help-13

[marble ermine]

uhhmmmm yess ok thankksss

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✅

[marble ermine]

wait, can you explain me why it means that the only nilpotent element of A/rad(A) is [0]?

[mental trail]

if x^m is in rad(A) for some m...

then what does this imply, by definition of rad(A)?

[marble ermine]

x^m is nilpotent so x is nilpotent

[mental trail]

so cl(x) = ...

or a = ...

[marble ermine]

i dont know, it depends on the equivalence class?

a = {y in A, x - y in rad(A)} and x is nilpotent

[mental trail]

We just showed that if x is such that cl(x) = a, then x is in rad(A)

so a = [?]

[marble ermine]

well if x is nilpotent and since 0 is also nilpotent, then they share the same class here so it's [0]?

[mental trail]

yes

[marble ermine]

ok thank you

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[gaunt hamlet]

Let f(x,y)=x^2y-y^3 compute f(x+h,y)-f(x,y)

[bright fiber]

Get your own channel rick

[timber linden]

oh

sorry i thought it was available

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[somber brook]

5 - (5/2) = 5 how?

[cerulean sail]

And where does it say that

[somber brook]

x = 5- 5/2

x = 5/2

[granite knoll]

yes

so 5 - 5/2 = 5/2

[somber brook]

how does that make sense

[granite knoll]

5/2 is 2.5

5 - 2.5 = 2.5

[somber brook]

ohhh

thanks

forgot basic maths

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[shut grail]

Just asking for clarification, but wouldn’t the answer be -2R3 + R1?

[warped coyote]

That could be, but one of the options finishes one of the rows, then clearing R1 is simpler

[shut grail]

Oh I see

[royal loom]

-2R3 + R1 would change the -2 in R1 to a -4

which is not very helpful

you likely want to get rid of the -3 in R1 first somehow, although the question is weird because you could just as reasonably try to clear the -2, or the 1

or even the -3 in R2 would be fine to remove

[shut grail]

That’s probably where I’m confused LMAO

[warped coyote]

Second row makes the most sense

[royal loom]

I think it probably gives you 3 nonsensical options (hopefully) and one that's like, okay that's fine

but sadly it appears not

[warped coyote]

3R3+R2 clears the second row then you clear the first row with multiples of rows 2,3,4

[royal loom]

that works

[shut grail]

Thank you so much for the help guys

I appreciate it

[royal loom]

np

[shut grail]

better close this and get out of your hair

Thanks again tho

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[knotty yoke]

How to visualize this in desmos

[royal loom]

you can graph y=sqrt(x) and use {0 <= x < 1} to get it to restrict the graph

and similarly for 1/x^2 with { 1<= x}

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[slim carbon]

would the answer be "quadratic function"?

[glacial sandal]

i think that it's inverse

because quadratic is $$x^2$$

[wraith dagger]

Juanjo

[glacial sandal]

lineal

sorry

[trim radish]

No it's not an inverse... An inverse would be like substituting x for y and then solving for y again.

[granite knoll]

no

it's asking whether it is even or odd

[slim carbon]

ohhhhhhhhhh

[glacial sandal]

it´s lineal, no?

[dim birch]

x^2 is an even function for example, x^3 is an odd function

[slim carbon]

ok

got it

thank you all so much

[glacial sandal]

im so confuse

[cedar kiln]

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[rustic steeple]

so for part a)

i got 2x^6 + 30x^4 y^2 + 30x^2 y^4 +2y^6

[earnest geyser]

That's probably correct

[rustic steeple]

not sure how to to relate it to part b tho

[earnest geyser]

U want b?

[raven shard]

remove the probably

[rustic steeple]

yes please

im a bit lost ofr

part b'

[earnest geyser]

X equals 5

Y equals 3

[rustic steeple]

yes

[earnest geyser]

Take 2 common

[earnest geyser]

If u put x =5 and y=3 you'll get the one as 2(b)

That's 2 times of second question value

[rustic steeple]

wait but

[earnest geyser]

So now substitute X and y in original equation

[earnest geyser]

?

[rustic steeple]

its

x^4

[sage sail]

.

[rustic steeple]

and y^2

but then in the 2nd one its

5^5 and 3^3

[earnest geyser]

?

[rustic steeple]

um

im not sure i get it

[earnest geyser]

Did u put x=5 and y=3?

[sage sail]

that is polynomials?

[rustic steeple]

wait sorry do u think

u could write it out

possibly

[earnest geyser]

You'll get $2(5^5+15.5^4.3^2+15.5^2.3^4+3^6)$

[wraith dagger]

Monarch of Eternal Night

[rustic steeple]

yes ok...

and then after that

[sage sail]

wth?

