help-0

[ocean seal]

RipeOrange

[topaz scaffold]

Just solve for the normal force

Which would be perpendicular to the wall

@fickle dew

[fickle dew]

Not sure I'm quite following, so I get the Ff from m . g then ÷ it by the u (dont have the character) to get the Fn?

[topaz scaffold]

mg is your force of gravity

Denoted by F_g here

μ is the coefficient of friction

[topaz scaffold]

But this would be correct

Just need to plug in numbers

[fickle dew]

I see I see, thank you!

[topaz scaffold]

No problem!

[ivory otter]

no clue how to solve it

i was thinking, what if i calculate the area of the triangle (everything above h)

then i subtract

eeeeeh not sure tbh

[topaz scaffold]

Hint

Actually I should have drawn the orange line in a different place oof

Do try to use the radius tho

[ivory otter]

i think they want me to solve it in another way

[topaz scaffold]

Finding the area would be a lot harder tho

[ivory otter]

no i think your way is the way

mb

hmmmmm

im just gonna pray i dont get this question during exam

best way to solve it tbh

[topaz scaffold]

lol

[simple stream]

question

you have a cup of coffee at temperature 70 C and you immediately pour in 1 part milk to 5 parts coffee. The milk is initially at temperature 1 C. Write the differential equation that governs the temperature of the coffee

[uncut tapir]

Some things to consider:

The milk will heat up and the coffee will cool down until they are the same temperature

The coffee will 'win' because there's more of it, meaning that the final temperature would be closer to 70 than 1

Are you given heat capacities?

[ivory otter]

https://cdn.discordapp.com/attachments/373217754666500097/880504326550855700/vb.png

https://cdn.discordapp.com/attachments/373217754666500097/880504418016063571/image0.jpg

I must have Done something wrong with the last calculation
can someone look at it?

[uncut tapir]

Why do you think it's wrong?

[ivory otter]

cuz the answer is 1.96 * 10^-4

doubt thats the answer

[uncut tapir]

Seems like it makes sense with your input and output though

Why did you do Sum xy and Sum x^2 though

Don't you need these formulae?

[ivory otter]

this is what we use

[uncut tapir]

They are probably the same tbh

I don't see anything obvious

[bleak basalt]

I have a #discrete-math question

how can inclusive or be used in such a way where p, q, and r, are statements like 'we will be using this coding language in the class', 'we will be using that coding language in the class', and 'we will be using the other coding language in the class'? I am supposed to write a sentence for (p and q) or r, with those statements. but i dont see how it could be inclusive or rather than exclusive

[placid zinc]

Inclusive or, usually given the symbol V, means "take option 1, option 2, or both options"

[sullen bobcat]

Hello ! How are you ?

[placid zinc]

Truth table explains all:
p q p V q
0 0 0
1 0 1
0 1 1
1 1 1

[uncut tapir]

For me, those statements seem to imply you are using all 3 in the same class?

[sullen bobcat]

I've lots of difficult in English. Can we speak a little French please ?

[sullen bobcat]

0 and 0 -> 1
1 and 0 -> 0
1 and 1 -> 1
0 and 1 -> 1

[placid zinc]

@bleak basalt
Did I help make it more clear? It's not all too clear what you're asking

[sullen bobcat]

I've lots of difficult in English. Can we speak a little French please ?

I'm level A2 in English CECRL

With Google translate

[bleak basalt]

I understand the difference between or and xor, i just dont understand how OR could possibly be applied to this specific situation

[placid zinc]

(p and q) or r?

[sullen bobcat]

Can you help me ?

[bleak basalt]

since the scenario, for example, is something like "we will be using either a combination of java and C, or python". But in that example, the or is exclusive

[sullen bobcat]

@bleak basalt

[placid zinc]

Do you mean this?

Expressing XOR with AND and OR?

[sullen bobcat]

@placid zinc Can you speak French ?

[bleak basalt]

i dont understand your question really. Im supposed to formulate a sentence for p and q, inclusive or r

and my problem is i can only think of sentences for the given values of p, q, and r, in which the or is exclusive

[placid zinc]

p XOR q = (q or p) and (p' or q')
Where ' means complement, or NOT

Is one way to express it

[bleak basalt]

but I mean i need to come up with an actual english sentence that would make the expression true

[placid zinc]

I have no idea what you're asking

[bleak basalt]

okay so lets say p is soup, and q is salad. My assignment question is "write a sentence for which s is true in the expression s=p^q". The correct answer for this question would be "i will give you both soup and salad"

[placid zinc]

"I will give you soup or salad, but not both"

[sullen bobcat]

@placid zinc @bleak basalt

HELLO !!!!!!!!

[novel siren]

@sullen bobcat le salon est déjà occupé, pose ta question dans #help-5 jvais voir si jpeux aider ou au moins traduire

[bleak basalt]

yes, and now I am trying to do something similar to the example that I have just given, except it is for the p, q, and r values, and expression that I mentioned above. Does that make sense?

[placid zinc]

We may be using a combination of Java and C, but if we don't, we will be using Python instead

[bleak basalt]

okay and that wouldnt be exclusive? because if we use python instead, doesnt that mean its only python and the combination is excluded?

[placid zinc]

That's a good idea, "only Python" to make it more clear

[radiant karma]

https://gyazo.com/aeca2dba4280733524c0381c064a260c

Hi can someone help me differentiate this

[placid zinc]

First do chain rule:
1/(xe^x) times d/dx(xe^x)

[bleak basalt]

but its supposed to be inclusive, not exclusive

[radiant karma]

I got (1+x)e^x / xe^x

[placid zinc]

Yes that looks right

Note the e^x can cancel

[radiant karma]

https://gyazo.com/0c25834c88cf5a54100aeafddf000420

why does the mark scheme say this

[jolly stone]

big brain way is simplify that expression first

log(xe^x) = log(x)+log(e^x) = log(x)+x

[assuming log is base e]

[radiant karma]

Ohhhh

I just realised lmao

theyre both equivalent haha

not a multiplication of each other

thanks guys!

