help-23

[fickle abyss]

0<x<= 4

[cosmic grove]

why

[fickle abyss]

wait

no

[faint seal]

$x^2>=0\forall x\in R$

[flat frigate]

kheerii

[fickle abyss]

$f(x)$= $\frac{8x+5}{2x+3}$, $x >\frac{-3}{2}$\ $g(x)$ = $16-x^2$ ,0≤x≤4 \ my equation there is fg^{-1}(x)

[flat frigate]

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

[fickle abyss]

idk where i did wrong in latex

but yh thats the equation

[safe radish]

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[velvet cobalt]

Can someone pls help me solve number 1

[velvet cobalt]

Integration by substitution

[safe radish]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

@velvet cobalt Has your question been resolved?

[velvet cobalt]

1

[faint seal]

this doesn't seem very basic

,w integral of x*sqrt(x^2-6x)

[flat frigate]

Results provided by WolframAlpha

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Requested by kheerii#8421

[faint seal]

yeah

[high mica]

damn

[faint seal]

well

@velvet cobalt pretty sure the question is wrong by the way they are calling it "basic calculus"

[velvet cobalt]

Yea

I emailed my teacher

No response

[faint seal]

especially since the other questions are literally just 1 u sub

[faint seal]

well

if you really want to know how to do it

you would need to complete the square firsdt

and then substitute

[velvet cobalt]

I got stuck at this part

[winged cloak]

for starters you can do the first integral

[faint seal]

have you done trig substitution

[velvet cobalt]

Yea

But only the basic ones

[faint seal]

what do you substitute in case of sqrt(x^2-a^2)

[velvet cobalt]

That one seems complicated aswell

[winged cloak]

try multiplying and dividing by sqrt(u²-9) on the second integral

and see where you get from there

are you allowed to integrate by parts here?

cause what i have said requires it

[velvet cobalt]

Im not quite sure

Maybe as long as i use the substitution

[velvet cobalt]

How?

[calm zenith]

try completing the square

[velvet cobalt]

3sqrt(u^2-9) •sqrt(u^2-9)?

[velvet cobalt]

I already did that first part

[calm zenith]

[velvet cobalt]

I can expand usqrt(u^2-9) into 1/3(u^2-9)^3/2

But idk what to do with the other

[safe radish]

@velvet cobalt Has your question been resolved?

[lone arch]

A similar questions has been asked on Math StackExchange before, with -4x instead of -6x:
https://math.stackexchange.com/questions/2996834/calculate-int-x-sqrtx2-4x-mathrmdx?noredirect=1

[velvet cobalt]

Wow

Looks like an advance one

Could anyone explain this?

I dont get it

[safe radish]

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[wet dragon]

For b (iii)

I want to answer this question using the limit comparison test

What’s the best way to choose the function g(x)

Any help would be greatly appreciated

<@&286206848099549185>

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[lean otter]

Here's a question from my calculus 2 homework. I struggle to determine the absolute value of a sub n+1 over a sub n when the denominator looks like that. I was able to get the absolute value of x times( (n+1)^2 times 9n)/n^2 times (9n+9). I'ms struggling to determine what R is based on the limit as n goes to infinity

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@lean otter Has your question been resolved?

[lean otter]

no

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

no

[tame charm]

Hmm

Can you rewrite the denominator somehow?

Looks like 9 * 9(2) * 9(3) * …

= 9^n * 1*2*3*…*n

Hm

Maybe combine the 9^n with the x^n on top?

I think you can then plug this into the limit test

@lean otter

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[steel gulch]

Does anyone know what test I should do to determine if this series is convergent

[steel gulch]

I've tried the ratio test, and that does't seem to work.

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@steel gulch Has your question been resolved?

[stoic dune]

Can you do a limit comparison? This looks a lot like 1 / ³√[n²log(n)²]

[steel gulch]

maybe

I'll try it

actually, no.

actually yes

nvm

.close

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[fiery valley]

in this DE can I use undermined coefficients for 15sin(x) and parameter variation for e^x*tan(3x) and then add both solutions?

[safe radish]

@fiery valley Has your question been resolved?

[crimson field]

Yes.

[fiery valley]

Yes?

<@&286206848099549185>

[crimson field]

If you find particular solutions for each separately, i.e., (3D^2 - 6D + 30)y = 15 sin(x) and (3D^2 - 6D + 30)y =e^x tan(3x), you can add the two particular solutions and know you have a particular solution to the original differential equation.

[fiery valley]

Thank you so much <3

[crimson field]

I thought this is what you were asking. They called it the principle of superposition.

[fiery valley]

:0

.close

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[hallow gulch]

i need help in understanding functions and linear graphs topic
i just did the basic graphs so far
i learned about x and y axis
i can mark the points on a graph if im given coordinates
but i dont understand the second part of the chapter

[hallow gulch]

hello??