[earnest geyser]

Now just put 15 as 5*3

[rustic steeple]

ohhhh

wait

OHH

okok thank u so much

i get it now

[earnest geyser]

Like $15.5^4.3^2=5^5.3^3$

[wraith dagger]

Monarch of Eternal Night

[rustic steeple]

yeahhh

yeahhh

ohhhh

[earnest geyser]

Now substitute in og equation

[rustic steeple]

alright alright

yep yep

got it now

okok thank u sm

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[timid crypt]

for this problem i think i want to express this function as a sum, but i am just stuck on the denominator, not sure how to express that

[dim birch]

$$n!$$

[wraith dagger]

Cyphercrit

[dim birch]

wait

hmm

its like a double factorial but it skips some

[timid crypt]

its like 3n! minus some terms

(3n)!

so the first term n = 0 has a denominator of 1

[dim birch]

well

[timid crypt]

im thinking you could put something in the numerator to cancel out some numbers in the factorial

but idk what

[crimson sedge]

Yes

[timid crypt]

hmm i think this would make sense

[crimson sedge]

But the 1

[timid crypt]

it’s not elementary function but it works out for the ratio test

[crimson sedge]

You won't get the first term with that

Sub n equals 0 you get -2

[timid crypt]

oh

true

uhhh

[crimson sedge]

Start with n equals 1

[timid crypt]

but then i would have x^3 as my first term

no x^0

[dim birch]

ooh

its like a triple factorial almost

so every 3 terms

https://en.wikipedia.org/wiki/Double_factorial

[timid crypt]

yea i just took the 3n factorial then put 1, 4, 7... in the numerator to cancel out stuff

wait what

i never learned that

interesting

[dim birch]

n!!! is the product of all positive integers from n down to 1 that are congruent to n modulo 3.

rarely used though

[timid crypt]

yeah

would you just be able to take the first term 1 out of the sum and start with the x^3 term?

ohh

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[plucky bolt]

please help me with this

[drifting fable]

what is the surface area in terms of x and h libster

@plucky bolt

[plucky bolt]

Im not sure

[drifting fable]

well, the surface area is just the area of each face added up, right?

[plucky bolt]

Yes but im having a hard time visualising the sides

[drifting fable]

ok no worries

think about it this way

lets suppose the top and bottom faces are x by x cm

and the height is h cm

[plucky bolt]

Wait so when it says each edge x cm, thats just the length of one of the faces

[drifting fable]

yes

[plucky bolt]

Ah ok

[drifting fable]

its basically a rectangular prism

or

its a cube, but one of the dimensions is elongated

what is the surface area of the top and bottom faces?

if the top and bottom are x by x cm

[plucky bolt]

2x^2

I think

[drifting fable]

yes good

now, what is the area of one of the faces in the middle

if the top and bottom are x by x cm, and the object has a height of h cm

[plucky bolt]

h*x

[drifting fable]

ok good

is it true that the area of each middle face is the same?

[plucky bolt]

Yes

[drifting fable]

ok

so the area of the entire middle portion is 4hx then

[plucky bolt]

Yes

[drifting fable]

area of the middle + top and bottom = surface area

[plucky bolt]

2x^2 + 4hx?

[drifting fable]

yes

[plucky bolt]

the answer says x^2 + 4hx

is that wrong?

[drifting fable]

actually

i read the question wrong

it asks for the area of an open box

so the top face does not exist

thus, the answer would be area of middle + area of bottom

[plucky bolt]

oh i see

Yes

[drifting fable]

and it tells you what the surface area is

75cm ^2

[plucky bolt]

so the open box is just a square with 4 other squares around it?

[drifting fable]

yes

[plucky bolt]

It was just that question i couldnt figure out

[drifting fable]

you can now set up an equation to answer b

ok

[plucky bolt]

Thank you

[drifting fable]

np

[plucky bolt]

Do you have any tips for doing worded problems like these?

[cedar kiln]

@plucky bolt Has your question been resolved?

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[worthy basalt]

hello

[worthy basalt]

question

how can I solve c?

[vale ginkgo]

Usually with those 1 markers you could use a calculator

[worthy basalt]

How can I use it here

plz

explain

[vale ginkgo]

You have graphical calculator?

Is it 12?

[worthy basalt]

yeah it is ?

oh no

just a natural one

[vale ginkgo]

What?

[worthy basalt]

yk those normal ones

scientific

[vale ginkgo]

Oh yeah classwiz

[worthy basalt]

casio

Well

that matrix transformation

is a rotation anticlockwise

150?

and I think Identiy is when it's 360#

so we have to find I think the lcm of both?

[vale ginkgo]

Is the answer 12?

