help-0

[jagged cobalt]

i cant really visualise what it is youre writing, but i dont think so

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

[ocean seal]

AℤØ

[tepid prism]

correct

[jagged cobalt]

then just do your derivatives with the chain rule, second derivative will need the product rule also

[tepid prism]

tried

but the answer is wrong

[jagged cobalt]

did you try expressing things in terms of u at the end maybe

yeah that should work

[tepid prism]

I got it

it worked

[jagged cobalt]

nice

[silk herald]

Hi , i need help with this its to work out the gradient and the y-intercept .

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[alpine sable]

Some help please

[alpine sable]

F derivable implies that f’(l) left and right are equal should find the f’(l)

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

<@&286206848099549185>

[alpine sable]

<@&286206848099549185>?

[alpine sable]

Yes

f and f’ should both be equal for both sides at x=2

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

I know how can I find a and b ?

Take the derivative from both sides

Then they are equal

You can sovle for a with that equation

Then use that value to solve for b with the equation that f has to be equal for both sides

[alpine sable]

I will do a system or what ?

And I will replace x by 2 right ?

What equation do you get for the f’ equal from both sides

[alpine sable]

Yes

[alpine sable]

what if I get the dénominateur equal zero ?

What denominator?

You will get $6ax^2=4x$ for x=2

[ocean seal]

Ryanstaal2006

[alpine sable]

Wait wait lemme try it

I thought I should use f(x)-f(2)\x-2

Do you know how to differentiate something like ax^n?

[alpine sable]

do u speak French ? Since I don’t study maths in English it’s quiet hard to understand

[alpine sable]

Yeah

[alpine sable]

Sorry I dont speak french

$f(x)=2x^2+b$ gives $f’(x)=4x$

[ocean seal]

Ryanstaal2006

[alpine sable]

And $f(x)=2ax^3+11a$ gives $f’(x)=6ax^2$

[ocean seal]

Ryanstaal2006

[alpine sable]

oh I see

$6ax^2=4x$ for $x=2$

[ocean seal]

Ryanstaal2006

[alpine sable]

I can’t use the limits here ?

I’m not sure

But this is just basic derivatives

Cuz we have that the second function is defined in ]2,+ linfine [

[alpine sable]

Well I can’t do the basic derivation until I find DF’

[alpine sable]

Did you understand how to get here?

[alpine sable]

Yes ofc

What value of a you find?

[alpine sable]

But I think I can’t do it in that way

Oh why not?

But I got 1/3

[alpine sable]

so I have to show that f(x) is derivable in 2 before using f’(x)

To show that I have to use the limit

The definition of derivation

Idk if u get it

[alpine sable]

Doesnt this imply differentiability?

Basically this

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[deep kiln]

help

[deep kiln]

How can i show that fn is infinitly differentiable

[lean forge]

have you tried induction ?

[deep kiln]

I understand that root x^2 is |x| which is infinitly differentiable just not in x=0

[deep kiln]

Yes but my brain hurts and it makes not really sense i can show tho

[lean forge]

sure

[deep kiln]

theres no simple formula for the derivatives

First 4 derivatives but i cant see any formulas

[lean forge]

hmm

idk

[lone heart]

@deep kiln Has your question been resolved?

[deep kiln]

<@&286206848099549185>

Ill play 5€ for someone who solves this with induction which is simple. No other way

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[deep kiln]

<@&286206848099549185>

[kind sparrow]

I don't really want to think about this very carefully, but I thought that the composition of differentiable functions is itself differentiable, so the only problem really is if you define something like g(x) = sqrt(x) in a neighborhood of zero. That just sidesteps the entire induction part doesn't it? I guess the purpose of the exercise is to show that a sequence of smooth functions can converge to something that is not smooth?

[deep kiln]

I dont need to show that compositions of differentiable functions are differentiable. Its already known. But how do you shot that fn(x) itself is infinitly differentiable all over |R ?. Like if you took the 1/n part out it would be f(x)=sqr(x^2):=|x| which is infinitly differentiable all over |R except 0 (so |R\0) but thats the problem right, which doesnt effect the fn(x) since 0 is not an element from {x^2+1/n | x€|R, n€|N} so it should be differentiable even if x=0, and it should be infinitly differentiable since its a function of degree 1 since n is one set number

[kind sparrow]

I didn't say you needed to show that. You're also not taking out the 1/n part.

In the limit 1/n goes to zero but for any fixed n, that term pushes the problem away from the problem point

So fiddle around with something like f(x) = sqrt(x + 1/n) and g(x) = x^2, or something and hope it works and if it doesn't examine why it didn't work and adjust your f and g accordingly until it does

I assume that's the whole point, you have a sequence of smooth functions that converge to, I assume uniformly, to a function which is not differentiable. If you had to worry about f(x) = |x| too you're not going to get anywhere because that's not differentiable at 0.

