help-10

[obtuse pebble]

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[fiery vapor]

does anyone know how i can find the equation to make this function?

[spark field]

make a piece wise

[fiery vapor]

what does that mean

[spark field]

1 function that is defined by multiple sub functions

make 3 equations

[fiery vapor]

ohh ok

[spark field]

for the highlighted sections

[fiery vapor]

do you know how you can find the derivative of that?

[spark field]

Draw tangent lines

and get an aprrox estimation

In some places the function is not differentiable

[fiery vapor]

but it would work if you just find the tangent of the right side?

[spark field]

no the function is not differentiable

it has a corner

[fiery vapor]

oh

[spark field]

wait im not so sure

[fiery vapor]

because the question on this problem is to sketch the derivative of that graph

[spark field]

Yea create your piecewise func then draw the derivative of the 3rd sub function

[obtuse pebble]

@fiery vapor Has your question been resolved?

[obtuse pebble]

@fiery vapor Has your question been resolved?

[obtuse pebble]

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[placid totem]

Im pretty confused about gaussian elimination

Or well, atleast how I should go about it

Is it just one of em things you gotta practise a bunch?

I feel like I always get stuck doing it

This is the beginning

<@&286206848099549185>

[obtuse pebble]

@placid totem Has your question been resolved?

[obtuse pebble]

@placid totem Has your question been resolved?

[obtuse pebble]

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[gleaming rose]

taking the x^2 to the other side

to be 2cos(theta)

then on the other side im left with

sqrt(4-4(2cos(theta))

thats all i could think of

1?

sin^2 + cos^2?

sry im confused

so it comes out to 1 because of pythagorean?

yes

pythagorean identity

i agree

[obtuse pebble]

@gleaming rose Has your question been resolved?

[gleaming rose]

i thought it was -1

now im workin on

im not very good at moving units

or i guess variables

im sorry im so confused

im using that

so for this one i would do x^2 to the other side right?

how do i solve these types of questions

im so confused on where to move stuff

how do i simplify it then im so confused

dudeeeeee

thats so helpful

actually

hold up

lol

hold up

am i looking at this right now?

how?

sorry just asking

oh yes whoops

thats it?

done

or whats next?

so wait what did you do there?

to the 25 aswell?

does this matter still or no?

or are we only working with

wait that still matters?

or just

one sec

so now you have this

so how did you get rid of the sqrt?

by squaring it?

5

wym 25 common

lol

whoops you mean

why do i square it

just curious

to know

is that to get rid of the sqrt?

yes

correct.

so i replace the x

we get thisd

why does that get csc aswell?

yes i get

so now we have

right?

where it wrong?

is it

wait is it

yes

why does it become 25

so now we have

now 😦

😢

you lost me at why we lost the 25

csc^2(thetha)

on the - side

this is wrong

how did you get this then

from this

this

from

25

so we should have this then right

not

^2

so this

ok

then what do we do with it

sqrt it?

yes lol

so now

we minus 25-25?

and we have

and then sqrt it

??

??

?

or 1

1,5,25?

how did you get rid of the 25?

??

no

but

how did you do this

**

from this

whats common?

can you elaborate how lol

ok we have

then what do i do

https://tenor.com/view/calculation-math-hangover-allen-zach-galifianakis-gif-6219070

@timid silo im super confused man

hello?

im still confused

sorta yeah

1,5

ok makes sense so we have

what do we do next

so

so like this

or

like that?

?

ok

so

yes

i agree

1-cot^2u?

so its now

yes

i do

or is it

??

i see cause they cancel eachother out

i agree

so then

how do we tackle the sqrt now?

and the 5

cot(theta)

then 5*cot(theta)?

holy crap

so lemme see if i acquired this right

is this right?

all the steps?

thanks for not just leaving bro!

[obtuse pebble]

@gleaming rose Has your question been resolved?

[obtuse pebble]

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[timid silo]

may someone help

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[forest sinew]

it helps if you can clarify what youre confused on, what you tried, where you got stuck, stuff like that

[timid silo]

i dont get what it is asking, sorry english is not my first language

[forest sinew]

it gives you the difference between the radius of two circles, and an upper bound on the area of the larger circle in terms of the area of the smaller circle

does that part make sense?

