help-28

[torpid stag]

Calculating the standard deviation would require you to expand the expression $\left(\sum_{i = 1}^{2000} X_{i} \right)^{2}$ where $X_{i} \sim \text{DUnif}(10)$

[glossy valve]

jan Mikkel

[foggy shore]

What is the DUnif(10)

unidentified distribution?

[torpid stag]

Discrete uniform

[foggy shore]

Okay well this helps a lot already

Thanks

[torpid stag]

You could also just run a simulation

Which would be much easier

To my knowledge at least

[foggy shore]

Yep somebody already did that but I thought actually calculating the S would be nice so I can graph it on Geogebra

[torpid stag]

How much silk did you get

[foggy shore]

Well it was a while back I did it but lowest I can remember the worker getting was around 10200+

[torpid stag]

Hmmmm

The expected value is pretty straightforward to calculate to 11.000

I tried running a simulation of 200.000 trials, and got a standard deviation of around 128

Since the sum of independent discrete uniform random variables has asymptotic behavior of a normal distribution you should lie within [μ - 2σ; μ + 2σ] = [10.744; 11.256] in most cases

[foggy shore]

Honestly, 128 might very well be accurate enough for this since its from 200k trials, ill try graphing it when I get home

[thin quartz]

isn't this equivalent to rolling 10-sided dice?
I found this https://math.stackexchange.com/questions/2245194/what-is-the-standard-deviation-of-dice-rolling

plugging the numbers in gives 128.452325787 so 128 seems good

[torpid stag]

Lmfao, you're right. I don't know why I went back to variance definition instead of just using the independence assumption

[full forum]

@foggy shore Has your question been resolved?

Channel closed

Closed by @foggy shore

Use .reopen if this was a mistake.

[foggy shore]

Thanks guys

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[unreal hull]

What do I do for 1a?

[torn jolt]

if you are allowed to use basic application of differentiation.
then calculate dy/dx at x= 2
so now you have slope
find out the y-cordinate by putting x=2 in f(x)
you would get the corresponding point on the curve

so now you have a point and slope at x =2
use slope point form and get the equation

[unreal hull]

oh thanks

.close

[full forum]

Channel closed

Closed by @unreal hull

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[buoyant wigeon]

How can I show that $\sum_{k=0}^{n} C^k_n \phi_k = \phi_{2n}$ where $\phi_n$ is the Fibonacci sequence ?
I tried induction but i can't seem to figure out how to proceed

[glossy valve]

Azenx

[buoyant wigeon]

$\sum_{k=0}^{n+1} C^k_{n+1}\phi_k =\sum_{k=0}^{n+1} (C^{k-1}{n}+C^{k}{n})\phi_k \ \
\sum_{k=0}^{n+1} (C^{k-1}{n}+C^{k}{n})\phi_k = \sum_{k=0}^{n+1} C^{k-1}{n}\phi_k +\sum{k=0}^{n+1} C^{k}{n}\phi_k = \phi{2n}+ \sum_{k=0}^{n+1} C^{k-1}{n}\phi_k
\\ \phi{2n}+ \sum_{k=0}^{n+1} C^{k-1}{n}\phi_k = \phi{2n}+ \sum_{k=0}^{n} C^{k}{n}\phi{k+1}$

[glossy valve]

Azenx

[buoyant wigeon]

For induction step

Now to finish we'd have to show why $\sum_{k=0}^{n} C^{k}{n}\phi{k+1}$ is $\phi_{2n+1}$ but i cant seem to show it

[glossy valve]

Azenx

[full forum]

@buoyant wigeon Has your question been resolved?

[full forum]

@buoyant wigeon Has your question been resolved?

[full forum]

@buoyant wigeon Has your question been resolved?

[full forum]

@buoyant wigeon Has your question been resolved?

[hollow sable]

Cant you say that the last sum in the second line is phi(2n-1)?

[buoyant wigeon]

Well I don’t think so, or at least maybe theres something I didn’t realize about the induction hypothesis that would allow us to do so

I also showed that $\phi_{n+1}^2-\phi_n \phi_{n+2}=(-1)^n$ if that’s any useful

[glossy valve]

Azenx

[hollow sable]

I’m not very well acquainted with induction but we can show that the result holds if it holds for n-1 and n, so our base step would be showing that it holds for n=1 and n=2.

[full forum]

@buoyant wigeon Has your question been resolved?

[tiny bridge]

As you showed here, proving $\sum_{k=0}^{n} C^k_n \phi_k = \phi_{2n}$ is equivalent to proving that $\sum_{k=0}^{n} C^{k}{n} \phi{k+1} = \phi_{2n+1}$. So simply expand your induction hypothesis to handle both of those.

[glossy valve]

chencking

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[minor creek]

i dont get how to solve e

[glacial pasture]

if you did c

then just solve 6=...

[minor creek]

ye but i get stuck

[glacial pasture]

show me

[minor creek]

What am I supposed to do after 0=1.23

[glacial pasture]

youre going to be missing solutions

if theres a solution at 1.23, theres another at pi-1.23

then you can do the adding of 2npi for each one

[minor creek]

how would i know which numbers would work though

the answer is supposed to be 3:30m and 12:30am, both were rounded to the nearest half hour

how do i get to it

my teacher was too lazy to post solutions

[full forum]

@minor creek Has your question been resolved?

[minor creek]

.close

[full forum]

Channel closed

Closed by @minor creek

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[ionic spear]

Yo

[ionic spear]

Can anybody help me find the bearings of b)i) and ii)

[full forum]

@ionic spear Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[abstract shard]

the top image is the question and the bottom is the answers

I'm trying to find the derivative but my question has more to do w algebra

how does 21 look like 1/ sqrt x+2 and 22 look like sqrt (1/t^2-2) but they both turn into (x+2)^-1/2 (for 21) and t^2-2)^-1/2

like how is their first stepts the same?

unless im trippin and they arnt the same

[smoky wing]

[\wrb{
\s{\f ab} = \f{\s a}{\s b}
}
]

[glossy valve]

Pure

[abstract shard]

woaaa its rainbow

ok wait yea

but

#21 isnt all square rooted ...

only the denom is

[smoky wing]

\[\wrb{
\s{\f 1{t^2-2}} = \f{\s 1}{\s {t^2-2}}
}
\]

well yeah.

