help-33

[woven plinth]

taylor series makes sense to me theres just so much you have to account for lol

[glass silo]

Yep there can be quite a bit also a style comment, but you can simplify the (n - 1)!/n! down to make your expression a bit neater, just in case you wanna write it out or something

[woven plinth]

oh yeah true i didnt even think of that i can just leave it as 1/n

also a more general question can you always take out that first number term like i did?

i did it to make it alternate smoothly

before it was + + - + - + so i wanted it to alternate better

[glass silo]

Yea you can always e.g. do the constant term separate and then have the rest where the general formula holds

[woven plinth]

ah ok thats helpful

thanks so much for your help

.close

[marsh citrus]

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[frail crane]

what is limx−→0 e−1/x2

[marsh citrus]

@frail crane Has your question been resolved?

[frail crane]

no

any answer?

[dry holly]

Can't just give answers out

What have you tried so far?

[frail crane]

i feel the answer is zero

but from left side and right side, is the limit the same

[dry holly]

The limit is the same from both sides, yes

But the answer isn't 0

Wait, do you mean (e^-1) / (x^2) or (e^(-1/x^2)?

[frail crane]

e power (-1/x^2)

[dry holly]

Oh, different function then 😭

It helps to clarify those kinda things with brackets

[frail crane]

thats the question there

[dry holly]

In that case then yes, the answer is zero

And it still is the same on both sides

[frail crane]

ok, thx....just answering the last part of the question...i can just define f such that f(x)=0 for x=0 right?

[dry holly]

Yeah, exactly, you would define the function so that f(x) = e^(-1/x^2) if x ≠ 0 and 0 if x = 0

[frail crane]

ok...

thx for confirming

[dry holly]

Np

[frail crane]

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[marsh nymph]

At what distance from the vertex of a convex (convex) mirror is the object located, if its clear image is created at a distance of 30 cm from the vertex of the mirror? The focal length of the mirror is 50 cm. What is the height of the image, if the height of the object is 5cm, what is the mirroring ratio?

[dry holly]

!status

[marsh citrus]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[marsh nymph]

1

<@&286206848099549185>

[marsh citrus]

@marsh nymph Has your question been resolved?

[marsh nymph]

<@&286206848099549185> help me

[grizzled horizon]

Do you know the mirror equation and the relationship between that and the mirroring ratio

[marsh nymph]

no

[grizzled horizon]

$\frac{1}{f} = \frac{1}{d_i} + \frac{1}{d_o}$

[elfin berry]

°Jason Parker°

[grizzled horizon]

$f$ is the focal length, $d_i$ is the image distance and $d_o$ is the object distance

[elfin berry]

°Jason Parker°

[grizzled horizon]

The mirroring ratio is given by $m = -\frac{d_i}{d_o}$

[elfin berry]

°Jason Parker°

[rapid flax]

i have no idea what that means

[marsh nymph]

thank you

closed

[marsh citrus]

@marsh nymph Has your question been resolved?

[marsh citrus]

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[still temple]

oioioi

<@&286206848099549185>

Yk how they said same amount of money?

Convert the denominators to 12

X/5=Y/4=Z/3=t

Make them in one variable

B is the correct answer

@still temple

ok

ah ok

wait nvm i got it

[still temple]

i still dont get

[split comet]

Do you want a simpler explanation of the first question?

[still temple]

yes

[split comet]

We know they give Otto the same amount of money correct?

the 3 friends

[still temple]

yes

[split comet]

Let us assume the amount of money given by each is 1$

[still temple]

ok

[split comet]

Then how much money each gave to Otto?

[still temple]

1/5 of 1?

1/4 of 1

[split comet]

And 1/3 of 1

[still temple]

yes

[split comet]

Moe gave 1/5 of her money which was 1 to Otto

How much money she had before?

[still temple]

4

[split comet]

It was after she gave right?

[still temple]

yes

[split comet]

I'm asking before

[still temple]

5

[split comet]

Exactly

Moe had 5

[still temple]

yes

[split comet]

How much Loki had?

[still temple]

4

and nick had 3

[split comet]

Correct

[still temple]

so add

12

one from each

3/12

[split comet]

total money given/total money of group

[still temple]

=1/4

yes?

[split comet]

exactly

[still temple]

ok thx

[split comet]

no problem

[still temple]

.clos

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[marsh citrus]

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[half stump]

m=sqrt(3)/3

3=2sqrt(3)/3+c

[proud basin]

what

[half stump]

how should i find c

[proud basin]

$c=3-\frac{2\sqrt{3}}{3}$

[elfin berry]

Skill_Issue

[half stump]

then y=sqrt(3)x/3+3-2sqrt(3)/3

also yo you cube and play gd?

[serene spoke]

y-3/x-2 = tan30°

[half stump]

?

nvm i get it

but like

how does that help

[grizzled hearth]

you use the point given and input it into your equation

to find c

@half stump

y=mx+c

[half stump]

^

[grizzled hearth]

ok, so you can find c then

your equation is given by y = mx+c

[half stump]

^ so is this right?

