help-36

[light violet]

so im a bit confused for that

because its upper

wait

i thought 5 was the upper

i think

but im not 100% sure

so upper is teh vlue that

p>=upper

is less than 0.025

[tulip coyote]

5's the lower, cause that's at the "bottom half"

[light violet]

ohhhh

i see

like on the graph

so now so i want

px>= upper

and that should be o.o25

but after that idk how to get the typ1 error

is ti 13?

i put x for the 'lower' bit i nmy calculator

idk if thats done x>13 or x<13

[tulip coyote]

Well, remember that you want P(X >= u) < 0.025, you can equivalently state that as P(X <= u - 1) > 0.975, and use the calculator for that one

[light violet]

ahh i see

but what i dont know

is if chagning from upper to lower flipped the sign

i thin it did

because when i put in 5

it now gives 1-my probability

0123619ive now got p x=<17 = 0

what do i do for the type 1 error

[tulip coyote]

For the type 1 error, that's the probability you "falsely convict", so you reject the null hypothesis but it's true, for which, add the probabilities of being in each critical region "tail"

[light violet]

im sorry but ive teried to udnerstand this and i dont know how i can relate my numbers to this

like im adding them

but i dont see why

[tulip coyote]

Because those are the probabilities that you're in each critical region "tail"

You want to know what the actual probability of being in those tails are, assuming the null hypothesis of p = 0.35 is true (as that's the probability that you observe a value that makes you reject the null hypothesis, possibly incorrectly)

[light violet]

hmm so

i add them

because they are the probabilities that i could incorrectly reject H0

so there being a probability of an type 1 error

dosent mean there is a type 1 error for sure

thank you 🔥

that explanation was great

(ps i love the cat gifs)

[tulip coyote]

Yep, not necessarily, the idea for rejecting the null hypothesis is that "you find a result so unlikely, it's probably not even true", but there is the possibility that it's true

[light violet]

i see

have a nice day

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[grand niche]

can anyone help me with 6?

[grand niche]

i dont really know the formulas and stuff here :c

[autumn geode]

Hmm

Let’s focus on one problem

And let’s see what we can get done

[grand niche]

sure

like 6?

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@grand niche Has your question been resolved?

[grand niche]

anyone? :c

[grand niche]

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[stray tapir]

So i'm trying to join a sine graph smoothly to the graph of f(x) =0.5(x-1)(x+1) for x<1 at the point (1,0) . I differentiated f'(x) which equaled x and subbed in the x value for the gradient at that point which was 1. So the requirement for the graph of sine would be that at (1,0) it has to have a gradient of 1, however i dont know where to go from there?

[worldly vale]

Did you miss out part of the equation? (x+)

[stray tapir]

oh yeah my bad

there we go

im thinking that i differentiate the general formula of sine and make that equal to 1

[worldly vale]

Sure yeah you want to find some point of sin(x) that has derivative 1

[stray tapir]

so for a simplified general formula it would be g(x) = aSin(bx) with a and b being variables?

[worldly vale]

Well maybe just see if sin(x) itself has any point with derivative 1 first

[stray tapir]

ohh okay

g'(x) = cos(x)

1 = cos(x)

do i do inverse cos here

[worldly vale]

Well you can just think of the graph of cos

And where it equals 1

[stray tapir]

oh 😭

at 0 and pi

OH

[worldly vale]

Yeah (and infinitely many more), but we only need one, so 0 seems like a good pick

[stray tapir]

OHHHHH

so i just have to shift the graph to the right

[worldly vale]

Yep, by how much?

[stray tapir]

1?

[worldly vale]

Nice

[stray tapir]

idk why i overthought abt it so much

ahhhh

[worldly vale]

Your general strategy with asin(bx) is good, it just wasn't needed in this case

[stray tapir]

yes i see now thank you very much

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[warm python]

so just A is right here, right?

sorry

A,B and D

as

oo

[trail mango]

you think A is true?

[warm python]

now that I examine it carefully

now

[atomic coral]

the answer is B

[warm python]

*no

[trail mango]

!nosols

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[atomic coral]

{1,{1,2},{1,2,3}} \ {1,2,3} --------------> {1,{1,2}}

[warm python]

yes

and {1,2,3} \ {2,3}---> {1}

[trail mango]

blud...

no

[atomic coral]

A is wrong since {1,2} U {1} --------> {1,2,1} which is not C S

[silver maple]

that is for multisets

[warm python]

{1,2}u{1}= {1,2}

[silver maple]

We are working with sets

[trail mango]

just for the record this isn't right

[warm python]

why isn't B right

[silver maple]

B is correct

[trail mango]

it is not

[silver maple]

But it isn't the only answer

[trail mango]

