help-33

[edgy kestrel]

Oooh I get it

Thanks

I really appreciate it

[split pike]

no problem maam

[edgy kestrel]

.closed

Wait how do I close the channel

[split pike]

i think its .close

[edgy kestrel]

Oh

.close

[marsh citrus]

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[stable verge]

If I have -y = -4 can I divide both sides by -1 to make y = 4?

[stable verge]

siiiick

[sharp harness]

you could also multiply both sides by -1, that's the same thing because 1/-1 = -1

so basically yes you can

[stable verge]

Thanks!

[marsh citrus]

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[stable verge]

.close

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[knotty shard]

!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

[knotty shard]

1

[glossy flint]

,, \frac{dy}{dx} = \frac{\left(\frac{dy}{d\theta}\right)}{\left(\frac{dx}{d\theta}\right)} \ \ \text{(by the chain rule)}

[elfin berry]

Alberto Z.

[glossy flint]

So you'll have to calculate dy/dtheta and dx/dtheta

[knotty shard]

ah

how does one find d theta 😅

[glossy flint]

Didn't the teacher explain this?😢 Otherwise how can you do the exercise? 😅

[glossy flint]

What do you mean?

[knotty shard]

yeah im confused on how to apply it to the equation 😭

[glossy flint]

You only have to calculate $$\mathbf{\frac{dx}{d\theta}} \ \text{and} \ \mathbf{\frac{dy}{d\theta}}$$

[elfin berry]

Alberto Z.

[knotty shard]

ohhhhhhh

i understand now

i forgot that from x i can turn it into dx/d theta and same for y

[glossy flint]

All good, don't worry 👍

[marsh citrus]

@knotty shard Has your question been resolved?

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[lilac sandal]

I think its
A Can Happen
B Can Happen
C Can Happen
D cant happen

but it said its wrong i get 1 more try

[marsh citrus]

@lilac sandal Has your question been resolved?

[lilac sandal]

<@&286206848099549185> can someone help out please

[true parcel]

where's the question

[rustic field]

@lilac sandal where is the question

the diagram

[lilac sandal]

there isnt one

thats all i got

i just have to mark if it can or cant happen

[rustic field]

A)Can happen

B)Can happen

C)Cant happen

D)Cant happen

I think

[lilac sandal]

i just submitted it with that and it said
Cant
Can
Cant
Can

[eager tinsel]

what is your explanation for D being impossible?

[lilac sandal]

idk

question is dumb

[rustic field]

u cant make a pentagon out of lines containg infinite lenght

[eager tinsel]

it is not

[rustic field]

it is

bruh who tf asks these questions

[lilac sandal]

not your question, the math question

[eager tinsel]

I am not familiar with that congruency thing
but C is impossible for sure

[rustic field]

Congruent means eqaul

in a sense

[eager tinsel]

you can't bisect a ray

[eager tinsel]

okok

but shouldn't they could just use equals symbol

?

[rustic field]

U can just say a figure is equal to the other

for example

Triangle ABC cant be equal to DEF

Its congruent

and also

figures have more parts than just lenghts

so if 2 figures are congruent

they are equal in every sense

[eager tinsel]

the thing is that maybe congruency might have something to do with orientation factor too

but anyways

[lilac sandal]

.close

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[sharp sedge]

when expanding this,
x^2-4(x^2 +4)
x^2-(4x^2+16)
with this term in the bracket would i make the whole thing negative or only the -4x^2 part

[sharp sedge]

x^2-4x-16 or x^2-4x+16

just a bit confused

im way past this level but for some reason i aint thinkin right today

[hard gull]

first one , consider the negative as -1
x^2 -1(4x^2 + 16)

[sharp sedge]

oh ok thanks

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[sharp sedge]

which 1 should i sub?

how do i find the easiest one

i can either go for x or y

[golden prairie]

the x or y in the first both work fine

[sharp sedge]

ah ok

[golden prairie]

i cant think of one in this case thats way easier than the other

[sharp sedge]

but for future questions what should i consider

[sharp sedge]

i see

.close

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[misty wigeon]

<@&286206848099549185>

is this graph linear appropriate

[main idol]

!15m

[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.

[misty wigeon]

i've posted this same question 3 times

and no one has helped me

i waited 15 minutes in the other times and no one has helped me

can someone please help

[main idol]

doesn't matter

[misty wigeon]

then help me

[main idol]

no. wait for someone

[misty wigeon]

<@&286206848099549185>

[marsh citrus]

@misty wigeon Has your question been resolved?

[misty wigeon]

<@&286206848099549185>

[hidden hearth]

Actually what do you want to do with this graph?

[marsh citrus]

@misty wigeon Has your question been resolved?

[misty wigeon]

is it linear appropriate

[marsh citrus]

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[misty wigeon]

.reopen

[marsh citrus]

✅

[elfin berry]

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

[misty wigeon]

@sharp wing

why is no one helpiong

[true parcel]

maybe no one knows

but i think it is linear appropriate

the residuals arent in some sort of pattern

just scattered over and under x axis

[marsh citrus]

@misty wigeon Has your question been resolved?

[marsh citrus]

@misty wigeon Has your question been resolved?