[grizzled hearth]

if you calculated everything and solved it correctly, yes

[half stump]

this is textbook answer

[grizzled hearth]

can you get the text book answer in your form?

[half stump]

no that i know of

3sqrt3-2+x/sqrt3

9-6+3x/3=y

x=y

😦

[grizzled hearth]

wouldnt it be 3sqrt3-2+x = sqrt(3) y?

y = 3-2/sqrt(3) +x/(sqrt)3

= 3-2*sqrt(3)/3 +sqrt(3)x/3?

=y

which is your ans??

[half stump]

y=3sqrt3-2+x/sqrt3

y=9-2sqrt3+xsqrt3/3

[grizzled hearth]

where did 9 come from

[half stump]

ah i get it

9 is over the 3 aswell

so it is the same

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[proud stratus]

hi

[proud stratus]

i need help

i am very stressed

I HAVE A EXAM ON SATURDAY

AND I FEEL STRESSED

this is the 2nd time of taken the exam

the frst time it was fine

but now im worried boiut the scind time

how do i manage alll the stress????

[mighty gyro]

......

meditate

but this math server

......

[proud stratus]

allg

il try

[marsh citrus]

@proud stratus Has your question been resolved?

[proud stratus]

yes

.close

[marsh citrus]

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[hoary wharf]

How do i find the mode in this situation? How am i supposed to find the next class frequency with reference to the modal class if the next interval doesn't exist?

[hoary wharf]

The modal class we have here is 134-139, d¹ = 10-9 =1, i = 6

d² is equal to the frequency of the modal class (10) subtracted by the next class frequency which doesn't exist.

im asking what do i do when i come across this situation?

[marsh citrus]

@hoary wharf Has your question been resolved?

[hoary wharf]

<@&286206848099549185>

[hoary wharf]

watch me ask a calculus question and yall would answer it but not this question

[still temple]

Ya because for me, I don’t quite get this lol

Statistical data analysis killed me

[marsh citrus]

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[hoary wharf]

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[knotty robin]

https://imgur.com/Z4dnT7M
What is the dot in the union?

[maiden parcel]

disjoint union

maybe

[maiden parcel]

just a symbol to say it is a disjoint union

[marsh citrus]

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[tender ibex]

In a casino we can play the game "Throw yourself rich." In this the player throws a die, and receives as many euros as the die has dots. Robbe participates.

(a) What profit can Robbe theoretically expect per game if you don't take into account the wager he has to make at each game? What is his average profit after 6 games?

(b) How big must a player's wager be to be sure that the casino does not make a loss in the long run?

[tender ibex]

idk how to start

it’s w stochastic variables

so I did X = profit of Robbe

But then idk what to do if you don’t take the wager into account

[marsh citrus]

@tender ibex Has your question been resolved?

[tender ibex]

<@&286206848099549185> 🫣🙏

[storm dagger]

Well for part (a) isn't it just the Expected value of the die roll, which is just the average of the number of die dots: (1+2+3+4+5+6)/6 = 3.5

[tender ibex]

and how can I use probability

[storm dagger]

im not sure what you mean?

[tender ibex]

is there a way to do it with chances

The chance that he gets 1 or 2 or 3 or 4 ..

[storm dagger]

well that's what i did basically. I added all the possible outcomes multiplied by their probability

so 1 * 1/6 + 2 * 1/6 + 3 * 1/6 +...

that gives the expected value (average winnings) of the game

[tender ibex]

okok

And the second question?

[storm dagger]

well we know the average profit for each game is 3.5

so if the casino needs the wager to at least be 3.5 so they dont make a loss

[tender ibex]

But if it’s the average profit for the player then im confused

Why not less than 3.5?

@storm dagger ?

[storm dagger]

ok lemme explain like this

imagine i set the wager = 3

then each person who plays the game will receive (on average) 3.5 - 3 = 0.5

that means the casino is losing (on average) 0.5 each time a person plays the game

so if 10,000 people play the game, the casino loses 5,000

[tender ibex]

ah I got confused thinking less than 3.5 was a loss but it’s only a loss if it’s less than 0

for the player

I got it tho ty

[storm dagger]

no worries :)

[tender ibex]

.close

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[shy spear]

Guys I'm taking calc 2 and need a graphing calculator (something where I can input two functions and it'll graph them and their intersection)

What would be good for that? Idk much about calculators since I've never used them so which one could do that?

[wary kite]

ti-84 plus ce

[storm dagger]

depends where you live

[cobalt sentinel]

U don’t really need the ce

ti84 plus is good enough

[storm dagger]

so im guessing that's American?

[shy spear]

yes

[storm dagger]

are you American?

[shy spear]

As long as it can graph two functions at the same time

[shy spear]

I am studying in America

[storm dagger]

ok, i cant help u lol. different product s in different countries

here in the uk, the Casio CG-50 is popular

[wary kite]

i just don’t like the ti-84 plus regular

[shy spear]

Question, is there a calculator that can straight up calculate the area under a curve?