[glossy valve]

Pure

[smoky wing]

and sqrt(1) = 1

[abstract shard]

ohhhh

[smoky wing]

So you can rewrite g(t) as 1/(sqrt(t^2-2))

Which looks similar to the expression in question 21.

[abstract shard]

so the steps to 21 and 22 are the same

okokkk

tysm!!

[smoky wing]

[abstract shard]

.close

[full forum]

Channel closed

Closed by @abstract shard

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[jolly girder]

How can i solve this ? (Worded problems involving ratios)

1. Divide 252 into 3 parts having the ratio 8:7:6 . What are the tree numbers?

[open igloo]

You can assume the numbers as 8x,7x,6x

Coz they still have the same ratio

[jolly girder]

Then what would i do next

[compact zodiac]

Solve

[jolly girder]

how do i solve it

[compact zodiac]

I mean did you understand this

[jolly girder]

not really

[open igloo]

You've to seperate 252 in 3 numbers

I've assumed those 3 as 8x,7x,6x
Since the 3 numbers also have to be in the ratio 8:7:6

[jolly girder]

so if im right

8x +7x +6x = 252?

[compact zodiac]

Now solve it

[jolly girder]

x = 12

then

ill multiply it with each ratio?

[compact zodiac]

You can always verify the answer yourself after computing it!

[jolly girder]

i added all the answrs

i got 252!

its correct

Will the same rul apply if the give nwas

was 2 ratios

like

9:8 and 187

[open igloo]

You mean two numbers in ratio 9:8 and sum 187?

Then yes

[jolly girder]

oh

and what if

the ratio is 5:1

but theres no sum

A pair of complementary angles has the ratio 5:1 find the number of degrees in each angle

thats the question

[open igloo]

There's a sum hidden in the question

[jolly girder]

is it 2 since it says pair?

@open igloo

[open igloo]

... no

[jolly girder]

is it

[open igloo]

What are complementary angles

[jolly girder]

5+1?

[jolly girder]

I kinda forgot

[open igloo]

Bruh

Search it up

[jolly girder]

60 and 30?

[jolly girder]

am i right

[open igloo]

So you're saying complementary angles mean 60⁰ and 30⁰?

Just search the proper definition bruh

[jolly girder]

oh

its 90 degrees

[open igloo]

Yes

You've the ratio and the sum

[jolly girder]

im too deep in algebra thanks

[open igloo]

So same thing

[open igloo]

I see

Np

[jolly girder]

.close

[full forum]

Channel closed

Closed by @jolly girder

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[cursive path]

why does sin (-1/2) = 11π/6 but sin-1 (-1/2) = -π/6

[thin quartz]

first statement is false

[cursive path]

maybe but its more about sin-1 (-1/2) = -π/6 because I dont see this in the circle

[velvet sedge]

negative angles are considered by going clockwise from the positive x-axis around the circle

[cursive path]

because cos-1 (-1) is pi and I can see it

[velvet sedge]

so sin(-pi/6)=sin(2pi-pi/6)=sin(11pi/6)

sin^-1 or arcsin is defined (as a function) only on interval from -pi/2 to pi/2

so it will only capture angles in that range, despite the fact that sin(x)=-1/2 has many answers that aren't just -pi/6, infinitely many in fact

[full forum]

@cursive path Has your question been resolved?

Channel closed

Closed by @cursive path

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[spice orchid]

. @verbal root put your question here

[verbal root]

Okay

[verbal root]

Write the equation of the line that passes through the given point M(3,2) and makes an angle of 45° with the abscissa axis

[buoyant pewter]

$y-y_{0}=\tan\alpha\cdot \left( x-x_{0} \right)$

[glossy valve]

Joanna Angel

[verbal root]

write the equation of the line that passes through the point M(2,1) and is normal to the line 2x+3y+4=0

[buoyant pewter]

$\text{If}\text{ }\text{ }k:y=ax+b\text{ }\text{ and}\text{ }\text{ }m:y=cx+d\\\text{ then}\text{ }\text{ }k\bot m\Leftrightarrow a\cdot c=-1$

[glossy valve]

Joanna Angel

[full forum]

@verbal root Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[ocean urchin]

doin some practice before my final and this one has me stumped

[ocean urchin]

the derivative of G would be g right?

so the critical points of G would be the points where g(s) = 0

but the issue is that...thats in terms of s and the function we want the critical points of is G(x)

What ive got so far:

critical points are 0, 1 and 2 (0 and 2 because they are endpoints, and 1 because of a jump discontinuity)

is the integral always increasing? my class is using the definition that "Integrals represent actual area"

so like...that would mean that 2 is a maximum?

since like, a larger "range" of integration would result in a larger area

[full forum]

@ocean urchin Has your question been resolved?

[verbal root]

Nuh uh

I don't understand anything

[full forum]

@ocean urchin Has your question been resolved?

[granite shore]

@ocean urchin I can likely help with this

Give me a few moments to draw g(s) so I can see what it looks like

[ocean urchin]

sure

sorry for my bad explanation im mentally drained atm

[granite shore]

studying calculus will do that lol

so I like the way you are thinking: idea here is to the the FTC to get the derivative $G'(x) = g(x)$, and then we simply want to find $g(0)$.

[glossy valve]

twitch.tv/pencenter

[granite shore]

Then, I agree with your logic that the next step would be to use the Extreme Value Theorem: a max/min must happen either when the derivative is zero, or we hit an end point. Now, the issue here is that you have the jump discontinuity, so you are correct in thinking that the max/min might also occur at the discontinuity

[ocean urchin]

right now the biggest hurdle for me is that g is given as a function of s, not x

[granite shore]

But when you take the derivative of G(x), then you get g(x), so it will be in terms of x when you go to solve the problem

[ocean urchin]

so in that case G'(x) or g(x) is

(1 - x^3)^1/2         if 0 <= x < 1
-1 - (1 + x^4)^1/2    if 1 <= x <= 2

[granite shore]

Yes

So now we note that g(x) = 0 has no solution, so we next check the endpoints g(0) and (2).