[deep kiln]

yeah but i dont need to look at the limit

Thats why 1/n will never reach 0

[kind sparrow]

I think we are just agreeing with each other

[deep kiln]

Yeah

[kind sparrow]

I think that is the right strategy, but either way I think finding the nth derivative or using induction in this particular way from the above conversation is not a good idea

[deep kiln]

the chosen f(x) and g(x) arent good for this tho

u(x)=sqr x and vn(x)=x^2+1/n is more suitable since you can differentiate easier

This is the plot which shows fn for lim n->oo it converges to f |x| but since were not looking for f just fn the "edge" doesnt exist just when you go to lim

but how can proof that its infinitly differentiable then

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[tight geyser]

hi

[tight geyser]

Can someone help me wit this question

[alpine sable]

/

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[quaint loom]

I need to do part a. "Write parametric equations for the ellipses." How would I figure out the equation of the circle? After I do that, Do i just have to change it back to

x = ? + ? cos t
y = ? + ? sin t

format?

[tardy stag]

an ellipse is just a circle that's been stretched or squished

so yes that idea of yours should work

[quaint loom]

ok

how do i resolve this

[tardy stag]

what i would do is get a graphing calculator and try values

and see what happens

what happens what you make them bigger? smaller?

[quaint loom]

k

tnx

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[alpine valve]

i'm not rly sure how to work this out

[alpine valve]

theres cusps at x=0,2

[lone heart]

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[alpine valve]

<@&286206848099549185>

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[unkempt compass]

trying to solve by completing the square. dunno where ive gone wrong but it looks like its not going to solve into the answer key. can anyone point something out to me?

[lone heart]

@unkempt compass Has your question been resolved?

[unkempt compass]

<@&286206848099549185>

[barren rapids]

so the original question is 7ksquared -16k +100 = 0 and you want to change it to the a(x-h)^2 + b = 0 form?

[unkempt compass]

yeah that was the idea, but then also just take have the squared difference on one side and solve for k

i kind of gave up after looking at this problem for a long time and idk where i went wrong. on the bottom just looking at it if i squared the -649/50 it didnt look like it'd be anywhere near the answer in the answer key

not squared but square rooted

and then add the 8/7

to isolate for k

[arctic lintel]

yeah i have a feeling that you shouldn't have coverted all that to 90.86

[unkempt compass]

ahhhh

maybe, that sounds like it could be right

but....everything else checks out if that were the case? just i used a calculator instead of keeping things in fractions?

[stark crater]

I think you had to get 32/7 rather than 16/14

When doing the completing the square part

[unkempt compass]

think or is it 100% sure thats it? i thought i had to take half of b and square it which would be 16/7 * 1/2 squared

[stark crater]

Yeah thats 32/7

[arctic lintel]

nah i have a feeling it should be 8/7

[stark crater]

Squared

16/7*1/2=32/7

Im not being an idiot am I

[unkempt compass]

that doesnt look right to me

[stark crater]

Yeah u right I am just dumb

[unkempt compass]

and 8/7 is 16/14 just not reduced yet

[arctic lintel]

yeah but much simpler to work with rather than 16/14

as 8^2/7^2 is much easier to figure out

aight so personally how i would solve this is take 100 to the other side

and get 7k^2-16k=-100

then divide by 7

and try to complete the square

[unkempt compass]

i was working on the not using a calculator part and does a number that comes up to 636/49 come up?

[arctic lintel]

yeah

[unkempt compass]

okay i feel like the calculator part really tripped me up

[arctic lintel]

hold up, are u working with complex numbers?

[unkempt compass]

it worked out

yeah complex numbers

[arctic lintel]

aight ur fine then

[unkempt compass]

2i something something

tyty

[arctic lintel]

all g

[unkempt compass]

.close

[lone heart]

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[glad aspen]

This seems logical to me, but I just want to make sure this is allowed. If im given lets say x/y could be between [0, 1] is it legal to say x could be between [0, y]?

[vale wigeon]

sounds sus as written

!original

[lone heart]

Please show the original problem, exactly as it was stated to you. A picture or screenshot is best.

If the original problem is not in English, then post it anyway! The additional context might still help helpers help you. Do your best to translate.

[glad aspen]

im doing a physics problem and this is quite far into the logic rabbithole

so the original problem dosen't really exist in this case

lemme look refresh my latex and see if I can show my thinking in a neater way

So after doing some problem solving I got to this

,, arcsin(\frac{2gD}{V^2}) = \alpha

[ocean seal]

Night

[glad aspen]

and im trying to get as much information out of what alpha could possibly be

arcsin has a domain of [-1, 1] right?

from the question itself we know g is negative, D is positive, and V is positive

so the only possible options are [-1,0]

so would it be allowed to say that for alpha to be a valid angle, 2gD would need to be between [-V^2, 0]?

