help-0

[gray isle]

where is
x-24 = 5(x-24)
coming from

[alpine sable]

x+24=5(x-24)?

not minus 24

wait but why? Gemma gives 24 of her sweets to betty

yes so gemma has x-24 sweets and betty has x+24

whcih is 5 times of x-24

Yeah technically

ohhhhhhhhhhh

Now I get it

x+24=5(x-24)

okay so I did this and I found 36 as my answer

so technically its 72 right?

[magic pine]

Is this question like a Trial and Error thing?

[alpine sable]

help someone

[stone minnow]

still need help?

[stone minnow]

Ok so volume = base * height right

[alpine sable]

ya

[stone minnow]

And the height is clearly 34 cm

So what we needa do is to find the base

[alpine sable]

yup

19 plus 13 plus 22?

[stone minnow]

Nope

[alpine sable]

but the shape is a trapezium

oh?

[stone minnow]

I mean the base area

[alpine sable]

oh ok

[stone minnow]

According to the question, section II is a square prism

[alpine sable]

ye

i did

[stone minnow]

i.e. its length = its width = 13 cm

[alpine sable]

1/2 times 34 times 54 plus 13 ans times 34 but it was wrong

[alpine sable]

o

yes

[stone minnow]

And as you may notice, it shares a same side with sections I and III

Rmb how to evaluate triangle area? b*h /2

[alpine sable]

yep

[stone minnow]

So section I = 19*13/2

[alpine sable]

oh

so i should

take the volume of the shapes

one by one?

i just made the whole a trapezium

[stone minnow]

You may do that

But I recommend you to add up their base areas and then multiply it by the height

This helps you to calculate quicker, as less steps are required

[alpine sable]

i just did that..

and i got the same answer

i got as the trapezium way

but its wrong apparently

i took the area of the base area of each shape 1 by 1

and times the final by 34

💀

[stone minnow]

Did you get 14807

[alpine sable]

no...

38726

[stone minnow]

I will show you my steps then

[alpine sable]

alrighty

[stone minnow]

V = [(1319/2) +( 13 * 22/2) + (1313)] *34
= (123.5 + 169 + 143) * 34
= 435.5 * 34
= 14807

[alpine sable]

o

i didnt

times them by 13

i times them by 34

[stone minnow]

Oic

[alpine sable]

why 13

[stone minnow]

Cause you are finding the base area

[alpine sable]

oh wait

[alpine sable]

oops

i was fidning the area of the

trapezium

the top oosp

alr i get my mistake tysm!

[stone minnow]

Lol

No wonder

Yw ~~

[alpine sable]

wait wait

oh nvm

alrighty tyyy

[lyric ocean]

hey can anyone show me step by step with explanation how to solve this question?

[stone minnow]

Do you know cos 60 = 1/2

Anyways that is one of the special angles for trigonometric functions

And after getting the value, as the question requires -2pi < theta < 2pi, we would certainly obtain more than 1 answers

This is because the cosine of (theta), (negative theta [cause they both locate in quadrants on the right of the y axis] ) and (theta+2pi) are all the same

[lyric ocean]

i have zero clue on what you said

[stone minnow]

Have you learnt the unit circle for trigonometric functions yet

[lyric ocean]

Well, not

yet

[stone minnow]

Ic

Well that is kinda hard to explain by words

[midnight sand]

Does anyone know what error intervals are?

[amber veldt]

Hey guys stuck on this question

[quaint trout]

First show that all r between 0 and p are not congruent.

Consider 0 <= r < s < p

Is it possible for r-s to be a multiple of p?

Then use Euclidean division

[amber veldt]

sorry but whats s?

[quaint trout]

@amber veldt i just considered two different numbers r and s between 0 and p

And show that they are not congruent

That means a cannot be congruent to two different things in that range(that's the unique part)

[amber veldt]

ohhhhh i get it

theres only one r on each multiple of p that equal to a

?

[quaint trout]

Only one r between 0 and p

This only shows that there is at most 1 though, it's still possible for there to be none

So you need to use Euclidean Division to get that there is an r

[alpine sable]

.<

[quaint trout]

Do your quiz yourself

[alpine sable]

Q16, struggling

Any help ?

[next chasm]

6m^3-4.5m times 8m times 12cm

12cm=0.12 m

6-4.5*8 times .12

1.68

[alpine sable]

oops i forgot about making it into 0.12

[tropic sail]

hey how do i make it so that a number resets once it hits another number

for example

i am working with circles and i can change the angle from 0 to 4pi once it gets past 2pi it goes back to 0 as it is starting again

how would i do this?

[quaint trout]

Your question doesn't make sense to me mchw

In what context do you want it to do this?

[tropic sail]

i am writing a computer program to do this

[quaint trout]

Okay

What exactly does your code have to do?

[tropic sail]

and i need to check if the angle is on the top or bottmo half of a circle

[next chasm]

so ur given the angle with pi or degrees

[tropic sail]

in radians

[next chasm]

ok

[quaint trout]

Okay, so

Input: Angle
Output: top or bottom

[tropic sail]

yes'

[next chasm]

what language u want your code in

c++, python, java

[quaint trout]

Don't write the code for them

Just describe how to do it

[next chasm]

ok so ur gonna write 2 if functions, one to check if the xradian >2pi, then from that value remove 2pi as many times as needed to pass that if function, then another function to see if that value is bigger than pi or no

[tropic sail]

what i am trying to do is check if the number is greadter thn or less than pi which will tell me if its top half or bottom half but i need a function which takes a number and carries it so it is between 0-2pi

[quaint trout]

Your angle can't be negative?

