help-0

[gusty gorge]

https://www.khanacademy.org/computing/computer-science/cryptography/modarithmetic/a/what-is-modular-arithmetic

you could read all of the articles

[cyan agate]

hello

[frosty flume]

don't have the time to do so right now but I appreciate the resources and help

[gusty gorge]

basically, you will compute $y^k \equiv cm^{-1} \pmod{p}$ but to compute $m^{-1}$, you will need to use the extended Euclidean algorithm or compute $m^{p-2}$

[ocean seal]

Saccharine

[frosty flume]

ok thanks! don't waste anymore of ur efforts because im not getting it haha ill go look up when i have the time

.close

[lone heart]

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[gray oxide]

Hello

[gray oxide]

Is

a=bc equal to a- bc = 0 or is it equal to a/bc = 1?

[gusty gorge]

a = bc and a-bc = 0 are equivalent

a/bc = 1 implies that a=bc, but the reverse is not true

now if b and c are nonzero, then all are equivalent

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[split cloud]

i dont have any parrelograms on my notes so idk how to even start this

[gusty gorge]

this is a trapezoid

notwithstanding that

draw a line from the top to the bottom corner

now it's a rectangle combined with a 30-60-90 right triangle

[vale wigeon]

are you just asked to find the values of a and b or something more sophisticated

[split cloud]

like from 60 to 90?

or there

[split cloud]

values

[pale kestrel]

try both

and see which helps

[vale wigeon]

perhaps it would make things a little easier if you gave names to all relevant points

then you would have a means to talk about specific stuff within the diagram by name

[gusty gorge]

right there

[pale kestrel]

Let them try

[split cloud]

i got a bit stuck on that one so i tried 60 to 90

isnt b the short side?

ohh no

nvm*

[pale kestrel]

How did u get stuck

[split cloud]

i got b

[pale kestrel]

uhhh can u show what u done

your working

or your answer for b

[split cloud]

is c=a?

or could they be different #s

[pale kestrel]

yes

think about why

[split cloud]

all cng angles

[pale kestrel]

you drew that line so it is perpendicular

All right angles make a rectangle

[split cloud]

oohhh i got a now too

a=15 b=30

right?

[gray isle]

b isn't 30

[split cloud]

oh yea now i c it isnt..

s=10

so the short side is 10 right?

or is it 5..

bruh thi sis soo confusing

[orchid stream]

hey i need a little help i dont know the right way to approach this question, Let f (x) = 2x where the domain is the set of real numbers. W hat is f(R)?

[split cloud]

oh i got it now nvm

[lone heart]

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[pale kestrel]

.close

closes channels

[split cloud]

oh i thought u delete it

[lone heart]

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[split cloud]

(20 radical 2)^2+20^2=c^2

[split cloud]

400 radical 4 +400=c^2?

800+400=c^2?

1200=c^2?

[open folio]

Can you use the bot

[split cloud]

idk how to use it sorry

[open folio]

Ah ok

Saying radical is confusing though

[split cloud]

20 radical 3=c?

yea ik sorry

[open folio]

Cause idk whats in the radical

[split cloud]

i got it right dw

just wanted to make sure

[open folio]

K

[split cloud]

.close

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[earnest lodge]

what general formula do I use

[solemn grove]

(1+x)^n expansion for non integer powers

[earnest lodge]

yea how can I solve it

couldn't find any vids on YouTube

showing how they got their general formula

[solemn grove]

1 +(n)(x)+ ((n)(n-1)(x)^2)2!

…

[earnest lodge]

how do I get this general formula

by working out

[solemn grove]

that’s the general formula

that’s the working out

[earnest lodge]

do it's something I have to memorise?

so*

[solemn grove]

sorta

[earnest lodge]

haiz okay

[solemn grove]

it’s just like your binomial expansion.

andd

@earnest lodge tl maths channel has really good maths videos

[earnest lodge]

wow

theres com sci here

thanks 🙏

[solemn grove]

com sci ?

and nws matey

[earnest lodge]

computer science

there are some algorithm vids there

I'll take a look at those when I have the time

NWS?

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[earnest lodge]

.close

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[orchid stream]

Let f (x) = 2x where the domain is the set of real numbers. W hat is f(R)? what is the right way to approach this question?

[pale kestrel]

write down the definition of f(R)

[orchid stream]

it is a function of all real number?

[pale kestrel]

Check your notes.

Alternatively, look up what the image of a set is

[lone heart]

@orchid stream Has your question been resolved?

