help-13

[kindred storm]

Yes, that's the new top.

[real bone]

All over x * 1/x

[kindred storm]

Why do you do x · 1/x?

[real bone]

X is the original

[kindred storm]

Oh, logarithmic differentiation there?

[real bone]

And ln x

Is 1/x as the derivative

[kindred storm]

It's easier to just use the power rule. (xⁿ)' = n xⁿ⁻¹.

Unless they tell you to use logarithmic differentiation.

So, (x¹)' = 1 x⁰ = 1.

[real bone]

I thought I had to take the ln of the top and bottom

[kindred storm]

No, you have to differentiate the top and bottom.

You can do that by different methods for the different parts.

[real bone]

Oh it's done separately

[kindred storm]

Yeah, top and bottom separately.

[real bone]

Ok then yea

Derivative of x is 1

[kindred storm]

Also, if there are multiple terms in the top, you can use the sum rule of differentiation to do the parts separately, too.

[real bone]

Yes

So if I plug in zero to what we have now

[kindred storm]

So, L'Hospital just says if you get an indeterminate form like 0/0 or ∞/∞, you can take the derivative of the top and separately take the derivative of the bottom, and those are your new top and bottom.

[real bone]

It's just ln11 - ln10

[kindred storm]

Good.

And that should be the answer, unless they want it rounded to the nearest something.

ln(11) - ln(10) is the best answer, though, since it's exact.

[real bone]

Yea webwork does the calculation

[kindred storm]

Oh, OK.

[real bone]

One last question

You said if e^x approaches inf it's a limit of inf right?

[kindred storm]

Yes, that's right.

As x gets higher, eˣ gets higher without any upper bound.

eˣ can get as high as you want it to by making x high enough.

When that happens, the limit as x goes to infinity is infinity.

[real bone]

Thanks for all the help

[kindred storm]

You're welcome.

[real bone]

.close

[cedar kiln]

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[verbal kernel]

Ok, I have multiplied 2r and -78 which equals -156. I’ve found -12x13 = -156 and -12+13=1 or r in this case. Now what?

[verbal kernel]

Factoring

[glad kestrel]

factor by grouping

[verbal kernel]

That’s right okay

I wrote down (2r-12r) (13r-78). I got (2r-6) (r-6)

It’s problem 2

[glad kestrel]

not sure how you got that

[cedar kiln]

@verbal kernel Has your question been resolved?

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[sweet rampart]

hey guys what am I messing up here? It says I have an argument error. "deSolve(y'=-2x+1 and x(0)=2,x,y)

[sweet rampart]

I'm trying to find exact solution of x(0)=2

[cedar kiln]

@sweet rampart Has your question been resolved?

[sweet rampart]

<@&286206848099549185>

[cedar kiln]

@sweet rampart Has your question been resolved?

[violet rapids]

why use a calculator

$\dv{y}{x} = -2x+1$

[wraith dagger]

sills

[violet rapids]

this is really easy to solve for the general solution

[cedar kiln]

@sweet rampart Has your question been resolved?

[sweet rampart]

our professor makes us put the input/output of our ti89 for the solution

so we have to take derivative normally but then do it with a calculator as well

[sand ether]

deSolve(y'=-2x+1 and y(0)=2,x,y)

[sand ether]

shouldn't it be y(0) = 2

[cedar kiln]

@sweet rampart Has your question been resolved?

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[glad kestrel]

show work

[lost python]

you take the subroots

[jaunty mural]

thats not work.

[merry beacon]

It should be on the numerator, right?

And times dθ

[cedar kiln]

@glacial ibex Has your question been resolved?

[jaunty mural]

no, you show your work.

🤦

doesnt hurt to show how you tried...

[cedar kiln]

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[deep pendant]

Hello, I am asked to write out this false statement in mathematic notation. The answer is wildly different to what I wrote so I am wondering if what I wrote is correct or makes sense

[unique bramble]

it should be n^2<0.

[deep pendant]

That is the answer yes

But I don’t understand why what I wrote also doesn’t correspond to the statement

[unique bramble]

so, the statement is quite straight foreward. There exist a number

the fisrt part

[deep pendant]

Yep

[unique bramble]

youve called that number n

so its root must striclty be nagtive

n^2 <0

[deep pendant]

I could have written the statement better

It it simpler, what you say

[unique bramble]

in this case striclty refers to not equal

[deep pendant]

But how is what I say not correct too even if it’s not pretty

[upper abyss]

Here's what you wrote:
There exists a real number n, for a real number x, x = n²
So you don't mention the negative thing anywhere

[deep pendant]

I wrote that x is in R-

[unique bramble]

cuz you define 2 numbers, but your x does not need to be negative

its the square

use the numbers you define

[upper abyss]

You're thinking of $R^-$

[wraith dagger]

Kaynex

[deep pendant]

Yes

[deep pendant]

Ah I see this makes sense

Okay I see my mistake now

[unique bramble]

You wrote: There exist a number called n, element of R and also assume x to be element of the negative R. Then you say that x=x^2, but it does not refer to 'Their exits'

Okay!!!

Glad to help!