[worthy basalt]

yeah

[vale ginkgo]

So it’s right then

[worthy basalt]

but How did u find it

[vale ginkgo]

Send pic of your calculator

[worthy basalt]

ehh i'm on pc

but is like a casio

it has no matrices

[vale ginkgo]

Yeah it is 150 degree rotation anticlockwise

Well that’s what you need for these questions

[worthy basalt]

I also have another one

like a brick one

where you can even make graphs

[vale ginkgo]

If it’s one mark it’s not asking anything special

[worthy basalt]

but they don't let me use it

[vale ginkgo]

So do you get it now?

[worthy basalt]

yeah ig I'm just trying to do everything correct

[worthy basalt]

yeah

ty bro

[vale ginkgo]

Ok cool

[worthy basalt]

how do I solve b?

[neon grotto]

isn't is summation of (n)(n+1) from 10 to 100

[worthy basalt]

idk

what do I do here

[neon grotto]

Try to think what is the pattern

[worthy basalt]

i found the first one

but b

[neon grotto]

Look

You have to identify the pattern

[worthy basalt]

i guess the common differnce between them

increases by 2

[neon grotto]

In other questions it will be different patter

Well depends on the problem

Here it is summation

So think of it as n, n+1, n+2...

How can you write 10*11 from only one variable

[worthy basalt]

ohhhhh

[neon grotto]

Write how you can form it as a summation

[worthy basalt]

uh

i guess

r^2#]

r^2+3r+2

it gives me 110

[neon grotto]

No

No

Dont multiply

Just take the numbers as it is

10*11

11*12

[worthy basalt]

10*11

[neon grotto]

The difference is one

let 10 be n

How will u write 11?

[worthy basalt]

n(n+1)?

[neon grotto]

Yup

And now if u start from 10

And go upto 100

It will form the series, that is in the question

[worthy basalt]

so this is like for every type of hard pattern questions

[neon grotto]

Yes

You have to identify the pattern

And sometimes simply and stuff but yea

[worthy basalt]

thanks bro

I understand now

[neon grotto]

Anytime

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@worthy basalt Has your question been resolved?

[cedar kiln]

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[wheat herald]

Hello i need to calculate AB.AC
Can someone explain me what my teacher did here ?

[wheat herald]

<@&286206848099549185>

[timber zinc]

vector stuff?

[wheat herald]

yes

[timber zinc]

wow this thing is so neat

[wheat herald]

i just wrote what teacher did

[timber zinc]

but I have a question why did he just use vector and non vector why don't he just use 6x7?

[wheat herald]

only 6x7 would be if the triangle was rectangle

i think

.close

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[fringe mauve]

,rotate

[fringe mauve]

does anyon eknow how to remap roots?

like done here

[cedar kiln]

@fringe mauve Has your question been resolved?

[fringe mauve]

<@&286206848099549185>

[worldly thistle]

Did u find the roots?

@fringe mauve

[cedar kiln]

@fringe mauve Has your question been resolved?

[fringe mauve]

wdym

[worldly thistle]

🤦🏻

[fringe mauve]

nah like i was asking does anoyong know how to do it in the way i outlined

cause finding roots and doing simulatnoeus takes too long

[cedar kiln]

@fringe mauve Has your question been resolved?

[fringe mauve]

<@&286206848099549185>

[crimson sedge]

@fringe mauve

Oh the given roots

[nimble veldt]

https://en.wikipedia.org/wiki/Vieta's_formulas

[crimson sedge]

The common term is alpha beta gamme

That is the product of the roots

The value which you already know

So it would be 3 alpha 3 beta 3 gamma

I guess now you can do it

[fringe mauve]

no wait

i cant find the value of teh roots

[crimson sedge]

?

[fringe mauve]

buthow do i find A B C D

like teh coeffs of the equation

[crimson sedge]

THERE Is no need to find the value of the roots to find the product of them

[nimble veldt]

you do not need them if you use vietas formulas-

[fringe mauve]

whats vietas formula

i need to find the eqaution of a new poly

with those roots

[nimble veldt]

i gave you the link for the explanation.

the product of alpha beta and gamma is 3.

[fringe mauve]

is that just product and sumof roots

after i get teh values

[nimble veldt]

the product of the roots of the new polynom is (alpha times beta times gamma)^4, so you know its 3^4.

[fringe mauve]

how do i find the enw polynomial

[nimble veldt]

so you know the constant term of the new polynom

and now do them same with the other values using vietas formulas.

[fringe mauve]

wait lemme show u

[wicked stag]

Hey descartes rule of signs may help

Which one are you doing?

[wicked stag]

,w x³ + x² -2x -3 = 0

[wraith dagger]

Results provided by WolframAlpha

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

Requested by itzmecairo

[cedar kiln]

@fringe mauve Has your question been resolved?

