help-36

[slender tendon]

unless I need to be using a different "Rule" or property

[soft zealot]

Ken_

Ken_
Compile Error! Click the reaction for more information.
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[slender tendon]

?

[void crest]

a random came in

[slender tendon]

oh

[void crest]

n used bot stuff

ok so whats

f'

[slender tendon]

did I break some rule? and to answer the question I don't know if I should be using the product rule or something else

[void crest]

eh

u can use product rule

but i think power rule works btr here

product rule wld b applied twice

power rule, once

but power rule comes w chain rule so lol

[slender tendon]

oh

so the answer would be......(Let me try this again)

[grim nebula]

product rule o boi

[void crest]

(fff)' = f'(ff) + f(ff)' = f'(ff) + f[ff' + f'f] = 3fff'

[slender tendon]

Sorry had to leave

[final saddle]

@slender tendon Has your question been resolved?

[slender tendon]

soo let me try this

-54?

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[unkempt swift]

the highlighted ones

[unkempt swift]

so from what i know

this is my proof for part b

im not sure how to prove the additive property though

[icy glacier]

Tried searching for counterexamples?

[unkempt swift]

erm

i thought i had to prove generally

oh wait its for all

so i just need one counter example

[unkempt swift]

ohhhh

thx

lemme write that down

so for these types of questions

how do i know if its true or false, lets say i cant think of a counterexample

[stoic mural]

hmm

step 1:

intuition

think whether it makes sense

step 2:
find a counter example if you think it has to be false

step 3:
if you can't find one or think it is correct
try to prove it

in b)
we would have
a=(w,x,y,z)
b=(w',x',y',z')
a+b=(w+w',x+x',y+y',z+z')
check if a+b is in the subspace
(w+w')(x+x')=(y+y')(z+z')
wx+wx'+w'x+w'x'=yz+yz'+y'z+y'z'

we know wx=yz and w'x'=y'z'

so we are left with

wx'+w'x=yz'+y'z

where we would be stuck

[unkempt swift]

is that what i did for additive property

XD

it seems awfully similar

[unkempt swift]

when i reached this point, i was asking myself if i missed out something

[stoic mural]

in this example i dont know how to find counter examples so i just tried out stuff, but in general when the proof fails it often either gives a contradiction or leads us in the way of a counter example

but yea in this case i just guessed

[unkempt swift]

ah i see

[stoic mural]

btw e) is not a subspace

[unkempt swift]

no pls why did u tell me

LOL

[stoic mural]

e) can be done by step one

intuition

[unkempt swift]

hmm

lemme finish up part b first

one sec

[stoic mural]

👍

[unkempt swift]

hmm

i dont see how its not tho

so we need these 3

the first one is def possibl

[stoic mural]

try additive

the third one

[unkempt swift]

oh

okay

hmm

but both the vectors are going to have numbers in the x and z coordinates

so wont the condition always hold true

[stoic mural]

uhm,

e) says that either x or y has to be 0

not both

[unkempt swift]

omg

[stoic mural]

so lets look at vectors where only one is 0

add them

boom

[unkempt swift]

ah yes

[stoic mural]

chaos

[unkempt swift]

i understand now

[stoic mural]

🙂

[unkempt swift]

lemme change it

ah

[unkempt swift]

how am i supposed to go about solving for g lol

any tips?

[stoic mural]

yeah

start by rewriting the subset

simplifying the rules

to get a general vector in the set

[unkempt swift]

hmm okay

so like

[stoic mural]

w+z=0 means w=-z

[unkempt swift]

ill sub the equations into each other

right

[stoic mural]

exactly

[unkempt swift]

lemme do that

so now i have x = -z

[stoic mural]

x=-z and -z=w
therefore x=w

[unkempt swift]

ohhh

right

okay so now this is mega simplified

[stoic mural]

so a general vector in terms of w looks like this:
(w,w,-5w,-w)

[unkempt swift]

right

hmm

lemme try using intuition

so the zero vector is def possible

[stoic mural]

just scaling it by a c won't change things, will still be in the set

yes

0 is possible

now for a+b

[unkempt swift]

right

now addition

hm

i would think its in the set

cuz im adding two coordinates with the same constant

so it should be the same

or am i missing an edge case

[stoic mural]

let a=(w,w,-5w,-w) and b=(w',w',-5w',-w')
a+b=(w+w',w+w',-5w-5w',-w-w')
=((w+w'),(w+w'),-5(w+w'),-(w+w'))

w+w' is in our field, R

[unkempt swift]

so its the same yes

[stoic mural]

yes

👍

[unkempt swift]

a ha

[stoic mural]

works

[unkempt swift]

thanks

lemme do it

thanks for the help sir

[stoic mural]

you're welcome^^

[unkempt swift]

.clsoe

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[fallow bolt]

how do I solve this?

in previous questions ive included my calculations but theyve been just confusing 😄

[brave elm]

Cos is 0 on 90°

[stoic mural]

and 270°

[zenith sierra]

and 450°

[fallow bolt]

damn guys, I need a graph?