[deep pendant]

I get it, thanks so much

[unique bramble]

yw

type .close

@deep pendant

[deep pendant]

I know o:

.close

[cedar kiln]

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[unique bramble]

sowwy

[deep pendant]

God knows I have too many messages in this discord

Luckily you guys exist

[cedar kiln]

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[hallow tinsel]

Does $A\cap \bigcap_{n=1}^{\infty} B_n = \bigcap_{n=1}^{\infty} \left(A\cap B_n\right)$?

[wraith dagger]

(𒀭)

[hallow tinsel]

Intuitively, I'd guess it is, but I just want to be sure

[narrow root]

Yeah bc set intersection is distributive over itself

[hallow tinsel]

cool, thanks

.close

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[narrow root]

Why not just make a truth table

[split vortex]

idk what that is i've been really behind

[narrow root]

Do you know what the symbols mean in the expression

[split vortex]

i don't

[narrow root]

Bro..

[split vortex]

yea i know

[narrow root]

^ is and

~ is not

Down carrot is or

[split vortex]

ok wait actually can i change my question i found out how to do those

[cedar kiln]

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[boreal blade]

hey

[boreal blade]

can anyone here point out the intuition behind this property of joint CDF ?

i mean how pointing one variable to infinity leads to CDF of other random variable

[dire geode]

F(x) goes to 1 as x goes to infinity for all CDFs

So if you treat F(x,y) like 1 for the y variable, then you're just left with the x variable

[cedar kiln]

@boreal blade Has your question been resolved?

[boreal blade]

so if F(x,y) as y goes to infinity then F(y)=1 and you leave with F(x) ?

[cedar kiln]

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[boreal blade]

.reopen

[cedar kiln]

✅

[cedar kiln]

@boreal blade Has your question been resolved?

[unique bramble]

if you need intuition you could see it like this @boreal blade

we know that probability will be distributed in a certain way

we dont know how, but we do know that each known given will tell us something about the unknown

eg: we know Y, we can estemate X (or its distribution)

so if we loop over all possibla Y

we know what X would be given every situation

the reason we can do this is cus they are independent

You could also see it like this: A function in 3D space. X,Y and Z as the result of F(X,Y)

imagine integrating over 1 var

and it should make more sense

[boreal blade]

makes sense

thanks

.close

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[coral surge]

How to solve this one?

What to do with the |x|?

In the numerator

Ping me if you help

[tropic oxide]

,rccw

[tropic oxide]

@coral surge

do you know how to make a sign table

...actually, wait

you don't need that here

|x| is positive for all x other than zero, so this inequality reduces to 1/(x-1) > 0 (so long as you remember to exclude x=0 from your answer at the end)

[coral surge]

Yeah

But, out of curiosity

[coral surge]

What is sign table?

[tropic oxide]

it's a method of solving inequalities that are in the form [product of stuff] > 0

[merry beacon]

Do you even need complex solutions? Or just real?

[tropic oxide]

(or <0, or ≥0 or ≤0)

[tropic oxide]

we're talking about an inequality here. you can't do that on complex numbers.

[merry beacon]

K

[coral surge]

Thanks a lot

[tropic oxide]

why are you thanking me

i said literally nothing

i was going to say that a sign table is constructed by noting all points at which one of the factors of the LHS changes sign, and partitioning the real number line based on those points, and then studying the sign of the entire LHS on each subinterval

but i suppose you don't want to hear that

[coral surge]

Yeah 😅

.close

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[warm vector]

I still don’t understand why we can just use the depreciation formula to and minus by the amount to get the depreciation for the third yr. I don’t understand why the found the depreciation of the second and third year and subtracted those 2 values

[livid hound]

they're asking for depreciation in the third year
NOT after three years

its like starting with a certain amount of apples and eating some each day
at the beginning of the first day i had 10
at the beginning of the second day i had 7
at the beginning of the third day i had 5
how many apples did i eat on day 2?

[warm vector]

So if they say ‘an object depreciates by a rate of something for 5 years find the depreciation’, what does this mean? Directly using the formula of depreciation?

[livid hound]

yeh...

[warm vector]

ok I got it thanks

.close

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[rugged tusk]

H is subgroup of G, show that gHg^-1 is subgroup of G

[upbeat carbon]

Well, what are the hypothesis you need to verify for gHg^-1 to be a subgroup of G ?

[rugged tusk]

subgroup

in this case multiplication closure

let a,b in gHg^{-1} => gag^{-1}gbg^{-1} = gaebg^{-1} = gabg^{-1}

[upbeat carbon]

Well, that works just fine

[rugged tusk]

then inverse closure

[celest ledge]

Which part you are proving? 1 is contained in it? Closed under Multiplication ? Closed under inverse?

[rugged tusk]

i dont know how to prove inverse closure

[celest ledge]

(gxg^-1)^-1=g(x^-1)g^-1

[rugged tusk]

hmm, why g**(x^-1)**g^-1 only x has ^–1

?

[upbeat carbon]

Try to multiply gxg^1 by g(x^-1)g^-1

[rugged tusk]

ok

[upbeat carbon]

You should get the identity element

[celest ledge]

You check it yourself

You don’t know (ab)^-1=b^-1a^-1?