[wary kite]

yea

ti-84

plus

[cobalt sentinel]

Ye ti84s are like a 100 bucks, but u can prolly get them used for cheaper

[shy spear]

bruh how is this allowed in exams then

I mean I need it because graphing the function without it seems like hell

But still

[wary kite]

exams i take don’t allow calculator but also they might want you to show work

finding the anti derivative and integrating by hand

[shy spear]

Yea but realistically speaking if you can graph the area on the calculator then just copy paste the graph on your paper

The only thing you'd have to do is integrate

For me graphing is the difficult part so if that's taken care of, it seems futile

I'll take it tho lmao, thanks guys

[marsh citrus]

@shy spear Has your question been resolved?

[marsh citrus]

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[still temple]

How can I find y and x of this?

[still temple]

Ive tried everything

Still nothing

One time I got 4.5 = y and x = 3.4

[serene spoke]

Hm

[still temple]

One time I got 5 for x

I just cant do this

Ive tried

Nothing works

[serene spoke]

x²+4²=y²

[still temple]

so x is 3?

[serene spoke]

Hey

[still temple]

Hold on

[serene spoke]

Wait one min

See arent they similar triangles

x/3 = 4/x

Or x = 2√3

[still temple]

so x is 3.46

[serene spoke]

Yeah

[still temple]

So y has to be

3.46 + 4

[serene spoke]

Why ?

[still temple]

Thought thats what you said

[serene spoke]

Use this yes

x² = 12

Therfore y² = 12+16

Or y = √28

[still temple]

5.29

[serene spoke]

You cant seperate like this !

[serene spoke]

Yeah

[still temple]

thank you, you helped me solve it faster than the other guy, he took 2 hours and didnt help me like you

[serene spoke]

Umm ok

But did you understand why similar ?

[still temple]

Yes

[serene spoke]

Ok cool 🙂

[serene spoke]

K bye have a good day

[still temple]

.close

[marsh citrus]

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[still temple]

thank you

Solve for x.

A
x = 2

B
x = 3

C
x = 7

D
x = 8

Im guessing I screwed up

or D

[marsh citrus]

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[still temple]

BRO

[still temple]

basically

ab=2b-32

BD=4b-4a

AD=6b-6a

OD=6b-4a

my two ways of getting OC are

OC=OA+ (lamda/x)AB

SO HENCE U GET

(Mew/y)

SO

OC IS

2a+2x-2xa

and MY OTHER WAY

IS

OC=OD+yDA

AND HENCE U GET

0C=6B-4A+6yA-6yB

IVE DONE IT TWICE

HOW D0 I MANAGE TO KEEO CANCELLING MY VALUES

WAIT

WAIT.

DE=3A+7B

HOLD ON

LADS

SO OE=3A+9B

WAIT

I GOT LAMDA =1/6

SO

1:5

BRILLIANT

BRILLIANT

MARVELOUS

I GOT IT

also

how do yk which one u use for the ratio

[marsh citrus]

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[vagrant swallow]

What does 4 indicate?

[sleek lake]

multiplication by 4

[proud ice]

$4\times\sqrt{98}$

[elfin berry]

SWR

[marsh citrus]

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[marsh citrus]

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[vagrant swallow]

So sqrt98*4?

.reopen

[proud ice]

sure

[marsh citrus]

✅

[vagrant swallow]

So sqrt392?

[proud ice]

Oh. No

I thought you meant $\sqrt{98}\times4$, not $\sqrt{98\times4}$

[vagrant swallow]

But IF we have 4sqrt98 + 3sqrt98, it’s gonna be 7sqrt98?

[elfin berry]

SWR

[proud ice]

yes

[vagrant swallow]

But if it’s multiply?

[proud ice]

!original

[marsh citrus]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[vagrant swallow]

Nvm

Alr

Bye

.close

[marsh citrus]

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[proud ice]

Bruh..

[vagrant swallow]

I wanted to ask smt

I don’t have any operation.

[proud ice]

operation?

[marsh citrus]

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[main mica]

ABCD trapezoid AB and DC legs cross in point E. Need BEC triangles perimeter if AB=4,BC=5,CE=7 and AD=12

[marsh citrus]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[broken dome]

How would you approach this?

[main mica]

Well the problem i got is thag I don’t know how to draw a diagram

Of this problem

.close

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[still temple]

.close

[marsh citrus]

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[hearty thicket]

Can someone just explain why in the question(which is asking: without derivatives determine the maximum and minimum of the function) in the last row why is it equal to + or - pi/2 why not just pi/2?

[hearty thicket]

and btw in a previous question you also had to determine where it's defined so thats how he knew to equal them to 1 and -1 fyi.

this is the function sorry

[merry pewter]

it is $\pm \frac{\pi}{2}$ as cos is equal to 0 at both those points

[elfin berry]

caspar

[hearty thicket]

Oh so im supposed to look at the cos alright

thanks

.close

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[merry pewter]

@hearty thicket not cos sry, but the term inside the sin is 2phi, so that it will be $\pm \pi$ inside the sin fuction

[elfin berry]

caspar

[hearty thicket]

the arcsin?