[lone heart]

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[white ledge]

hello, all calc 2 taylor sieries help

[white ledge]

the tailor series abot x=0 for a certain function f converges to f(x) for all x in the interval of convergence The nth derivitive of f at x=0 is givven by

f^(n)(0) = ((-1)^(n+1) (n+1)!)/5^n(n-1)^2 ```
for n>=2. the graph of f has a horizontal tangent line at x=0 and f(0)=6

[warped zephyr]

<@&286206848099549185>

[white ledge]

you have your own channel?

why

how do i find if its a relitive max or min

thats second derivitive

but how do i get it

could i get help finding it? <@&286206848099549185>

if you want i could try my best to format it more mathamatically

[lone heart]

@white ledge Has your question been resolved?

[white ledge]

no

[lone heart]

@white ledge Has your question been resolved?

[solemn grove]

no worries = nws

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@white ledge Has your question been resolved?

[lone heart]

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[buoyant aurora]

Can someone explain to me how x->3 became x->1?

[little drum]

would you believe me if I said... "by mistake"

[buoyant aurora]

A typo?

[little drum]

indeed

[buoyant aurora]

Actually u know what i think ur right lol

Ok thanks

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[echo socket]

This is the same as saying 0 = 2pi because sin(0) = sin(2pi)

[pale kestrel]

How did you get from the 1st to the 2nd line

[echo socket]

Euler's formula

Oh

Nvm

It should be 2pi*i = 1

But still

[pale kestrel]

huh?

no

it should be 2pi n i or similar

the complex logarithm is multivalued (depends on your definition)

If you consider it to be not, then that still isn't right.

[little drum]

https://en.wikipedia.org/wiki/Complex_logarithm#:~:text=In mathematics%2C a complex logarithm,is denoted by log z.

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[raven rover]

Is that wrong?

sin(x) looks good to me

[native temple]

yep

uhh where did I go wrong

@ helpers help!!

[buoyant kayak]

this is the same problem you were asking about the other day

you're correct

[native temple]

yea

wait what

I am?

[buoyant kayak]

yes

[native temple]

oh I must be inputting my answer wrong then

[raven rover]

Maybe type in sin x or sin(x)

Idk

[native temple]

got it thanks

I might close if I don’t need more help

sheesh fractions

they will always be a pain won’t they?

[raven rover]

Not if you get fast at them 🙂

Practice, practice, practice

[vast pawn]

How to start on this

[raven rover]

#❓how-to-get-help

[vast pawn]

Oh mb

[raven rover]

This channel is in use

Np np

Open a new channel and I can help you there

[native temple]

B what!

In my openstax textbook

where’s the chapter on solving inverse trig functions by hand?

[raven rover]

Not sure - Idk what textbook you're on

You can probably google whatever skill you want to learn online

[native temple]

algebrw and trig

openstax

[raven rover]

Don't think I recognize that textbook unfortunately

It may not have it

[native temple]

It’s free

openstax

I got it for nothing

you see it?

[lone heart]

@native temple Has your question been resolved?

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@native temple Has your question been resolved?

[lone heart]

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[empty snow]

quadratics question, just need help forming the equation, not sure how to make it work when given the maximum point and also the intercepts

[formal bolt]

so from the given

you could tell that at x=40 and at x=0 y is equal to 0

those are the formula's roots

also h(root of h')=40

h is always positive obviously.

if we take the domain just from [0, 40]

modelling this throw

h=x(x-40) maybe? I am not sure

I will check my answer

[empty snow]

well, i thought that too, but I took into account the maximum point

i got either -x(x-40), or 12-(x+20)^2

[formal bolt]

well yeah then that's a wrong answer

mine I mean

[empty snow]

maybe they are factors of each other? not sure

[formal bolt]

hmm

I really dk I have never done those kinds of problems

I have only drawn equations

I haven't done the reverse

[marsh rapids]

You can stay with x(x-40), you just need to multiply it by the right constant such that it equals 12 at x=20

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[alpine sable]

1. How long does it take to pay off the higher-interest card?
2. What is the amount of the last payment on the higher-interest card? Why?
3. At the end of the month that you pay off the higher-interest card, after you have started to pay down your debt on the lower-interest card, what is the balance of the lower-interest card? Why?

Complete the following two tables to help you answer questions 4–5.
4) Rework the problem so that you pay off the lower-interest card first.
5) How much money do you save by paying off the higher-interest card first?

[lone heart]

@alpine sable Has your question been resolved?

[tacit arch]

You're likely to get help if you show what work you've done so far

[alpine sable]

I did

I'm clueless though

[lone heart]

@alpine sable Has your question been resolved?

[tacit arch]

putting in numbers don't count as "work"

share some equations and manipulations you've done

[alpine sable]

Like I said, I'm clueless

[tacit arch]

you inputted some numbers. how did you get them?