@meager igloo

<@&286206848099549185>

[clear blade]

!15m

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[hallow gulch]

...

i need help

[outer raven]

specify ur question.

[hallow gulch]

so i have questions in which

im given graphs to draw functions such as y=2x+4 and y=2-3x

i dont understand it

[outer raven]

i dont know why u dont understand it.

use desmos or geogebra to draw it.

[hallow gulch]

whats that

[outer raven]

https://www.desmos.com/calculator

[hallow gulch]

no

i have to do to it in notebook

or graph book

i dont understand the 2x+4 and what do these values mean

[outer raven]

...i mean you can learn how to draw by websites.

two points can determine a line.

choose two points, and draw your line.

[hallow gulch]

i know how to draw graphs but i need to understand this type of questions

i got exam tomorrow

hello?

[outer raven]

i dont know what you mean to understand it.

[hallow gulch]

the question is On a sheet of graph paper using a scale of 2cm to represent 1 unit on x axis and 1cm to represent 1 unit on y axis draw graphs of the functions y=2x+4 and y=2-3x for values of x from -2 to 2

i can do the scaling but i don't know what to do with functions

[outer raven]

just draw the part satisfying x from -2 to 2.

[hallow gulch]

do i have to solve it?

.close

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[quasi bison]

those black bands are like 10 times wider than the image itself 💀

for everybody else's sake (and my own), this is the problem

@cunning rampart no, you don't have to draw a graph.

in fact, a graphical solution would go against the problem requirement to use either substitution or elimination

[cunning rampart]

Wait sorry wrong one

[quasi bison]

can you take the black bars off this time please

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[cunning rampart]

This one

[quasi bison]

augh

[quasi bison]

You deleted your original post. The channel will abruptly close and possibly lock. (This is irreversible).
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[cunning rampart]

Shit

[safe radish]

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[analog burrow]

Can someone help me with this

[analog burrow]

How do I find the angle goh?

[lean otter]

alr @analog burrow let's do this together

im going to help you with diagrams so i need you here with me.

are you here?

[analog burrow]

Yes

[analog burrow]

Alright

[lean otter]

so do u understand that any length from the center of the circle to a point on the circle is called radius

[analog burrow]

Yes

[lean otter]

good. so can u tell me the radius from the figure?

[analog burrow]

10cm

Which is OH

[lean otter]

well done.

or OG

same thing

[analog burrow]

Yes

[lean otter]

now im going to use trigonometry and dissect things.

watch close

[analog burrow]

Ooh alright

[analog burrow]

So we cut it into half?

[lean otter]

lets say the angle we need to find is theta.

yeah

[analog burrow]

Okay?

[lean otter]

can tell me what would "?" be

if assuming our answer to find, GOH is theta. what would GOD be?

[analog burrow]

We'll have to use sin inverse right?

To fund the angle

[lean otter]

yes but please answer what "?" would be

[analog burrow]

23.6 degrees

[lean otter]

huh

no in terms of theta...

theta/2 right?

[analog burrow]

Oohh

Yes half theta

[lean otter]

idk how you arrived at 23.6 degrees but let's go my way and see if i can get to ur answer yeah?

[analog burrow]

I did X = sin^-1(4/10)

Idk if it's good though 🥲

[analog burrow]

Yes your way please

@lean otter ?

[lean otter]

does this make sense @analog burrow ?

length GD will be GH/2. because we're dissecting, or a better term would be, bisecting, cutting in half

so GD has to be half of chord length, which is 8/2 or 4cm.

I used trig in triangle GOD.

[analog burrow]

Yes

[lean otter]

sin(theta/2) = 4/10, 10 because its the radius OG.

good

so you were right, theta/2 = sin inverse of (4/10)

[analog burrow]

Yes

[analog burrow]

Which is also the hypotenuse

[lean otter]

good job!

[analog burrow]

It's a lot more clear now tysm

So we'd have to do sin^-1(4/10)*2

👍 tysm

[lean otter]

so this is (theta/2) = 23.58 degrees, meaning your total angle GOH would be twice of that, or roughly 47.16 degrees

[lean otter]

yep!

[analog burrow]

Yes 😌

Tyyy

.close

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[silent narwhal]

with the question "if you have the numbers 1,2,3,4,5 how many ways can you arrange it if the number arranged is less than 40,000 and ends in an even number?" How would@u get to the answer

[silent narwhal]

What I thought is first u have all the even numbers which u get by doing 4!*2=48

Then you do 48 take away all numbers whihc start from 4 or 5 for whihc I did 2* 3!*2

Then I took that away from all outcomes 48-24=24

The answers 30 what did I do wrong

[safe radish]

@silent narwhal Has your question been resolved?