[tropic sail]

it can be negativ

[quaint trout]

use a while loop to subtract 2pi until it is the range you want

Okay

[next chasm]

ye, or add if negative

[quaint trout]

Then you need to consider two cases, greater than 2pi then subtract and less than 0 then add

[tropic sail]

is there no sawtooth looking function to do this instead of the loops?

[next chasm]

until it falls in range of 0 to 2pi

[next chasm]

man we giving you tips, just write the code and test if there are any errors

[tropic sail]

ok thanks

[quaint trout]

No, don't ping random people to help you

[next chasm]

ok

[quaint trout]

@tropic sail some programming languages might have a built in option to "mod 2pi" but I don't know

[next chasm]

ye like c++ has that sort of function

but dunno bout the others

[tropic sail]

yes mine has mod

[quaint trout]

Does it just allow modding for integers?

If not you can use mod 2pi and it will give you what you want

[tropic sail]

integers and floats

ooh thanks

its working now

[quaint trout]

[magic warren]

how?

i have to solve it using the roots

[next chasm]

try solving for 1 integer solution idk

like +-1 +-3 +-5 ...

for 105 divisers

see which one works

[magic warren]

i doubt thats the way i should do it

[next chasm]

ye it works

[devout summit]

Have you tried Vieta’s formulas?

[next chasm]

1,3,5,7

a=1,k=2

[magic warren]

i have never heard of it

[next chasm]

theres a good way of solving these long equations

so like if the numbers ahead of them

like x^4 is 1 right

-16x^3 is -16, and so on

if their sum=0

then x=1 is a solution

[magic warren]

oh wait i know what they are i just didnt know the name

[next chasm]

ye

basically 1,3,5,7 are the solutions

[magic warren]

oh ok

[next chasm]

i guess you can figure out the value of k

[finite grove]

[next chasm]

f(2)=6

f0f(2)=-2

[alpine sable]

anyone here good at chem?

[alpine sable]

Which class ?

[alpine sable]

grade?

[next chasm]

like class

11th

12th

10th

[alpine sable]

Yeah

ya

[next chasm]

what ya

[alpine sable]

Yeah short form

😐

[next chasm]

ik

but like

i said 12 11 10

he said ya

[vapid edge]

Guys i have a question from conic section
So the eccentricity of a circle is zero right?
And the eccentricity of a hyperbola is always greater than 1.
Basically, higher the eccentricity, more uncircular is the curve.
And if the eccentricity is infinite, we obtain a straight line.
Does this mean that i can convert a hyperbola into a straight line by making it's eccentricity infinite?

[alpine sable]

yeah .

[next chasm]

im asking exact grade my man

like are you 12th grade

[alpine sable]

How can he/she tell ?

[next chasm]

bro wym

[alpine sable]

This question isn't from him/her

[next chasm]

i can tell what grade im in rn

[alpine sable]

10th.

[next chasm]

oh right

lol

didnt look

soryr

not u

[alpine sable]

@alpine sable need to answer it

[next chasm]

yeah

didnt look at usernames

lmao

my bad

[vapid edge]

So does anyone know the answer?
I really need to know this

[lapis valley]

Any algebra experts

[next chasm]

just use wolfram alpha))

[lapis valley]

Idk how to

Can u do it for me plz

[alpine sable]

11

[alpine sable]

11

this is the question

[alpine sable]

Oh sry i'm in 10

9x^2 - 3x - 20 > 0

[raw nebula]

Why does this happen in geogebra?

[bleak ridge]

It must think its log base 10 for some reason

[humble orchid]

I dont get question 7

Why is it 3/7

[sinful juniper]

Can someone help me? This question is under the topic of Remainder and Factor Theorem

[grizzled ember]

Wouldn't the area of this trapezoid be 66 units^2?

[craggy stream]

whats the most basic formula for working out a triangle's area

[grizzled ember]

A=1/2bh

[craggy stream]

exactly

now draw a diagram and try to use this formula

let h be the height then

and the b be the base

the b is the length of side AB

[grizzled ember]

H =12 b = 9

[lone heart]

From

#❓how-to-get-help

Rule 3

Stick to one channel and don't post the same question in multiple channels. Please don't ask for help in other channels if no one is responding in the one you have posted your question in.

[vale wigeon]

in fact maybe it's best if all of you move out of this channel, seeing as it is the most crowded of the ten

[grizzled ember]

?

How is anyone violating the rules

I'm asking a question, the channel isn't in use?

[dreamy otter]

answer is 78

[grizzled ember]

Yeah it is but my question is.

[wary stream]

Don't give out answers

[dreamy otter]

u want me to explain why or?

[grizzled ember]

OK nvm

I made an arithmetical error

[dreamy otter]

oh unlucky, at least u get it now

[grizzled ember]

I was using the area formula for trapezoid and getting wrong answer but I used base as 9 not 11

Base 1

Yeah I see now.

