help-0

[ocean seal]

Cicopath

Cicopath

[alpine sable]

Do you see the resemblance?

[vagrant tinsel]

I little bit

[digital turtle]

you want to solve for t?

[vagrant tinsel]

so how do we find out long it will take to grow?

yes

but there is no P I can calculate

[alpine sable]

Now that we have an equation set up, simply use your algebra skills

We don't need to calculate what P is

We want to figure out what t is for how long it will be until P quadruples

Before I continue to help, can you take a larger screenshot?

Just want to verify it's not a test or such

[digital turtle]

why don't you work backward

[vagrant tinsel]

How would I work backwards

[digital turtle]

3P=(12.11)^(12*t)

[vagrant tinsel]

3?

[digital turtle]

divide both side by p -.-

[vagrant tinsel]

it’s a test but the teacher is literally letting us cheat

[digital turtle]

then log both side and divide by 12

[alpine sable]

I should've asked if it was a test early on, I will not continue to help, I apologize.

[vagrant tinsel]

alri

[alpine sable]

You aren't supposed to be asking questions from tests/exams on here that you are currently taking

[digital turtle]

so can I ask my question now?

[vagrant tinsel]

go ahead lol

[vagrant tinsel]

ok 🤣

[digital turtle]

what is the possibility that after n rounds the total sum of the die equal to m

sorry for the quirkiness, English is not my first language

anyone?

[topaz scaffold]

Hmmmm

There's multiple ways to add to m

[digital turtle]

thta's what I thought

[topaz scaffold]

If m = 6 and there's 4 rounds

You can get 1, 1, 1, 5

1, 5, 1, 1

And so on

Tricky...

I have no idea

[gritty gull]

The SUM Sn, therefore is simply n times the ___ ? ___ of the first and last term of the series. ? =

anyone got an idea

this is related to sequences and series

• average
• product
• difference

numbed it down to those 3

[ionic jewel]

we need the rest of the question lol

[gritty gull]

ohhh lol

its

[minor elbow]

what the answer for this?

i think i got it wrong

[pearl marlin]

what answer you are putting in box?

[minor elbow]

x^3+8*x^2+3

[minor elbow]

but it says its wrong

[pearl marlin]

can you show your work?

[pseudo igloo]

Can someone help me do 39 in voice chat?

[twin haven]

sin 4t can be written as sin 2t+2t

then use the identity of sin(A+B)

Sin(a)cosb+sinbcosa

this is how i think

ask the experts tho i'm an amatuer

[pseudo igloo]

the confusion stems from the cube

thank you

[dawn wraith]

@pseudo igloo does it have to be in a voice chat?

[pseudo igloo]

nope

[dawn wraith]

All right, I’ll help you then.

[pseudo igloo]

i appreciate it

[dawn wraith]

So firstly, I’d take out a factor from the RHS.

[pseudo igloo]

rhs?

[dawn wraith]

Right hand side

[pseudo igloo]

okay

so if i were to factor

how would you do this

[dawn wraith]

I’d take out the similar terms,
Such as cosine of t and sine of t

[pseudo igloo]

so id multiply them

[dawn wraith]

Nono, you factorise them out.

[alpine sable]

Use double angle formula on sin 4t

[dawn wraith]

$$ \frac{\sin(4t)}{4} = \cos(t)\sin(t) (\cos^2(x)-\sin^2(t))$$

[ocean seal]

Hunnydrips

[alpine sable]

I think you are being too straight forward @dawn wraith

[pseudo igloo]

thank you, i am pretty bad at math

[dawn wraith]

That’s all I’m giving though, from there it’s just using properties.

[twin haven]

where does the 1/4 go?

[alpine sable]

sin 2A is congruent to 2 sin A cos A
sin 4t can be written as sin ( 2(2t) ), now you can proceed from here I guess

[alpine sable]

he just skipped to a step, I mean use the double angle formula, it will cancel the 4 in the denominator (in this context)

[twin haven]

hmm still in 10th grade never learnt that

[alpine sable]

same (in 10th grade)

[twin haven]

wow you a genius mate

[pseudo igloo]

my brain is exploding @dawn wraith thank you though

[dawn wraith]

You’re most welcome.

[alpine sable]

not really I am not good, I just read more

[twin haven]

wait wait sin can someone explain me tho ik sin2a= 2sinacosa

[alpine sable]

thats pretty much the double angle formula

[twin haven]

and cos2a= cos^2- sin^2

so its 4 right

thats why i recommended spliting it to 2t+2t

then sin(A+B)?

[alpine sable]

sin 4t
sin ( 2(2t) )
=> sin(2t) cos(2t)
then apply double angle formula again

[dawn wraith]

The double angle formula is just a peculiar case of the sum of two angles formula, both of the “distinctive” angles are the same.

[twin haven]

is this way wrong ?

[dawn wraith]

No, not at all.

[twin haven]

ok

thanks

[alpine sable]

its just another way of writing 2(2t), and so is 2t + 2t another way of writing 2(2t)

[gritty gull]

By finding the second term, a2= 7 +3(2) = 7+6=13, we can say what the COMMON DIFFERENCE of the series is _

anyone know what common difference is?

[twin haven]

its the difference between each no, in an arithmetic progression

[gritty gull]

how would you implement that into a equation

[vale wigeon]

is this all that the problem says?

or does it say something right before that you chose not to show us

[gritty gull]

the first term is

[vale wigeon]

the first term is what

[gritty gull]

a subscript 1 = 7 + 3 (1)

which is 10

[vale wigeon]

so $a_1 = 10$ and $a_2 = 13$

[ocean seal]

Ann

[gritty gull]

ah so 3

thanks alot

[tulip sedge]

help

[twin haven]

square both sides

[tulip sedge]

yeah i did that but i have no clue what to do next

[twin haven]

then youll get x^2= -1-x

[tulip sedge]

ooh

[twin haven]

then solve the quadratice

[tulip sedge]

i see

thanks

[vocal drum]

Would someone mind helping me plot f(t)=4-2cos(2pi t) for tE[0,2]

E is the greek letter

I dont understand how to fit in tE[0,2]

[vale wigeon]

E is the greek letter

you mean $\in$?