[alpine sable]

I don't remember

[alpine sable]

plz help

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[alpine sable]

Can someone please explain this with steps ?

[small linden]

move $\frac{x^2}{a^2}$ to the 1 side

[ocean seal]

Hamburglers

[alpine sable]

Like that?

[small linden]

yeah

[alpine sable]

What next?

[small linden]

now multiply by b^2

[alpine sable]

Like that?

[small linden]

the answer u gave is wrong

[alpine sable]

But

[alpine sable]

Better?

[bright ravine]

hello ?

any one there?

<@&286206848099549185>

[white jolt]

@bright ravine lad you don't know how to find radius and centre of a circle?

[small linden]

yeah thats correct

[alpine sable]

How do they do it?

[small linden]

$y^2=\frac{b^2}{a^2}\left(a^2-x^2\right)$

[ocean seal]

Hamburglers

[alpine sable]

What was the first step

What part did they move first

[small linden]

from here $y^2=b^2\left(1-\frac{x^2}{a^2}\right)$ u already wrote

[ocean seal]

Hamburglers

[small linden]

factor out 1/a^2

[bright ravine]

yes bro i dont know 😦

i stop 4 years in school

and i want to pursue bro

i appreciate if you teach

im from ph

thanks 🙂

[white jolt]

@bright ravine ok ig centre is (-g,-f). And radius is root of g^2+f^2 -c

[bright ravine]

i think

that answer is A?

[alpine sable]

What

[white jolt]

@bright ravine so circle has the genera equation of x^2+ y^2 + 2gx+2fy+c

@bright ravine now just count it

Everything is int front of u

[small linden]

from here $y^2=b^2\left(1-\frac{x^2}{a^2}\right)$ factor 1/a^2 out from right side

[ocean seal]

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

[bright ravine]

am i correct the answer is A ?

[white jolt]

@bright ravine yes

[bright ravine]

can i ask 2 more question bro ?

[white jolt]

@bright ravine ask on other help section

[bright ravine]

i need badly help bro

okay bro thanks

i appreciate bro

[white jolt]

Yeah

[lone heart]

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[raven fog]

I need to put this in a grid. I know that the answer is 24 , but I don't know how to put it in a grid

[ripe rain]

4ways of wearing pants

3 ways of waering polos

2 ways of wearing shoes

These are independent events

So

[ocean seal]

Deep Hariya

[raven fog]

yea

I need it to be something like this huhu

[ocean seal]

Deep Hariya

[ripe rain]

For pants

[ocean seal]

Deep Hariya

[ripe rain]

$(s_1,s_2)$ for shoes

[ocean seal]

Deep Hariya

[ripe rain]

Then you can do this I guess

Can you?

[ocean seal]

Deep Hariya

[ripe rain]

Like that you’ll have 24 elements in your set

[raven fog]

yea. thank you

thank you:))

.close

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[alpine sable]

Help guys is my solution and answers correct?

[pale kestrel]

no

u should multiply the last by -1, then add, instead.

[alpine sable]

so the last one is supposed to be -40 x -1, then it would be 40?

[little drum]

⁉️

scratch that and start over again.

you'll know your mistake (probably)

[lone heart]

@alpine sable Has your question been resolved?

[formal bolt]

yeah except for the coefficient of X

it should be -6

[lone heart]

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[shy veldt]

how many solutions for this form of exponent

[hasty elk]

Hint: excepting a special case, you can take logarithms

[shy veldt]

Does f(x) = -g(x) on condition h(x) is an even number counts ?

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[shy veldt]

.close

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[alpine sable]

any idea how to approach this?

[little drum]

$f'(x) = 0$ and $f"(x) > 0$ , ?

[ocean seal]

Ansh

[little drum]

unless you can deduce that you don't need to check the f" condition.

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

why do i need f''(x) @little drum

how does it help me prove that the extreme point is the minimum

[little drum]

f'(x) being zero only suggests that the slope of tangent at the point is zero

which implies that the function has went an extreme change and might wish to decrease/increase now

but

you need f"(x) to be able to say for certain whether this point is your maximum point

or the minimum

basically f"(x) tells whether your curve is convex shaped or concave

[alpine sable]

i see

ok but

how do i even continue from here

is this correct anyway?

[little drum]

f'(x) = 0

check

find solution

and you have the answer

[alpine sable]

i never learned how to solve such equations lol

[little drum]

oiiiiiiiii

$e^y = 0$ has no solutions

[ocean seal]

Ansh

[little drum]

so your best bet is only

$1+\ln x = 0$

[ocean seal]

Ansh

[alpine sable]

so ln x has to equal -1

alright so reverse ln on calculator got it

then go for 2nd derivative

can i ask another question please

could u give me some guidance with this

im lost here

anything is appreciated

like i went on bruteforce mode when i got to this question lol i just started doing anything that i thought could help but left the question when i left like i wasnt progressing

so im not sure if what i did is correct

probably not lol

[little drum]

ouch

Are you not allowed to use chain rule?