[forest sinew]

maybe you can try to explain what you think problem a is asking, to see if it makes sense?

[timid silo]

this chapter is named linear inequalities in one unknown, i dont get how do I use the given information to set up an eqation

[forest sinew]

I think a good first step is to identify the things you are interested in.

So try to find if you want to know radius, or area, or height, for the problem

[timid silo]

i have to find the height

[forest sinew]

Then define some variables that represent the quantities you want to know. You should be clear about what they mean when you write them

[forest sinew]

You should start by defining the variables really clearly. Just a suggestion but I think it's a good first step

then you have the tools to start writing equations

Variables + Information ----> Equations

[forest sinew]

also, you may want to start with part a? Unless you already have that done

[timid silo]

i have thinked for a bit but what i worked out is 2A-4>40𝝿

and that doesnt make sense

[forest sinew]

I guess you'd have to explain what the variable means

[timid silo]

r=radius a=area

rB=rA-4
2rA-4=rA+rB

aA-40𝝿>aB

these are the information

but idk how to link these up

[forest sinew]

but what is A and B?

and area of what circle

and radius of what circle

or do you mean like

[trim hawk]

Hey Jan

[forest sinew]

oh i get what youre writing now

aA is area of A

[timid silo]

yes

[trim hawk]

I need help with my algebra homework.

😂

[forest sinew]

well then u should get your own channel

[trim hawk]

I did

Nobody responds

[forest sinew]

youre only 3rd in line

rB=rA-4
2rA-4=rA+rB

aA-40𝝿>aB
these are the information
but idk how to link these up```

@timid silo where are you getting that second equation? 2rA-4=....

[timid silo]

'it is given that the area of circle A is not greater than of circle B by 40𝝿 cm' , doesnt that mean aA-40𝝿>aB

because like it is 40𝝿cm squared shorter

[forest sinew]

well it says not greater than

so if you take aB + 40pi

aA cant be bigger than that

I think this one would be aA - 40pi <= aB

but I was asking about the other equation, right above it

[timid silo]

umm sorry i always mess up with bigger or smaller, the < >s

[forest sinew]

youre good

I'm not sure where youre getting the 2rA - 4 = rA+rB is all but

just starting from what you have i think is good

so

aA-40pi <= aB```

you want the greatest area for aA, which i read as asking for like aA <= .... where ... is some number

[timid silo]

yes... i meant this in my head, i dont know how to write it out

[forest sinew]

they say in terms of pi which is weird

but I think what youll want to do is try to rewrite aB using the first equation

[timid silo]

rB = rA-4
aB = rB * hB * pi
rA-4 * hB * pi = aB
rA-4 * hB = aB / pi

[forest sinew]

wait arent you on part a?

[timid silo]

I tried to rewrite this

[forest sinew]

right but youre using height?

[timid silo]

oh sorry i always mess up the formulas... then should it be
rB = rA-4
aB = pi * rB ^ 2
aB = pi * rA-4 ^ 2
aB / pi = rA-4 ^ 2

[forest sinew]

i think you have the idea

you can write like

$test$

is the bot back up yet

dang

aA <= aB - 40pi

aA <= pi (rB)^2 - 40pi

aA <= pi (rA-4)^2 - 40pi

you can do various factorings or whatever here

I'm not sure they make it much more clear

[timid silo]

but i dont see anywhere that i can factoring here

[forest sinew]

i mean you could rewrite it as like

aA <= pi [ rA^2 - 8rA - 24 ]

or something like that

i dont think anything cleans up nicely if you start playing with it

[timid silo]

i dont think this is taught in school yet tho, this is so confusing

[forest sinew]

these kind of problems are usually very hard for people

since its a combination of a lot of skills

dont worry about the factoring

[forest sinew]

does getting to this answer seem okay?

[timid silo]

yes i guess

[forest sinew]

oh, theres a sign error

[forest sinew]

this should be a plus

aA <= aB + 40pi

aA <= pi rB^2 + 40pi

aA <= pi ( rA - 4 )^2 + 40pi

[forest sinew]

do you have equations for part b?

