help-28

[foggy tree]

I’d recommend simplifying the exponents then distributing

[copper sequoia]

Wait lemme try

[teal wigeon]

distributing then simplifying would be easier i think since u just add the exponents

[foggy tree]

U rite

[plush egret]

yea and then mostly drop out

[copper sequoia]

Figured it out. I was just messing up in first step

[copper sequoia]

Right i forgot to simplify

Got another doubt.

[hushed spear]

How do you get from x to (x-3)²?

[copper sequoia]

Ugh what do you mean?

[hushed spear]

If you have x, what do you need to do to get to (x-3)²?

[copper sequoia]

I am not sure how do I find the final answer.

[foggy tree]

Try expanding the (x-3)^2

Then plug in x

[copper sequoia]

Let me try it.

Got the answer

I would close this thread now.

.close

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[copper wharf]

How do I find the pronumeral letters

[copper wharf]

of z and y

I found x already

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@copper wharf Has your question been resolved?

[tight glen]

since you already know x and 39, can you find the third angle that is the part of that triangle

@copper wharf

[copper wharf]

Which one x or y?

[copper wharf]

Can you draw it for me pls

[tight glen]

ye wait

[copper wharf]

ok

...

[tight glen]

that triangle

you know two angles

can you find the third one

[copper wharf]

102

180 - 39 - 39

[tight glen]

x is 39?

are you sure?

[copper wharf]

Nah i'm blind it's 23

Which equals to 118

[tight glen]

Ok so consider that angle and y

their sum would be?

[copper wharf]

Would z be 118 because it's a larger angle

[copper wharf]

180?

[tight glen]

So?

you can find the angle y now

yes?

[copper wharf]

give me a sec...

[copper wharf]

I'm not quite sure

[copper wharf]

141

[tight glen]

wait why?

why would their sum of 141?

[copper wharf]

118 + 23

=141

[tight glen]

32?

where did that come from?

[copper wharf]

You mean 23

???

[tight glen]

yes sorry

sum of angles on a straight line?

is equal to?

[copper wharf]

A straight line is approximately 180

[tight glen]

not approximately

it is always that

[copper wharf]

Who said it was?

[tight glen]

wdym?

[copper wharf]

Who justified it was 180 degrees

[tight glen]

justified as in? like proved that it is always 180?

[copper wharf]

I think a straight line is 180 because a right angle is 90 degrees and double that is 180

[tight glen]

that is kind of right

[copper wharf]

I'm sorry btw I'm going to have dinner right now because my momma is calling me

Can I dm you and continue you this later?

If that's fine

[tight glen]

Ok, lets continue this later

[copper wharf]

Thanks, I appreciate it

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[surreal acorn]

yo

[torn jolt]

yo

[surreal acorn]

idk how the answer is 79.6

i know how to solve it

but the answer is strange

[hot herald]

show work

[surreal acorn]

i dont have my phone

@torn jolt

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[brisk sage]

Hi, ive tried to do this by doing 9C3 to find all combinations, its 84 which is the denominator.

Ive tried finding the numerator by doing

3C3 + 4C3

i got 30/84 but the answer sheet the teacher gave said its 5/84, i need some help understanding why this is

[static leaf]

uhm we can just solve this by listing combos

GGG, BBB

but I imagine each ball is different

so like

[wild sleet]

5/84

[brisk sage]

theats what the teacher said too

but i need to understand why

[static leaf]

,w solve 3c3 + 4c3

[wild sleet]

5 is the outcomes that work, GGG, BBB,BBB,BBB and BBB

[static leaf]

,w solve 3choose3 + 4choose3

[brisk sage]

i did, permeatations instead of combinations

yeye 4chose3 is 4, and 3chose3 is 1

so 4+1 is 5

[wild sleet]

that's also what you did

3C3 + 4C3

[static leaf]

,w solve 3C3 + 4C3

FOJHDBKLJHJOIFHBKLKJOIPFOHKBjn;l

[brisk sage]

i originally did permeatation, but i now understand it is combination, i misstyped my original question

so it would be combination because order does not matter right?

[static leaf]

yeah

it does not matter, cause they only care about color not like the id

[brisk sage]

alright

thank you very much

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[wanton mesa]

how did it get there?

[wanton mesa]

from 👆 to ☝️

[kind jay]

do u know how they went from 4^(..) to 2^(..)

[wanton mesa]

no

that was the initial question

[kind jay]

whats 4 equal to

2^x=4

what would x be here

[wanton mesa]

2

[kind jay]

so u can write 4 as 2^2

[wanton mesa]

so 2(3x-2)?