[jolly stone]

had the same story with my calc professor lol, gave a whole page to find derivative of (x^-3+x^-2)/(x^-1). people did shittons of work with product rule and such, and then me and my friend did this in 2 lines

[prime lake]

I need help clarify something for me. The square root property is when you got x^2=9 u get x=squareroot9 or x=-squareroot9 but the thing is, ive seen some people put parentheses on minus x=(-)squareroot9, what does that mean? is it to define that it's positive only?

[jolly stone]

not sure what specific context that is, but when x^2 = 9 -> x = -3 or 3

but when if you want to find sqrt(9), it is defined as the only positive value sqrt(9) = 3

so if someone said -sqrt(9) it means -3

the parenthesis thing i've never seen it before

[prime lake]

Same here, but they do it in a way of x=+-sqrt(9) and put the parantheses on the minus

for an example, the length of a side is never negative

i think thats why?

[jolly stone]

did you see that on the geometry problem or just anything in general

[prime lake]

but it's fallacy still, square of two negative and positive yield positive anyway. but if we are saying that a pythagorean theorem u have c^2=a^2+b^2 and if u square root, u never get negative one

[jolly stone]

cuz it's just weird to write out negative

yeah exactly

i mean, it's true if x = -3, x^2 = 9

but if x is a side length, x can never be -3 anyways

[prime lake]

it can but its not practical. lets say one side is negative and another is negative depends where u put your origo xD yield then positive area 😄

but the question is, what is the name called that u put the parantheses on the minus? i dont find any website or books yet that show the definition and explanation

[crude viper]

Why is it that a/b*b/a = 1 no matter what?

[wary stream]

Because the numerators and denominators cancel out and make 1

$$\frac{a}{b}\times \frac{b}{a}$$

[ocean seal]

dldh06

[crude viper]

Can I have an example?

[wary stream]

$$\frac{4}{6}\times \frac{6}{4} = \frac{4 \cdot 6}{6 \cdot 4}$$

[ocean seal]

dldh06

[wary stream]

The 6 in the numerator and denominator cancels to be 1, and same with the 4

[thorn kindle]

you can prove this using the mathematical principle of induction

[crude viper]

Go on.

[crude viper]

I thought of this, but it didn't really "click", at least the inner workings of it.

[alpine sable]

$$ test $$

[ocean seal]

shira ツ

[alpine sable]

To do this I just need to change x and y to 1?

$$ f(1,1) = ln(x + y - 1) $$

[ocean seal]

shira ツ

[topaz scaffold]

Yea

[crude viper]

sorry to bug you, but what do you mean by this?

[faint oasis]

https://gyazo.com/f18f565715fc1ca27e9098a5b5de1bbf find a and b

[crude rose]

when something is notated as (g o f)(x) is that the same as g(f(x))

[thorn vortex]

when two inscribed angles intercept the same chord, the y have the same measure

[novel siren]

yes

[arctic delta]

anyone know what happened here

i know you sub in 2-x for u and stuff like that

but am unsure how to fit u into the other terms like x-1

[placid zinc]

If u = 2 - x
Then x = 2 - u
And finally x - 1 = (2 - u) - 1

Or x - 1 = 1 - u

[arctic delta]

ahh i see

whered the powers come from?

[faint oasis]

can you simplify that to the point where a 8th grader can understand

[thorn vortex]

what don't you understand in what i just said

[faint oasis]

basically the entire thing

well mostzly the part where u talk about the same chord

[thorn vortex]

don't you know what is a chord

[faint oasis]

like a striaght line

[thorn vortex]

it is a segment that joins two points of a circle

[ivory zodiac]

so here's the first part of that question

plugging everything in, F is equal to 28.936

[prime mural]

?

[surreal sphinx]

what is the law of exponent in (2x^3)(3x^5)

<@&286206848099549185>

[oak chasm]

@surreal sphinx Rearrange it so that the nonvariables are together and all the variables are with the same variable.

2 · 3x³x⁵.

Then multiply the different groups together.

2 · 3 = 6

x³x⁵ = x⁸

6x⁸.

[ocean seal]

Chai T. Rex

[alpine sable]

Hello can anyone help me with this question ?

https://cdn.discordapp.com/attachments/328208536029102081/880604620622291014/unknown.png

<@&286206848099549185>

need help with wheer to start

[wanton beacon]

Ik this a dumb question but i forgot, would (6 2/7 * 6 2/7) + (196 * 98) be the association property of addition or multiplication?

Pls someone answer lol

[sly mantle]

there are 2 steps to prove unique existence, existence & uniqueness. to show existence, we must show there exists a definition of addition & multiplication on F satisfying the above conditions. to show uniqueness, we must show that if there exist two pairs of definitions of addition & multiplication on F satisfying the above conditions, let's call em +/* & [+]/[*], then +=[+] & *=[*] (the equality here means equality of functions since addition & multiplication are formally functions FxF->F)

[wanton beacon]

Could someone pls quickly answer my question

[west bronze]

neither, it's just an expression
the associative property of addition is a + (b + c) = (a + b) + c
the associative property of multiplication is a * (b * c) = (a * b) * c

[wanton beacon]

Ty very much

[tranquil sierra]

How do they get that pi/6 value?

[glass lichen]

unit circle

[tranquil sierra]

Where do we get the 30˚?

nvm I'm an idiot

[median tendon]

Just curious, why is the integral of a square wave a triangular wave? Since integration is the area, shouldn't the triangular wave start with a step? (the area under the square wave starts with a number larger than 0)

[topaz scaffold]

The square wave has constant values

So when you integrate it you get the linear increases and decreases of the the triangular wave

You could also go backwards and imagine what the derivative of the triangular wave would be

@tranquil sierra

[orchid tapir]

is there precal tutors or something? I'm new to this whole discord tutoring thing

[glass lichen]

#rules #❓how-to-get-help

[quasi bloom]

What

I fucked up

Someone please explain

[quasi bloom]

I can't figure out how that is the correct answer

I obviously am missing a big portion of trig

Since I wasn't making trig functions negative when they needed to be

[wary stream]

It was because one of the given values was negative

[split slate]

How did I get this wrong?

