help-42

[marble pendant]

As k approaches 56, n approaches inf

[exotic cosmos]

hard to interpret it that way i guess

i just saw division by zero and got rid of it

but like no other choice works too

Lol

I mean B got pretty close

hmmm okay thanks

weird question 😭

[marble pendant]

Loll

Btw what exam are you preparing for?

[exotic cosmos]

School exams

There was another question i think idk if you're down to help but like

the standard deviation of 140-a, 140, 160, and 160+a where a > 0 is 50

what is a

i could use the formula but that takes a lot of effort

probably there's an easier way

which i'm trying to find

[marble pendant]

I think you can add or subtract by the same number and still get the same standard deviation

[exotic cosmos]

oh yeah

[marble pendant]

Like 1, 2, 3 and 7, 8, 9 has same standard deviations

[exotic cosmos]

Var(x + C) = Var(X)

cuz dispersion isn't changed by translation of data points

[marble pendant]

Yup

That will simplify this alot

Try doing it and then ping me when you are back

[exotic cosmos]

still long right?

i shifted it down by mean

so we're operating with 0 mean

only saved one line i think

[marble pendant]

What are the numbers now?

[exotic cosmos]

-10-a,-10, 10, 10+a

[marble pendant]

Yup

I dunno but it's easier to calculate (10+a)² than (160+a)²

[exotic cosmos]

no i mean

you get (10 + a)^2 regardless no?

,, \operatorname{Var(x)} = \frac{\sum_{x \in D} (x_i - \overline{x})^2}{n}

[potent lotus]

mmmm7

mmmm7

[exotic cosmos]

so effectively the numerator of Var(x) is the same thing

you'll get the 10 thing

but okay so $400 + 2a^2 + 40a = 50^2 n$

[potent lotus]

mmmm7

[exotic cosmos]

I don't think i could've solved all this in time lol

[marble pendant]

I think school exams are like 3hrs long right?

[exotic cosmos]

the answer is also nice

[marble pendant]

And they have like 20-30 ques

[exotic cosmos]

it's 2 hours

but there are that many questions

[marble pendant]

I mean exams mostly have easy questions

[exotic cosmos]

if u take more time for this then you have to make up in other questions

[marble pendant]

You will definitely have time left

[exotic cosmos]

the questions are like this 😭

pretty hard i guess

to solve with time limits

at least for me

[marble pendant]

If it's hard for you then it's hard for everyone

No need to worry

[exotic cosmos]

so the only option is to solve the quadratic?

[marble pendant]

This quadratic?

[exotic cosmos]

yeah

the quadratic itself isn't easy

😭

even worse

[marble pendant]

I think you have done it wrong

Their should not be an n there

[exotic cosmos]

n is 4

[potent lotus]

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[marble pendant]

Ohh

You should solve quads yourself

[exotic cosmos]

i know how to solve quadratics 😭

[marble pendant]

Or else you won't be able to such questions in under a minute lol

[exotic cosmos]

oh LOL

😭 my exam is in 2 days

i can't change

but it's always these tedious questions

however there's usually

nnice solutions

which is why i was asking

[marble pendant]

Yup

[exotic cosmos]

the answer was nice

which means maybe there's a nicer solution?

[marble pendant]

I don't know
I haven't done stats yet

I just know some "extra" things

[exotic cosmos]

Oh

I just know the formula too lol

[marble pendant]

lol

[exotic cosmos]

yeah i think this definitely takes 3 minutes at least

idk why this exam is a racing game

i'll skip the question i guess

if i get something like this

the data is symmetric

[marble pendant]

Lol

[exotic cosmos]

maybe there's something about it

[marble pendant]

If you get options you can put the options instead of solving the quad

[exotic cosmos]

no options for this

[marble pendant]

Ooh

[marble pendant]

Yeahh

So I think we can just calculat for one half

[exotic cosmos]

yeah i think i'm positive they don't want u to solve the quadratic

also the quadratic isn't even that easy that solve

[marble pendant]

10, 10+a will give the same deviation from 0

[exotic cosmos]

well it's not that hard but we have alot of divisors of 4800 to look for

[marble pendant]

100 + (10+a)² = 50² * 2

IT WORKSA

Do you see what I did here?

[exotic cosmos]

I'm confused 😭

[marble pendant]

You don't need to solve quad here

[exotic cosmos]

what works?

[marble pendant]

Both sides are perfect squares

50² * 2 - 100 = 4900

[exotic cosmos]

where did you get all these numbers from?

[marble pendant]

^

Cause (-10-a)² is the same as (10+a)²

Same for 10 and -10

[exotic cosmos]

I'm confused LOL

okay i get the gist

but that is a thing?

Never knew u could do such things

[marble pendant]

I didn't too

Just realised this

I have to go now

Good luck for your exam

And good night

[exotic cosmos]

Ohhh

good night

Thanks for the help

[calm coral]

@exotic cosmos Has your question been resolved?