[timid silo]

nope...

[forest sinew]

The height of cylinder X is shorter than its base radius by 4cm

how about this part into an equation?

[timid silo]

hX < brX - 4

[forest sinew]

sure, but whats brX?

[timid silo]

base radius of X

[forest sinew]

yea but what is it

what circle forms the base of that cylinder?

[timid silo]

diameter / 2

[forest sinew]

theres no reason to guess, its given in the previous sentence

[timid silo]

circle A

[forest sinew]

right

so circle A is the base of cylinder X, so what's brX...

[timid silo]

radius of circle A

[forest sinew]

alright, so create your equation

[timid silo]

hX < rA -4

[forest sinew]

did you maybe wanna take a break?

or if youre not finding this super helpful maybe theres something else youd wanna try

[timid silo]

i just really want to solve this question but i cant

[forest sinew]

youve made a lot or progress so far

[forest sinew]

are you sure this makes sense to be < ?

[timid silo]

it said shorter

[forest sinew]

yea

but you could interpret that like

i mean in the original sentence

[timid silo]

then it means smaller so < ?

[forest sinew]

radius of circle A is greater than that of circle B by 4 cm

this gives us rB + 4 = rA

right

or if you are 5cm shorter than your friend paul

then hP - 5 = your height

[timid silo]

yes

[forest sinew]

so do you think its equality or inequality?

[forest sinew]

here

[timid silo]

inequality

[forest sinew]

man what if youre right and im just dumb

i do not think its inequality

since it says by how much

[timid silo]

sorry math is not the thing for me... you can close the channel maybe

[forest sinew]

we could take a break

you should write down the equations you have for part a at least

since that is good progress

sorry you ran out of steam, good luck finishing it out later

[timid silo]

you can close the channel, i will try to work it out later

[forest sinew]

.close

[obtuse pebble]

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[stable rain]

hi i was looking at principal value integrals. so is every pv integral an improper riemann integral? but not the other way round

[stable rain]

namely when the improper riemann integral doesnt exist, the pv integral might exist

that right?

[obtuse pebble]

@stable rain Has your question been resolved?

[obtuse pebble]

@stable rain Has your question been resolved?

[wild swallow]

you got it wrong way round

riemann => pv

pv not necessarily riemann

[stable rain]

hmm

but

oh

OH

haha

good joke by me

got caught

nice catch

ok

thanks

💕

.close

[obtuse pebble]

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[silver plover]

help plz

dont really get the k part

[wind flower]

I think it can't be b).
a=1; b=6
there is no 2*k that will get 7

[silver plover]

could u explain to me what these statements acc mean first plz

cuz im confused how the k comes into play

so for a it says : there exists a and b in the set S and there exists k in the set 1 2 3 4 ?

where a + b <= 4

?

[wind flower]

i think that you can ignore 'k' in a)

[wind flower]

but yes

[silver plover]

ok

[old sail]

what is x square divided by 6 plus x +989720?

[silver plover]

a is defo false

[silver plover]

bro

im in a middle of a help session

[old sail]

dang i need a empty one

[silver plover]

anyway

a is defo false

i think

[wind flower]

3 and 2

a=3 b=2

[silver plover]

ye doesnt work

as 3 + 2 = 5

[wind flower]

yeah i am dumb

[silver plover]

yh lol

ahhaha

[wind flower]

so not a) or b)

so now c)

i think that could actually be it

[silver plover]

hmmm

yh i think it is

[wind flower]

the smallest a and b can be 2 and 3

[silver plover]

and k is 1

[wind flower]

and if you take smallest k... 1

it will work

so you should be able to get any higher value right

[silver plover]

yh ight

ill check ms soon and lyk

but pretty sure its c

thanks

[wind flower]

what if k=2

lets test that

so a+b>=10

so 2+3 is not >=10

so

c is aslo wrong?