[stoic mural]

and when adding 360 of course

[brave elm]

Yup

[fallow bolt]

cant we do it with a pure equation (without re-writing too much)

[stoic mural]

,w (arccos(0)-1)/2

[soft zealot]

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Requested by ~Martin#3125

[stoic mural]

0.5(0.5pi-1)

however

0.5(0.5pi+n×pi-1) where n is an integer

[fallow bolt]

thats insane

this is what the result (should) be

I wouldnt think it to be too complicated, since this is just the first course on engineering mathematics

[fallow bolt]

I can't even read these (not knowing the more complex formulas)

skill issue, I know, but still

[fallow bolt]

how do I expand to this form??

from 1/4*(Pi-2) that is

and even so it doesnt explain what the addition of Pi+number means

[final saddle]

@fallow bolt Has your question been resolved?

[fallow bolt]

<@&286206848099549185>

deep knowledge is needed

[distant hawk]

It depends on what level you are in.

You could be one of the following.

(1) You may be learning simple right-angled triangle perspective, in which your trig knowledge is only within 0 to 90 degree.

(2) You may be learning trig in unit circle, in which you will need to solve for possible solutions btw 0 and 360 deg.

(2.5) You may be taught with radian when you learn the unit circle trig topic, in which your solution will be between 0 to 2pi

(3) You are beyond all the above, and really want to find the so-called general solution for trig equation, in which your solution can go beyond 360 degree.

The question is, which one are you in? 🙂

[fallow bolt]

an example equation, but it has two functions together which makes it easier.

[distant hawk]

Then CAST / ASTC diagram should be helpful for you.

[fallow bolt]

ill have to look into it

thank you 🫡

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[keen fog]

Hey, I skipped lot of my maths classes and now I need help. Just a quick stupid question that I arised when solving quadratic equation. Can some one explain me the why 1st one is wrong. I swap the factors. 43 as 34 why this is wrong. Please help me

[supple jolt]

Becuase

The order doesnt matyer

Matter

You didnt factor correctly at the 1st one

[tired walrus]

@keen fog you typo'd in the last line in #1

should've had (x+4)(x+3) = 0

that's the only thing that is wrong

[supple jolt]

Yes

[keen fog]

Thanks @tired walrus and @supple jolt. But this is not a typo I think I haven't much idea on factorization. I just take it like this. I followed product sum technique like this. Can anyone tell me is there any specific way that we need to follow when doing this

[supple jolt]

The 3 and 4 are correct

Only the last step is wrong

[supple jolt]

This is correct

[tired walrus]

talking about this here

the four became a three

this is a typo

unless you're gonna tell us that you consciously decided to make that four into a three

[keen fog]

I did it consciously. I thought that the expression inside the brackets are the pairs that we can obtain

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[tired walrus]

you can't

it's false

take a=b=1/2

LHS will be 2/3 while RHS will be 3/4

[harsh marlin]

yes i should have checked also but i trusted authors of the book 🙂

ok

now i have another similar problem

@tired walrus

[tired walrus]

...bound each fraction from below by 1/(2n) and win

[harsh marlin]

like this ?

but how do we know that k is not greater then n ?

@tired walrus

[tired walrus]

k is n

you have n fractions

1/(n+1) + 1/(n+2) + ... + 1/(2n) is a sum of n terms

1/(n+1) + 1/(n+2) + ... + 1/(2n) > 1/(2n) + 1/(2n) + ... + 1/(2n) [still n terms] = n/(2n) = 1/2

[harsh marlin]

tnx

i got that

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[sullen mauve]

A hexadecimal string consists of hex digits:
0,1,2,3,4,5,6,7,8,9,𝐴,𝐵,𝐶,𝐷,𝐸,𝐹
d) How many hexadecimal strings of length 𝑛 have exactly 𝑘 letters? 6^k * 10^(n-k)
Is this correct? I am told to multiply what I have by a combination of (16 6) which does not make sense to do because then tests don't pass (ex: n=2 and k=1)

[sullen mauve]

or could it be (n k) * 10^(n-k)

[dusty harbor]

oh god sorry yes it would be (n k)

i confused the two my bad

[sullen mauve]

so what would be the full thing

oh i figured it out thank you

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[ripe gull]

I don’t know how to do B, I know for A u just plug in the t to verify

[ripe gull]

Nvm I got it

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[slim shell]

Hii

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Please don't occupy multiple help channels.

[slim shell]

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[tranquil pine]

‘Explain in details of following scenarios when solving linear equations’

[tranquil pine]

Need an explanation in details of one solution, no solution and infinite solutions

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[heavy loom]

one solution is when the two lines intersect once

no solutions is when they're parallel

infinite is when they coincide

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[tranquil pine]

in detail

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[blissful blade]

Hi, Can somebody help me with Multivariable Calculus Problem, the t belongs to -infinity to +infinity.
<@&286206848099549185>

[final saddle]

Please don't occupy multiple help channels.