[marsh citrus]

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[marsh citrus]

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[topaz latch]

How do I disprove this, I know the cancellation holds for right side and left side cancellations

[desert dirge]

you could make a counterexample

[mellow kraken]

consider the group of integers under multiplication. 4 · 0 = 6 · 0 clearly doesn't imply 4 = 6. why?

[final skiff]

should use rational numbers, not all integers have inverses.

[spark otter]

0 still doesn't have an inverse

[final skiff]

True

[spark otter]

try something like

S_3

the group of permutations of {1,2,3}

there are only 6 of them in there, should be pretty easy to find one that doesn't work

(example : take c a 3-cycle and a,b permutations)

@topaz latch I hope this helps

[marsh citrus]

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[lavish wharf]

I’ve tried solving this

But I says it’s wrong and I don’t understand why

First I took 7-4

So it became 4x-2.5x=3

Then I did 4x-2,5x and that’s 1,5x

So it became 1,5x=3

And then I divided 3 by 1,5

And it became

Oh

I had clicked smt wrong on the calculator nvm🥲

.close

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[humble lichen]

hey yall, trying to figure b) here and struggling to find the answer, I understand that the goal is to turn |(pi*x_n - 2)x_n -(pi - 2)| basically into a variation of |xn - 1| and choose my epsilon to prove that equation is less than epsilon... but I'm kinda stuck

[humble lichen]

I changed it to this form but the singular 2/xn is making it hard

.close

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[glass silo]

Any ideas for either of those?

[mellow kraken]

plot out the graph, and then work out the integral piecewise.

[placid grotto]

the 2nd one I just do the integral twice on the 2nd derivative to find the original function?

I did plot out the graph it doesnt show anything

[mellow kraken]

integrate twice, using f(0) = 2 and f'(0) = 3 to work out the constants of integration.

[placid grotto]

what do you mean using?

[mellow kraken]

I'll give an example

Suppose f'(x) = 4x + 3 and f(0) = 4. Then, we integrate f'(x) to get f(x) = 2x^2 + 3x + c. And, using f(0) = 4, we get c = 4. So f(x) = 2x^2 + 3x + 4

[placid grotto]

how do we get 4

I don't know where 4 is coming from

oh right it's the constant

?????

[marsh citrus]

@placid grotto Has your question been resolved?

[placid grotto]

????

@mellow kraken can you explain it more?

[placid grotto]

??????

<@&286206848099549185> can someone help me

[placid grotto]

@wooden sedge can you help me

@mellow kraken can you help me

[placid grotto]

.close

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[low sapphire]

can someone point me in the right direction for d)?

[glass silo]

e.g. assume C is obtuse: then the "height" of the triangle is not "inside" the triangle

(or choose another angle and draw a similar diagram, then take it from there, you might get the cosine rule in another order maybe )

[low sapphire]

ty

:)

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[manic portal]

How do i solve this question?

[glass silo]

Do you know any identities that link tan and sec?

[manic portal]

Umm i dont know

[analog thistle]

I got you hold on

[manic portal]

Thank you

[versed canyon]

nor really
but theres some for tan^2 and sec^2

[analog thistle]

Want me to explain it or do you want an answer?

[manic portal]

Ohh

[glass silo]

!nosols

[marsh citrus]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[manic portal]

Step by step answer please and some explaining

[glass silo]

And same thing the question was for OP though

[analog thistle]

oh ok I just joined this and I didnt read the rules lol

[analog thistle]

Ok do you recall a Pythagorean identity that relates tan^2x and sec^2x?

[manic portal]

1 =sec2x -tan2x
Tjis one?

[analog thistle]

Its this one

1+tan^2 x=sec^2x

Understand it?

[manic portal]

Yes

But how do i get sec2x

Oh wait

Nah too hard

[analog thistle]

For that we use the pythagorean identity which is sec^2x=1+tan^2x

[analog thistle]

lol

[analog thistle]

if you just want the answer dm me

i cant share here

[manic portal]

.close

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[trim laurel]

any integration gods?

[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.

[gilded cedar]

do u know relation between sinx and cos2x

[marsh citrus]

@trim laurel Has your question been resolved?

[trim laurel]

.close

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[cunning chasm]

do you say the limit as x approached 4 doesn't exist or approaches infinity

[main idol]

+inf

[late geode]

depends on the specific wording of the question

if just asked whether the limit exists, you'd say no

[marsh citrus]

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[limber oasis]

(a)

[calm harbor]

Can you translate it?

[limber oasis]

theres English there lol

[calm harbor]

mb

[limber oasis]

having trouble to find the angle, im missing something 😭😭

[limber oasis]

any luck?

.close

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[limber oasis]

.close

[calm harbor]

It’s closed

[marsh citrus]

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[twin goblet]

hi my teacher solved this q a while ago may i know how the heck did she do these steps because i don't really understand what did she do..
(i got this from my friend's notes)

[true parcel]

,rotate

[twin goblet]

[true parcel]

simplify $\frac{2x^2 - 3x + 4 + 5x - 4}{x}$

[elfin berry]

Astar777

[true parcel]

u get $\frac{2x^2 + 2x}{x}$

[elfin berry]

Astar777

[true parcel]

split the numerator

$\frac{2x^2}{x} + \frac{2x}{x}$

[elfin berry]

Astar777

[true parcel]

thats 2x + 2

factor out 2

so you're left with 2(x+1)

what?