Originally the question has you leveraging pythagorean theorem to solve for unknown side length then calculate area

Ty

[warped phoenix]

How is the x-coord of the vertex -2?

to find the x coord of the vertex of a factored form equation, wouldnt i do (-3 + 7) / 2?

which is 4/2

=2

[indigo jetty]

you should be taking the difference between the larger and smaller number

7 - (-3)

[zenith dome]

3.cos^2A - 4.cosA + 1 can anyone factorize this ?

[glass lichen]

yes

[rapid nova]

replace cos A with x and factorize as quadratic polynomial

[glass lichen]

replace cos(A) with x*

[rapid nova]

yes

[vivid pecan]

Somone can help me?

in call?

[glass lichen]

dont ask to ask

[vivid pecan]

theres no voice channels?

[glass lichen]

Well you never posted a question and expect help

so...

hopefully you can see the issue.

[limber bear]

assume x and y are postive

x must be bigger than y

which means x and y are not equal to 2

so x>2 and y <2

but i cant quite find the exact minimum

[gritty jungle]

is there anyone active that can help me

[rapid nova]

do you know derivatives?

[limber bear]

yea

how can i relate

[rapid nova]

from $xy = 4$ you know that $y = \frac{4}{x}$

if you substitute it in your equation you get $x + \frac{16}{x}$

[ocean seal]

rept1d

[rapid nova]

now you just need to find the minimum of the function

[limber bear]

yea still

it remain unsolved

i might be not very good at derrivative

[rapid nova]

do you know when derivative is equal to 0?

[limber bear]

u mean for my eqn?

[rapid nova]

i mean in general

[limber bear]

i know is limit approach to zero

[glass lichen]

have you done optimization problems before?

[limber bear]

is that what u r referring

[gritty jungle]

https://cdn.discordapp.com/attachments/269573202018041856/903270647071907850/Screen_Shot_2021-10-28_at_9.11.38_AM.png

helpp

[glass lichen]

dude channel's clearly in use

[zenith dome]

idk how to factorize polynomials

[gritty jungle]

ok

sozz

[rapid nova]

even quadratic ones?

[glass lichen]

stop spamming, use one of the other 9 channels or #geometry-and-trigonometry

not a hard concept

[zenith dome]

nope

[rapid nova]

no

im referring to the fact that if the function has a local maximum/minimum point at x0, its derivative at this point is equal to 0

[limber bear]

yea

[rapid nova]

so if you find all the points where your function's derivative is 0, one of them will be your minimum (if it exists)

[limber bear]

and derive it again to know whether its max or min

[glass lichen]

if you use 2nd derivative test, yes..

[limber bear]

im familiar

[tawny fable]

Hi, I am having an issue with the 5.b.
I was able to prove wrong the first one (with the number 27)
but on the second one, I got nothing...
I realize that n is an odd number since n = 4k + 3, but I don't know what to do with that..

I tried proving wrong that sqrt n is a rational number and got stuck with no contradiction.

Any help please? 🙂

[rapid nova]

ok, so can you solve it?

[limber bear]

-x=32

-x^2

right?

am i in the right path

[alpine sable]

Can someone give me a workout and explanation for these please? I am not sure how to do it, you can ping me, thanks in advnace

[rapid nova]

how did you get 32?

[limber bear]

x+16/x

so is 1+-32/x2

oops

[rapid nova]

no, the derivative should be 0

not the function itself

[limber bear]

yea

im doing the derivative first

[rapid nova]

it's $1 - \frac{16}{x^2}$

[ocean seal]

rept1d

[limber bear]

we did it bois

u are sick rept1d

it all make sense now

[tawny fable]

any help pleasE?

[warped phoenix]

that still doesnt make sense though

7 - (-3) = 10, divide by 2 = 5, the x coordinate of the vertex is not 5 though

it's -2

[indigo jetty]

ok i think i saw wrongly, the x-intercepts should be -7 and 3, so if you're using the midpoint theorem, then it should be (-7+3)/2

[warped phoenix]

ohhhhhhhhhh you do the opposite ones

i see

mb 🤦‍♂️

ty!

[indigo jetty]

because (x+7)(x-3) has roots -7 and 3, not 7 and -3

[alpine sable]

Without using any area formulas, estimate the area of the floor, clearly describing how you estimated the area.

how am I supposed to accomplish this?

I was thinking because from the left side it starts from 6 squares in first column and keep adding by one
so for example: 6 + 7 + 8 + 9 + 10
and do the same from the other half
is there a better way?
because it doesn't account for the half and quarter squares

<@&286206848099549185>

[alpine sable]

Just put it in your calculator

[pine igloo]

Give the vertices in each of the three strongly connected components of the below graph.

[alpine sable]

umm my question hasn't been answered

..

[rapid nova]

{0, 1, 4}, {2}, {3}

[pine igloo]

i'm confused, am i supposed to have a graph to use for this?

[pine igloo]

<@&286206848099549185>

[unborn dome]

can someone help me out with this

[alpine sable]

which?

All of them

@alpine sable

@unborn dome First is 18x^2+18x and second is 36x + 18

[raw shard]

they don’t need help with the derivatives lol

[alpine sable]

Use power rule

[novel frigate]

Take the first derivative and set that equal to zero, solve for x. Use the 2nd derivative test to verify if the x-values you found are a max or min.