@merry pewter oh okay I got it thanks

[marsh citrus]

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[ornate ruin]

sketched the parallelogram not sure how to solve it

[broken dome]

Probably wanna do some substitutions here

like clearly you have x+3y repeating in multiple places

and -x+5y

so subtitute those for, let's say u and v, and then that converts area A_xy into area A_uv

Did you get that?

[broken dome]

Do you want me to explain it to you in greater detail?

[ornate ruin]

yeah that would be great

[broken dome]

Right so first let's set x+3y = u

and -x+5y = v

that changes our integrand function to u/v

now applying these substitutions to the bounded area we get

u = 0, u = 6, v = 1, v = 8

so we these are now our bounds of integration basically

We also have to rewrite dA = dx*dy in terms of du and dv

[ornate ruin]

oh okay

i got 9log8/4

not sure if its correct

[broken dome]

Uh wait

we didn't rewrite dA ye

yet

[ornate ruin]

oh okay

[broken dome]

Let me just recheck on how to do that

[ornate ruin]

no problem

[broken dome]

Are you familiar with the jacobian?*

[ornate ruin]

not exactly is there a calculator I can use

[broken dome]

So basically when you do a change of variables in integrals like these

dA = |J| dA_new

Where J is the Jacobian

defined as

[ornate ruin]

oh okay

[broken dome]

so you have to express x = x(u,v)

y = y(u,v)

then do the partials

partial derivatives

and then calculate the determinant of the jacobian

[ornate ruin]

got it then I plug it into the integral?

[broken dome]

Yeah so now you have double integral of u/v times absolute value of the Jacobian dudv

And now you solve that

[ornate ruin]

okay got it

[broken dome]

Here's more resources

https://tutorial.math.lamar.edu/classes/calciii/changeofvariables.aspx

For you to use a reference

[ornate ruin]

thank you

is the integral upper bound 8 lower bound 1 f upper bound 6 lower bound 0 f u/v -1/16 dudv?

[broken dome]

the u bounds are 0 to 6

v bounds are 1 to 8

so yeah

wait

what did you get

for the jacobian?

[ornate ruin]

-1/16

[broken dome]

I got 1/8

also jacobian is absolute, so plug it in positive

[ornate ruin]

oh okay

is it 1/8 or 1/16

[broken dome]

Let me recheck

[ornate ruin]

okay

[broken dome]

I got 1/8 again

can you recheck your work?

[ornate ruin]

sure

oh okay i see my mistake ur right

for my final answer with 1/8 i got 4.67874

[broken dome]

Let me check

So I got (6/8) * ln|8|

How did you solve the integral?

Oh nevermind

hold on

yeah it's correct

[ornate ruin]

urs?

[broken dome]

(36/16) * ln|8|

I messed up a bit

[ornate ruin]

i got it right thank you sm for ur help bro

[marsh citrus]

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[marsh citrus]

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[dry sedge]

i dont understand this at all

and i have a final tomorrow man

[uncut cipher]

triangle interior angle sum is 180, while it is 360 for circles. therefore:

[dry sedge]

I get that it should be double but how can an arc have degrees? sorry if this question is stupid

and how does it prove BCE and BAC are equal

[uncut cipher]

since BOC is an isosceles triangle other two angles are 90-alpha

and we proved angle BCE and BAC are equal

assume all 6 six pieces are identical

[uncut cipher]

does it make sense now

[marsh citrus]

@dry sedge Has your question been resolved?

[dry sedge]

I’ll check in a sec

[dry sedge]

Kind of, but I don’t even know what alpha is. We aren’t taught abt alpha at my level I don’t think

Is it just a substitution for x?

[vagrant swallow]

No.

[dry sedge]

uh oh

what’s its importance to the question

[uncut cipher]

alpha is name of symbol i used in this question

[uncut cipher]

COB is 2 alpha

[dry sedge]

Draw isosceles triangle (COB)
COB = 2x, CAB = x (angle at centre subtended by same arc as angle at circumference)
OCB = COB = 90 - x
OCE = 90°
BCE = 90 - (90 - x)

But how is 90 - 90 - x = x
Shouldn’t it be -x @uncut cipher

in mine I substituted alpha for x sorry

I but what I got was BAC = x
and BCE = -x

[marsh citrus]

@dry sedge Has your question been resolved?

[marsh citrus]

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[still temple]

why is it - for |T1|

did they magically assign coordinates and not specify

[vivid basin]

i think they just assumed that the right side is positive

and that would mean the left side in negative

[marsh citrus]

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[still temple]

Can someone explain how to solve a completing the square problem. Like X^2-4x-7=0

[rugged spindle]

essentially, $(x+a)^2=x^2+2ax+a^2$, so if you have anything of the form $gx^2+bx + c = 0$, you can do a=b/2, and do $x^2+2ax+a^2-a^2+c=0$ to $(x+a)^2-a^2+c=0$.