[twin goblet]

nvm

[true parcel]

so $\lim_{x \to 0} 2(x+1)$

[elfin berry]

Astar777

[true parcel]

no indeterminate form here

so just put x=0

and you get the answer

[twin goblet]

2(0+1)

[true parcel]

yes

[twin goblet]

which comes to??

2+1?

3

💀

[true parcel]

[twin goblet]

Real

[true parcel]

2(0+1) -> 2(1) -> 2

[twin goblet]

oh

ok thanks

.close

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[weary karma]

can we get the value of alpha + beta/2 from here?

[stark sandal]

I don't think so?

You'd need more

[weary karma]

i cant really solve the question without that value tho ;-;

[stark sandal]

!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.

[stark sandal]

oh fuck coord geo

[weary karma]

dw this one is easy we just have to apply the formula

thing is the formula has cos ( alpha + beta /2)

and sin (alpha +beta/2)

[marsh citrus]

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[night lion]

quick question is this property only to be applied as a whole to the integral

[night lion]

or can i do it to specific functions of x?

[sinful thistle]

wdym

[night lion]

say i have integral of tanxcotx

[dusky viper]

yeah gonna need some details

[night lion]

can i just use it for cot x

[sinful thistle]

no

not how integration works

[dusky viper]

nah u have to apply for every function of x

[sinful thistle]

@night lion we done here?

uh

[night lion]

yea

[night lion]

yea makes sense

[sinful thistle]

.close

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[stoic trench]

.close

[jade notch]

can someone help me tackle 8(b)(ii)?

this is my solution

the problem is that how to turn 2^r to 2^-r to satisfy the proved equation in 8(a)

[weary karma]

maybe expand the bracket?

[jade notch]

I have

but I still cant use the equation in part(a)

[sinful thistle]

notice

it's -r2^r from r = 1 to 1000

[weary karma]

2^r(2000) + 2^r(-r)?

[sinful thistle]

maybe subs?

[weary karma]

the first part is a GP

[jade notch]

like this ?

[jade notch]

this is my alt account

.close

[marsh citrus]

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[sweet mesa]

ik i could get the answer simply by considering section formula

but treating them as vectors, since they're collinear, when i use the condition:
PR=k.PQ
i get k=3/2
and when i substitute that value am getting the coordinates all wrong

why so

nvm i made a dumb calc mstk wtf

.close

[marsh citrus]

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[misty jacinth]

How to solve without guess and check?

[hidden dawn]

do u know how to modelise this problem by two simple equations?

[misty jacinth]

No

[hidden dawn]

just consider a the length and b the width

and make equations off the values u have from the problem

[misty jacinth]

That’s what I did but idk which one works

[hidden dawn]

it becomes a system of equations

[misty jacinth]

That’s what I got as well, but it turned into zero

[hidden dawn]

wait what

[misty jacinth]

Idk I might have done something wrong

[hidden dawn]

did u write out the equations?

[misty jacinth]

Ye

[hidden dawn]

show

js to verify

[hidden dawn]

so 1/2 l² - 21l = 6860

this is a big quadratic tbf

[misty jacinth]

I just guessed numbers and got it right

[hidden dawn]

Oh

[misty jacinth]

I can’t figure it the quadratic thing

[hidden dawn]

i believe this was meant to be solved by a quadratic equation

[hidden dawn]

calculator

[marsh citrus]

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[marsh citrus]

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[austere mountain]

The value of

$$\sin^{2} \ang{1} + \sin^{2} \ang{3} + \sin^{2} \ang{5} + \ldots + \sin^{2} \ang{89} =$$

[sinful thistle]

uh

do you mean

[elfin berry]

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

[sinful thistle]

is texit down

weird

finally

[austere mountain]

n := odd numbers

[sinful thistle]

ah

[austere mountain]

for the natural numbers, i used identities

[sinful thistle]

well recall that sin(90 - x) = cos x

therefore sin^2 (90 - x) = cos^2 x

[austere mountain]

ooo

let me try

i got it

$$\sin^2 89\degree = \cos^{2} 1\degree$$

$$\sin^2 87\degree = \cos^{2} 3\degree$$

etc

$$\sin^2 47\degree = \cos^{2} 43\degree$$

[elfin berry]

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

[austere mountain]

it should be

$$22 + \frac{1}{2}$$

$$= 22,5$$

[austere mountain]

Thank you so much!!!

[elfin berry]

raymondclie

[sinful thistle]

np!

[marsh citrus]

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[austere mountain]

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[waxen breach]

for both a and b, it's absolutely not true that for any case of x as a linear combination of y and z, you can necessarily write it as a combination of y and z AND w (if it's not coplanar)
like if u have 2 dimensions and a line along x axis
(1,0) to (2,0) for y and z
if u have a w (0, 1) that's not gonna give u a linear combination that follows that line
but how do u write that mathematically

[sinful thistle]

a is true

[spark otter]

... you can always add 0w

[sinful thistle]

^^

0w is always possible

x = ay + bz = ay + bz + 0w

the second one is false

[waxen breach]

bruh

i see

what about b tho how do u prove b

[sinful thistle]

"give an example"

[spark otter]

well b is false

[sinful thistle]

you don't need to prove it

[spark otter]

give a counterexample

[waxen breach]

prove it/counterexample yea

[sinful thistle]

no

those are most definitely not the same thing

[waxen breach]

i see

[spark otter]

"prove it's false" implies "prove it's always false", which is different from "give an instance where it's false"

[waxen breach]

well i can't think of an example anyways

[sinful thistle]

how

[spark otter]

think about 3D for example

where each of the components in a basis (maybe take the simplest one) is important to describe a vector x

[waxen breach]

i, j, k would work

[spark otter]

which of x,y,z,w would those be?