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[arctic wren]

To solve that in term of a, b , c d

i could just equal a = 4

and solve it

ok

but if i "send" the right matrix to the left side

i would get a - 4 and son

but what do i pu in the right side 0 or a 2x2 matrix with 0 ?

[little drum]

a 0 equated to a mxn matrix is assumed to have mxn dimension with 0

but it'd be convenient if you just write 2x2 matrix with zeroes

[arctic wren]

oooo ok

so my line of though wasn't wrong

thank you

.close

[lone heart]

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[sudden palm]

@leaden tiger

E

[leaden tiger]

yes, so did u get the value for q?

[sudden palm]

I didn’t

I got stuck

[leaden tiger]

ok so the orginal equation is cos(35) = 8/x

you need to rearrange for x

[sudden palm]

Right

Idk gown

How

I didn’t learn that syntax

[leaden tiger]

does this help? , theta is 35 and the adjacent is 8

just input and re arrange for H

[sudden palm]

Okay but I don’t know what to do

I wrote it

Idk what rearrange means

[leaden tiger]

make H the subject

H = ....

[sudden palm]

I don’t know what that means either

H e X

Idk what to do

I’m so confused

[leaden tiger]

hmm, im not sure how to explain this to you if u dont know what re arranging an equation is....

[sudden palm]

I’m crying

[leaden tiger]

hm, you may want to learn some of the basics of equation manipulation online or smthing

[sudden palm]

Can you just tell me what to do though

Pls

[leaden tiger]

search "how to re arrange eqations" on youtube

[sudden palm]

This is how I was taught to do it

Idk rearrange that seems complicated

I forgot how to enter into Desmos past that though

[leaden tiger]

yes, that is exactly wat u need to do, that process is called equation manipulation

so you have cos(35) = 8/x

[sudden palm]

Right..

[leaden tiger]

so multiply both sides by x

giving....

x cos(35) = 8x/x

[sudden palm]

Mhm

[leaden tiger]

and then you can cancel the x's out on the right

[sudden palm]

??

[leaden tiger]

and so on....

[sudden palm]

So on is what I don’t know

[leaden tiger]

you written out the process here

[sudden palm]

Ye

How do I get

To the equation

Though

The answer

[leaden tiger]

so you hav x = 8/cos(35)

do u get that...?

[sudden palm]

Yes

[leaden tiger]

then just throw it into a calculator

and done

[sudden palm]

In degrees ?

[leaden tiger]

yes

[sudden palm]

Im getting .81

.819

Is that what im supposed to be getting

[leaden tiger]

no, uve inputted it wrong

[sudden palm]

Is it 9.766

[leaden tiger]

yes

[sudden palm]

Okay so it’s 10

Thank you

[leaden tiger]

yes if u want to round up

[sudden palm]

.close

[lone heart]

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[proven oriole]

What would the limits be for finding this? What I tried so far is:

[versed crater]

Where’d you learn this stuff

[proven oriole]

uni. Pls @real ore if you have a hint or smth

its been a while since ive done double integrals and thinking about limits so...

[lone heart]

@proven oriole Has your question been resolved?

[placid zinc]

Limits? What limits?

Indeed, can't move x out of an integral that uses x

So the inner integral can be done first, just as a regular single integral

[proven oriole]

Integral bounds? Is that what you call it?

[placid zinc]

Bounds, yeah

[proven oriole]

Yeh I did the inner integral. The outer one I can’t get rid of the y

[placid zinc]

You won't have any y after doing the inner integral

[elder sedge]

i would advise you to draw the region for this fatum

[placid zinc]

Since that integral is dy, y is used up.

[proven oriole]

I know it’s the outer one that messed me up

[placid zinc]

Oh, I'm realizing that indeed the bounds are incorrect. Yeah, drawing the region is huge.

[proven oriole]

For y < x < 2 should I sketch y < x?

[elder sedge]

y=x and proceed

[proven oriole]

Ok gonna temporarily close this and try

.close

[lone heart]

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[lean plover]

i see this

i see association

i think spearmans rank

but theres only 2 things to rank?

sum of spearman rank becomes 2

so spearman rank coefficient becomes -1

spearmans rank is not mentioned on the mark scheme anywhere

so i dont think this is correct method to do it

[lone heart]

@lean plover Has your question been resolved?

[lone heart]

@lean plover Has your question been resolved?

