help-33

[marsh citrus]

@opaque sluice Has your question been resolved?

[opaque sluice]

can u hel0p me with one mpre

<@&286206848099549185>

[unreal adder]

you can estimate it

if you know one square is a 1 by 1

the form triangles were it is sloped

and find the length (hypotenuse) of the triangle

and add all of the the lengths needed

[opaque sluice]

im not sure how to precisely do that

[unreal adder]

well you can't be precise since you only have a large 1 by 1

[opaque sluice]

i did this but the answer was 1 or 2 metres off so im wondering how i precisely do it

[unreal adder]

ok, try to use the a^2 + b^2 = c^2

[opaque sluice]

i have i have

[unreal adder]

did you use an estimate on the rope?

or did you use the full box?

[opaque sluice]

i used the pytha and I calculated the hypotenuse

so all of the ropes

but as it goes decimals or like

yeah

[unreal adder]

yes yes, but for the exact place the rope is in or for an estimate in regards to the outlines of the boxes

since all of these are just y = mx + c lines

you can calculate the gradient

input x as the base

and get y

then you have the accurate base and height

[opaque sluice]

right I used the estimate

so youre suggesting to use the gradient formula and calculate the precise numbers

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[opaque sluice]

.reopen

[marsh citrus]

✅

[opaque sluice]

@unreal adder

[unreal adder]

mhm

thats the way to get it to be more precise

you can also reverse it to find the base if you have a better estimate of the height

[opaque sluice]

well then whats the faster way

[unreal adder]

more precise; y = mx+c
less precise but faster = estimating by eye

[opaque sluice]

how about using a^ + b^2 = c^2

would that worjk

[unreal adder]

thats if you are estimating

but as you said you were off by a bit

depends on the margin of error that is allowed on the question

[unreal adder]

also you round up in this question

no matter what

[opaque sluice]

no but it was like 23

the answers 25

[unreal adder]

ye i got around 23 as well just by estimating

but thats the exact amount

but that is not to safely complete

[opaque sluice]

aight ty

.close

[marsh citrus]

Channel closed

Closed by @opaque sluice

Use .reopen if this was a mistake.

[opaque sluice]

yup?

@unreal adder

[marsh citrus]

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.

[marsh citrus]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[noble radish]

i dont know how to start question 5.

[whole compass]

,rotate

[tawny forge]

just start equating them xd

so the opposite sides in rectangles are equal

so equate the values on both sides

So let's take diagram a

[noble radish]

yea

[tawny forge]

On the left there is 5y+3 and right there is 17

Since opposite sides in a rectangle are equal

5y + 3 = 17

5y = 14

[noble radish]

yea

i got that

[tawny forge]

y = 14/5

[noble radish]

soooooo one sec

[tawny forge]

yea?

[noble radish]

so 2.8?

[tawny forge]

U can just keep it in fraction honestly but yea

[noble radish]

ok so it will be

[tawny forge]

Now we go to b

instead of the y there just replace it with 14/5 or 2.8

[noble radish]

no but what about 2x-4 and 10

[tawny forge]

Oh shit i forgot

[tawny forge]

Don't mind this btw

[noble radish]

so it will be 14/7 + 3 and 17

[tawny forge]

Yea we just equate them

[noble radish]

yea

[tawny forge]

What?

[noble radish]

what does that mean

equate?

[tawny forge]

just put an equal sign

[noble radish]

oh wait so like

2x-4 = 10

and like

[tawny forge]

yes exactly

[noble radish]

5y + 3 = 17

and than

thats

5y = 14

which is

y = 2.8

so

[tawny forge]

good job

[noble radish]

the final result for that question

is

[tawny forge]

so u found y for diagram a

[noble radish]

14 +3=17

[tawny forge]

now you have to find x too

[noble radish]

okkii thankss !!

[tawny forge]

only the 3rd diagram is different

others all can be using same method

[noble radish]

wait for diagram b - the y and 13x how do i do that?

[marsh citrus]

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.

[flat pawn]

Let (V, ‖·‖2) = (Mn,n(C), ‖·‖2)
Show that for all A ∈ V the sequence
Sum (...) converges to (V, ‖·‖2)

Note: The limit is denoted by exp(A) = (...).

[flat pawn]

(...) is this sequence

I have considered estimating the exponential function with cauchy in order to show that the sequence converges, but I cannot find a suitable cauchy sequence

[maiden parcel]

I think the norm 2 on matrices lets you to say norm (AB) ≤ norm(A).norm(B)

So try to show abs conv

[flat pawn]

ok i try that ty

[marsh citrus]

@flat pawn Has your question been resolved?

Channel closed

Closed by @flat pawn

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.

[marsh citrus]

Please don't occupy multiple help channels.

[sour ruin]

Help

[tawny forge]

Bro

How old are you

[bitter terrace]

Mate dont occupy two channels

[sour ruin]

Sorry

[tawny forge]

are u 13?

[sour ruin]

Ye

[tawny forge]

fr?

[sour ruin]

Yes

[bitter terrace]

Just safe lmaooo

[tawny forge]

if you're like under 13

nvm

[sour ruin]

I'm 13

?

[tawny forge]

even if he is he won't

[bitter terrace]

Nah i can see a 13yr old do congruency

[tawny forge]

yea actually

[sour ruin]

So, help me

[bitter terrace]

What do you know

Are ypu completely new to the topic?

[marsh citrus]

@sour ruin Has your question been resolved?