[waxen breach]

x = a[1,0,0] + b[0,1,0] + c[0,0,1]

[spark otter]

yeah great

[waxen breach]

unit vectors for 3 dimensions

[spark otter]

just pick some specific values for a,b,c

[waxen breach]

and then if u try making x = [1,1,1] with c = 0 (remove w vector) then u cant

[spark otter]

so that you can't just "remove" c

[spark otter]

yeah exactly

[waxen breach]

cool thanks

[marsh citrus]

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[karmic shale]

9+8(6 - 5^1 ÷ 9(99(6 × 5)) × (9% × 2)) - 21 + (-(-8))+ 2110 + (((-2)×(-6))-19)-246+950+1)0+1

[karmic shale]

Please help me with this question

my friend think the answer is 1 and I think the answer is 2852

[still temple]

,w 9+8(6 - 5^1 ÷ 9(99(6 × 5)) × (9% × 2)) - 21 + (-(-8))+ 2110 + (((-2)×(-6))-19)-246+950+1)0+1

[elfin berry]

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Requested by anjaliji_74295

[still temple]

486

[velvet cedar]

9(99(6×5))
To juxtapose or not to juxtapose

There also seems to be errors in the parsing

950+1)0
Becomes 950 + 10 in WA

,w 9+8(6 - 5^1 ÷ 9(99(6 × 5)) × (9% × 2)) - 21 + (-(-8))+ 2110 + 0(((-2)×(-6))-19)-246+950+1)+1

[elfin berry]

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[still temple]

2 difference off

[velvet cedar]

Hmm, I think parentheses are misplaced

Yeah

+1)0
This is missing an opening one

[marsh citrus]

@karmic shale Has your question been resolved?

[karmic shale]

idk

Step 1: Simplify powers and multiplications.
5^1 = 5
6 × 5 = 30
99 × 30 = 2970
Now the expression becomes:
9 + 8(6 - 5 ÷ (9 × 2970) × (9% × 2)) - 21 + (-(-8)) + 2110 + (((-2) × (-6)) - 19) - 246 + 950 + 1)0 + 1
Step 2: Simplify modulo or percentage operation.
9% × 2 = 0.09 × 2 = 0.18
Now the expression becomes:
9 + 8(6 - 5 ÷ (9 × 2970) × 0.18) - 21 + (-(-8)) + 2110 + (((-2) × (-6)) - 19) - 246 + 950 + 1)0 + 1
Step 3: Simplify division and multiplication.
9 × 2970 = 26730
5 ÷ 26730 ≈ 0.000187
Now the expression becomes:
9 + 8(6 - 0.000187 × 0.18) - 21 + (-(-8)) + 2110 + (((-2) × (-6)) - 19) - 246 + 950 + 1)0 + 1
Step 4: Simplify the result in parentheses.
0.000187 × 0.18 ≈ 0.000034
6 - 0.000034 ≈ 5.999966
Now the expression becomes:
9 + 8(5.999966) - 21 + (-(-8)) + 2110 + (((-2) × (-6)) - 19) - 246 + 950 + 1)0 + 1
Step 5: Multiply 8 by 5.999966.
8 × 5.999966 = 47.999728
Now the expression becomes:
9 + 47.999728 - 21 + (-(-8)) + 2110 + (((-2) × (-6)) - 19) - 246 + 950 + 1)0 + 1
Step 6: Simplify remaining terms
-(-8) = 8
(-2) × (-6) = 12
12 - 19 = -7
10 + 1 = 11
Now the expression becomes:
9 + 47.999728 - 21 + 8 + 2110 - 7 - 246 + 950 + 11
Step 7: Perform the final addition and subtraction.
9 + 47.999728 - 21 + 8 + 2110 - 7 - 246 + 950 + 11 = 2861.999728

Final answer: 2862

This is how I got the answer

[marsh citrus]

@karmic shale Has your question been resolved?

[karmic shale]

so

does is make sense?

[velvet cedar]

,w 9+8(6 - 5^1 ÷ (9 × 99(6 × 5)) × (9% × 2)) - 21 + (-(-8))+ 2110 + (((-2)×(-6))-19)-246+950+10+1

[elfin berry]

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Requested by strangequarkal

[velvet cedar]

Same answer but there's still this issue

[velvet cedar]

If you can clarify by posting the original question, that would be great (though I imagine it was intentionally presented in this format)

[karmic shale]

okay

9+8(6 - 5^1 ÷ 9(99(6 × 5)) × (9% × 2)) - 21 + (-(-8))+ 2110 + (((-2)×(-6))-19)-246+950+1)0+1

that's the question

[velvet cedar]

950+1)0
There's no matching opening parenthesis

In your work, you treated 1)0 as 10

(Also, I'm not certain but the formatting of your answer looks AI generated)

[marsh citrus]

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[marsh citrus]

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[normal bough]

Is 160 the correct answer?

[normal bough]

or was I supposed to replace the 96 with 16?