[elfin berry]

fish

[rugged spindle]

In your example, you would have a=-2, since 2ax=-4x, so the expression becomes $(x-2)^2-4-7=0$

[elfin berry]

fish

[still temple]

👍

[rugged spindle]

does my explanation make sense?

[still temple]

Yeah

[rugged spindle]

ok good.

[still temple]

.close

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[stable zealot]

someone pls help

[marsh citrus]

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

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[nova bobcat]

can someone help me with the Pyagorthean Theorem of however you spell it? I dont have work right now but its kind of difficult for me. i know how to do A2+B2=C2 but i cant solve it for the life of me when its asking like if its a right triangle given the measurements or when C is already given

[nova bobcat]

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[stuck marsh]

hello, can someone explain me how sloving $exp(\psi(t)) = exp(t)$ is going to help me to find $\psi^{-1}$? $\psi$ is the digamma function

[elfin berry]

abyssworld

[stuck marsh]

<@&286206848099549185>

[stark trail]

!15mins

[marsh citrus]

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.

[stark trail]

But can you show the original question please

[stuck marsh]

i need to create a function on python that can give me $\psi^{-1}(t)$ for t in R and they say we have to solve exp(psi(t)) = exp(t) first, i dont see the correlation

[elfin berry]

abyssworld

[stuck marsh]

we can use newton raphson for the coding part

[stark trail]

This seems wrong at first glance since taking the log of both sides will imply that psi(t)=t

Which isn’t the gamma function as you said it was

[stuck marsh]

wait typo sorry

exp(psi(x)) = exp(t)

[stark trail]

?

Oh

x

[stuck marsh]

yes srry my bad

[stark trail]

Okay so psi(x) = t. I’m confused still what the question is

[crystal lintel]

[stark trail]

Am I missing something maam?

[crystal lintel]

no i don’t understand either

[stuck marsh]

yes now sorry i understand, i didnt read well

.close

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[still temple]

can i ask a quixk question

[still temple]

for sets

n(so and so)

if its a number

you add

if its a letter or wtv

u count

[sharp sequoia]

1. What do you mean by so and so

[still temple]

liek

[sharp sequoia]

2. Is n an operator

[still temple]

you know your

(A u B)

[sharp sequoia]

Can you type in one sentence

[still temple]

ok

n(A u B)

and lets say

its numbers

[sharp sequoia]

What does n represent? It's cardinality?

[still temple]

yh

but when its a number you add them all up and if they are letters count how many letters there are right?

[sharp sequoia]

Are you saying that A and B are sets

[still temple]

yep

[sharp sequoia]

You don't "add" them up. "Add" would mean, at least to me, that it's some sort of bijection to prove cardinality lol.

A union B consists of all elements in A and B.

Is that what you mean?

@still temple

[stiff pumice]

more like count not add

i think

[still temple]

well

thing is

like

the element is a number

i forgot how to explain it

but when its a number

it has that value

[stiff pumice]

oh

then maybe?

[sharp sequoia]

Is it an operation on a set?

[still temple]

.close

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[hexed umbra]

can someone explain how this error happened wallahi im so confused

[woven plinth]

i think its on the -2log 0.5

[hexed umbra]

-log6-2log0.5
log(1/6)+log(4)
log(4/6)=log(2/3)

is another way it can be simplified

[woven plinth]

actually wait

oh

that looks right

[woven plinth]

^

alternatively you can distribute the negative and get -log 1.5 which turns into log 2/3

[hexed umbra]

my question is why is -log(6)-2log(0.5) != -(log(6*0.5^2))

[woven plinth]

first you can distribute negative

then move the two coefficient into log 1/2

so square the 1/2

then multiply the numbers inside the logs

[hexed umbra]

almost yea

its just not supposed to be negative

its supposed to be postiive log i think

[woven plinth]

wdym

its supposed to be + log 1.5?

[hexed umbra]

yes

[woven plinth]

i dont think it is

[hexed umbra]

i probably made a mistake somewhere else

[woven plinth]

thats criminal for them to make you show work like that

[hexed umbra]

'determine the exact vlaue of x in form log(m)/log(n)'

[hexed umbra]

im just lazy and dont want to write it out then take a picture then upload it so im doing this,, lmao

[woven plinth]

why is log (0.5/6) = log (12)

last two steps

[hexed umbra]

because it just is

wait nvm

o shit

[woven plinth]

yea it is if you flip the sign

so then x = +log(1.5)/log(12)

[hexed umbra]

i think i understand

i dont understnad

ohhh shit i get it

tysm

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[red cairn]

hiii i dont know how to start on this problem

[zinc condor]

What is the definition of secant in terms of sine and cosine?

[red cairn]

would that refer to meaning like secant is 1/x

because its the reciprocal of cosime

[zinc condor]

Yes

So $\sec\theta=\frac{1}{\cos\theta}$

[elfin berry]

otheol

[zinc condor]

Right?