[ocean urchin]

g(0) = 1
g(2) = ~-5.12

[granite shore]

Yep.

Now you want to deal with the nasty things happening at x=1

[ocean urchin]

g(1) would be - 1 - sqrt(2)

but thats not a max/min so why would it be important to calculate that?

[granite shore]

Maybe the idea here is to notice that on the interval $x \in (0,1)$ you are always decreasing, same with $x \in (1,2)$. So the max must necessarily happen on (0,1) and the min on (1,2)

[glossy valve]

twitch.tv/pencenter

[ocean urchin]

ok i get that

but right here is the major disconnect

this is the graph of g(x)

[granite shore]

Yes I agree

[ocean urchin]

is the area not maximised when G(x) is integrating from 0->2?

[granite shore]

So since the function is always decreasing the max has to be at the left end point and the min at the right endpoint

[ocean urchin]

since the G(x) is the integral of g(x), i.e., the "area"?

that was an issue that the professors ran into as well at the very last like 2 weeks of the course; and they reached the conclusion that integral will represent the "absolute" area of a graph, so no negatives

at least for the definition used in this course

[granite shore]

Here, G(x) will give the "net" area and will consider the areas under the x axis as negative

In blue is G(x)

[ocean urchin]

wait but that graph shows that G(x) is max at 1, not 0 nor 2

[granite shore]

I think I was explaining something wrong, so I'll try again lol

Basically the max/min for G must happen either at a critical point, endpoint, or at a point of discontinuity. We have the endpoints evaluated already, there are NOT critical values on the interval we are working on since the derivative is always decreasing. So that last step would be to see what happening at x=1

[ocean urchin]

I'm listening

[granite shore]

I'm just spitballin here, you'll maybe have access to something else we can use. But I think the idea here is that we know G(x) will be continuous (but not necessarily differentiable) at x=1 since it is keeping track of area

[ocean urchin]

yeah I'm just not entirely convinced yet because if it was maximized at anything except 2, (like 1), that would mean that the area from 0-1 is less than the area from 0-2

because that doesn't seem possible if we're not taking negative areas (which the professor said not to)

[ocean urchin]

.close

[full forum]

Channel closed

Closed by @ocean urchin

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[unborn moth]

What linear algebra books do you recommend

[versed tendon]

#books

[cedar pumice]

Looks like an oligopoly graph lol

[full forum]

@unborn moth Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[rigid cedar]

Hello. How do I read this and why is there the dash above the "∪"? I know it's supposed to be complement of, but it being above the U is confusing me.
The while thing for context.

[velvet sedge]

that's just a notation error yea

it's just treating (AUB) as one set

[rigid cedar]

but on 2 different editions?

[velvet sedge]

oh wait

no it isnt

(AUB)^c means complement of AUB

[rigid cedar]

ohhhh

[velvet sedge]

A^c U B^c means union of A complement with B complement

[rigid cedar]

thank you so much!

btw

do you know what this means?

or how i read it?

[velvet sedge]

complement of A

[grim skiff]

Technically A complement or B complement, the combined set, if I'm not mistaken

[rigid cedar]

this book really loves throwing stuff without saying what it is

even though it has two dashes on top?

[velvet sedge]

reworded for clarity :)

[rigid cedar]

gotcha

[grim skiff]

Double complement

[velvet sedge]

oh wait

didn't see the other dash

[grim skiff]

Complement of the complement of set A

[velvet sedge]

yeah complements cancel

[rigid cedar]

oh. it does say that A two dashes = A

[velvet sedge]

yes

[rigid cedar]

but i thought it was a bit unnecessary so i thought it had to mean something else

[velvet sedge]

nah it's just basically saying complement of the complement of a set is itself

[rigid cedar]

argh. kinda funny

thanks you two

[grim skiff]

It's more common when you see in like $\overline{(\overline{A} U B)}$

[rigid cedar]

oh

[glossy valve]

CaptainNova22

[grim skiff]

You get what I'm trying to say

[rigid cedar]

yeah i do

interesting. seems a bit hard to understand at first though. hopefully i'll be able to read it easily soon

[grim skiff]

Because then you do de morgans to get $\overline{\overline{A}} \cap \overline{B}$

[glossy valve]

CaptainNova22

[rigid cedar]

huh

[grim skiff]

De morgan this

[grim skiff]

You get this

[rigid cedar]

yeah, the book mentions De Morgan's law

[rigid cedar]

but in this case isn't it just easier to write A?

or is there something i'm not getting

[grim skiff]

Yes it simplies to A but if you were showing work, that's what it would look like

[rigid cedar]

ah, to show some kind of specific thinking or something?

[grim skiff]

If your teacher wants full work in the proof

[rigid cedar]

understood

thanks again!

@velvet sedge too

.close

[full forum]

Channel closed

Closed by @rigid cedar

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[cunning sorrel]

i know how to do it kinda because on the platform im using it gives me a guideline of what to do but I don't understand why its telling me to do what its telling me to do

i dont understand the thought process behind figuring out what is supposted to go in the blank

I assume is 116 but I don't know why

[hot herald]

same side interior angles

[cunning sorrel]

ik they are supp

supplementary

[hot herald]

yeh, its literally just applying that

[cunning sorrel]

but why is it angle 1 + angle 2 +116 is 180

isnt angle 2 +166 =180

[hot herald]

whats your definition of supplementary?