[desert dirge]

did you just find the maximal height?

thats not what it asked for

[normal bough]

oh.

[desert dirge]

its asking for the set of (valid) t values such that h>16

[normal bough]

😐

[desert dirge]

im not a mind reader

if you have an issue youre going to have to say it

[normal bough]

what do i do for this problem then?

[desert dirge]

solve h>16

solving h=16 can be a start

[marsh citrus]

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[normal bough]

.close

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[simple gull]

i need help with d) e) and f)

[simple gull]

I need to say whether they are true or false but dont know where to start

[onyx flume]

first of all it is a parallelogram so the parallel sides are in the same direction and have the same magnitude

@simple gull

[calm harbor]

Do you have any idea how to resolve question a?

[marsh citrus]

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[elder crag]

Hi! Could someone help me understand this?

[elder crag]

what is $$f = \sum_{k=1}^{N} a_k \chi_{R_k}$$

[elfin berry]

woomy

[elder crag]

And i dont understand how this relates to riemann integrals

and what do they mean by "building blocks of integration theory"

ALSO why is f a step function?? how is that a step function

im just so clueless right now...

I understand why the step functions would be important to riemann integrals as that is how you construct them

[elder crag]

but i dont understand how this is a step function, what is (\chi) doing there?

[elfin berry]

woomy

[elder crag]

If someone could explain it I will be extremely grateful!! thanks in advance :)

If i dont respond then feel free to ping me

<@&286206848099549185>

[unique basin]

What is the set E?

I might be able to help with that part but probably the rest is above my paygrade

[elder crag]

its just a set

doesnt have any specific characteristics

like it isnt defined to be anything

just any set

[fringe temple]

what level of mathematics is this?

[elder crag]

I assume measurable though but it isnt specified

[elder crag]

Real anaylisis, measure theory

[unique basin]

Ohh nvm i misread it no i can't help unfortunately

[elder crag]

no problem!

[elder crag]

Im just not sure what this function reppresents and how exactly would it be a step function

[cobalt sedge]

According to the definition of the riemann integrals, you divide the domain into small sections of width dx, and create rectangles with height equal to the value of the function at that point in the domain. So, you have a superposition of multiple such functions that "resemble" the original function f.
Here in this figure you can see we have 3 such functions red, green and blue. Each is scaled with different a_k so it achieves the proper value; and they are each different \chi functions individually.
their superposition gives you orange function which is f
[This is the idea that I get from the description]

[elder crag]

Okay till here i understand

[cobalt sedge]

If you take the difference you can convert the step function into the rectangles as you desire

[elder crag]

So would $$f = \sum_{k=1}^{N} a_k \chi _{R_k}$$ be whats taking this difference?

[elfin berry]

woomy

[cobalt sedge]

you have the various corresponding values of a_k, those values would ensure that you get the function

think of all the lil chi functions as the basis of your function space

so with some linear combination of those, you can recreate your function

[elder crag]

could you maybe draw out an example if you have the time?

[cobalt sedge]

take this for an example

the red and green are individual chi functions that are the basis

and you can compose the hat function if u choose a_k1 = 1 and a_k2 = -1

[elder crag]

whats the hat function?

[cobalt sedge]

now you only chose 2 functions as the basis, so the function space doesnt span over all C_0 functions or anything

[elder crag]

oh nvm i guess that would be the basis

[cobalt sedge]

hat is the difference

[elder crag]

oh ok

[cobalt sedge]

coz it looks like a hat

[elder crag]

AA hahaha

[cobalt sedge]

you might have heard of its cousin, the tent function

its a famous basis for finite elements

[elder crag]

also sorry i vaguely understand what you're saying cause this book is supposed to introduce the topics you are talking about so i havent really reached that point yet

[cobalt sedge]

Oh finite elements is entirely different

[elder crag]

but im guessing when i finish the book it will all become clear

[cobalt sedge]

it wont be in measure theory course

its about numerical methods on differential equations

but functions spaces and basis of function spaces might get covered in your course

[elder crag]

the book is about real analysis in general and the first chapter is measure theory, it then gets to integration theory and hilbert spaces

[cobalt sedge]

Oh, then youd see more of this later on for sure

[elder crag]

Do you think its a problem that im only following a book and not a course/lecture

also sorry i have to go to eat, ttyl!! thanks :)

[cobalt sedge]

npnp

[cobalt sedge]

it depends on the way you study yourself. If you feel like you get stuck and you need help, following a lecture might be beneficial. But since this is not a graduate course, you can find video lectures for the course that you find comfortable. If you want one, I can recommend The Bright Side of Mathematics. They have very nice lecture series on this

[marsh citrus]

@elder crag Has your question been resolved?

[elder crag]

Thanks alot!

ill close this now

.close

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[lavish owl]

how do i solve this?

[glossy flint]

Which number to the 5th power gives you -1?

(unless you want to go in the complex field)

[stoic slate]

You should give more context

[next raft]

should give*

[stoic slate]

[next raft]

isnt sqrt generally the principal root

[stoic slate]

Yes but we don’t know who wrote that, could be him so I would prefer the whole context to be sure.

[slate yarrow]

generally yes afaik \sqrt[n]{x} is about principal root

[lavish owl]

i have to solve that

[stoic slate]

That is not too much of a context, can you provide the whole screenshot with the original question?