$Pop_{\text{in 4 years time}} = 3425 - ((3425 \times 0.03) \times 4)$

[ocean seal]

HappyAlt

[split slate]

Should equal 3014

[wary stream]

Isn't supposed to be an exponential function?

[split slate]

Then how would I do it?

Could you please explain?

[quasi bloom]

I don't understand how to work with that

[split slate]

oh nvm I got my thingo

carry on

[wary stream]

Given here, (-3.5, 6.8)

[quasi bloom]

is that all?

i meant i don't know how to solve them

[wary stream]

You did everything correctly, you just forgot to account for that negative value that was given

[quasi bloom]

am i not supposed to work with an obtuse angle?

also wouldn't -6.8^2 + 3.5^2 = 58.49

where did 5849 come from

[faint oasis]

https://gyazo.com/e4de5e9ec620da92410f384633a3014e i missed out on some classes about analytic geometry can someone give me some hints or explain the process

[kind solstice]

I don't know what to do with the "x+" and "1-". How to solve it? I'm stuck with those two things, but I don't know how to proceed, I know the answer but don't know how to solve the question! I need to simplify the fraction! Thanks for the help!

[faint oasis]

<@&286206848099549185>

[sage bronze]

$\frac {x+ \frac {y-x}{1+xy}}{1 - \frac {xy - x^{2}}{1+xy}} = \frac {\frac {(y-x) + x(1+xy)}{1+xy}}{\frac {1(1+xy) - (xy - x^{2})}{1+xy}}$

[ocean seal]

HELLOBELLO

[kind solstice]

Thanks!!

[sage bronze]

np

[ember night]

Hey so I have a number that get's multiplied by 0.25, for example 100, which is 75. How can I find out by how much I need to multiply 100 in the first place so that value - 75 = 100, the same number?

[placid zinc]

So (0.25)100 = 25

You'd multiply 25 by 4, in order to get 100 back

[ember night]

yea i know.. it's hard for me to explain

I need to provide a formula

like

if I multiply 100 by 1.25 (add 25%) and then by 0.75 (substract 25%) I get 93.75

And I need to get back to 100 again

In the first step I need to multiply by something that gets me to 133 which is the value that after 25% (1.25) gets me to 100

But I don't know how to find it as a formula

[placid zinc]

93.75x = 100
x = 100/93.75

[ember night]

right.. and multiply by 1.25 and then that by 100

[placid zinc]

You're very unclear. Can you list out, like with steps, what exactly you are doing to this number?

And what you are trying to have the number match?

[ember night]

you already solved my issue

[placid zinc]

Okay! Great haha

[opal gulch]

there was a family

they ate garlic bread every day

3 of them in total, two parents and an only child

they where in bliss

but then

another gremlin child was born

now 4 people ate garlic bread

what fraction of garlic bread did each of the original three lose

[vale wigeon]

depends on how much garlic bread the new child eats in relation to the parents and the first child
and whether or not the total amount of garlic bread eaten by the family has changed with the birth of the new child

[opal gulch]

no

they all eat the same amount of garlic bread

an equal amount

and the amount of garlic bread is the same

I think I know the answer but I might be wrong

[vale wigeon]

and what do you think the answer is?

[opal gulch]

1/3 = 33.3333333333
1/4 = 25
33.3333333-25 = 8.33333333
100/8.33333 = 12

12 3

•      ===>       -
  

100 25

I think they all lost three twenty fifths

[placid zinc]

Imagine there's 12 loaves of garlic bread every day. How many each did the 3 eat? How many each do the 4 eat now?

[opal gulch]

oh no

but if you carry the 44 around the three it equals the answer

yep makes sense

[next hatch]

how do i do b?

im a bit confused

seems like integration by parts but i tried it and it doesnt work

[split oriole]

You can solve 1st by substituting 2x^4+16=t

[thin urchin]

so they gave me a distance formula and asked me to calculate the average velocity

[next hatch]

ive done the first part

[thin urchin]

am i starting about this right?

[next hatch]

its b im confused on

sorry boss question's already being asked

ive tried doing ln(x) = du/dx and the other one being v(x)

and vice versa

and both scenarios have lead me to weird integrals

[split oriole]

Split the integral

[next hatch]

wdym

[split oriole]

Take log with x^1/2 , and other ,then try to apply the integration by parts

[next hatch]

ohhhhh

OHHHHH

huge brain

gimme a secf

[split oriole]

👍

[astral dagger]

rewrite (x^{\frac{1}{2}}-6x^3) as (\dfrac{x^{\frac{3}{2}}-6x^4}{x}), then (u=\ln(x)), there you go

[ocean seal]

SubGui

[next hatch]

im still confused with that

[astral dagger]

maybe it works, maybe not

lemme double check before

[next hatch]

yep

is this right so far?

[rigid smelt]

Instead of expanding

Just do ibp right away

[next hatch]

i tried that

[rigid smelt]

You just have to integrate (...) as a whole

[next hatch]

it gave me some fucko answer

[rigid smelt]

Can you show your work?

[next hatch]

i kinda crossed it out lol

[rigid smelt]

Sigh

[next hatch]

,t 270

,r 270

,rotate 270

[next hatch]

there we go

if u can read that props to u

if not ill try it again

[rigid smelt]

If you had
(x^(1/2)-6x^3)/x -
integral of (3/2 * x^(3/2) - 3/2 * x^4)/x dx

Then thats correct

[next hatch]

so the x^1/2 part is the derivative

[rigid smelt]

No

[next hatch]

no no

i mean like

[rigid smelt]

ln has to be u

Because integrating ln(x) is troublesome

[next hatch]

yes

i meant like

that x^1/2 at the start

is dv/dx

[rigid smelt]

Uh no, (x^(1/2) - 6x^3) is dv

[next hatch]

yes

thats what i meant

[rigid smelt]

Then yeah

If you make no mistakes then you are on your way

And by the seem of it

You were doing good

The integral after the ibp is not very hard

Oh nvm, you messed up your uv

but the integral vdu is good

[next hatch]

this is right yeah?