[ocean seal]

Ann

[vocal drum]

yes

[vale wigeon]

that's the set membership symbol, not a greek letter

anyway,

,w plot f(t) = 4 - 2cos(2pi t) for t in [0,2]

[vocal drum]

ah thank you for clearing that up haha

[ocean seal]

Results provided by WolframAlpha

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

Requested by Ann#0413

[vale wigeon]

here you go

[vocal drum]

um im sorry but do you mind explaining what happened to the ? that graph looks the same regardless of the t=0 to 2 what am i not understanding? what does t=0 to 2 do?

to the graph?*

[alpine sable]

the value of t (check x axis) varies between 0 and 2 @vocal drum

[vocal drum]

Ok this is going to be a stupid question, but the graph never hits 0

[alpine sable]

the value at the y axis, is going to be the value of f(t), for t ∈ [0, 2]

[vocal drum]

OH

[alpine sable]

the value of y doesn't hit 0 because it wont be 0

the x axis ranges from 0 to 2

[vocal drum]

ah hyes

I understand

Thank you very much for clarifying

What would happen to the plot if it was 0,4?

[alpine sable]

x axis would range between 0 and 4

,w plot f(t) = 4 - 2cos(2pi t) for t in [0,4]

[ocean seal]

Results provided by WolframAlpha

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

Requested by Shivansh Jaiswal#0042

[vocal drum]

Ahh yes

Ok that makes alot of sense

[alpine sable]

@vocal drum it is going to be the same, plot it to 100 or 2000

[vocal drum]

You are a legend thank you my friend

Yeap you have taught me wel

[alpine sable]

I'm not, thank ann lol

[vocal drum]

Oh yeah and thanks ann i appreciate you aswell ❤️

[tulip sedge]

help pls

[alpine sable]

what have you tried

[tulip sedge]

i dont understand how to simplify z^101

[tulip sedge]

i dont have any clue

[alpine sable]

or multiply it by i

to simplify it

I have no clue after that

sorry

okay @tulip sedge by multiplying it by i you get omega

(root(3) + i)i => -1 + root(-3)/2

[tulip sedge]

oh yea

[alpine sable]

which is the value of omega apparently

Hello

How r u

[tulip sedge]

yeah i got z= -iw

yeah i can solve this now, thanks @alpine sable

[tulip sedge]

good , btw you can use #discussion for chatting

[alpine sable]

Gud nght

[alpine sable]

Im beyond confused what do I have to do next. (1 & 2)

[vale wigeon]

why did you write 7x - 34 = 4x + 2?

what reason do you have for declaring these two angles equal?

[alpine sable]

I honestly have no clue.

What formula am I supposed to use?

@alpine sable you first fine what is bca

It is given triangle abc is isoceles, I hope you understand what I am saying

and then calculate the value of x

after that it should be pretty simple

How do I find bca?

the triangle is isoceles

ab = ac

Oh

I hope you can solve it from here

How do I find AB?

you don't

you have to compare angles here

ab = ac
angle bac = ange bca

you know this property right?

I'm still confused I'm sorry. This work wasnt taught to me for some years. They just handed me an entire packet with work and didnt teach.

okay I will explain

so there is this property of a isosceles triangle, that the angles of the opposite sides are equal.

For instance the 2 with the lines?

and then there is another one which states, the exterior angle a = angle b + angle c

[alpine sable]

yes

everything else should be clear now

angle sum property of a triangle implies sum of all angles is 180

[tough hatch]

angles opposite the congruent sides*

[alpine sable]

yes

So how would I set it up?

say a triangle abc
in this ab and ac are the same sides, so the angles abc and acb are going to be same

sorry I don't know latex

@alpine sable you got your answer?

Im beyond confused on what I should do first.

Would I do 4x+2=180 and solve that or?

I dont understand sorry.

no don't worry

okay so first of all

@alpine sable you know the angle sum property for a triangle?

It basically says that the sum of all interior angles of a triangle is 180

and there is another property that says that the congruent sides of a isosceles triangle are same

which basically means angle BAC = angle BCA in this case

you now know all the angles of the triangle except for BCD, but we will get back to it in a moment

so angle ABC = 7x - 34, angle BAC = angle BCA = 4x + 2

sum of all angles is 180

now find x @alpine sable from this

[eager marten]

x = 5(2x - 4)
x = ?

[vale wigeon]

@eager marten is this unrelated to pazerx's question?

[eager marten]

no @vale wigeon

it's an equation

could you pls solve x?

i mean yes @vale wigeon

[vale wigeon]

nobody's going to do this for you.

[eager marten]

i didnt read properly

why?

[vale wigeon]

read #❓how-to-get-help

[eager marten]

ok

[vale wigeon]

we will help you but we will not just do things for you

anyway, this is a linear equation. have you solved linear equations before?

[eager marten]

no

[vale wigeon]

so if i gave you an equation like 2y + 11 = 39 you would be unable to solve it?

[eager marten]

ys

yes

[vale wigeon]

...have you done algebra at all before

[eager marten]

no

[vale wigeon]

then you do not have the necessary tools to solve your equation

seeing as you have not yet learned how to solve the simplest kinds of equations

[eager marten]

ok @vale wigeon

[glass flare]

@vale wigeonam i bad at algebra or his equation has no solultions

[vale wigeon]

x = 5(2x-4)?

this equation does have a solution. you must be bad at algebra.