[kind jay]

yes

[wanton mesa]

to get 6x-4

what about 1/2sqrt2

2^1/2?

[kind jay]

do u know exponent laws

[wanton mesa]

is it 2^1/2 times by 1?

[kind jay]

no

[wanton mesa]

oh wait

2^-1/2?

times by one

[kind jay]

2^(-1/2)*x?

no

needs to have same bas

base

to use multiplication exponent law

[wanton mesa]

where does the x come from

[kind jay]

2*(-1/2) ** 2^x=2^(-3/2)

what would x be

[wanton mesa]

i don't get that

[kind jay]

do u know exponent laws

[wanton mesa]

1 min

yeah

could you show me it in micorsoft paint or paper ?

[kind jay]

$a^x*a^y=a^{x+y}$

right?

[glossy valve]

Triangular Hebesphenorotunda

[kind jay]

for us a is 2 here

so u just need to

add the exponents together

basically (-1/2)+x=-3/2

solve for x

[wanton mesa]

which part of the equation is this?

[kind jay]

this

[wanton mesa]

what does the double "**" mean

[kind jay]

multiplication

[wanton mesa]

for the first part do you mean 2^(-1/2) and not 2*(-1/2)?

[kind jay]

aha ys

yes

[wanton mesa]

the question says to solve this btw so i wouldn't know that 2^(-1/2) * 2^x is equal to 2^(-3/2)

[gritty rose]

$4^y = (2^2)^y = 2^{2y}$

[glossy valve]

riemann

[wanton mesa]

ok thanks i got it finally

!close

[gritty rose]

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[torn jolt]

can someone plz help??

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[magic canyon]

Im confused on finding a

[gritty rose]

https://socratic.org/questions/what-do-a-and-b-represent-in-the-equation-of-a-hyperbola

[magic canyon]

would it be 6 or 36?

i squared 6

[tidal citrus]

6

Notice that a and b are squared in the equation.
36 isn't anywhere on that graph even

The distances are a and b, not squared.

[magic canyon]

ohh...
im a little confused on the graph

Center: (5,6)
Slope = 4/3

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[kind jay]

do u know your log properties

[rustic stump]

I might be wrong but I think when adding logs you actually multiply them, so it would actually be logxy. Then you can use the power rules and bring the 4 up to the top, so the answer would be A logxy^4

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[tepid pasture]

How would I find the entropy (how random) a 2d boolean grid is?

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[fathom saddle]

You've got to explain that a little better

Why do you have Boole's grid? He needs that!

[wild sleet]

i read about shannon entropy, so naively it's about how close the amount of zeroes is to half the grid

that seems not very useful, you certainly don't want that

here https://stats.stackexchange.com/a/17556

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[wild sleet]

they don't suggest a way of using all the scales at the same time but the rest makes sense

so basically you start with sums of all 1×1 windows, which is just the original grid, the ehtropy of that is 1 when there's equal amount of 1 and 0, otherwise it gets smaller
then you do 2×2 windows and entropy of that is maximum at 2.3 when there's equal amounts of 0 and 4, and 1 and 3

and so on, larger windows have higher max entropy, and you want to add up all scales, but i don't know at what weighting

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[valid snow]

A pet store has 8 dogs and 4 cats. If you were to adopt 3 pets in total, what is the probability that you adopt 2 dogs and 1 cat?

[valid snow]

Im doing probabilities right now

[torn jolt]

Adopting 2 dogs and 1 cat means : picking 2 dogs from 8 , and 1 cat from 4. how many possibilities then ?
And how many total possibilities are there ? (picking 3 pets randomly)

recall : the number of possible combinations of k elements taken from n elements is $\binom{n}{k}$ (order doesn't matter here)

[glossy valve]

AimaneSN

[valid snow]

1320

because its 12 factorial

thats the amount of combinations

[torn jolt]

the amount of which combinations?

[valid snow]

Nevermind I solved it its good now

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[plush egret]

could someone help me track the answer for b?

I do have the form of the posterior but im having trouble seeing how this falls out

[gritty rose]

Did you do the integral?

[plush egret]

the integral?

well were not supposed to

were supposed to use the form

[gritty rose]

something like this?

[plush egret]

no, were supposed to just use a given form

given prior $N(\mu, \sigma)$ and likelihood $N(\tau, \theta)$ then posterior is $N\qty( \frac{ \tau ^2 \mu + \sigma ^2 t}{ \sigma ^2 + \tau ^2 } , \frac{\sigma ^2 \tau ^2}{\sigma ^2 + \tau ^2 } )$

[glossy valve]

jan Niku (@pomodoro role)

jan Niku (@pomodoro role)

[plush egret]

but it seems like were missing the wrong parameter?

i realize this is probably a dumb question im just trying to jog my memory since i will not be able to do that integral on the exam

[gritty rose]

oh jesus

[plush egret]

isnt out prior the prior for theta

[gritty rose]

So $\mu=2$, $\sigma=3$ ?