[silver plover]

ummmm

[wind flower]

right? xD

[silver plover]

the ms says

c is right

[wind flower]

annnd again, i am dumb. it says that 'k' exists

and we found one k

[silver plover]

ye lol

[wind flower]

then c is correct

[silver plover]

ye cool

[wind flower]

i should not be helping

too dumb

xD

[silver plover]

hahah nah

its calm

cheers man

[wind flower]

no idea

[silver plover]

likewise

lol

[wind flower]

nice

if you put tan(2y) the function will be twice as fast, so it will be from -pi/4 to pi/4 instead of -pi/2 to pi/2

and i see pi/4 only in c)

[silver plover]

sadly

u r incorrect

[wind flower]

f

ask someone else xD

i have no idea

you can ping helpers

[silver plover]

yh dw

thats calm

thanks pal

.close

[obtuse pebble]

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[daring kestrel]

why did the thing at the bottom just get removed like that

the denominator

[final thunder]

a fraction is equal to 0 iff the numerator is 0 (and the denom is not 0)

or you could say we multiplied both sides by (x^2 +4)^2

[daring kestrel]

i was gonna do that but thought itd be pointless cuz 0 * denominator

wouldnt change anything

but now i see it

ty

[final thunder]

yw

[daring kestrel]

.close

[final thunder]

[obtuse pebble]

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[shadow lava]

How would I solve for x?

[shadow lava]

The x in the exponent is throwing me off and not sure what to do

[thick oracle]

4^2 is the last term?

[shadow lava]

yes

Here is a better screenshot

[teal turret]

Do u know ur exponent rules?

[thick oracle]

split the exponents

and use u sub

@shadow lava

what happened

did you solve it?

[obtuse pebble]

@shadow lava Has your question been resolved?

[obtuse pebble]

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[astral flare]

I have to sketch graphs the equations is usually in the form y = ax^2 + bx + c but this one is in the form y = ax^2 + bx and i'm not sure how to find the intercepts

[teal turret]

Well if u factor out an x, you get:

,, y = x(ax +b)

[warm shale]

Stephen

[astral flare]

ahh thank you this is so obvious idk why is slipped my mind, Thank you!

[teal turret]

Then to find ur x intercepts, let y = 0

[teal turret]

Sure np

[astral flare]

!close

[teal turret]

Use a period

(.close)

[obtuse pebble]

@astral flare Has your question been resolved?

[astral flare]

.close

[obtuse pebble]

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[urban needle]

Trying to find the recursive formula for the following sequence (4,12,36,108,324), I found the explicit form to be (4)3^(n-1)

[upbeat gazelle]

What's your question?

[urban needle]

How do I find the recursive formula? My notes say an= ra(n-1)

But a0 is 4 so that formula doesn't make sense to me

[stable rain]

um

[stable rain]

u also define base term

[urban needle]

Unless the recursive formula isn't used to find the first term and I'm being dumb and it's only used to find the next term?

[stable rain]

in this case as u found, a0=4

[stable rain]

the first term, u define it separately

[urban needle]

Ok, so it would be just be 3a(n-1)

Thanks

[stable rain]

er

yes

[urban needle]

.close

[obtuse pebble]

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[stable rain]

[obtuse pebble]

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[plain summit]

The question is: Find the smallest value for M such that |1/x| is less than or equal to M for all x in the interval [2, 7]. I'm not sure how to answer this question since M doesn't have any properties?

[stable rain]

its like

wait crap

[plain summit]

so the smallest value is 1/7?

[stable rain]

sup of |1/x| for x in [2,7]

|1/x| is less than or equal to M for all x in the interval [2, 7]

upper bound

smallest value

thus smallest upper bound

or sup

[obtuse pebble]

@plain summit Has your question been resolved?

[plain summit]

Sorry- question is resolved.

[obtuse pebble]

@plain summit Has your question been resolved?

[obtuse pebble]

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[balmy steeple]

you saw that I was typing and u send a picture without text

idiot

[final thunder]

bit agressive

[somber hound]

Sorry I didn’t see u typing I was taking a picture

[thick oracle]

[final thunder]

[somber hound]

Give me a motivational speech oogway

[thick oracle]

You are the master of your destiny: No one and nothing can come in between you and your destiny except you. Take destiny by the horns and have fun.