[calm coral]

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[wheat wyvern]

u = cos(7t)
du = -sin(7t) 7 dt

-1/7 int e^u du

-1/7e^u + C

-1/7e^(cos(7t) + C

[eternal stirrup]

Beware of the sign again

And also u forgot to apply chain rule

[wheat wyvern]

ok I fixed the sign

I applied chain rule to du

du = - sin(7t) 7 dt

Thank you

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[undone bear]

I need help with a geometry problem

[undone bear]

The bisector from an acute angle of a right triangle has length 3√5 and divides the opposite leg into segments of length 3 and 5. Find the length of the other two bisectors

I have already found out BF but I dont know how to find AE

<@&286206848099549185>

[sinful moon]

Hmmm looks like u could use Stewart’s theorem here maybe

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[red locust]

v

[red locust]

am i right with B here?

[final haven]

yes you’re right

[red locust]

i also thought it would be C but it cant right

[stray tundra]

are you just asking the solutions to your test in different channels?

[delicate lantern]

lmao

[red locust]

dont you have to open new each time

[stray tundra]

you're not supposed to cheat, nor get simply the answer handed to you

[red locust]

im not i already worked it out on paper just wanted to confirm

[stray tundra]

!show

[calm coral]

Show your work, and if possible, explain where you are stuck.

[red locust]

i would send a pic but i dont even have a phone

[final haven]

it can only be either (-5x-3)/(x-1) or the answer you put because they factored out the negative

[red locust]

ohhh okay i understand that

thank you

[stray tundra]

mspaint is a pretty handy substitute for pen and paper

[red locust]

someone told me abt that yday

i need to try it out

i already did all these on paper but i will forsure

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[vestal apex]

Programming something for fun to automate a tedious task, but I'm not sure how to figure out the position of v4. In real life I'd use a compass, but that's not possible in my case. I'm wondering if there is a certain equation I can use to figure out the position of v4. I wrote down a bunch of other points that might be useful, but I couldn't find any connections that might help me figure this out.

[vestal apex]

i got the red x by using a compass with the length of 450px on v2 and v3 (i hope that makes sense)

i was thinking of using a rotation matrix and multiplying with it at first, but I thought that there might be an easier solution

[rough arrow]

(x,y) and (500, 460) have a common coordinate, if that's what you're asking for.

[serene geode]

you mean the green line has length 450?

[vestal apex]

yeah, shouldve mentioned that

[serene geode]

well (x,y) could be anything unless you know the angle between the green and gray line

or do you want (x,y) as a function of theta

[vestal apex]

what if i treat the points as circles

and get the intersection point

[serene geode]

w h a t

[vestal apex]

ill draw it up real quick

[serene geode]

do you mean (x,y) is length 450 from v3 and v2

because then its very simple to get it

[vestal apex]

should be yeah

[serene geode]

ok

[serene geode]

then

[vestal apex]

this is what i started thinking of

[serene geode]

no need

draw a line from v3 to v4

then v2, v3, v4 make an equilateral triangle

[vestal apex]

ooohh

its starting to form in my head

thanks

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[worthy matrix]

can someone help me on #4? im trying to graph both but my line for g(x) keeps coming out weird

[hallow rock]

What is g(x)

[worthy matrix]

4^0.5x -3 @hallow rock

[viscid zenith]

what does the question says

[worthy matrix]

it says describe the transformation but i have to graph both @viscid zenith

[indigo grove]

4^x-3 being a parent function seems a little criminal

[worthy matrix]

its exponential functions

[indigo grove]

Yea ik

[indigo grove]

Ok what input x in f(x) would give us g(x) ?

[worthy matrix]

wdym

[indigo grove]

like what value we put in f(x) that makes it the same as g(x) ?

[worthy matrix]

i think none? because for gx you divide the x by 2 (or times by 0.5)

[indigo grove]

It’s like the case where you input other variables other than x
like f(x+h) would be 4^(x+h)-3
using the function in question

[worthy matrix]

i dont think i learned that yet

[indigo grove]

so f(x) means a function at x
if we want the function at some point x+h we say f(x+h)
and input x+h as a whole in the function

[worthy matrix]

whenever i graph it i get this line? but they dont look similar to me

[indigo grove]

The function should look a little expanded

[worthy matrix]

so is the line right?

[indigo grove]

The one using the pencil is right
But the blue line isn’t

[worthy matrix]

how do i make the blue one correct

[indigo grove]

It should look like f(x) but like a little expanded

[worthy matrix]

like ik they have the same intercepts

for when x=1 i get y is -1

and when x=2 i get -2

[indigo grove]

doesn’t look correct

[worthy matrix]

i did 0.5(1) whixh is 0.5 and then i did 4^0.5 is 2 and 2-3 =-1

is that wrong?

[indigo grove]

At x=1 f(x) would be 1

[worthy matrix]

how?