[glossy valve]

riemann

[plush egret]

yea

but then tau = theta and theta = tau?

im not quite sure how an X gets introduced

[gritty rose]

what's little $t$ here ?

[glossy valve]

riemann

[plush egret]

thats what im trying to determine

i guess you would uhm

[gritty rose]

same as $t = \theta$?

[glossy valve]

riemann

[plush egret]

you would integrate away your unknown

[gritty rose]

$\tau^2 = 16 \implies (16 \cdot 2 + 9 \cdot t) / (9 + 16) = \theta$ ?

[plush egret]

hmm let me look

[glossy valve]

riemann

[plush egret]

oh geez

i think i see what you mean

X just switches place with theta

somehow

maybe through the integration

actually no, im still confused

shouldnt we have an X^2 then?

at least according to the formula

unless the mean and variance switch places

there was a switcheroo at some point in my notes

thank you riemann

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[plush egret]

glad i caught that before the exam lol

my cheat sheet makes no sense

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[unborn flicker]

I need help

[unborn flicker]

<@&286206848099549185>

[kind jay]

dont ping helpers right away

[unborn flicker]

ok

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[atomic blade]

Draw a line of best fit

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[harsh meteor]

Hello, I didn't really understand how they solved this one

[harsh meteor]

my solution is here

[low bloom]

$sin^2x$ doesn't mean $sin^2 \times x$

[glossy valve]

Swas.py

[low bloom]

so you can't use the product rule

$sin^2x$ means $(sin(x))^2$

[glossy valve]

Swas.py

[harsh meteor]

I thought it was $sin^2x*(x^2+2)$

[glossy valve]

InactiveBella

[low bloom]

no, sin^2 is never written by itself

[harsh meteor]

So I don't have to do anything with "(x^2+2)"?

[low bloom]

there needs to a be an argument to the function

[low bloom]

you do, you have to apply the chain rule

[harsh meteor]

Thank you so much for the help!

I think I understood what to do

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[fresh brook]

I am confused since I got the wrong asnwer

correct asnwer is7499

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[undone harness]

Hi, i have to find every solution in complex that satisfies the condition. can anyone help me

[fresh brook]

-(z^2+1) = 0

(z^2+1)=0

absolute just means it can be either positive or negative

[boreal stump]

not for complex numbers

[light sonnet]

There is one complex solution I can think of

[boreal stump]

i meant this is not true for complex numbers

[burnt pendant]

means 0 distance from origin on complex plain

so just the origin

z^2 + 1 = 0 + 0i = 0

[undone harness]

but i need to have 2 solutions right?

[burnt pendant]

there are two solutions to z^2 + 1 = 0

you're solving for z not for z^2 + 1

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[tall lagoon]

I'm trying to decode a game formula that links between:
Base stats
Level
Rank
I do not know what to do next and the values seem to be rounded to the nearest integer as there are some oddities around

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@tall lagoon Has your question been resolved?

[tall lagoon]

<@&286206848099549185>

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[twin ember]

😢

[gritty rose]

https://jwcn-eurasipjournals.springeropen.com/articles/10.1186/1687-1499-2014-95

Where did you hear the phrase from

[twin ember]

thanks!

[gritty rose]

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[faint wind]

This is my working out for it so far, but I dont know how to connect it back to n+1

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@faint wind Has your question been resolved?

[faint wind]

<@&286206848099549185>

[faint wind]

Then ig you can do this but idk what this means

<@&286206848099549185>

[faint wind]

I think I have it...?

So you have this

and any value n is, the term will always be n+1 terms bc it follows the same principle as parcel's triangle

I think I have it

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[severe basin]

,tex If two numbers when divided by a certain divisor give remainder 35 and 30 respectively and when their sum is divided by the same divisor, the remainder is 20, then the divisor is

[glossy valve]

QuantumBee

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[edgy lily]

Can someone help me solve this disequation?

[edgy lily]

$e^{2x}+2e^x-8\le 0$

[glossy valve]

Lyuka

[edgy lily]

i put this disequation on symbolab but i dont understand how he factors it

and finds log

[hearty ferry]

try looking at the LHS as a quadratic

maybe substituting u = e^x is better?