Channel closed

Closed by @sour ruin

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.

[frosty bronze]

how do I solve this question?

[marsh citrus]

@frosty bronze Has your question been resolved?

[spark otter]

try to write AX = B

and from here...

[marsh citrus]

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.

[low mica]

`

[low mica]

c = -13?

[dusky viper]

how'd u come up with that

[low mica]

dscriminant

$b^2 -4ac = 0 \ \ (-2)^2 - 4 \cdot 1 \cdot (-12 - c) = 0 \ 4 + 48 + 4c = 0 \ 52 + 4c = 0 \ 4c = -52 \ c = -13$

[elfin berry]

pixel

[dusky viper]

yeah that looks right

[low mica]

how would I go about doing this

[dusky viper]

yo sorry i didnt see this

do u know the point gradient formula for the equation of a line?

[marsh citrus]

@low mica Has your question been resolved?

[low mica]

y2-y1 / x2-x1

that one?

wait

no

y-y1=m(x-x1)

[dusky viper]

right

where (x1,y1) is a point that it passes through

so i'd first start with that

[low mica]

$y+2 = m(x-1) \ y=mx-m-2 \ y=x^2 \ \ x^2 = mx-m-2 \ x^2-mx+m+2 = 0 \ \ b^2-4ac = 0 \text{(tangent)} \ \ (-m)^2-4 \cdot 1 \cdot (m+2) = 0 \ m^2 - 4m - 8 = 0 \ y= \frac{-b \pm \sqrt{b^2-4ac}}{2a} \ \ \frac{4 \pm \sqrt{16-4 \cdot 1 \cdot -8}}{2} \ + = 5.46 \ -=-1.46$

[dusky viper]

right, now expand everything and make y the subject

yep

[low mica]

mmm

would we do discriminant next?

or na

would that do anything

[dusky viper]

yeah we can take the discriminant

[low mica]

uhhhhhh did i do something wrong

[dusky viper]

yeah take the discriminant of the resulting quadratic

mx-m-2 is just a straight it doesnt have a discriminant

[low mica]

oh

so we take discriminant

of

m^2

?

[dusky viper]

no, make our two equations y=x^2 and y=mx-m-2 equal eachother

[low mica]

oh right

[dusky viper]

yeah this looks more like it

[low mica]

ok now

quadratic equation

we solve for values of m?

[dusky viper]

yeah

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[elfin berry]

pixel

[low mica]

.reopen

[marsh citrus]

✅

[dusky viper]

u have the right idea just wrong execution

-6 and 2 dont multiply to -8

you will have to solve the quadratic using the quadratic formula or by completing the square

[low mica]

💀 dude

im autistic

$y+2 = m(x-1) \ y=mx-m-2 \ y=x^2 \ \ x^2 = mx-m-2 \ x^2-mx+m+2 = 0 \ \ b^2-4ac = 0 \text{(tangent)} \ \ (-m)^2-4 \cdot 1 \cdot (m+2) = 0 \ m^2 - 4m - 8 = 0 \ y= \frac{-b \pm \sqrt{b^2-4ac}}{2a} \ \ \frac{4 \pm \sqrt{16-4 \cdot 1 \cdot -8}}{2} \ + = 5.46 \ -=-1.46$

[elfin berry]

pixel

[low mica]

@dusky viper doing it right so far?

[dusky viper]

yeah, i'd just keep the answers in exact form

[low mica]

ok

ty

[marsh citrus]

@low mica Has your question been resolved?

[marsh citrus]

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.

[uneven imp]

need help

[sand kindle]

what have you tried?

[uneven imp]

in the end i got (- p v q) -> r

where it ask me to prove p v r which i feel impossible

since i cant eliminate q

[sand kindle]

can you show your derivation?

[uneven imp]

okay gimme a min

this is the second step i did

i got negation p v q ^ tautology

the last one i use the formula p -> q = -p v q

[sand kindle]

a -> (b -> c) is different from (a -> b) -> c

[uneven imp]

wait which part

[sand kindle]

nvm, the main issue is something else. Here are your first three lines with proper parentheses:

• (p → q) ∧ (p → r) → r
• (p → q ∧ r) → r
• (p → q ∧ ¬r) ∨ r

can you see the error?

[uneven imp]

(p → q ∧ ¬r) ∨ r

this

i cant use r inside the bracket to imply p -> q which implies on r

unless i change ^ to v ?

idk if im wrong

[sand kindle]

yes, that's the error

try it again, but be more careful with parentheses

[uneven imp]

ok so i need

reset it back to default

(p → q ∧ r) → r

this right?

[sand kindle]

this is ambiguous, for example

[sand kindle]

yes

and to be clear that's (p → [q ∧ r]) → r

[uneven imp]

got it

so what do i need to solve first

like the q ^ r

or inside the bracket ( )

i shouldnt be touching -> r right?

[sand kindle]

change one of the implications to a disjunction (∨)

[sand kindle]

you can do either one

[uneven imp]

negation p v [ q ^ r ]

possible?