[indigo grove]

Typo

[worthy matrix]

still how

[indigo grove]

4^(1)-3=4-3=1

[worthy matrix]

but 0.5(1) =0.5 not 1

[indigo grove]

That’s for f(x)

Not g

[worthy matrix]

oh

[indigo grove]

You did g correctly

[worthy matrix]

huh?

you said the blue one was wring

that was g(x)

[indigo grove]

I meant here

[worthy matrix]

thats for g(x)

[indigo grove]

But ok for the graphing
Both function at x=0
Would be -1

[worthy matrix]

but anything to the power of 0 is one, so 1-3=-2

i got that they both have a y intercept of -2

[indigo grove]

ok the two functions would look similar but g(x) is horizontally stretched

[worthy matrix]

i really dk what your saying sry, im just confused on how to do the points for g(x) and why my line was wrong

like if x=1, what would g(x) be

same for x=-1

[indigo grove]

For x=1 4^0.5(1)-3=2-3=-1
for x=-1 4^0.5(-1)-3=4^-0.5-3
0.5-3=-2.5

[worthy matrix]

if x=2 would it be 1?

[indigo grove]

Yea

[worthy matrix]

is this correct

could i say stretched horizontally?

[indigo grove]

Looks correct but it’s a little rouge

[indigo grove]

Ye

[worthy matrix]

yeah i cant rly draw

[indigo grove]

It’s ok

[worthy matrix]

@indigo grove i have one more question

[indigo grove]

ask

[worthy matrix]

is 11 right?

[indigo grove]

Send 11

[worthy matrix]

i did

[indigo grove]

Shows only to 10

[worthy matrix]

i sent a photo of what i wrote for 11

and the equations

[indigo grove]

Is -3 on the exponent ?

[worthy matrix]

yes

[indigo grove]

Then yea looks correct

[worthy matrix]

ok thx

if the blue line is a transformation of y=2^x what is the equation? @indigo grove

[indigo grove]

The (0,1) point got shifted to the right 3 units

[worthy matrix]

i’m talking about 16 mb

i dont get it

is it up 5?

[indigo grove]

It got shifted upwards
The point (0,1) changed to (0,12)

[worthy matrix]

so up 11

??

[indigo grove]

Yep

[worthy matrix]

then the equation would be y=2^x+11 correct

[indigo grove]

Yea

[worthy matrix]

if its like 3(2)^x compared to 2^x, does that mean the line is steeper

[indigo grove]

Would look vertically stretched

[worthy matrix]

is that the same as steeper or is it just taller

[indigo grove]

Yea it’ll look steeper

[worthy matrix]

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[quiet ice]

The table mentioned is basically what's written on the bottom left

[quiet ice]

I'd elaborate but idk what went wrong lol

[marsh valley]

Try (2n)! in the denominator

[quiet ice]

🗿

thanks lol

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[idle ore]

How do I go about solving questions like these?

I am studying and the solution just provides the counterexample immediately how would I get to that? As I started to simplify the equation\

[ripe spade]

Maybe draw a picture

[idle ore]

How would I draw an equation like that?

[ripe spade]

Venn diagram

So u can see if it's actually true before u start proving

[idle ore]

Mmm okay that makes sense ive never drawn them out before just straight to solving and if its tough I would see if theres a counter. Makes snese

If you are familiar with proofs do you have any tips for solving using strong induction>?

Ive tried to make it into a step by step but doesnt always work bc the questions vary quite a bit

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[mossy geode]

how do yall estimate this

[calm coral]

@mossy geode Has your question been resolved?

[prime yacht]

What are the statements @mossy geode

[calm coral]

@mossy geode Has your question been resolved?

[mossy geode]

whcih one is greater or less than 2/3

[cosmic holly]

cos is greater

Expand sin and cos to x^2

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[sacred anchor]

is this correct?

[sacred anchor]

i don’t exactly know how to check if i used the formula for the riemann sum correctly

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[fickle flume]

What's the direct comparison test and when do I know how to use it?

[fickle flume]

Is it when a function with two terms that are on their own functions as well, where one of the terms/functions reaches infinity faster than the other?

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[obtuse parrot]

Unsure when to do what in mathematics :-

Long story short I was reading serge langs book , its not the most straight book but i want to finish it.

I am not sure when to do what in mathematics like theres this equation where we " multiply 60 on left side and then take the left side and subtract it by right side"

better would be to give a screen shot

I am very new to mathematics and i dont know when to do what, i dont know what to do with a step i dont even know exists

[obtuse parrot]

how am i supposed to work with it, i know practice is a option but i am asking how am i supposed to deal with a step or expect a step i dont know exists

[midnight falcon]

well for this question, what i would do is multiply the first one with 60 as the explanation says. then i would write them side by side and i would compare them

"hmm if had 30y more i would get 480, so i think 30y = 80"

thats kinda logic thing

but yeah

[obtuse parrot]

So basically i need to practice my logic towards mathematic

[midnight falcon]

yes that would be more useful

[obtuse parrot]

alright!

any books u would recommend for that?