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@glad aspen Has your question been resolved?

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@glad aspen Has your question been resolved?

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[uneven wedge]

What can x^2 congruent with 1 (modulo 8) be rewritten as with x?

[golden canyon]

You mean that x^2 == 1 (mod 8) would imply x == 1 mod 8?

In that case: no 7^2 == 1 mod 8

[uneven wedge]

No I’m asking what it Would imply I guess

[upbeat hornet]

notice that x cannot be even

then you can test all 4 cases to see if they work

[golden canyon]

It would be the easiest to check all cases, yeah

Other way would be difference of squares

[uneven wedge]

I’m trying to understand how to solve dipphantine equations

Like this

[upbeat hornet]

does (7) mean mod 7

[uneven wedge]

Yes

[upbeat hornet]

you can complete the square

and then solve the first equation

and then you know x mod 7

and you can find x and a mod 91

[golden canyon]

*Remember that 7 being prime means that this works like you are used to

[uneven wedge]

You mean solving for x?

[golden canyon]

ab = 0 implies a or b = 0

Only works mod primes

[upbeat hornet]

oh you don’t even need to complete the square

you can just factor it

[lone heart]

@uneven wedge Has your question been resolved?

[lone heart]

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[primal lance]

how do i calculate the derivative of 1/x??

[primal lance]

providing my steps wait...

[jagged cobalt]

you gonna post your steps or...

[primal lance]

here

readable?

[jagged cobalt]

oh, youre doing it like that, okay

its fine i guess until the last line

[primal lance]

ok

[jagged cobalt]

the h and the 1/h cancel

[primal lance]

what did i do wrong?

lemme see

[jagged cobalt]

so youre left with -1/(x^2+hx)

[primal lance]

wait

Oooooooohhhhhhhhhhhhhhhhhhhhhhh

i am stoopid

i got the answer:

-1/x^2

is it correct?

[jagged cobalt]

uh huh

[primal lance]

?

[jagged cobalt]

yes

[primal lance]

Oh nice

thx

.close

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[gray isle]

!status

[lone heart]

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

[rich vine]

1

[storm musk]

Expand the form

Compare the variables

Solve the system of equations

[rich vine]

ill try

[gray isle]

don't do that

[rich vine]

alright

[storm musk]

oh ok

[gray isle]

i mean you can solve it that way, but not ideal

have you done completing the square before?

[storm musk]

Oh I thought it was illegal to do it here

[rich vine]

no

[storm musk]

How about you expand the form instead

[gray isle]

what were questions 1-4

[rich vine]

standard simplifying and expanding

[storm musk]

So you should be able to expand the formula with the variables

[gray isle]

i suppose you could go the expansion route then

[rich vine]

hmm so have it go to 3(t^2-30t)+70?

[storm musk]

no

wait

yeah but you have to take the 3 out of 30t too

[rich vine]

so that becomes 3(t^2-10t)+70?

[storm musk]

3 and yes

Now you can complete the square, that is if you know how to

[rich vine]

no need explanation

[storm musk]

Alright, good luck

[rich vine]

i need explanation i mean

not great at words lol

[storm musk]

Oh, what language do you speak well

[rich vine]

english im just terrible at typing lol

[storm musk]

oh

So, can you expand (t-x)^2

[rich vine]

to t^2-tx-xt+x^2?

[storm musk]

We normally do -2xt

[rich vine]

forgot the vaiables where the same lol

[storm musk]

2xt = 10t

2x = 10

Solve for x

[rich vine]

5?

[storm musk]

Yeah

Now what is x^2

[rich vine]

25

[storm musk]

Yeah, so you do +25-25 into the brackets

[rich vine]

like that?

forgot to write as25

gimme a sec

[storm musk]

25

[rich vine]

that?

[storm musk]

Yes

No

Put the +25 in front

[rich vine]

done it

[storm musk]

It might look like it doesn't matter, but it does. kinda

Also, t^2

[rich vine]

fixed

[storm musk]

So now, do you see the $t^2-10t+25$ part?

[ocean seal]

RomeNunt

[rich vine]

yes

[storm musk]

Now you can make that into a perfect square

[rich vine]

what

[storm musk]

The $t^2-10t+25$ part

[ocean seal]

RomeNunt

[rich vine]

yeah i see it in the equation

[storm musk]

It becomes a $(t-x)^2$ part

[ocean seal]

RomeNunt

[storm musk]

What was x earlier?