[wind kite]

u didnt consider all the cases

[wind kite]

what if i starts with 2 at the start

then your first calculation 4!*2 =48 wouldnt work

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[safe radish]

@lean otter Has your question been resolved?

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@lean otter Has your question been resolved?

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[wind kite]

find the number of arrangements in the word ABA

[safe radish]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[wind kite]

is it 6 or 3

define an arrangement

[hushed minnow]

could you define an arrangement?

Is the question how many different words can you make up with 2 A's and 1 B?

[wind kite]

yes

[hushed minnow]

well it's 3, choose a slot for B and then you have no choice

you can also think about it by choosing slots for A's first and the you have no choice so binom(3,2)=3

also you could just write down all the arrangements

[wind kite]

okay

how about

find the number of arrangements that can be made from the word

ABACUS

[hushed minnow]

it's the same reasoning, jest put down all the letters and leave the A's for last

[wind kite]

so would it be 6! or 6!/2!

[hushed minnow]

that would be 6 * 5 * 4 * 3

so the second one

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[safe radish]

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[sonic geyser]

Isolate $\sin^2(v)$ in the identity

[tall bough]

just solve for sin²(v)

[flat frigate]

Rub05

[tall bough]

real

fr

[sonic geyser]

Then, integrate the result

[tall bough]

which you basically get an another identity

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[lean otter]

Find a set of unique rationals in the form 1/x that sums to 1 with x greater than or equal to 2 and less than or equal to 2023

i was here a day ago and ive made progress with this but i need as bit more help

[lean otter]

ive gotten an equation with 168 rationals but its extremely time taking and there must be a more effecint way

ive written two programs that can find fractions but the main problem is duplicates and no more routes of expansion

the programs:

number 1:

#n1 and n2 are factors of your desired fraction

x = 1
while x == 1:    
    n1 = int(input('number: '))
    n2 = int(input('number: '))
    frac1 = (n1*(n1 + n2))
    frac2 = (n2*(n1 + n2))
    print(frac1, frac2, "\n")

number 2:

# the amount of frac variables can be expanded for the amount of fractions that add up to 1 

# 1/2+1/5+1/6+1/30+1/10 is a working equation

# so you could set more frac variables to n* 1 2 5 6 30 10


x = 1
while x == 1:    

    n = int(input('number: '))
    frac1 = (n*2)
    frac2 = (n*3)
    frac3 = (n*6)

    print(frac1, frac2, frac3, "\n")

https://tio.run/##bY7BasMwEETv@xVDThLIjZ0eCqG@6gt6Kz2IRm4FsSRWcou/3lUqQR3oHmfmzU5c82fwj11c47ptE4cZE5v37IJPcHMMnKGbAJOgiYxP35Yx4vWNiC52QgrXLyvSMiukbDjLMxGAKTAcnAcb/1H8m6UwKHRDSeD3UukpIDoMOEILJ5vhSi2e0Z/RBIBtXthDm2uy1NQ65sHEaP3lRu/xcfyPf@HF7mN1vILbzboPV8WWt39@exxDFPXp/braqsVhOJ76/iAVnk69pMjOZ1FZuW0/

and also this made by bongcloud but this is more chance and hoping for random fractions, which is also quite ineffecient due to duplicates

there must be a mathematical way to find the longest possible equation

<@&286206848099549185>

<@&286206848099549185>

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

<@&286206848099549185>

helpers really said nah 💀

<@&286206848099549185> ?

[calm zenith]

is this py?

[lean otter]

yeah

[carmine fable]

speaking of "more efficient way" of programming implementation , try asking here https://discord.gg/python

[lean otter]

ill try

[lean otter]

no help sadly

.close

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[plucky breach]

can someone help me at stochastic?

[plucky breach]

easy task actually

[fast gazelle]

just ask the question

[plucky breach]

In a small cloth bag there are four balls that are identical except for the color. One is yellow, one green, one red and one blue. Without looking, two balls are removed one after the other, with the first ball not being put back.

E: " Both balls drawn have the same color".

P(E)=...?

[grizzled shoal]

!status

[safe radish]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

@plucky breach Has your question been resolved?

[plucky breach]

1

[grizzled shoal]

what was your reasoning until you got stuck?

[plucky breach]

ohh I meant 1

not 2

[plucky breach]

is it not 1/4 * 1/3?

[grizzled shoal]

let's not get into the math first

think about it logically

let's say our bag is: {y,g,r,b}

and we take one out, like let's say we take out the yellow one

then our bag becomes: {g,r,b}

what is now the chance to get a yellow ball?