[lone heart]

@lean plover Has your question been resolved?

[lone heart]

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[edgy cape]

I am struggling with 4ii

my general method was to set up simultaneous equations to solve for c and k

but I did it wrong

I got my integral to be: t=[(2*x^1/2)/(-k)]+c

I am not sure if my integral is correct

After plugging in the given values I set up the simulataneous equation to look like this:

0= (2√2 /-k)+c 5=(2-2√2)/-k + c

idk if maybe that is also wrong

what

what did i say that you don't understand?

[tacit arch]

<@&268886789983436800> pls

[sly mantle]

@alpine sable cut it out

[lone heart]

@edgy cape Has your question been resolved?

[edgy cape]

<@&286206848099549185>

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@edgy cape Has your question been resolved?

[tacit arch]

share your work for part (i)

[lone heart]

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[mighty zinc]

My answer is simple

Find as much info of the circle as you can

Find all possible Info as possible

Ok

So what is the angle of the cut out piece?

Noice

What is the length of the cut out piece?

[tacit arch]

formula's here: https://www.cuemath.com/geometry/arc-length/

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@alpine sable Has your question been resolved?

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@noble marlin Has your question been resolved?

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[next sage]

hello, just curious on one thing, which one am i supposed to type in the calculator..? and why..

[alpine sable]

the first one is the correct inverse of the function

assuming thats what your looking for

[next sage]

i have seen instances where they remove negatives when finding the angles, so i am a bit confused

[alpine sable]

$f(a) = b \Rightarrow f^{-1}(b) = a$

[ocean seal]

aspwil

[alpine sable]

hmm

[next sage]

i understood that

[alpine sable]

im not very in depth about about it but i only think that would work for cos(x)

hold on wait

[pale kestrel]

Do you understand the problem?

There exists no inverse for tan

unless you restrict its domain

[alpine sable]

OH YEAH I WAS ABOUT TO SAY

[pale kestrel]

If that is the issue here.

[alpine sable]

sorry caps lock

[next sage]

but example we’re resolving resultant forces, after finding the resultant force using pythogoras, we used tangent inv to find the angle but its all absolute numbers inside the inverse func

[alpine sable]

tan(-2)

[next sage]

o

thankyou.

.close

[lone heart]

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[stone granite]

Can someone dumb this kind of question down to me bc I can’t find practices for this kind of question anywhere nor do I know what kind it is

[lone heart]

@stone granite Has your question been resolved?

[stone granite]

<@&286206848099549185>

[lone heart]

@stone granite Has your question been resolved?

[abstract fractal]

I disagree with question 25. √x is defined as the principle square root. It is always positive when x is positive.

For question 30, just think about it. Plug in numbers. If A is less than -7, then let A = -8 and see what B is

[wary stream]

No that’s not true

[abstract fractal]

How so?

[wary stream]

You can’t have numbers less than 2 for that one

[abstract fractal]

I said when x is positive for √x. In this problem, x is C - 2

[wary stream]

Were you disagreeing with the red answer or the green?

[marble coral]

25A is correct

[abstract fractal]

I think both A and B are true. B is true since the radicand would be negative, and A is true because √x is always positive for positive x

[marble coral]

But complex numbers are a solution

[wary stream]

It’s referring to real solutions

[abstract fractal]

That's true. However, judging by the coloring of the answer, it seems the question makers deemed B to be true and A to be false

[gray isle]

there are multiple valid options to that question

[violet quail]

help

please

[wary stream]

#❓how-to-get-help

[marble coral]

Use another channel

[abstract fractal]

C is true too! If B is negative, then there are no solutions, since √x is never negative

[marble coral]

Look at what they have in common

[wary stream]

It does say pick the statements, meaning multiple

[marble coral]

No

"Which of"

I think it's one

[abstract fractal]

This question is wack

They must've confused √x for ±√x

[wary stream]

It is highlighting B green and green is normally the correct answer

[abstract fractal]

B is true, but so is A and C

And it says A is wrong

[wary stream]

Wack question

[lone heart]

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[late parcel]

I have some math questions

[late parcel]

I think I did number 1, 5, 9 and 10 wrong. Can someone help me with any of those?

[lone heart]

@late parcel Has your question been resolved?

[late parcel]

Anyone?

[lone heart]

@late parcel Has your question been resolved?

[late parcel]

<@&286206848099549185>

Help on number one please

A half life problem

[alpine sable]

one sec

a half life is how long it takes for the amount of radioactive material to get cut in half right?

[late parcel]

Correct

Abs I know the formula is

Initial times .5^ t/half life

However in this example they don’t give us the initial so how can you do it?

[alpine sable]

whats a curie? is that the amount of radation being released?