2nd Derivative Test: if f''<0 local max, if f''>0 local min

[alpine sable]

I am using a microsoft math solver, it shows the workout but i am kinda afraid it might be wrong, I am not sure

I got -91 for the first answer, my original answer was 3 or something like that

[raw shard]

@alpine sable post the question, i can probably help

[alpine sable]

here it is

[unborn dome]

i got no clue what ure talkin about

we were supposed to learn this today but im feeling a bit feverish

so

18(x+1) = 0?

[raw shard]

take the first derivative and find where it is zero

then take the second derivative at that point

[unborn dome]

okay first derrivative is just 18x + 18x^2 = 0

[novel frigate]

yes

[raw shard]

factor out 18x and it’s an easy solve

[novel frigate]

you'll find two x-values, take the 2nd derivative and plug those x values in

plug the x-values from the first derivative in, I mean.

[unborn dome]

whaat.

nbow im lost

how do i factor this again?

[raw shard]

@alpine sable when someone doesn’t know how to do something, don’t just tell them to put it in a calculator, because that doesn’t help

factor out 18x

[unborn dome]

uh

18(x+1)

?

[novel frigate]

Distributive property

[raw shard]

18x*(1+x)

[novel frigate]

no, 18x(1+x)

[unborn dome]

but

theres two 18x's

when u get 18x(1+x) what happened to the other 18x

[novel frigate]

Yes, but the distributive property is defined as a(b+c) = ab + ac

[unborn dome]

AH

RIGHT

[next pulsar]

numbers have a neat property: a(b + c) = ac + bc

not all numbers

but some

[novel frigate]

Definitions are king 😉

[unborn dome]

bruh how do i forget this im super dumb 😦

[raw shard]

yes all numbers

[unborn dome]

okay

now we got 18x(1+x)

[raw shard]

wait technically not but whatever

yeah

[unborn dome]

uh

[raw shard]

find where that’s zero

[unborn dome]

we want to find out x values

so

18x so 18 x 0 = 0

[next pulsar]

i think octonions lose that property

[unborn dome]

and

[next pulsar]

or 16-ons

[unborn dome]

1 + -1 = 0?

[next pulsar]

cant remember

[unborn dome]

so 0 , -1?

[novel frigate]

2nd one is correct

[raw shard]

yeah they do i think, but no one talks about those lol

yes 0 and -1

[unborn dome]

okay

[unborn dome]

now we get the second derrivative?

so

18x + 18x^2

second derrivative of that would be uh...

[raw shard]

18+36x

[unborn dome]

18 + 36x?

[novel frigate]

yup 🙂

[unborn dome]

right

now we plug in 0 and -1?

[raw shard]

yes

[unborn dome]

or....

[novel frigate]

yes

[unborn dome]

okay

so

18 + 36(0) is just 18

[novel frigate]

which is bigger than zero

[raw shard]

so it’s a minimum

[unborn dome]

and 18+36(-1) is 18

wait

phol up

[raw shard]

-18

[novel frigate]

no, haha

[unborn dome]

yeah

lmfao

[novel frigate]

there ya go!

[unborn dome]

so

[golden fjord]

i need some help plz

[unborn dome]

what do we do next

[raw shard]

at least you realized the mistake lol

if it’s greater than 0, it’s a minimum

local minimum maybe

right?

[novel frigate]

Your question just wanted you to find max/min stuff, so I think once you determine that you're done.

[unborn dome]

hm

thats wrong

[novel frigate]

no no, don't use the values from f''

it's either 0 or -1

[unborn dome]

neither values give u 8 tho

[novel frigate]

it might want the y-value?

[raw shard]

probably

[novel frigate]

Is that ALEKS?

[unborn dome]

https://tenor.com/view/walter-white-shocked-fall-4k-4160p-gif-21623835

[raw shard]

this channel is occupied bruh

[unborn dome]

so

wut do we do for the y value

[novel frigate]

plug in the x-values to the original equation

[raw shard]

plug in -1 and 0 into the original equation

[novel frigate]

so find f(0) and f(-1)

[unborn dome]

ah

8 n 5

poggies

[novel frigate]

there's the 8

[unborn dome]

thats so strange though

it never asked for y values

[next pulsar]

its not, its very natural

[raw shard]

it asked for the minimum and maximum values

[novel frigate]

yeah, some of the software is not so great

[raw shard]

implies y values

[novel frigate]

To you, but to a lot of students it should be more explicit in my opinion

[raw shard]

true

[unborn dome]

ty ty, u guys are doing a lot of help figuring out this topic for today since i missed class

[next pulsar]

yeah a common highschool pitfall is y = f(x)

catches everyone

[novel frigate]

I find the homework software vague for a lot of students 😦

[unborn dome]

uhh.......

how do we approach this. through anti derrivatives or.....?

[raw shard]

no

[next pulsar]

look at the first line that needs to be satisfied

f'(x) represents slope, so the first line is basically asking you "which of these graphs have the same slope at x=2 and x=4?"

[unborn dome]

the last one?

atleast well that one has two curves

so id assume

wait no

[next pulsar]

the last one is the only one which DOESNT satisfy this line actually

[novel frigate]

Since you missed class... Here's the important part of the way the derivative works for this stuff. A horizontal line has a slope of 0, so when we set our derivative equal to zero, f'(x) = 0, we're finding either a maximum point or a minimum point of our curve. So, this question is giving you the local max/min locations.

