan latch]

YES

[prime shadow]

sure I get this

so

[cyan latch]

there's one more step if you wanna get fancy

[prime shadow]

I'm wondering

[cyan latch]

but let's do another practice or two

[cyan latch]

ask away

[prime shadow]

the guy in the vid said

it doesn't work for quadratic functions

why?

[cyan latch]

huh

[hidden compass]

It does work, as well

[cyan latch]

yeah see it works just fine

[prime shadow]

https://youtu.be/ASwOZYbfBjI

first twenty seconds

he says it doesn't, is he just wrong?

[prime shadow]

2.5, -2.5

[cyan latch]

i think so

[prime shadow]

it doesn't bounce or anything

so 1

[cyan latch]

I'm sorry what?

[prime shadow]

(x-2.5) (x plus 2.5)

[cyan latch]

oh

yeah

[prime shadow]

broke my plus button so ignore that

[cyan latch]

technically it's 3 but that's just from reading the numbers wrong

[cyan latch]

nw

alright r you ready for a practice one? @prime shadow

[prime shadow]

yep

[cyan latch]

oops

gave the answer away

[prime shadow]

woah dude

[cyan latch]

😭

lemme make another

[cyan latch]

always be prepared for scuffed windows

[prime shadow]

do I always just assume the lowest even or odd

or is there some way to figure it out

[cyan latch]

there probably is a way

but dw about it for now we have a bigger problem

[prime shadow]

ok give me a sec

[cyan latch]

nw

[prime shadow]

x*(x-20)^2

and liek from there

like

what is the y value for x 0

[cyan latch]

hm?

[prime shadow]

y value for x = 0

[cyan latch]

0

[prime shadow]

oh right

[cyan latch]

so you're right

[prime shadow]

lol

[cyan latch]

x(x-20)^2

alright now for the "hard" part

[prime shadow]

so uh a*x(x-20)^2 = y

[cyan latch]

so we know how functions behave at x intercepts and we have some sort of idea of how to give them multiplicty right?

[prime shadow]

yes

[cyan latch]

right now I'll explain the "a"

[prime shadow]

ok

[cyan latch]

so the "a" is whatever number is being multiplied by all those factors in order to get the "true" function

it's like how y = 2x^2 has mostly different values than y=x^2 even though they have the same intercept and multiplicities

in that case we have y = ax^2

y = 2x^2 means the a is 2

y = x^2 means the a is 1

y = x^2 = (1)x^2

following?

[prime shadow]

0.5x^2 means a would be 0.5?

[cyan latch]

yup

[prime shadow]

ok

[cyan latch]

so

see this

[prime shadow]

yes

what is with that

[cyan latch]

make the function for me pls

and add just the a for now

[prime shadow]

a* x*(x-2)

[cyan latch]

yay

now

remember how a changes the behavior of functions

[prime shadow]

yep

[cyan latch]

it changes every point but the x intercepts

[prime shadow]

yup

[cyan latch]

what do we know about the graph I showed you?

[prime shadow]

it has two turning points so it is at least of the third degree

[cyan latch]

ok

but what about its values

is there a an easy point on the graph that I marked 😉

[prime shadow]

goes to infinity

[cyan latch]

try again

[prime shadow]

x value doubles

[cyan latch]

you're still correct tho!

[prime shadow]

maybe that?

[cyan latch]

still correct

but it's looking at you

[prime shadow]

oh

hold up

you mean

substitute here

[cyan latch]

it crosses the point (3,6)

YES

GENIUS

we know that this graph will have a point where y=6 and x=3

therefore we substitute those values into the function we made with the multiplicities and solve for "a"

[prime shadow]

6 = a * 3* * 1

so 3a

a = 2

[cyan latch]

yup!

now we know the value of a

[prime shadow]

yep

[cyan latch]

so we just put it back in to the general function

and viola

[prime shadow]

holy shit dude you are one awesome teacher

I've been at this for a while

no o ne explained it as well as you did

[cyan latch]

thanks man that means a lot to me

[prime shadow]

Okay, maybe you can help me with this other problem too

[cyan latch]

I'm not the best at math, but I wanna teach when I grow up 🙂

[prime shadow]

how old are you?

[cyan latch]

first you wanna do a practice problem for that one?

[cyan latch]

16

[prime shadow]

sure

wow, wild

[cyan latch]

hbu?

[prime shadow]

where are oyu from

19

[cyan latch]

Iran

don't live there anymore tho

anyway, lemme make you the question!

alright have a crack at this one

@prime shadow Imma go grab a snack rq I'll brb to check ur work tho/help you if you need more help

[prime shadow]

x * (x-2)

4 = a * 1 * -1

a = 4/-1

so a = -4

[cyan latch]

only (x-2)?

where did its multiplicity go :0

[prime shadow]

oh right

x-2^2

so basically a = 4

[cyan latch]

yeah that works

kinda funny though because the actually graph is (x-2)^4 (see how the bounce is a little more stretched than last time)

it's the only point that works 😭

[prime shadow]

yep

[prime shadow]

I see

[cyan latch]

that's my bad on the making the question part

[prime shadow]

so how does one tell the degree

[cyan latch]

for now just take note of how "stretched" the bounce is

or how "stretched" the flex is

[prime shadow]

alright

next uh

so

with functions from the degree 5-2

[cyan latch]

is that the whole question? 😭

[prime shadow]

what are some of their characteristics

[cyan latch]

https://www.desmos.com/calculator

play around

[prime shadow]

If I'm just given the function

how can I calculate the intercepts?