[rugged tusk]

i got the identity

[rugged tusk]

i know it, but in this case we have 3 elements like (abc)

[celest ledge]

Then what

[celest ledge]

Exam it yourself

[upbeat carbon]

Well, (abc)^1 = (c^-1)(ab)^-1 = (c^-1)(b^-1)(a^-1)

[rugged tusk]

then just the middle element stays in the middle

[rugged tusk]

thanks, got it

but what does it mean when i ended up with identity element?

identity is in subgroup, so then its closed ?

[cedar kiln]

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[upbeat carbon]

ô.o

[upbeat carbon]

It means you found the inverse of gxg^-1

(The channel is bugged I think)

[rugged tusk]

but i need to find if its closed

under inverse

[upbeat carbon]

Well, you wrote the inverse g(x^-1)g^-1. Isn't this in gHg^-1 ?

[celest ledge]

You really need to be fed directly? Any x from H, x^-1 is from H.

[chrome edge]

Let me just say something: Make sure you understand the properties/conditions of groups and subgroups

[rugged tusk]

and the last thing i have to check

if gHg^-1 is not empty

[celest ledge]

What? Why you always say that? You just check 1 is in it

[upbeat carbon]

The two properties are equivalent, but proving 1 is in gHg^-1 is faster and easier

Most of the time

[rugged tusk]

if i take a = e then geg^-1 is in the subgroup

[upbeat carbon]

Yep, so it's not empty

[rugged tusk]

ok thanks guys for help

[upbeat carbon]

np

.close

[rugged tusk]

.close

[cedar kiln]

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[cedar kiln]

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[terse roost]

You want something like tan(alpha) ?

[dusty hazel]

Probably alpha.

[worldly atlas]

is it alpha

[dusty hazel]

What is your question?

[terse roost]

Alpha = Arctan(4)

[worldly atlas]

i mean it is alpha

i need to find the alpha

[terse roost]

Arctan(4)

[worldly atlas]

ok thnks

[terse roost]

You see how I found it ?

[worldly atlas]

trying to figure it out

[terse roost]

Call E the orthogonal projection of B on DA

[dusty hazel]

You now get a rectangle.

And a triangle.

[terse roost]

And look at the right triangle AEB

[worldly atlas]

i see that

[terse roost]

You can get its lengths pretty easily

[worldly atlas]

the thing is how do i find the degrees

[terse roost]

Mmh

Do you know trigonometry ?

[worldly atlas]

lis sinus and stuff

like

[terse roost]

Yes

[worldly atlas]

yes

[dusty hazel]

This is something you should have asked before using arctan4

[terse roost]

Do you know what tan(alpha) is in the right triangle like this ?

[terse roost]

Since we needed it to answer I assumed he/she studied it already

[dusty hazel]

That makes sense, however some people try questions in the internet so it makes sense to ask.

[worldly atlas]

is tan
ctg or tg

[terse roost]

tg

Tangent is the full word

[worldly atlas]

oh ok i get it now

[worldly atlas]

will keep in mind

thnks!

the response ime is very quick

.close

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[strong anchor]

hello, sorry for such a juvenile question but i've got this question which asks " solve the following for x"

[strong anchor]

does that mean expand? cos i got

6x -2x^2 + 15 -5x = 0
1x -2x^2 + 15 = 0 

[crimson sedge]

why would you expand?

what do you know about a product which equals 0?

hello?

[strong anchor]

nothing comes ot mind

[crimson sedge]

ok if I tell you that I have a* b * c = 0

what are the solutions?

[strong anchor]

are they all zeros?

[crimson sedge]

that is one of them

[rigid ridge]

it could still happen that a=0 and b=1 and c=1

[crimson sedge]

but is that all?

[rigid ridge]

so not all zeroes

[limpid meadow]

You might be able to do that using quadratic formula but the other way is simpler

[strong anchor]

there could a negative number which takes the positive to zero

[crimson sedge]

let @strong anchor respond

[rigid ridge]

a negative number times a positive number making zero?

[crimson sedge]

no

[rigid ridge]

could you give an example

[crimson sedge]

this is NOT a sum

[modest warren]

2x + 5 = 0 and 3 - x = 0

[crimson sedge]

HL why

[rigid ridge]

but why

[strong anchor]

I HAD THAT EARLIER BUT I DIDNT UNDERSTAND IF IT WAS CORRECT

[rigid ridge]

it's not

i mean, strictly speaking :P

[crimson sedge]

huh

bro it is correct

[rigid ridge]

because of ||and||

[crimson sedge]

but @strong anchor does not know this rule

[strong anchor]

this has to do with quadratics though

[crimson sedge]

oh right

yeah it's "OR"

[rigid ridge]

ofc they mean the right thing tho

[strong anchor]

i just cant for the life of me understand what the question's meaning

[rigid ridge]

What values of $x$ make \[ (2x+5)(3 - x) = 0 \] a true statement?

[wraith dagger]

Lance

[crimson sedge]

solve an equation means to find such values that make it true

[modest warren]

the value of x that makes the equation equal to 0..