[rigid smelt]

Yes

[next hatch]

okay

[rigid smelt]

Your work was almost correct

[next hatch]

and to find v(x) i integrate dv(x)/dx

[next hatch]

this is confusing me now

cuz if ln is u

[rigid smelt]

Again, dv=ln(x)

[next hatch]

then wouldnt the equation be ln x * v(x)

[rigid smelt]

What equation?

[next hatch]

didnt u say it was u

[rigid smelt]

We dotn have any equation

[rigid smelt]

No

Oh wait

[next hatch]

^

[rigid smelt]

Ughh nvm

Brain fart

I need my coffee

[next hatch]

so we have to integrate ln?

lmao feels

[rigid smelt]

No no, u=ln(x)

Its just me having a stroke

Yeah nvmyour work is good

Continue with the integral

[next hatch]

lmao aight

i got this so far

[rigid smelt]

Yes

[next hatch]

so then its uv - integral(v * du)

[rigid smelt]

Uyep

Basically just copy the whole expression that you crossed out above down

The thing you crossed out was correct

[next hatch]

okay yep

now that integral looks a bit wack

for me at least

do i split it?

or wait

would the x cancel one of the x's on top

[rigid smelt]

Yes

[next hatch]

so 2/3 x ^1/2

it would become

and 3/2 x^3

and then i integrate that

[rigid smelt]

Firstly v=2/3 * x^(3/2) - 6/4 * x^(4)

[next hatch]

yes

[rigid smelt]

And secondly 1/2 + 1 is not 3

[next hatch]

idk if im just writing out retardedly

i meant

[rigid smelt]

I dont know how you came from 1/2 to 3 tbh

[next hatch]

2/3 x ^3/2

becomes the same but ^1/2

this is before integration

and the 3/2 x ^4

becomes 3/2 x ^3

[rigid smelt]

Oh ok this clears up more

Because i have absolutely no clue what you were writing

[next hatch]

lmao sorry im mathematically illiterate

[rigid smelt]

Anyway to sum up, if you have integral 2/3 * x^(1/2) - 3/2 * x^3 dx then you are heading in the right direction

No its just that i cant read minds

So it probably would help if you write out the full work

[rigid smelt]

Yeah looks good

[next hatch]

so that'd be the final answer

or do i have to do anything else

[rigid smelt]

+C

[next hatch]

fuck

every fucking time

god damnit this stupid + C

[rigid smelt]

Welp everyones nightmare

[next hatch]

in high school we were told we can ignore it since the questions told us to find AN integral which could omit the C

now in uni thats fucking us in the ass

[rigid smelt]

🤷‍♂️

[next hatch]

oh well is what it is

thanks for the help

just one more thing

[next hatch]

with parts c and d its standard integrals yeah?

[rigid smelt]

Standard as in?

[next hatch]

like standard integrals

uh

already existing

like the standard triangles

for trig

but for integrals

[rigid smelt]

I guess its in those forms(???)

For d you might have to manipulate using a bit of algebra

But yeah, those integrals are fairly common

[next hatch]

okay bet

and e ill ask another time lmao that looks nightmareish

thanks again for ur help

[arctic delta]

integral related, how do i go about solving this

[vale wigeon]

differentiate both sides

[arctic delta]

is that from a rule?

[vale wigeon]

what?

sorry, do you think there's some kind of Book Of Correct Courses Of Action that lists the one and only proper procedure one must engage in when solving any math problem?

[arctic delta]

no lol, like a law or rule stating for general blanket stuff y know

[placid zinc]

See the first fundamental theorem of calculus, to see that derivatives can "undo" integrals

[vale wigeon]

no there is no rule

i should probably have suggested that you differentiate both sides and see what happens

[wary badge]

:sus:

[cinder finch]

[surreal sphinx]

what is the GCF of 4m^3 and 6m^6

[dark granite]

well, determine gcd(4,6) and determine gcd(m^3,m^6) and then figure out what you need to do with those answers to get gcd(4m^3,6m^6).

[agile ruin]

How the angles $\theta$ and $\alpha$ on the plane got equal to angles on the circle?

[ocean seal]

Bkas

[alpine sable]

the inclined plane is tangent to the circle so the radius is perpendicular to the plane

the dashed line is also tanget

@agile ruin

[agile ruin]

Thanks

[next hatch]

how do i go about doing d?

i've completed the square to get (x-3)^2 + 13

but thats it

[rigid smelt]

try factoring the denominator and do fraction decomposition

[next hatch]

wdym

[vale wigeon]

partial fractions

that's what waler is suggesting

[next hatch]

like 1/(x-3)^2 * 1/13

no wait

no i cant do that

[vale wigeon]

wat

[next hatch]

i was thinking of the multiplication thingo

nah that dont work

let me have a look at my notes

okay so i need to split it into (x-3)(x-3) + 13

but what do i do with that 13, its the bit thats confusing me

[rigid smelt]

you have to factor x^2 -6x + 22

(x-3)^2 + 13 is not factored

[next hatch]

one sec

how do i factor it

[rigid smelt]

tho wait nvm its not factorable

[next hatch]

yeah i was gonna say

thats why i completed the square

[rigid smelt]

completing the square wont help, i suppose something to do with ibp?

and then u-sub probably

[alpine sable]

i suggest two methods

either integrate it's infinite series

or differentiate under the integral sign

[rigid smelt]

oh wait, bruh how didnt i see it

yeah completing the square

and then trig sub

[next hatch]

wdym trig sub

[rigid smelt]

using the identity tan^2(x) + 1=sec^2(x)

you have (x-3)^2 + 22

looks fairly similar doesnt it?

[next hatch]

somewhat

[rigid smelt]

yeah so try to apply it

[next hatch]

would rearranging to get 1 on its own work?

and then put it on the numerator?