[versed tendon]

they are looking at the triangles formed by dividing the rhombus in 2

[cunning sorrel]

like two angles adding up to 180

[cunning sorrel]

what about the triangles

[hot herald]

the relevant parallel lines are marked there

green + red = 180

and that green is <1 + <2

[cunning sorrel]

ohhh

i forgot that angle 1 and angle 2 are congruent

not supplementary

[hot herald]

doesn't matter if they're congruent or not for what they're applying in that first step

[cunning sorrel]

ok but

shouldnt angle 2 be supp to 116

my question is like why is it both

[hot herald]

no

[cunning sorrel]

cuz only 2 and 116 are on same side of transversal

[hot herald]

you need to consdier the position of your parallel lines

[cunning sorrel]

should i try rewriting the figure but like without all the extra lines

just parallel and transversal

[hot herald]

if may help

[cunning sorrel]

ok im gonna do that rq

i dont think it works

cuz i need the extra lines to form the angles

[hot herald]

when consider the same-side angle / co-interior angle to the 116 that involes angles 1 and/or 2:

that red line would be the transversal

just going to erase the 1 and 2 entirely

[cunning sorrel]

oh i see it now

i was using the diagonal as the transversal

so that green angle is supplementary to 116

and that green angle is made up of angle 1 and 2

so angle 1 + angle 2 +166 =180

ok thank you

.close

[full forum]

Channel closed

Closed by @cunning sorrel

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[glossy valve]

Mycobacterium

[full forum]

@torn jolt Has your question been resolved?

[velvet sedge]

i think it'd be easier to do them as separate sums then take their difference :)

[buoyant pewter]

they are ordinary geometric series

no need to use any criterion for that

just verify if | q | <1

like in school

$\sum_{n=0}^{\infty }q^{n}=\frac{1}{1-q}\text{ }\Leftrightarrow \text{ }\left| q \right|<1$

[glossy valve]

Joanna Angel

[velvet sedge]

ye, and q^(-n)=(1/q)^n

[buoyant pewter]

defintion you want to know ?

[velvet sedge]

this is almost correct

yea, and for your sum above, you just needed to put the odd number index inside the -

[glossy valve]

Mycobacterium

[velvet sedge]

$\sum_{n=0}^{\infty} 5^{-2n}-3^{-(2n+1)}$

[glossy valve]

Moosey

[velvet sedge]

this also works :)

[full forum]

Channel closed

Closed by @mint light

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[glacial flame]

I just watched a video on a simple math problem 6÷2(1+2)=??? and it didnt make sense to me. in the video he states it could be 2 answers but does math work that way? I understand as you go higher up you and sqrts and stuff but how can a simple problem have multiple answers?

[glacial flame]

https://www.youtube.com/watch?v=Irv7ioa-1II

the video in question

[glossy valve]

ℝαμΩℕωⅤ

[glacial flame]

I see

.close

[full forum]

Channel closed

Closed by @glacial flame

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[vocal niche]

How to solve 38

[vocal niche]

How to divided by (x-5)(x+2)

.close

[full forum]

Channel closed

Closed by @vocal niche

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[amber palm]

Find the points of non differentiability of the function

[amber palm]

,, f(x) = (1/2) - x + 1/2 [2x] - 1/2 [1-2x] in [0,1]

where [.] represents GIF

[glossy valve]

naxtisy

[onyx glen]

$f(x) = \frac{1}{2} - x + \frac{1}{2} \floor{2x} - \frac{1}{2} \floor{1 - 2x}$

[glossy valve]

Ann

[onyx glen]

this?

@amber palm confirm/deny that this is the correct function

[amber palm]

wait its loading

sorry wifi was off

is still slow

yep

thats the function @onyx glen

[onyx glen]

ok

[amber palm]

So like

[onyx glen]

and you want to find how many discontinuities it has in [0, 1].

[amber palm]

the way i was thinking

[amber palm]

no no

point of non differentiabilities

[onyx glen]

oh, not discontinuity. non-differentiability. my bad.

[amber palm]

yes yes

no worries

[onyx glen]

so what were you thinking?

[amber palm]

right

[amber palm]

so breaking off the function in 3 parts

1/2 - x and then the other two

[amber palm]

now [2x] is ND at 2x = Z so x = Z/2

[onyx glen]

not very good choice of notation there

but ok continue

[amber palm]

and yeah same for the second one

x = 1 - Z/2

[onyx glen]

bad notation again. don't like using the same letter for a set and for an arbitrary element of that set.

[amber palm]

huh

its the same thing

[onyx glen]

no, it is not.

[amber palm]

Z represents integers

for both the things

[onyx glen]

Z represents the set of all integers.

[amber palm]

i am treating them separate

[onyx glen]

you can't use the symbol $\bZ$ to refer to an arbitrary integer.

[glossy valve]

Ann

[amber palm]

.

[onyx glen]

this is like conflating an individual human with all of humankind.

anyway

[amber palm]

i am also solving it for all general values

and then i check the domain

[onyx glen]

from this you should have concluded that in your domain [0, 1] you get the following points as suspect for discontinuity (from which follows non-differentiability):

0, 1/2, 1.

[amber palm]

mhm

[ionic trout]

Bro how can I learn integral

[amber palm]

!occupied

[full forum]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[onyx glen]

!occupied

[full forum]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[onyx glen]

ok, so did you continue from here?

[amber palm]

nope

[onyx glen]

well then continue! for the function g(x) = floor(2x) - floor(1-2x), calculate at x = 0, 1/2, 1:

• the value
• the left-hand limit (except at x=0)
• the right-hand limit (except at x=1)

you will get discontinuities this way

[amber palm]

hm

how did you do it

[full forum]

@amber palm Has your question been resolved?

Channel closed

Closed by @amber palm

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wheat furnace]

no idea how to solve this

[buoyant pewter]

look at scuh examples:

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

[glossy valve]

Joanna Angel

[buoyant pewter]

in an analogous way, you can evaluate your expression

[frosty meteor]

nasty case of identities but solvable

[wheat furnace]

how

[wheat furnace]

I got this thing but how do I apply this to ^7 of something

[frosty meteor]

[x^7 + \frac{1}{x^7} = \left(x^3 + \frac{1}{x^3}\right) \cdot \left(x^4 + \frac{1}{x^4}\right) - \left(x + \frac{1}{x}\right)]

[glossy valve]

GigaChad

[wheat furnace]

oh is this thing correct?