[glass flare]

[vale wigeon]

...

[glass flare]

?

[vale wigeon]

what's with the troll face

[glass flare]

let me actually try to solve it

[vale wigeon]

what made you come to the conclusion that it has no solutions?

[glass flare]

wait

[alpine sable]

How would I set this up?

[vale wigeon]

oh pazerx is back

[alpine sable]

Yes sorry.

[vale wigeon]

@glass flare we are gonna need to move

[alpine sable]

@alpine sable what do you ask?

you want to proove that?

My question is how would I find x from all that.

I understand it all adds to 180. And the 2 sides are the same.

But I dont understand how to find the x.

oh yeah that's good

so you have all the angles

and the angle sum property says that sum of all the angles is 180

sum you see?

you have all the angles

so make an equation from all the interior angles which equates to 180

and then solve for x

So would it be 7x-34+4x+2=180?

And then I solve from that?

angle bac = angle bca

there are 3 angles

not 2

there are 2 angles with the measure of 4x + 2

you get it? or not?

No :c

okay, the sum of all the angles is 180 degree

I understand that there are 2 4x+2's

what are the 3 angles in our triangle?

But how would I setup the equation

[alpine sable]

first this

4x+2
4x+2
7x-34

okay very good

now sum of all angles is what?

180

[alpine sable]

so sum of these angles will be what?

180

very good

now put that into an equation

a + b + c = 180

where a, b and c are angles of our triangle

4x+2+4x+2+7x-34=180

yeah!

solve it for x now

that was so easy

Thank you

I'm going to solve that rn one sec

[proud sentinel]

Do anyone have idea with Normdist function in MS excel or just some idea with probability density functions?

[alpine sable]

you mean MS Excel stuff?

#computing-software I guess @proud sentinel

[proud sentinel]

actually its not exactly computing based, question is somewhat on density functins

[alpine sable]

then #help-3 this channel is busy

[proud sentinel]

okay

[alpine sable]

@alpine sable you solved it?

Yes sorry.

x=14?

@alpine sable

[rancid vale]

Hi

help

im stuck

[alpine sable]

<@&286206848099549185>

[rancid vale]

thx

[alpine sable]

I pinged for myself lol

[alpine sable]

yes

Okay so now what.

now,there is a property

let there b a triangle ABC, and D be extended from bc

then angle acd = angle a + angle b

[alpine sable]

guys i need help

ask @alpine sable

find modz that satisfies mod z+2i and argz = pi /6

they dont have the same centre so its hard to find the angle to determine if the triangle is isocelces etc

sorry i made a mistake

it should be mod z+2i= 3

[quaint pond]

hey guys I have problem understanding one math exercise

I know the answer is 215 but i just don't know how to solve it

it might be because i dont really understand what multiple means

im not very fluent in english so

yeah

[strong furnace]

5,10,15... Are multiples of 5

5n for n in Z basically

[quaint pond]

so multiple means that it should be able to be divided without any remainder?

[strong furnace]

Could say that yes

[strong furnace]

Consider the geometric representation of mod (z+2i) =3

[alpine sable]

i have drawn the loci and the half line but dont know where to draw the 90 degrees triangle

[strong furnace]

wdym by that?

you have a circle and a line and you want point of intersections...

[alpine sable]

?

Im confused

[alpine sable]

@strong furnace

i have found the point of intersection

but to find the length of the line

i need to know what kind of triangle it is

to do cosine

or pythagorean

[strong furnace]

if you have the point of intersection you have the coordinates

you just need the norm now?

[alpine sable]

yes but to get the co ordinates i need to find the length of the line and add or subrtract to the centre of the circle

well thats how my textbook says you have to do

do u know how to do it

[strong furnace]

I really don't understand wym , I would rather just do it using analytic geometry (cartesian) but if there's an approach your book has it would be better if you had a name or if you could show what it said

[alpine sable]

cause it says you have to draw a line form the centre of the circle to the point of intersection

and use that same line to from a triangle

find the length of that line

and using that length and the centre of the circle co ordinates

you can find the point of intersection

does that make it more clear?

[strong furnace]

oh

I kind of see what they are going for

[alpine sable]

yh

[strong furnace]

if the line

is tangent

to the circle

it would be perpendicular

[alpine sable]

yes

[strong furnace]

and then you can use pythagoras

I mean I had potentially 2 possible points in my heads so you can't blame me for not thinking of that

this is a special case so yeah that works

[alpine sable]

no worries

[strong furnace]

now what is the problem you are facing here

[alpine sable]

umm

this

[strong furnace]

so you have a right angled triangle

right angled at your point

[alpine sable]

ind modz that satisfies mod z+2i = 3and argz = pi /6

they dont have the same centre so its hard to find the angle to determine if the triangle is isocelces etc

[strong furnace]

the other 2 points on this triangle

are the center of that circle

and origin

[alpine sable]

yes

Okay so I got to this point, how do I do the next step.

[strong furnace]

bruh

[alpine sable]

@alpine sable

I was in this channel previously, sorry.

[strong furnace]

move to some channel and ping me?

[alpine sable]

ok

Wait lemme show

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle.

@alpine sable

The measure of the exterior angle is going to be the sum of the two non adjacent angles as can be seen in the above figure

@alpine sable

?

Apply this to your question and you will find all the angles

What are the two non adjacent angles.

The interior angles which are not adjacent to the exterior angle

@alpine sable I hope you are getting me

So its the 2 angles added up?

Yes

So would it be 128?

Yeah I guess

No

122

I did 64+64

7(14) - 34 + 4(14) + 2 = angle DCB

11(14) - 32

154 - 32 = 122

Ohhhh ok

Okay so I got that.