[cedar kiln]

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[buoyant latch]

Set up your disks

What do each of the ΔV look like

[celest marsh]

all i rmmbr was V = Area dx

so V = pi * r^2 dx

[buoyant latch]

Well if I gave you a disk how would you find the volume of said disk

[celest marsh]

and theres no numbers here

which is kinda tripping me out

[buoyant latch]

It’s more like ΔV = pi r² Δh where h is the height

Do you agree?

[celest marsh]

oh wait

so ΔV is big sphere minus cylinder thing

ri?

[buoyant latch]

Nope

[celest marsh]

oh nvm

[buoyant latch]

Have you done the disk method before?

[celest marsh]

thats what where calculating

i hv for an easier question

[buoyant latch]

Could you show that easier question?

[celest marsh]

I just used v = pi * r^2

[buoyant latch]

Perhaps we can use that question as a stepping stone for this one

Did you draw a picture?

[celest marsh]

it gave a picture lol

[buoyant latch]

Ok would you be able to draw this picture yourself?

[celest marsh]

well x=2 and y=1 yeah but not the other function

[buoyant latch]

Can you show the steps you did for this question?

[celest marsh]

i can you tell you

all i did was use V = integral from 0 to 2 (pi (2-e^-x)^2)dx

from A = pi * r^2

plugged in the function for r because for some reason thats the radius

[buoyant latch]

You should’ve drawn a picture like this

Have you seen something like this before?

[celest marsh]

yeah

[buoyant latch]

Do you think you could reproduce a picture like this?

[celest marsh]

probably yeah

[buoyant latch]

Alright I want you to do this picture

For this question

Draw it and show me

Remember to label all the relevant pieces like I have done here

[celest marsh]

there are no values in the question

which is confusing me

[buoyant latch]

Label the inner ring r

And outer ring R

That’s what the values are (at the equator)

You’ll need to think a little bit to get the outer ring length

Think for a sphere as you move up the z axis, how far away is the edge of the circle horizontal to you?

[celest marsh]

acc before i get to this question, because i kinda need to think about this one

is it cool if ask a quick question about another one

thats easier for me but not entirely sure

its on shells

[buoyant latch]

Sure thing

[celest marsh]

thanks appreciate it

i answered a question similar to this

but im confused about the x = y^3

usually we get all in terms of y ri?

also we only care about quadrant 1

i checked the graph on desmos and we have two volumes

[buoyant latch]

Well there should be 2 parts that need to be rotated about y = -1

Was the answer not that?

[celest marsh]

wdym?

[buoyant latch]

There should be 2 volumes

[celest marsh]

yeah here

[buoyant latch]

Yeah

[celest marsh]

but i can only do 1

i can choose 1 of them

[buoyant latch]

Do it in pieces

[celest marsh]

which ever is easier i guess

[celest marsh]

i only need one tho?

[buoyant latch]

You should need both

[celest marsh]

no i mean were allowed to choose one its in the textbook

just in first quadrant for example

just to make it easier

assume we only care about quadrant 1

anyways

i know we need to find intersections

so would i do x^3 = cuberoot(x)

[buoyant latch]

Yeah

[celest marsh]

ngl i dont know how to factor that

[buoyant latch]

I mean you can just inspect the intersections at -1 0 and 1

[celest marsh]

i know

but if this question was on exam

[buoyant latch]

Inverse functions intersects themselves at x = y

[celest marsh]

then i would have no idea

right

[buoyant latch]

You can abuse that as well

[celest marsh]

im terrible with graphs

[celest marsh]

ohh

rlly

[buoyant latch]

Well they have to

They are mirrored on that x = y line

If you imagine drawing a graph then mirroring it

The only places it can intersect itself is where it touches the mirror

[celest marsh]

but if i wasnt able to see graph, i would need to find intersections right

[celest marsh]

makes sense thanks

[buoyant latch]

For x³ and cbrt(x)

[celest marsh]

yes

[buoyant latch]

I think it can be expected that you can graph yhem

[celest marsh]

so 0 = cbrt(x) - x^3

[buoyant latch]

They shouldn’t give you too difficult a graph to do or they would break it up instead parts

[celest marsh]

ok

[buoyant latch]

I mean for x³ = cbrt(x)

You can cube both sides

Get x⁹ = x so x⁹ - x = 0 so x(x⁸ - 1) = 0

This is difference of 2 squares

x(x⁴ - 1)(x⁴ + 1) = 0

More difference of 2 squares

x(x² - 1)(x² + 1)(x⁴ + 1) = 0

And another

x(x - 1)(x + 1)(x² + 1)(x⁴ + 1) = 0

Hence the real solutions are x = -1, 0, 1

[celest marsh]

makes sense

thanks for explaining

now i can answer normally

but this time its through y-axis right

with y = -1

[buoyant latch]

For this question I’d want a way to describe the distance here

[buoyant latch]

.