[rich vine]

5

[storm musk]

So

[storm musk]

It's not done yet

You still haven't accounted for that -25 you added earlier

[rich vine]

what do i do with it?

[storm musk]

You multiply it with 3, the number in front and add it to 70

[rich vine]

now i got no A lol

[storm musk]

No, you don't lose the 3

The three is still there

[rich vine]

alright

[storm musk]

You're just multiplying the -25 to the 3 to move it(-25) out of the parenthesis

[rich vine]

ok

thats done?

[storm musk]

Yes

So now, just put the a b and c

You should be good

[rich vine]

alright

yeah all good thanks

.close

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[chilly stag]

For this problem:
A colony of bacteria doubles in size every hour. If the colony initially contains 500 bacteria. Give the explicit formula for the sequence representing the bacteria population at each hour.

I am having trouble whether to start with P(0) = 500, with explicit formula P(n) = 500 * 2^n or if it should be P(1) = 500 with the explicit formula P(n) = 500 * 2^(n-1). Should I go with the first one? Thank you!!

[arctic lintel]

it says initially, which means its when time = 0

500t

wait im dumb

500*2^t

[chilly stag]

I was talking about this with other students, some of them did P(n) = 500 * 2^(n-1), so we reached different answers.

[arctic lintel]

why n-1?

that would be saying after one hour the bacteria would still be at 500

[chilly stag]

I think they got confused since the only examples given to us where for geometric and arithmetic sequences, both having "n-1" in them.

[chilly stag]

Yes, and if that actually happened where did those 500 bacteria came from?

[arctic lintel]

i dont think its that deep, at hour 0 the bacteria was at 500 is what the question is saying

[chilly stag]

Anyways, I really just need some assurance. I was about to get swayed by their side lol. Thanks!

[arctic lintel]

all g

[chilly stag]

.close

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[supple tree]

sqrt(25-5^x) >= 0

25-5^x >=0

idk why x becomes x <= x and not x>=2

[zealous lichen]

when you multiply/divide negative number you switch the inequality

for example, 1 < 2 but -1 > -2

[supple tree]

oh wait mb im trippign

thanks

.close

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[oblique plover]

this is rlly simple lol it’s just the last question on my homework but i can’t do it

[zealous lichen]

!status

[lone heart]

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

[oblique plover]

3

tried to answer it about 10 times. now i think im rounding it incorrectly

[gray isle]

show work

[oblique plover]

wait nvm

sorry

i got it

.close

[lone heart]

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Use .reopen if this was a mistake.

[manic briar]

can any1 help

[upbeat gorge]

!status

[lone heart]

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

[manic briar]

3

[upbeat gorge]

Show your work

[manic briar]

ok

[manic briar]

here

[lone heart]

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[primal lance]

How do i find the derivative of sin(x). Here's my current work

[upbeat gorge]

Factoring and splitting stuff up

[primal lance]

no like am i going on the right direction?

[upbeat gorge]

Yes

Oh wait actually

[primal lance]

so will the cos(h) and sin(h) wil cancel out?

yea?

[upbeat gorge]

Please notate lim before every line since you haven’t evaluated the limit yet

[primal lance]

oh right

i forgot

[upbeat gorge]

what do you mean by this

[manic briar]

what about the question up

[upbeat gorge]

open another channel, I didn’t notice you posted in a channel that was closing

[upbeat gorge]

Oh ofc not

[primal lance]

💀 .

what do i do now??????

[upbeat gorge]

^

[primal lance]

oh

[upbeat gorge]

There are two special trig limits you need to know to evaluate this fwiw

[primal lance]

what are those?

[ocean seal]

CST (please ping when replying)

[upbeat gorge]

and $\lim_{x\rightarrow0}\frac{1-\cos x}{x}$

[ocean seal]

CST (please ping when replying)

[primal lance]

ok....

[ocean seal]

CosmicDev

CosmicDev

[upbeat gorge]

sinx /x first

Do you know what that is?

[primal lance]

nah

=1?

[upbeat gorge]

It is 1

[primal lance]

nice

[upbeat gorge]

You can now use this limit to solve the other one

[primal lance]

right

0?

ok so now

[ocean seal]

CosmicDev

[primal lance]

@upbeat gorge ?

[slim nova]

Can anyone help me with 2x + 4y, -5y

[primal lance]

?

[primal lance]

this channel is taken

[primal lance]

https://discord.com/channels/268882317391429632/903463351789694986

<@&286206848099549185>

[upbeat gorge]

Ok hold on

Yeah this is why I told you that you need to break stuff up

You can’t just willy-nilly things

[upbeat gorge]

Any terms on the top that share a common factor?

[primal lance]

sin?

[primal lance]

sin?

[lone heart]

@primal lance Has your question been resolved?