Now what.

Now what?

I will leave it to you from now

No more help sorry

Your question has already been solved lol

@alpine sable

It says select 2

I selected C

And then find the other yourself

Brute force check yourself

[small holly]

-3y-(3y-6)=12
  -3y-3y+6=12
    -3y-3y=6
         0=6

is this correct?

[vale wigeon]

last step is wrong

-3y - 3y is -6y, not 0

[small holly]

oh im so dumb lol

my bad

[alpine sable]

@alpine sable

please

I would be greatful

?

@alpine sable I have posted the question in #help-1

[rich basin]

what should f(x) and g(x) be when trying to find the integral of between two curves

forexample a question like

would f(x) be x+1 or x^2/4 -2

i don't really quite get which one i should denote as f(x)

[pliant oracle]

is that choice not entirely arbitrary, or are you using some set formula with f and g in it?

[rich basin]

Yeah i am using a formula

But i'm trying to get the intuition of the formula

[paper oar]

the f(x) is the one on top

[pliant oracle]

do you know the geometric meaning of ∫ f(x) dx and ∫ g(x) dx

[rich basin]

@paper oar what do you mean by on top?

[paper oar]

in this case f(x) would be y = x+1

[rich basin]

@pliant oracle It is the area under the curve

[pliant oracle]

indeed

[paper oar]

I mean there is a more mathematical term but I always remembered it by the function that was "on top" or infront of the other

when graphed that is

[pliant oracle]

so to find the area between the two, you take the larger area ∫ f(x) dx and subtract the smaller area ∫ g(x) dx

[rich basin]

but why exactly woudl we know which one is larger when finding the premitive

I mean I see which one being f(x) and g(x) based on there differences

but how can we generalise this without having to do that

[pliant oracle]

well it's the region bounded between the two curves, so find where the curves intersect and between those two points one will always be smaller than the others

[rich basin]

But i don't know which one is smaller than the other?

[misty mountain]

can someone explain this ∑?

[alpine sable]

do you mean that how do you know which function is smaller than the other on the interval [a,b]?

[rich basin]

You can tell by the number difference

but this is in terms of xs which can be dynamic

[ripe osprey]

write the equation of condition given in question, and then solve it to arrive at asked parameters

as a shortcut, or general rule
for 3 qty X Y Z in ap, write the eqn as 2*Y=X+Y
for 4 qty W X Y Z in ap, write eqn as X+Y=W+Z

[onyx delta]

can you please send whole solution, i already tried this

[rich basin]

what is the difference between the two questions?

[alpine sable]

I might be wrong here, but I believe that you can treat the x axis as the line y=0

[rich basin]

@alpine sable But isn't it x > 0

so it wouldn't even matter

[ripe osprey]

answer to 5th will be infinite
so its not a correct question

[rich basin]

@ripe osprey But it is also bounded by the line 3 though

[ripe osprey]

thats on the right side
its not bounded by anything on below side

[rich basin]

@ripe osprey but there is also a x > 0 restriction as well

[alpine sable]

it looks like you are conflating x>0 with y>0.

[ripe osprey]

which is, on left side
there is nothing on down side given

Im talking about Q5

[rich basin]

what do you mean by downside?

you can't get it below y < 0

[alpine sable]

still don't know what you mean by this.

[rich basin]

because of x^2 and 1/x^2

[rich basin]

I mean the they are contaiend with unknown values which can be anything

[alpine sable]

which unknown values are you talking about? you can take any input of x and evaluate it with your given function

[rich basin]

But how would we know which one is greater or smaller?

which would do we place as f(x) or g(x)

[alpine sable]

okay, now you are being clear.

[alpine sable]

let's take this one as an example.

[ripe osprey]

Try to do something after this...
Im not very clear after this

[alpine sable]

to start off, you want to study and analyse these both functions, ie you want to know their behaviour as well as to have a rough idea on how they look like on a graph.

in the analysis of those functions, you want to know certain points that will be important, which are in this case, the points where both functions intersect.

are you able to find those intersection points?

[rich basin]

yeah

[onyx delta]

thankyou ! do you know physics, physical chemistry ?

[alpine sable]

what are those points?

[rich basin]

make both of them equal

[alpine sable]

if you already found them, ofc. if not, try and give it an attempt

[alpine sable]

yeah, that's how you get the points, but have you found those points?

[ripe osprey]

Physics, yes

[rich basin]

I get it now, I was just looking if it is possible rather than just obversing the functinos or just minusing thme to understand their differenmces

[alpine sable]

find the range of values for theta , -pi < theta < pi , for which arg ( z-4+2i) = theta and mod z+6+6i = 4 have no common solutions

[grim shadow]

which part??

[rich basin]

part a

so i found the intersections to be +- root(2)

[grim shadow]

ya then thats it

just integrate

[rich basin]

and then i made it a and b

but then i got the wrong answer

i then did x^2 - 4 +x^2

4-2x^2 actually

[grim shadow]

nope thats wrong

[glass lichen]

x^2 clearly isnt the top function

[grim shadow]

ya

so whats the problem??

[rich basin]

and then i integrate it with the boundaries of +- root 2

but then it is the wrong answer

the answer suppose to be 4/3

this is my answer

[grim shadow]

thats correct

mb the ans 4/3 is wrong

[rich basin]

yeah i think the answer is wrong

[grim shadow]

coz square roots will def come

to remove square root u would need a even powered term in x

and when u integrate ur getting 1 and 3 in x

[rich basin]

I looked at the wrong section for it

[grim shadow]

xd

[rich basin]

Oh yeah i did the wrong section question

this was the actual question i had trouble with

nevermind

[alpine sable]

Open channel?