[sand kindle]

missing the → r at the end, but yes

[uneven imp]

letss goo

[sand kindle]

All three of these are equivalent

• (p → [q ∧ r]) → r
• (¬ p ∨ [q ∧ r]) → r
• ¬ (p → [q ∧ r]) ∨ r

[uneven imp]

but the thing is

how do i prove p v r

likes it feel super impossible

[sand kindle]

keep going

your full statement now is (¬ p ∨ [q ∧ r]) → r

[uneven imp]

cuz there is q

got it

i try

now

can i use associative law

([¬ p ∨ q] ∧ r) → r

[sand kindle]

there is no associative law for ∨ and ∧

there's a distributive law

[uneven imp]

oh shiii

unless there ^ ^ or vv i can use

associative

sorry my bad

(¬ p ∨ [q ∧ r]) → r maybe i can expand q = q ^q or q v q as in idempotent law

[sand kindle]

• (the sky is blue OR ice is cold) AND grass is pink
  is different from
• the sky is blue OR (ice is cold AND grass is pink)

[uneven imp]

ok that makes sense

[sand kindle]

rather,

• (the sky is blue OR ice is cold) AND grass is pink
  is the same thing as
• (the sky is blue AND grass is pink) OR (ice is cold AND grass is pink)

hence distributive not associative

[uneven imp]

so you want me to use disributive

[sand kindle]

you can do that

or you can get rid of the →

[uneven imp]

but the thing is

if i use distributive

it gonan revert back to question

[sand kindle]

why not get rid of the →'s first

[uneven imp]

since( p -> q )^( p-> r) -> r

become (-p v q ) ^ ( -p v r ) - > r

[uneven imp]

which part btw

implies r ?

-(( - p v q ) ^ ( -p v r )) v r

[sand kindle]

yep

[uneven imp]

ok bro now i show u my working

seems good?

i can use associative law now right

since i got V V

[sand kindle]

is this (p ∧ (¬q ∨ ¬r)) ∨ r or p ∧ ((¬q ∨ ¬r) ∨ r)?

[uneven imp]

(p ∧ (¬q ∨ ¬r)) ∨ r

so its not associative law

,

https://tenor.com/view/взгляд-2000-ярдов-война-war-soldier-gif-3632617944134077161

[sand kindle]

You have a ¬r and r, so why not try to combine them?

from here

[uneven imp]

jeeez i forgot

[sand kindle]

or actually, this works

use the distributive law again to bring the r inside the parens

[uneven imp]

got it

wait how

(p ∧ (¬q ∨ ¬r)) distributive law on this

or

(¬q ∨ ¬r)) ∨ r this

[sand kindle]

[p ∧ (¬q ∨ ¬r)] ∨ r

[uneven imp]

woah

[sand kindle]

one of those is not valid

[uneven imp]

how is that

[sand kindle]

I mean the proposition is [p ∧ (¬q ∨ ¬r)] ∨ r

[uneven imp]

not valid?

[sand kindle]

this doesn't make sense

[uneven imp]

so you want me to go back to original distri law

right

[sand kindle]

(see how there are two ))'s in a row?)

[uneven imp]

yep

[sand kindle]

so [p ∧ (¬q ∨ ¬r)] ∨ r is fine

now bring the r inside

with the distributive law

[uneven imp]

idk how tho

like i know p v ( q n r ) = (p ^ q )v (p ^ r )

but now im facing 3 variables

[sand kindle]

(¬q ∨ ¬r) acts like a single variable because it's in parentheses

[uneven imp]

so i can assume (¬q ∨ ¬r) as q

[p ∧ q] ∨ r

[sand kindle]

those "q"s are not the same, but yes

[uneven imp]

okay

lemme show

[uneven imp]

@sand kindle is this okay

am i reaching the end yet

[sand kindle]

no, don't reuse variable names

you're overcomplicating it

[uneven imp]

aww

[sand kindle]

• [p ∧ (¬q ∨ ¬r)] ∨ r
  is equivalent to
• (p ∨ r) ∧ ((¬q ∨ ¬r) ∨ r)]

[uneven imp]

is that the same

to my answer

[sand kindle]

oh wait it is

I misread that bit

[uneven imp]

yea

[sand kindle]

but you still shouldn't reuse "q"

you can use another letter if you really want to do that

[uneven imp]

noted

what should i do next

my head when spinning looking at formula tbh

[sand kindle]

nearly done!

[uneven imp]

wew lets go and i got to eat

what should i do next

[sand kindle]

remember we wanted to get the ¬r and r together

[uneven imp]

it become T then

r v -r = T

[sand kindle]

yep

[uneven imp]

so ( t v -q ) ^ ( r v p )

[sand kindle]

yes

[uneven imp]

what formula then

it doesnt show in

laws of logic

so far

[sand kindle]

T v -q

[uneven imp]

q -> T

[sand kindle]

you're not wrong

but it's simpler than that

[uneven imp]

how

[sand kindle]

"True OR <something else>"

what does that simplify to?

[uneven imp]

domination law ?

[sand kindle]

yes

[uneven imp]

wait HOW

i thought the formula only apply to non negation

[sand kindle]

think about it logically

"1 + 1 = 2 OR <anything else>" is always true

no matter what <anything else> is

[sand kindle]

that p can be anything

(in this case ¬p)

[uneven imp]

@sand kindle this good?

[sand kindle]

looks fine to me

[uneven imp]

whats next

[sand kindle]

you try to figure it out

you're very close to your goal

[uneven imp]

wait a min

if i could assume that ^ (AND) which either both must be true in order the entire statement to be true

therefore i just prove( p v r )

yes?

[sand kindle]

yep

yep!

[uneven imp]

oh my god

wtf

for 6 hours i been stuck on this

now i got it

💀

@sand kindle thx for the help btw

also for the last part what law is it

welp identity laws

.close

[marsh citrus]

Channel closed

Closed by @uneven imp

Use .reopen if this was a mistake.