[late parcel]

Correct

[alpine sable]

so half as much radaiation mean half as much radioactive material?

[late parcel]

?

I’m not sure what you mean

[alpine sable]

if you douvble the ammount of substance you have it will create double the ammount of curies?

[late parcel]

I believe

Want me to give you an example we did in class together?

[alpine sable]

so if the amount of radaition goes down by 1/2 the total material goes down by 1/2

[late parcel]

These 2 are similar but unique

[late parcel]

Correct

[alpine sable]

question 1 says, at the start were producing 2 curies, at the end were producing 1 curie,

[late parcel]

I posted my work for the problem above. Do you disagree with what I put? I’m hesitant because they don’t give an initial amount

It means how long until 1 curie is all that’s left

[alpine sable]

we start at 2 curies being prduced and end at 1 curie being produced. the curries have gone from 2 -> 1, or there at half of there original right?

[late parcel]

That’s my takeaway

[alpine sable]

so we have lost half of the radioactive material, how long does it take to lose 1/2 of the radio active material?

[late parcel]

That’s the question

[alpine sable]

.

[late parcel]

What about it?

[alpine sable]

it takes 1 half life, for us to lose half of the radio active material.

if we have lost 1/2 of the radio active material how many half-lifes have passed

[late parcel]

10?

[alpine sable]

1 half life has passed, so yes 10 years

[late parcel]

Ok thank you!! With half lives in mind can you also help me with number 5

It’s similar

[late parcel]

Yes

Wait first

Timeout

[alpine sable]

yes?

oh you need to go afk for a moment?

[late parcel]

Trying to do number 1 by hand

No Calc because no Calc on test

How can I isolate t

[alpine sable]

oh by pluging into the equatuion?

[late parcel]

When it’s in an exponent

But I have .5 ^t

How can I get T by itself

[alpine sable]

can you give me the default decay equation?

[late parcel]

See that thing under T just means half life

That t 1/2 means half life

So it’s N(.5)^t/(half life)

[alpine sable]

so you want to get the exponent down?

[late parcel]

Yes

Some log rule right?

[alpine sable]

yeah with logaritums. do you know how to use logarithums?

[late parcel]

Not anymore, can you refresh me

[alpine sable]

for $ a^{b} b = log_{a}(a^{b}) $

[late parcel]

Wait what?

[alpine sable]

come on math bot

[late parcel]

Lol

[alpine sable]

for $a^{b} b = log_{a}(a^{b})$

im not the best at tex

for $a^{b} : b = log_{a}(a^{b})$

[ocean seal]

aspwil

[alpine sable]

so pulling loga on a^b will result in just b

[late parcel]

What’s the :

Is that supposed to be times?

[alpine sable]

no, its just a sperator. we dont really need it it just made a bit more sence, its a mathematical sentance.

just pay attention to

$b = log_{a}(a^{b})$

[ocean seal]

aspwil

[late parcel]

Then how do you know what log.000977 is?

Do you need a calculator for that

[alpine sable]

uhh log what now?

where did you take that number from?

[late parcel]

.5^10

[alpine sable]

what equation are you tring to solve for t?

[late parcel]

Yes T

Look at the top line

[alpine sable]

oh so

$1 = 2(frac{1}{2})^{\frac{t}{10}}$

$1 = 2(\frac{1}{2})^{\frac{t}{10}}$

[ocean seal]

aspwil

[alpine sable]

first we devide both side by 2 to get the exponent expressikon by itself

[late parcel]

Ok

[alpine sable]

$\frac{1}{2} = (\frac{1}{2})^{\frac{t}{10}}$

[ocean seal]

aspwil

[late parcel]

Correct

I got that

[alpine sable]

if we want to get b (the exponent down) we need to take the log base a

[late parcel]

Ok

Let me see

I think I did that wrong

[alpine sable]

looking at the right side

which part is a and which part is b?

what is a and what is b in this case

[late parcel]

A is 1/2

B is t/2

[alpine sable]

now repalce a and b in this with the values

for $\frac{1}{2}^{\frac{t}{10}} : \frac{t}{10} = log_{\frac{1}{2}}(\frac{1}{2}^{\frac{t}{10}})$

[ocean seal]

aspwil

[late parcel]

Du confused why you have the :

What does that mean?

[alpine sable]

just take : to mean the phrase "we do"

[late parcel]

Ok

[alpine sable]

so its for $a^{b} $we do$b = log_{a}(a^{b})$

so its for $a^{b} $ we do $b = log_{a}(a^{b})$

[ocean seal]

aspwil

[late parcel]

How how do you get the number 10 from that mess of log?

[alpine sable]

we have this right?