[plucky breach]

Yes

if: {y,g,r,b} then 1/4

[grizzled shoal]

yes, but we already took out a yellow ball

so our bag is not {y,g,r,b}

it is {g,r,b} now

[plucky breach]

there is no yellow ball in there, so there is no any posibility

[grizzled shoal]

👍

[plucky breach]

oh

I got it now, okey. bruhhh. Okey, thanks for it first

[grizzled shoal]

we are kinda trying to get two of the same thing out of a bag, when only one is inside

[plucky breach]

Yes it is a problem of reading

[safe radish]

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[plucky breach]

.reopen

[safe radish]

✅

[plucky breach]

I have four more question. Can help me for a short? @grizzled shoal

[grizzled shoal]

just ask them here

[plucky breach]

okey wai

t

A wheel of fortune is divided into 60 fields of equal size. 20 fields are blue, 24 fields are green, 12 fields are red. The rest has the color yellow. The wheel of fortune is spun twice. Determine the probabilities.
Task:
a) P (red twice). P(r twice)= 12/60 * 12/60 ? Correct?
b) P(once blue, once yellow)
c) P(blue at least once)
d) P(red at most once, but no yellow)

At b I would say, 20/60 * 4/60?

At c I would say, 20/60
At d I would say 1 - 4/60?

all wrong I know…

[grizzled shoal]

a) looks good

60 total
20b, 24g, 12r, 4y

b is asking for once yellow, once blue

however, it does not say in which order

so getting blue and then yellow works, and so does getting yellow and then blue

[plucky breach]

hmh

[grizzled shoal]

with task c), we can take a look at two cases:

1. we get yellow in the first try
2. we dont get yellow in the first try, but do get it in the second try

[plucky breach]

wait a moment. Lets finish b. So if there would be an order like yellow, blue then its: 4/60 * 20/60 but because there isnt an order its: 2 * ( 4/60 * 20/60)

?

[grizzled shoal]

yes

[plucky breach]

.

okey important to know

now we can do c)

[plucky breach]

didnt you mean blue?

[grizzled shoal]

yes

[plucky breach]

So it could be: 1) 20/60 * (something else) or (something else) * 20/60?

[grizzled shoal]

20/60 + "not blue" * 20/60

[plucky breach]

why?

[plucky breach]

why "not blue"

[grizzled shoal]

the second path is that we didnt get blue in the first place

[plucky breach]

because blue at least once? Could write it mathmatical so that I can follow you better?

[grizzled shoal]

we are just looking at all possible paths

and then add them up

that's all

[plucky breach]

how do i write not blue

[plucky breach]

okey then lets go on d

[grizzled shoal]

d) P(red at most once, but no yellow)

so here we have three paths

1. no red
2. red first
3. red second

we get each probability

and then add them

each time, given that no yellows

[plucky breach]

thats it?

[safe radish]

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[cloud zephyr]

I dont really understand how to do the Ind Step

[cloud zephyr]

I started my base case of N=1 cause thats the first positive integer

then I assumed that 10k = 5(k)^2+5k

So then I started my ind Step by doing 10(k+1) = 5(k+1)^2+5(k+1)

but i dont really know what to do next

[safe radish]

@cloud zephyr Has your question been resolved?

[grizzled shoal]

10k=5k^2+5k is not true

10+20+...+10k=5k^2+5k

i would advise you use sum notation

this is what we want to show

for n=1 we get
10=5+5
so that checks out

then via induction we look at n+1

and want to show this identity

when we are dealing with such sums, it is always a good idea to "pull out" the last term of the sum

that way, we will get the original sum back

for which we have shown the identity

[safe radish]

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[sleek spear]

can anyone help me

[cloud zephyr]

na

[sleek spear]

ivfe been trying trial and error and trying to find a pattern but it wont work

[sleek spear]

bru

[safe radish]

@sleek spear Has your question been resolved?

[sleek spear]

<@&286206848099549185>

[sleek spear]

@sleek spear

[safe radish]

@sleek spear Has your question been resolved?

[safe radish]

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[cunning crypt]

Could someone help me with parts d and e

i think for D you are supposed to just do the dot product

but im not entirely sure

[lean otter]

yes

[cunning crypt]

this is the work i have so fat.

so far

[lean otter]

looks fine

[cunning crypt]

for part e, however, i do not know if i found the correct matrix P

[lean otter]

you are correct

[cunning crypt]

the matrix p is just the two eigenvectors together in the same matrix right?

[lean otter]

yes

[cunning crypt]

oh great

tahnks

thanks

[safe radish]

@cunning crypt Has your question been resolved?

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[queen parcel]

Match the coefficients

[oblique trail]

Where?

Do I mean factorise the 2abx and ax?

[queen parcel]

Well the coefficients to x^2, x, and x^0 should be the same on both sides

[oblique trail]

Oh so like a^2x^2= 4x^2, ax=14x?

I’m rly bad at math so pls bear with me

[queen parcel]

yes! Keep in mind you also have 2abx on the LHS

[oblique trail]

Hmmm what do I do with that

I’m not really understanding

<@&286206848099549185>

[queen parcel]

(a^2) x^2 + (2ab + a)x + b^2 + b

4 x^2 - 14 x + 12

Do we agree?