S\{1,2,3} is S with the elements 1 2 and 3 removed

not S with the set {1,2,3} removed

[warm python]

isn't S \ {1,23}= S-{1,2,3}

[silver maple]

Ah I see, I missed that detail

[worldly vale]

it is not S \ {{1,2,3}}

[warm python]

ah

ok

oh, so C isn't right either

[atomic coral]

then C is the answer

[polar gale]

only C is right

[warm python]

but that would be {{1,23},{1,2}}

[atomic coral]

{1,2,3} U {1,2} = {1,2,3} and its in S

[atomic coral]

its a set

[polar gale]

no

that's not how union works

you add all elements from both sets into one set

so you put 1, 2, 3 and 1, 2 into one set, which means you just get a set with 1, 2, 3

[warm python]

ah yeah

my bad

got it

thanks

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[ancient basalt]

this means that we are differentiating dy/dx multiplied by itself right

[ancient basalt]

like

we are doing the same differentiation twice?

[humble swift]

yes

we are differentiating the function twice

"double differentiation"

[ancient basalt]

with the same variables right

[humble swift]

for example take x^2

[humble swift]

dy/dx is 2x

s^2y/dx^2 is 2

thts it

[ancient basalt]

like over here we just put the value of y and differentiate where x is the variable right

[humble swift]

combine parametrics into one equation

[ancient basalt]

twice

[ancient basalt]

i didnt understand ;-;

[humble swift]

find t from y=2at

wht is it?

[ancient basalt]

y/2a

[humble swift]

yes put that in x=at^2

[ancient basalt]

oh

[ancient basalt]

then i differentiate this twice?

[humble swift]

yep

[ancient basalt]

oh alr

lemme try it wait

[humble swift]

ok

[ancient basalt]

I don't understand 😭

[ancient basalt]

I know it's completely wrong 😭

But like

How to do it then

[humble swift]

dude chill

what is dy/dx?

[humble swift]

it is y^2 = 4ax not 40x

[ancient basalt]

Oh 💀

[humble swift]

...

[ancient basalt]

We will put y and differentiate it with x as the variable

[humble swift]

no like solve for dy/dx

and tell me wht u got

[ancient basalt]

Okay

[humble swift]

yes diff again

[ancient basalt]

ohhhhh

ok wait

I GOT THE CORRECT ANS

TYSM

[humble swift]

No problem!

[ancient basalt]

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[odd escarp]

Im trying to find the total equivalent resistance to this question as part of my homework

but I keep getting different answers

is 1203 correct?

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[odd escarp]

@spring depot

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[oblique moat]

How do i know which is which

same with like this question

<@&286206848099549185>

[sinful flume]

what do you mean

??

[oblique moat]

how do i know if its oscillation and not

or the type of damping

[oblique moat]

.

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[oblique moat]

<@&286206848099549185>

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@oblique moat Has your question been resolved?

[oblique moat]

<@&286206848099549185>

[livid carbon]

you sure the correct answer is option c ?

[oblique moat]

yeah thats the makr scheme

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[atomic fern]

hi! i need a bit of help, i wanna know what i did wrong here. this is systems of equations btw
i consulted a few apps (because i absolutely did not understand my teacher) and they said x=3, and i wanna figure out how they did that

[tardy vortex]

you forgot a -1

in the third last step

[atomic fern]

where can i put that?

[tardy vortex]

this bit

when you expand the bracket

youve missed out -1

-(-2x+1) = 2x-1

that last -1 is missing

[atomic fern]

ok icic ima try :3

[tardy vortex]

yh

[atomic fern]

i got it!!! thank you !!

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[modern onyx]

How do i calculate this limit?

[solar glade]

Show your work

[modern onyx]

i got nothing... im stuck

[runic needle]

perhaps consider different paths to approaching zero

[modern onyx]

it comes nothing to my mind

that is why i went to get help

any tips?

[runic needle]

i mean actual paths to the point (0,0)

if the limit exists the limit along any path must be the same

[modern onyx]

but it gives 0/0

[runic needle]

which path?

[modern onyx]

first one

if u sub the x and y with 0

[runic needle]

that's not path

[modern onyx]

wdym path

[runic needle]

i mean like u start somewhere close and approach that point

like $\lim_{t\to 0} f(t,0)$

[soft zealot]

mayer-vietorUs

[modern onyx]

oh so not subing both x and y

[runic needle]

yes

[modern onyx]

one at a time

[runic needle]

or $\lim_{t\to 0} f(t,t^2)$

[soft zealot]

mayer-vietorUs

[modern onyx]

hmm

lemme do and send it to you

@runic needle

like this?