I can cancel out the square roots here right

[vale wigeon]

yes but you're missing the dx and also your pi got swollen

[alpine sable]

Lmao, thanks for the cynical help :)

[minor heath]

do you know the formula for the sum of an infinite geometric series?

or maybe just the general formula for the sum of terms in a geometric series?

[glass flare]

google ez

[minor heath]

i didnt ask you

[glass flare]

[onyx delta]

yeah unable to break the question

[minor heath]

wdym

thats a clear question

[boreal musk]

The irreducible fraction of the number 0.16 is:

[minor heath]

channel occupied

[boreal musk]

ah ok

[alpine sable]

you still need help with that?

[minor heath]

anyways, just if you dont know whats the formula for that then you at least know the general formula for the sum of terms in a geometric sequence-

um

[alpine sable]

welcome!

but not here

[minor heath]

id rather go to #discussion than here

[alpine sable]

yea

[minor heath]

@onyx delta are you still with me or do you not want me to help you with your question?

[alpine sable]

you can ask your question in any of the other channels, since someone else is using this one

[onyx delta]

actually i got the answer, thankyou !

[minor heath]

ok

[thick shard]

Guys, does anyone know how to use the bot? I need to simplify [m - n + (a + b) - 1]².

[glass lichen]

there's not much to simplify there

[thick shard]

Eh... Yeah. I just wanna square the thing.

[glass lichen]

Ok, so distribute it like normal

[thick shard]

Yeah. I'm bad at it. I've tried it twice.

Lemme show you my work.

[glass lichen]

$(m+a+b-n-1)^2=m(m+a+b-n-1)+a(m+a+b-n-1)+b(m+a+b-n-1)-n(m+a+b-n-1)-(m+a+b-n-1)$

[ocean seal]

Mosh

[glass lichen]

yeah you get 25 terms in the expansion... no clue why you'd want to expand it out

[thick shard]

Eh... So, is it (a+b) or without the bracket? I need the a + b inside a bracket.

Okay. Lemme try this.

[gray isle]

do you have the original problem or the end goal you're trying to acheive?

[thick shard]

$[m - n + (a +b) - 1]^2

[gray isle]

the end goal you're trying to achieve

expand completely? you mentioned

I need the a + b inside a bracket

[thick shard]

Yes. I need it expanded.

Could you please guide me?

[gray isle]

follow what mosh did

[thick shard]

Thanks a trillion! @glass lichen @gray isle

So, again, sorry for the constant disturbance, I actually need a+b inside the bracket. Like, you can't remove the bracket. Although, yes, you can. But, I need it not removed.

[gray isle]

that's what i was trying to clarify...

what's the end goal? why do you need a+b inside parentheses?

[thick shard]

Eh... Well, I was given the value of a + b, but not individually. Like, I don't know what a is or b is individually, but I know the value of a + b.

[gray isle]

in that case can't you just replace (a+b) with whatever a + b is first?

[thick shard]

Yeah. But, I also need.... Ok. Just wait. I'll ask again later.

[gray isle]

you should really post the entire question with full context

otherwise with the info you're giving me,
the best i can recommend is to do something similar to what Mosh suggested but keep (a+b) in parentheses

[glass flare]

how do i represent b^x=y as x=something

[alpine sable]

how do i express 0.00000001??

in standard form

[smoky harness]

https://cdn.discordapp.com/attachments/866737142915137587/867055868884549662/unknown.png https://cdn.discordapp.com/attachments/866737142915137587/867055969959149578/unknown.png https://cdn.discordapp.com/attachments/866737142915137587/867056115195969576/unknown.png https://cdn.discordapp.com/attachments/866737142915137587/867056458130915358/unknown.png

[glass flare]

@alpine sable you mean in the form of 1*10^d?, d<0

there is 7 zeros so 1*10^-7

[alpine sable]

no i meant how do i express it in scientific notation (aka standard form)

oh

uh

[glass flare]

wdym then what i said is correct

no

[alpine sable]

oh sorry i have not learnt it like that so i did not know

[glass flare]

[alpine sable]

hahahaahh

[glass flare]

lol

@alpine sable also you can say 1e-7

[alpine sable]

ok thanks a lot

[unkempt lava]

can any1 help? thanks

[river hearth]

stuck on this worksheet problem

[topaz scaffold]

This would be more suitable for a physics server

You can check out #old-network for one

[topaz scaffold]

You know the Law of Sines right?

For that you need to have at least one set with an angle to the opposite side

[river hearth]

how would that work?

Ive been out of school for a couple days so Im kind of working through missed assignments

[vale wigeon]

in the standard labeling of a triangle, an angle and the side opposite to it are labeled with uppercase and lowercase versions of the same letter

like C and c

[topaz scaffold]

Yea

[vale wigeon]

there's only one answer option which contains a pair like that

[river hearth]

so it could be A

[vale wigeon]

it could only be A

[river hearth]

ok thank you that helps alot

[topaz scaffold]

My beautiful drawing doesn't load

[spice mauve]

b^x = y
x ln b= ln y
x= ln b / ln y

using the concept of Natural log

[topaz scaffold]

It would be easier to just use log base b too as well

Doofid's is kinda like switching base

[spice mauve]

i learned math in korean so i have no idea wtf a base is

[topaz scaffold]

Oh

[spice mauve]

but we mostly use ln in that situation

[topaz scaffold]

$x = log_b(y)$

[ocean seal]

RipeOrange

[topaz scaffold]

Works too

[spice mauve]

wolfram is OP.

[muted lark]

can someone help with finding this questions answer?