[blissful blade]

previous one got lost -_-

hello there ? 👨‍🦯

[wraith crater]

This means the least distance?

[blissful blade]

yes, more like displacement.

because the point is perpendicular to the plane

[wraith crater]

Well Least distance = displacement

[blissful blade]

yes.

Main problem here is that the vector eqn has a variable t

which belongs to -infinity to +infinity

[wraith crater]

Let’s say the point on the line is $\begin{pmatrix}
2+2\lambda \
1+6\lambda\
3\
\end{pmatrix}$

[soft zealot]

Pure

[wraith crater]

For some lambda

Call this point Q

Find the vector from (2,1,3) to Q

This must be perpendicular to the direction vector of the line

Which is (2,6,0)

[blissful blade]

the point P(2,1,3) is the point from where I have to calc the distance to the plane

[wraith crater]

Ye

Find lambda first

[blissful blade]

okay, the best method of finding the value of lambda is ?

acc to this situation ?

[wraith crater]

PQ dot (2,1,3) =0

[blissful blade]

this gives me the value of lambda right?

Just double-checking, can't mess up rn ! :(

[wraith crater]

This gives you a linear equation in lambda

[blissful blade]

okay.

right.

then I solve that for lambda & my problem is solved.

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[timid oyster]

Hello, I know i need to integrate the function and i need f'x/fx but how do i go about this when the numerator is 'ax' rather than like '4x' for example?

[vestal frigate]

If A is a constant, treat it like you would any other constant

For example

[timid oyster]

oh okay, so make is 2ax?

[vestal frigate]

If A is a constant: $\frac{d}{dx}Ax^3 = 3Ax^2$

[soft zealot]

lexitorius

[vestal frigate]

Just like how $\frac{d}{dx}2x^3 = 3(2)x^2$

[soft zealot]

lexitorius

[vestal frigate]

(My numbers are different from your problem)

[timid oyster]

hmm okay i see, i just wanted to see if there were any differences for integration

thanks for that

[vestal frigate]

Just pretend it's any other number, the same properties apply

$\int A dx = Ax + C$

[soft zealot]

lexitorius

[vestal frigate]

Where C is also a constant lol

[timid oyster]

ok cool ty

[dusty harbor]

$\int A dx = A \int dx = Ax + C$

[soft zealot]

Gijs

[vestal frigate]

If A is a variable, that's when it throws this for a loop, but assuming A is a constant these are true

I think we can assume it is since we're given A > 0 and x is the only letter stated to be a variable

[timid oyster]

yeah all good, now treating it as a constant my working aligns with the work solutions 👍

[vestal frigate]

👍

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[swift stag]

what is displacement?

[dusty harbor]

like with water

[swift stag]

displacement is the net amount of distance moved?

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@swift stag Has your question been resolved?

[pine valley]

Yup, basically displacement is just the net amount of distance traveled

Like, here's an example of distance vs displacement

I move 10 meters north, and 10 meters south

Displacement would be 0, since I have moved a net 0 meters, while distance would be 20 m, since I traveled 20 meters in total

[swift stag]

that makes sense, thank you! @pine valley

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[dull orchid]

is this B

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[tranquil pine]

how do i do thiks

how do i do this?

Given: \angle A \cong \angle EBC∠A≅∠EBC and \overline{AB} \cong \overline{BC}.
AB
≅
BC
.

Prove: \overline{BE} \parallel \overline{AC}
BE
∥
AC
.

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[fossil geyser]

My guy. You spammed the same question four times in somebody else's help channel

Read #❓how-to-get-help

@dull orchid I'm gonna close this channel since it got kinda hijacked and I see you already opened another one

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[jaunty zinc]

Help

[final saddle]

Please don't occupy multiple help channels.

[exotic hill]

Can you share your solution?

[jaunty zinc]

@exotic hill

[exotic hill]

Better to use y^2 = 7+sqrt(7+sqrt(x))

Y^2-7= sqrt(7+sqrt(x))

Task will be more easy

[jaunty zinc]

Where u get y from

[final tangle]

don't multipost

i've already responded in your original channel

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[floral wind]

how did my teacher know that its a horizontal ellipse?

[floral wind]

also how did they get the a and b values

[honest carbon]

From the foci coordinate

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[light brook]

can i get help on problem #9 please

[exotic hill]

Flip it

You will see magic happens

It will be 87x^5 * 8/21 x^2

[light brook]

is it 232/7 over 237/7

i’m stuck between those

[exotic hill]

Where is your x?

[light brook]

nvm

it’s 232x^3/7

😩😩😩

[exotic hill]

👍

[light brook]

thank u!!!

🙂

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[tranquil pine]

can someone pls help me with this

[muted prairie]

how much money went in?

[tranquil pine]

1689.8 mil ?

[muted prairie]

nah

[tranquil pine]

in like total ?

[muted prairie]

that's starting balance

8 people are in a house

6 more people walk in the house, and then 2 people leave

how many people are in the house now?