[cyan latch]

tbh idrk what that question is getting at. You seem to have a solid grasp of end behavior. Odd degrees have one side approaching infinity the other approaching negative infinity based off the sign value of "a". Evens are up up or down down again based off "a". Number of roots is based of degree

[cyan latch]

hmmm

do you have a sample question?

also if you want we can just call if it's easier

[prime shadow]

sure thing

[obtuse pebble]

@prime shadow Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

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>.
• 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.

[tepid pilot]

The height h=5m of an equilateral triangle is given. Calculate the side length a, the area A and the perimeter u.

[tepid pilot]

hhi idm dont know how to solve this problem

[strong pike]

start by drawing it out

[tepid pilot]

i did

i made a sketch

[woeful edge]

in equilateral triangles, theres a relation between their sides and their heights

[strong pike]

then you should identify a pythagorean triplet.

[tepid pilot]

ermm waht is that

[strong pike]

do you know the pythagorean theorem?

[mortal mason]

triangles

yeah

[tepid pilot]

yes

[strong pike]

so when you draw it out, the equilateral triangle can be split into two right triangles

[tepid pilot]

yes

[strong pike]

doing so, you can calculate the side length of the triangle

[tepid pilot]

huuh

but i only have the height

how do i

[strong pike]

is that not a right triangle?

[tepid pilot]

it is

[strong pike]

then can't you solve for the side length, b, using pythagoreans theorem?

[tepid pilot]

sorry these english terms confuse me cause i have maths in german 😓

[strong pike]

the right triangle is a traingle with a 90 degree angle

pythagoreans theorem, a^2+b^2=c^2 applies to right triangles

[woeful edge]

theres like a straight forward formula

but sure

[mortal mason]

Rechtwinkliges Dreieck

[tepid pilot]

ja

[mortal mason]

thats right angled triangle

[terse tendon]

that is the formula

[strong pike]

by splitting the equilateral triangle (a triangle whose sides are the same length) into two, you can make a right triangle with height 5, and solve for b

[woeful edge]

this is the demonstration

of the formula

so u would win more time

[terse tendon]

what?

[thorny idol]

math aint about memorizing formulas

[woeful edge]

it is

with understanding it too

[mortal mason]

y'all going off track

[terse tendon]

it isnt, a majority of large tests will give you a reference booklet with formulas in it.
but anyways, back to topic.

[mortal mason]

we have to help nyx understand the problem

[woeful edge]

😔

[mortal mason]

true

@tepid pilot you still here?

[tepid pilot]

yes

im here

[mortal mason]

okok

lets continue

[tepid pilot]

can someone translate this

[mortal mason]

so after getting the Rechtwinkliges Dreieck

i don't speak german i just translated it

[tepid pilot]

i got to 5² + (b/2)² = b²

but i dont understand how u can just solve b

[mortal mason]

so thats a equilateral triangle

right?

[tepid pilot]

yes

[mortal mason]

what is the property of a equilateral triangle

[tepid pilot]

equal angels and sides are the same length

[mortal mason]

yes nice

[tepid pilot]

angles *

[mortal mason]

have you learned about cos, sin and tan?

[tepid pilot]

nno

[mortal mason]

ok thats fine

[mortal mason]

so what you got is actually good

idk why i went away from it

do you have an idea how to solve this?

[tepid pilot]

no 😓

[mortal mason]

ok thats fine

so you want to isolate b

how can you rewrite (b/2)^2

[tepid pilot]

2²? caus u said to isolate b

www sorry i dojt knnow

[mortal mason]

no its okay if you don't know

we'll go through it together

so (b/2)^2 can be rewritten as b^2 / 4

becasue 2^2 = 4

[tepid pilot]

OOH

RIGHT

oops

i forgot about that

[mortal mason]

yeah there we go

no worries

so now you have 5^2 + b^2/4 = b^2

you want to isolate for b

what can you do

subtract something from both sides maybe?

[tepid pilot]

minus b²? am i allowed to do that

[mortal mason]

yeah but why do you want to do that

you'd get ... = 0

think of (b^2)/4 as x

if you want to move it to the other side you'd have to subtract the whole thing

so (b^2)/4

[tepid pilot]

OOH

can i also rmove the 4 by multiplying by 4

[mortal mason]

YESSSS

you can

[tepid pilot]

YAAY

sso

20^2+b^2=4b^2 ?

nohwh

huh

ok ther

[mortal mason]

eeeh

no

[tepid pilot]

but

[mortal mason]

4* 5^2 =/= 20^2

[tepid pilot]

OH

[mortal mason]

you can compute it to see that they aren't equal

and where did the b^2 come from on the left side

[tepid pilot]

cause exponent before multiplying thingy

[tepid pilot]

from the b^2/4 ?

[mortal mason]

yeah

nono

ah wait yeah

i though you did something else but that works too

[tepid pilot]

YAY

trhen war

[mortal mason]

so you have 4*5^2 + b^2 = 4b^2

you can do 1 more thing before being able to find the value for b

[tepid pilot]

5²=25
25*4=100

emrrm

i think

[mortal mason]

yes okay

yea that is correct

but now you have 100 + b^2 = 4b^2

[tepid pilot]

minus b^2?

to get 100 = 3b^2

[mortal mason]

yesssss

you're almost there

now to get b on one side and the rest on the other

[tepid pilot]

wat do u mean

isnt b already ln one sjde

3b^2 = 100

then divide by 3

b^2 = 100/3

and then wurzeln

i dont know the term in english

swuare root

b = sqrt(100/3)

[mortal mason]

yeuhh

thats it

you got it

nice

[tepid pilot]

YAY

then b = 5.77

[mortal mason]

i didn't compute it but it should be it

since it has to be larger than 5 it should be correct

[tepid pilot]

YIPE THANK U€!!