[unborn dome]

i see

max at 4 and min at 2?

so this one?

[next pulsar]

nah, f'(x) = 0 does not tell you whether it is a local maximum or minimum

it tells you that the slope at that point is flat

[unborn dome]

oh...

[next pulsar]

dont worry about maximums and minimums just yet

[unborn dome]

im so sorry im so clueless lol

[next pulsar]

do you see that only first three graphs have are flat at x=2 and x=4?

[novel frigate]

but he just had to answer a question about max/mins...

[unborn dome]

had it not been for this damm wisdom teeth i would be in class rn

[next pulsar]

yes and it was answered and hes on a new question now

[novel frigate]

yes, and I was trying to relate it to the question he just did...

[raw shard]

this question definitely needs knowledge on minimums and maximums

[next pulsar]

i was about to get to them

was going to go through the lines one by one

[raw shard]

@upbeat helm occupied

[next pulsar]

occupied

[upbeat helm]

sory'

[unborn dome]

anyways...

id have to look for when those 2 points are flat?

i'm kinda lost here but i have a good feeling its one of these two then

[next pulsar]

ok cool, let's get to the next line then, if f'(x) = 0 implies that a slope is flat, then what does f'(x) > 0 imply?

[unborn dome]

that the slope is not flat?

[next pulsar]

yep

is it going up or down?

[unborn dome]

up

ah

so it cant be the highlighted one

[next pulsar]

correct

[unborn dome]

okay

[next pulsar]

yes!

[unborn dome]

so

[next pulsar]

because the slope is going down in the specified region

[unborn dome]

dang

that wasnt that bad actually

[next pulsar]

wait

i read the bounds wrong

[unborn dome]

the answer was right

[next pulsar]

f'(x) > 0 if x < 0 is basically saying "the slope is increasing for negative x", right?

[unborn dome]

can we uh do one more question?

[next pulsar]

yeah im sure it is but oh well 😔

[unborn dome]

i have a few more but u guys must be busy

[novel frigate]

Today's actually my day off lol

[unborn dome]

pog

[alpine sable]

I'm using the rational zero theorem on an equation at the moment and using it I found that I did it correctly but once I hit the part where I need to use synthetic division it ends up with a remainder?

What do I do in this case?

[unborn dome]

this question looks borderline insane

[next pulsar]

do you know about derivative rules? namely chain and product rule

[unborn dome]

uh somewhat yes

very hard to memorize

but

[next pulsar]

its ok you will do so many of these that the rules will be etched into your brain

[unborn dome]

thats the goal

[next pulsar]

but basically you know how (fg)' = f'g + g'f

[novel frigate]

You just need to split these things into intervals, -2,3, and 5

[unborn dome]

how did you uh

turn them into opposite symbols?

[novel frigate]

and plug in test values into the given f' to see if hte sope is positive or negative

[unborn dome]

the

nvm

nvm silly quiestion

-2 + 2 = 0

[novel frigate]

Set them equal to zero

[next pulsar]

oh yeah wait you can actually just sub in values

bruh im slow tonight

[novel frigate]

yeah, they gave f', so you just need to do the increase/decrease tests

[unborn dome]

me every day

so we got -2, 3 , and 5.......

[novel frigate]

So, choose another value in the interval, such as -3, plug that into the given f' and see if it's positive or negative

The actual output values aren't important, just whether they are positive or negative

[unborn dome]

oh

so just plug any value

of -2 , 3 , and 5

back into the original equation

?

[novel frigate]

in between

[unborn dome]

ah

[novel frigate]

choose the nearest whole numbers

so between -2 and 3, choose 0

[unborn dome]

okay

[novel frigate]

between negative infinity and -2, choose -3

[earnest sequoia]

suppose you have an interval (a,b). if f'(x) > 0 on (a,b), then f is increasing on (a,b). if f'(x) < 0, then f is decreasing on (a,b).

[novel frigate]

Yeah, those the increase/decrease rules,

*those are the

[next chasm]

btw you can edit your message

[unborn dome]

jesus @novel frigate

[novel frigate]

like I said, the number is not important

[unborn dome]

oh right

positive or negative

[novel frigate]

just that it is negative or positive

[unborn dome]

in this case its negative

[novel frigate]

VERY negative haha

[unborn dome]

so

(-oo, 0)?

[novel frigate]

nah, negative infinity to -2 is your intervale

[unborn dome]

why stop at -2?

[novel frigate]

since f'(-3) was negative, use the rules Lawsick posted. This means your slopes are going down

Because that's your interval split from the original question, -2, 3, 5

[unborn dome]

hm

i dont think its -2

[novel frigate]

Well, you just found it was decreasing on that interval

since you said f' was negative

[unborn dome]

OH

it says increasing

jesus

so

(-2, infinity)?

[novel frigate]

no, next interval is -2 to 3

you need to test that one too

[unborn dome]

huh

so

plug in -2 and 3

in to original equation?

[novel frigate]

no, you'll just get zero

[unborn dome]

ah it flatlines...

[novel frigate]

yah! So, you need to choose values in between the flat lines

and see what they do

[unborn dome]

can i try -1?