[upbeat gorge]

Yep

So can you factor out sin(x) from those two terms?

[primal lance]

i'll try

[primal lance]

3 terms

right?

[upbeat gorge]

no

sin(x) and sin(h) are different

[primal lance]

oh understood

$\lim_{h\rightarrow0}\frac{sin(x)(cos(h)-1) + cos(x)sin(h)}{h}$

[ocean seal]

CosmicDev

[upbeat gorge]

Yes

Now split them into two limits

[primal lance]

alr

$\lim_{h\rightarrow0}\frac{sin(x)(cos(h)-1){h} + lim_{h\rightarrow0}\frac{cos(x)sin(h)}{h}$

[ocean seal]

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

[primal lance]

wha

$\lim {h\rightarrow0}\frac{sin(x)(cos(h)-1){h} + lim {h\rightarrow0}\frac{cos(x)sin(h)}{h}$

[ocean seal]

CosmicDev

$\lim {h\rightarrow0}\frac{sin(x)(cos(h)-1){h} + lim {h\rightarrow0}\frac{cos(x)sin(h)}{h}$
```Compilation error:```! File ended while scanning use of \frac .
<inserted text> 
                \par 
<*> 950998776540188692.tex
                          
I suspect you have forgotten a `}', causing me
to read past where you wanted me to stop.
I'll try to recover; but if the error is serious,
you'd better type `E' or `X' now and fix your file.```

[primal lance]

$\lim {h\rightarrow0}\frac{sin(x)(cos(h)-1){h}} + lim {h\rightarrow0}\frac{cos(x)sin(h)}{h}$

right

$\lim_{h\rightarrow0}\frac{sin(x)(cos(h)-1)}h + lim_{h\rightarrow0}\frac{cos(x)sin(h)}{h}$

[ocean seal]

CosmicDev

[upbeat gorge]

eh whatever i get your point

yes this is correct

[primal lance]

i can understand

[upbeat gorge]

Now it’s evaluation time

[primal lance]

yea

let's follow this

[ocean seal]

CST (please ping when replying)

[primal lance]

...

oh

[upbeat gorge]

left one first

[primal lance]

ya

[upbeat gorge]

Actually if it helps you, you can factor out sin(x) and cos(x) from their respective terms

since they don’t have h anyway

That should make it really obvious now

[primal lance]

yea...

?

[primal lance]

like this?

[upbeat gorge]

Yes

[primal lance]

alr

so

${\sin(x)}*\lim{h\rightarrow0}\frac{\sin(x)(\cos(h)-1)}{h} + \cos(x)*\lim{h\rightarrow0}\frac{\cos(x)\sin(h)}{h}$

wth

[ocean seal]

CosmicDev

[primal lance]

nahh

[upbeat gorge]

When you factor stuff out, you can’t leave it in the fraction lol

[primal lance]

$\sin(x)*\lim{h\rightarrow0}\frac{(\cos(h)-1)}{h} + \cos(x)*\lim{h\rightarrow0}\frac{\sin(h)}{h}$

[ocean seal]

CosmicDev

[primal lance]

YES

also wrong(the limits)

but np

[upbeat gorge]

Ok

Now you should know these two limits by now

[primal lance]

yea

lemme try

[upbeat gorge]

Yes

Oh wait

No

[primal lance]

alr

[upbeat gorge]

.

[primal lance]

oh

b-but

[upbeat gorge]

Not how derivatives work

[primal lance]

right again

right

[upbeat gorge]

But I see you got cos(x) as your answer

[upbeat gorge]

What happens to the thing on the left?

[primal lance]

doing...

correct?

[upbeat gorge]

That limit is 0, but that’s not how it’s derived lol

[primal lance]

then?

[upbeat gorge]

Well you literally have one thing left

[primal lance]

right

and?

[primal lance]

.close

[lone heart]

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[spark moss]

How do i convert f(n) = 36f(n-2) into non recursive form?

[spark moss]

Base values are f(1) = 60, f(2) = 504

[rigid sail]

So, you might want to consider odd and even numbers seperately.

[spark moss]

So will non recursive be piecewise function?

[rigid sail]

Yeah, this needs to be defined piecewise

[spark moss]

This is the series btw

[rigid sail]

Looks good. I think the pattern might become more apparent if you don't evaluate the products.

[spark moss]

Soo its like
f(n) = 60 * 36^(n-1) for n odd
f(n) 504 * 36^(n-1) for n even

[rigid sail]

Well you get the idea, but try checking some inputs to see if it matches what you have.

[spark moss]

Ok thanks

.close

[lone heart]

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[limpid terrace]

can anyone help me find this knowing that a>0 and b>0

[golden canyon]

Do you know about AM-GM?

[limpid terrace]

i don't think so but i could because maybe in French it's called something

else

what is it?

[golden canyon]

(x + y)/2 >= sqrt(xy)

[limpid terrace]

Oh

no then

[golden canyon]

Do you have any idea on how to prove this?

(this is the second part of the inequality btw)

and it only holds for x, y >= 0

[limpid terrace]

I'd probably prove that through the (a+b) ^2>0

Btw

[golden canyon]

Yes that's the right direction

[limpid terrace]

I've kind of done that

but i got stuck here

1 sec

[golden canyon]

= 0 actually

If we want to prove it for x, y >= 0

[limpid terrace]

the square root is the problem

it should be a 2

[golden canyon]

What about (a - b)^2?

[limpid terrace]

(a-b) ^2>=0?

[golden canyon]

Yeah, t^2 >= 0 in general

[limpid terrace]

Oh yeah

True

Missed that

That'd give us a^2 +b^2>=2ab

[golden canyon]

Yeah (a^2 + b^2)/2 >= ab

but let x = a^2 and y = b^2

what would it become then?

[limpid terrace]