[red cairn]

yes

[zinc condor]

Can you use your calculator to find the value of $\cos\theta$?

[elfin berry]

otheol

[red cairn]

would theta be the 100 degrees shown on the graph ?

ahhhh nevermind thank you so much for the guidance !!!

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[worn radish]

Hello. I do not know how my answer to this question is wrong. Can someone check for my mistake?

[pliant birch]

your answer is right

i believe

[worn radish]

Alright, it might just be the answer key that's wrong. I'll check with my teacher tomorrow. Thanks for confirming!

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[median peak]

i dont get how the greedy alg works for picking the best tree

[marsh citrus]

@median peak Has your question been resolved?

[marsh citrus]

@median peak Has your question been resolved?

[marsh citrus]

@median peak Has your question been resolved?

[marsh citrus]

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[minor acorn]

10f I keep on getting y=5/6+1/6 but in the answers it says it’s -5/6 instead what are the steps to solve that question

[marsh citrus]

@minor acorn Has your question been resolved?

[uncut cipher]

so you found slope of AB

it is 6/5

and what's the slope of PQ?

using m(AB) × m(PQ) = -1

it is -5/6

[minor acorn]

Oh ok thank you

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[main mica]

ABC right triangles AB is the hypotnus. We have P and Q points so that AC=AP and BC=BQ. Need to find PQ if AB=16 and angle is 60 degrees

[heady lark]

where is p and q on triangle

[valid cape]

• does P and Q necessarily lie on the triangle or it can be any points as long as it satisfies the equation?
• which angle is 60 degrees?

[marsh citrus]

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[lusty girder]

this gotta be false right

[lusty girder]

also this has to be true cuz it converges for all real numbers

using root test or am i tripping

yaeh im trippin

the second one i got intervals -4<x<-2

When i substitued i got (-1)^n and (1)^n

but its center -3 is between -4 and -2 so it has to converge at it right?

[storm dagger]

what is it's center? x = -3 ?

[lusty girder]

yeah

[storm dagger]

it converges for it's center

[lusty girder]

W but i have a question

how do i know if (-1)^n is divergent

[cunning fiber]

You don’t even need to find the interval of convergence, just note that it’s the sum of 0^n

[cunning fiber]

Test for divergence

[lusty girder]

so find if lim of (-1)^n is = 0 ?

[storm dagger]

check the limit

it isnt 0

therefore it diverges

[lusty girder]

and the (1)^n same process?

[storm dagger]

thats the one im talking about

[lusty girder]

oh okay

thanks

[storm dagger]

np

[lusty girder]

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[tardy vessel]

A rectangle is inscribed in an isosceles, right-angled
triangle ABC as shown in the figure.
The hypotenuse AB in the triangle has length 2a.
Investigate how large the area of ​​the rectangle can be.

[supple marsh]

are the other points named? is this the correct diagram?

[twilit grove]

why would the other points need to be named

[tardy vessel]

i was thinking that the 2 other angels of one of the triangles was 45 meaning that it was 45 45 90 triangel. since ab=2a then A to 0 = a and therfor 2b^2=a^2 meaning that the sides has a length of sqrt(2)*b. i also know that for every "a" the A to C its "increasing" ( dont rememver the engilsh word think the derivatie of the line) would be sqrt(2)*b. and i was also thinking that when x = 0 on the line g(0) would be sqrt(2)*b witch means that maybe g(x)=sqrt(2)bx+sqrt(2). then for the area of the rectangle would there for be a point on the g(x) witch i could call p (for point) the area of the recktangle would then be Ar(p)=g(p)*p. but i unsure if this is the correct way? could someone give me a hint to how to solve this?

[twilit grove]

you're given that it's isosceles, so the angles at A and B are 45, yes

[tardy vessel]

no there is no other points named and this is the correct diagram form the problem.

[supple marsh]

for explanation simplicity, I was just asking.

[supple marsh]

I dont understand everything you're saying, but the beginning is correct.

[tardy vessel]

what part do you not understand so i could try to explain it better?

[marsh citrus]

@tardy vessel Has your question been resolved?

[marsh citrus]

@tardy vessel Has your question been resolved?

[marsh citrus]

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[gentle steppe]

Hey I have a question about general mathematics since i'm going into class 9 and physics is getting hard because i dont have a grasp on concepts from grade 6,7,8 If there anything particular way i should resolve this issue I'm having trouble with fractions decimals and equations

[leaden monolith]

Understanding the theory gives you the ability to do the questions

Doing a lot of questions makes you fast

[gentle steppe]

would you recommend any particular resource for this purpose

[leaden monolith]

Does your school use a textbook?

[gentle steppe]

ncert

[low ruin]

Hit the textbooks. Lot of fractions is just knowing the theorems. For, decimal should know rounding and conversions

[leaden monolith]

Usually the Cambridge one (which my school used) has a lot of questions

[gentle steppe]

I'm looking for like a refresher course or website so i can revise these concepts quickly and then practice lots of questions

[low ruin]

Khan Academy

If you have troubles refer to the Q/A

[gentle steppe]

never heard of it i'll check it out

[low ruin]

check top-voted, trending and recent questions for questions. Go through every post possible before asking a question

[gentle steppe]

Q/A channel?