[lavish owl]

1.99

Write the numbers in ascending order

[stoic slate]

Ok so then, because it implies order, it implies you want the principal root

[lavish owl]

yeah

in the solution it's written like this

[stoic slate]

Well, do you understand that solution?

[lavish owl]

i dont get how he gets the extra ^5

[stoic slate]

You have two things

They say they are equal and you can see they are equal except in some spots where u see differences

That leans the difference is also equal

[next raft]

they casually tossed out 4 solutions

[stoic slate]

You can start by proving that (-1) = (-1)^5

[lavish owl]

how

[stoic slate]

Do you know what x^5 means?

[lavish owl]

yeah okay i get that part now

[stoic slate]

Ok, then look again to see if u have any other question

[lavish owl]

.ckise

[stoic slate]

Typo

[lavish owl]

.close

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[quick orbit]

how would i perform calculations without any values for these vectors?

i know i want to form triangles to calculate resultant vectors but not sure how to approach the problem with the information given

i suppose i could give arbitrary values given that they have th same speed and the same speed of river flow

but then they would all have the same value after working with the given triangles...

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.close

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[wanton bolt]

How do you graph exponentials w/ transformations?

[wanton bolt]

I kinda don't get it

[marsh citrus]

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[patent vault]

how do I find the value of p if my y coefficient is greater than 1

[patent vault]

in the general form of a parabola

[calm harbor]

What does p represent?

[patent vault]

like in (y-k)^2 = 4p(x-h)

[calm harbor]

p stands for the focus of the parabola

[patent vault]

ah

so how do I find it in an equation with the y coefficient bigger than 1

[calm harbor]

wdym

Like 2(y-k)^2 = 4p(x-h)?

[patent vault]

no like in an equation such as 4y^2 -4y+x=2

I've tried pretty much everything to my knowledge

[calm harbor]

Ah

First of all, move x to the right side

Next, make a square to turn it into the form above

[calm harbor]

Let’s take this for example

[patent vault]

so like
4y^2 - 4y = 2-x

[calm harbor]

Yes

[patent vault]

and completing the square

to get uhh

[calm harbor]

Correct, for an easier move, you can divide both side by 4 in the first place

To make the coefficient of y become 1

[patent vault]

4y^2-4y+4=2-x-4?

then simplify rhs to get -x-2

[calm harbor]

Gimme a sec

[patent vault]

then convert lhs to a perfect square

like 4(y-1)^2=-(x+2)

soo what do I do next

[calm harbor]

Just move 4 to the right

And convert it into 1/4

aka division

[patent vault]

so p = -1/4?

[calm harbor]

Nope, remember the right side is supposed to be 4p

4p = -1/4

Are you there?

[patent vault]

yup

so p = -1/16

?

hello?

[calm harbor]

Correct

My apologies, I wasn’t available

Ping me when you’re back

[patent vault]

ah thanks

@calm harbor

.close

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[calm harbor]

np

[marsh citrus]

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[rancid junco]

But what is the distribution? Is it a scaled (central) chi square now?

[marsh citrus]

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[rancid junco]

<@&286206848099549185>

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[tight spruce]

Did I formatted incorrectly

it said at least one of the ans is wrong

assuming the bottom is incorrect

[late geode]

1st issue:
writing the powers like that is ambiguous / may not be accepted
you'd want stuff like (sin(x))^6 or sin^6(x)
2nd issue:
why division by x?

[sinful thistle]

look at how they've denoted (sin x)^5

your notation is different. use theirs.

[true parcel]

both answers are wrong too

[sinful thistle]

yeah, division by x for some reason

and coefficients are missing

[true parcel]

and the power for the first one is wrong

[sinful thistle]

@tight spruce u there fam

[sinful thistle]

no, it's correct

[true parcel]

nvm yes

it is

i thought it was 5

my bad

[slim turtle]

Why x in denominator, shouldn't it be 6 and 3 respectively?

[marsh citrus]

@tight spruce Has your question been resolved?

[tight spruce]

no

wait brb

[marsh citrus]

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[tight spruce]

I go tit guys!

[sinful thistle]

good job

also *got it

anyway

you accidentally opened a channel

sooooooooooo

@tight spruce

are you
going to close this

or

[marsh citrus]

@tight spruce Has your question been resolved?

[marsh citrus]

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[marsh citrus]

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[void elm]

any suggestions for this proof?

[marsh citrus]

@void elm Has your question been resolved?

[long osprey]

How do you know that B_i is a subset of U_i, which is also something you need to prove for (a)

[void elm]

where am I looking?

[long osprey]

nowhere, you never even said it

[void elm]

I’m a little bit confused by what you mean

hold on, let me see

ahh, I see what you mean for part a) now

but part b) is an unrelated proof

[long osprey]

For (a) you need to show X is a subet of closed B_i such that each is a subset of some U_i

nowhere in your proof to you mention why your B_i are a subset of soem U_i

[void elm]

yes, I see it now

hmm

[long osprey]

(In fact technically the B_i you chose don't satisfy this though there is a relatively easy fix)

[void elm]

ah, well if V_i is in U_i, then W_i is in U_i too, where W_i denotes the open ball around x with half the radius of V_i

then the closed ball with the radius of W_i is contained in U_i, I think

[long osprey]

👍

also btw I wouldn't use i as an index until after you take the finite subcover, and rather use x as the index

[void elm]

sure, that’s a fair point

I will fix that

how is my proof of b)?