[novel frigate]

yup!

[unborn dome]

or

just

okay

[novel frigate]

0 is technically easiest from an arithmetic stand point though

[unborn dome]

rip

okay

let me try uh 1

they're all negative

pain

[novel frigate]

yeah, so it just keeps decreasing... but there are still two more intervals (3,5) and (5, infinity)

[earnest sequoia]

in general, when you check whether a function g(x) is positive or negative on some interval (a,b), you try plugging in some number between a and b for the input, and then check if you get a positive or negative output

edit: this happens when g(a)=g(b)=0

[unborn dome]

gotcha

😮

plugging in 4 gives me 36 @earnest sequoia @novel frigate

[novel frigate]

whoo an increase!, check the last one

[unborn dome]

5?

thajt just gives me 0

cuz 5 - 5 is 0

and then you know

[novel frigate]

yup....

[unborn dome]

yeah..

so

(-oo, 4)?

[novel frigate]

so what other number can you choose between 5 and positive infinity?

[unborn dome]

wait no

4, infinity?

wouldnt any number

after

4

[novel frigate]

yes, so 4 is not an option

[unborn dome]

right

[novel frigate]

no, after 5

[unborn dome]

6 , infinity

[novel frigate]

yah

[unborn dome]

mbad

cuz after 4 is 5

and 5 gives u 0

in this

[novel frigate]

choose 6

[unborn dome]

6 , infinity it is

[novel frigate]

see if that gives you a positive

[unborn dome]

rip

oh and 6 does give me a positive

[novel frigate]

yeah, so the intervals (3,5) and (5, infinity) are increasing

You do NOT choose your test values as part of the interval

[unborn dome]

(3,5)U(5,oo)

[novel frigate]

yeah, if it wants unions?

[unborn dome]

well

dont u need unions

in this problem

[novel frigate]

increase/decrease answers are usually just a list

[unborn dome]

since on the intervals 3,5

and 5 infinity

[novel frigate]

Yeah, this is why I don't like software haha, typically you'd just answer (3,5),(5, infty)

Unions are usually a domain/range thing, because you're talking about the sets of values

[unborn dome]

rip

also tried unions that didnt work

[novel frigate]

get rid of the comma?

[unborn dome]

that doesnt work as well

god i hate lumen

[novel frigate]

try 3 to infinity

cut out hte middle man

[unborn dome]

but

3 to infinity

5 gives it 0

[novel frigate]

just try it

[unborn dome]

so just try (3,oo)?

[novel frigate]

yeah, if it it works I know why

[unborn dome]

HOW

HOWWWWWW

[novel frigate]

Ok, soooo, the nuance that happens with the definitions/theorems in this topic is that

when you plug in f'(5) you get zero, you MAY or MAY NOT have a max/min there

[unborn dome]

ty so much for the help @novel frigate btw, lmao i must admit im quite slow

May or may not?

tf

[novel frigate]

It's okay... you seem to be doing better than my students

Yeah, that whole "maybe" aspect is why you need to do test values.

[unborn dome]

deff not, i was supposed to come in class today :/

gotcha

ty so much for the help man

[novel frigate]

no problem 🙂

[unborn dome]

my niece came over and i gotta babysit, she's 2

[novel frigate]

lol, good luck with that

[unborn dome]

if u can, maybe we can do some more practice later?

[novel frigate]

harder than calculus!

[unborn dome]

lol yes.

[novel frigate]

Yeah, you can friend me if you want

[unborn dome]

🙏

I owe u one

[novel frigate]

No problem!

I just joined discord today, so I'm new to this thing

[unborn dome]

so

are you like a professor or?

think u mentioned students before

[novel frigate]

yeah, I'm a professor... answering rando math questions, you'd think I'd have enough...

[topaz flower]

is this channel now open?

[novel frigate]

yeah, you're good

[topaz flower]

okay perfect, i just want to check and see if i did this problem correctly

oop sorry its sideways, lemme retake the picture

[velvet osprey]

It's good

Parentheses are missing ln 3rd line tho

[novel frigate]

Should be -5x

[velvet osprey]

And may be = symbol

[novel frigate]

yeah, equals would be nice 😉

[velvet osprey]

Give a name to your polynomial too like P

[topaz flower]

Ok ok thank you

[velvet osprey]

There is a calculous mistake

Line 4

You didn't square 2i but only i I think

[topaz flower]

-i^2 would be +1, i did -2i^2 and did +2 in the next line

or is that wrong?

[velvet osprey]

It's not 2i^2 but (2i)^2

[topaz flower]

ok let me fix it one second

not quite done in here lol

i have one more after sorry

[next chasm]

lol

i had a question

3 people asked right after

im like i had a question

one of them wasnt in the server anymore

[topaz flower]

so the answer should end up being f(x)=x^3+2x^2-11x-12

[alpine sable]

Can someone help?

[topaz flower]

i think thats correct but when i type the question in on mathway it gives me x^3-6x^2+13x-20

i cant figure out where i would have went wrong?

[alpine sable]

Can someone help?

[topaz flower]

@velvet osprey does this look right to you?

[brittle crater]

uh hi?

can i send my question?