[low ruin]

The above is in reference of Khan Academy

[gentle steppe]

k i'll use it

[low ruin]

Yes khan academy has a Q/A section for each video

[gentle steppe]

ohh

k thx

!close

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[lusty girder]

is this false cuz its not in its pure form of x^2/a^2 - y^2/b^2 = 1

[crystal wraith]

you can even rewrite this in that form, but whether or not a hyperbola is in that form doesn't actually affect the fact it is one.

[floral rapids]

is the equation in an equivalent form to its pure form?

[lusty girder]

yeah

im just trying to get rid of any tricks by making sure with you guys

i have a quick question tho

do i use ast with this

cuz its be divergent if i did

[mystic minnow]

correct

[lusty girder]

alright thanks

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[exotic wolf]

hello

[exotic wolf]

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[minor tinsel]

i need help

[whole compass]

The question pls

[minor tinsel]

answer....?

[mystic minnow]

if they're similar quadrilaterals, their side lengths all have the same ratio

so AB/EF = AD/EH

plug in numbers and solve for x

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[north marsh]

Guys

[north marsh]

Some questions about using sign analysis

So I've done the table and got my signs on the "product" column

So the + sign and - sign.....what tf do they even mean? How did that help me determine my final answer

[late geode]

,rotate

[late geode]

positive, negative

tells you whether something is greater or less than 0

[north marsh]

OK so how do I grt my final answer from that info?

Compared to something like this

I just don't understand what is going on with this table bro

Ph wait

Wait wait wait wait wait wait

OHHHHHH

Ok

[merry cloud]

How to solve number 6

?

[minor tinsel]

use gaumath on app store

[merry cloud]

@minor tinsel Okay I try

[marsh citrus]

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[chrome relic]

Hey, I was wondering if their was a way to add the perfect squares at the bottem of the pic without having to do that much work.

[twilit grove]

need a clearer picture. is that a door???

[still temple]

sorry for the irrelevancy, but are you doing math on your... window?!

[chrome relic]

Yes, lol

One sec

This is as clear as I can get

[shell ether]

I know only how to add the cubes

[chrome relic]

So there is no other way?

<@&286206848099549185>

[shell ether]

Maybe to get prime numbers...

fr like 8² is 2⁶

[chrome relic]

Ahh yes, thank you!

.close

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[chrome relic]

WTF

[old plinth]

<@&268886789983436800>

[chrome relic]

<@&268886789983436800>

[marsh citrus]

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[sage gate]

so I know how to do passing through pints but the y

do I just solve for x?

x-3^2 * x+2 = -1.8

like that

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[brisk saffron]

Why must the second row be 7 and not 1?

[brisk saffron]

For context this was the original matrix

nvm didn't read the solution properly

.close

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[minor tinsel]

.

[marsh citrus]

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[outer lodge]

s

[outer lodge]

Having trouble computing the Ricci tensor for the following line element
[ \dd s^2 = \dd r^2 + \tanh^2(r) \dd \varphi^2 ]

[elfin berry]

shsgd

[outer lodge]

I have the following non-zero Christoffel Symbols:
[ \Gamma^r_{\varphi\varphi} = \tanh (r) \sech^2 (r) ]
[ \Gamma^{\varphi}{r\varphi} = \frac{1}{\cosh (r) \sinh (r)} ]
[ \Gamma^{\varphi}{\varphi r} = \frac{1}{\cosh (r) \sinh (r)} ]

[elfin berry]

shsgd

[outer lodge]

Then, I computed the following Riemann tensor
[ \text{R}^r_{\varphi r \varphi} = - \frac{2 \tanh^2 (r)}{\cosh^2 (r)} ]

[elfin berry]

shsgd

[outer lodge]

Thus, by the symmetries,
[ \text{R}^r_{\varphi r \varphi} = -\text{R}^r_{\varphi \varphi r} = \text{R}^{\varphi}{r \varphi r} = -\text{R}^{\varphi}{r r \varphi} ]

[elfin berry]

shsgd

[outer lodge]

The Ricci tensor is given by
[ \text{R}{ab} = \text{R}^{\lambda}{a\lambda b} ]
Which results in
[ \text{R}{rr} = \text{R}{\varphi\varphi} = - \frac{2 \tanh^2 (r)}{\cosh^2 (r)} ]

[elfin berry]

shsgd

[outer lodge]

But I'm told that
[ \text{R}{\varphi\varphi} = \frac{2 \tanh^2 (r)}{\cosh^2 (r)} ]
[ \text{R}{rr} = \frac{2}{\cosh^2 (r)} ]

[elfin berry]

shsgd

[marsh citrus]

@outer lodge Has your question been resolved?