<@&286206848099549185>

[gray isle]

what have you tried?

also don't ping helpers immediately

[muted lark]

mb

That's what I did so far

Idk if it's right

[gray isle]

sin(3t) isn't 2sin(t)cos(t)

-1/2 is a nice ratio,
you have enough information to outright determine the nice value of theta,
and hence 3 *theta
and hence sin(3 theta)

[dim acorn]

i hope i am not

interuppting anyones question

can anyone answer this with explanation

yes

i got no clue of this question

it was in my olympiad

[shut wadi]

is the exam over yet?

[gray isle]

The question implies it doesn't really matter what a,b,c are,
since it's multiple choice, instead of doing tedious algebra you can consider what happens when
a=b=c = 2

[warped phoenix]

Apparently the solution is (1/3, 8/9, 2/9)

But I’m not sure what I did wrong

This was the original question

First I got x by itself in the third equation, and substituted x into the second equation. I then got z by itself, and substituted x and z into the 1st equation. I then got y and substituted that into z and x and got my answer from there

[alpine sable]

Damn I never realised this was a possibility

[gray isle]

you need to work on how you structure your work

You shouldn't have to tell me the order you did things in

Anyway, you fjed up the sub of x into the first equation

[topaz scaffold]

You know linear algebra btw? Cause that would be easier

[warped phoenix]

um i know how to do gauss jordan elimination

thats it

[topaz scaffold]

That's what you'll use here lol

[warped phoenix]

:0

[thorn tapir]

You can also express a coefficient matrix A and solve for the matrix X from the relation AX = B

[glass lichen]

vector x*

[thorn tapir]

yeah, my bad there

[warped phoenix]

im not sure how i would 🥲 , just organize it better? thats why i divided it into three sections

[gray isle]

work in one direction

Instead of zigzagging

[proper loom]

isnt cramers rule easier

[gray isle]

If you didn't say what order you do things in, it would've been near impossible

5x doesn't mean that the 5 only gets multiplied to the summand that appears first in an expression equivalent to x

[warped phoenix]

5 2 1 | 3
-1 1 2 | 1
1 1 -1 | 1

like this?

[glass lichen]

that'd be the augmented matrix, yes

[topaz scaffold]

Definitely not for 3D matrixes

Determinants are a pain

[warped phoenix]

whats an augmented matrix

"augmented"

[topaz scaffold]

This

[warped phoenix]

oh i didnt know there were different types of matrices lol

[glass lichen]

$[A|b]$ is the matrix A augmented with vector b

[ocean seal]

Mosh

[warped phoenix]

oh so that line

"|"

[proper loom]

ah well u can also do augmented then rank ig

[warped phoenix]

means augmented

i see

[proper loom]

im just too used to cramers

[topaz scaffold]

It's probably easier for numerical computation

I'm not sure

[glass lichen]

I mean 3x3 matrices are relatively easy to compute their det, but if they openly said they only know Gauss Jordan...

[proper loom]

i think thats the standard method taught in schools so questions usually at that level will have simple determinants because its intended to solve using that

atleast here its like that

[glass lichen]

they said they only know gauss jordan

[topaz scaffold]

Idk, I've been told that Gaussian elimination is faster in most cases

[thorn tapir]

Wait, just asking - finding the vector X* in AX = B is in essence the same thing as Gaussian Jordan Elimination, as we're simply using Row Operations in finding the inverse of A - and the rest is similar.

[topaz scaffold]

Yea (?)

[proper loom]

the actual method is slightly different

you dont actually find the inverse in augmented form

[thorn tapir]

But the inverse is directly multiplied to the B, and yeah that's why I said it's "same in essence", not same

[proper loom]

yeap

[glass lichen]

$[A|b]\to [I|b']$ means the solution is unique. In $Ax=b$ this is equivalent to saying $x=A^{-1}b$ where we know A is invertible since its RREF is I

[ocean seal]

Mosh

[glass lichen]

however if A isnt invertible you cant use Ax=b to find the solution space or the fact there is no solution and thus need to do $[A|b]\to [R|b']$ and interpret

[ocean seal]

Mosh

[glass lichen]

where R is the RREF of A

[thorn tapir]

So if we do try to solve an inconsistent system of equations - we might be actually able to solve it that way?

Oh I got what you mean

Thanks

[drowsy fern]

Jasmin has 5 blue shirts, 2 green shirts, 3 pants and 4 shorts, What is the probability that she chooses to wear a blue shirt and a short?

[oak chasm]

@drowsy fern Do you know about probability distributions?

[glass lichen]

Yes cause a system of linear eqn has either 0 1 or inf solutions, so if there are infinitely many then we want a way to describe the hyperplane we'd get

[dim vector]

I need help please
Calculate the annual simple interest rate if $6395 it is settled with a loan $5837 within 6 months

[oak chasm]

@dim vector What is the formula for simple interest?

[oak chasm]

M = C + niC

So, what two variables do we know?

We know the amount they borrowed, $5837. Which variable is that?

[dim vector]

$6395 $5837

[oak chasm]

Right, which variable is $5837? M, C, n, or i?

[dim vector]

idk

[oak chasm]

OK, so M is the amount you pay at the end.

C is the amount you borrow.

[dim vector]

yes

[oak chasm]

Not sure what n and i are.

What are n and i?

[dim vector]

maybe within 6 months

[oak chasm]

No, I mean n and i stand for interest rate and time.

Which one is interest rate?

Which one is time?

[dim vector]

6395 =5837 + ______

[dim vector]

6 months

[oak chasm]

No, which variable is time?

n or i?

[dim vector]

Hmmm i

[oak chasm]

OK, I looked it up. i is interest rate and n is time (https://matematicasecundariavideos.blogspot.com/2018/02/interes-simple-interes-compuesto.html?m=0).