[crystal oyster]

Lots of questions helps to build up pattern recognition

[midnight falcon]

as he said yeah

[obtuse parrot]

alr

ty

[midnight falcon]

im not an expert for that topic lol

[crystal oyster]

I dont rlly know many books

[obtuse parrot]

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[finite kindle]

how do I calculate
the intervalls at which a function is strictly monotonic
for example
1/4x^4 -2x^2

[ocean cypress]

strictly monotonic doesn't make sense

[finite kindle]

yeah?

tell that to my analysis book

[ocean cypress]

i mean it's either monotonic or it's not. strictly increasing or decreasing makes sense

[finite kindle]

alright

lets assume I meant that

as I had to translate it

and we might have some minor differences in sciency language

[ocean cypress]

just take the derivative

look at the points where it's non negative

[finite kindle]

sure I have the derivative

but how do I do the 2nd part

[ocean cypress]

what's the derivative

[finite kindle]

x^3-4x

[ocean cypress]

find the zeros

[finite kindle]

ok

give me a sec

x(x^2-4)= 0

from here it is?

oh

x (x-2) (xplus2)

so 0, 2, -2

broke my plus button on my keyboard

is that correct?

@ocean cypress

[ocean cypress]

yep but i gtg. just identify the intervals where the function is positive

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[dusky crescent]

What makes a degree sequence valid in graph theory?

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@dusky crescent Has your question been resolved?

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[remote mural]

Hello

so first i differentiated this function and got 3x^2 - 10x + 3

[lost flint]

if you help me ill help you

[remote mural]

and i used the quadratic formula to find x = 3, and a 1/3

No

[lost flint]

why not

[remote mural]

I dont have time to assist

I want help

[lost flint]

my question prolly easier

just check it out

[remote mural]

No

No

[remote mural]

Leave my Chat

[lost flint]

ur one is easy

[remote mural]

This is my help chat

Leave

[lost flint]

On bro i can do it in 4 min

[remote mural]

.close

[calm coral]

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[calm coral]

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[wheat pewter]

Hi I have a question on why b is 4 and how this works. I thought exponential functions would have output values that are proportional but why does this funciton have rate of changes that are proportional, not the output values

I thought it would be 12/6 = 36/12 and so on

[serene geode]

exponentials also have proportional values

i don't know if you know calculus but calculus shows that the rate of change of an exponential is also an exponential

🙂

[serene geode]

this would be true if k was 0

[wheat pewter]

Ohh I see so if it says there is an exponential function but the first output values aren't proportional, I cna find B through finding if the rates of hcanges are proportional?

[serene geode]

yes, that can identify b

you can also find k first

and then subtract k from all output values

and then try it

like (12-4)/(6-4) = 8/2 = 4

(36-4)/(12-4) = 4

🙂

does that make sense

[wheat pewter]

Yes I get it now! Thanks

[serene geode]

YAY

[serene geode]

you'll learn this if you take calc

🙂

[wheat pewter]

Okay I see thanks for your help!

[calm coral]

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[torpid summit]

whats derivative of r=costheta/5

[torpid summit]

well ok

no

what is it split into

x = r cos theta

y = r sin theta

x = cos t/5 * cos t
y = cos t/5 * sin t

right?

[lusty sand]

nono

the answer is 1/5sin(theta/5)

[lusty sand]

nope thats wrong

[torpid summit]

wait how would you split it into x and y

[lusty sand]

it should look like this: y= 1/5sin(x/5)

where theta is x

does that make sense?

[torpid summit]

nope lmao howd u get there

[true wasp]

chain rule

[lusty sand]

alright so, youre probably confused here because of all the rules you have to memorize, in your case youre confused because of "product rule"

you dont use that there

[torpid summit]

nonono

i wasnt talking about derivative for that

just splitting the polar into rectangular

[lusty sand]

oh, i'm not familiar with that one sorry for not answering your question, mind pinging a helper instead?

[torpid summit]

lol ur fine

<@&286206848099549185> anyone

[serene geode]

what

$x = r\cos\theta, y = r\sin\theta$

[potent lotus]

rain

[torpid summit]

basically how do u split r = cos theta/5 into x /y

[torpid summit]

is this right

t = theta

[serene geode]

um that looks right

[torpid summit]

alr thx

.close

[calm coral]

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[vernal portal]

$\begin{tikzpicture}
\draw[thick,->] (0,0) -- (4.5,0);
\draw[thick,->] (0,0) -- (0,4.5);
\draw (4,0) arc (-5:180:2cm);
\end{tikzpicture}$

[potent lotus]

wasu

[vernal portal]

original question is

Find the maximum area of a rectangle that can be inscribed in a semicircle with radius 1.

i know its a square, not sure how to find side lenght of it

[vernal portal]

its the lenght of the square?

[odd moon]

yes, right?

[vernal portal]

huh

we dont know angle

[odd moon]

i know

i'd represent the area of the rectangle/square in terms of theta and then maximise the expression

[vernal portal]

so we want to maximize

$\sin^2(\theta)$

[potent lotus]

wasu

[odd moon]

uh im still
working it out

[vernal portal]

ok

[odd moon]

idt thats it

ok wait

nvm

its a square yes

then

$2 cos(\theta) = sin(\theta)$

[potent lotus]

kitten

[odd moon]

?