[tranquil pine]

12

[muted prairie]

yeah

same principle here

323.3M money enters the company

and 171.4M leaves

[tranquil pine]

151.9M

what abt the 1,689.8 mil ?

[tranquil pine]

is this the right answer ?

if it is thanks

.close

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[muted prairie]

add that to the start as well

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[wind spire]

How can I do this

I know how to do the first one

But what about d/da and d/db

[wraith crater]

Treat other variables as constants

When differentiating wrst a, treat x and b as constants for example

Assuming they are all independent

and a and b are not constants

[odd dove]

I find it concerning they didn't use partial derivatives here, so yeah, we have to assume they are independent.

[wind spire]

Can you show me how its done, please

[soft zealot]

Pure

[odd dove]

Essentially the same you have always done with x, but instead a is your variable and everything else is constant.

The purpose of this exercise is to presumably get you comfortable with the fact that using x as the letter for your variable is arbitrary.

[wind spire]

Can you show me step by step what do I do

I have only defined d/dx

Derivatives

[wraith crater]

Did you not see why this is the result of b?

[wind spire]

Not exactly

My teacher hasn't teached this type of things yet

[odd dove]

$\dv{(b^2)}{b}$, could you compute this?

[soft zealot]

Remavas

[wind spire]

No

[odd dove]

What about $\dv{(x^2)}{x}$

[soft zealot]

Remavas

[wind spire]

I don't know how to deal with that

[wraith crater]

How did you deal with part a?

[odd dove]

$\dv{x} (x^2)$?

[soft zealot]

Remavas

[odd dove]

maybe it's the notation

I hope

[wind spire]

With part a I did 3 * 2x - b * 1 + 0 , 6x - b

[odd dove]

well yes.

so you differentiated it with respect to x

can you differentiate b^2 with respect to b?

[wind spire]

Its 2b

Isn't it?

[odd dove]

🥳

[odd dove]

As you can see, you just do the same you always did.

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[oak kraken]

Do you ever use the words minuend, subtrahend, and/or addend on a regular basis with math? If not, how come?

[oak kraken]

Factor, dividend and divisor (numerator and denominator) seem a lot more common place words to me .. just wondering why that is?

[tired walrus]

addend maybe sees occasional use

minuend and subtrahend no

[oak kraken]

With calculus?

[oak kraken]

Hmmm I wonder why this is…

[tired walrus]

🤷

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[cunning axle]

hi

please i need help in this question

[amber holly]

Just keep adding 4 to 14

[cunning axle]

lol should i write that in the solution

[odd dove]

No, you do that until you have six terms

[cunning axle]

and what about that ?

[odd dove]

well, what are your thoughts?

[cunning axle]

actually i don't have an idea

[odd dove]

Well, what do we do each time with the number to get the next one?

[cunning axle]

adding?

multiplying by 3 ?

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[rare lily]

Hello! I have a concern rather then a specific math question. I am currently taking AP Calc BC and have taken Precalculus before however I am struggling in class. I finished Precalculus with a 99 in my first semester and a 100 second semester however in Calc I have a 90 right now. I struggled with derivates and am not sure how to move forwards. I was wondering if anyone had any advice as to how I can get better grades.

[topaz bone]

Better for #math-discussion

or just #discussion

[odd dove]

I much prefer https://www.derivative-calculator.net/

Here are some pretty great notes: https://tutorial.math.lamar.edu/

Specifically, you might want to check out https://tutorial.math.lamar.edu/Extras/StudyMath/HowToStudyMath.aspx for tips on how to study math

[rare lily]

Thank you so much! I apologize if I posted in the wrong place! My teacher said that my concepts were fine so I was wondering if there was a place where I could take practice tests for certain units?

My points are mainly taken off because of formatting issues rather then math itself however my teacher does not emphasize that on any reviews he gives so I was wondering if there was a guide for things like that

[odd dove]

has a lot of practice problems

[rare lily]

Thank you! Also, are there any recommendations for self-studying such as the 5 steps to a 5 book or should I use these online notes?

[odd dove]

hm.

Demidovich has a massive amount of practice problems. I think there is an English version.

Otherwise, you can't go wrong with most calculus texts

I do recommend these online notes however.

[rare lily]

Ok thank you so much! I will look into both sources!

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[rustic tangle]

im confused on how to solve this, "if sin 0 (theta) = 3 find, in exact form, the possible values of sin 0 (theta)

[rustic tangle]

any help is appriciated

[dusty harbor]

what is sin 0 (theta)

[delicate quest]

I don't think thats solvable

he means 0 is the theta symbol

[dusty harbor]

oh aight

[dusty harbor]

it has complex solutions

[rustic tangle]

yeah sorry 0 means theta

[dusty harbor]

$\sin{\theta} = 3$

[soft zealot]

Gijs

[odd dove]

well, let's ask the OP whether theta is complex or not.

[rustic tangle]

what does that mean

[odd dove]

theta is real then.