[rigid smelt]

well in a way, you can see the identity as 22tan^2(u) + 22=22sec^2(x)

so you just have to try to make 22tan^2(u) appear

the only way is, like i have mentioned, trig sub

or u-sub but people dont like to call it that and just wants a different name

if you are stuck ||substitute x-3=sqrt(22)tan(u)||

[next hatch]

so u = (x-3)?

[rigid smelt]

no not quite

we want tan^2(u) and not just u

very close

[next hatch]

(x-3)^2 = tan(u)^2

[rigid smelt]

yes every closer

[next hatch]

so arctan(x-3) = u

[rigid smelt]

but now we want to have 13tan^2(u) appear

so it should be sqrt(13)tan(u)=x-3

oh wait, its +13

nvm

[next hatch]

so replace all 22's with 13

bet

[rigid smelt]

yeah

[next hatch]

so (x-3)^2 = 13tan(u)^2

[rigid smelt]

no, (x-3)^2 = 13tan^2(u)

or x-3=sqrt(13)tan(u)

[next hatch]

and multiply everything by 13

yes

[rigid smelt]

?

[next hatch]

sorry i was typing without seeing the message

so the whole identity

multiplied by 13

to give us the +13

[rigid smelt]

yeah

anyway, find du and just substitute

[next hatch]

but isnt the identity this

so where does the u come from

[rigid smelt]

yes it is

?

its just a different variable?

it doesnt affect the identity at all

[next hatch]

oh right

[rigid smelt]

tan^2(8) + 1 =sec^2(8)

doesnt matter what i put in there

[next hatch]

okay yeah gotcha

sorry im just tryna understand this as much as i can

so 13tan^2(u) + 13 = 13sec^2(u)

[rigid smelt]

u*

13tan^2(u) + 13 = 13sec^2(u) because we already used x in our integral

now thats the substitution in the integrand, you still havent found the substitution for dx yet

[next hatch]

hm

[rigid smelt]

just go back to x-3=sqrt(13)tan(u) and find dx in terms of u and du

[next hatch]

implicit dif is needed yeah?

[rigid smelt]

yeah

[next hatch]

fuck

[rigid smelt]

its not so bad

[next hatch]

gimme a sec

[rigid smelt]

take your time

[next hatch]

wait where does the sec go

from the identity

[alpine sable]

wait

you have to put bounds on u

[next hatch]

it can't be pi/2 yeah?

and any factor of it

[rigid smelt]

when you substitute x-3=sqrt(13)tan(u) into the integral, you have 1/(13tan^2(u) + 13) which simplifies to 1/(13sec^2(u)) if thats what you were asking

[next hatch]

oh yeah gotcha

[alpine sable]

u can yonly be in first and third quadrant

[rigid smelt]

u is every real number except pi/2 + kpi for k in Z

[alpine sable]

no

you are letting (x-3)^2 = 13tanu

tanu can not be negative

[rigid smelt]

im not letting (x-3)^2 = 13tan(u)

[alpine sable]

oh my bad

[next hatch]

should i just disregard that or is it important

cuz tryna understand it is confusing me

[rigid smelt]

it is not important in this problem since you are just finding the integral

just find dx in terms of du and u

[next hatch]

aight mad

[rigid smelt]

what did you get?

[next hatch]

sorry im in the middle of work im a bit on and off atm

imma try now

is it possible to use y instead of u or does that fuck up stuff

like cuz y = f(x) sorta shit

[rigid smelt]

it is

[next hatch]

aight mad cuz dy/dx looks neater to me

[rigid smelt]

you can just use anything you like as long as its not causing trouble for others to understand your work

[next hatch]

oh okay sweet

[alpine sable]

i have a quesiton

question

[next hatch]

yes

[alpine sable]

how do the bounds of the substitution affect the integration

[rigid smelt]

then you probably should use a different channel

[alpine sable]

it's re;ated

and no need to be rude

[rigid smelt]

im not being rude

if you have a question which i supposed was a math problem then i asked you to move to another channel.

its just part of how the question channels work

#❓how-to-get-help

[next hatch]

wait so for x-3 = sqrt(13)tan(y)

im a bit confused as to how to do implicit diff

its been like 3 weeks since i last did it

[rigid smelt]

ok so here x is a function dependent on y

and we will differentiate both sides with respect to y

so for the left side what do you have?

[next hatch]

x-3

[rigid smelt]

no i mean after the differentiation

[next hatch]

1

[rigid smelt]

not really

x is a function of y

[next hatch]

oh

wait

so is it dx/dy

[rigid smelt]

yes

[next hatch]

okay

[rigid smelt]

and the right side, what do you have?

[next hatch]

oh wait thats the answer lol whoops

i meant like dx/dy is the derivative

anyways

right side would be

uh

one moment

sqrt(13)sec^2(y)

[rigid smelt]

uh no

sqrt(13)sec^2(y)

or sqrt(13)/cos^2(y) if thats what you were intending to write

[next hatch]

oh wait i was thinking of the 1/cos^2(y)

yes

that

[rigid smelt]

so in summary, dx/dy = sqrt(13)sec^2(y)

so dx = sqrt(13)sec^2(y) dy

[next hatch]

yes that

[rigid smelt]

and i messed up

[ocean seal]

waler

[next hatch]

isnt that the same

[rigid smelt]

are you clear why we got this?

[rigid smelt]

no, i was missing the 13 in the denominator

[next hatch]

ah right

okay so

that trig identity * 13 = the sec denominator

and the dx is treated as a variable

[rigid smelt]

yeah

[next hatch]

which is sqrt13 sec^2(y)dy

[rigid smelt]

yes

so now the integral simplified down to 1/sqrt(13)

however the variable of integration is y

so be careful about that

[next hatch]

one moment

so the secs cancel out

and i get root13/13

how does it become 1/sqrt(13) again

divide by root13?

[rigid smelt]

1/sqrt(13) = sqrt(13)/13

[next hatch]

yes yes cuz with trig root2/2 = 1/root2

[rigid smelt]

i mean you can write it either way

doesnt matter anyway

[next hatch]

gimme a sec

is it just y/root13 +C

[rigid smelt]

yes

dont forget the constant tho

and then just change it back into terms of x

[next hatch]

but then what is y

[rigid smelt]

x-3=sqrt(13)tan(y)

solve for y

[next hatch]

ah

bet

so the final answer is arctan(x-3) + C?