[somber hound]

[daring rock]

Your destiny, of course, being to determine whether this set of vectors is linearly independent

[thick oracle]

[somber hound]

Pls tell me the result of my destiny

Is it linearly independent or is it not linearly independent

[daring rock]

Can you solve the system laid out at the bottom?

If that system has only one solution, then they are independent

[somber hound]

No I cannot

I am not 100%

Can someone confirm?

[obtuse pebble]

@somber hound Has your question been resolved?

[somber hound]

<@&286206848099549185>

[wispy wadi]

it's independent indeed

you should think of a solution tho, because there is one

you probably checked for solutions where the coeff are not zero

[obtuse pebble]

@somber hound Has your question been resolved?

[obtuse pebble]

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[silent imp]

https://gyazo.com/4d9b335454aeeeb21aca83097dec1d01

[silent imp]

why are my concavities wrong

[atomic pasture]

Where did you get (7,9)

[silent imp]

will its going up right

[silent imp]

yeah from that point it concaves upwards

[atomic pasture]

i think its 0,5

im not sure

but try it

[silent imp]

for concaves dwon?

down*

[atomic pasture]

yes

[silent imp]

its not right ima go look on utube

[atomic pasture]

ok

[obtuse pebble]

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[lavish arch]

my question revolves around fitch proofs, but does anyone know how to prove thus

[obtuse pebble]

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@lavish arch Has your question been resolved?

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@vestal trench Has your question been resolved?

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[bronze tendon]

i need help im not sure where to start

i know volume is LxWxH

but im not sure where the height and width are

[fierce lagoon]

You have the area of the cross section

Volume is also (cross section) x (other dimension)

@bronze tendon

[bronze tendon]

yes hi

[bronze tendon]

okay

so

uh

[fierce lagoon]

Think about a cross section being a 2D piece of paper. If you stack a lot of these papers, you get a rectangular prism.

That's essentially what you're doing here. You're gonna multiply the area of the cross section by 3

[bronze tendon]

ohh ok

so 28^2 x 3

what is that

2352?

[fierce lagoon]

Not 28^2

Why are you squaring it

[bronze tendon]

uh

i saw 28m^2

so i thought you sqaure it

[fierce lagoon]

m^2 is a unit

Metered squared

[bronze tendon]

ohhh

ok

[fierce lagoon]

You need to understand that area is 2-dimensional

[bronze tendon]

so 3x28=84

[fierce lagoon]

Yes

[bronze tendon]

okay

so like

what now...

[brisk matrix]

that's the volume of the solid

[bronze tendon]

oh

thats lovely

[brisk matrix]

notice that the units match up

[bronze tendon]

wdym?

[brisk matrix]

the cross section is 28m^2, the length 3m

so 28m^2 * 3m = 84m^3

[bronze tendon]

ohhhhhhhhhh

[brisk matrix]

so we're still dealing with volume

do you want to try the second question?

[bronze tendon]

yeah syre

sure

wait

i dont have time actually

[brisk matrix]

so do you not want to do it

[bronze tendon]

i dont think i can no

thanks tho!

.close

[obtuse pebble]

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[ionic summit]

is this just wrong

[ionic summit]

I thought critical points is where x = 0 when you take the derivative or where x is undefined

considering the derivative is 4x-64/sqrt(x)

x cant be 0 or its undefined so

[pulsar tree]

yep

0 and 4 is correct

[ionic summit]

11/10 homework thing

.close

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[spark field]

could someone explain how to solve this using limit trig func

[obtuse pebble]

Please don't occupy multiple help channels.

@spark field Has your question been resolved?

[timid silo]

for all 3 questions, if x tends to some constant 'a', then change the variable of limit to h = x-a
Since x tends to a, x-a tends to 0, and so h will tend to 0
Then simplify using trig identities

[spark field]

how

[timid silo]

Which part you didn't get

[spark field]

Ok so

[spark field]

so like this?