[vernal portal]

huh

how

[vernal portal]

i dont really understand it but ok

so tan(theta) = 2

[odd moon]

ehm sure?

[vernal portal]

so find theta

then plug into sin^2(theta) for answer

?

[odd moon]

i guess

[odd moon]

sin is y and cos is x

sin theta is a side length

so cosine theta should be half

[vernal portal]

i got 4/5

[odd moon]

is it 4/5

im not confident

[vernal portal]

i can check

nope

(sin(arctan(2)))^2

[odd moon]

thats the same thing

[vernal portal]

its wrong

[odd moon]

well

[vernal portal]

maybe i did something wrong

[odd moon]

is this the answer?

or your answer

[vernal portal]

my answer

[odd moon]

oh

whats the answer

[vernal portal]

it doesnt say

[odd moon]

what

Oh

[odd moon]

lol aops

[vernal portal]

yeah

[odd moon]

ohh what class you taking at the academy

[vernal portal]

calculus

[odd moon]

yep ok so we should probably be using calculus

[vernal portal]

optimization class

[odd moon]

are u sure its a square

thats the most area

[vernal portal]

im 83% sure

its a square

[odd moon]

i mean in most contexts yes

butttt

im not so sure

[vernal portal]

oh

[odd moon]

ok again like i said

set up some kind of equation or expression

find the maximum of it with calculus

sooo

[vernal portal]

oh

i just

guessed the answer

as 1

[odd moon]

💀

[vernal portal]

uh

Find the maximum volume of a cone that can be inscribed in a sphere with radius 18.

[odd moon]

sin^2(theta)

so it was really

just as easy asy

maximising

sin^2(theta)

lmao

[vernal portal]

lol

[odd moon]

i definitely overthought it

[vernal portal]

What about this one

[odd moon]

broo

im getting flashbacks from ap calc

[vernal portal]

volume of a sphere is 4/3 pi r^3

,calc 4/3 * 18^3

ok thats not good

[potent lotus]

Result:

7776

[vernal portal]

volume < 7776pi

im def not guessing this one

[odd moon]

good start ill add volume > 0 too

[vernal portal]

ok

volume of a cone is

i forgot

[odd moon]

1/3 b * h

[vernal portal]

wait does it have to be a right cone

[odd moon]

[vernal portal]

might be oblique cone

yeah i have o idea

no idea

[vernal portal]

e

[odd moon]

i would assume its a right cone

https://math.stackexchange.com/questions/225718/find-the-volume-of-the-largest-right-circular-cone-that-can-be-inscribed-in-a-sp

[vernal portal]

huh

ok i think i got it

.close

[calm coral]

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[edgy knoll]

hi. could i get help

[edgy knoll]

i have no idea how to approach this, i was off

[sweet shard]

No clue

Sorry

[edgy knoll]

oof

[sharp narwhal]

just find each area

let the side length be a

of the square

[edgy knoll]

okay

[sweet shard]

👍

[sharp narwhal]

?

[edgy knoll]

wait

then what

ad = 2de

[sweet shard]

What?

[edgy knoll]

?

[sweet shard]

?

[calm coral]

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[tough star]

sin(6pi/5) = cos(x)
find all x between 0 and 2pi

can someone do this real quick

[tough star]

and let me know what they got

i got 13pi/10 and 7pi/10

[void frost]

You can confirm computations like this via WolframAlpha

,w sin(6pi/5) = cos(x) find x

[potent lotus]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by kepe_5235

[tough star]

wheres the answer?

[drifting seal]

cos(x) = sin(pi/2 - x)

[void frost]

Ok that one didn't work out

[drifting seal]

also, why do you need these verified

you could always graph it yourself

[tough star]

oh

true

[drifting seal]

are you taking a test

[tough star]

nah 💀 ong

i forgot i can check with a calculator

my bad

.close

[calm coral]

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[void frost]

,w sin(6pi/5) = cos(x) for x = 7pi/10

[potent lotus]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by kepe_5235

[void frost]

,w sin(6pi/5) = cos(x) for x = 13pi/10

[potent lotus]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by kepe_5235

[void frost]

From the plot you also see these are the only two

[calm coral]

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[hollow sphinx]

How do I reduce this?

[tame spire]

wdym

[calm coral]

@hollow sphinx Has your question been resolved?

[hollow sphinx]

How do I get it reduced row echelon form

[calm coral]

@hollow sphinx Has your question been resolved?

[severe nebula]

Idk if i did it but i did something

Probably a way easier way tho

I got 1:5 tho

Through name thing other unknown 2 areas , naming a side as a and doing simultaneous equations

[calm coral]

@hollow sphinx Has your question been resolved?

[severe nebula]

Nvm this is hell

[calm coral]

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[rancid rock]

What does it mean by “Set your working out down the page. One column per page…”?