[strong anchor]

yeah but how is 2x+5 = 0 a valid answer

cos if x is 0, wouldnt the equation expression in the bracket not equation 0?

2 * 0 + 5 = 5
and
3 - 0 = 3

[modest warren]

there are two somutions not 1

[limpid meadow]

then use the quadratic formula if you're asked to do so

[modest warren]

*solutions

in quadratics there are mainly two solutions to x

so the other would be - 5/2

x = -5/2 and 3

[strong anchor]

i learnt 2 formulas for quadratic equations, and this is end product of both equations i think

[limpid meadow]

when we have something like a.b = 0, for the statement to be true, either a has to be 0 or b has to be 0. In this case a is (2x + 5) and b is (3 -x), both include x which can take any value , that means at some value of x, either one of them can be zero, so we find those value of x which make either a or b equal to 0

[cedar kiln]

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[crimson sedge]

Hi,

when we have 8 Apples and want to share them among 4 people we would calculate 8apples/4people which equals 2apples/people, speaking 2 apples per person.
So we are dividing our amount of apples into several equally large amounts of apples. (Every person gets the same amount of apples.)

However, when we have a road with 8km length and we drive 4km/h, then we obviously need 2hours. 8km/(4km/h) = (8km*h)/(4km) = 2h.
But is there an intuitive way like above where we can say, we split the length of the road into equally large pieces of .... ?

Like we split the length of the road into equally sized pieces with "size" 2 hours? That seems false

[cinder portal]

It's not exactly abstract but I think if you try too hard to find intuition for things in maths especially trivial things such as this you will end up wasting a lot of time

Just understand that distance/time = speed so distance/speed = time

[crimson sedge]

I mean, it is intuitively totally clear that 8km/4km/h equals 2 hours. I just thought we might find this easy formulation like with the apple/person example.
I think why we can not find it here is because the denominator does not contain a "unit."

8apples/4persons <=> 2apples/person speaks like 2 apples per person.

But 8km/(4km/h) <=> (8km*h)/4km <=> (2h/1) since the km cancel each other out. So we are left with a denominator that does not have a "unit" so we can not say 2 hours per something

[cedar kiln]

@crimson sedge Has your question been resolved?

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[valid nexus]

Hola

[valid nexus]

In 2.8 (a), do I need to find dot product?

[cinder portal]

I believe so which will just be the magnitude of u

[valid nexus]

I don't think so.

[foggy merlin]

yea it's a dot product

[valid nexus]

Thank you 🙂

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[echo scroll]

How do I find the excepted value of C when T is uniform distributed on the interval (1, 3)

[dense wing]

find E[T^2]

then just compute E[C]

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[echo scroll]

how do I do that

[dense wing]

definition of E[] and LOTUS

[echo scroll]

yeah i don't know how to compute it when it is T^2

[dense wing]

$E[g(X)]=\int_{\mathbb{R}}g(x)f(x)\dd{x}$

[wraith dagger]

Mosh

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[crimson sedge]

Yo

[crimson sedge]

how tf is cos(x-pi) equal to -cos(x)?

im so confused brah

[livid hound]

consider unit circle and/or compound angle identities

[native halo]

bro

coem

help

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[indigo oasis]

the determinant of matrix B is 0

therefore other matrix in place of matrix A will also multiply to produce matrix C

how can I find such a matrix Z

https://media.discordapp.net/attachments/486841106298961930/952551531075485727/unknown.png

^ This is the first row of C

with help from @tough osprey, I get

https://media.discordapp.net/attachments/486841106298961930/952557868664635432/wolf.png

[tough osprey]

Yay

So Z is either does not exist or not unique

Can u get the system of linear equation of the 2nd row and the 3rd row of C?

[indigo oasis]

ok let me do that

[indigo oasis]

Z is not unique, there is more than one such Z

[tough osprey]

Yay

[tough osprey]

Lol just list out the equations and let wolfram help us

[indigo oasis]

hhahahaha yeah imma do it rq thanks :)

,w d+2e-f =6, d+3e-2=5, d+e=7

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[tough osprey]

Opps

[indigo oasis]

im double checking

[tough osprey]

Then Z does not exist …..but this is obviously not true

A is already a counter example

[tough osprey]

U miss the f in the second equation

[indigo oasis]

oops mb

,w d+2e-f =6, d+3e-2f=5, d+e=7

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[tough osprey]

Noice

[indigo oasis]

nice ok

,w g+2h-i=12, g+3h-2i=11, g+h=13

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[indigo oasis]

b = 1 - a
c = 2 - a
d = 7 - e
f = 1 + e
g = 14 - i
h = -1 + i

[tough osprey]

Now u can write Z in terms of a, e, i only

[indigo oasis]

what do you mean?

oh yeah

sec

[tough osprey]

$Z=\begin{pmatrix}a&1-a&2-a\7-e&e&1+e\14-i&-1+i&i\end{pmatrix}$

[wraith dagger]

Trenton

[indigo oasis]

oh damn thanks

[tough osprey]

That is beautiful

[indigo oasis]

lmaooooo

wait so any values of a, e, i in Z where Z*B will give C?

i dont know if that makes sense

what I typed

imma try

[tough osprey]

Yes

If we didn’t make any error during the computation

[indigo oasis]

ok imma try to calculate

[tough osprey]

Btw if u want to show that the answer we obtained is correct

U cant just substitute some a,e,i

[indigo oasis]

it must be values from C right?