[edgy lily]

Wow thats smart

But when i get $U \le -4 and U \le 2$

[glossy valve]

Lyuka

[edgy lily]

what do i do?

i change it back to U=e^x

[hearty ferry]

so when you factor, you have (u+4)(u-2) <= 0

which means -4 <= u <= 2

[edgy lily]

Yes

[hearty ferry]

now you change back to e^x

[edgy lily]

yes, how can i solve $e^x \le -4 $for example

[hearty ferry]

e^x is always positive so it would never be <= -4

(for real x)

[edgy lily]

you are right

but how do i get ln2 from $e^x \le 2$

[glossy valve]

Lyuka

[cold tangle]

Take the ln of both sides

[hearty ferry]

^

[edgy lily]

thank you guys

.cloise

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[vapid geyser]

what do they mean by use induction on structure

but proofs for prop 2.1.19 and 2.1.20 i

but I can do ii

given i.)

<@&286206848099549185>

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[restive barn]

how do you solve the equation $x^2 - 9x^(-2) = -1/8$ ?

[glossy valve]

Synoxa

[restive barn]

bruh idk how to use this

[wanton turret]

multiply 8

both sides

[restive barn]

yea did that but

how do i get rid of that ^-2

[wanton turret]

multiply x²

[restive barn]

multiply both sides by x^2 ?

[wanton turret]

yez

[restive barn]

so you get 8x^4 - 72 = -1

[wanton turret]

both sides

[restive barn]

ohhhh

yeah forgor

💀

[latent perch]

(8x^4-72+x^2)/8x^2

[restive barn]

where did the 8x^2 come from

i currently have 8x^4 + x^2 - 72 = 0

[wanton turret]

yeah factor

[latent perch]

its the same, because its =0 and you go to your current state

[shy tide]

multiply both sides by 8 to get rid of -1/8
8 * x^2 -9x^-2 = -1/8 * 8
8x^2 - 72x^-2 = -1
multiply both sides to get ride of x^-2
x^2 * 8x^2 - 72x^2 = -1 * x^2
final answer?
8x^4 - 72 = -x^2

[restive barn]

never mind

i did the steps before getting this eqn wrong

made it harder for myself

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[torn jolt]

hello

[clear ermine]

hi

[torn jolt]

how do i find Ef

[clear ermine]

Idk sorry

[light sonnet]

You provided nothing

[clear ermine]

Thanks, I was scared to ask it lmao

[torn jolt]

no. 18

i need to find Ef

@light sonnet

[light sonnet]

One don't ping me

Two, there is not Ef listed

Your question does not make any sense

[torn jolt]

Df and Ef?

do u know what those are?

[light sonnet]

There is no Df or Ef

What are you referring to?

[wise wyvern]

Can you translate what your original question says?

[torn jolt]

idk what the thing is called in english

[wise wyvern]

What language is this?

[torn jolt]

but we write it as Ef

[torn jolt]

lithuanian

[wise wyvern]

It's range.

You have to find the values of f(x) right?

For all possible x values.

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[viral oriole]

hello, how can i demonstrate that: for α ∈ ℕ, x ∈ ℝ : α⌊x⌋ ≤⌊αx⌋

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[burnt pendant]

i like floor(x) <= floor(ax)/a better
anyway, consider the interval (z ∈ Z) z <= x < z + 1
on this interval, floor(x) = z.
on this interval also, floor(ax)/a has initial value z and is not decreasing (x1 < x2 implies f(x1) <= f(x2))
since it’s not decreasing, it will never be less than z on this interval.
thus, floor(x) < floor(ax)/a on this interval
since this interval works for all integers z, and since all integers z for intervals make up all real numbers, this works for all real numbers

@viral oriole

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[sweet void]

So when integrating a trig function, do I multiply or divide by the integral or derivative of the inner function ?

[sweet void]

Like I’ve done the substitution and have the integral of cos(u), what would the integral of that be? I know it becomes sin(u) but like do I multiply or divide by the derivative or integral of u?

[deft tulip]

you can't really think of chain ruling the same way you do when you take a derivative

[sweet void]

So what do then?

[deft tulip]

do you have an example problem?

[vernal ice]

for just 1 trig function, you divide by the derivative if you think about integration as reverse differentiation afaik.
If i had sin(2x), its derivative would be 2cos(2x), you're multiplying by the derivative inside the brackets.
So going backwards you will divide by the derivative

[sweet void]

So would it be 3x^2sin(u)?

I’m confused because these answers don’t match that

[deft tulip]

the u substitution itself took care of the "inside function"

thats what replacing the dx with the du does

[sweet void]

I know

[deft tulip]

so youre getting $\frac{1}{3}\sin(x^3)+C$

[glossy valve]

Sooshon

[deft tulip]

if you go back and replace the u with x^3

[sweet void]

Oh okay

I get it

[deft tulip]

how did you end up with an 3x^2 in the denominator therer at the end?