[kindred estuary]

That's something you should ask your teacher

[rancid rock]

…

[kindred estuary]

How are we suppose to interpret what your teacher meant?

So you should ask them

[severe nebula]

No idea

[rancid rock]

I thought there’d be someone who had a similar task like this… that’s why I asked for help.

[remote mural]

You’d probably not get help with this around here

[rancid rock]

Wether they done it or not

[remote mural]

These channels are made for maths questions typically

Probably ask your teacher as Nova said

:)

[kindred estuary]

This server has people from all over the world, the chances of someone who has your teacher is slim

[rancid rock]

I want to point out how Silly (not in humorous way) this was from me but I can’t word it out. And I want to say that I am sorry that I did this. I just wanted to start this task right away but after looking at that one submission rules, I became frustrated.

[amber bolt]

it measn you can't write a vertical line

and use the page like it's two pages

that would be two columns

[rancid rock]

So not like this? (I would like a reference please).

[amber bolt]

like the left is messy but they are saying right is also bad even though it's tidy

this would be fine i assume

[rancid rock]

So an answer along with working out to the side pretty much? (Because that’s what my irl friend suggests).

[amber bolt]

yeah that's what they don't want is my guess

[rancid rock]

Got it!

[calm coral]

@rancid rock Has your question been resolved?

[calm coral]

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[split glen]

A family has five children. The youngest child is x years old, and the oldest is 2x years old. The other three children are aged (x + 2) (2x-1) and (2x-3). If their average age is 14 years, then determine the age of the middle child

[split glen]

A family has five children. The youngest child is x years old, and the oldest is 2x years old. The other three children are aged (x + 2) (2x-1) and (2x-3). If their average age is 14 years, then determine the age of the middle child

How do i know who is the middle child

I found x

[viscid zenith]

nice

[split glen]

Who is the middle child

[viscid zenith]

list the values x, 2x, x + 2, etc

[trail hull]

Calculate all possibilities given your equations and the median value

[viscid zenith]

and find which is in the middle

[split glen]

Wait

There?

That?

No?

[viscid zenith]

you need to put in order

11 goes before 18

[split glen]

Oh sorry

[split glen]

9,11,15,17,18

The third goes to 15

[viscid zenith]

yep

[calm coral]

@split glen Has your question been resolved?

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[remote mural]

what?

[calm coral]

@hollow minnow Has your question been resolved?

[manic hawk]

what do you want help with? Posting a question tells us nothing. Do you know what a function is? Do you know what a transformation is? Do you know what f(x) = sqrt(x) looks like?

[hollow minnow]

Maybe posting a question means I need help with how to answer the question 🤯

[viscid zenith]

!showwork

[calm coral]

Show your work, and if possible, explain where you are stuck.

[hollow minnow]

i got starting point (-1/5, 4)

so i thought it was D

so going from the start wouold be good

since it was incorrect

<@&286206848099549185>

[trail hull]

@hollow minnow with a negative x value, you would have a negative value under the square root which cannot happen

Your starting point will be whenever the value under the square root stops being negative, or when it =0

[hollow minnow]

okay

so it's 1?

[trail hull]

That’s your first x value

But then find the y value

& you know your function will start there

[hollow minnow]

-4

[trail hull]

Yes

[hollow minnow]

so (1, -4)

[trail hull]

Yes

That’s your starting point

[hollow minnow]

so it cannot be D

or C

or F

[trail hull]

Correct

[hollow minnow]

so now we have possibilities A, B, and E

[trail hull]

It’s also worth pointing out that it wants you to know that the starting point of any function sqrt(x-h)+k will be (h,k), which we can see is true in this case since our h is 1 and our k is -4

Does that make sense or I feel like that’s too clunky of a way to say it

[hollow minnow]

right okoay

clunky but makes sense

[trail hull]

Alright

So now do you know what y=sqrt(x) looks like normally?

[hollow minnow]

if we find the value not to have any zeros

then the answer would be A

[trail hull]

It seems unrelated but this is how they want you to understand it

[hollow minnow]

or am i misinterpriting

[hollow minnow]

just sqrt(x)

looks like

hm

a wave pointing right

not a steep slope

nothing on the negative axis

[trail hull]

You’re right and I like your reasoning, but I also want you to know the reasoning the question wants 😅 as annoying as it is

[hollow minnow]

alright

[trail hull]

It flattens after a while?

[hollow minnow]

thank you for putting the time in

[trail hull]

I don’t mind

[hollow minnow]

ye im pretty sure at least

i havent spent a lot of itme looking at it

[trail hull]

So if you take any y value on sqrt(x) and you multiply it by -5 what happens

The negative is an easy start

[hollow minnow]

you flip over y axis right?

[trail hull]

Do you mean the vertical line or the horizontal line

[hollow minnow]

wait horizonotal so x

[trail hull]

Yes

[hollow minnow]

and then stretch by 5

[trail hull]

Exactly

[hollow minnow]

and then you go down four

[trail hull]

So the whole (1,-4) thing took sqrt(x) and just moved where it started

[trail hull]

Yep

[hollow minnow]

or "shift downwards 4 units"

so it's A?