x+y/2=sqrt(xy)?

[golden canyon]

Yeah, brackets and >= though

so (x + y)/2 >= sqrt(xy)

which is what we wanted!

[limpid terrace]

Yeah

does replacing those a and b with x and y make it a general case?

[golden canyon]

What if we plug in x = 1/a and y = 1/b?

[golden canyon]

Yeah, because we can use it for the first part too

[limpid terrace]

(1/a+1/b)/2>=sqrt(xy)

?

[golden canyon]

Yes, and sqrt(xy) becomes?

[limpid terrace]

Oh yesss

sqrt(1/ab)

then we make the inverse or whatever its called

which changes the sign

nice!

thanks so much for the help

[golden canyon]

Yup, because sqrt(1/ab) = 1/sqrt(ab)

[lone heart]

@limpid terrace Has your question been resolved?

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[gray heart]

.close

[lone heart]

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[weary abyss]

Can someone help me integrate by parts

[glacial patrol]

U don't need parts

[weary abyss]

i wrote the wrong thing

let me fix this

[glacial patrol]

let u = 2x + 1 and dv = cos(3x),

U got this I believe in u

[weary abyss]

what should be my v

antiderivative of dv?

[glacial patrol]

yeah

[weary abyss]

how do i do that in my head

sin3x/3 + C

thats what the calculator says

[lone heart]

@weary abyss Has your question been resolved?

[weary abyss]

i have my variables what should i do next

<@&286206848099549185>

[glacial patrol]

uh

Show work ig?

[lone heart]

@weary abyss Has your question been resolved?

[lone heart]

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[lone heart]

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[polar spire]

boolean algebra problem:

[polar spire]

Does there exist such expression "I" which is dependable only on variables "p" and "q" so that
(p ⇒ (I ∧ q)) ⇔ ((p ∨ q) ⇒ I) is contradiction?

How do I approach this problem? What is the key idea? I tried using the truth table so far, but don't really understand what I should look for. Perhaps treat the "I" as a variable?

[lone heart]

@polar spire Has your question been resolved?

[polar spire]

<@&286206848099549185>

[jovial ridge]

Yes?

I can't really do that.

[prime badge]

i don't understand what it's asking

[polar spire]

so an expression I can plug in that consist of some combination of "p" and "q" that then evaluates to tautolgy or contradiction (apparently there is no solution for contradition)?

[prime badge]

it should be impossible, yeah

if p false and q false, the expression is true

so it's never a contradiction

i don't need to consider any l at all

but i don't understand what makes ⇒ and → different maybe i'm missing something

[lone heart]

@polar spire Has your question been resolved?

[alpine sable]

Hurt

!claim

!occupied

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[lone heart]

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[remote kernel]

'

[alpine sable]

Claim

!occupied

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[woven ledge]

move each point one by one

[remote kernel]

i did it \

[lone heart]

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[mystic nebula]

why is it

how do i graph this

[gaunt crane]

basically, you should graph it, intersecting X-axis in -1, 2.5 and 5, starting from negative y

[mystic nebula]

whats multiplicity

like odd multiplicity

what does that mean

[gaunt crane]

it'll look like this

[gaunt crane]

one moment

[mystic nebula]

like the way that it curves

[gaunt crane]

oh, that's basically number of roots

[mystic nebula]

i understand the end goals

[gaunt crane]

no, but like the way it "starts", and where "finishes"

[mystic nebula]

yea i understand that it starts negative and increases in x as y increases

but how do i decide what the valleys are

im just in general confused

[gaunt crane]

wait, valleys? wdym?

[mystic nebula]

okay so i have a positive cubic function

and the intercepts -1, -2.5, and 5

[gaunt crane]

+2.5

[mystic nebula]

yes right

so it rises all the way to the y value which is 25

fuck i cant explain this over text

[gaunt crane]

you mean, why it goes downwards after about y=25?

[mystic nebula]

yea

that

[gaunt crane]

ohhh

[lone heart]

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[tawdry ibex]

hi broskis simple math question here

[tawdry ibex]

i dont understand why its 2^8

[lone heart]

@tawdry ibex Has your question been resolved?

[tawdry ibex]

and why is this displaying the method wrong but the result right

how is 101011 43 and 171 at the same time

[lone heart]

@tawdry ibex Has your question been resolved?

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[ebon hornet]

q14e

[ebon hornet]

have no idea where to start

[keen mason]

for

which

part

[ebon hornet]

e

[keen mason]

u know these?

[ebon hornet]

yep

[keen mason]

lets use these to our advantawe

reform as much as the left as you can using these equations

[ebon hornet]