[rigid smelt]

no

[ocean seal]

waler

[rigid smelt]

the sqrt(13) is inside the argument

[next hatch]

oh right

so final answer is arctan([x-3]/root13)/root13 +C

awesome thank you so much again waler

you da mvp

[low topaz]

Can there be sigma notations with decimal limits

[rigid smelt]

do you mean something like sum of 0.1 + 0.2 + 0.3 + ...?

[low topaz]

How could you calculate this

Would it be 0+.5+1+2+3+4

[vale wigeon]

no

you would just not use this notation in the first place

what did you attempt to write with this?

0 + 0.5 + 1 + 1.5 + 2 + 2.5 + 3 + 3.5 + 4 + 4.5?

is this what you wanted to write as a summation?

@low topaz

[formal patrol]

is there a simple and fast way to get the zeropoint of a function f.e. x^3-4x^2+x+6?

[old fjord]

what is spiral square root ?

[low topaz]

No. Im wondering if the upper limit could be a number In the Decibels.

[vale wigeon]

no

[low topaz]

Ok

[slim reef]

what is maths?

[shell widget]

@alpine sable For the first, it's 3f(x) + 30

For the second, first a vertical stretch by 2 and then translation upwards by 3 units

hm, f(x) + 3/2 and then 2[f(x) + (3/2)] = 2f(x) + 3

yeah same

First a horizontal compression by a factor of 2 and then shifting the graph horizontally to the left by 4 units.

sec

Yes

You're right!

mb

[silver current]

this is a little easy but my answer isnt in the options

[vale wigeon]

what answer did you get?

[silver current]

5

[vale wigeon]

you got x=5 as the only solution, right?

[silver current]

yes

[vale wigeon]

yeah, i got the same

looks like the question is messed up

[silver current]

the other solution is 5/3 which would satisfy the option B

[late cedar]

Why is the denominator 5! times 6!? Shouldn't it be only 11! using the permutation formula?

[silver current]

but it doesnt satisfy x<0

[vale wigeon]

yeah x=5/3 doesnt solve your equation

@late cedar 11!/11! would just be 1, you know...

[silver current]

Maybe the options are wrong

[late cedar]

yes but it would be (6-5)! therefore the answer should be 11! only?

[vale wigeon]

???

[late cedar]

Im following the permutation formula

[vale wigeon]

can you show what formula you're trying to follow here

i'm pretty sure either it doesn't apply or you're not following it properly

[late cedar]

but I am substituting the numerator with the total number of books

and the denominator as 6-5

[vale wigeon]

n=11 in your case

[late cedar]

yes

[vale wigeon]

but then you say you put 6-5 in the denom

how did 11 suddenly transform into 6

(also nPr isn't even appropriate to use here)

[late cedar]

oh ok

i get it now

[silver current]

is |(-4)^(1/2)| a pssible number

is it imaginary

[vale wigeon]

if you allow yourself to work with complex numbers then yes it is a thing that makes sense

no it's not imaginary

$|2i| = 2$

[ocean seal]

Ann

[silver current]

ah

it doesnt say x belongs to R+

[vale wigeon]

........what's up with these questions that have no correct answers

there is only one real solution here

[silver current]

2 actually

+- 2

[vale wigeon]

-2 doesn't work

-2 * |-2| = -2 * 2 = -4

[silver current]

oh right

fu

[vale wigeon]

can i see the entire homework assignment

the fact that not one but two questions ended up without correct answer options is kinda concerning

[vale wigeon]

do any of these allow picking multiple answers?

[silver current]

only the first one

[vale wigeon]

right

[silver current]

or if instructed

[alpine sable]

A table of size n rows and n columns will be filled with the number 1 or –1
so that the product of all the numbers in each row and the product of all
the numbers in each column are – 1. How many different ways to
fill in the table?

stuck at this

I even do not have any idea for this question

[sudden kayak]

Can someone please help me with this assignment

[carmine lion]

assignment?????????//

yo wtf

[idle rune]

does "D (or P)" alphabet have angles?

[frozen shale]

Hi, what are my options for online Bayesian inference? I'm trying to update a posterior $P(\theta \mid y_{t+1}) = \frac{P(y_{t+1}\mid \theta) P(\theta \mid Y_{t})}{\sum_{\theta} P(y_{t+1}\mid \theta) P(\theta \mid Y_{t})}$ on observing a new datapoint $y_{t+1}$

[ocean seal]

jowlz

[alpine sable]

All?

[cobalt coyote]

Did anyone ever come across this formula. If so, can you explain what is the name of formula and where was it used. Thank you

[spark zenith]

Help him

Idk how to help

[alpine sable]

Bruh.

[spark zenith]

Wtf is ur problem

[spark zenith]

<@&268886789983436800> help him idk how to help him

[alpine sable]

I already mentioned it.

[sly mantle]

@spark zenith do not use the mod ping like this

[cobalt coyote]

Thank you for ping for moderators to help

[spark zenith]

Ok

[sly mantle]

the mod ping isn't for hw help

[spark zenith]

Ow

[spark zenith]

I saw your msg

[sly mantle]

@alpine sable knock it off with these comments

Do it yourself, it's ezz.
I only help girls.

[cobalt coyote]

Please help me anyone with this one.

[spark zenith]

Its not allowed for help

[cobalt coyote]

Yes I understood..

[vale wigeon]

this doesn't look like any particularly well-known formula

what do you need it for?

[cobalt coyote]

It's actually a coding problem, hence for that coding problem I want to find a mathematical notion to solve in general

[vale wigeon]

???

[cobalt coyote]

That was the final mathematical formula I got from my friend, but can't figure out where it was used

[vale wigeon]

then ask your friend maybe??

or share the coding problem here

[cobalt coyote]

Can I share coding problem here as it was a maths questions here?