[trail hull]

Then we just flipped it, and stretched it

[trail hull]

Yes, for the reason that it takes sqrt(x), moves it right 1, down 4, flips it, and stretches it by 5

[hollow minnow]

okay awesome

this is the next issue

it dooesnt tell me what i got right either

the point of origin must be wrong though

x = 5

so [5 on x

then 2 on Y

so the point of origin is (5,2)

ah nvm wait i got it, your way of teaching gave me that needed aha moment thank you

.close

[calm coral]

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[rough mica]

If the remainder is 70² when the number 50! is divided by the number 48!-a, where a is a digit, what is a?

[rough mica]

If anyone wonders, this is AYT 2024 Math problem

[tall moon]

50!=50×49×48!

[rough mica]

U thinking bro?

[tall moon]

?

[calm coral]

@rough mica Has your question been resolved?

[rocky flower]

|| from here I think you just do 50 * 49 * 48! - 70^2 and then factorise into 2450(48!-2) which should clearly give you what you want ||

[rocky flower]

if your stuck, just consider what happens when you minus the remainder, which is 70^2 from 50!. What do you notice?

[rough mica]

So a = 2 thanks, Btw, I wonder if this question can be solved using modular arithmetic?

[rocky flower]

yeah it can be solved using modular arithmetic, just consider what I said before

[rocky flower]

which is here

[rough mica]

Yeah i get it thanks again, what do u think about this questions hardness level is?

[rocky flower]

It’s actually pretty easy if you think correctly. Usually these type of problems want you to factorise from which you just spot the answer

[rough mica]

You know 2 million student entered this exam and 1.9 million of them including me failed to answer this

i really reel bad now

[rocky flower]

Maybe they haven’t learned this technique. It requires just some creative thinking, so I can see why many people wouldn’t get this right

[rocky flower]

You don’t have too. It’s all good, especially once you learn the techniques of solving this problem, you can apply it to other problems

[rough mica]

I hope so, the questions consisting of large numbers can be intimidating during the exam 😕

[rocky flower]

Yeah, but remember to not be intimidated. The problems are made such that there is a way of solving them in the exam, id like to think of it that way

[rough mica]

Actually u re pretty right, anyway i should take no more time of yours thanks again dude have a nice day 🧡

[calm coral]

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[rocky flower]

No problem, and you too!

[calm coral]

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[minor hollow]

for part b

[minor hollow]

idk how they got 2450

i keep getting 2250

[hasty fiber]

!show

[calm coral]

Show your work, and if possible, explain where you are stuck.

[tribal osprey]

wait i'm getting that too

when
t = 0, P = 1000
t = 2, P = 1500

a)
A = 1000
k = ln(3/2)/2

b)
P = 1000e^(4k)
= 2250

[minor hollow]

alr probs an error in the working out then

they have the same working out too

ill show

[neat yoke]

transcription error

[neat yoke]

i mean

[tribal osprey]

they got a decimal?

[neat yoke]

pretty obvious ur answer is right

if u put their 3rd last line into calc

u get 2250

[tribal osprey]

yea

[minor hollow]

alr dawg was js verifying 😭 thanks lads

.close

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[lethal dawn]

The points A(1,2), B(m, m - 3) are given in the perpendicular coordinate plane. Since the line passing through points A and B makes an obtuse angle with the x-axis, which of the following can be the value of m?
A)4 B)6 C)8 D)10 E)12
Translated by deepl
I dont understand the question doesnt all of them work? If im not wrong to get an obtuse angle m needs to be larger than 1

[remote mural]

obtuse angle with the x axis implies the slope of the line should be negative

find out the slope and then check the intervals of m for which it is negative

[remote mural]

as the slope is tanθ where θ is the angle your line makes with the positive x axis and tanθ is negative for θ between pi/2 and pi

[calm coral]

@lethal dawn Has your question been resolved?

[calm coral]

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[calm coral]

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[ancient lynx]

if I have this and I want to turn it into an explicit function of x, can I just take both sides to the power of e and subtract 1? or does the absolute value create difficulties

[ancient lynx]

this is the original differential equation if that helps in some way

[pseudo socket]

The absolute value is just there so that ln(1+y) can be defined for all value

So u can just use e

[prime yacht]

Take the constant as ln C

Final result will look better

[remote mural]

⬆️

It’s a common convention to follow

[ancient lynx]

So wouldn’t I lose solutions if I take to the power of e

[calm coral]

@ancient lynx Has your question been resolved?

[ancient lynx]

<@&286206848099549185>

[ancient lynx]

Also if I do this do I have to specify anyrhing

[prime yacht]

No

[prime yacht]

You wouldnt

[ancient lynx]

ight thanks

.close

[calm coral]

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[calm coral]

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[wintry echo]

Hi

What is the question?