[marsh citrus]

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.

[grizzled coyote]

do a and b represent the digits of the number?

[twilit grove]

ah, represent them as multiples of the digits

for example, 21 = 2 * 10^1 + 1 * 10^0

treat them as variables

literally take my example, change "2" to "a" and "1" to "b"

yeah, and you can write ba = 10b + a. see if that helps

the same way you represent ab = 10a + b

just switch a and b

it is another way of representing ba

[marsh citrus]

Channel closed

Closed by @sour quest

Use .reopen if this was a mistake.

[marsh citrus]

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.

[mossy widget]

need some help with b plz

[marsh citrus]

@mossy widget Has your question been resolved?

[mossy widget]

<@&286206848099549185>

[marsh citrus]

@mossy widget Has your question been resolved?

[hallow crown]

@mossy widget you can separate f(z) into two terms, one polynomial and the other rational, polynomial is just the first part of the laurent series expansion while for the rational part you can use that hint

[mossy widget]

yh i did that

wait one sec

[mossy widget]

here

[hallow crown]

k would be from -inf to 2 no?

[mossy widget]

ok thats what i dont get

why

i dont get it

[hallow crown]

the substitution you used

k = 2 - n

[mossy widget]

ye

[hallow crown]

since n >= 0 then 2 - n <= 2

[mossy widget]

yh

thanks

so much

[hallow crown]

no problem

[mossy widget]

why does it change to n + 3?

[hallow crown]

they took the terms for n <= -1 and just changed n to -n

[marsh citrus]

@mossy widget Has your question been resolved?

[marsh citrus]

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.

[cyan dove]

confusing ts out of me

i divided the function and got 20.039 but theres no indication to round

[latent coral]

try just directly putting the function instead of dividing yourself

[cyan dove]

i used mathway

[latent coral]

like 643.885/1.944 * sqrt(K/273.15)

[cyan dove]

oh

returns the same answer

the answer seems to be right but im not rounding correctly

cuz i plugged in the second part and got a correct answer

<@&286206848099549185>

[marsh citrus]

@cyan dove Has your question been resolved?

[cyan dove]

<@&286206848099549185>

<@&286206848099549185>

[balmy magnet]

w h a t

[balmy magnet]

just replace v(K)

$$\frac{643.855\sqrt{\frac{K}{273.15}}}{1.944}$$

[elfin berry]

amwn0tyk

[marsh citrus]

@cyan dove Has your question been resolved?

Channel closed

Closed by @cyan dove

Use .reopen if this was a mistake.

[cyan dove]

.reopen

[marsh citrus]

✅

[cyan dove]

this didnt work

i tried it already

.close

[marsh citrus]

Channel closed

Closed by @cyan dove

Use .reopen if this was a mistake.

[marsh citrus]

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.

[crude leaf]

what does the length of an arc represent?

[jovial star]

Imagine if you walk along an arc
It tells the distance you travel

[quaint elm]

the amount of string it would take to line it

[jovial star]

Which isn't the straight line displacement but longer

[crude leaf]

i still dont understand

for example

if i had a pos vs time graph

and lets say my line is y=x

from t=0 to t=1

i travel 1 unit of position

but the arc length from 0 to 1 is sqrt(2)

but my total displacement was only 1

[latent coral]

arc length represents the length of the graph itself

[crude leaf]

so what doe sthe sqrt(2) represent

[latent coral]

not the physical interpretation of the graph

but the graph itself

[crude leaf]

how would the arc length be useful

[latent coral]

there are applications in stuff like physics, other math

you can find perimeters of cool stuff

[crude leaf]

oh

[latent coral]

also just nice to be able to do that

[crude leaf]

couldyou give me a simple example

[latent coral]

an example of where it would be useful?

[crude leaf]

yes

[latent coral]

https://www.quora.com/What-are-some-real-life-applications-of-finding-the-arclength-of-a-curve-using-integration

examples

useful for minimizing things too like lengths of curved objects

roads, bridges, etc

[crude leaf]

alright

thank you!

.close

[marsh citrus]

Channel closed

Closed by @crude leaf

Use .reopen if this was a mistake.

[marsh citrus]

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.

[desert prairie]

What excatly is this question asking me?

[glass silo]

,rccw

[glass silo]

“When the ball has traveled a horizontal distance of 55m, is its height less than 3m above ground or not?”

[desert prairie]

My brain is so slow

I didn’t realise they playing cricket

So ofc it would be from the ground 😭

[glass silo]

Hehe, well, to be fair it doesn’t matter so much that it’s the “ground” but that you want to be less than 3m from the point you hit it from, so can consider that as the “ground” for the question

[marsh citrus]

@desert prairie Has your question been resolved?

[marsh citrus]

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.

[sturdy bobcat]

I need help with geometry. I have to prove that a rectangle is a parallelogram.

Give me a hint

[leaden monolith]

List what makes a shape a rectangle

List what makes a shape a parallelogram

Observe that the conditions for a parallelogram are weaker than that of a rectangle

This means the rectangle is only a special case of a parallelogram

[sturdy bobcat]

It's a quadrilateral in which all angles are right angles

[sturdy bobcat]

It's a quadrilateral in which opposite sides are parallel

Are there any conditions besides these?

[leaden monolith]

Try to say this with angles

Because you used angles for the rectangle

[marsh citrus]

@sturdy bobcat Has your question been resolved?