[timid silo]

no

x-π/3 = h

And so h tends to 0

x = h + π/3

you replace x with h + π/3

[spark field]

so like this

[timid silo]

yes

now expand cos(h+π/3)

[spark field]

cos(h) + cos(pi/3)

[timid silo]

No

[spark field]

oh then what do you mean

[timid silo]

cos(A+B) = cosAcosB - sinAsinB

[spark field]

oh lol

that

[obtuse pebble]

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[sterile bluff]

quick question

[sterile bluff]

what is

e^integral(-1/x)

when solvinf a differenti

differential

so this is the integrating factor

[obtuse pebble]

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[echo steppe]

Hi

[finite glen]

hello mate

[echo steppe]

Using this information how would I find c(13, -20)?

[finite glen]

im sorry i dont understand this stuff

[obtuse pebble]

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[hollow grail]

I dont understand this

[thick oracle]

It gives me another solution

Lol

For the derivative

[knotty crow]

it's chain rule

[hollow grail]

Whats the rule again if you can remind me?

[hollow grail]

In so confused

[thick oracle]

The derivative of f(g(x)) is f'(g(x))*g'(x)

[obtuse pebble]

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[low pagoda]

Is this D?

[hardy widget]

,w solve sinx + xcosx > 0, 0 \leq x \leq \pi

[warm shale]

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[hardy widget]

,w solve sinx + xcosx < 0, 0 \leq x \leq \pi

[warm shale]

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[hardy widget]

You solved for when it's decreasing tbh

[low pagoda]

So concave down = dec

[hardy widget]

It gave you the first derivative tho, increasing just means f' > 0

[low pagoda]

Yeah

Wait

I read the answers wrong

I meant B

[hardy widget]

The graph can be increasing or decreasing when concave down

,w graph y=-x^2

[warm shale]

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[low pagoda]

I thought D said [0, 2.029]

I read it wrong

So B is correct right?

I misread D I thought it said [0,2.029] only

Lol

.close

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[rare shore]

how do i do question 2? i drew the graphs of both on desmos and used a slider for k but idk what to do afterwards

<@&286206848099549185>

[fossil crag]

3 is positive, you can factor it inside the absolute value

Then you're left with an inequality $|A| \geq |B|$

[warm shale]

rafilou2003

[obtuse pebble]

@rare shore Has your question been resolved?

[rare shore]

sorry i don’t understand ;-;

[obtuse pebble]

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[slow viper]

Why when I integrate this, I can just raise the power by 1? I don’t have to expand the equation?

[untold flax]

becuase the derivative of the inside is 1

so it wouldn't change

[slow viper]

So if the derivative of inside is 1, just leave it as it is?

Then raise the power by 1 and continue?

[untold flax]

yeah

cus if you differentiate ((x-k)^3 )/3

you'd get (x-k)^2 x 1 from product rule

chain rule**

[slow viper]

Ohhh

Thanks

.close

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[untold flax]

np

[slow viper]

.reopen

[obtuse pebble]

✅

[slow viper]

How come e^loge(1/2) become 1/2?😭

Is that something that I have to remember?

[old dagger]

$a^{log_{a}x} = x$

[warm shale]

Noone

[old dagger]

This is the rules

[obtuse pebble]

@slow viper Has your question been resolved?

[slow viper]

Ohh okay

Thanks

.close

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[unique spear]

I’m trying to prove the law of cosines in an obtuse-angled triangle. However, I seriously don’t know what I did wrong to prove the law wrong.

[unique spear]

If possible, I only want to prove it by using Pythogorean’s Theorem since I have yet to learn about trigonometry identities.

[obtuse pebble]

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[little tinsel]

Karcsi thought of a two-digit positive integer and multiplied its digits together. He then got a two-digit number and multiplied its digits again. He got ta two-digit number again, so he multiplied its digits again. The multiplication was then eight. How many numbers could Karcsi think of?