[celest marsh]

yeah

i'd say 0 to 1

[buoyant latch]

No

If I give you some z value

How can you find ?

Hint: ||pythagoras theorem||

[celest marsh]

wdym by distance tho?

like the distance from 0 to the line y = -1?

[buoyant latch]

Not to the line y = -1

[buoyant latch]

Are you asking this problem

[celest marsh]

yeah

[buoyant latch]

Yeah

From 0 to 1 for x

[celest marsh]

but i only need distance for first quadrant tho or 3rd quadrant

just 1 of them

[buoyant latch]

No

You need both

The answer should include both parts

You need to do them individually

[celest marsh]

i get that normally we need both but I was told, "it was intended to only be the region in Quadrant 1 being considered. That is, it was intended you only look at the region where x and y are both positive."

so wouldnt that mean 1

or am i just tripping

[buoyant latch]

Sure

Then you go

From x = 0 to 1

We consider disks that have radius ???

The ??? Depends on the x value

[celest marsh]

disks?

[buoyant latch]

Oh you’re doing shells

[celest marsh]

arent we doing the shell question

[buoyant latch]

Yikes

Shells kinda suck here I think

[celest marsh]

so in that case i know the start we have 2 * pi * integral from 0 to 1

cant we just use the formukla

[buoyant latch]

Draw the shells out

Drawing is always the best for these questions

If you can’t draw what you’re calculating you’ll struggle lots

[celest marsh]

ngl i dont like drawing lmaooo

but i know we can use this formula: 2 * pi * integral (radius) * height * (width)

its just a matter of what to plug in

correct?

[buoyant latch]

You can’t get out of drawing

Improve your drawing skills if you can’t do it

[buoyant latch]

The formulas might not always work

It depends on the set up

It will depend on if you can draw the question

[celest marsh]

im assuming y = -1 can be the same as y = 1 here

right

they are the same size anyways

[buoyant latch]

No???

You’re revolving around that y = -1 line

[celest marsh]

oh ok thought we could do that lol

in that case because we only care about one of them wouldnt it be easier if we just find the one in quadrant 3 or no

[buoyant latch]

What…

They are both revolved around the y = -1 line

[celest marsh]

rmmbr how i mentioned that for this question specifically we only want to get the one in quadrant one (for simplistic purposes)

[buoyant latch]

Then you only rotate the 0<x<1 part about y = -1

[buoyant latch]

Nowhere in the question does it say anything about y = 1

[celest marsh]

yeah i see

and hypothetically if i only care about quadrant 3

it would be -1<x<0part about y = -1

[buoyant latch]

Yes

[celest marsh]

in your opinion which is easier

if we had to choose one

[buoyant latch]

They lead to different answers

[celest marsh]

i get that but hypothetically if we want to just find one of them, which would be the easier volume to calculate

because im just practicing i want to just to the easier one

i feel like quadrant 3 one might be easier

[buoyant latch]

They are both just as hard

[cedar kiln]

@celest marsh Has your question been resolved?

[cedar kiln]

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[deep plume]

I cannot figure out why I got #2 wrong? calculator issue?? I keep getting the same answer.

(Trigonometry. Easy solve)

[cedar kiln]

@deep plume Has your question been resolved?

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[crimson sedge]

hi just trying to confirm my answer on this:

integrate using integration by parts:
x^3 root (4-x^2) dx

[crimson sedge]

sorry idk how to type maths on my phone LOL

[torpid cipher]

alr

whats your ans

[crimson sedge]

sry for awful handwriting my dom hand is broken

[torpid cipher]

its fine im checking rn

[crimson sedge]

thank youu ❤️

heres a better version

[torpid cipher]

thats so much better

thx

[crimson sedge]

question is 2b

[torpid cipher]

something might be wrong here

shouldn't the nominator be -2x

oh 2/2

sorry kinda dumb rn

[crimson sedge]

no its fine

u most likely know more than me

[torpid cipher]

so u=sqrt(4-x^2) right

dv=x^3 dx

v=(x^4)/4

[crimson sedge]

ya

[upper abyss]

Note the question is asking for integration by parts, but your work goes for a u-sub instead

[torpid cipher]

im not sure about the sub part but still checking

this part might be wrong

[crimson sedge]

here is the first page sry shouldve added this

hello

[torpid cipher]

seems off

oh

[crimson sedge]

yeah teacher said its fine

why complicate with u sub

[upper abyss]

You've wrote
"sub x³ with u²x"

I don't follow that

[torpid cipher]

yep

i think you overcomplicated that part

ill solve it myself then compare

[crimson sedge]

choose u = 4-x^2

trust me

hang on im going over it agn sry

sure

take your time

[torpid cipher]

it becomes smthing like this

[crimson sedge]

can be done without ibp too

just pure u sub

[torpid cipher]

u=?