[sweet void]

I thought you said divide by the derivative of inside

[deft tulip]

he meant that if you were just doing that in your head without doing the u substitution

in your case the u sub takes care of that

[sweet void]

Okay

Thanks

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[deft tulip]

stick to u sub until it becomes more automatic when you have $\int \cos u,du$ then its just sin u + C, simple

[glossy valve]

Sooshon

[deft tulip]

and doesnt matter what the original x expression is

[vernal ice]

you are still dividing by the derivative, but because it's du, you divide by the derivative of u which is just 1

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[dim wolf]

Not sure what it means by rule, but do you know composition of functions?

[torn jolt]

yes

[dim wolf]

So basically you are putting f into h for the variable in h. Its kinda hard to explain without giving the answer. Give it your best shot first

[torn jolt]

ok

[torn jolt]

i got 3x-4

but that is wrong

[dim wolf]

How did you get that. We’ll walk through it

[torn jolt]

well i did

h(f(x)) = h(x-7) then i combined like terms with h

[dim wolf]

The step of doing h(x-7) is correct so if so you plug that in you get 2(x-7) + 3

[torn jolt]

oh thats how u do it

so 2x-11

[torn jolt]

How would I do it opposite

?

as in

[dim wolf]

Yup

[torn jolt]

f(h(x))

[dim wolf]

So h(x) = 2x+3. So plug that in and get f(2x+3)

Then I’ll let you do the rest

[torn jolt]

ye thats what i got to

alright hmm

would it be

2(x-7)+3

[dim wolf]

So take f(x) = x-7. When we want to do f(2x+3). You put the (2x+3) where x is above

That make sense?

[torn jolt]

not really

[dim wolf]

Look at what we did in the last example its the same concept

[torn jolt]

(2x+3)-7?

[dim wolf]

Bingo

[torn jolt]

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[bitter yacht]

If X ~ Bin(16,0.4) what is the mean of X?

[plush egret]

,w mean of a binomial distribution

[glossy valve]

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[plush egret]

,w binomial distribution

[glossy valve]

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[plush egret]

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[mortal musk]

Quick question, can we make the assumption in purple based on the two statements in black?

[mortal musk]

I know that for intervals that are added we can add the two "extremities" together but I'm not sure how to handle a minus for intervals

Thanks

[swift shore]

not correct

[formal plover]

this

[deft tulip]

well if $y\in[\frac{-\pi}{2},0]$ then $-y\in[0, \frac{\pi}{2}]$

[glossy valve]

Sooshon

[swift shore]

basically for the lower bound, find the minimum of 2x and -y and add them together, same for the upper bound

[swift shore]

this

[formal plover]

also this

[mortal musk]

Okay, I see

So we basically just convert the angle into a negative

and then add those two intervals together

so it's [0,pi]

[glossy valve]

Sooshon

[mortal musk]

so $2x+(-y) \in [0,\pi]$

[glossy valve]

rice

[mortal musk]

thank you so much that makes a lot of sense

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[mortal musk]

Wait another stupid question but I just want to be sure, I have $y \in [- \frac \pi 2, \frac \pi 2]$, so -y is also in $[- \frac \pi 2, \frac \pi 2]$?

[glossy valve]

rice

[mortal musk]

ok thank u a bunch!!

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[storm trellis]

Can someone please explain how to do this?

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[storm trellis]

<@&286206848099549185>

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[rigid belfry]

Yoo uhh does the answer here come out to 17.65?

[civic surge]

use a calculator dude

even I don't know the value for it

[rigid belfry]

no I meant yea on ur calculator

its cus idk if I misinputted smthng or am I seeing things

2 hrs ago it came out as 17.65

but now it comes out as 72.35

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[rigid scaffold]

Hello. here is a high school statistics-probability problem (hypothesis testing). is this a typo (see bolded text) or can I really use a 0.05 level of confidence to compute for the critical value?

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[stone phoenix]

z

@everyone

[rigid scaffold]

<@&286206848099549185>

[candid ice]

You can. A 0.05 level of confidence means a 5% level of confidence

They probably phrased it wrong, and meant 5% level of significance

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@wicked shore Has your question been resolved?