[little tinsel]

i know that at the end the number will be 81 or 18

or 24 or 42

[royal basin]

"squeezed his digits together"?

are you translating this from another language

[little tinsel]

ya

let me fix

[royal basin]

what language are you translating from?

maybe it is a language that i speak

[little tinsel]

Hungarian

fixed it, here you go

[royal basin]

...okay, nevermind

i don't speak hungarian unfortunately

still don't know what "squeeze" is supposed to mean lol

[little tinsel]

its okay

multiplying

the digits of the number

wait i still didnt edit

[royal basin]

and what about the "multiply the digits by 8" thing at the end

[little tinsel]

lets start over

i thought deepl has accurate translates

[royal basin]

no machine translation is perfect

they all screw up sometimes

[little tinsel]

you are right

here

so we have a positive two digit integer

multiplied the digits -> two digit number x3
answer 8

how many numbers Karcsi could think of

[royal basin]

oh, so we took a 2-digit number [ab], then a * b = [cd], then c * d = [ef], and e * f = [gh], and g * h = 8?

is that it?

[little tinsel]

yes

[royal basin]

right

perhaps it is best to work backwards from this

see what numbers could've given you a product of 8 at the end

[little tinsel]

24 42 81 18

[royal basin]

and see how those numbers could've arisen as products, if any

and so on

[little tinsel]

3x8 4x6 8x3 6x4
6x7 7x6
9x9 9x9
2x9 9x2 3x6 6x3

---

38 46 83 64
67 76
99 99
29 92 36 63

====

8x8

6x6 6x6 7x9 9x7

---

88

66 66 79 97

this numbers cannot be achieved with multiplication of 1 digit numbers

so i fricked up somewhere

ey

i dont know

[obtuse pebble]

@little tinsel Has your question been resolved?

[little tinsel]

<@&286206848099549185>

okay i got it

here is the solve if someone is interested

.close

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[mystic spindle]

Hey, guys. Can anyone tell me why the rate of change of the distance between the buses is 1320/13? Shouldn't it be 1320/26?

[zealous cape]

Does this bad sketch help?

[mystic spindle]

Yeah, that is what I drew, except my triangle is inverted

[zealous cape]

So we want to turn the 55 on the freeway to something "in the direction" of the other bus. What do you get for one of those buses?

Don't simplify anything, so we can see where every number is coming from.

[mystic spindle]

Mmh, I'm not sure I'm following you.

What I did was use the pythagorean theorem, differentiate it on both sides, and then plugged in known values

Was that wrong?

[zealous cape]

No, that's fine. Can you show your work before plugging in known values?

[mystic spindle]

Yep. Hold on.

[zealous cape]

As in, the last step before plugging in

[mystic spindle]

2a•da/dt + 2b•db/dt = 2c•dc/dt. The b term cancels, though, since the rate of change between the highways does not change

[zealous cape]

right, so I have 2* 12* 55+ 2* 5* 0 = 2* 13* dc/dt

[mystic spindle]

Yep

[zealous cape]

So that's the speed of bus B.

[daring rock]

Shouldn't that da/dt be -110?

[mystic spindle]

Wait. Are you saying that solving for dc/dt equals the speed of bus B?

[zealous cape]

That's the crux. 🙂

yes, 55 describes bus B. 110 describes both buses moving.

[daring rock]

Both buses are driving toward each other at 55mph, so the length of that leg of the triangle is shrinking at 110 mph

[mystic spindle]

Wait a sec

Wth. How did you figure that da/dt is 110? It is correct (I just solved the problem using 110 for da/dt), but I didn't think to make da/dt 110 😐

[zealous cape]

one bus is moving with da/dt=55. But both buses are moving

[mystic spindle]

Ohh. The question asked to find the rate of change of the distance between the buses when they are heading towards each other. Wow lol

It's always the details, man

Or maybe I understood that wrong lol

[obtuse pebble]

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[obtuse pebble]

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[young solar]

I have no idea on what to do

I am supposed to make it so that one of these notable limits appear so that I can simplify it

But I literally don’t know how to get to any of these forms

[haughty coyote]

My first thought would be to set u = pi/2 - x to have a limit to 0

I didn't fully check, but I think it works

[young solar]

?? Wait what do you mean?

[haughty coyote]

substitution

[young solar]

Oh so for example
Pi/2 - x = t ?

[haughty coyote]

u or t, whatever

[young solar]

Alright ! Let me try it

But wait

How do I go from there?