[crimson sedge]

4-x^2

[plain ridge]

why are u guys doing u sub over i by p
regardless of which is easier the question specifically wants ibp

[torpid cipher]

yeah also that

[torpid cipher]

i found something pretty close

[crimson sedge]

really

[torpid cipher]

kinda.

re-doing with pencil now

[torpid cipher]

can you revise this part

i just can't understand that

[crimson sedge]

yeah hang on

wait can u dm me bc im outside rn and i dont want to keep hogging this chat 😭 dont wanna get in trouble

[cedar kiln]

@crimson sedge Has your question been resolved?

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[deep plume]

.reopen

[cedar kiln]

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[deep plume]

I cannot figure out why I got #2 wrong? calculator issue?? I keep getting the same answer.

focus on far right of page.

<@&286206848099549185>

[granite knoll]

don't be rude. he did it once. if you don't want to be a Helper, remove the role

[deep plume]

it’s a simple problem. i’m a rookie bro. you guys are wizards

nothing but respect

you gotta take care of us peasants

[granite knoll]

<@&268886789983436800> he stealthily deleted some profanity

[granite knoll]

it looks right at a glance

but the ratios don't equal one another... lemme see

[deep plume]

@granite knoll is there anyone on this server who specializes in trig? I will pay them via cashapp for help during finals week.

[granite knoll]

payment is against the rules FYI

[deep plume]

thank you man. take your time

ahhh dang.

that’s strange

pretty far from prostitution

[granite knoll]

you can also ask in #geometry-and-trigonometry

[deep plume]

thx. lemme know if you can’t figure it out and i’ll post it there

[slim jasper]

Clarification: Paying people for help (rather than for cheating assistance) is not forbidden as such, but we prefer that it's not arranged through the server, because we don't want to be involved in the inevitable disputes about whether the help given was worth the agreed price or not.

[deep plume]

awesome. thanks for the clarity. I shall not arrange it on off of grounds.

server grounds*

woah I fucked that sentence up

ykwim

[granite knoll]

you should ask in #geometry-and-trigonometry ; the ratios aren't coming out correct but I don't know why

[deep plume]

woah. didn’t expect this problem to stump. will do

[granite knoll]

lol well I haven't taken geometry in 25 years so

[cedar kiln]

@deep plume Has your question been resolved?

[cedar kiln]

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[blazing kraken]

so i have a question, it's a simple one and i might look stupid for it but im kinda confused, is 5x + 7 a polynomial?

[hidden mural]

yes

[blazing kraken]

im studying math for an exam and it says that it isn't a polynomial in our book so im confused

also
x^2

and 6^x

[vagrant elbow]

this is a polynomial

[blazing kraken]

idk ask the one who made our math book

[vagrant elbow]

this is not

surely you misunderstood something

[blazing kraken]

"x ^ -3, sqrt(x), 5x + 7, 6^x, x^2, all of these are not polynomials"
this is exactly what's written in my school's math book

[vagrant elbow]

5x + 7 and x^2 are certainly polynomials

Unless for some reason your book thinks monomials and binomials don't count

[blazing kraken]

(also im kinda confused about 6^x)

[vagrant elbow]

That's an exponential

[blazing kraken]

so 5x + 7 and x^2 are polynomials, x^-3 and sqrt(x) and 6^x aren't

not sure about 6^x but ima assume it isn't

[vagrant elbow]

The power needs to be an integer

You can't have a power as a variable

[blazing kraken]

yeah i also thought that was the reason

[cyan eagle]

polynomial is defined as $a_nx^n+a_{n-1}x^{n-1}+\dots a_1x+a_0$, so $6^x$ can't be. also maybe your textboox is saying 5x + 7 and etc are not polynomials because they want distinction between number of terms. like, 5x+7 has 2 terms, so it's a binomial, which is a polynomial.

[wraith dagger]

fish

[blazing kraken]

i misread one of them actually lol

it was written 6^x + x^2

but i didn't misread the 5x + 7 one tho

[cyan eagle]

i said "which is a polynomial"

[vagrant elbow]

let n --> infinity, bam everything is a polynomial

[blazing kraken]

(i did)

for some reason i only notice these small details after it's too late it's been more than half an hour now since i got confused

ok this is so embarassing

[vagrant elbow]

It's alright

[blazing kraken]

.-.

not my fault! it's my eyes fault! (which is my fault)

i saw a comma between the sqrt(x) and 5x + 7 even though there wasn't

how do i close the channel

.close

[cedar kiln]

Channel closed

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[blazing kraken]

.close

ok ig that does it now

thanks !

why isn't it going to the available channels

eh ig i will get back to studying

anyways, thank yall !