[heady tree]

The second one 😭

[placid heath]

what the hell

[wintry echo]

Source ?

[heady tree]

Is this even possible 😭

[heady tree]

My teacher challenging me

[wintry echo]

Why is there a 209?

[placid heath]

ok so uh

this looks like simplification heaven

[heady tree]

He js wanted it too look like a textbook question

[placid heath]

is that an integral inside of the second integral?

[heady tree]

Yes 😭

[placid heath]

ok but where does it end

just cos²(3x)?

[heady tree]

idk my teacher probably pranking me

i need the extra credit

[placid heath]

there are a lot of simplifications you can pull off

for example

the exponential

when your professor says log does he mean natural or base 10?

[heady tree]

base 10

[wintry echo]

@heady tree But why are there faces drawn?

[remote mural]

oi el patron

[placid heath]

ok it won't be a big issue, add a exp(log(10)-log(10))

by inserting it via multiplication

[heady tree]

why not?

[placid heath]

it's gonna clear out the exponential

[heady tree]

i always draw on my hw

[wintry echo]

Ah ok, anyway you can use wolfram to do the evaluation

[placid heath]

no wolfram

[heady tree]

is that an application?

[placid heath]

we doing this real human style

[heady tree]

bro we need to show work

[wintry echo]

Yes

[heady tree]

😭

[placid heath]

like i said

start by destroying that annoying exponential

i hate it

[wintry echo]

@heady tree But what would you do anyway?

[heady tree]

u right huh id prob js photomath

[placid heath]

photomath would crash

[heady tree]

step one, then break it down

oh my days this gonna take so long 😭

[placid heath]

there has to be something

really

he's not going to give you an addition of two massively complex integrals like that

and not have a hidden trick to it

[heady tree]

deadass it is refused to solve and told me to ask google 😭😭😭

[placid heath]

i told you

[heady tree]

i dunno

but i’m gonna solve it

step by step

[wintry echo]

@heady tree But why in the series is written i=2, but the i does not appear in the integral?

[heady tree]

I KNEW IT

MY TEACHERS JS PRANKING ME 😭😭

good eye

[wintry echo]

<@&268886789983436800> This user is trolling

[heady tree]

???

[placid heath]

what

buddy you didn't tag mods because you don't know silent variables don't have to be part of the term of a series

💀

[heady tree]

so my teacher isn’t pranking me with an unsolvable problem?

[wintry echo]

@placid heath I'm sorry but can't you see that he doesn't even know what he wrote?

[heady tree]

i copied the whiteboard😭😭

hello???

[wintry echo]

Yes, so a professor in your opinion starts trolling

👍

Your teacher didn't even explain these topics, can you explain to me how you do this exercise?

[heady tree]

so my teacher is giving me an unsolvable problem over thanksgiving break as extra credit

[heady tree]

its integration

anti derivative

[wintry echo]

But do you know what a series is?

[heady tree]

i’m assuming it’s a series of anti derivatives that continue similar to double prime and triple prime

[wintry echo]

+Why do you think its a troll?

Can you show me esercise 208

I assume you've done it

[heady tree]

i js told u he put it on the whiteboard

it’s not even a textbook he js wanted to make it look like a textbook question

[wintry echo]

Ah ok then it can't be solved

[heady tree]

then my teacher is pranking me

[wintry echo]

Why do you keep writing that it's a prank?

[heady tree]

something my teacher would do

[wintry echo]

Ah ok, the exercise is yours anyway. Write what you want

[heady tree]

thanks

[calm coral]

@heady tree Has your question been resolved?

[calm coral]

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[timid cape]

Marvin had a birthday on Tuesday, May 27 in the leap year 2008. In what year will his birthday next fall on a Saturday?

[placid heath]

leap years happen every 4 years

[timid cape]

i thought this would be 2012

but it's wrong

[placid heath]

hang on

[timid cape]

?

[timid cape]

anybody get why this is 2017?

[placid heath]

how did you reason?

[timid cape]

sorry for the late reply

[timid cape]

do u mean how did i solve this?

since 2008 is Tuesday and each consecutive year, it's +1

so 2009 is Wednesday

2010 is Thursday

and 2011 is Friday

[timid cape]

<@&286206848099549185>

[silent basin]

That would make sense

[placid heath]

ok so here's the thing

2012 is a leap year

so you're gonna do +366

so it's gonna send you to sunday

[timid cape]

oh huh

nvm continue please

[placid heath]

so yeah u do the additions taking into account you have to do +2 instead of +1 when you hit a leap year

so you're gonna hit saturday on 2017

[calm coral]

@timid cape Has your question been resolved?

[calm coral]

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[calm coral]

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[brisk yarrow]

Each DFA is an NFA

[tender vessel]

i get it.. but i think i am require to make at least 2 paths for 1 option or block option in one state

it really was written as: Build a NFA for each task

[brisk yarrow]

Yeah Yeah

[tender vessel]

so i have no idea haha

i was curious if its possible to make it "more" NFA