so ive got (1 + 2sinacosa)/(2cos^2(a))

but idek if its the right cos substitution

[ebon hornet]

holy crap mate

thats amazing

thanks

.cose

.close

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[fringe pike]

Can someone help me? 🥹

[fringe pike]

I don't know what the question "Write the coordinates of the endpoints of a line segnment that intersects the y-axis and the write the coordinates of the endpoints of a line segment that is not parallel to either acis, and does not intersect either axis" means

[lone heart]

@fringe pike Has your question been resolved?

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@fringe pike Has your question been resolved?

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@fringe pike Has your question been resolved?

[lone heart]

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[radiant karma]

Can someone explain

[lone heart]

@radiant karma Has your question been resolved?

[radiant karma]

.close

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[modern wyvern]

im unsure what thsi question is asking me to do?

[stark crater]

Replace the entire u-7 with g(u), then for g(x) write the appropriate function (it should have x in it)

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@modern wyvern Has your question been resolved?

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[coral cedar]

can somebody help me with 7c?

[alpine sable]

what's your confusion? which question?

[coral cedar]

7c

[alpine sable]

alright

whats confusing you

[coral cedar]

i dont get what to do

like do i minus 24

or divided 2

[alpine sable]

the general principle is this

you want all the variables on the left side of the equation

and you want all the numbers on the right

[coral cedar]

yea

[alpine sable]

you have 6x on the left and 2x on the right

so you want to get rid of the 2x

make sense so far right?

[coral cedar]

yea

[alpine sable]

okay question is how do you get rid of the 2x

well answer this

[coral cedar]

divide 2?

[alpine sable]

2x + ____ = 0

answer this

what term should should we put in the blanks

basically

[coral cedar]

not sure

[alpine sable]

do you know about like terms

[coral cedar]

yea

[alpine sable]

yeah right

so 2x +3x =5x

you add up the coefficients yes?

[coral cedar]

yes

[alpine sable]

okay let's remove the x

2+ ___ = 0

can you answer this

[coral cedar]

-2

[alpine sable]

yes!

put back the x

what do you have

[coral cedar]

-2x

[alpine sable]

yes

2x-2x = 0

this is making sense I hope so far?

[coral cedar]

yes

[alpine sable]

okay

so back to our original question

8x = 2x +24

[coral cedar]

yes

[alpine sable]

you know now that if you add -2x to 2x you get 0

[coral cedar]

mhm

[alpine sable]

so it gets rid of it

can you connect the dots

[coral cedar]

o

so it turned into 8x+24

=

[alpine sable]

no

think again

[coral cedar]

6x=24 mb

[alpine sable]

yes!

now you want to isolate the x

do you know how to

[coral cedar]

yes

x=4

[alpine sable]

wooOo

good jov

[coral cedar]

cheers

im doing exams soon and i forgot what i did in term 1

i strate this stuff like a year ago and forgot

thanks a lot

.close

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[scenic hedge]

Please help me solve this

[scenic hedge]

please help me solve this

#help-0

.close

[lone heart]

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[quiet cosmos]

.open

what are the commands if i am in need of help some one

[quiet cosmos]

i need help with exponancial sequnces with indices included in the mixture please

[lone heart]

@quiet cosmos Has your question been resolved?

[lone heart]

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[alpine sable]

What is the maximum value of Q in 5P9 + 3R7 + 2Q8 = 1114?

[alpine sable]

.close

[lone heart]

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sterile beacon]

explain the equation

[lone heart]

@sterile beacon Has your question been resolved?

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Available help channel!

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tall crag]

hi can someone please help me with a year 10 level physics question

[lone heart]

@tall crag Has your question been resolved?

[tall crag]

,close

.close

[lone heart]

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Available help channel!

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[misty moat]

is this correct?

[lone heart]

Please don't occupy multiple help channels.

[misty moat]

are they all concave up

[cold cargo]

if a function f(x) is concave up/down at x, what do you know about f''(x)?

[misty moat]

what?

[cold cargo]

do you know what the concavity of a function is?

[misty moat]

yes

[cold cargo]

So for example f(x) = x^3, do you know what the concavity is at different points?

[misty moat]

bro

that isnt the question

[misty moat]

.

[cold cargo]