[oblique trail]

yea but why did u factorise thise specific variables

those*

[queen parcel]

Because you can match coefficients

[oblique trail]

oh i understand

now what do i divide both sides with x?

[queen parcel]

Well in order to make these equal, set

a^2 = 4, 2ab + a = -14, b^2 + b = 12

[oblique trail]

one sec

ok and then i solve?

[queen parcel]

Ye

[oblique trail]

so a=2, b=-4

now do i substitute into the equation?

[queen parcel]

Ye

That's one function

There's another a, b pair which makes it true

[oblique trail]

how do i find that?

[queen parcel]

If a^2 = 4, then a = what and what?

[oblique trail]

ohhh + or - 2

b as well?

or is it only -4

pic doesnt load

[queen parcel]

#❓how-to-get-help

[oblique trail]

@queen parcel so now what?

[queen parcel]

Correct, now what is b for a = -2?

[oblique trail]

+2?

i mean +4?

oh wait

my bad

one sec

so b=3?

[queen parcel]

🙂

[oblique trail]

ok so

how do i write the answer now

would i just substitute the numbers in f(x) = ax+b

got it, thanks man

.close

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[lean otter]

Please help quickly

[lean otter]

What is the formula for the surface area of a one quarter of a sphere closed

and the formula for the volume of one quarter of a sphere closed

Please i need now

<@&286206848099549185>

😭

is that 1/4 of a sphere?

no all of it

ahhhhh 😭

wdym ahh

divide by 4

its 1/4

that doesnt work

too late

.close

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[final halo]

too late for what?

[lean otter]

ill have to do my self

[safe radish]

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[obtuse kettle]

circle theorums q:
I've had a look at the tutorial provided with the question but I still don't understand how to solve this..

[green bane]

what is the sum of all the angles in a hexagon

[obtuse kettle]

(n-2)x180 which is 720

but i don't think that will help much until i get the other values

[green bane]

could uh i have the tutorial

[obtuse kettle]

i can't rlly send it to u bc otherwise you'll need to log into my acc but i can send clips

[green bane]

ah

[obtuse kettle]

does that help?

[green bane]

ye

[obtuse kettle]

me rn:

[green bane]

hint

[obtuse kettle]

360-136-136/2?

sorry im a bit confused

[green bane]

no

both are opposite angles

[obtuse kettle]

uh so (180-136)+(180-103)?

[green bane]

yep

[obtuse kettle]

RLLY?

[green bane]

yep

[obtuse kettle]

OMG TYTY

[green bane]

[obtuse kettle]

LIFESAVER

[green bane]

:D

[obtuse kettle]

.close

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[lean otter]

Should I be trying to work out the work done against friction or am I going about this wrong?

[ember sphinx]

Maybe try P = F*v

[lean otter]

what would F be?

[ember sphinx]

you work it out

So

you know the power of the vehcile

wait

Yea

just use P = F*v

maximum velocity is when accelration is 0 (the net force is 0)

and so force would be 1500

[lean otter]

it's that 5 tonne bit that confused me thought I'd need it somewhere

thanks

[ember sphinx]

Becuase i think you could use Ke

and than derivitives

but im not too sure

[lean otter]

I tried using KE

but then I thought I'd use work against friction = Fx

and have no x

basically couldn't work out how to use 1500N with KE

but P = Fv works anyway

thank you

.close

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[daring thistle]

find the exact value of sin 23pi/12

[daring thistle]

i need help understanding how to do this problem

[ruby sand]

no calculator im guessing?

[daring thistle]

yeah

i know i have to factor it down

i have my sheet

[ruby sand]

ok well do you know the difference of sums

[daring thistle]

can you look at it

[ruby sand]

im not the best versed at this chapter but I finished it last tri

go ahead and attatch it

[daring thistle]

the top side

just want to make sure all is good

[ruby sand]

yep

its right

[daring thistle]

what do you think

okau usweet

can you check my second one

the question is state the exact value of csc 23pi/12

i started in the bottom by using the answer igot from previous question

but i want practise so heres finishedd:

ornot finished

close

[ruby sand]

seems about right

Imma check again though

my unit circle knowledge is failing me

[daring thistle]

ok

im not done

do you know the final answer?

[ruby sand]

trynna figure it out rn

[daring thistle]

kk

[ruby sand]

ok when I simplified it completely I got sqrt(6) - sqrt(2)

sorry

-sqrt(6) - sqrt(2)

[daring thistle]

shit

ok

[daring thistle]

i got this

over 4 though?

[ruby sand]

nah

just regular

try doing the second step again

[daring thistle]

when its at -4 sqrt(3) over -sqrt(6) + 3sqrt(2)

what do you do

reciprical ye

can you just flip it and factor or no

[ruby sand]

well you cant flip it because it's not an equation

[daring thistle]

this is what i did

ah

did you rationalize ?