[cedar kiln]

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[umbral crow]

If f(0) = f(1)

And f is continuous

Wouldn’t MVT state that f’(x) must equal 0 at least once

And prove the question wrong

Or am I missing something

[umbral crow]

Since it says f is strictly increasing

<@&286206848099549185>

[dim birch]

Remember that an open interval doesn’t include the endpoints

Not sure why we’re talking about MVT

It doesn’t say that the closed interval is continuous

It only says that the open interval is

[umbral crow]

ohhh

I missed that

So it looks like this and answers D

thanks

.close

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[undone rapids]

can someone help me solve this differential equation ? There are ways to make it simpler if you do notice that 1/2sin(x) = cos(x)sin(x) and then see quickly a solution but I'm not someone with that kind of intuition in math, if someone could help me solve it entirely through a method that works all of the time it would really help

[dim birch]

$$y=\frac{1}{e^{sin(x)}}(\int \frac{1}{2}sin(2x)e^{sin(x)}dx)$$

I believe

https://youtu.be/gd1FYn86P0c?si=fCh7FLrC1Kq9rwhz

[wraith dagger]

Cyphercrit

[undone rapids]

okok good this is what I found but i don't manage to finish this

it feels endless

[dim birch]

The integral?

[undone rapids]

yes

[dim birch]

And I’m guessing you’re doing integration by parts?

[undone rapids]

yes

[dim birch]

Watch the last example of this and it should become clear what you need to do

https://youtu.be/sWSLLO3DS1I?si=h1Po515mrAOCbICw

[undone rapids]

okok thank you a lot

[dim birch]

No problem

[cedar kiln]

@undone rapids Has your question been resolved?

[undone rapids]

i carry around an extra cos(x) is it a problem ?

I know that sin(x)cos(x) = 1/2sin(2x) so I think it can be solved the way the video shows, but basically it's if you don't know that sin(x)cos(x) = 1/2sin(2x) you can't really do it, right ?

nevermind even knowing that property i have an extra thing, do you maybe see where the problem is ?

[cedar kiln]

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[wide badger]

I missed like a week of classes because I had some medical issues, and I'm pretty lost on how to solve this question that is to catch up on the materials covered in class. The question asks: Determine the exact value of the trigonometric expression. Express your answers in simplified radical form.

[wide badger]

i did begin by changing the angles to their exact values in radical form, but as for simplifying it i am lost

[cedar kiln]

Show your work, and if possible, explain where you are stuck.

[wide badger]

here is what i've done (not much 😭😭)

[plain ridge]

well for starters you have $2 \frac a 2$

[wraith dagger]

b

[plain ridge]

which is just a

[wide badger]

right so just root 2

[plain ridge]

mhm

then you multiply that by ½

[wide badger]

ahh so i was doing the right things, just not in the correct order which messed it up

[plain ridge]

probably🔥

[wide badger]

honestly that happens so often it sucks so bad lmaoo

thank you though, i think im good to solve it now 🫶🫶

.close

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[hidden hound]

(0, 6.3)
(6, 0)
(21, 0)

these are my three coordinates right?

2 x intercepts

and a y intercept

y intercept = c

6.3

right?

y = a(x-6)(x-21)

[slate lintel]

yes

[hidden hound]

6.3 = a(-6)(-21)

6.3 = 126a

a = 6.3/126

y = 6.3/126(x-6)(x-21)

is that correct

minimum height is 30

so

(x, 30) --> turning point

to find x

we use axis of symmetry

$\frac{0+180}{2} = 90 \ \ \text{turning point} = (90, 30) \ \ y=a(x-90)^2+30 \ \ \text{sub (0, 75) into turning point equation} \ \ 75 = a(-90)^2 + 30 \ \ 45 = 8100a \ a = \frac{45}{8100} \ \ \text{final equation:} y=\frac{45}{8100}(x-90^2)+30$

[wraith dagger]

pixel

[cedar kiln]

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[midnight ridge]

Numero 3!