[topaz flower]

i mean im still trying to figure out if mine is correct

just waitinng on a response from a helper

[brittle crater]

ok

[lethal furnace]

I have three questions that I need help in solving

[lethal furnace]

<@&286206848099549185>

[magic pine]

@lethal furnace ping me if someone answers your question, I would like to know how it would be solved

[lethal furnace]

ok

[topaz flower]

Im still waiting for an answer on my ongoing question above sorry

[plucky crow]

is p AND if q then r = p OR if not q then not r

[wanton folio]

hey

[plucky crow]

then just draw a truth table

@lethal furnace

you know what each of those means rihgt

and, or

if

[bright remnant]

hey just a quick question, I got the equation -3(x-1)^2+9 and the vertex is (1,9)

its telling me to find the maximum value, is it the y value of the vertex or the x value of the vertex?

[alpine sable]

It looks like your function will yield a parabola

[bright remnant]

yes i know

[alpine sable]

And due to the - on a, that its a reversed one

Therefore the maximum point is Y

[bright remnant]

yes

thanks

[alpine sable]

The point of symmetry would be X (i hope thats what it was called)

[bright remnant]

mhm

[alpine sable]

But for max and min its Y.

And it can be found with the Y=-Delta/(4a)

help

Where a is the coefficient of x^2

[topaz flower]

please wait and dont post your question in a occupied channel

[alpine sable]

Transform every value into something with powers to take advantage of reductions

For example (9/16) = ((3/4)^2)^(5/2)

The powers multiply and the 2 gets simplified.

Do that for all and it shoudl be solveable

For example on 3/2 you have power 0 and n^0=0, n∊R* and regardless on what power you raise 1 to its still 1 so it disappears.

Thats the main idea or so it looks like it.

I didnt calculate it to check.

It may look ugly and "hard", but its made to be easy.

It forces you to use the properties of exponents.

[topaz flower]

Gonna repost this as it seems his question is solved and I never got an answer on if this is correct or not.

[vital timber]

when i do f_y is that chain rule?

[topaz flower]

#❓how-to-get-help please wait

[plain halo]

why is -(2i)^2 equal to -4

isnt it 4

[alpine sable]

How do you solve this ?

[topaz flower]

the person who was helping me before said it was -4

[meager barn]

i solved it, lemme send picture of solution

[alpine sable]

The calculations look right to me, exept the -1*-1 = -1, the fundamental theorem of algebra was used. Dont see anything wrong with it.

[alpine sable]

i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1

divide the powers by 4

[topaz flower]

sounds good

[meager barn]

so I did something wrong??

[alpine sable]

How come ?

[topaz flower]

im not sure, i think you did it correctly and i did it wrong somehow

mathway.com says you are correct, so im inclined to believe you lol

[alpine sable]

Thats how i behaves under certain powers.

I remember it by imagining a trigonometric circle with i

and imagine i to thee sides and up and down.

[meager barn]

see 4th step, there's mistake, - (2i)^2 = - [4(-1)= +4 , see it??

[topaz flower]

ah

that would do it

[alpine sable]

And using the property of i you can divide the powers by 4 and get the remainder.

That will be the power of your i, because i is cyclic (like sin and cos).

[topaz flower]

I see it now, thank you so much. I appreciate you solving it aswell.

[alpine sable]

Thanks!

Np, i hope i was of help.

[meager barn]

np

[topaz flower]

Hey PillDealBro you done here? I wanna throw in another question just want to make sure you are all done first

[analog nymph]

[meager barn]

you can also take conjugate

[topaz flower]

Unsure of how to solve this

[analog nymph]

width * length

oh x

[topaz flower]

I know A = W x L but i dont know what it actually wants me to do

[analog nymph]

me neither

there are many possible combinations

the question didnt specify if the side lengths are integers

if it did, then A=x^2

[topaz flower]

yeah thats what i was thinking but it seems too easy

and i also dont want to asume and get it wrong

I dont understand modeling functions at all

[meager barn]

but its reactangle ig

[analog nymph]

oh that stuff. yea idk modeling functions

[analog nymph]

square is a special rectangle

[unborn dome]

can someone help me with this?

[meager barn]

oh thanks

[unborn dome]

pretty sure I use quotient rule here

[meager barn]

already occupied

[topaz flower]

I honestly dont even know how to get started

Seems like the question doesnt give enough info

[meager barn]

check this??

[topaz flower]

Errr

It looks like you are doing it correctly, but im honestly not sure

[meager barn]

tbh I m also not sure, just started doing this stuff recently

[topaz flower]

I plugged 5 into X and it doesnt really check out

Just was trying to test it

[meager barn]

but here we don't know the "x" right??

[topaz flower]

we dont

but with the function we should be able to plug in an X and see if it checks out, no?

[meager barn]

lemme find x

well it seems there's mistake, sorry

[topaz flower]

No worries

I would be even more lost without you lmao

[prisma adder]

I have a question about matrix decomp

so I know how to decompose a matrix A = L*U

where L is a lower triangular matrix and U is an upper triangular matrix

Now let A = [4,-1,-1;-1,4,-1;-1,-1,4]

I was able to decompose it into LU but one of the question asks me to decompose it to Ltrans(L)

But I don't know any method of doing that

Any help would be appretiated

[topaz flower]

I think you were actually on the right path

It should be solvable by plugging in a variable as its a function

[topaz flower]

Might get an answer quicker if you go to a channel thats not occupied currently

[alpine sable]

How would I go about solving this for x?