[runic needle]

yes

[modern onyx]

the exercice says "calculate if exists"

what do i say

[runic needle]

if it did exists u would get the same answer for both paths

so it doesn't exist

[modern onyx]

ohh

wow is that simple?

[runic needle]

yep

[modern onyx]

this is university exam level

im suspicious

[runic needle]

www.math3d.org

maybe plot it to convice urself

[modern onyx]

i have another question

how do i study the continuity of this limit?

or i already did

[runic needle]

wdym continuity of the limit

limit dne

[modern onyx]

i translated it

Let f : Df ⊆ R2 → R and (a, b) ∈ R2 be an accumulation point of Df .
The function f is said to be continuous at point (a, b) if and only if they are verified
the following three conditions:
— there is the image f (a, b), that is, (a, b) ∈ Df ;
— there is the limit lim(x,y)→(a,b) f (x, y);
— the guaranteed elements in i are equal. and ii., i.e.

that is supposed to be Continuity

i dont know if it has a different name in English ..

[runic needle]

yeah basically if the limit equals f(0,0) then it's continuous

but limit dne

[modern onyx]

limit dne is the same as continuous?

[runic needle]

does not exist

[modern onyx]

i saw the solutions of the exam it says that the limit doesnt exist but is continuous in R^2 \ {(0,0)}

[runic needle]

yeah that's true

but it's not continous at (0,0)

because $ \lim_{(x,y) \to (0,0)} f(x,y) $ doesn't exist

bruh

[modern onyx]

then why it says its continuous

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[thin leaf]

how do i do # 3

[thin leaf]

and # 4

this is actually driving me mad

book says answer is 16/25 for both

i just dont get how

[waxen loom]

does anyone understand this ??

[thin leaf]

ace

dude

go to #help-18

@waxen loom

[waxen loom]

a

[thin leaf]

bro im already occupying this channel

[waxen loom]

SORRY

[thin leaf]

k? can you like delete your messages or sum?

[fathom walrus]

@thin leaf what have u tried for 3

just send the problem again

[thin leaf]

here

i've tried adding and multiplying fractions

grouping them and doing other stuff

to no avail

i have absolutely no clue what im supposed to do

[fathom walrus]

so we want the probability that we get a different color on each of the 2 spins

[thin leaf]

yes

[fathom walrus]

list out all of the possibilities that we can land on for 2 spins

[thin leaf]

like in a sample space?

a spin?

[fathom walrus]

like for example

(b,g) , (y, b)

like that

[thin leaf]

alr

one sec

it's just 6?

BG,GB,GY,YG,YB,BY

those are all the combinations??

[fathom walrus]

no, ur missing some

think about it

[thin leaf]

am i tripping

[fathom walrus]

all of those are right, but ur missing 3 of them

[thin leaf]

GG,BB,YY?

[fathom walrus]

correct

[thin leaf]

i thought we couldn't have same colors?

it says different colors

[fathom walrus]

oh shoot u right sorry

[thin leaf]

right

[fathom walrus]

so yes this

[thin leaf]

so

that turns out to be 6/25?

or something

idk

book says 16/25 is correct answer

idk how to get there though

[fathom walrus]

did u calculate each of them individually

whats the probability of BG

[thin leaf]

2/10

= 1/5

[fathom walrus]

no

[thin leaf]

isn't it 2/5 * 1/5

[fathom walrus]

whats the probability of B

[fathom walrus]

yes

[thin leaf]

ooooh

2/25

srry i added

right so 2/25

[fathom walrus]

yes, now do that for rest of them

[thin leaf]

so do i have to do all those combinations and add them together?

or multiply together

[fathom walrus]

what do you predict? all those possibilities, would we add their probabilities or multiply

[thin leaf]

add

because

it turns out to be 16/25

[fathom walrus]

lol correct answer wrong reason

[thin leaf]

💀

wait

lemme count them

alr i got it

so

4 of 2/25

and 2 of 4/25

add em all up

16/25

alright i got that but how is it that # 4 is also 16/25

wouldn't it be 12/25?

[fathom walrus]

what are the possible combinations

[thin leaf]

well

BG,GB,BY,YB

GY and YG are excluded

so that's just 2/25 + 2/25 + 4/25 + 4/25

which adds up to 12/25

[fathom walrus]

ur missing 2 of them

[thin leaf]

wait

BB?

[fathom walrus]

yes BB and BB

[thin leaf]

it can't

because

ill tell you why

[fathom walrus]

oh yea just BB

[thin leaf]

because the final answer in the book is 16/25, and since it's just BB,BG,GB,BY and YB

yeah

so

alright thanks a lot good sir

[fathom walrus]

np

[thin leaf]

i gotta continue grinding my math hw

[fathom walrus]

gl

[thin leaf]

ttyl mb

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[lapis wedge]

How do you get the rhs starting with the lhs

[solar glade]

Using algebra?