[sturdy bobcat]

I know from a previous theorem from the book I'm using that, in a parallelogram, opposite angles are congruent

[leaden monolith]

React to the bot

Or this channel will close

[leaden monolith]

Aha

[sturdy bobcat]

Since in a rectangle all angles are right, opposite angles are congruent

Therefore it's a parallelogram

[leaden monolith]

Yep!

That’s exactly it

[sturdy bobcat]

Alright, thanks

[leaden monolith]

You can also use parallel-ness of the sides

Parallelogram requires opposing sides to be parallel yes

So do rectangles!

They just also require them to be perpendicular to adjacent sides

[sturdy bobcat]

I see

Thanks for helping me out

.close

[marsh citrus]

Channel closed

Closed by @sturdy bobcat

Use .reopen if this was a mistake.

[marsh citrus]

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.

[grave crag]

hi

[grave crag]

idk how to simplfy

[storm dagger]

you have a quadratic equation

move all the terms to one side and solve using quadratic formula/completing the square/factorisation (whichever you're more comfortable with)

[marsh citrus]

@grave crag Has your question been resolved?

[marsh citrus]

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.

[earnest siren]

Assume we are given 7 distinct points in the plane R2 with the following property: any line that goes through two of the points is going through at least three of the points. Prove that all 7 points have to lie on one line.

[earnest siren]

I proved this in a very horrible method

You can start with assuming that a line only goes through 3 points

prove that wrong

and then if one line goes through four points easily prove that all points go on the same line

[earnest siren]

but I did this just with a kinda of a brute force way

You can assume A = {1,2,3} forms a line (1 through 7 are the 7 points)

B = {1,4,5} forms a line

and C = {1,6,7} forms a line

then consider the line {3,5,p}

if p = 1 or 2 (Eg: {3,5,1}, {3,5,2}) then {3,5,p} shares two points with A, so then these two are the same line and 4 points go through a line

if p = 4 then you get the same problem but with B

p = 6 is the hard one

If you consider {2,5,q} then you find the only possible q value is 7

then you consider {3,4,r} and find that the only valid r is 7

then you consider {2,6,x}. I can prove that all of them don't work besides x=4 but I don't know how to show x=4 can't happen without a picture

All the conditions combined would be {1,2,3}, {1,4,5}, {1,6,7}, {2,5,7}, {3,4,7}. And I need to show that if you also have {2,6,4}, then some line has atleast 4 points on it

I can show this with a picture and complete the proof

is there some better way to do this

[marsh citrus]

@earnest siren Has your question been resolved?

[marsh citrus]

@earnest siren Has your question been resolved?

[earnest siren]

<@&286206848099549185>

[earnest siren]

You can ignore what I have and just look at the question, because my proof is ugly and I need to know a better way to solve it

[marsh citrus]

@earnest siren Has your question been resolved?

[marsh citrus]

@earnest siren Has your question been resolved?

[marsh citrus]

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.

[low mica]

how to calculate the angle between two vectors

[fervent rampart]

use the dot product formula: [ \va a \cdot \va b = \norm{\va a}\norm{\va b} \cos \theta ]

[elfin berry]

cloud

[fervent rampart]

knowing the magnitude of the two vectors and their dot product, you can solve for the angle

[low mica]

mm ok yes i got that

new question

PQRS is a parallelogram. If PQ = p and QR = q, then SQ is equal to?

have i drawn it correctly?

.close

[marsh citrus]

Channel closed

Closed by @low mica

Use .reopen if this was a mistake.

[marsh citrus]

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.

[weak patrol]

How do I prove this

[marsh citrus]

@weak patrol Has your question been resolved?

[glass silo]

What does g being even and h being odd mean? Can you write a statement for that in terms of f?

[weak patrol]

f(x)=g(-x)+-h(-x)?

[glass silo]

Well, I mean, that is correct at least

[weak patrol]

nvm I did it

.close

[marsh citrus]

Channel closed

Closed by @weak patrol

Use .reopen if this was a mistake.

[marsh citrus]

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.

[flat grail]

is it true that if u=u(x,y), and $x = e^s \cos t, y=e^s \sin t$ i want to find $u_x$, is $u_x = u_s s_x + u_t t_u$

[elfin berry]

lewis_f04

[marsh citrus]

@flat grail Has your question been resolved?

[marsh citrus]

@flat grail Has your question been resolved?

[flat grail]

<@&286206848099549185>

[marsh citrus]

@flat grail Has your question been resolved?

[marsh citrus]

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.

[frosty gyro]

are the bounds of the cardiod and dimpled limacon always 0 to 2pi

[frosty gyro]

.close

[marsh citrus]

Channel closed

Closed by @frosty gyro

Use .reopen if this was a mistake.

[marsh citrus]

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.

@turbid talon Has your question been resolved?

[marsh citrus]

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.

[hollow dawn]

I don't really understand proofing and stuff and its actually like frustrating me at this point cs im good at math

[hollow dawn]

5 would be AAS and 7 would be parallelogram

[mighty pier]

a

what is aas?

[glossy solstice]

angle angle side

[mighty pier]

wait

[hollow dawn]

this is geometry btw 😭

[mighty pier]

both are 90 degree

[hollow dawn]

yeah

[mighty pier]

definition of rectangle?

[hollow dawn]

so its a rectanlge

😭

[hollow dawn]

yeah

[marsh citrus]

@hollow dawn Has your question been resolved?