[frosty meteor]

wdym

[wheat furnace]

didnt know you could rewrite x^7+1/x^7 as (x^3 etc

well didnt know is the wrong word but couldnt see it

[frosty meteor]

you can expand it and check

[full forum]

@wheat furnace Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[devout grove]

How to do
(4ab + 2a² + 2b²) ÷ (4a + 4b)

[keen shoal]

what are you trying to do with that

[devout grove]

İm tryna solve a question i find the numbers but cant solve it

[full forum]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[simple ridge]

so you want to simplify it ?

[devout grove]

Yeah

[simple ridge]

ok so as a hint start by taking 2 as a common fact in the num and 4 as a common factor in the denom

then check if you see something nice

[devout grove]

English is not my main language so i didnt understand what do you mean

And by the way the problem is
There is (a + b) cups all cups have (2a + 2b) tennis balls inside it and they want to share all tennis balls to players there is (4a + 4b) players

[simple ridge]

same as you did

check common factor

[devout grove]

İs the answer a² + b²

[simple ridge]

no

Notice that $\frac{4ab+a^2+b^2}{4a+4b}=\frac{2(2ab+a^2+b^2)}{4(a+b)}$

[glossy valve]

calculus is fun

[simple ridge]

can you continue from here

[devout grove]

(2ab+a²+b² ) / (2(a + b) )

[simple ridge]

dont expand the 2 on the bottom

does the above look familiar

[devout grove]

is it (A+b) / 2

Thx

.close

[full forum]

Channel closed

Closed by @devout grove

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lilac junco]

i dont really understand this part of the proof? from d = ..... why have they let it equal x -a > 0

[devout valley]

The idea is that by $x$ being a boundary point, for any choice of $\delta > 0$, you have said interval $(x - \delta, x + \delta)$ must have a point of $S$ in it - but because you assumed $x > a$, you know that $x - a > 0$, so choosing $\delta = x - a$ is valid

[glossy valve]

@devout valley

[devout valley]

The fact that you know that $x - \delta = x - (x - a) = a$ allows you to simplify things a bit nicely to lead to the contradiction you do

[glossy valve]

@devout valley

[lilac junco]

ah this is the part i was getting confused with that, thanks for clearing it up

im still unsure as to WHY they would think to do that though, that would be hard for me to think of in an exam situation i think

is there a hint im missing that would lead me in that direction of thinkning? or just practice

[devout valley]

It can be pretty tough to think along those lines - the idea here is that being a boundary point is as per that definition you had, so you want to think about whether there's a valid way to get a positive distance you could work with (and the assumption that x>a lends you to the idea of noticing x - a > 0, and thinking "hey, that's strictly positive, why don't I use that!")

Then of course you spot you can make those simplifications, and what it ends up to you concluding

[lilac junco]

ok thank you so much for your explanation, it was very detailed but concise! have a good day

.close

[full forum]

Channel closed

Closed by @lilac junco

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[gilded tapir]

Need to prove 5 and 6

[twilit leaf]

Lets work on 5

What have you tried?

[gilded tapir]

writing ctg as 1/tg

[twilit leaf]

I suggest breaking it down even more to sin and cos

[gilded tapir]

ok

Like this?

[twilit leaf]

Watch out, the ones on the right are beta

But yes

[gilded tapir]

oh yea

ok now what

[twilit leaf]

Make everything have a common denominator

[gilded tapir]

that would be?

sina cosb?

[twilit leaf]

The numerator and denominator would have different ones

[twilit leaf]

This one would be for the denokinator

[gilded tapir]

yea

this?

@twilit leaf

[twilit leaf]

Close

You have plus in the very bottom

[gilded tapir]

whats bad about it

oh mb

ok now what

[twilit leaf]

Do the numerator and denominator of the big fraction have something in common?

[gilded tapir]

yea

numirator

[twilit leaf]

Yes, you can cancel those out

[gilded tapir]

the whole one?

[twilit leaf]

The whole thing

[gilded tapir]

ok so i have left with what

[twilit leaf]

Take a guess

[gilded tapir]

cosasinb/sinacosb

[twilit leaf]

Not quite

(1/cosasinb)/(1/sinacosb)

[gilded tapir]

oh yea

now what

[twilit leaf]

What do you think we should do next?

[gilded tapir]

idk

[twilit leaf]

Hint: we arw dividing fractions

[gilded tapir]

cosasinb/sinacosb?

[twilit leaf]

Thats what you put last time

So no

[gilded tapir]

mmm

[twilit leaf]

Are you familiar with keep and flip?

[gilded tapir]

yes wait

no idk what do i do

@twilit leaf

[twilit leaf]

We keep the first fraction the same and multiply by a flipped version of the second one

[gilded tapir]

yea ik that

sinacosb/cosasinb?

[twilit leaf]

Yup

Now youre really close to the finish line, can you figure out the last step?

[gilded tapir]

tg*ctg?

[twilit leaf]

tg what?

[gilded tapir]

a

[twilit leaf]

And ctg what?

[gilded tapir]

i dont think thats right tho

b

[twilit leaf]

you have tga*ctgb

ctgb is the same as?

[gilded tapir]

yes

1/tgb

or cosb/sinb

[twilit leaf]

So you replace ctgb with that

[gilded tapir]

oh yea

6

now

pls

[twilit leaf]

I suggest opening a new help channel, i have to go eat

[gilded tapir]

can you not help me quick?

i have to go too

[twilit leaf]

Cant, sorry

[gilded tapir]

ok thanks

.close

[full forum]

Channel closed

Closed by @gilded tapir

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lunar bramble]

Can I get the first step

Ping when respond pls

[cold quarry]

sin2x = 2sinxcosx

@lunar bramble

[full forum]

@lunar bramble Has your question been resolved?

[lunar bramble]

Sin(x+2x)?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[royal fox]

i can’t figure out what the bounds of integration are after i change variables

i know it’s 0 <= x <= 1 and 0 <= y <= -x +1

but plugging in the transformed forms is confusing me

idk how to manipulate them right

[full forum]

@royal fox Has your question been resolved?

[royal fox]

<@&286206848099549185> pretty please

[full forum]

@royal fox Has your question been resolved?