[ruby sand]

like 1/2 = 1/2/1

[ruby sand]

always

[daring thistle]

can you show me your steps

[ruby sand]

you flip and you get

[daring thistle]

yeah i see

it

so do i just multiply top and bottom

by

[ruby sand]

by conjugate

[daring thistle]

-4 sqrt(3) over sqrt(6) -3sqrt(2)

[ruby sand]

thats what I did

[daring thistle]

okok

ill try that

[ruby sand]

alr

I gtg

[daring thistle]

kk thanks appreciate it

[ruby sand]

but I wish u luck

this is some hard stuff right here

ngl

[daring thistle]

thanks bro

[ruby sand]

I miss when problems only took like 5 minutes

;-;

[daring thistle]

hah tell me about it

[safe radish]

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[soft forge]

Can I use L’hopitals rule in any of these circumstances?

[green bane]

yep

[soft forge]

.close

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[whole merlin]

5. In a small toy shop, a 3D printer is used to build toy airplanes and toy spaceships. The machine can be used all day (up to 24 hours), but can only build one type of toy at a time. Each toy airplane takes 1.5 hours to build, and each toy spaceship takes 2 hours to build. The owner of the shop wants to build at least 4 airplanes each day, but has decided that the number of spaceships built must be greater than or equal to three fourths the number of airplanes built. Let 𝑥 represent the number of toy airplanes built each day, and let 𝑦 represent the number of toy spaceships built each day.
   a. (8 pts) Set up a system of inequalities that represents the possible numbers of each type of toy built in a day, and draw the solution to this system (also called the feasible region in class). Label all the vertices with ordered pairs (𝒙, 𝒚

[whole merlin]

Would this be started with y>3/4(x)

And x>4

[safe radish]

@whole merlin Has your question been resolved?

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[grizzled meadow]

i’m really stuck on c

[grizzled meadow]

why is the 1/(10-2) there

nvm got it

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[fast beacon]

How do u do question C?

[uneven veldt]

now, could you tell me what happens at the point of intersection between two lines

Hint: Think what happens to the equations of the lines specifically

[fast beacon]

they equal each other

simplify all of that it gives u px^2+tx-4p = 0

[uneven veldt]

yes, but note, this is a quadratic equation, and we want there to be 2 real solutions. So what condition can you think we can use here

[fast beacon]

b^2 - 4ac > 0

which gives t^2 + 16p^2 > 0

[uneven veldt]

Now, also note, that t^2 + 16p^2 no matter what will always be > 0

[fast beacon]

yup

[uneven veldt]

Now, I think you can understand why the given statement is true

[fast beacon]

the vertex is above the x axis

wait nvm thats when its <0

because its squared

so its never negative

[uneven veldt]

yes

and also note that p cannot be = 0 otherwise the second equation would no longer be a quadratic

[fast beacon]

yup

does that mean t > 0 and p is >= 0?

[uneven veldt]

It is given in the question that p is not equal to zero

[fast beacon]

oh shi yea p>0

i had a brain fart

[uneven veldt]

And also the square of -ve number are positive, hence p can be any number except 0 while t can be any number

[fast beacon]

oh right it includes negative values because they become positive anyway

so would it be TER and P not equal to 0?

the same as what's given in the question?

[uneven veldt]

yep

[fast beacon]

got it, thank you!

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[regal granite]

can anyone explain why its C

[regal granite]

im a lil lost

[tall cedar]

do you think its C?

[regal granite]

process of elimination

[light shoal]

that's the most simpleminded way, but entirely legitimate for a multiple choice question

[regal granite]

si

[light shoal]

if you want a solution that doesn't require elimination, just find two examples of f and g that satisfy the given conditions but give different answers for the integral in C

e.g. for one example you could choose f and g so that their domains don't overlap, so the integral in C is zero.. so for the other example, look for an overlapping case

[regal granite]

okay, thx amigo

,close

.close

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[regal granite]

idk where to start for this question

[regal granite]

o nvm

.close

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[mild lion]

help q11 pls

[plucky elk]

Figure out the angle using the arc length and radius

[mild lion]

i tried doing that but i got ir wrong

[plucky elk]

Show your work and the answer

[mild lion]

This was what I did

But I gave up after that cos yea

[plucky elk]

Why did you give up

[mild lion]

I thought I couldn’t minus 27820 from 6336 cos it would be a negative number

[plucky elk]

Also I can't tell how you got those numbers in the 3rd equation

[mild lion]

Idk either 😭

I multiplied both sides by 360 I think

[plucky elk]

,calc 2* pi *12.3/360

[flat frigate]

Result:

0.2146754979953

[mild lion]

To get rid of the 360

[plucky elk]

Do you know what 360/360 equals?