[tough osprey]

You should keep them in algebraic form

Ya

[indigo oasis]

oh

[tough osprey]

The a,e,i will cancel out each other

Then gives the matrix C

If we get C

Then we are correct

[indigo oasis]

holy hell

plugged into online matrix calculator and got the same C

damnnn

thank you so much

can i pm u real quick

@tough osprey

[tough osprey]

Ok

[indigo oasis]

awesome dude

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[crimson sedge]

Problem no.12

[crimson sedge]

I have no clue how to start

P(n)/q(n) is I can multiply and divide by p(n)

And then I write q(n) as p(n).s(n) + r(n)

But this isn’t helping at all

Ik why this will go to 0 but how to show that

[jaunty mural]

hint: you have a nice fraction (write it out explicitly)

I would divide numerator and denominator by something

[crimson sedge]

P(n) ?

And this becomes a continued fraction ?

Is that the approach

@jaunty mural

[jaunty mural]

huh?

sounds mad.

there's an elementary approach.

[crimson sedge]

Oh shit

I divide by x^m

Hahahahaha

[jaunty mural]

yes.

[crimson sedge]

Why didn’t see that

Ty Shuri

U rock

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[hardy mountain]

Hi, does someone have a source or a video that can help explain whatever's going on on this image ?
I understand the Gaussian Elimination Method and what the Row Echelon Form is, I'm just confused as to what's happening in this specific example.
Any time there's more variables than there is equations I get confused.

[upper garnet]

since there's 3 equa and 4 variables

you choose 4th variable be a random real number let's say x_4=s

then solve the equation and you'll see there won't be one unique solution

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[hardy mountain]

Oh I see, thank you I'm going to try this again with this new knowledge !

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[smoky fox]

could someone explain to me how we know b has double the perimeter after we use r * Θ
(a is unrelated, ignore)

[smoky fox]

oh wait

im actually a dumbass

it has radii in two places

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[late pike]

how come there is no inflection point at pi and no relative max

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[wintry mural]

Which is that formulae in the 3rd step ?
I actually tried to find the formulae of central angle but that's completely different than the one mentioned in 3rd step

[quartz vale]

yeah the RHS of the 3rd line ought to be 50

[wintry mural]

What ?

[quartz vale]

umm

the LHS is the formula right?

that yields 50 right?

[cedar kiln]

@wintry mural Has your question been resolved?

[wintry mural]

@quartz vale
I actually couldn't understand the whole formulae that's why I asked

[quartz vale]

yeah that formula isnt right... its only the RHS that is correct

but the value of that formula is 50

[wintry mural]

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[crisp anvil]

Should i study matrices first or determinants?

[sand ether]

matrices

then determinants

[crisp anvil]

Okay thank you✌️

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[limpid grail]

Can anyone tell me what's happened between these two steps

[steady imp]

Yeah two things

First they cancel out the x

Then they cross multiply the fractions

[limpid grail]

I see thank you.

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[civic wren]

hi i have a problem regarding the epsilon delta definition of a limit

[civic wren]

the problem is this

i want to prove this limit....

that is where ive got up to

and the problem is that i dont have a clue how to get to the point where one of my abs values is |x-3|

[celest ledge]

|x^2+4x+4-25|=|x-3||x+7|

[civic wren]

oh silly me

sorry abt that lol

forgot i needed to minus the 25

[celest ledge]

Lol

[civic wren]

thanks for the help

have a good day :)

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[elfin tulip]

What is the age of amber in terms of m

[elfin tulip]

find ambers age in terms of m

<@&286206848099549185> can u help me find ambers age in terms of m

[glad kestrel]

• After 15 minutes, feel free to ping @Helpers.

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

[elfin tulip]

hasnt it been

[elfin tulip]

oH

(SORRY)

ok so i did Kyle = 3x Amber 5 years ago.

Kyle was : 5m-3 years old but i dont know how to find amber

[glad kestrel]

i don't think that's what the problem intended

looks like it's saying kyle is thrice as old as amber present day, and 5 years ago, kyle was 5m-3 years old

[elfin tulip]

i dont understand how to work it

its a new topic what we did

and i didnt understand when it was being taught

[glad kestrel]

let kyle's age be K, and amber's age be A

how can you express 5 years ago in terms of K?

[elfin tulip]

uh

5m-3 / 3?

[glad kestrel]

not quite

think about yourself: you are currently some age. think about how old you were 5 years ago. how would you determine your age 5 years ago given your age today?

you don't need to actually tell me your age, just think about that

[elfin tulip]

uh

[glad kestrel]

then express kyle's age 5 years ago in terms of K

[elfin tulip]

well i wud do

my current age -5?

[glad kestrel]

right

so if kyle's age is K, how old was kyle 5 years ago?

[elfin tulip]

so its 5m-3 -5?