[royal fox]

<@&286206848099549185>

[full forum]

@royal fox Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[ruby vale]

hello people, can anyone provide a playlist of an introduction to partial differential equations? I am looking to study PDEs from the very start, any help is appreciated 👍

[ruby vale]

(i do not prefer books for topics I find difficult, like PDEs. I much so prefer being taught by someone from like a YouTube video)

[gritty rose]

Help channels are for specific problems or questions

#book-recommendations or #discussion

.close

[full forum]

Channel closed

Closed by @gritty rose

Use .reopen if this was a mistake.

[ruby vale]

wtf is wrong with u man

if u dont wanna help just move on

im asking FOR specific problems

[gritty rose]

Don't misuse help channels

[ruby vale]

its not a misuse?

i used help channels to ask for help on other topics i wanted to learn, they were very helpful too

[gritty rose]

Good for you

It was still a misuse

[ruby vale]

???

im not looking for fucking book recom

i literally mentioned that

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[flint dew]

i did solve it but it took me a while to find the trick

[flint dew]

is there a faster way to find tricks and stuff

like the trick to this was to double it and add one to get (2a+1)(2b+1) = 675 and factorize from there

but it was really hard to find

does anyone have tip to intuitively find stuff like this

[reef palm]

is 704 the right answer?

i think the solutions are

(1, 112)
(2, 67)
(4, 37)
(7, 22)
(12, 13)

so 112 + 67(2) + 4(37) + 7(22) + 12(13) = 704 so yes it is nvm

so i'm sure a genius would know a better way but

but,

1. find an expression for the number of matches used in a nxm rectangle

2. find n in terms of m

3. find when both are integers. note that 337 is prime and you dont need to check above sqrt(337)

[full forum]

@flint dew Has your question been resolved?

Channel closed

Closed by @flint dew

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[torn jolt]

guys

[torn jolt]

how do i find inradius of a triangle

like a triangle inscribed inside a circle

if i know coordinates of its vertices

[stiff summit]

The inradius of a triangle is the area over the semiperimeter

there’s a nice geometric way to see this

let ABC be a triangle, and let r be its inradius, with O its incenter

[torn jolt]

okay

[stiff summit]

then the perpendiculars from O to AB, AC, and BC are all r units long

then, consider the areas of the triangles OAB, OAC, and OBC

[torn jolt]

yeah

[stiff summit]

they are (1/2)r*AB, (1/2)r*(AC), and (1/2)r*(BC)

and these must add up to the area of ABC, which you can see if you draw a picture

[torn jolt]

wait a second

let me try an draw

[stiff summit]

but when you distribute while adding them together, and move a few things around, you get r*(1/2)(AB+BC+CA)

(AB+BC+CA) is exactly the perimeter, and half of that is called the semiperimeter

so, we get that the radius of the incircle times the semiperimeter is the area

[torn jolt]

something like this right

i got it

@stiff summit is there some nice geometry to find circumradius aswell

[stiff summit]

I just googled it and it turns out there is

https://artofproblemsolving.com/wiki/index.php/Circumradius

the formula is nice and symmetric, but the method they used isn’t as nice as the one for the inradius

[torn jolt]

for right triangle its intuitive and obvious

[torn jolt]

i have no idea about eulers theorem for triangle

i think they used it there

[stiff summit]

See the proof following the first diagram in the link I sent

[torn jolt]

hmm

i got it

they used inradius to prove it

.close

[full forum]

Channel closed

Closed by @severe plover

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[dull mauve]

If A(3,1), B(5,7) and C(6,4) are three consecutive vertices of a parallelogram:

[dull mauve]

At what point do the two diagonals intersect?

[queen crater]

If it's a parallelogram, they intersect at their midpoints

[fossil wren]

yeah you're gonna need section formula as far as i know

[dull mauve]

and there is not other way?

[fossil wren]

nope

at least i don't know any other way

section formula isn't that hard

it just takes a few problems to get the hang of it

[queen crater]

Not sure what the section formula is but it sounds more complicated than what you need here

A midpoint is just the average between two points

[fossil wren]

that is the section formula

at least, section formula describes the point between two other points if the point is dividing the line in any ratio

a midpoint is just a specific application of the section formula where the ratio is 1:1

[dull mauve]

can you teach me how to do it?

[fossil wren]

just add the two points and divide it by two

[dull mauve]

like AC=(3,3) and the average of this?

[fossil wren]

for example if you have (2,3) and (4,5), just take the average of the x and y coordinates

(2 + 4)/2 and (3 + 5)/2

(3,4) would be the mid point

[dull mauve]

ok tysm

[dull mauve]

What is the fourth vertex? About this question do you have any way to find it without using section formula?

[queen crater]

Vector addition

The vectors AD and BC are the same

[dull mauve]

but how i can know that is AD and not AB?

[queen crater]

Draw a figure

[dull mauve]

and i can know it without drawing that?

[queen crater]

I mean you can draw a figure in your mind too

A, B, C are consecutive vertices

If D is the fourth one, then it comes after C and closes the parallelogram with A

So AB and DC are opposite sides

And AD and BC are also opposite sides

So when you take direction into account, the vectors AB and DC are the same, and the vectors AD and BC are the same

[dull mauve]

sorry for my ignorance, but what does consecutive verticals mean?

[queen crater]

consecutive: following each other continuously

Start at A, go to B by drawing one side, then go to C by drawing another side, then to D, then back to A

Instead of going from A to C to B to D for example

[dull mauve]

like this?

[queen crater]

Yes for example

[dull mauve]

thank you for your patience and teaching😊

[queen crater]

[dull mauve]

.close

[full forum]

Channel closed

Closed by @dull mauve

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[stable dew]

hii, im stuck in another linear combination question again

[stable dew]

Determine the set of all vectors in R2 that are linear combinations of:
(b) (1, 2);
(c) (1, 2) and (-2, 4);
(d) (1, 2) and (0, 0);
(e) (1, 2) and (2, 1).

idk wth im supposed to say

when we have two vectors, it can be the whole set or a plane

but when do i know whether it is one or another?

[reef palm]

if they are linearly independent

[stable dew]

then what

???