[mild lion]

Um

1

[plucky elk]

Yes

Use that in equation 2

[plucky elk]

When you do this step

[mild lion]

I don’t understand

[plucky elk]

Which part

[mild lion]

I don’t understand what u mean by multiplying 360/360

[plucky elk]

When you multiplied by 360 on the left side, you should have cancelled the 360 in the denominator

[plucky elk]

I didn't say to multiply by 360/360

[mild lion]

I thought I did this tho

[plucky elk]

Doesn't look like it in your third equation

[mild lion]

I am soooo confused

[plucky elk]

Start over then and explain all your steps one by one

[plucky elk]

,calc 2 * pi * 12.3 * 81.9/360

[flat frigate]

Result:

17.581923285815

[plucky elk]

And why is that wrong

[mild lion]

Idek

[plucky elk]

If it's not wrong why did you say it was

[mild lion]

No I said my other working out was wrong

[mild lion]

This

[plucky elk]

This is correct

[mild lion]

Ok ty

.close

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[quasi sun]

Lil help pls?

[feral thicket]

Phythagoras

C = 13

144+ 25 = 169

Sqrt 169 = 13

Sin theta = opposite on hypotenuse

[stark flame]

Hello

I need help with my math homework

[feral thicket]

Send

[quasi bison]

@stark flame open your own channel. #❓how-to-get-help

[quasi bison]

don't encourage channel intrusion

[quasi bison]

!nosols

[safe radish]

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.

[rocky gazelle]

pythagorean theorem:
$$a^2+b^2=c^2$$
use the mnemonic SOHCAHTOA -- SOH ($\sin = \frac{\text{opposite}}{\text{hypotenuse}}$) CAH ($\cos = \frac{\text{adjacent}}{\text{hypotenuse}}$) TOA ($\tan = \frac{\text{opposite}}{\text{adjacent}}$)
$$\csc{\theta} = \frac{1}{\sin{\theta}}$$
$$\cot{\theta} = \frac{1}{\tan{\theta}}$$
$$\sec{\theta} = \frac{1}{\cos{\theta}}$$
you should memorize all of these

[feral thicket]

Okay sorry

[flat frigate]

Dogecode

[safe radish]

@quasi sun Has your question been resolved?

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[waxen moon]

Find two positive numbers whose sum is 18 and the product of the first number and the square of the other is a maximum

[waxen moon]

For this problems, I set it up initially as:

x * sqrt(y) = 18

x + y = max
x + y = 18

What should I do after this?

[gritty glacier]

$f(x) = x + y^2$

[flat frigate]

bettim

[waxen moon]

Btw, this is applications of derivatives

[gritty glacier]

right?

[waxen moon]

Oh

It's not square root?

[gritty glacier]

same thing

square would be easier

[waxen moon]

I see

[gritty glacier]

now convert it all to same variable

x+y=18

so

y = 18-x

now

$f(x) = x + ( 18 -x)^2$

[flat frigate]

bettim

[gritty glacier]

this should be maximum

[waxen moon]

I see, so we could substitute for x or y, but it would give this exact equation correct?

[gritty glacier]

yes

then it would be f(y)

nothing much differs

[waxen moon]

Hmm

I'm getting a decimal

[gritty glacier]

i dont think so

[waxen moon]

When I took the derivative

[gritty glacier]

$f(x) = x + 324 -36x + x^2$

right?

[flat frigate]

bettim

[gritty glacier]

$f'(x) = 1 - 36 + 2x$

[flat frigate]

bettim

[waxen moon]

Oh

[gritty glacier]

$f'(x) = 2x - 35$

[waxen moon]

Yeah, I got this when I did direct derivative

[flat frigate]

bettim

[gritty glacier]

yes its decimal ig

whats the answer

[waxen moon]

It's supposed to be two whole numbers

It doesn't say
The teacher only said it's two whole numbers

[gritty glacier]

shit wait

[gritty glacier]

product not sum mb

$f(x) = x(18-x)^2$

[flat frigate]

bettim

[waxen moon]

I see

[gritty glacier]

so its uhhh

$f(x) = 324x - 36x^2 + x^3$ right?

[flat frigate]

bettim

[gritty glacier]

$f'(x) = 324 - 36 x + x^2$

[waxen moon]

Wouldn't there be a square root?
If we isolate for x, it would be y = sqrt(18-x) before substituting

[gritty glacier]

?

[flat frigate]

bettim

[gritty glacier]

theres no square root so ??

[waxen moon]

I see

[gritty glacier]

f(x) = xy^2

ight/

wait let me do with y

$f(y) = (18-y)(y^2)$

[flat frigate]

bettim

[gritty glacier]

right?

[waxen moon]

I'm confused about the power of 2 exponent

Is it from x + y = 18?