[wicked shore]

someone pls help

[wicked shore]

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[simple palm]

.reopen

can anyone explain me why 6^0 is equal to 1

[static leaf]

#❓how-to-get-help delete ur message

[static leaf]

so 6^2 = 6 * 6

so 6^1 = 6

so 6^0 = 6/6

so 6^-1 = 6/6/6

[latent perch]

6^0=6^1*6^-1=6^1/6^1=1

[static leaf]

and so on

[simple palm]

what

i dontunderstand

[latent perch]

6^0

[simple palm]

what do you mean by 6/6

[latent perch]

6^0=6^1*6^-1= 6^1
----- = 1
6^1

[simple palm]

let me say it again

so 6^2 is gonna be two six

and 6^1 is gonna be only one six

but why did 6^0 became 1

is it almost the same with every number?

[latent perch]

i just explained

[simple palm]

like for example

2329842407^0 = 1

[latent perch]

every number to the power of zero is 1

yes

[simple palm]

i didnt understand it

ok

thx

[latent perch]

anything else?

[simple palm]

no but i will ask again if im confused later

[latent perch]

okay

[static leaf]

6 divided by 6

[simple palm]

OHHHHHHHHHHHHHHHHHHHHHHHHHHHAHhh

sry caps

[errant abyss]

a^0=1

[simple palm]

ok im confused at another question

wait lemme send cuz i cant type it

[static leaf]

👍

[simple palm]

Ok can u tell me how to workout the evaluate question

Is it 3^4????

[errant abyss]

$x^{n}\dotx^{n_1}=x^{n+n_1}$

[simple palm]

no please im not in that level

[errant abyss]

Not related

[simple palm]

twthat im confused

[errant abyss]

Disregard

Ok

3*2^9/2^6

You see the 2^9/2^6

?

[simple palm]

WBAT

what

[errant abyss]

9 and 6

[simple palm]

dude what are you even saying

i dont understand

[errant abyss]

Ok

[simple palm]

;;-;

[glossy valve]

aol

[simple palm]

no look at the pic i send again

wait gimme a se

c

Here

This is what I see

[errant abyss]

You can break it into $\frac{3}{1}*\frac{2^9}{2^6}$

[glossy valve]

aol

[errant abyss]

So

[simple palm]

is it cuz when theres nothing it means theres an 1?

[errant abyss]

Yes

[simple palm]

ok tell me what i do after

[errant abyss]

Ok, using what you must have learnt

You subtract 6 from 9

[simple palm]

Ywes

[errant abyss]

$\frac{2^9}{2^6}=\frac{2^3}{1}$

[glossy valve]

aol

[errant abyss]

$2^3=222=8$

[simple palm]

Why

[glossy valve]

aol

[errant abyss]

What why

Oh

[simple palm]

The

[errant abyss]

$\frac{2^9}{2^6}=\frac{2^{9-6}}{2^{6-6}}$

[glossy valve]

aol

[simple palm]

your not an native speaker right?

[errant abyss]

Yes

Why

[simple palm]

dude i feel like im talking to siri

but only will see 1 word

[errant abyss]

No im just bad at explaining

[simple palm]

yes maybe i should just ask my tr tmr

[placid cypress]

maybe you should get some bitches

[errant abyss]

stop

[simple palm]

can you help me?

[surreal trail]

Gottem

[simple palm]

or are you a trol

[surreal trail]

Do you know that x^a/x^b = x^(a-b)?

[simple palm]

yes

[surreal trail]

Perfect

Here

X=2

[simple palm]

/ is divide right?

[surreal trail]

Indeed

[simple palm]

ok

[surreal trail]

So can you simply the fraction for me

Using that fact

[simple palm]

wh

a

t

[surreal trail]

2^9/2^6

Right?

[placid cypress]

damn you guys have some patience

is this guy actually serious (in which case im sorry)

[errant abyss]

whats the number 9 and 6 called im just not english

[kind jay]

good luck being a math teacher

[surreal trail]

You’re not helping. Get out.

[kind jay]

exponents

[errant abyss]

so how is x^n called

[simple palm]

3 x 2^9 = 6^10

    2^6

2^6 / 6^10 = 3^4 is this correct?

[errant abyss]

No

[errant abyss]

^

[surreal trail]

Use this fact first

[simple palm]

i cant be good at it if i dont understand, im trying my best as i can

[surreal trail]

Don’t worry about him he’s mean

[placid cypress]

im sorry man, i just thought you were trolling because you were calling the other guy siri

we all gotta start somewhere man, no worries :))

[simple palm]

o j/

[surreal trail]

2^9/2^6 =?

[surreal trail]

Using this

[simple palm]

2^3???

[surreal trail]

Good!

[placid cypress]

yeah!

[simple palm]

omomgomgomgomg omogm

[surreal trail]

Lol

And what’s 2^3?