[devout valley]

In this case, you're in R^2, so the "plane" happens to just be a line (for example, in R^3, there's the whole space, but also a plane and a line, and there are similar "in-betweens" for higher dimensions)

[devout valley]

The idea is that if you have two linearly independent vectors in R^2 (which has dimension 2), you get the whole space, and if you don't, then it's probably a line

Any vector by itself (with one exception!) is linearly independent with itself - though of course you won't get the whole space...

[full forum]

@stable dew Has your question been resolved?

[stable dew]

so in R3, when do we know whether its the whole space, a plane or a line?

[devout valley]

Depends on how many linearly independent vectors you have

if 1, it's a line,
if 2, a plane
if 3 or more, you get all of R^3

[stable dew]

ok

so in the examples i got, b) is a line, c) is the whole space d) is a line that crosses de origin and e) is a plane?

[devout valley]

Yes - but for e) R^2 is "the only plane", and for b)/d) all lines you'll find must pass through the origin

[devout valley]

To clarify, the lines and planes here for R^3 also must be through the origin

[stable dew]

ok so in conclusion we have b) line c) the whole set d) line e) the whole set

?

another question, is this a subspace?

[devout valley]

Yea that’s fine

[devout valley]

And you tell me

[stable dew]

i dont think it is, but like

my brain is NOT braining today

so idk

because if x = 1 and y = 1, the statement is false

bro

its a subspace, isnt it

[granite shore]

hate those days lol

[granite shore]

totally

[stable dew]

im in my finals week

is it my final week tho=

?

stay tuned

[stable dew]

bro why

im so confused

[devout valley]

Do you know how to show if something is a subspace or not?

[stable dew]

no 💀

like, i know the properties

nvm i dont know them either

ARGHHHHHH

[devout valley]

Well the very basic one is that you’re a subset such that if you copy and paste the definition of vector addition and scalar multiplication, you still get a vector space

There are quicker ways to check whether something is a subspace though, a lot of things get inherited from the larger space(!)

You just need to show that you aren’t empty, and that you’re closed under linear combinations

In a bit easier, if U is the subspace of the vector space V, then if you take u1, u2 from U, then u1 + u2 must also be in U

And also if you take some u in U, and some scalar a, then a.u needs to be in U as well

Does that sound familiar?

[stable dew]

yeah yeah

i just didnt know how to verbalize it, english is not my first language

damn

i think i got this

[devout valley]

[devout valley]

Awww

There’s also a faster way to kind of check too - notice that as 2x + y = 0, then y = -2x

So then if you think about (x,y), then…

[stable dew]

(i totally didnt get this btw, im just coping)

im getting this SLOWLY

but i will at the end of the day

[stable dew]

we have x, -2x

but what do i do with this information

[devout valley]

Yep, or basically x(1, -2) - a line that goes through the origin

[devout valley]

Wonder whether something like that was said somewhere

[stable dew]

ok so, if i have a linear combination with two elements like a(1,2) and b(3,4), its automatically considered a subspace?

because its the whole set in R2?

[devout valley]

Yep - because it should hopefully be easy to see that the sum of two things of that form is also of that form, as with scalar multiples

[stable dew]

yeah yeah

ok i think i got this

thanks!!!

u da goat

.close

[full forum]

Channel closed

Closed by @stable dew

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[soft agate]

how would i change the vertex form y= -0.48(x-0)^2+3 into standard form and factored form

[soft agate]

<@&286206848099549185>

[full forum]

@soft agate Has your question been resolved?

[pallid tiger]

is this graph or sth

[spare panther]

your trying to get it into standard form

you could expand the (x-0)^2

but it would be redundant since 0 wouldn’t change anything so then -0.48x^2 + 3

standard form

[soft agate]

would i be able to use foil?

like at the end i got

-0.48x^2 + 3 = 0

[spare panther]

You could use foil

FOIL works for sure but

If u want a short cut you can see that the 0 is redundant

So it would just be (x)^2 which is x^2

Just a little faster but both work

[soft agate]

so does this seem okay?

.close

[full forum]

Channel closed

Closed by @soft agate

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[shrewd crystal]

I'm new to functional equations and I was trying these questions involving equations on Natural numbers as range. But this one has R+ as range and I can't seem to find a way to crack this. Someone help

[full forum]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[plush egret]

lol looks like someone is testing out the bot

[shrewd crystal]

I understand till the 2^k<_l^n part but how did he get equation 1?

[devout valley]

But this one has R+ as range
what, the one in your picture? Assuming your natural numbers don't include 0, then (b) and (c) mean that you can't get any reals strictly between 0 and 1

[velvet sedge]

applied f() to everything

well

to the inequality 2^k <= m^n <=2^(k+1)

and f preserves the inequality

[shrewd crystal]

Yes thats right the range contains all reals from 1 to infinity

[velvet sedge]

$2^k \leq m^n \leq 2^{k+1} \to f(2^{k}) \leq f(m^{n}) \leq f(2^{k+1})$

[glossy valve]

🫎 A Certain User(Moosey) 🫎

[shrewd crystal]

Okay but how applying f() gets 1/2??

[velvet sedge]

oh wait

equation (1) is the second equation

lmao

[devout valley]

(oh, I see, usually R+ implies all strictly positive reals)

[shrewd crystal]

Yeah

[shrewd crystal]

Sorry my bad its not R+

Its [1, infinity)

[velvet sedge]

OH

they divided by l^n?

[shrewd crystal]

That would explain the (m/l)^n term but I don't see how 1/2 and 2

[devout valley]

[also note that as $2^k \leq l^n < 2^{k+1}$ for example implies that $\frac1{l^n} \leq \frac1{2^k}$ and $\frac1{l^n} > \frac1{2^{k+1}}$]

[glossy valve]

@devout valley

[shrewd crystal]

Ahh

Oh yeah

Got it thanks

.close

[full forum]

Channel closed

Closed by @shrewd crystal

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hushed jackal]

can someone check if my process is what you're suppose to do for this problem

[harsh pilot]

Yeah, it looks good.