[late parcel]

I understand that part

[alpine sable]

and we have this

notice how the red box is the same as the right side of that equation

[late parcel]

Yes

[alpine sable]

so to get t/10 on the right side of this equation down we need to take log base 1/2

[late parcel]

See that 1/2 under the log?

That came from the left side of the equation right

[alpine sable]

1/5?

[late parcel]

1/2

[alpine sable]

ahh

[late parcel]

Which 1/2 did that come from

The base of the log

[alpine sable]

a is 1/2

[late parcel]

So what happened to the 1/2 on the left side?

[alpine sable]

for a number A^B take the log base A and you will be left with B

[late parcel]

Ok

[alpine sable]

$\frac{1}{2} = (\frac{1}{2})^{\frac{t}{10}}$

[ocean seal]

aspwil

[alpine sable]

see this equation?

were solving for t in this

[late parcel]

Yes

[alpine sable]

for a number A^B take the log base A and you will be left with B

[late parcel]

Ok

[alpine sable]

we want to take the log base a (in this case a = 1/2)

[late parcel]

Ok

Is that .5 from the left or right

Their are 2 1/2s

[alpine sable]

the right

[late parcel]

Ok

A =1/2KKK

And left 1/2 = 1/2JJJ

[alpine sable]

$\log_{\frac{1}{2}}(\frac{1}{2}) = \log_{\frac{1}{2}}((\frac{1}{2})^{\frac{t}{10}})$

[ocean seal]

aspwil

[late parcel]

Oh ok see

[alpine sable]

we take the log base 1/2 of both sides since thats the number on the right

giving us this

[late parcel]

Ok

So then what

[alpine sable]

look at the right side of both the equations

[late parcel]

Yes

[alpine sable]

hold on

if we have an equation like this

[late parcel]

Yes

[alpine sable]

we cancel out by drawing this and the crossed out things disapear

the x cancel eaother out

[late parcel]

Right

[alpine sable]

in the same way the a cancel out

leaving us with just b

log base a and a^ are opaite operations

[late parcel]

Ok

[alpine sable]

so in this if we look at the right side, the A's cancel out

leaving us with just t/10 on the right side

its really dificult to explain why.

im just trying to find a way that works well

we get

$\log{\frac{1}{2}}(\frac{1}{2}) = \frac{t}{10}$

$\log_{\frac{1}{2}}(\frac{1}{2}) = \frac{t}{10}$

[ocean seal]

aspwil

[late parcel]

Ok

[alpine sable]

theres a rule $log_{x}(x) = 1$

[ocean seal]

aspwil

[alpine sable]

so the left side is 1

$1 = \frac{t}{10}$

[ocean seal]

aspwil

[alpine sable]

and its finishable from there

sorry if this has been really confusing

[late parcel]

No worries

[alpine sable]

logarithums are notorius for being difficult to explaine. i had to flounder around for hours with them, but then suddenly it clicked and i was like "OH thats how it works"

[late parcel]

Ya

Well thank you very much

I really appreciate the help

Have a good one!!

[alpine sable]

yeah good luck, maybe watch some youtube videos on logaritums to get a better understanding (might help more)

(at the end btw type .close)

like this

.close

[lone heart]

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[late parcel]

.close

[lone heart]

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[celest trail]

find the pattern

[celest trail]

<@&286206848099549185>

[blissful whale]

I don't think there is a pattern or if there is, it's not enough numbers to be sure.

Because it looks pretty random for me

[blissful whale]

After 15 minutes, feel free to ping @ Helpers.

[lone heart]

@celest trail Has your question been resolved?

[celest trail]

hmm

but it has to be

some patern

[celest trail]

sorry

[lone heart]

@celest trail Has your question been resolved?

[gray kiln]

106

maybe

8*4+2=34

34/2 -3=14

14*4+4=60

60/2 -5=25

25*4 +6=106

[lone heart]

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[candid minnow]

how do we know that x_p is (3,1,0,0)

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@candid minnow Has your question been resolved?

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[lone heart]

@median bridge Has your question been resolved?

[median bridge]

<@&286206848099549185>

[ripe rain]

I think it is false

Take a look at this graph for eg

Here at k f’(x)<g’(x)

I don’t know how to disprove it but i think it is false

I guess I have made my point clear

[open linden]

Yeah I'm pretty sure it's false

Because you can increase the value of a function however much you like without changing the derivative

just by adding a constant

so comparing the size of derivative shouldn't have anything to do with the size of the functin

[ripe rain]

Ya

[lone heart]

@median bridge Has your question been resolved?

[median bridge]

Much appreciated, it's all clear now! @ripe rain @open linden

[lone heart]

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[whole wadi]

Can someone show me how we get a minus sign in front of sin in the second step?