[lapis wedge]

yeah

[solar glade]

Add and subtract xy

[lapis wedge]

oh ok thank you

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[hoary hamlet]

i got the answers but idk how to make sure theyre the smallest number

like for q10 i got 4 but the correct answer was 3

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[ruby quarry]

How do you answer this

[ruby quarry]

how do I start going about this question

<@&286206848099549185>

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[vernal cobalt]

hi

[vernal cobalt]

about the graph

i’m confused about integrals like what does this integral even tell me

is it the area from 2 to 1? or like what

i don’t get what it’s telling me

about the graph

[eager saddle]

yes it's the signed area

[tranquil pine]

"area"

[vernal cobalt]

thanks so much

i’m also confused on this

to figure this out do u need to figure out the equation of the graph

and would u do that by finding the 1st and 2nd derivative equations in reverse using the critical points?

like that seems too complicated

or is that the only way bc u need the equation to figure all these things out

except the first one for that u can use y=mx+b but we aren’t doing that rn so i don’t think that’s what ur supposed to do

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[solar glade]

How did you get -4?

Also, you don’t put (+5), only 5

() not needed

-1+5

Like this

[sturdy ocean]

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[slender pewter]

please help

<@&286206848099549185>

[mossy bridge]

Get the points for each corner

For example, (2,6)

Flip those coordinates, so (6,2)

Change sign of the Y coordinate

So (6,-2)

And plot that point

Do so for all the corners @slender pewter

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[void cipher]

I think this will be an easier way to ask my question, I made it using my glorious MS Paint skills

[void cipher]

so far i've been able to solve a few of these kinds of problems, but this one threw me for a loop

and i keep thinking why use 8^2 specifically, why not 9^2 or 10^2?

[hardy tendon]

9^2 doesn't go into it

you're trying to isolate perfect squares

[void cipher]

i thought i was doing that and i wound up with 2^6

sorry ive been at this for hours and my brain is fried

[hardy tendon]

your solution is actually correct by the way, you just typed it in wrong

instead of 2^3 you should have simplified it to 8

both factorisations work

[void cipher]

i see it now

[hardy tendon]

khan academy is rather picky with simplifications

[void cipher]

i can factor it out the way i did, and then like you said just simplify the exponents out (if possible)? so basically if it's an integer, a regular whole number and not a variable, ill just apply the exponent and write that number

so 2 times 2 times 2 times b^3 becomes 8 times b^3

[hardy tendon]

yes

you can't simplify b^3 any further, but you can simplify 2^3

[void cipher]

you are amazing

thank you very, very much

[hardy tendon]

happy to help

[void cipher]

have a wonderful night

.close

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[hushed musk]

Hii i dont understand how to do this

[astral moss]

Maybe try splitting up the cot into sin and cos first?

[hushed musk]

But how would i evaluate theta - pi/2

[astral moss]

Remember from symmetry that sin(theta + pi/2) = cos(theta)

[hushed musk]

Wait what

Why

Then would sin(theta-pi/2) = -cos(theta)?

[astral moss]

Try graphing it and it makes more sense

Or think of the unit circle

If you go to where sine normally starts and do a quarter rotation and start from there instead, you end up overlapping with cos

[astral moss]

And yes this is true

[hushed musk]

Omgg wait i get it now

Its just a phase shift

[astral moss]

Yeah

[hushed musk]

Okk thank you :DDD

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[astral moss]

Your welcome

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[ivory vessel]

A line and a plane is given: [
\begin{cases}
\Delta : \frac{x-2}1=\frac{y-2}1=\frac{z-1}2\
(\alpha):x+y+z-1=0
\end{cases}
]
Let d be the line that belongs to $(\alpha)$, cuts $\Delta$ and the $z$-axis. Find the equation of d

[ivory vessel]

not sure how to approach this

how do i know if 2 line equations cut each other?

[tranquil pine]

Which one is plane

[ivory vessel]

...

[tranquil pine]

Equate all to lambda

[tranquil pine]

Add an extra equal to

To the first equation

And equate it to p

Z=2p+1

y=p+2

X=p+2

[ivory vessel]

ok yeah, convert it into parametric

then? plug it into alpha?