I will have
t multiplied to sin x / cos x

[haughty coyote]

rewrite x as a function of t

[young solar]

So I write
t multiplied to sin (t + pi/2)/ cos (t + pi/2)?

[haughty coyote]

you should get x = pi/2 - t

[young solar]

Alright

I did it and now I have
t multiplied by cos t / sin t

[haughty coyote]

which brings you back to one of known limits

[young solar]

Wait which one??

[haughty coyote]

sin t / t

[young solar]

OH

YOU ARE RIGHT

Thank you !!

.close

[obtuse pebble]

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[dark orchid]

How do i solve number 1

[sage geode]

Find the gcd of 8 and 20

That will be the number you'll be able to factor out

[dark orchid]

So gcf of 8 & 20 is 4

[sage geode]

Yes, can you factor the 4 out?

[oak bear]

You can try to memorize or read divisibility rules

[dark orchid]

?

[sage geode]

What did you get?

[dark orchid]

What am i supposed to do once I factor outed the gcf?

[sage geode]

That's it

As long as you got 4(2x + 5) that's the answer

[oak bear]

Or start from the bottom up, like finding the smallest number you can divide 8 and 20, then factor it out.
The smallest number you can divide by both 20 and 8 is 2
8/2 = 4
20/2 = 10
2(4x+10)
It can still be divided by 2 so divide again,
4/2=2
10/2=5
2x2(2x+5)
4(2x+5)

[dark orchid]

Oh

I get it now.

Gcf goes outside of ()

[oak bear]

This method isn't really complicated and can be used without actually finding out the gcf

But if you want to find out the gcf, then you gotta know the divisibility rules

[oak bear]

https://www.mathsisfun.com/divisibility-rules.html

[dark orchid]

Thanks

.close

[obtuse pebble]

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[teal osprey]

I have a somewhat hard question

[sage geode]

Just post it

[tardy epoch]

if it's better suited for an advanced channel i'll let you know

[teal osprey]

I need to solve this integral by partial integration

And it needs to be one of these as a result

[silver fox]

Ok so your gonna integrate x/squareroot(1-x^2) using usub

[tardy epoch]

pretty standard integration by parts. try something

[distant moth]

These are results?💀

[teal osprey]

I tried solving it but I can only come to (9) as a solution, but the sign is wrong

Yes

And no, it needs to be partial integration, not u-substituion

[silver fox]

It will be both

[teal osprey]

Anyways. I only get (9) but with a minus sign. Can’t figure it out

Can someone help me with this?

[tardy epoch]

show your work then

[teal osprey]

Ok just a sec

This is what I have currently

But I think my thought process is wrong and I need to use some special rules or something. Am i wrong?

[tardy epoch]

both answers are correct. x * arcsin(x) is an even function

,w plot x arcsin(x)

[warm shale]

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Requested by riemann#2529

[tardy epoch]

arcsin(x) is odd because sin(x) is odd

and x is odd. so odd function * odd function is odd

[teal osprey]

Hmm. Could you further explain a bit what you mean about an odd function?

[tardy epoch]

no wait that's wrong

your calculations are correct. there's a sign error here

tell you instructor

[teal osprey]

Are you certain?

My math instructor is a somewhat (locally) famous mathematician so he often creates tasks that have twists in them

[tardy epoch]

yes

[teal osprey]

Ah okay then, Thanks!

[obtuse pebble]

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[shell hull]

I know this formula.
But how can I find the formula for the sum of squares of odd numbers?

[tardy epoch]

add the two equations

[shell hull]

So what?

[tardy epoch]

did you do it?

oh you don't have a formula for the first eqn

nevermind

[shell hull]

No but imagined what will happen

[stable rain]

er

uve sum of squares

u can use the same formula but with some sub to get the sum of odd and even squares till 2n or 2n+1

then manipulate again to get it till n

ud need floor or smt i think

[tardy epoch]

is your question the sum of odd squares 1^2 + 3^2 + 5^2 + ... + n^2 or your alternating expression?

[stable rain]

wait arent those cubes?

whered they come from

[tardy epoch]

yes typo, fixed

[shell hull]

1^2 - 2^2 + 3^2 -... - 1400^2