Channel closed

Closed by @hollow dawn

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.

[vague tendon]

how does the first expression simplify into the second <@&286206848099549185>

[cedar smelt]

Take the second bracket common

[mystic blade]

are you familiar with the distributive property

[vague tendon]

i think ive covered it before but i dont remember exactly rn

what does that imply

oh right i have

[cedar smelt]

(a1 + a2)(b1 + b2) = A1(b1+b2) + a2(b1 + b2)

[vague tendon]

yes fair enough

thanks

[mystic blade]

np

[vague tendon]

ye ofc ik the distributive property but i didnt recognise it my bad

[mystic blade]

u good fr

it happens

[cedar smelt]

in General
a(x±y) = ax±ay

[vague tendon]

appreciate it

.close

[marsh citrus]

Channel closed

Closed by @vague tendon

Use .reopen if this was a mistake.

[marsh citrus]

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.

[novel juniper]

Let P(x) be a polynomial with real coefficients let $\alpha_1, \alpha_2....\alpha_k$ be distinct real roots of P(x)

[elfin berry]

ƒ(Why am. I here)=I don't Know

[novel juniper]

If P'(x) is its derivative

show

$\lim_{x\ \rightarrow\alpha_i}\left(\frac{\left(x-\alpha_i\right)\left(P'\left(x\right)\right)}{P\left(x\right)}\right)=r_i$

[elfin berry]

ƒ(Why am. I here)=I don't Know

[novel juniper]

for some positive integer $r_i$

I was able to show that it's some real value

but why must it be $r_i$

[elfin berry]

ƒ(Why am. I here)=I don't Know

[novel juniper]

I mean an integer

[elfin berry]

ƒ(Why am. I here)=I don't Know

[novel juniper]

I'll send my proof here

so $ln(P(x)) =ln((x-\alpha_1))+ln((x-\alpha_2))......+ln((x-\alpha_k))$

[elfin berry]

ƒ(Why am. I here)=I don't Know

[novel juniper]

or $\frac{1}{P\left(x\right)}P'\left(x\right)=\frac{1}{\left(x-\alpha_1\right)}+\frac{1}{\left(x-\alpha_2\right)}.....+\frac{1}{\left(x-\alpha_k\right)}$

[elfin berry]

ƒ(Why am. I here)=I don't Know

[novel juniper]

so I have

[leaden monolith]

What if you took log of this

Do some handwave magic and move the log inside the limit

[novel juniper]

just a min

Let me write my thoughts first

$\frac{\left(x-\alpha_i\right)P\left(x\right)\left(\frac{1}{\left(x-\alpha_1\right)}+\frac{1}{\left(x-\alpha_2\right)}......+\frac{1}{x-\alpha_{k\ \ }}\right)}{P\left(x\right)}$

[elfin berry]

ƒ(Why am. I here)=I don't Know

[novel juniper]

or I have

$\frac{\left(x-\alpha_i\right)\left(\frac{1}{\left(x-\alpha_1\right)}+\frac{1}{\left(x-\alpha_2\right)}......+\frac{1}{x-\alpha_{k\ \ }}\right)}{ }$

[elfin berry]

ƒ(Why am. I here)=I don't Know

[novel juniper]

why is this necessarily an integer

[still temple]

if its an integer cant you assume x-a_i divides x-a_n

or something

something with proof of contradiction

[still temple]

suppose that if it doesnt turn out then its not an integer

[novel juniper]

no, I mean this is supposed to be true for any general polynomial , right

why is that true

<@&286206848099549185>

[upbeat sable]

Expand the thing out

You will see a nice cancellation

(in the ith term)

[novel juniper]

yeah, I noticed that

[upbeat sable]

And every other term, what does it become?

[novel juniper]

oh, right

shit

I was so close

0

[upbeat sable]

Yes

[novel juniper]

damn it

I could have scored 10 in the exam on this

😭

got everything else right

[elfin berry]

quickdoom

[novel juniper]

yeah, that's pretty easy

so the limit is always 1

[upbeat sable]

(the alpha(j)s are distinct, so the denominator in this fraction is never 0)

[novel juniper]

yeah

[upbeat sable]

Yes

[novel juniper]

Btw, you writing CMI's entrance too?

thanks

[upbeat sable]

Oh also, i am too trying to solce the last problem

I think i have a solution to the fiest part in #discrete-math

I am having trouble proving the other inequality

[novel juniper]

that's way above me, but looks cool

don't know any graph theory

good luck

[upbeat sable]

I just used language to make it concise, but the concepts dont involve any real graph theory

[upbeat sable]

☺️ thanks!! Same to you

[novel juniper]

.close

[marsh citrus]

Channel closed

Closed by @novel juniper

Use .reopen if this was a mistake.

[marsh citrus]

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.

[vagrant sedge]

I have solved the question but dont know why its 3 equal parts isnt it 4?

[sand fable]

“The sides of another square are divided into three equal parts”

[vagrant sedge]

still dont get it

[sand fable]

you can see the tick marks on each side to see how they did that

[vagrant sedge]

Ohhhhh

i get it

thanks

.close

[marsh citrus]

Channel closed

Closed by @vagrant sedge

Use .reopen if this was a mistake.

[marsh citrus]

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.

[desert prairie]

why does square rooting the det of this give me k?

