help-27

[timid peak]

is there a more calculation type of way to do it? Like the characteristic polynomial method for sequences where theres both an and an-1 term

@upper schooner

ahh wait

for d, we know subsequences nk =2k-1 (odd terms) are increasing

and mk=2k (even terms) are decreasing

thats it not sure how to find the limit that both subsequence converge to

<@&286206848099549185>

[timid peak]

@zealous bloom

do you think you'd able to help?

nevermind 6.4 for now..

do you know how to do these?

[timid peak]

oh my goodness

im giving up for today

ahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

ok

i'll be back

.close

[devout snow]

Channel closed

Closed by @timid peak

Use .reopen if this was a mistake.

[devout snow]

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.

[gusty merlin]

Hi

[gusty merlin]

Js need help w this

I’ll rotate

[tardy mulch]

The volume of a prism is the surface area of the side multiplied by the length

[gusty merlin]

So it’s 4x17?

[tardy mulch]

Yup

[gusty merlin]

Which is 64

68*

[tardy mulch]

Yep 68

[gusty merlin]

So the volume of the hexagonal prism would be 68m^2

[tardy mulch]

M^3

[gusty merlin]

Thank you

Could u also help me with the second one?

7. B

[tardy mulch]

That one seems alot harder, let me have a think

[gusty merlin]

Ik that to calculate the volume of a prism it is v= 1/3 a h

So would it be 1/3x17x4?

[tardy mulch]

It is hexagonal based

[gusty merlin]

Yes

[tardy mulch]

I'm not sure what the intended method is, but there is a formula here

[gusty merlin]

Oh

So it’ll be square root /2 a^2 h

Which part is a and which part is h

[tardy mulch]

And a is different here I think

H is 4

But a is the side length of the hexagon

This seems like the wrong method

It's very annoying to calculate a

[gusty merlin]

Yea bc we don’t have a n stuff

[tardy mulch]

Yeah sorry mate not sure

You could try calculate a using formula for surface area of hexagon

[gusty merlin]

I figured it out thanks so much for the first one tho

.close

[devout snow]

Channel closed

Closed by @gusty merlin

Use .reopen if this was a mistake.

[devout snow]

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.

[modern spear]

I need exact value for q and p to tell that this is dividable. What do I do next?

[modern spear]

I know that I need to tell that q and p must equal to 0 but not sure what to do next

[solar goblet]

synthetic division

[green kelp]

No

Simple remainder theorem

[solar goblet]

oh yeah that i forgot

[old nimbus]

i dunno how to solve it guys who can help me?

[solar goblet]

!occupied

[devout snow]

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).

[modern spear]

In the previous task, the remainder was x(p-14)+12+q and from here I can say that p is 14 and q is -12, but I don't know how here?

Well the problem here is +1

[devout snow]

@modern spear Has your question been resolved?

[modern spear]

<@&286206848099549185>

[modern spear]

.close

[devout snow]

Channel closed

Closed by @modern spear

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.

[proud rock]

Two candidates were standing in an election. Of the total number of people in the electoral roll in that election, 10% did not use their votes and 60 votes were declared invalid. The winning candidate secured 47% of the total votes of the voter list and he won the election by 308 votes. How many votes were cast in that election and how many votes did the losing candidate got?

[twilit comet]

[proud rock]

anyone ?

[proud rock]

hey

.

.close

[devout snow]

Channel closed

Closed by @proud rock

Use .reopen if this was a mistake.

[devout snow]

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.

[ripe ore]

Hello, could someone please guide me through understanding the intuition of the definition of local maximum?

[uncut crow]

everywhere “near” x*,the function is less than or equal to f(x*)

“near” means the points less than epsilon distance away from x*

so there is some, perhaps very small, region around x* where nothing exceeds f(x*)

[ripe ore]

hmm ive been trying to understand that, maybe i need to visualise it. Lets say for this graph what could a good epsilon value be

so i can yk visualise it myself and use real values to understand it properly

[jaunty mantle]

Say you’re standing on the line

If you look to your left the floor isn’t going upwards

[jaunty mantle]

If you look to your right the floor isn’t going upwards

So you are “higher than your surroundings”

And you can kinda shrink “surroundings” to as small as you like, cantered at you but not 0

[ripe ore]

what I dont get is why is it not using f(x) < f(x*)

but its using x < x*

????