So, we have M = C(1 + ni)

We know M is the amount you pay, which is $6395.

We know C is the amount you borrow, which is $5837.

We know n is the number of years, which is 0.5.

So, we fill in the values we know:
M = C(1 + ni)
$6395 = $5837(1 + 0.5i)

Does it make sense so far?

[elder roost]

A.Produce a function f(x) that satisfies the following conditions:

I.Its domain is all real numbers.

II.It has no maximum and no minimum on the interval [ 1,3] .

III.It satisfies f(1) = 1 and f(3) = –1, but there does not exist a c between 1 and 3 such that f(x) = 0.

B.Construct a function f(x) that satisfies the following conditions:

I.f is continuous for all x.

II.–10< = f(x) < = 10 for all x.

III.f does not have a maximum or minimum on the interval [negative infinity, infinity]. i legit can’t do this

[oak chasm]

@elder roost Sorry, channel is busy.

[dim vector]

I'm trying to do it on a sheet

[oak chasm]

OK, but does what I said so far make sense or do you need an explanation of some of it?

[dim vector]

yes

[oak chasm]

OK, so now we use algebra to solve for i, the interest rate.

So, write:
M = C(1 + ni)
$6395 = $5837(1 + 0.5i)

Then, what do you do next to solve for i?

[dim vector]

Is a sum made? 6395=5837+2918.5i or it may not be with the sum

[oak chasm]

Yes, that's a way to solve it.

What do you do next?

[dim vector]

12232 + 2918.5i ?

What I don't know is if it happens by subtracting to remove the i

[oak chasm]

No, we want to get i by itself.

So, we want to get rid of 5837 on the right.

So, we subtract 5837 from both sides.

6395 = 5837 + 2918.5i
6395 - 5837 = 5837 - 5837 + 2918.5i

[dim vector]

i think 558=2918.5i but u say that we want to get i by itself.

[oak chasm]

Yes, now the right side is closer to having i by itself.

Before, the right side was 5837 + 2918.5i
Now, the right side is 2918.5i

The right side is closer to just having i.

Does that make sense?

[dim vector]

ohh yes

[oak chasm]

OK, what do we do next to the right side to get i by itself?

[dim vector]

Sorry i'm not sure

[oak chasm]

OK, so here's how to find out. What do we do to calculate the right side?

We multiply 2918.5 times i.

[dim vector]

Then would i pass over to the other side? or it would be eliminated

[oak chasm]

No, so that's the last step in calculating the right side.

So the last step is multiplying.

What's the opposite of multiplying?

It's dividing.

So, we divide both sides by 2918.5.

558 = 2918.5i
558/2918.5 = 2918.5i/2918.5

As you can see, on the right we end up with just i.

So we got closer to just having i.

[dim vector]

0.1911941

[oak chasm]

Good, so that's your interest rate.

If you want it in percent, multiply by 100.

[dim vector]

Ohhh

tysm!!!! :D

[oak chasm]

You're welcome.

[river hearth]

?

[oak chasm]

@river hearth So, what is secant in terms of sine and cosine?

[river hearth]

secant?

[oak chasm]

Yes, what sec is short for.

[river hearth]

oh

Im thinking A or D

I dont think it would be the others

[oak chasm]

Well, what is secant in terms of sine and cosine? If you don't know, let me know.

[river hearth]

I dont

[oak chasm]

OK, tangent is sine over cosine.

For the other three, cotangent, cosecant (csc), and secant (sec), you look at the third letter in the full name of it.

So, cotangent is 1/tangent, cosecant is 1/sine, and secant is 1/cosine.

So we have secant.

That's 1/cosine.

What's the cosine?

1/2

So, the secant is 1/(1/2)

What's that?

[river hearth]

cos?

wait whats what

[oak chasm]

cosine

[river hearth]

1/2?

[ocean seal]

Chai T. Rex

[river hearth]

ok

so cos is 1/2

over sin?

[oak chasm]

No.

sec is secant. The third letter of secant is c. C is for cosine. So, secant is 1/cosine.

[river hearth]

1/(1/2)

[oak chasm]

Right.

[alpine sable]

guys does a^3 mean a multiplied twice or thrice?

[oak chasm]

@alpine sable Sorry, channel is busy.

[river hearth]

so what is next?

[river hearth]

thrice I think

[oak chasm]

So, now, what is 1/(1/2)?

[river hearth]

1/2

or 2

oops

[oak chasm]

Right, it's 2.

[river hearth]

so the answer is 2?

[oak chasm]

Yes.

[river hearth]

thank you very much

[oak chasm]

You're welcome.

@alpine sable The exponent tells you how many of the base to multiply together.

[ocean seal]

Chai T. Rex

Chai T. Rex

[alpine sable]

i knew that but different dictionaries have different definitions so i wasnt sure

[oak chasm]

Oh, OK.

[alpine sable]

is this channel available?

cuz i need help

[vale wigeon]

if you're looking for math definitions in a dictionary you're doing it wrong

[alpine sable]

oh 😦

anyways i should introduce myself, im arjon from bangladesh, studying in 10th

i need help

[sleek elbow]

https://dontasktoask.com

[alpine sable]

o k

how do i do 5

[full canopy]

Well we know that once they meet their combined distances will be 448km, if you write that as an equation you can solve for time

[alpine sable]

so then its 65x+75x=448?

[full canopy]

yep

[alpine sable]

i feel like i didn't get my point across... when we multiply 3 by 3, isn't 3 multiplying by itself once? then in the case of 3x3x3 isn't 3 multiplying by itself twice? some say in case of cube the given number gets multiplied by itself thrice which doesn't sit right with me

[sleek elbow]

sounds pretty logical, but I think we just count how many numbers we are multiplying together 🤷‍♂️

[alpine sable]

tyy

[alpine sable]

how did you guys took where both cars gonna meet?

i took the time of both the cars which they will take to cover from A to B

ping me please if someone tells it

[topaz scaffold]

Eh?