[storm dagger]

i dont think it's the square root

k is the determinant of the enlargement matrix P

[twilit grove]

i'd write arbitrary transformation matrices first

[storm dagger]

yep

[desert prairie]

that what the mark scheme says tho

[storm dagger]

but since rotations preserve size, the determinant of M is equal to the determinant of P

[desert prairie]

i might be saying it wrong tho

[twilit grove]

wouldn't it be k^2?

[storm dagger]

is it asking for area scale factor or or length scale factor ?

[desert prairie]

this is it

i dont get why that the case tho

[storm dagger]

ok it must be area scale factor mb

[storm dagger]

2 things

|M| = |PQ| = |P||Q|

and |Q| = 1 since transformation Q is a rotation

[copper raven]

3rd thing, what's the matrix of P supposed to be ?

[desert prairie]

it would be k 0 k 0? in matrix form

i mean k 0 0 k

[copper raven]

yeah

what's the det of that

[desert prairie]

k^2

ohhhhh

i think it get it now

ty

.close

[marsh citrus]

Channel closed

Closed by @desert prairie

Use .reopen if this was a mistake.

[marsh citrus]

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.

[main garnet]

cannot lie

[main garnet]

do not know where to start lol

acc wait yes i do gimme a sec

ok now i dont

gg

help

[devout mauve]

how did you do (a)

[main garnet]

set it = x then just solve a polynomial

[devout mauve]

ok I had hoped you had done something different. but I suppose that was much easier here

so anyway, you want to solve f(x)=x

equivalently, f(x)-x=0

and you know that f is continuous

do you have a theorem which gurantees you the solution to some equation involving some continuous function?

[main garnet]

ohh f is continuous and x is continuous so

so f(x) - x is a cts function too?

[devout mauve]

yes

[main garnet]

so if i said

g(x) = f(x) - x

and the domain of g is [0, 1]

can i assume the range of g os [-1, 1]

or is that leaping in logic

[devout mauve]

that is leaping

why should that be true

[main garnet]

ye ur right

hmmm

[devout mauve]

also note the difference between range and codomain

[main garnet]

oh so what i said is the codomain

but the range is somemthing else

that makes sense

[devout mauve]

why is that the codomain

[main garnet]

because ive said that the values have to exist between -1 and 1

but it's not true that the function takes all vlaues between -1 and 1

hence it cant be the range

well it can be true but

u cant assume that

[devout mauve]

why

[main garnet]

because the codomain of f is [0, 1]

and the codomain of x is [0, 1]

so the co-domain of f(x) - x has to be [-1, 1] as the lowest poss value is 0-1

and the highest poss value is 1-0

[devout mauve]

ok

so now g:[0,1]->[-1,1] is continuous

and you want to find a root

how could you do that

which thm do you want to use

[main garnet]

wait g is cts

ohh

so then

by IVT wouldnt it follow that for all y in the interval[g(0), g(1)] there exists a c in [0, 1] s.t. f(c) = y

and as g(0) = f(0) - 0 = f(0) which exists in [0, 1] and g(1) = f(1) - 1 which exists in [-1, 0]

that means there must exist a d in [0, 1] s.t. g(d) = 0 by IVT?

so f(d) - d = 0 which implies there exists a fixed point d of f?

[devout mauve]

yup

[marsh citrus]

@main garnet Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[marsh citrus]

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.

[wind whale]

let A and B be square matrices of order 2 such that tr(A) = 7, |A| = 22, tr(B) = 4, |B| = 11, tr(AB) = 33, solve for x such that |A+xB| = 272

[wind whale]

im not so sure i have enough ideas to start the problem

tr(A) is trace of A

[marsh citrus]

@wind whale Has your question been resolved?

[cold sonnet]

was this in a test

i remember seeing this

anyways, $|A+xB|=|A|+x^2|B|+x|\mathrm{tr}(A)\mathrm{tr}(B)-\mathrm{tr}(AB)|$ this should help

[elfin berry]

bo

[cold sonnet]

@wind whale

[wind whale]

is this true for all square matrices or order 2 specifically

[cold sonnet]

order 2 specifically

[wind whale]

maybe? i had someone share this to me

[wind whale]

is there a general expression for a general square matrix?

[cold sonnet]

preparing for some exam?

[wind whale]

we both are, yes

[cold sonnet]

not that i know of

[cold sonnet]

jee?

[wind whale]

well yes

actually

did you also have this in your test

[cold sonnet]

i had this

[wind whale]

considering you asked that question

[wind whale]

was it rather recently?

[cold sonnet]

last sunday

[wind whale]

okay, i know where you live lmao

which means you also have an exam today

because my friend does

[cold sonnet]

where 👀

[wind whale]

are you fine with me saying that just like that

[cold sonnet]

sure

[wind whale]

lol

[cold sonnet]

nah that's not where i live

[wind whale]

sure you do mate

[cold sonnet]

i don't

allen test?

[wind whale]

okay wait

it might have been an all india test

[cold sonnet]

yes

aioot

[wind whale]

they do have those too sometimes

ah then that's that

[cold sonnet]

it was an all india test

[wind whale]

what'd you score

[cold sonnet]

i didn't check

[wind whale]

there's no way

[cold sonnet]

it wasn't allat 💀

[wind whale]

actually

this is not the place, ty for the help it does work

[cold sonnet]

most of the questions were quite easy

[wind whale]

#discussion

.close

[marsh citrus]

Channel closed

Closed by @wind whale

Use .reopen if this was a mistake.