[tranquil pine]

The coordinates are equal at cutting point right

So.... why not

Yea

And find p

[ivory vessel]

delta would cuts alpha at (1, 1, -1)

[tranquil pine]

Wait delta is the plane or line

I learnt this as a vector equation or something

It was long ago

[ivory vessel]

delta is the line, alpha is the plane

[tranquil pine]

Alr

What are u asked

In question

I can't see last part

[ivory vessel]

find the equation of d

[tranquil pine]

Think of a format

Of line equation

[ivory vessel]

$(x, y, z) = (x_0, y_0, z_0) + \lambda(A, B, C)$

[ivory vessel]

yeah sure, whats next

i do know that A + B + C = 0

since it belongs on the plane, the vector (A, B, C) must be perp to the plane's normal vector

[tranquil pine]

Wait... determine intersection point with z axis

[ivory vessel]

x = 0, y = 0, z = lambda is the z-axis yeah?

[tranquil pine]

It's 0,0,1

[ivory vessel]

yeah its the directional vector for the z axis

[tranquil pine]

Putting x=0 and y=0 in x+y+z-1=0

Since line lies on plane

[ivory vessel]

oh i see what you mean now

i got the directional vector of d as (1, 1, -2)

which got the final line eq as

$(x, y, z)=(1, 1, -1) + \lambda(1, 1, -2)$

[tranquil pine]

Go for this

[ivory vessel]

seems to check out

already got it, thanks!

[tranquil pine]

Cool

[ivory vessel]

.close

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[jagged flare]

ABC is a 90 degree triangle with incircle O, if FG=4 and EG=2, find the area of ABC

[jagged flare]

answer choices are
8
27
54
108

[cobalt briar]

afg and abc is similiar

but idk how that would be useful

if cf and ab is parrelel though

[jagged flare]

af??

[cobalt briar]

cfg

[jagged flare]

it is

acf and the point line at the bottom is a rectangle

[cobalt briar]

i found 54

[jagged flare]

how?

[cobalt briar]

im trying to make that

ok i made a mistake

[jagged flare]

i dont understand what the hell im seeing

[cobalt briar]

neither me

im bad at drawing

[cobalt briar]

similiar traingles ş used a lot

i can say that but

the intersection of incricle and line from middle of incircle is 90 degrees

and there is a similiar triangle there

bc angles

im a bad helper

[cobalt briar]

sorry if i was unable

[final saddle]

@jagged flare Has your question been resolved?

[jagged flare]

how do you suddenly conclude that A=54??

[vestal yoke]

He solved it using similar triangle two times

[vestal yoke]

First in these two triangle to find the value of x or radius of incircle

[jagged flare]

then?

[vestal yoke]

Then similar triangle in ABC and CFG to find the side AB

[jagged flare]

x=3 right

[vestal yoke]

Yes

[jagged flare]

what like
3/4=AB/12
AB=9

ah ok

[vestal yoke]

Hmm

[jagged flare]

new question (i have 10 questions to ask lmao)

[vestal yoke]

Ask then, I will help If I can

[jagged flare]

there are 10 boxes arranged in a row, if you can swap a box for a ball (you can do this as many times as you want), but there cant be a ball thats right next to another ball, if there is atleast one ball in the row, how many ways are there to swap the balls

if you want i can skip tbis for now

[cobalt briar]

thanks for clarifiying my stupid answer

[vestal yoke]

It’s ok, it wasn’t stupid

[vestal yoke]

No, I’m trying

We can swap maximum 5 balls

[jagged flare]

i forgot the answer choices but one of them was 2025

i didnt know so i chose that one since my completely innacurate method completely went over the others

the others werent even like 300

[vestal yoke]

We can do like this, the lines are the balls and x values are number of boxes between the balls

[jagged flare]

i have no idea any of the notations are

[jagged flare]

ohh thats smart

[vestal yoke]

And x_2,x_3,x_4,x_5 can’t be 0 as balls can’t be next to each other

[jagged flare]

but, what about cases with less than 5 balls, and what about boxes that are to the left of the first ball

like bobobobobo b=box o=ball

[vestal yoke]

We will do like this for 4,3,2 balls

[jagged flare]

okay

isnt this basically like stars and bars

[vestal yoke]

Stars and bars?

[jagged flare]

nvm

so cases for 5 balls has 2 possibolities right?

[vestal yoke]

6

[vestal yoke]

Here, I subtracted 1 from all those which should be minimum 1 and then used the formula

[jagged flare]

for 4:
x1|y2|y3|y4|x5
since balls take 3, then x1+y2+y3+y4+x5=7
since y>=1 we can say yi=xi+1
x1+x2+x3+x4+x5=4

[jagged flare]

oh yeah

[vestal yoke]

Balls take 4

But yeah you are doing it right except no. of balls

[jagged flare]

so 8c3 right?

56?

[vestal yoke]

No, 7c3

[jagged flare]

${5+4-1}C{4-1}$ no?