[glad kestrel]

not quite

forget about the m expression for now

just use K

how old was kyle 5 years ago

if K is kyle's age now

[elfin tulip]

uhh

[glad kestrel]

it's exactly what you were thinking about here

[elfin tulip]

oh

uhm

K = 3x A -5?

[glad kestrel]

you're overthinking this quite a bit

if kyle is K years old right now, how old was kyle 5 years ago

[elfin tulip]

sorry its just so confusing

[elfin tulip]

K-5

?

[glad kestrel]

yep

so kyle was K-5 years old 5 years ago

[elfin tulip]

yea

[glad kestrel]

but he was also 5m-3 years old 5 years ago

so what can you say about K-5 and 5m-3?

[elfin tulip]

multiply by 3?

because of amber?

[glad kestrel]

not thinking about amber yet

[elfin tulip]

oh

[glad kestrel]

just thinking about kyle's age

you know two things now:
Kyle was K-5 years old 5 years ago
Kyle was 5m-3 years old 5 years ago

[elfin tulip]

well do u do k = 5-3?

[glad kestrel]

no

[glad kestrel]

think about this

google the transitive property if you need to

[elfin tulip]

K= 5m-3 -5?

[glad kestrel]

you're very close

but there was a step you skipped that resulted in a mistake

[elfin tulip]

uhhh

K=5m (-3-5)

[glad kestrel]

seems you're just guessing here

think about this logically

[elfin tulip]

its hard ;_;

[elfin tulip]

but what is that step

[glad kestrel]

that's what i want you to figure out

5 years ago, kyle was K-5 years old and he was 5m-3 years old

i want you to write an equation relating K-5 and 5m-3

if you know he was both K-5 years old and 5m-3 years old, what can you say about those two expressions?

[elfin tulip]

that they are similar??

[glad kestrel]

they are indeed very similar, how can you write that mathematically

[elfin tulip]

hm

K = 5m (3-5) ?

[glad kestrel]

how did you arrive there?

[elfin tulip]

i seperated it

[glad kestrel]

separated what?

[elfin tulip]

but alike terms together

put*

[glad kestrel]

what alike terms?

[elfin tulip]

3 and 5

[glad kestrel]

how'd you get from K-5 and 5m-3 to K=5m(3-5)?

[elfin tulip]

i figured to seperate the 5m from the 3 and 5

[glad kestrel]

why?

[elfin tulip]

i just thought of it

[glad kestrel]

does it make sense to do that?

[elfin tulip]

not really

[glad kestrel]

then think about something that would make sense

kyle was K-5 years old
kyle was 5m-3 years old
relate those two expressions

[elfin tulip]

K =5m-3 -5

?

[glad kestrel]

you're close... but you're skipping a step

[elfin tulip]

uh

[glad kestrel]

why are you subtracting 5 from 5m-3?

[elfin tulip]

K-5 = 5m-3?

[glad kestrel]

there you go

[elfin tulip]

:o

[glad kestrel]

if kyle was K-5 years old 5 years ago and kyle was 5m-3 years old 5 years ago, K-5 and 5m-3 are representing exactly the same thing

so you can set them equal to each other

now solve for K

[elfin tulip]

K = 5m (-3+5)

[glad kestrel]

the parenthesis imply multiplication, best to leave those out in this scenario

[elfin tulip]

the what

[glad kestrel]

the () you wrote imply multiplication

[elfin tulip]

OH

[glad kestrel]

looks like you're writing 5m times (-3+5)

[elfin tulip]

so is it K = 5m -3+5

[glad kestrel]

right

and you can simplify that a bit

[elfin tulip]

K=5m + 2

[glad kestrel]

yep

so now we think about amber

[elfin tulip]

A = - 3?

[glad kestrel]

?

it tells you in the problem that kyle is thrice amber's age

[elfin tulip]

bc kyle is thrice as old as amber

[glad kestrel]

if kyle is K years old and amber is A years old, relate K and A

[elfin tulip]

so its -3 from kyle?

A = 5m-2-3?

[glad kestrel]

i don't know how you're arriving there

[glad kestrel]

you said something almost correct here in your very first statement

if right now kyle is K years old and amber is A years old

and you're given that kyle is 3 times older than amber

K=?

[elfin tulip]

K = 5m -2 x3?

+2*

[glad kestrel]

you're getting a little ahead of yourself here

i just want you to relate K and A

Kyle is 3 times older than Amber

[elfin tulip]

K = 5m +2 /3?

[glad kestrel]

missing parenthesis, but yes

the way you wrote it implies $K=5m+\frac23$

[wraith dagger]

a disappointing son

[glad kestrel]

K=(5m+2)/3

[elfin tulip]

i got it

so its the answer

?

[glad kestrel]

yes

[elfin tulip]

k

how do i close

[glad kestrel]

.close

[elfin tulip]

.close

[cedar kiln]

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[flat pawn]

y=2x^2+4x

[flat pawn]

how to get the vertex on this quesiton

*question

[dull anchor]

bist du deutscher?

[glad kestrel]

the vertex of a quadratic can be found using $x=-\frac{b}{2a}$

[wraith dagger]

a disappointing son

[flat pawn]

no not technically my parents work for the dutch embassy in berlin

[flat pawn]

jes i tried that

[glad kestrel]

what did you get?