#❓how-to-get-help

[misty moat]

?

answer the question

[alpine sable]

no one is going to answer it for you

[misty moat]

i already answered it r u good?

im asking whether its correct

[misty moat]

go away if youre not gonna help

[exotic canopy]

looks correct to me

[misty moat]

.close

[lone heart]

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Available help channel!

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[ionic sedge]

How to apply chain rule to cos(2pi - a) when differentiating

[echo socket]

First come up with a pair of function whose composition is cos(2pi - a) and whose derivatives you are familiar with

[ionic sedge]

oh yeah, sorry i have not done any math in like 3 to 4 months and now suddenly have to do calculus, so i am a bit out of the loop

1 min

i have notes on this

somewhere

ty

.solved

.close

[lone heart]

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[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[main cedar]

i need help

[vale wigeon]

!status

[lone heart]

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

[vale wigeon]

!nosols

[lone heart]

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.

[ionic sedge]

oh okay

[vale wigeon]

you've been on here long enough to know better.

[ionic sedge]

well ive been mostly asking questions

[vale wigeon]

!status @main cedar

[lone heart]

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

@main cedar Has your question been resolved?

[vale wigeon]

👻

[ionic sedge]

its not even like you where in responsive lol

[vale wigeon]

pardon?

[lone heart]

Channel closed

Closed due to timeout

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Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[alpine sable]

In question two which asks for Fourier's series, the answer doesn't seem to have an (a not) but from what I have wrote so far, (a not) does exist which makes me believe that I made a mistake of sorts

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

<@&286206848099549185> Is the question too complicated?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

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Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lost flax]

solve for P

[storm musk]

I suggest you remove the denominator

[lost flax]

why

I already tried

[storm musk]

Is the question specifically asking for P?

[lost flax]

yes

you need to calculate the amount of P

[storm musk]

Just say that a is 0

And solve for b

[lost flax]

but you dont have the amount of P so you cant find b

[storm musk]

Look at the equation on top

There is no P

You can solve the top equation with the assumption that a = 0

[lost flax]

mean I need to minus the left to the right ?

[storm musk]

?

Substitute a = 0

[lost flax]

yes

[storm musk]

And find b from that information

[lost flax]

ok let me try

[lost flax]

oh tks

but I have a another option

[storm musk]

??

[lost flax]

you dont need to care about letter

just look at the calculation

[storm musk]

Their logic is really difficult to understand

I prefer my way more since you don't need to look for patterns

[lost flax]

me too

[storm musk]

I know you get b = 0,4

[lost flax]

but I m not sure that it can have maximum point

[storm musk]

But we know that if b is 0, then the denominator will be 0

If it works, it works

[lost flax]

b=4

[storm musk]

Yeah exactly

[lost flax]

so

P= 16

[storm musk]

Yep

[lost flax]

tysm

[storm musk]

Np

[lost flax]

How can i close this conversation =))))

.close

[lone heart]

Channel closed

Closed by @lost flax

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Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[alpine sable]

How can we find where y=2^x starts?

[frozen compass]

You could plug in points

[barren portal]

What do you mean by starts?

[alpine sable]

The y coordinate

So that i can figure out where y=2^x - 1 is

[barren portal]

Plug x=0

what you get?

[alpine sable]

1

Oh

[barren portal]

So (0,1) is a point in the graph right?

[alpine sable]

So c is the correct option?

[barren portal]

Hold on, plug x=0, you got y=1?

[alpine sable]

2^0 = 1

[barren portal]

yes so, 2^0-1= 0 right?

[alpine sable]

Yeah

C is the correct option

Right?

[barren portal]

(0,0) belong to the graph not (0,1)

[barren portal]

Do you understand this?

[alpine sable]

Dude if it asks for y=2^x - 1 then we move the graph one down

We moved it from (0;1) to (0:0)

Am i wrong?

[barren portal]

It’s asking you which of the following is the graph for y=2^x-1

[alpine sable]

Yeah

It's c

[barren portal]

It’s not

[alpine sable]

Then which is it

[barren portal]

Let me explain why it’s not c

if it was c, x=0 should give you y=0 right?

[median oar]

How is it not c

[alpine sable]

It's literally c

[barren portal]

Ahh

C

I thought the last one is C

mb

yes, it’s since (0,0) is in it