[soft zealot]

Skill_Issue

[vestal yoke]

First correct this mistake

[jagged flare]

wdym

oh ywah

sry

x1|y2|y3|x4
x1+x2+x3+x4=4

7C3?

also, isnt it 7c4 instead? for the 4 thing

[vestal yoke]

This is for 3 balls?

[jagged flare]

yeah?

[vestal yoke]

Then x1+y2+y3+x4=7

[jagged flare]

aaa

ok i understand the gist of it but im too lazy, is it fine if we move on

[vestal yoke]

Yes, if you understood then go ahead

[vestal yoke]

!ss

[final saddle]

Please post images (such as PNGs or JPGs) of the question rather than other filetypes such as PDFs which have to be downloaded. Non-image downloads can potentially contain viruses or other security risks.

[jagged flare]

ABC is a triangle that lies in a semicircle with diameter AB, E is a point on AB such that AB=4EB, if ABC=30° and EC=13, what is area BCE

does this work

[vestal yoke]

Now, you can find R and then get the area

You got what I did here

[jagged flare]

uhh

why does area of cbe use the base of the triangle DB?

[vestal yoke]

Oh sorry, I did a mistake there it should be EB

[jagged flare]

and how do i find EB? i know EB=BD-DE but how do i find BD?

nvm

ok i get it

ty

[vestal yoke]

np

[jagged flare]

assume c is a constant where c>0, line l has the equation y=2kx+3k^2, it intersects with parabola y=x^2 at point P which is at quadrant 1 and Q which is at quadrant 2, if point O is on (0,0) and the area of the triangle of POQ is 48, what is the slope of line l?

[vestal yoke]

Where you used c and isn’t line l is y = constant

[jagged flare]

wait

sorry

[vestal yoke]

Oh ok

Find the points where line l cuts the parabola in form of k

Then find area by determinant method

Then solve and get value of 2k which is slope

Got it?

[final saddle]

@jagged flare Has your question been resolved?

[jagged flare]

what is determinant method?

also how do i find points that cut the parabola?

$$y=2kx+3k^2$$
$$y=x^2$$
$$x^2-2kx-3k^2=0$$
$$\frac{2k \pm \sqrt{4k^2+12k^2}}{2}$$
$$\frac{2k \pm 4k}{2}$$
$$x=k \pm 2k$$

like this?

[soft zealot]

Skill_Issue

[vestal yoke]

Yes

[jagged flare]

how do i use it

[final saddle]

@jagged flare Has your question been resolved?

[final saddle]

@jagged flare Has your question been resolved?

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[graceful badger]

helloo

[sharp goblet]

Hii

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[vestal yoke]

@jagged flare if you still have questions you can ask, I was busy today

[ornate knot]

combine the log together

$$log_{0.2} (x^3+8) - 0.5 log_{0.2} (x^2+4x+4) = log_{0.2} (x^3+8) - log_{0.2} (x^2+4x+4)^{0.5}$$

and then simplify further

[soft zealot]

JustToPro

[ornate knot]

$$log_{0.2}\frac{x^3+8}{(x^2+4x+4)^{0.5}}$$

[soft zealot]

JustToPro

[tranquil pine]

(x² + 4x + 4)⁰'⁵ = (x + 2)

[ornate knot]

!help

[final saddle]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[vestal yoke]

.close

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[chrome hemlock]

excuse me

[chrome hemlock]

how do i do this

where do i start

[final saddle]

@chrome hemlock Has your question been resolved?

[chrome hemlock]

GUYS..

<@&286206848099549185>

[final saddle]

@chrome hemlock Has your question been resolved?

[chrome hemlock]

<@&286206848099549185>

[oblique violet]

it's the same as a person swimming againt the flow of the river

he has to swim opposite to the flow at an angle so the relative velocity is in the shortest direction between two coasts

[chrome hemlock]

pardon

[final saddle]

@chrome hemlock Has your question been resolved?

[chrome hemlock]

<@&286206848099549185>

[final saddle]

@chrome hemlock Has your question been resolved?

[wooden lion]

have u drawn it?

[chrome hemlock]

I need help drawing it

[wooden lion]

could be like that?

im actually not sure where y is in relation to x

ok wait ig the 065 has significance

im guessing the waves are moving at 45 degrees

or 135 ig

u have a system of linear eqns then, just solve them

@chrome hemlock

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@chrome hemlock Has your question been resolved?

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@chrome hemlock Has your question been resolved?

[chrome hemlock]

.close

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[chrome hemlock]

.reopen

[final saddle]

✅

[chrome hemlock]

Guys i am cooked what is B

Isi t

Ethylbenzene

No its

3 carbons

[craggy plank]

Name the red one, and the yellow one

[chrome hemlock]

Butylbenzene?

Monkeys eat peanut butter

Propylbenzene?