[flat pawn]

for the x coordinate i got x=-1

[glad kestrel]

looks good

now find the y coordinate

[flat pawn]

but my book gives the answer of 0

[glad kestrel]

,w graph 2x^2+4x

[wraith dagger]

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[glad kestrel]

doesn't look like it

if your book says the x coordinate of the vertex is 0, it's wrong

[dull anchor]

maybe its talking about the zeros?

[cedar kiln]

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[signal bane]

how do you factorise 4f^2+f

[flat pawn]

2F(2F+1)

you take out the common factor

[cedar kiln]

@signal bane Has your question been resolved?

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[crimson sedge]

Could someone tell me if the answer is 1?

[crimson sedge]

I simply considered this as x and did the math then got

$\frac{17x+3}{30x+7}+\frac{13x+4}{30x+7}$

[wraith dagger]

feliipe

[crimson sedge]

and got 1

[celest ledge]

Yes correct

Left being x right being y, $\frac{1}{\frac{1}{x}-2}=\frac{1}{\frac{1}{\frac{1}{y}-1}-1}$

[wraith dagger]

Cogwheels of the mind

[celest ledge]

I got (2y-1)/(1-y)=(1-2x)/x, x+y=1 too

[crimson sedge]

thank you

just needed a confirmation that it was correct

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[granite pecan]

tried this many times, i can seem to get the answer they got

[celest ledge]

What’s your question?

[granite pecan]

how they managed to simplify that

i made it to the far right cant get any further.

[celest ledge]

So there is no original question,.. just simplify the thing in your picture…

[granite pecan]

yes

[celest ledge]

And it is correct

[granite pecan]

im confused how they managed to simplify the above expression into the answer at the bottom

[celest ledge]

I mean there is no mistake. But you said simplify, it doesn’t have a standard answer

[granite pecan]

yes i keep getting a different answer which would make it wrong in other work

[celest ledge]

It =1+2^(n+1)(1-(1/2)^(n-1))=1+2^(n+1)-4=2^(n+1)-3

[granite pecan]

but how does 2^n turn into 2^n+1

[celest ledge]

You divided by 1-(1/2)=1/2

[granite pecan]

okay i see thank you

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[frank nest]

hello

[frank nest]

i just have this question on integration

im confused because of the last interval

for the right endpoint

im not sure if my last endpoints are correct

for left and right endpoint answers

specifically. when doing right endpoint, i did delta x times fx. Which i got (pi/2-pi/3)(f(pi/2))

but thats weird as last endpoint for left endpoint was delta x = pi/2-pi/3

im confused

<@&286206848099549185>

<@&286206848099549185>

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[trim sentinel]

The triangle ABC is given. If the length of the center of gravity from the vertex C is equal to half the length
side AB, prove that the triangle ABC is right-angled.

[trim sentinel]

Can i just say because circle?

Oh wait a sec

No nvm it can be just proven by circle right

,w triangle in circle

This?

CO = r
AB = 2r

[trim sentinel]

Is that what this means

[mighty drift]

I'm not going to pretend to be good enough at geometry to solve this, but I don't think the center of gravity is o, since o is on the edge

[trim sentinel]

Well the big problem is i cant even draw this triangle bc im so bad at geometry

[cedar kiln]

@trim sentinel Has your question been resolved?

[trim sentinel]

Ok i checked meaning of line

Idk why it translated to center of gravity

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[wraith dagger]

Andreww

Andreww

Andreww

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[sick mirage]

Hi I have a related rates question - did I get the right answer to this?

[dense wing]

Post your work?

[dense wing]

,rotate

[sick mirage]

my bad had to use phone

[dense wing]

yeah that looks right

[sick mirage]

Ok true - thanks for checking that out!

@dense wing got it right yewww! haha

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[fathom mural]

this would be 2^4 = 16 right

[flint plinth]

yep, X has 4 elements so its power set has 2^4

[fathom mural]

cool thanks

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[flint plinth]

how many ways are there if you don't consider rotations to be equivalent?

[fathom mural]

im confused whether the 10 guests will be arranged with respect to the table or among themselves

[flint plinth]

there are ten chairs and ten people, how many ways are there to arrange the people onto the chairs?

[fathom mural]

(10-1)! then

[flint plinth]

why -1?

[fathom mural]

cuz its circular

and the seatings are the same if rotated

[flint plinth]

right, if you don't consider the rotations then there are 10! ways

[fathom mural]

ya

[flint plinth]

but you can partition them into groups of 10 that are just rotations of each other

so 10! / 10 = 9! = (10-1)!

[fathom mural]

also in induction hypothesis

this question

[flint plinth]

well you would induct on n

so any correct statement must include "for all 0 < r < 1" which rules out the first and last ones

[fathom mural]

so the third

[flint plinth]

the third one is a restatement of what you're trying to prove (for induction you don't assume it's true for all n)

so it should be the second one

[fathom mural]

oh

[flint plinth]

assume it's true for some particular n and for all 0 < r < 1

[fathom mural]

ahh ic

[flint plinth]

then you want to prove that it's true for n+1 and 0<r<1

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[fathom mural]

cant be one to one cuz codomain will have some elements that are mapped to more than once, right

is it option 1 or 3?? or some other

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[bold marten]

i dont understand how to graph

[rigid ridge]

do you know what graphing means?