[topaz scaffold]

Notice that they moved the log3 to the other side by dividing

[river hearth]

https://tenor.com/view/elmer-sheep-thumbs-up-like-approved-gif-7569635

[lofty stream]

Q. Prove that diameter is the longest chord of a circle.

Please help me with this. Thank you.

[alpine sable]

measure it and compare it to other chords in the circle

in all seriousness, I recall having to draw a triangle

and using the triangle inequality

[lofty stream]

line segment joining any two point of the circumference of a circle is called a chord

[alpine sable]

Draw a triangle that two of it's sides are the circles radius and it's third side is any chord connecting these two radii

you don't really need to do that tbh, not sure if you can answer the question this way but ...

triangle inequality states that AB < OA + OB

and OA and OB are both radius of the circle

so we can substitute 2r

which is the diameter

hope this makes sense

can you even draw a triangle like that anyways?

just say as long as AB does not equal 2r

problem solved

[lofty stream]

Thanks a lot

[median hound]

i have had troubles with this prob before so can someone help

[alpine sable]

oh right

but close enough 🙄

[median hound]

also im pretty sure YN is 2.925

[median hound]

so LN should be 8.125

[median hound]

but beyond that is above my small knowledge

im having trouble getting LT and TN so can someone explain that?

on how to get it not the answer

wait i think i know how to get TN

thats how im getting TN

[alpine sable]

but a circle can't really have a radius of zero I mean I sorta get what u are saying but I still can't wrap my head around having a triangle inscribed into a circle with two sides = to the diameter

oops sorry for interrupting

[median hound]

TN is 23.765625 right?

wait i forgot a part of it

4.875?

[median hound]

im pretty sure the perimeter of LINT is 22.75 so can someone fact check that?

hello? lmao

[ocean seal]

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[median hound]

22.75 was correct

[ocean seal]

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[mellow canyon]

hey how do you go about operations on radicals and the such?

[celest root]

i got a quick question for a self practice

i searched this up online but idk the correct answer

The medication order is to adminster diazepam (Valium) 0.2 mg/kg IV STAT. The infant weighs 15 pounds.
Available: Multidose vial labels Valium 5 mg/ 2 ML (round to the tenths place)
How many mL will/should the nurse administer?

yessir

i got 0.5ml (my answer)

[ocean seal]

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[celest root]

i have no idea what you just did

but wow

[ocean seal]

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[celest root]

ah

so i was right

oh

ima just write that down real quick

the next question i did was similar but i did get wrong

The medication order is to administer gentamicin sulfate 6mg/kg/day. The child weighs 35 pounds. Available: gentamicin sulfate 10 mg/2 mL. (round to the tenths)
How many mL will you administer

i had like a 9.7

i checked my asnwer and yet it was 13.7

[ocean seal]

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[celest root]

wow

i think it was a typo on the website but mine, yours and the websites are completely different

i thank you for the help

[manic glade]

someone asked if this is the right way to define the set of ordered pairs whos sum of squares is equal, going by the reasoning that "if they are all equal to a specific number then they are equal"

this seems like the wrong way to go about doing that, am i just wrong?

also if it is indeed wrong what is the correct way to define that

ive no idea what they were trying to do honestly just passing on the question because im curious

seems to me like it would "check" for a different z for every pair it "looks" at

so their idea of comparing everything to a unique z value doesnt apply

tru

but is it possible to define the set they were trying to?

they described it as all the pairs with equal sums (of squared elements)

they wanted ordered pairs

course semantics

they use pointy ones for whatever reason

i mean

it may not be what youre used to

or even the most popular notation

but its certainly is the way its used

thats just handwriting..

i mean thats hardly what matters heres ;p

is there a way to define a set they described?

or in general something of that kind

yeah i guess it does

can you do something like define an arbitrary specific z value

let z something something

sure?

so how would that definition look like

[ocean seal]

Hurubon

[ionic jewel]

shouldn't it be (x,y)

i see

using wrong notation

[manic glade]

its pointy on the wiki too, just weird local notation

the english one uses ()

[ionic jewel]

guess you could read it as a vector

[manic glade]

hebrew

i gave them your definition

[small holly]

what does 'in terms of x' mean in the question

so f(x)?

ohh alright i get it

ty

[small holly]

why did my teacher switch the operations in the 4th step

oh alright

thanks

[narrow basalt]

wha is this?

[iron hull]

2 multiplied by the square root of 2?

[narrow basalt]

oh ok

thanks

[small holly]

how do i find the t-intercepts for this

and how do i get the turning point

[alpine sable]

t-intercepts are values of h for which t=0

[alpine sable]

The turning points are the points of a function where the derivative is 0

[small holly]

isnt the t-intercept h=0

[alpine sable]

Ah yes, i beg ur pardon

[small holly]

yeah but i dont know what to do when the equation becomes
0=20t-5t^2

[alpine sable]

Factor out t

[small holly]

so t(20-5t)

[alpine sable]

Precisely

[small holly]

should i factor 5 as well?

[alpine sable]

U could, if u wanted, yes

[small holly]

so then itll be 5t(4-t) right

[alpine sable]

Yes, set that equal to 0

Wht values of t will u get then?

[small holly]

idk

[alpine sable]

Use the fact that if ab = 0, then a = 0 and b = 0

[small holly]

so then t=0

[alpine sable]

Yes, and?

[small holly]

it will then be 0(4-0)

and then the equation would be 0=0

[alpine sable]

Not quite

[bitter sage]

leadersheir when done can you help with this?