[gritty glacier]

they told square of a number nah/

[gritty glacier]

yes that is info 1

[waxen moon]

Oh

Makes sense then

[gritty glacier]

$f'(y) = 36y - 3y^2$

[flat frigate]

bettim

[gritty glacier]

when we do for 0 thenn

[waxen moon]

It's 6 then

[gritty glacier]

0 = 3y(12-y)

[waxen moon]

Oh

[gritty glacier]

how six?

yea fine yes

12 and 6

[dense condor]

$y=0, y= 12$

[flat frigate]

AltoHail

[gritty glacier]

yes but

the ques said two positive nums

0 isnt positive so y =12

[waxen moon]

Where did 36x come from?

[gritty glacier]

nah thats wrong leave it

[waxen moon]

It's 12 and 6

[gritty glacier]

use this

[waxen moon]

If we plug it into the equation

Of x+ y = 18

[gritty glacier]

yess

so max value would uhh

,calc 61212

[flat frigate]

Result:

864

[gritty glacier]

yes that

[waxen moon]

How did u get this derivative?

[gritty glacier]

$f(x) = (18-x)^2 \times x$

[flat frigate]

bettim

[waxen moon]

I'm getting 3x^2 -72x - 324 tho

I found out

I'm getting x^2 -36x + 18 tho

[safe radish]

@waxen moon Has your question been resolved?

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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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[high horizon]

I don't know where to start.

[high mica]

what does gradient 0 say about the line?

[wise blaze]

slope=0

[high mica]

yes but what does it say about the line?

[wise blaze]

the slope of AB =0

[proud cosmos]

it's a horizontal line

[high mica]

yes this

[high horizon]

Yes

I drew a diagram so far thats all Ive done

[proud cosmos]

you have the middle of the horizontal line and you know the full length

[wise blaze]

y coord of A and B =2

[proud cosmos]

AB is 10 in total

mp's x is 1

[high horizon]

Alright

..I'm lost after this

Is there some equation we have to equate?

[proud cosmos]

you know that mp is in the middle of AB

[wise blaze]

let x1 and x2 be the x coords of A and B

x1-x2=10

(x1+x2)/2=1

[high horizon]

Ohhhh we can make a simultaneous equation individually for the x'ys and y's

[high horizon]

Hold on why does this work

[wise blaze]

cuz distance = 10

and its a horizontal line

[proud cosmos]

AMP = MPB since it's the middle

[high horizon]

Oh of course

So a side track question

[proud cosmos]

try finding one of these

[high horizon]

for example the distance in this random line would be 14 right

[proud cosmos]

yes

[high horizon]

What about the y's?

[wise blaze]

2

[proud cosmos]

same y if it's horizontal

[high horizon]

Oh right

It's horizontal

If it were a slope it would be a different case

Right?

[wise blaze]

yes

[high horizon]

If it were a slope we'd use the pythagoras theorem

And equate that somehow

Right?

[wise blaze]

no

[high horizon]

Actually the second question is for a slope

So I understood the first question so far

[proud cosmos]

depends on what you're given and what you're searching for

[high horizon]

Now it's a slope

S

For part b

Actually let me do this myself I'll brb

Thanks guys @proud cosmos @wise blaze

[high horizon]

Do I repeat the same thing for y1 and y2?

[wise blaze]

yes

what you get for tha answer

[high horizon]

I solved x

[wise blaze]

What

[high horizon]

x1 = -4 and x2 = 6

But I cant solve y

I always keep getting -y1 in the equation

Which means u cant solve it

[wise blaze]

actually

When the line is horizontal

[high horizon]

Isnt y the same?

LOL

YO

[wise blaze]

which means all y coord are the same

[high horizon]

WHY DIDNT I THINK OF THAT

JESUS

IM STUPID

[wise blaze]

Yes

[high horizon]

YEA

The straight line thing threw me off

[wise blaze]

lol

[high horizon]

Btw I love chuuniboyu @wise blaze

Based anime

My guilty pleasure

[wise blaze]

me too death

[high horizon]

I would never admit I love that anime to my friends

Theyd bully me

😭

Let me try to solve part b now one sec

[wise blaze]

bruh thats cringe

everyone love it death

[high horizon]

Can u help me on part b too 😭 @wise blaze

Just a little hint

[wise blaze]

ok

distance formula

[high horizon]

The pythagoras thing

[wise blaze]

sqrt[(x1-x2)^2+(y1-y2)^2]=10

[high horizon]

Yes

A lot of unknown variables

It scares me

OH

I GOT IT

[wise blaze]

ok i give you 4 formulas

solve x1 x2 y1 y2

all understand right?

[high horizon]

thank you

i got it

.close

[safe radish]

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• 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.

[patent lodge]

Could someone help me with part c ii)?

i can send the solutions to the previous questions if it helps