I also need to do it using the quadratic formula

[topaz flower]

Might get an answer quicker if you go to a channel thats not occupied currently

[meager barn]

so my solution is correct?? or still not sure??

[topaz flower]

no i dont think it is, but i think you were on the correct path

the problem is i dont think your solution was solvable by replacing X with a number such as a 5

Using 5 for X we can go backwards and see that the area would be 100m not 25m

[meager barn]

ohh, lets give it another try then

[topaz flower]

im not sure

i cant seem to figure out a way to make it solvable

is it supposed to be solvable, right?

its a function

[meager barn]

i got it right now

[fresh quail]

$$"\answer {-\frac {1}{4} , \pi {\left (\cos \left (49\right ) - \cos \left (16\right )\right )}}$$'

[topaz flower]

i cant quite read the second to last line, its ? x A(x) = 25/? x X

[meager barn]

does it make sense??

[alpine sable]

Yeah

It makes

[topaz flower]

Yes I get it!!

[alpine sable]

Oh sorry for intruppting

[topaz flower]

no worrie

im just happy i finally get it

@meager barn thank you my man

i was overthinking that so hard

[vestal hollow]

(This is for deriving the solution to the wave equation)

So here it says F_n(x) = Csin(xnpi/L)

But the question is asking for this

Where does C go?

This is the only explanation I can find, but I don't understand it

[meager barn]

yw!

[next pulsar]

I have a problem which requires me to determine whether or not some variables in a multiple linear regression model are needed

what are some ways I can determine if a variable is "needed"?

check p values?

[lapis sluice]

ok so I want to write that my equation is equal to 0 because of s = 0, but i don't want to do it this way.
$$equation... = 0 \hspace{50pt} \text{because} s = 0$$

[ocean seal]

Danajax

[polar egret]

hi

[lapis sluice]

would it make sense if i write $$equation... = 0 \because s = 0$$

[ocean seal]

Danajax

[novel frigate]

I say phrasing it like "Since s = 0, equation... = 0" makes more sense.

[lapis sluice]

ah thx, that is possible too

i have never used that $\because$ notation, therefore i was wondering

[ocean seal]

Danajax

[novel frigate]

Yeah, I've never really seen it either, so I'm not sure how common it is. I see $\therefore$ a lot though.

[ocean seal]

nullset

[craggy stream]

yeah

im lazy so i avoid using words whenever i can

[lapis sluice]

Ok thx, It's common sense that mathematicians are lazy xD

[ivory gulch]

so far i've rewritten like this

$\lim _{x\to \infty }e^{2x\ln \left(1+\frac{1}{x^2}\right)}$

[ocean seal]

ski

[craggy stream]

do u know l'hopital's rule

[ivory gulch]

yes

i just dk how it applies here

[craggy stream]

it applies to fractions of the form 0/0 or infinity/infinity

so can u somehow rewrite the power as a fraction

ignore the e for now and focus on 2xln(...)

[alpine sable]

the solution is i

[ivory gulch]

i could distribute and combine

[craggy stream]

its simpler than that

[ivory gulch]

then i’m not sure

could i get another hint

[craggy stream]

$\frac{2log(1+x^{-2})}{x^{-1}}$

[ivory gulch]

haha

cursed latex

[ocean seal]

AKS

[craggy stream]

now its of the form 0/0

[ivory gulch]

ok so derive

one sec

[craggy stream]

differentiate

[ivory gulch]

yes

2(-2x^-3 * ln(1+x^-2))

#❓how-to-get-help

[ivory gulch]

2(-2x^-3 * ln(1+x^-2))

?

[craggy stream]

i havent checked xD

[ivory gulch]

oh ok haha

[craggy stream]

it doesnt matter what it is actually

can u find the limit of it now

[ivory gulch]

no idk how to find the limit

[craggy stream]

oklemme differentiate it myself too

[ivory gulch]

$\frac{2\left(ln\left(1+x^{-2}\right)\cdot -2x^{-3}\right)}{-x^{-2}}$

[ocean seal]

ski

[ivory gulch]

yeah i haven't changed the negative exponents back

[craggy stream]

u forgot to differentiate the ln bit

[ivory gulch]

oh ur right

$\frac{2ln\left(1+x^{-2}\right)}{x^{-2}+x^{-4}}$

[ocean seal]

ski

[ivory gulch]

@craggy stream

?

[craggy stream]

i dont think thats right

oh it is nvm

[ivory gulch]

nah it's not

i just realized haha

$\frac{-4x^{-3}}{x^{-2}+x^{-4}}$

[ocean seal]

ski

[craggy stream]

yeah lol

also it should be +

[ivory gulch]

ok so now what

why would it be +

[craggy stream]

u can rewrite it as 4x/(x^2+1)

[ivory gulch]

d/dx x^-2 = -2x^-3

-2x^-3 * 2

[craggy stream]

yeah but theres x^-1 on the denominator which gives -x^-2

[ivory gulch]

makes sense

forgot ab that

[craggy stream]

.

now its easy

[ivory gulch]

yes so easy

but if u want u can explain it to me

for fun

[craggy stream]

xDD

[ivory gulch]

like obvi i already know how to do it

but just for fun

🤣