,w tangent to graph of y = sqrt(x) at x = 9

[glossy valve]

Results provided by WolframAlpha

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

Requested by onetrackpony

[harsh pilot]

Wolfram agrees

[full forum]

@hushed jackal Has your question been resolved?

Channel closed

Closed by @hushed jackal

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[smoky wing]

well, (\s{x-2}) will be undefined if (x<=2)

[glossy valve]

Pure

[smoky wing]

What rules?

Not sure what you mean by this. The fact that (-inf,1] can't be in the domain follows directly from the calculations.

We need (\unb{\p{(-\8,1] \cup [2,\8)}}{\t{from the quadratic}} \cap \unb{(2,\8)}{\t{from the denominator}}).

[glossy valve]

Pure

[smoky wing]

god awful spacing

[neon basin]

You find the intersection of all solutions (conditions)

[smoky wing]

[\unb{\p{(-\8,1] \cup [2,\8)}}{\t{from the quadratic}} \qq\cap \unb{(2,\8)}{\t{from the denominator}}]

[glossy valve]

Pure

[smoky wing]

Better

[neon basin]

$(x \neq 2) \cap (x \geq 2) \cap (x \in (-\infty, 1] \cup [2, \infty))$

[glossy valve]

USS-Enterprise

[smoky wing]

You need all the conditions to hold at the same time

[x-2 > 0\9x^2-3x+2>=0]

[glossy valve]

Pure

[neon basin]

0 is fine for the top root, you get sqrt(2), but in the bottom root you get sqrt(-2), which isn't fine

That's why you need the intersection and not union

[smoky wing]

Yes.

[neon basin]

and x != 2 🙂 if we had greater or equal on both this would matter

[smoky wing]

x != 2 is implied by x-2>0

[neon basin]

I know, that's why I added the second part of the message

Not everyone sees it

[smoky wing]

Same idea; you look for the overlap

[smoky wing]

Gotcha.

Where all the conditions overlap.

You need all the conditions to hold on the domain.

[neon basin]

$\8$

[glossy valve]

USS-Enterprise
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[neon basin]

What

[smoky wing]

[neon basin]

Oh

I thought this was universal

Thought I could save myself from typing infty every time 😦

[smoky wing]

Not sure what you mean about directions and all this but quadratic can be one or two directions depends on whether it's >= or <=

[smoky wing]

It's not hard to do just add \let\8\infty to your preamble

Yeah we need all of them to overlaps

for example

[\4{\s{x-2}}{\s{2-x}}]

the domain is empty

[glossy valve]

Pure

[smoky wing]

because we need

[x>=2 \77\9 x<2]

at the same time

[glossy valve]

Pure

[smoky wing]

Cool

No

[x>=2 \77\9 x\71<2]

[glossy valve]

Pure

[smoky wing]

Yeah

the domain is nothing here

[full forum]

Channel closed

Closed by @tulip lantern

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[gilded tapir]

Every side of this hexagon is equal fc splits it into two trapezoids ac eaquels 13 ae eaquels 10 need to find the area

[gilded tapir]

<@&286206848099549185>

[pale oriole]

!15m

[full forum]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[gilded tapir]

Can yoh help me?

[torn jolt]

Angle F is the same as angle B right

[gilded tapir]

What?

The sides are all equal

[torn jolt]

Well yes then the angle should be too right

[drowsy summit]

Gz on active role @pale oriole

well done

[pale oriole]

hm?

[torn jolt]

But that doesn’t make sense I guess, because if angle B and angle F are equal and also AB=BC=AF=FE, that would make triangle ABC congruent to triangle AFE

[gilded tapir]

Yes

[torn jolt]

But that would mean that AC=AE

Which is clearly not true

[gilded tapir]

The hexegon is split into 2 trapezoids

Ac is a diagnal

[torn jolt]

That’s not what I‘m saying, see triangle ABC and triangle AFE, they’re congruent to SWS

[gilded tapir]

Yea

But thats what the problem says

[torn jolt]

But then AC=AE

Which is false because 13 is not equal to 10

[torn jolt]

Hmm that’s weird

[gilded tapir]

So what is the problem wrong?

[torn jolt]

I think the construction is wrong, it should be formulated different, because AC=AE, which is false

[gilded tapir]

Ac and ae are both diagnals

Yea drawing is bad ik

But how would i draw it then?

[torn jolt]

Yes but they‘re equal

[torn jolt]

No no I don’t mean your sketch I mean the construction of the problem

What does the problem exactly say?

[gilded tapir]

cf is common

its in another language but it says that exactly

[torn jolt]

No matter what the problem says, we should not get into any contradictions

And the fact that the both triangles I mentioned are congruent is a contradiction

Perhaps I‘m wrong, but I think there‘s some problem in the task

[gilded tapir]

ok i have 1 more problem i need help with

so i have a isosceles trapezoid and there is a circle inscribed in it trapezoids area is 8 and the trapezoids cornor is 30 degrees i need to find the sides

@torn jolt

[torn jolt]

What’s the corner?

[gilded tapir]

30 degree

[torn jolt]

No I mean which angle

The one on the bottom, on the top, where

[gilded tapir]

bottom

[torn jolt]

Bad how does the information with the inscribed circle help, there‘s not anything given about it

[gilded tapir]

idk what are you thinking what do i do?

@torn jolt

[torn jolt]

I‘m thinking we must use some formula for the area of a trapezoid

[gilded tapir]

ok what?

[torn jolt]

Are you sure that the circle is inscribed and not around the trapezoid?

[torn jolt]

Well I‘m not sure yet, we must use the given information

[gilded tapir]

trapezoid is outside the circle

[torn jolt]

This can help us

[gilded tapir]

ok what do we do?

i need the legs only

[gilded tapir]

so there is not a problem? in the task?

[forest widget]

also didn’t i tell you what to do yesterday

[gilded tapir]

yea but i couldnt

[forest widget]

ye, problem is fine, your diagram is a little misleading

[gilded tapir]

ok so what do i do?

[torn jolt]

Hmm, it seemed first wrong to me

[forest widget]

make the hexagon a rectangle

[gilded tapir]

how tho?