[craggy plank]

n-propylbenzene

[chrome hemlock]

Isnit 3

How do i know the number

2-propylbenzene

[craggy plank]

You don’t need the number

[chrome hemlock]

Oh so its just propylbenzene

[craggy plank]

There’s only one possibility

[craggy plank]

yes

[chrome hemlock]

YAY

THX U

omg my uber is so slow

[sonic crystal]

Imagine doing organic

[craggy plank]

It took me a minute to translate it from Mandarin to English

[final saddle]

@chrome hemlock Has your question been resolved?

[craggy plank]

.close

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[floral atlas]

Lets say

[floral atlas]

Y = sqrt x

Technically speaking

Y can never be neg, unless its i, which in this case is irrelavant

But if we were to square both sides

Y² = X

Now Y can take a neg value

[pale oracle]

I mean

[floral atlas]

How does that work-

[pale oracle]

sqrt(9) = +-3

[floral atlas]

oh.

oh...............................

i forgot about that....

oopsies 🤭🎀

[pale oracle]

Yeah the premise there isn't correct

[shadow aspen]

Usually sqrt is a function so that is not the case

[feral ginkgo]

that's kind of a bad example though if they mean y = sqrt(x) which is just positive sqrt by defn

[pale oracle]

They didn't limit the question that Y is a function of X

[floral atlas]

uhuh

[feral ginkgo]

even if x is a fixed real number, sqrt(x) is still positive wdym

[floral atlas]

ur cooking

ur cooking

[floral atlas]

Oh

I mean

[shadow aspen]

I would say the default is sqrt(x) is a function

[pale oracle]

3*3 = 9 and (-3)(-3) = 9

[floral atlas]

It does say f(x) is sqrtx

😭

It is a func yea

[pale oracle]

Ok then

Thank you for that detail

[floral atlas]

yesyes

Ur welc

Sooo

How does that change anything

Again???

[shadow aspen]

In the original equation y=sqrt(x), y can only be a positive number, so unless you are creating a new equation for a different context, you would still have that y can only be positive

[floral atlas]

it js says f(x) = sqrtx

[young bridge]

squaring both sides yields extra solutions because the 'squaring' function (f(x) = x^2) is not injective. That is, f(a) = f(b) does not imply a = b.

[floral atlas]

pls speak englis

[young bridge]

yeh lemme get to it x

d

[floral atlas]

i dont understand einstien

🔥

[young bridge]

a function is injective if it maps every distinct input to a distinct output

the square function maps x and -x to the same output, meaning it is not injective

[floral atlas]

ohh

[young bridge]

this means applying it to both sides of an e quation will change the equation and hence the solutions

[floral atlas]

gyat

damn

wtf

when did math get so complex

wtf

i was learning addition js a few years ago

[young bridge]

this is uni level maths

dont worry u dont need ot know this for most courses up till university

[floral atlas]

okk

[young bridge]

but it's just something to keep in mind

[floral atlas]

okok

Fair fair

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[sacred lichen]

Im not sure how to solve this question

<@&286206848099549185>

[final saddle]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[vital surge]

consider the divisibility rule for powers of 2

[sacred lichen]

what does that mean?
]

like i tried dividing them all by 64

but they all dont work

[vital surge]

why 64?

[sacred lichen]

cuz thats 2^6?

[vital surge]

but why 2^6?

do you know what the divisibility rule for 64 is? work backwards from the divisibility rules for 2 and 4

[sacred lichen]

4 is like the last two digits right?

[vital surge]

yes

[sacred lichen]

and 8 is the last 3 digit?

[vital surge]

also yes

[sacred lichen]

but what next

I get that the last 4 digit has to be 6336

but theres two of them

nvm

im stupid

thx for the help

.close

[final saddle]

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[sacred lichen]

.reopen

[final saddle]

✅

[sacred lichen]

what about this one?

[faint kayak]

split it into 2 right triangles

[sacred lichen]

can I assume triangle abc is a 30,60,90 triangle?

[faint kayak]

theres prob a way to prove it

triangle adc is a 45 45 90

[sacred lichen]

yes but waht about abc?

[vital surge]

a lot of the work for this problem can be avoided

notice how it seemingly gives you zero information about the shape

you can make any assumption of your choosing and solve the problem like that

[sacred lichen]

so we can just make assumptions ?

so if I set ab as x

then I get root3 x plus x is 20

[vital surge]

there’s an easier assumption you can make here, one that lets you arrive at a correct answer very quickly

..the diagram is a bit misleading

[sacred lichen]

is we assume they are all 45 45 90 triangle?

oh shoot

so then it will just be 100?

[vital surge]

yeah

you can prove this by setting up an algebraic expression for the area and simplifying it (the result is a constant 100 regardless of what any side length is)

though in a competition you would just take the easy way out

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@sacred lichen Has your question been resolved?