[vale wigeon]

i literally just told you to share it

coding problems are ok here in general

[cobalt coyote]

Yes.

#include <stdio.h>

int foo(int x,int y, int q)
{
    if ((x<=0) && (y <= 0)) 
        return q;
    if (x <=0)
        return foo(x, y-q, q);
    if (y <= 0)
        return foo(x-q, y, q);
    return foo(x, y-q, q) + foo(x-q, y, q);
}

int main()
{
    int r = foo(15,15,10);
    printf("%d", r);
    return 0;
}```

This was the problem

[vale wigeon]

so your question is why this code represents the formula you gave earlier?

[cobalt coyote]

Exactly

[vale wigeon]

(three backticks for a code block btw)

hm

well your friend's formula only works when q > 0

also the program goes into an infinite loop if q = 0

[cobalt coyote]

yes of course q>0 granted

[vale wigeon]

okay

i can kind of see it, i think

[cobalt coyote]

It will always be some multiple of q for any two random integers x,y. That's for sure

[vale wigeon]

then it looks like your friend's formula is not quite right

and it should instead be q times what she wrote

[cobalt coyote]

Yes sorry there should be q

I forgot to say

[vale wigeon]

so if x and y are both nonpositive we get q

[cobalt coyote]

yes , take x,y as both positive and also q too

[vale wigeon]

...you said before that q is always positive...

[cobalt coyote]

all are postive there are no contravarsies here

[vale wigeon]

anyway, it looks like f(x,y,q) = q even if x is positive and y is not (or vice versa)

[cobalt coyote]

Yes, but take x,y,q as postive

[vale wigeon]

i'm getting there

[cobalt coyote]

This is the most general form

[vale wigeon]

patience

[cobalt coyote]

yes

[vale wigeon]

okay so let's fix q and imagine the input space of f as an infinite two-dimensional grid

like a coordinate plane but we're only considering points with integer coordinates

[cobalt coyote]

haa sure

x,y as two dimesional coordinates

in flat space

[vale wigeon]

it looks like the recursive definition of f implies that it'll be constant on certain q by q squares within this grid

for example if x and y are both between 1 and q (inclusive) we'll have f(x,y,q) = 2q

because its recursive definition always refers to its values at points q units to the left and q units below

[cobalt coyote]

I understood the answer is always 2q

in between

[cobalt coyote]

What is the point here i didn't get it

it's also recursive function

[vale wigeon]

what i'm saying is

we can partition the positive integers into ranges, each of length q

1 to q, q+1 to 2q, 2q+1 to 3q, etc

[cobalt coyote]

Haa i agree

[vale wigeon]

the value of f(x,y,q) only depends on which ranges x and y fall into

[cobalt coyote]

Yes surely that's correct

[vale wigeon]

this explains the ceil(x/q) and ceil(y/q) in the formula

[cobalt coyote]

Haa yes

So that's reverse engineering formula

[vale wigeon]

the values of f within each range form a sort of rotated pascal triangle

[cobalt coyote]

you just said right

[vale wigeon]

i didn't reverse engineer the formula no

[cobalt coyote]

Sorry i got confused but your explanation i can get it

[cobalt coyote]

pascal triangle

Actually we have divided the whole coordinate system of x,y as 1 to q, q+1 to 2q, 2q+1 to 3q

such that x and y values take in this range.

nice divison of this coordinated system

[alpine sable]

Hi guys

Can anyone solve this?

Point O is the center of a circle around triangle ABC, with BOC 120 ° and AOB 140 ° as shown. Find ABC in degrees?

[finite scroll]

well they are all radii

and isosceles triangles

20+30

so 50 right

@alpine sable

[cobalt coyote]

Could you please explain what you said I'm not getting

[alpine sable]

Thank you!

[finite scroll]

np

[cobalt coyote]

Can you draw the diagram and explain what you were saying

[opal gulch]

hello friends

[cobalt coyote]

Actually for q=3 I have written the diagram as follows

[finite scroll]

hi

does everyone have phds here

[cobalt coyote]

No I'm student not phd

Hey dosto please explain me if anyone are familiar with the given formula.

Where did you see this formula in your learning any ideas

There will be a multiplication Factor of q

In the formula

Both x,y,q are positive integers

[gentle ocean]

For this geometric sequence, is it possible to solve it using log?

[finite scroll]

bro im doign this stuff rn

but at a basic level

[gentle ocean]

😭

[finite scroll]

hold on

is that sadler?

the textbook

[ocean seal]

This may only be done by a moderator!

Aug 27, 2021, 1:30 PM

[gentle ocean]

Nelson

[finite scroll]

ah

[gentle ocean]

yea

[finite scroll]

this seems hard tho

[gentle ocean]

i just get confused :<

[finite scroll]

don't you use this

that's what we've been using

[gentle ocean]

yes

yos

[finite scroll]

1/128=8(-1/2)^(n-1)

you need log tho

[gentle socket]

yes

[gentle ocean]

but im finding value of n

[finite scroll]

to solve

[gentle ocean]

yes

but when i did it

i have log as negative

[finite scroll]

i'm sorry i haven't leant about log yet so i cant help

[gentle ocean]

log(-0.5)

which is undefined

so i got confused

sequences and series is confusing a bit

[finite scroll]

i agree

[sage canopy]

The sequence is formed by just multiplying (-1/2)
There is no need to complicate it by using log

[cursive frost]

What does the apostrophe mean?

Everything else is straightforward with union and intersects if sets

[sage canopy]

So just write the eqn. 8*(-1/2)^x=1/128 and solve this eqn
U will get x=10

[wary stream]

You are taking a test?

[hearty quail]

tsk tsk tsk

[wary stream]

Compliment or negation

What exactly don’t you understand?

[untold sequoia]

Oh ic

[sage canopy]

Hope u understood this solution @alpine sable

Its alr

Lol

No worries

[wary stream]

Don't do people's work for them

The goal is to assist the person, not finish their work

[sage canopy]

Ok

[cinder finch]

Don’t assist the person by doing 100% of the work; that just terminates the intent the work had towards the student. Another alternative for assisting people with work could include explaining them the concept?