Now, what is the range of sine?

[rustic tangle]

it doesznt say just says find the possible values of sin theta

[dusty harbor]

you know what the range of sine is

what values can sine take on?

[rustic tangle]

sorry internet went out

no

just that theta is the same in tan theata and sin theta

[odd dove]

what is the smallest and biggest sine can ever become?

[rustic tangle]

im not told

[odd dove]

.........

,w plot sin(x)

[soft zealot]

Results provided by WolframAlpha

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

Requested by Remavas#3737

[odd dove]

Any guess as to what the range of sine is now?

[rustic tangle]

ive got no clue

how about a different question, "if s = sin x and 90 degrees < x < 180 degrees, express cos x in terms of s

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[rustic tangle]

.close

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[crude dust]

Hello so I’m trying to Derivate this

[crude dust]

And I tried multiple times

The answer just can’t be like what my teacher gave me

[thorn grotto]

Did you try to move all y's to one side and all x's

[pulsar rampart]

xy²+y²+x = 0

What is the question?

[thorn grotto]

Use separation of variables

[crude dust]

Yes and this is how It came out

Way different from what my teacher gave me

He said that there’s a trick

[thorn grotto]

You started with dy/dx = -y^2/2x^2 right?

[crude dust]

It’s been like a while trying figuring it out

[crude dust]

Wym?

[crude dust]

This is how I started

[thorn grotto]

Can't you factor the y as well?

[crude dust]

Should I factor 2y?

Or just y?

[thorn grotto]

Doesn't really matter

[crude dust]

So it’s like this

[thorn grotto]

And multiply by 2y

Then write y' as dy/dx

And move the dx over

[crude dust]

Like this?

[thorn grotto]

Yes

[crisp plover]

Their final answer looks wrong unless there is additional context and so is yours. You are missing the product rule. The implicit derivative of xy^2 is y^2 + 2xyy'. Not what you wrote.

[thorn grotto]

Omg, thought it was a differential equation

Ima go to bed

[crude dust]

Sorry I didn’t pay attention

[crisp plover]

I just thought you went off the rails but I can totally see that now

[crude dust]

It should come out like this right?

[crisp plover]

no

[crude dust]

How so

[crisp plover]

I would hope it is obvious if you spend more than seconds looking at your work before asking.

[crude dust]

Cant see it.

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[twin knot]

So I have a question regarding "What are the last two values in 7^123" I am supposed to use Euler's phi and modulo to calculate this I think

[twin knot]

If I set the mod to 100, then I will get only the last two values

[desert mantle]

yes

[twin knot]

That said, phi(123) = 80

So I don't think it can be used?

[desert mantle]

wrong phi to calculate

[twin knot]

...

Oh yeah

Woops

Sorry, it's late

Thanks for the help

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[languid adder]

Hi

[languid adder]

Hi

Don’t get 27, 28, 29

[languid adder]

Anyone?

.close

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[languid adder]

.reopen

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✅

[languid adder]

i need help

[vale python]

So you know what the sun of the angles of a triangle add to, right?

[languid adder]

ye

180

[vale python]

Do you know what it is for any quadrilateral? Aka a four-sided figure

[languid adder]

360

[vale python]

How many sides does the shape in 27 have?

[languid adder]

4

[vale python]

So, what is the sum of the angle measures for 27?

[languid adder]

360

[vale python]

Right

[languid adder]

thats it?

[vale python]

For that one, yeah

[languid adder]

bruh

[vale python]

I suppose you could draw a diagonal to split it into two triangles

Then it would be 180+180

[languid adder]

oh ye

[vale python]

Same answer tho

[languid adder]

how about 28

[vale python]

But yea, it wants you to draw an edge between two vertices on 28 and 29 so that you break it into smaller shapes that you know the angle measure of

[sinful terrace]

Cut them into triangles is a good way to think about it, cause each triangle has 180 degrees in it

[languid adder]

ye how would 28 work

i split them into triangles

[sinful terrace]

Here's a shortcut to get your answer quickly for any regular shape.

Count the number of sides the shape has.
Minus 2 away from that number (e.g. if you have a pentagon you have 5 sides, so take away 2 gives you 3).
Then times that new number by 180

[languid adder]

really?

[sinful terrace]

for real yo :v

[languid adder]

so 28 is 540?

[sinful terrace]

(Number of sides -2) times 180

seems right to me

[languid adder]

wait

so basically the same thing as

[sinful terrace]

cause you can split it up into 3 triangles

[languid adder]

180+180+180

add 180 everytime theres one more side

[sinful terrace]

yep :v

[languid adder]

oh bruh

i also need help with something else

[sinful terrace]

because with each side your adding its like you add the potential for another triangle (starting with triangle at 3 sides, then square with 4)

[languid adder]

oh ye

31

can u explain 31

im bad with proofs

[sinful terrace]

Okay so in english I think its saying
Givin the Line GK bisects (stops at? Goes through?) the angle JGI
and the angle at H is the same as angle at I
Prove that the line GK is paralell to HI

[languid adder]

ye ik

lol

[sinful terrace]

Im not use to this language myself so I had to write it out lol

[languid adder]

ohh

ok

how do u it then

[sinful terrace]

The only other bit of information we have is thatthe anfle JGK is 1 and the angle at KGI is 2?
Also, the line GJ appears to be paralel with GH

hang on, tryna work it out xd

I should know this its just been a while

[languid adder]

xd

[sinful terrace]

Calling them angles "1" and "2" is dumb; you're teachers taught you algebra yet?