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[opaque tiger]

guys what is a prime function? for example f'(x)

[ocean stratus]

Likely derivative of f

[opaque tiger]

what is derivative

[formal trail]

the derivative is a measure of the instantaneous rate of change of a function at a given input value

introductory playlist: https://www.youtube.com/watch?v=WUvTyaaNkzM&list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr

[ocean stratus]

why yawn lol

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[stone tangle]

how?

[rocky tusk]

because what’s sin^2+cos^2

[stone tangle]

i think 1 right

i see

genius

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[versed crater]

That’s a common trick in polar coords

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[chilly beacon]

i don’t understand this simple stuff

[chilly beacon]

like i’m supposed to find x right but how did they just know how to do that

.clode

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[fierce willow]

Hello! I just want to ask if my proof is sufficient and if this is really a direct way of proving?

[desert mantle]

if you want to use(3) in that way you have to show that a^r=e

[final saddle]

@fierce willow Has your question been resolved?

[fierce willow]

hmmm i think i did something similar to this, hold on

[desert mantle]

yes that works

[fierce willow]

The problem I have with that is, I declared on (1) that k is greater than or equal to n, but in (3), it shows that k=0, and in (4) r=0, therefore k=0, which will contradict by claim in (1), or did I make some sort of fallacy here?

Lastly, it is a direct proof? thank you so much for responding

[desert mantle]

you didnt show at all that k=0

(which would be false)

from a^k=a^r you cannot conclude k=r

the whole proof is about from having a^n=a^k=e only being able to conclude that n divides k

yes its a direct proof

gtg

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[fierce willow]

oooooohhhh thank youuu!

[fierce willow]

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[amber holly]

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[gentle zephyr]

being $f : \mathbb{R} \to \mathbb{R}$ defined as $f(x) = \begin{cases}
\frac{e^{(x-2)} - 1}{5 \cdot \left(x-2\right)} & \text{if } x > 2 \
\frac{1}{10}\cdot\left(x-2\right) + \frac{1}{5} & \text{if } x \leq 2
\end{cases}\\$
decide, by using "coeficiente incremental" if $f$ is differentiable in $x_0 = 2$

[soft zealot]

938c2cc0dcc05f2b68c4287040cfcf71

[gentle zephyr]

this was translated but idk what coeficiente incremental translates

I believe in english is Incremental coefficient

this is the original question

if I translated it right its Incremental coefficient or something

[solid cobalt]

Coeficiente incremental is this (f(x+h)-f(x))/h

[gentle zephyr]

h being?

[solid cobalt]

$$f'(x_0)=\lim_{h\rightarrow 0}\frac{f(x_0+h)-f(x_0)}{h}$$

[soft zealot]

Categorist

[solid cobalt]

That's the definition of derivative of a function at a point

It's the limit of the coeficiente incremental

It can be written as

[gentle zephyr]

so it was just fancy wording to use the limit definition of derivative

mayhaps?

[solid cobalt]

What does mayhaps mean?

I'm a spanish speaker

It's like maybe and perhaps?

[gentle zephyr]

maybe and perhaps

[solid cobalt]

I think so, yes

[gentle zephyr]

okay so should I check continuity or wtf

right and left side limit of x_0

[solid cobalt]

derivability at x0=2

[gentle zephyr]

how to check continuity and differentiability of this piecewise

did I said it right?

[solid cobalt]

You have to study this limit

$$\lim_{h\rightarrow 0}\frac{f(2+h)-f(2)}{h}$$

[soft zealot]

Categorist

[solid cobalt]

So do h→0- from the left and h→0+ from the right

The definition of f(2+h) changes

In each one

[gentle zephyr]

im so confused, what are we doing here? analyzing differentiability or continuity

[solid cobalt]

continuity of derivative ≠ derivability ≠ continuity

[solid cobalt]

Differentiability

So the existence of that limit

You have to check if that limit is equal both sides

[gentle zephyr]

well for f(2) we need to use the second case of the piecewise

[solid cobalt]

Yes

[gentle zephyr]

1/5 that one is easy

[solid cobalt]

Yes

[gentle zephyr]

what about f(2+h) tho

[solid cobalt]

$$\lim_{h\rightarrow 0}\frac{f(2+h)-\frac{1}{5}}{h}$$

[soft zealot]

Categorist

[solid cobalt]

But f(2+h) depends on the sign of h

So you do two limits

[gentle zephyr]

$f(2^-)$ and $f(2^+)$?

wtf

[soft zealot]

938c2cc0dcc05f2b68c4287040cfcf71

[solid cobalt]

Sorta yes