[cold sonnet]

dms would be better ig, discussion is general

if you're ok that is

[wind whale]

ok i suppose

[night yew]

hey! can someone help explain me how to do this problem regarding derivatives ?

i’m assuming we use chain rule but the professor doesn’t cover material too well in lecture

[tight furnace]

Ye so chain rule is used when you have the composition of two functions

Can you find the two simpler functions which compose to make cot²(x)

[tight furnace]

Also #❓how-to-get-help

this channel will close any second

[marsh citrus]

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.

[chilly quarry]

How would you use to solve this if it had an infinity on top and is it possible to solve it in desmos

[marble shore]

what kind of series is that?

[broken dome]

You can graph sums in desmos like this

mind the x instead of infinity

[chilly quarry]

I’m not sure I just started learning this

[marble shore]

would it help point you in the right direction if i told you that type of series was called a geometric series?

[sharp sequoia]

I think so yeah

Would help them out

[marble shore]

its hard trying not to give the answer away haha

[chilly quarry]

What’s the difference between arithmetic and geometric series

[sharp sequoia]

YEAHHH

[sharp sequoia]

What are you doing in arithmetic sequences?

[chilly quarry]

I do these type of problems but I never saw a infinity on top and only learned arithmetic

[sharp sequoia]

Oh in arithmetic sequences it’s normally unbounded

Doesn’t really converge to a number

In geometric it does

That’s why we could use infinity

[chilly quarry]

So it’s 2?

[sharp sequoia]

Well depends on the ratio used

[chilly quarry]

Yeah I got the geometric formulas

I don’t understand what r stands for

[finite pine]

r just stands for the beginning point

so where the series will start

[quartz moth]

Who is fluent in geometry

[chilly quarry]

Oh alright thanks

[marble shore]

would that not be the a value, and r is the common ratio?

[finite pine]

u seem smarter, we can just go with your explanation

[chilly quarry]

Common ratio between what?

[marble shore]

if we took the series of 1, 3, 9, 27, 81 for eg

the intial term would be 1

[sharp sequoia]

If you have a question plz open a new channel.

[marble shore]

and if we're using a * r ^ (n-1) as a formula for the series, waht would r be?

[chilly quarry]

3/1?

[marble shore]

yeah, 3

that's your common ratio for the sequence

n / (n-1) = 3

[chilly quarry]

That makes a lot more sense now.

[marble shore]

in your original question, do you know what that symbol means?

[chilly quarry]

The sigma notation?

[marble shore]

yeah

[chilly quarry]

Writing a sequence in shorter length?

I’m going to try to solve it now since I know what r means now

[marble shore]

the sum of expression inside the sigma, with the lower and upper bounds of the sigma

so what you're essentailly calcualting here is the infinite geometric series of (2/3)^n

where a sequence is a bunch of numbers in a particular order (1, 3, 9, 12, 15, etc)
and a series is the sum of that bunch of numbers in a particular order (1 + 3 + 9 + 12 + 15, etc)

[chilly quarry]

So it would be (2/3)/(1-2/3) equaling 2 because the r term is (4/9)/(2/3) which gets you the bottom part of the formula, (1-2/3) and if you divide that by the numerator which is 2/3 it would be 2.

[marble shore]

yep exactly

[chilly quarry]

Ok thanks for the clarification and help

.close

[marsh citrus]

Channel closed

Closed by @chilly quarry

Use .reopen if this was a mistake.

[marsh citrus]

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.

[spring stirrup]

did i set this up right?

[tight furnace]

Looks right

how much linalg do you know?

You could try computing the value of <a,b> directly by using <3a-4b, 3a-4b> = 361, expanding using linearity and plugging in for <a,a> and <b,b>

[marsh citrus]

@spring stirrup Has your question been resolved?

[ashen lake]

Someone please help me

[marsh citrus]

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.

[wheat shell]

Part c, im not getting the show that, i have a factor of pi^2 on the top and missing a factor of 3 on the bottom, not sure where im going wrong

[still temple]

unreadable for me 😭

[wheat shell]

Fixed by subbing in hbar

.close

[marsh citrus]

Channel closed

Closed by @wheat shell

Use .reopen if this was a mistake.

[marsh citrus]

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.

[woven plinth]

i have a quesion about taylor series

[woven plinth]

so im trying to work out the taylor series of log x about center of 10

i cant tell if this is right

[glass silo]

"log" referring to log base 10?

[woven plinth]

yeah

took derivative as 1/xln10

[glass silo]

Remember that you're evaluating all derivatives at 10 of course

[woven plinth]

oh wait looking at it i think i did my derivatives wrong

1/xln10 -> -1/x^2 ln10 -> 2/x^3 ln10

i forgot to add a numerator coefficient

[glass silo]

(so evaluate this when x = 10, and same with the other derivatives upon correcting)

[woven plinth]

so the (n-1)! would be the coefficient in the numerator at each term

n = 3 youre multiplying it by 2, n = 4 youre multiplying it by 2 x 3 etc.

is this right though i cant tell

[glass silo]

The x in the denominator

[woven plinth]

what about it

is the exponent wrong?

[glass silo]

(other than that, looks basically like it)

[glass silo]

And see the comments here: while you have "1/xln10 -> -1/x^2 ln10 -> 2/x^3 ln10", you're evaluating each of those derivatives at x = 10, remember the form of the Taylor expansion

Once you do, you put that with the evaluated at 10 versions into the series

[woven plinth]

ohh so i have to substitute that x for 10 as well

nice