[outer lodge]

Turns out these symmetries hold for lower indices only, so have to perform some index raising/lowering
[ \text{R}^{r}{\varphi r \varphi} = g^{rr}\text{R}{r \varphi r \varphi} = g^{rr}\text{R}{\varphi r \varphi r} = g^{rr}g{\varphi\varphi}\text{R}{\varphi r \varphi r} ]
[ \implies g^{rr}g{\varphi\varphi}\text{R}_{\varphi r \varphi r} = \frac{2\tanh^2 (r)}{\cosh^2 (r)} ]

[elfin berry]

shsgd

[outer lodge]

.close

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[sweet pawn]

Prove that (p-1)! = -1 mod p

[sweet pawn]

1 × 2 × 3 × 4 × ... × p-1 =
(1 × -1) × (2× -2) × (3 × -3) × ((p-1)/2 × -(p-1)/2)

[marsh citrus]

@sweet pawn Has your question been resolved?

[hallow crown]

consider how Z/pZ is now a field (because p is prime) so every number has an inverse for k in {1,2,3,4,...,p-1}

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[mental yew]

factor 27a^3-125d^3

[mental yew]

need help to figure out the steps to factor

[late geode]

hint
27 = 3**^3**
and 125 = 5**^3**

[mental yew]

uhh

do i do like 3a-5d

[sweet pawn]

Let's see if I can remember it off the top of my head.

x^3 - y^3 = (x-y)(x^2 + xy + y^2)

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[mental yew]

sorry wasnt paying attention

so (3a-5d)(9a+15ad+25d)

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[marsh citrus]

@dawn zodiac Has your question been resolved?

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[rare fractal]

need answer

[stark trail]

!noans

[marsh citrus]

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

[rare fractal]

you an opp bruh

[stark trail]

what have you tried

[rare fractal]

yes bruh

why do you think im here.

[stark trail]

I was asking what you had tried, not if you had

like explain what you did so far and why you're stuck please

[rare fractal]

can i just have thhe answer tbh

[stark trail]

no

[rare fractal]

well that stinks

[stark trail]

if you're not going to be receptive to getting help here, maybe try clicking on "Show Examples"

[rare fractal]

I did and have tried. I have my math Final tomorrow and this was just missing work needing to be done

thats just me being straight forward telling u i was only here for the answer

[stark trail]

ok well no one is going to just give you the answer, that's not the point of the help channels

[sharp sequoia]

Yeah we're here to help, not being answer-givers.

Unfortunately if that is your intention then you are not going to benefit from here.

[upper timber]

Get real

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[haughty tusk]

Hello,
I got a math problem about permutation and I dont know how to solve it

[haughty tusk]

I think it is 30% but I dont know why the correct answer is 10%

[elfin prawn]

How many combinations are there in total?

And how many combinations are there that do not contain a constant?

[haughty tusk]

I think it is P(5,2) that would be 20

[haughty tusk]

And for this I think it is P(3,2) which would be 6

[wooden elbow]

That's the combinations that contain a consonant

[whole sleet]

This is the number of words that contain only consonants

[haughty tusk]

Oh
Yeah Idk how I missed that
Thanks to both of yall @whole sleet @wooden elbow

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[vernal basin]

this kinda makes sense to me, but i tried to do (13 choose 1) * (4 choose 2) * (12 choose 1) * (4 choose 2) * (11 choose 1) * (4 choose 1) which is wrong

the only difference here is that the solution does 13 choose 2 and I do (13 choose 1) * (12 choose 1). Why is the difference arising? what is the difference between the first and the second ways

[bitter terrace]

i’m pretty sure it’s because doing 13C1 and then 12C1 can lead to a repeated hand. Eg (22,33 and 33,22)

doing it by just 13C2 eliminates that

[normal sky]

Notice 13C1 * 12C1 = 2 * 13C2

[normal sky]

and this

[vernal basin]

ahhh i see

didn't even think of that, i guess ill just build that inuition

thanks

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[fair path]

can someone help me get from 1 -> 2?

[fair path]

i understand it's all algebraic manipulation but i don't see how we get the numerator?

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[sturdy bobcat]

How do I prove that, given a circumference C(O;r), and points a point P inside the circumference and a point Q outside the circumference, the intersection between PQ and C(O;r) is a single point?

It's easy too see, but I need a hint on what properties to use

[sand fable]

you could consider this by thinking of the distance PO and QO and what happens when you go from P to Q

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[gentle remnant]

When proving a limit using epsilon-delta proof, can I split epsilon into cases? like if epsilon is even, then pick delta s.t. and if epsilon odd, then pick delta s.t.

[gentle remnant]

cuz it's like for every epsilon > 0 there exists delta > 0, so if epsilon is even, there does exist a delta, and if epsilon odd, there does exist delta

[wanton ferry]

yes

prove for both even and odd cases

[hazy lion]

👀 for what proof

usually epsilon is just some positive quantity

it might not be even or odd

[gentle remnant]

no its not a secific proof

just in general

like can I split epsilon into rational and irrational

and take two cases