[simple palm]

what

[placid cypress]

you got to read 2^3 as (222)

[simple palm]

o

8????

[placid cypress]

2 times 2 times 2

[surreal trail]

Good!

[simple palm]

ok

[placid cypress]

Yeah exactly

[surreal trail]

And finally 3*8=

[simple palm]

• is multiply?

[surreal trail]

Yea

[placid cypress]

Yeah

[simple palm]

24

the answer is 24??

[placid cypress]

SIIIIIUUUU

[surreal trail]

Yup

[placid cypress]

Nice work!

[placid cypress]

There are 3 symbols that can be used for multiply: * x and a dot

so 2x3 is 6

2*3 is 6

And a dot is only used on paper

[simple palm]

Ok so let me say it again, first i have to divide 2^9 and 2^6 which is 2^3 then i have to multiply 2 three times which is 8 then multiply it with 3???

[kind jay]

never usd a dot nor seen someone using a dot lol

[placid cypress]

exactly!

You got the hang of it man, good stuff

[simple palm]

omgromgomggomgomg ththhanksss and on god i have to sleep now welp bbyeeeee

/ropen

,open

.rope

.ropen

.reopen

[errant abyss]

its

[simple palm]

i mena.

.clsoe

[gritty rose]

.close is what you want

[simple palm]

bruh i am gonna faint anymoment

.close

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[pine shard]

hello guys i have a question regarding this defferential

[pine shard]

do i integrate both sides and then solve it as a first order one ?

[cloud shore]

yes

[pine shard]

ok thank you

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[thorny anvil]

Is the equation "5 + 300% correct? Is it the same as 5 + (5 * 300%)?

[gritty rose]

yes

[thorny anvil]

Thanks.

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[brittle rune]

Why this is true?

[kind cypress]

Well, let's study a simpler case first, and we'll see that it's all we need to get the general rule

Let's consider 1/(1/x) for nonzero x

1/x is the answer to the question "if a cake is evenly split between x people, what proportion of the cake does each person get?"

Or equivalently and more generally, "what is the number i need to multiply by x in order to get 1?"

Indeed, x*1/x = x/x = 1

So then 1/(1/x) is the number you need to multiply by 1/x in order to get 1

But notice, x*1/x is still equal to 1

So 1/(1/x) = x

[brittle rune]

Ok let me now see it

[kind cypress]

From here, we can just use the fact that $\frac{xy}{zw} = \frac{x}{y}\frac{z}{w}$ (that notation is convenient for a reason)

[glossy valve]

Syst3ms

[kind cypress]

So we get $\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a\frac1{b}}{c\frac1{d}} = \frac{a}{c}\frac1{b}\frac1{\frac1{d}} = \frac{a}{c}\frac1{b}d = \frac{a}{c}\frac{d}{b} = \frac{ad}{bc}$

[glossy valve]

Syst3ms

[kind cypress]

it's okay if this isn't obvious, you're learning, and you get this down by being used to it

[brittle rune]

Oh wow that's nice way to think awesome thx for helping

[kind cypress]

Honestly, as long as you remember 1/(1/x) = x, you can derive the rest from classic manipulations

[brittle rune]

Ok

What does an angle mean. I know that how it used in various ways but I never had feel about what 1 degree actually means like you have feel of what does walking 1km or 1 mile is.

[kind cypress]

if you consider a circle of radius 1, then 1 degree is 1/360th of the circumference of that circle

In mathematics, angles are formally defined on a circle (of radius 1) by the length of the circlde they take up

https://usercontent1.hubstatic.com/14049118_f520.jpg

[brittle rune]

Ohk

[kind cypress]

If you take R=1, then the angle is a certain multiple of that arc length

This is why in mathematics we typically use radians instead of degrees

Because they lend themselves very nicely to a circle description like this

In radians, the angle is the arc length, no multiples involved

So a 180° angle is half of the circle, that is an arc length of π

Thus 180° = π radians

As for why degrees are nice, it's because 360 can be divided by a lot of things, so it's easier to talk about fractions

[brittle rune]

Yeah that's right

[kind cypress]

(also sorry, I don't take friend requests for this)

[brittle rune]

Ok fine I'm just new to the discord I don't know what to do and not to just trying to learn

[kind cypress]

make sure to close the channel when you're done

you can reopen one later if you need to

(also check out #❓how-to-get-help )

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[hoary briar]

My question is for part b specifically, as I know that the probability of at least two shifts will be represented is 1 - ( (10 choose 4) + (8 choose 4) + (7 choose 4))/(25 choose 4))
~ 0.975

[hoary briar]

I am not sure what exactly they are asking for when they say unrepresented

I tried to take the union of all events but since they are mutually exclusive I dont know what to do

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[brittle rune]

.close

[hoary briar]

.close

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[junior edge]

Confused on what I did wrong,
9-3/24 = 6/24 = intervals of 1/4

[junior edge]

What did I mess up on? Thank you in advance!