[long osprey]

I think you've overcomplicated showing that this epsilon works

[void elm]

ah, did I?

[long osprey]

like every ball in the subcover T lies in some element of the cover U (from definition)

oh wait no

I misread the question

you specifically need balls centred at x

[void elm]

yes, which I did, didn’t I?

[long osprey]

yeah, it's me that was forgetting that condition

[void elm]

ah

[long osprey]

(b) is fine

[void elm]

okay, I shall go and fix my proof of a) whenever my laptop decides to stop freezing up on me

thank you Edward!

.solved

[marsh citrus]

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[long osprey]

aaah epsilon <= ri/2 not just < somewhere in there

[void elm]

oh yes, this was fixed already

I typoed that

[marsh citrus]

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[spare elm]

if the graph of f(x) the same as the graph of g(x)?

[main idol]

Factor the denominator of g

[spare elm]

nah i think it is the same right

because it simplifies to 1/x+5

i shouldve asked, I think they are same, are they?

[main idol]

One is undefined at x=-1

[spare elm]

but how?

they are the same equation

[main idol]

Nope

x/x is also undefined at x=0

But it simplifies to 1

[spare elm]

what am i doing wrong here

[glass silo]

That cancellation only works when x is not -1

[glass silo]

[spare elm]

can u show the work

idk if u can

im just confused

[glass silo]

Well, I mean, what do you think 0/0 works out as?

[spare elm]

undefined

[glass silo]

If x = -1, that’s effectively what you get, is the reasoning

[spare elm]

whats the point of getting x=-1???

it doesnt play into factoring

[spare elm]

like why would u even do this?

[spare elm]

how are you supposed to know this? what does this even mean

[glass silo]

As you agreed, 0/0 is undefined - it’s also worth considering the domains of both f and g

Because you’re not allowed to divide by zero, -1 can’t be in the domain of g

[glass silo]

And while it doesn’t play into the factoring itself, it does for the cancellation

[main idol]

you're learning it now

or your teacher should have taught you

[main idol]

maybe a simpler example like this one

[spare elm]

so why isnt their a discontinuity at x=-1 for f(x)

[main idol]

1/(-1+5) = ?

[spare elm]

but g(x) factored is 1/x+5

[main idol]

you're going in circles

[main idol]

.

[spare elm]

ok so the domains are the same though???

[main idol]

it only cancels if x+1 isn't zero

[main idol]

no. read it again

[main idol]

.

[spare elm]

but im not trying to divide by zero

[main idol]

you are if you're cancelling

[spare elm]

k

.close

[marsh citrus]

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[honest pagoda]

Find an equation of the largest sphere that passes through the point (-1,1,4) and is such that each of the points (x,y,z) inside the sphere satisfies the condition x^2 + y^2 + z^2 < 136 + 2(x+2y+3z)

I think I solved it but I feel the way I did it was too straightforward to be correct:
I multipled out the parentheses in the right hand side and rearranged to rewrite the inequality as:
(x-1)^2 + (y-2)^2+(z-3)^2 < 150.
Then I simply plugged in the coordinate (-1,1,4) into the equation (x-1)^2 + (y-2)^2 + (z-3)^2 = r^2 and got that r^2 = 6.
Therefore I got my answer: (x-1)^2 + (y-2)^2 + (z-3)^2 < 150.
But then what the heck was the point of the 150? I didn't really use the 150 part to get my answer, right?

[long osprey]

(x-1)^2 + (y-2)^2 + (z-3)^2 < 150 isn't the equation of a sphere; a sphere is only the outer shell, e.g. (x-1)^2 + (y-2)^2 + (z-3)^2 = 150 would be a sphere

now while (x-1)^2 + (y-2)^2 + (z-3)^2 = 150 would be a sphere such that (-1,1,4) is inside it, it still wouldn't pass through the point

[marsh citrus]

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[marsh citrus]

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[lavish owl]

why does the solution have e^ln x = e^3

i did

ln x = 3
x = e^3

[honest pagoda]

they’re both correct

[fervent rampart]

they applied the inverse function, e^x, on both sides

[honest pagoda]

your way is probably simpler if anything

yeah they just took both sides to the power of e. and due to logarithmic properties the left hand side simplified to x after step 2

[lavish owl]

that rule doesnt show in my book anywhere so thats why i am confused

[fervent rampart]

e^x and ln(x) are inverse functions, it's a general rule for inverse functions

[lavish owl]

is it something i should remember?

[fervent rampart]

if $f(x)$ is a function and $f^{-1}(x)$ is its inverse function, then [ f(f^{-1}(x)) = f^{-1}(f(x)) = x ] is a general rule worth remembering

[elfin berry]

cloud

[lavish owl]

that made it more confusing to me

[devout mauve]

e^lnx=x is just the definition of lnx

lnx is the number such that when you put e^that number you get x

[lavish owl]

.close

[marsh citrus]

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[marsh citrus]

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[soft beacon]

If a question asks for a limit approaching from the left, but the graph doesn't exist left of the point, is the answer does not exist?