[languid adder]

ye

[sinful terrace]

Alright, just cause it'll confuse me otherwise, I'm gonna call angle "1" x
And angle "2" y
I'd tell your teachers off if I saw them giving you this paper >:I badly written

nonetheless the system needs to be appeased T-T

[languid adder]

ye

[sinful terrace]

right, so we know that the angle at H is the same at the angle at I, lets call this angle z

That means you have an isoceles triangle

[languid adder]

ye

[sinful terrace]

we know that angles in triangles equal 180, so the angle at the top of the triangle bit (HGI) is 180 - 2z
You don't necessarilly need to know this, I'm just writing out as im analysing the problem

[languid adder]

oh ok

[sinful terrace]

Okay so I looked up definition, turns out bisects means to divide into equal parts so angle 1 is equal to angle 2

[languid adder]

ye

ik xd

[sinful terrace]

so if angle 1 is equal to angle 2, then that means that these must have the same angle as z (the angles at H and I), because they share in common the anfgle at G (HGI)

yeh Ikr, check me out, big time mathematician I is....

[languid adder]

lol

its fine if you dont know how to do it xd

[sinful terrace]

anyway, the angle HGI is 180 -2z
but the angle at the same place from the line HGJ is also 180 cause its a straight line. As it happens we know that this angle must be angle 1 + angle 2 + angle HGI
We know that HGI = 180-2z, so since angle 1 and 2 are equal
Angle 1 must be: 180-(180-2z) - angle2 = 2z - angle 2
And Angle 2 Must be: 180-(180-2z) - angle1 = 2z - angle 1

Tldr angle 1 and 2 are equal and they are both the same as the angles at H and I.

When you take the angle to go "up" from angle H you go up an incline of z but when you come back down again by angle 1 you also come "down again by an angle of z, meaning the lines dont deviate from each other and they are paralell

there's probably a much much neater way to explain it but its beyond my pay limit xd

good luck

[languid adder]

thats it?

[sinful terrace]

I mean, I can see it but I cant really explain it well and your teacher will probably want a more clear explaination but what do they know, they call angles 1 and 2 >:I

angles 1 and 2 are the same as those at H and I

[languid adder]

ye

oh well thx

ill try it

[sinful terrace]

good luck :v

[languid adder]

ye

my teachers high

she just gives us work wihout explaining

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[hearty spruce]

Hi, just wondering how to frame this question: Factor fully; px ^3 + (p-q)x^2 + (-2p -q)x +2q

[hearty spruce]

Factor fully; px ^3 + (p-q)x^2 + (-2p -q)x +2q

[dreamy shadow]

I would most likely just write "Factor the polynomial px ^3 + (p-q)x^2 + (-2p -q)x +2q as far as possible" or something like that. Don't think you have to do anything fancy, not sure what it's for or if there is any restriction you need to adhere to

[hearty spruce]

No restrictions really, just know that the furthest my knowledge spans to regarding factoring this, is the factor theorem and remaind theorem.

Currently Gr. 12 University Math.

Advanced Functions if you're familiar.

[dreamy shadow]

wait are you asking how to solve this or how to write this as an exam question (as a teacher)? sorry i'm abit confused now sorry

[hearty spruce]

How to solve haha

No worries.

[dreamy shadow]

ohh sorry i thought with "how to frame" you meant you weren't sure how write it up as an exam question. ohh god now i need to actually use my brain XD

[dreamy shadow]

okay so i might have figured out what they are going for

start by resolving the parentheses

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[hearty spruce]

Sorry, spaced out.

YK what, I think a friend will send me an answer

Its ok man

Thank you for the help

-close

close

?

oh

.close

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[hearty spruce]

Noice

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[stray stump]

Is the variance correct?

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[nova fractal]

the sum of int angles of a reg poly is 200 degree. what is the measure of its ext angle

[cold gorge]

Sum of interior angles of a regular polygon is 200 degrees? Are you sure?

[nova fractal]

exactly

I was so confused

[grim badger]

Where is the question from? Book? Paper? Because post a picture of it

[nova fractal]

it's from a book

[grim badger]

Then post a picture of it

[heavy loom]

don't you love a -0.89 sided polygon

[nova fractal]

I'm trying to

[nova fractal]

LOL

[grim badger]

Technically it's a 28/9 sided polygon

[nova fractal]

It keeps saying error. Anyway, it's just as simple as ext + int = 180 soo I don't really mind

thank you anyway

[heavy loom]

o yeah you add 2 i screwed it up

[nova fractal]

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[lapis forge]

is this a quadratic expression where a=4,b=-1,c=10? or does the presence of the "2/___" not make it quadratic?