[midnight ridge]

This is about Statistics (nomal distribution)

Here's my obviously wrong workings

[violet flume]

On a production line making cameras, the probability of a randomly chosen camera being substandard is 0.072. A random sample of 300 cameras is checked. Find the probability that there are fewer than 18 cameras which are substandard. (Ans: 0.180)

might help someone help, idk the answer

[midnight ridge]

yep, thanks

[fresh patio]

at first glance it seems as though you are not bounding your normal random variable below

don't think it would make the answer that off since mean is positive and large, but normal can be negative so you need to bound below

also wait, is your calculation of np(1-p) correct?

[midnight ridge]

AAAAAHHH

[fresh patio]

yeah you did np^2

[midnight ridge]

this is why i lose so much marks in exams 💀 💀

thanks, im going to correct that rq

i got the answer!!

thank you!

[fresh patio]

cool

[midnight ridge]

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[severe elm]

simplified all the exponents and then took the stuff from the denominator and put into the numerator to cancel out the exponents

leaving n^2 p

<@&286206848099549185>

[candid mason]

yes it is correct

[severe elm]

unfortunately the checker returns incorrect

[candid mason]

maybe swap p and n around. Mostly likely there is coding error with the checker so nothing can be done

[severe elm]

nvm i needed to abs the p

[candid mason]

Ah that make sense. The sqrt is always positive

!done

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[strong jacinth]

question 8a

[crimson sedge]

so basically

@strong jacinth

[strong jacinth]

hi

[strong jacinth]

yreah

[crimson sedge]

oko

the length is 20

[strong jacinth]

yea

[crimson sedge]

and each section of the clock is 30 degres

[strong jacinth]

huh

oh yea

alr

oh so ur saying that it was be 96 degrees.?

[crimson sedge]

yes

[strong jacinth]

welll

the answers approached the question differently

[crimson sedge]

how?

[strong jacinth]

i dont understand how they did it

[crimson sedge]

the answer is the same

[strong jacinth]

yah ik

but do u get how they did the questin

[crimson sedge]

nah

im only grade 8

[strong jacinth]

oop ok'

do yk how to do b

[crimson sedge]

lemme se

no sorry

[strong jacinth]

nvm

[crimson sedge]

i dont get it

[strong jacinth]

i know how to do it

all g

thanks lad

.close

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[radiant scaffold]

hi i just want to ask, can i add m1u1 and m2u2 together like vectors?

[hollow trail]

momentum is a vector quantity, yes

[radiant scaffold]

ahhhh that’s right

thank you

.close

[cedar kiln]

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[cedar kiln]

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[crimson sedge]

B. 𝑝→𝑞

¬𝑝 ∴¬𝑞 is supposedly an invalid arguement, is this an error?

[crimson sedge]

if p and q are false, the arguement is valid, no?

[royal loom]

I agree with that reasoning

[crimson sedge]

my worksheet is saying the answer is b for finding the invalid arguement

[royal loom]

I'll forward this to my philosophy sir

[crimson sedge]

oh apologies, the conclusion has to be true where hypothesis is true, b has a true and a false

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[frank dove]

1/7(80i+1560j) km/hr

[cedar kiln]

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[ember otter]

can anyone help how numerator is seprated among the denominator terms

[ember otter]

can anyone help how numerator is seprated among the denominator terms

I have tried dividing numerator by denominator but neither quotient nor remainder is the answer written on RHS

[dim birch]

do you know about partial fraction decomposition?

[ember otter]

Sorry no but if it is that i can google it

Thing is, i don't even know what to search on internet to get my answer

[dim birch]

this should definitely help :)

https://www.youtube.com/watch?v=QKkdYW77xNI

[ember otter]

I only want to know about the highlighted part

Oh ok thanks

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[cedar kiln]

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[shut tree]

yo

[shut tree]

x+y > =140
2x+5y>=610
3x+2y>=ge360
y<=36

Are these all the contraints or is there more?

[cedar kiln]

@shut tree Has your question been resolved?

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[strong jacinth]

<@&286206848099549185>

[crimson sedge]

hello

what have you tried

[strong jacinth]

and

[strong jacinth]

uh so

i equated

2t+5 = 3t-15

and got t=20

[undone slate]

Make cot into 1/tan

[strong jacinth]

which is a correct answer

so i tried to do the same for question 15 but that idnt work

[undone slate]

It wont

That's just a fluke

[strong jacinth]

dang

[undone slate]

This

[livid hound]

that doesn't really help

[undone slate]

rlly?

what do we do

[cinder siren]

1/tan(2t + 5) = tan(3t + 5)

[strong jacinth]

mhm

[undone slate]

yea?

[strong jacinth]

ye thought so

[livid hound]

note that
cot, cotangent is short for complementary tangent
apply complementary relation between tan and cot

[nimble veldt]

3t-15

[undone slate]

Which is?

[livid hound]

its pinned in #geometry-and-trigonometry

[strong jacinth]

nvm got it

tyyy

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