Nevermind! I have discovered what I did wrong

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[hearty ice]

Can someone explain the part where they say hitting perpendicular to the edge of the cliff?

Im not sure what that means and how it would be drawn in the picture

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@hearty ice Has your question been resolved?

[hearty ice]

<@&286206848099549185>

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@hearty ice Has your question been resolved?

[soft pier]

I think its meaning that the direction of the ball is relative to the plane of the golfers feet

[hearty ice]

What do you mean by relative to the plane?

[soft pier]

So the cliff edge makes a 90 degree angle

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[hearty ice]

Thank you

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[red surge]

Hi.
How is the box true?
Can you write a logarithm as a summation?

[torn jolt]

ya

$log(ab)=log(a)+log(b)$

[glossy valve]

Pi Creature

[torn jolt]

and $100!=1009998*...*1$

[glossy valve]

Pi Creature

[torn jolt]

so ya

[red surge]

But each you are multiplying numbers not adding?

Each time

[torn jolt]

$log(1009998*...*1)=log(100)+log(99)+log(98)+...+log(1)$

[glossy valve]

Pi Creature

[torn jolt]

which they wrote as a summation

[red surge]

OH I see it now

Thanks

.closr

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[hexed hare]

Need the answer for this if anyone can DM me or something

<@&286206848099549185>

[shadow parcel]

• After 15 minutes, feel free to ping <@&286206848099549185>.

is that a test? @hexed hare

[hexed hare]

Review

[static leaf]

🤨

[hexed hare]

It’s a review but I’m stuck on the same question for the past 10 minutes

@shadow parcel

[shadow parcel]

i believe the x^4 terms must cancel to become a quadratic

i recommend you foil the righthand side

[hexed hare]

How do I do that

[shadow parcel]

i mean expand

using the FOIL method

[hexed hare]

Idk how to use the foil method

[shadow parcel]

it stands for First Outer Inner Last

tells you how to properly expand an expression in the form (a+b)(c+d) = ac + ad + bc + bd

cus its true

(a+b)(c+d) = a(c+d) + b(c+d) = ac + ad + bc + bd

[errant abyss]

ahhhh i hate that i msut relearn math just because of language

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[static bolt]

hello

[static bolt]

i have a problem

Idk how to continue my homework from this: The two opposite sides of the parallelepiped meadow are 550m and the area is 23.1ha. Find the distance between these sides.

1. 23.1ha=231000(m2)

2. Height: h=S:a=231000:550=420(m)

I just google translated the text idk if it makes sense

this is how the square looks like

I didn't have to actually draw it but idk what's it called in english

idk how to find the other two sides I'm confused

<@&286206848099549185>

[tired quarry]

you can't, but the question doesn't ask for it

[static bolt]

Do I just write the height as an answer then?

[tired quarry]

yes, it's the distance between those sides

[static bolt]

okay thank you

I will just write that

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[hushed spear]

You can use heron's formula

Though I'm guessing that's not what is expected

[errant abyss]

use herons formula

[hollow egret]

https://cdn.discordapp.com/attachments/756558609806000139/972367307160563732/Fish_yodel.mp4 fish

[errant abyss]

Xd

180-120=60

[hushed spear]

It tells you the area of a triangle given its 3 sides

[
A = \sqrt{s(s-a)(s-b)(s-c)}
]
where $a$, $b$, and $c$ are the sides of the triangle and $s = \frac{a + b + c}{2}$

[glossy valve]

castroploiin

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[rare otter]

how do i write this ellipse equation in standard form?

[swift shore]

divide by 25*9 on both sides

[rare otter]

25 times 9? and not 25 + 9?

:<

[swift shore]

times

[rare otter]

ok!

i dont really get what to do from here

is the 1 supposed to end up as .004?

[swift shore]

oh wait im stupid

ok, forget what i said

[rare otter]

alrighty!

[swift shore]

do you agree that $\frac{x^2}{1/25}=25x^2$

[glossy valve]

R31_

[rare otter]

um
im not sure?

i mean if thats right then yes

[swift shore]

ok here look $25x^2=\frac{25x^2}{1}=\frac{\frac{1}{25}25x^2}{\frac{1}{25}1}=\frac{x^2}{\frac{1}{25}}=\frac{x^2}{\left(\frac{1}{5}\right)^2}$

[glossy valve]

R31_