[trail mango]

that makes it not quadratic 🙂

[lapis forge]

gotcha. i understand that the opposite like "/2" is still quadratic where A=1/2 of whatever A is in the original ""

just wanted to make sure that "2/____" wasnt quadratic

ty

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[sinful steppe]

How would I find part (b) if I already know that the equation is y = -2.36cospi/6(x-4)+3.89

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[fathom walrus]

Set ur eqn equal to 4

Then solve for x

Assuming ur eqn is correct ofc

Keep in mind u start at 4AM

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[sinful steppe]

do you know how i would know what quadrant it would be in ?

like in relation to the unit circle since it is sinusoidal

[sinful steppe]

because i did this and did not get the right answer

[fathom walrus]

Not sure abt the quadrants, but what did u get for the values of x

[sinful steppe]

i got 3.94617932122

the answer sheet says i shouldve gotten

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[dusty harbor]

where are you stuck?

[tranquil pine]

I don't know how to get expected value given sigma and phi function

the only equation I found was an integral for PDF which my professor said was very difficult to work with

[dusty harbor]

yeah dont even try that lol

did he give a distribution table?

[tranquil pine]

no

he will give it next class

I was thinking you wouldn't need the distribution table for part a since part c wants a general expression

[dusty harbor]

nothing like this?

[tranquil pine]

he said he will give it next class

[dusty harbor]

alright

so they probably expect you to use

that formula thats N(0,1) distributed

something like this

[tranquil pine]

I will try this problem again tomorrow after class

thanks for your time

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[tranquil pine]

use rational root theorem to find a root, then polynomial divide (or continue using rational root)

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[chilly stream]

is there some place online where i can type math equations in latex and get a nice looking png as output?

[chilly stream]

like in a nice looking font

the websites i saw online didnt produce it with a nice font

similar to this for example

$\forall x \in X$

[soft zealot]

Gigabyte

[chilly stream]

this looks very clean

,help

[soft zealot]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[chilly stream]

ohh it now DMed me

(the bot i mean)

i can use it now

.close

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[untold parrot]

help

[crystal lily]

#❓how-to-get-help

[untold parrot]

can somebody explain to me how i can factor this?

if it helps anyone apparently the answer is (a-b-5c)(a-b+5c) i just dont know how to get to it

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[charred kestrel]

where do i start with these questions?

[final saddle]

@charred kestrel Has your question been resolved?

[charred kestrel]

no

[tranquil pine]

Okay first

What happens when you add 2pi to a trigonometric function

[charred kestrel]

oh sorry

yeah i figured out 29

i'm not sure about 31 though

@tranquil pine

[tranquil pine]

Ah yeah that's good then

[charred kestrel]

i tried finding coterminals there but

kinda led me to a dead end

[tranquil pine]

31 is the same story, 8pi/3 - 2pi is 2pi/3

That's just 120 in degrees, we can find what's that in a lot of ways, but that's just the same as the angle 60 from the negative x axis

So you are really just taking -cos(pi/3) here, which is - 1/2

I can explain to you why this is the case if you don't understand how we can find angles outside of the first quadrant

[charred kestrel]

wouldn't it be 6pi/3 because you have to multiply 2pi/1 by 3 in order to get common denominators?

[tranquil pine]

Yes it would be 6pi/3 which is 2pi

But i just subtracted it directly into 2pi/3

Because 2pi is just making a full rotation around the unit circle, so it doesn't matter if we add it or subtract from it

[charred kestrel]

ohhhhh

ok

[tranquil pine]

It's the angle 360 for example

[charred kestrel]

so ok

[tranquil pine]

Yeah

Did you understand the process of how I computed cos(2pi/3) though?

[charred kestrel]

into degrees?

[tranquil pine]

No, just the process of evaluating it into - 1/2

[charred kestrel]

kind of?

is it because of cos

[tranquil pine]

Yeah sure

[charred kestrel]

actually yeah

you found the degree and angle

then just find x since its cos

[tranquil pine]

It's hard to imagine it, but you don't need to do any fancy calculations, you just need to imagine the unit circle in your brain

[charred kestrel]

i got it yeha

yeah*

ty lex

[tranquil pine]

Ofc, good luck with the rest

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[untold estuary]

how did (...)/(5/2) became (2/5) * (...)

[tranquil pine]

whats that called

ima learn it rq

or try too

[untold estuary]

integral

[fossil geyser]

That's how you divide by a fraction

dividing by a number is equivalent to multiplying by its reciprocal

[untold estuary]

[tranquil pine]

alr hold on

gimmie like 10 minutes

ill try

[fossil geyser]

My guy is about to go learn integration in ten minutes lol

[tranquil pine]

well 30minutes

[untold estuary]

so

f(x) / g(x) = reciprocal(g(x)) * f(x)

[fossil geyser]

Yes

[untold estuary]

I should have this in my formula booklet

[fossil geyser]

$\frac{a}{b} = a \cdot \frac{1}{b}$

[soft zealot]

tatpoj

[fossil geyser]

Basically this.