[alpine sable]

:0 what your opinion

[wary stream]

No, it's based on the denominator

What value of a makes the expression not possible

[sage canopy]

Ok

[alpine sable]

:0 okey

[wary stream]

For more details, what value can the denominator not be?

[alpine sable]

Ok, thank you, the truth is, I don't know much about math, but thanks.

[wary stream]

If the denominator equals 0, math breaks

Does that help a bit more?

[alpine sable]

I think I understand something, thank you

[cinder finch]

Can someone explain this to me?

[wary stream]

Isn't that least squares method?

[cinder finch]

It’s actually linear regression

[wary stream]

Yeah, least squares regression

[cinder finch]

Yeah

[gray crag]

when im drawing the angle in standard position for the unit circle, is the triangle a 45 45 90 or 30 60 90

[wary stream]

Depends on how you want to draw it

[gray crag]

when is it 30 60 90 and when is it 45 45 90

[gray isle]

depends on the values in your question

[gray isle]

it should be clear if you can convert radians to degrees

[fierce frigate]

HELP THE B ONE

T-T

IM OS CONFUSED RN

[tribal wasp]

What's the issue?

Are you familiar with sine rule?

[gray isle]

Sine rule isn't needed

[versed light]

Is anyone Indian here

[tribal wasp]

Yeah it isn't. Just realised.

[versed light]

Nvm wrong channel

[gray isle]

start by drawing the line segment AB

use a protractor to measure the respective angles and draw rays

[tribal wasp]

Wait which part of the qtn are you having trouble with @fierce frigate ? The area or sketching

[gray isle]

their intersection will be the third point of your triangle

[fierce frigate]

area

and sketching

but

i already found someone

but i neede help

in A

nvm

no

no need

thx

[alpine sable]

Hi, does anyone know a website/tool for solving sequences and series and detecting what kind it is(arithmetic,geometric,fibonacci etc)
I currently use "Atozmath number series calculator", but its flooded with ads/a bit to slow for my liking.

If anyone knows a website please let me know! 🙂

Atozmath solution example

[gray isle]

wolfram

[alpine sable]

I have tried wolfram before and I get no solution pretty often. Am I using the wrong one?

[jolly stone]

for very general cases it's better to just manually find it

[wispy olive]

Is this channel free?

[alpine sable]

Yeah for these ones it is. But I also need to use it for bigger problems and more difficult numbers which are really time consuming to do by hand

[jolly stone]

wolframalpha helps you with arithmetic and geometric sequence, but probably not some variations of fibonacci sequence like your example

[alpine sable]

Alrighty

[gray isle]

you could try oeis

[jolly stone]

tried OEIS for that example and didnt work also, and OEIS only keeps most important sequences

[wispy olive]

How do we multiply and/or divide a number like 2 * √6 or 4*√7 by another number?

[jolly stone]

so general cases like that won't work

[alpine sable]

can somebody help me on how to integrate this one?

ln = natural log

[alpine sable]

For example 2√6 * 4√7 is 2 * 4 * √6 * √7 =
8 * √42

2√6 / 4√7. = √6 / 2√7

[bronze pelican]

What is a modulus function

[alpine sable]

A function with Range ≥ 0

[bronze pelican]

can u explain better

That's just a fact

[alpine sable]

It doesn't give any -ve value like
|x| = √x²

[bronze pelican]

|x|=?

[bronze pelican]

Ik but it's still just a basic

[alpine sable]

Wym?

[alpine sable]

still looking for help?

[bronze pelican]

Like it doesn't help too much in solving tough questions

[alpine sable]

I didn't understand that like give example?

[junior vigil]

@alpine sable it gives the 'magnitude of a number', especially useful for complex numbers

distance from the origin

0

[alpine sable]

Yeah ^

[junior vigil]

@bronze pelican you were asking ye

[bronze pelican]

|x+4|-|x|=4 , find the value of x

[bronze pelican]

nope

[alpine sable]

Graph it or solve seperately by splitting domain

[bronze pelican]

do it ik the process

[junior vigil]

think about the set of all 2 numbers that add to 4 that are positive

i.e. 2+2

3+1

1+3

anything inside the | | becomes positive

[alpine sable]

yeah I have to check if that series is convergent, I integrated by parts but what I'm getting doesnt seem to be convergent

[alpine sable]

1st) For x+4 > 0 and x<0
i.e. -4<x<0
Its x+4+x = 4
x = 0

2nd) For x+4<0
-(x+4) x = 4
Doesn't satisfies for any x < -4

3rd) For x > 0
(x+4) - x = 4
Satisfies for all x>0

So answer combined is
x≥0

[unborn sleet]

HI guys, I have a dumb question, on my book it's written that this expression, c^2-2c+1-25f^2 has no common factors other than 1 and -1, I get the 1 but why also -1

[stray prism]

is there a way to simply this?
-6x^4 + 3x^3 - 6x^2

I think there would be some solution to make it a single N x^n +- ....

[gray isle]

wdym by make it a single N

[stray prism]

like number

[alpine sable]

hey i kinda... did it maybe.. sending u the pic in 5..

[stray prism]

k

[alpine sable]

can you post in an unoccupied channel and tag me there with your work?

@alpine sable

[alpine sable]

check ur dm

[gray isle]

your question is still very unclear

[silver current]

help

[alpine sable]

Is there an easier way to do this other than just listing them all out

[warm carbon]

Hey all I have a quick question. I'm starting Indefinite integrals, but my algebra skills are a little lacking. How do handle an integral with x in the denominator?

[thorn vortex]

no

[warm carbon]

Nvm found it. it's the natural log

[upbeat helm]

Could I get some explanation on how to do it? Don't tell me the answer pls

[gray isle]

Apply inscribed angle theorems

[fluid moth]

first time posting here - can we ask questions on statistics, calc, and linear algebra? is this kind of an all purpose discord for anything related to maths? im starting my masters and i will definitely be coming to this channel