[soft beacon]

🙂

[sand kindle]

the limit doesn't exist if the function doesn't (in any neighbourhood of the limit point)

[soft beacon]

thank u my g

have a good one

[lilac light]

that kinda sounds like a asymptope

[soft beacon]

:/

ima dip

.close

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[open flower]

I am curious what this means as the expressions are not set to 0 , do I have to do anything differently?
I set 6x^5 to M and 1 to N
Solve the partial of M with repect to Y and got and 1 with respect to X and got 0 , does this mean it is exact? that feels wrong

[marsh citrus]

@open flower Has your question been resolved?

[open flower]

<@&286206848099549185>

[vale panther]

they are exact if the derivative of the x component wrt y is equal to the derivative of the y component wrt x

because clairaut and we assume that the function space is continuous

[open flower]

my main confusion is that when we find the derivatives, theyre not an equation, so are they continous? Is it like dM/dy = 0 = output
So the output is always 0 so it is continous?

because they have to be continous to make an exact derivative I believe

[vale panther]

yes

assume the initial function is x+y. it's continuous

and both it's combined second derivatives are 0

so it's exact

[open flower]

ok one final quesrtion

for a , d, and e are all the partial derivatives 0 ?

[vale panther]

if they are constants, yes

[open flower]

they are all constant wrt the variable we are differentiating by

so I guess so

[marsh citrus]

@open flower Has your question been resolved?

[marsh citrus]

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[jade hamlet]

i hit a ball from 30 yards into the goal,it got in the goal in 2 seconds,how fast was the balls speed going at in mph?

[worldly spire]

it travel 30 yards in 2 sec, so thats 15 yards a sec.

then convert 15 yards to miles

[cobalt sentinel]

was the ball going perfectly horizontal, or no?

[jade hamlet]

it was going straight

[marsh citrus]

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[wooden lava]

how would I solve for the domain of 2 quadratic functions that have f(g(x))?

[wooden lava]

so like if I have x^2+1 and 2x^2+2

how would i find it's domain?

[uncut oasis]

I assume you're asking about the domain of the function resulting from composing f and g?

[marsh citrus]

@wooden lava Has your question been resolved?

[marsh citrus]

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[desert gyro]

how am i supposed to simplify this... is this not the most simplified form?

[proper bolt]

whats the rest of the question

[desert gyro]

thats it. the original form was 5xy^7 * xy^9

[naive fox]

like, we need the original problem to help you figure out.

[desert gyro]

the original problem

[cloud field]

this is not simplified

[cloud field]

but this is

[desert gyro]

i am aware? i know....

[desert gyro]

i put this in for the answer and its saying that its not simplified

[naive fox]

simplify $5{x^{y^{7}}} xy^9$ is original problem?

[elfin berry]

everyone

[desert gyro]

um like that but its not x raised to y

sorry

i mistyped

[naive fox]

ok, it is $5xy^7xy^9$

[elfin berry]

everyone

[desert gyro]

yes

[naive fox]

so your original problem is to simplify that? or that is intermediate step? because what you have should be it

[desert gyro]

yes that is why i am asking

i was wondering if i was just msising something

but its saying it can be more simplified and im quite sure it cant

[naive fox]

just talk to your teacher

[cloud field]

unless

you can factor that power of 2 out

[naive fox]

yeah, you can do that

[desert gyro]

but that would leave a rly dumb number for the 5 right? square root 5 (xy^8) ?

[naive fox]

why would you have square root?

you can just factor one that can be factored

[desert gyro]

oh ok got it let me try something else

.close

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[tulip bridge]

i need help with this

is there a mathematical way to solve it? i dont know

it says estimate

so thats what i did

nvm

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[small agate]

how to solve ii)

[glass silo]

If you found the area of the whole triangle, you could consider that "another" way to find the area of a triangle is (1/2) * base * height...

[small agate]

huh

i need to find length for BD

[little granite]

how does BD being perpendicular to AC relate to its length 😭

only thing that does is make angle abd = 90 degree nah so you can use sine law if theres another side length but there aint?

good luck bro

[small agate]

.

im cooked bro

but thanksss

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[bright sundial]

is this true i dont want to get it wrong and restart

[meager badger]

round the 9.9

cause from the table

you see that as x approaches 3

it gets soooo clsoe to 10 right

If we do lke 3.00001 its prob gonna be 9.99999

or smt like that

[bright sundial]

tysm

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[whole sleet]

You're basically picking the closest answer to 9.99.

Note that 10 is closer than 9.9

[marsh citrus]

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[humble river]

is this in need of another equation

cuz there is 2 unknown it seem

Ik i shud put context

one second sry

.close

[marsh citrus]

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[marsh citrus]

@exotic apex Has your question been resolved?

[slate yarrow]

<@&268886789983436800>

[zenith escarp]

Nah what

[winter tendon]

Someone’s angy

[zenith escarp]

Bro is tripping

Bro gotta cope with failing a math test somehow I guess

[static quarry]

calls us racists

[buoyant geyser]

You are a highschooler

[open palm]

Jesus

[buoyant geyser]

Math can be frustrating sometimes

[open palm]

Yeah brings out the worst of us that's true

[zenith escarp]

Oh he got banned I think

[knotty shard]

How did blud accuse us of racism and then follow up with a slur

[slate yarrow]

sure,doesnt mean that someone lashes out

[buoyant geyser]

Lol

[open palm]

Hahaha ironic

[slate yarrow]

yes