It shouldn't really be anything new tbh

[untold estuary]

I forgor this

[tranquil pine]

what kevel math even is this

[untold estuary]

I didn't have a good understanding of fundamentals back then

[untold estuary]

12th grade

[tranquil pine]

oh

[fossil geyser]

It's calculus

[tranquil pine]

oh

[untold estuary]

basic calculus I think?

or is it calculus in general

[fossil geyser]

Like Calc 1 probably if this is your first introduction to integration

[fossil geyser]

That's fair. Maybe just review operations with fractions. Lots of functions you'll deal with in calculus have the form of a fraction.

[untold estuary]

there's a lot of radicals too

teacher already teaching this to us

and he taught us this within an hour

[tranquil pine]

yea i foing that rn

[untold estuary]

[untold estuary]

let me see

[tranquil pine]

my phone not focusing

hate that

[untold estuary]

oof

[tranquil pine]

this the antiderivative right?

[untold estuary]

yes atleast Ithink os

[tranquil pine]

ok

[untold estuary]

when this x^-1/2 was getting distributed why is it positive in x^3/2 - 3x^1/2

[tranquil pine]

wouldnt you get rid of the radical by squaring the top then dividing by x?

to get rid of the x on the bottom

[untold estuary]

easy one at a time

my brain is dumb

[untold estuary]

I think it's because sqrt(x) = (x)^1/2

then turn it to negative because of exponent rules?

[tranquil pine]

hmm

im still learing too

[fossil geyser]

Yeah it's in the denominator

$\frac{1}{\sqrt{x}} = x^{-\frac{1}{2}}$

[soft zealot]

tatpoj

[fossil geyser]

Then when they distribute it

$x^n \cdot x^m = x^{n+m}$

[soft zealot]

tatpoj

[fossil geyser]

So $x^1 \cdot x^{-\frac{1}{2}} = x^\frac{1}{2}$

[soft zealot]

tatpoj

[fossil geyser]

That's where the positive 1/2 comes from

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@untold estuary Has your question been resolved?

[tranquil pine]

based on my knowledge(photo math) u have it right. but what exactly are you asking? maybe im dumb and cant read or u just worded it weird

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[long galleon]

in a right triangle one leg measures 14 inches more than the other leg. The hypotenuses is 2 inches longer than the longer leg. What are the lengths of the threes ides of this triangle?

[long galleon]

I get kind of how to do this

I also however have to show my work so simple answers wont be much help

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@long galleon Has your question been resolved?

[topaz cypress]

Ok, so let x be the length of the short leg

The length of the long end is therefore x+14

And the length pf the hypotenuse is x+14+2=x+16

We also know that the length of a hypotenuse is the square root of the sum of the squares of the legs

So the hypotenuse is also $\sqrt{x^2+(x+14)^2}$

[soft zealot]

Estebson

[topaz cypress]

So we equal these 2

$x+16=\sqrt{x^2+(x+14)^2}$

[soft zealot]

Estebson

[topaz cypress]

We can square both sides to get rid of the square root

$(x+16)^2=x^2+(x+14)^2$

[soft zealot]

Estebson

[topaz cypress]

We do the squares

x^2+32x+256=2x^2+28x+196

We pass everything to one side

$x^2-4x-60=0$

[soft zealot]

Estebson

[topaz cypress]

This quadratic can be factorized into
$(x-10)(x+6)=0$

[soft zealot]

Estebson

[topaz cypress]

Thus, we get our answers of x=10 and x=-6

But of course, this is geometry, so the negative answer can be dicarded

So x=10

Therefore, the short leg is 10in long, the long leg is 10+14=24in long, and the hypotenuse is 10+16=26in long.

And we can confirm that $\sqrt{10^2+24^2}=\sqrt{100+576}=\sqrt{676}=26$

[soft zealot]

Estebson

[long galleon]

Thank you

[long galleon]

-close

How

Or wait

Can I ask another question

it says do not solve but tell me the type of solutions to this equation -5x+16x-3x^2=0

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[final tangle]

there is no question

also

!15m

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[final tangle]

the question is cut off

well the presence of y already means that you're wrong

no

x=0 isn't the only asymptote

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@candid wind Has your question been resolved?

[final saddle]

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[pseudo karma]

Could someone explain to me what $\widetilde{D}(h^2)$ is? "We recognize that $D_{sym}(h)$ is a function of $h^2$, i.e., $D_{sym}(h) = \widetilde{D}(h^2)$". I can see that it's a function of $h^2$ but I still can't see where $\widetilde{D}(h^2)$ comes from? Has $\widetilde{}$ a specific meaning in this example (my intuition is that it's just any arbitrary function of $h^2$)?