$\sin \left(x\right)=-\sin \left(x-\pi \right)$

[ocean seal]

Theophania

[whole wadi]

Like this?

[open linden]

Yeah

check it for yourself on a graph of sin x

[whole wadi]

These are the identities I have in my textbook

Which one is it?

[open linden]

sry the picture sucks

ok lemme see

From sin(180-v)=sin v we have sin(pi - v) = sinv

And since sin(x) = -sin(-x)

[little drum]

sin(x) = sin(180 - x) = sin(-(x - 180)) = -sin(x - 180)

[open linden]

We have sin(pi - v) = - sin(v-pi)

🙂

[whole wadi]

How do we know this?

sin(-v) = -sin(v)

I don't know about sin(x) = -sin(-x) though

[open linden]

They're the same thing

multiply your equation by -1

Also it's good to check these identities by looking at the graph of sin x

and cos x

will help u remember it better

[whole wadi]

So -1 * sin(π-v) = -sin(v-π)?

[whole wadi]

$$sin\left(-\left(x:-:180\right)\right):=:-sin\left(x:-:180\right)$$
Isn't it like this?
$$sin\left(-\left(x:-:180\right)\right):=:-sin\left(180-x\right)$$

[ocean seal]

Theophania

[little drum]

YOOOOOOOOOOO =_=

$\sin( - x) = -\sin x$

[ocean seal]

Ansh

[little drum]

What you just wrote was your own invention?

[whole wadi]

the second line

[open linden]

yep

[whole wadi]

the first one you wrote

[whole wadi]

.

[little drum]

what?

are you also unable to read properly?

I wrote $\sin (180 - x) = \sin(-(x-180))$

[ocean seal]

Ansh

[little drum]

Yeah what about that?

[little drum]

Yeah so?

[whole wadi]

My question below it

[little drum]

what do you mean by the second line?

[whole wadi]

Second line, row, etc

[little drum]

?

How did you come to that conclusion?

[whole wadi]

@open linden Is this correct?

https://www.symbolab.com/solver/step-by-step/prove sin\left(-\left(x - 180\right)\right)%20%3D%20-sin%5Cleft(180-x%5Cright)?or=input

What you wrote above is wrong @little drum

That's what I am saying

[open linden]

yeah

waitwait

[little drum]

$sin(-(x-180)) = -sin(x-180)$ is wrong?

[ocean seal]

Ansh

[open linden]

no ansh is right

theophania you mistyped it

[open linden]

into the proving engine

[whole wadi]

Look carefully lol

[little drum]

Not "MISTYPED"

[open linden]

THis is rigt

[whole wadi]

How?

[open linden]

asjdflkjahd

idk how to explan

[little drum]

it's totally inability to read properly

[little drum]

show the result?

🤷

[whole wadi]

Okay that's weird

Wolfram alpha says it's true

[little drum]

obviously

even symbolab says it's true

[whole wadi]

They're identical so I don't know why it said that

[little drum]

It's only you who thinks, from idk where and what reasoning, that it's not true

:/

Anyways, doesn't look like you're asking anything over here. So I'll head out lol

[whole wadi]

.close

[lone heart]

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[lone heart]

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[delicate temple]

hello, i'm trying to solve a problem in which i'm trying to figure out how many packs of [collectable item] someone would need to buy in order to have a 90% <= chance of obtaining all 12 collectables.

• all 12 have the same chance of appearing in a pack
• there is only 1 toy per pack

at first i thought it'd simply be binomial distribution problem but now i can see that it's not; could you point me in the right direction or perhaps some methods i could look up to find my answer?

[delicate temple]

(i asked this question yesterday, but was unable to get an answer & couldnt renew the channel as i went to sleep skdjhkjh)

[lone heart]

@delicate temple Has your question been resolved?

[delicate temple]

<@&286206848099549185>

[lone heart]

@delicate temple Has your question been resolved?

[lone heart]

@delicate temple Has your question been resolved?

[solid cargo]

Well if the number of packs available for buying is not defined the the solution will be infinite…

How many total packs are there from which u need to choose 12?

[lone heart]

@delicate temple Has your question been resolved?

[lone heart]

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Remember:
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• 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 oar]

Help idk how to answer

[covert agate]

angle sum of triangle = 180°

[tall oar]

The x’s are what mess me up

.close

[lone heart]

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[thick lynx]

$$x + (x + 70) + 28 = 180$$

[ocean seal]

Kepe

[thick lynx]

$$2x + 98 = 180$$

[ocean seal]

Kepe

[thick lynx]

$$2x = 82 --> x = 41$$