[bold marten]

yes

but i do not know how to grahp equations

[rigid ridge]

y=4x and y=x+3 are lines, so they are already determined by 2 points

so find 2 points that the line passes through and draw the actual line

[bold marten]

Ok , thanks

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[muted charm]

is it possible to convert a recurring decimal to a terminating decimal? sorry im stupid lol

[bright surge]

...no?
recurring decimals can be written as fractions (which, by the way, those fractions can not be converted to terminating decimals) though

[muted charm]

ok, thanks

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[simple viper]

What's the mathematical term for this?
For example, I'm calculating a probability of a certain something, and the answer is 1/3, and the question asks for the numeric form, and we only keep two numbers next to the decimal points only. So the answer is 0.33. I know this phrase in my first language, but not in English, so please help!

[cinder portal]

Its said 2 d.p. meaning 2 decimal points

[ancient talon]

you also may see tenth/hundreth/thousandth place (.x, .0x, .00x)

[cinder portal]

Another example would be 0.555 is 3 d.p.

[simple viper]

Yeah, but how would they state them in a math question?

Like: Calculate the probability of getting heads or tails (keep up to 2 decimal points)?
I guess?

[cinder portal]

Calculate the probability of getting heads or tails (round your answer to 2.d.p)

I think

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[pale kiln]

.close

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[stable monolith]

Hi, was wondering if i could get help for this question, its related to lin alg

[stable monolith]

on top theres some equations with their corresponding matrix, and on the bottom is an equation we want to represent in matrix form

my prof did this lol, but im pretty sure you cant just divide matrices like that, so what's actually going on?

[cedar kiln]

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[stable monolith]

@toxic thistle

wtf

<@&286206848099549185>

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[uneven dove]

For (b), I do not get why the solution uses choice instead of permutation. why shouldn't it be order-sensitive?

[cedar kiln]

Please don't occupy multiple help channels.

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[crimson sedge]

How would I do C?

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

<@&286206848099549185>

[kindred gale]

If you did a and b then just substitute your variables by their relationship equation if I'm not wrong x+2y+4z<=40 and 15x+25y+40z<=700

Oh it's 60 and not 40 beds

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[worthy snow]

i forgot how to answer this question

[worthy snow]

all i remember is that y(1/x) is for dilations horizontally and 1/y for vertical i think

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@worthy snow Has your question been resolved?

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[crimson sedge]

|A∪B|=|A|+|B|−|A∩B|.

[crimson sedge]

how can I read this ?

[dense wing]

|S| is the cardinality of S

[crimson sedge]

cardinality of A or B = cardinality of A + cardinality of B - cardinality of a and B ?

[exotic furnace]

For the last one, “and” instead of “or”

[dense wing]

• cardinality of A and B

[exotic furnace]

Otherwise yes

[crimson sedge]

thanks for helping me

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[rigid pelican]

Need help with 6

[rigid pelican]

Just confused about how to actually do this

[cedar kiln]

@rigid pelican Has your question been resolved?

[hazy trench]

Right, all you need to do is to find the volume of the given cuboid.

According to me, convert the given dimensions to centimeters

And then, use the formula for the volume of a cuboid ( L x B x H)

[rigid pelican]

Alright so when converted to cm we should get 94, 61 and 21 cm

[hazy trench]

Yep

Now, multiply them

L x B x H = Volume of cuboid

[rigid pelican]

120414

[hazy trench]

Bingo

Now, back to meters

[rigid pelican]

1204.14

[hazy trench]

Yep

That looks right to me

[rigid pelican]

What does it mean by suitable degree of accuracy?

[hazy trench]

Suitable degree of accuracy probably means to keep the answer as accurate as possible without rounding

We've done just taht

That

[rigid pelican]

So what now?

[hazy trench]

That's the answer

Wait a second

Hold on

I see something

You got 120414 cm^3 we need to convert that to m^3

My mistake

I told you to divide the value by 100

[rigid pelican]

Umm

I don't see it

You didn't

[hazy trench]

You got a value when multiplying 94, 61 and 21 cm, right?

[rigid pelican]

120414

[hazy trench]

Exactly, that value you got is in cm^3

[rigid pelican]

I did 94 X 61 X 21

[hazy trench]

Volume is always measured in cubic units

[rigid pelican]

Wdym?

[hazy trench]

Take a look at this: https://www.google.com/search?q=why+is+volume+measured+in+cubic+units&oq=why+is+volume+measured+in+cub&aqs=chrome.0.0i512j69i57j0i22i30l2j0i10i22i30j0i22i30l5.5953j0j7&sourceid=chrome&ie=UTF-8#:~:text=Any object possesses a volume by virtue of the object being three-dimensional. Explanation%3A All three dimensions must be multiplied while calculating the volume. Therefore%2C volume is measured in cubic units such as cubic meters%2C cubic inches%2C etc.

There's nothing wrong with your steps, all you need to do is to throw in a cm^3 beside the value