[uncut crow]

oh lmao that’s a typo

[jaunty mantle]

Oh, yeah

[ripe ore]

so is this a typo too

[uncut crow]

no

well that’s weird

it doesn’t introduce a function in the definition

[jaunty mantle]

I mean actually

[uncut crow]

so it looks fine

[jaunty mantle]

This is right too

There’s just a red herring picture of a function

😭

[ripe ore]

im still confused

[uncut crow]

it is probably supposed to be an example where A is the image of f

but it’s not written well

[ripe ore]

can one of yous rewrite the definition in a way i should understand

so i can make a link with your definition and what the slide's definition tries to imply

[uncut crow]

the maximum def there is fine, although it should clarify x* should be in A

[ripe ore]

in this case are the x and x* the "heights" of the functions? (the y axis)

[uncut crow]

in the local max definition, x <= x* should instead be f(x) <= f(x*) but is ok otherwise

[ripe ore]

and why is that different to global max, shouldnt it be f(x) too?

[uncut crow]

yea there should be a f(x) <= f(x*) in the definition of global max too

[ripe ore]

okay tysm

i think i understand it, i was just so confused and trying to wrap my head around why it wasnt including f(x)

i was soooo confused why it only depended on the input values

[uncut crow]

[ripe ore]

so its less of an understanding the logic issue more of a bad definition

[uncut crow]

yes lol

[ripe ore]

ty for help

[uncut crow]

[ripe ore]

.close

[devout snow]

Channel closed

Closed by @ripe ore

Use .reopen if this was a mistake.

[devout snow]

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.

[wary oxide]

test

[wary oxide]

i cant find the way

pls teach me

[frank summit]

try synthetic division

[covert root]

x^100 + 1 = quotient*divisor + remainder

The remainder should be at least one degree lower then the divisor in other words in the form ax+b

[wary oxide]

wait, i'm trying to understand

my English to math kinda bad

sorry, i still don't understand how to get the ax+b form

[covert root]

So what is the divisor

[wary oxide]

(x-1)²

[covert root]

So we have x^100 + 1 = quotient*(x-1)^2 + ax + b

When we sub x=1 we get:

1^100 + 1 = a+b

So at the very least we can eliminate option A

[wary oxide]

ooohhh i get it now

[covert root]

Try to think about what to do next

x^100 + 1 = (x^50 - i)(x^50 + i)

[wary oxide]

is the i necessary?

[covert root]

I am just thinking. I don't know what to do

[wary oxide]

i don't know what's next

[covert root]

Maybe take the derivative

Taking the derivative we get

$100x^{99} = q(x)2(x-1) + q'(x)(x-1)^2 + a$

[woven radish]

team132

[covert root]

From there when you sub x = 1, you can find a

From there it is easy to find b. Since we know a+b = 2

[devout snow]

@wary oxide Has your question been resolved?

[untold bough]

factor theorem

/ remainder theorem in this case

(x - 1)² has two roots but they're the same so let's treat it as a linear factor

as we know x - 1 = 0
x = 1

sub 1 for x¹⁰⁰ + 1
= 2

remainder theorem states that
given a linear / (can be any degree) divisor, the remainder can be found using f(-b/a) / f(solution to polynomial = 0)

[untold bough]

he had the idea already

unfortunately he didn't compute the fact that 1^anything = 1

[wary oxide]

i think i get the idea

sorry for the late response

I'm not very good at understanding math at other languages

Thanks for helping

🙂

.close

[devout snow]

Channel closed

Closed by @wary oxide

Use .reopen if this was a mistake.

[devout snow]

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.

[bold peak]

can someone help me write the contrapositive of this statement:

In Powerlifting getting a successful lift is equivalent to gaining a point. In a power meet if there does not exist a competitor such that they bench less than 100kg, then all competitors are strong because they have big muscles.

[devout snow]

@bold peak Has your question been resolved?

[topaz axle]

"because" can be replaced with "and"
"if there's one competitor who is weak, or there's one competitor who doesn't have big muscles, then there's one competitor who can bench less than 100 kg"

one is short for "at least one"

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[devout snow]

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.

[wooden cairn]

hi

[wooden cairn]

in the u and v plane, ie the real line

why do we exclude 0?

.close

[devout snow]

Channel closed

Closed by @wooden cairn

Use .reopen if this was a mistake.

[devout snow]

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.

[sleek bough]

Can some one help me with this question

[sleek bough]

I am on the step in which I got the squares under the roots

[solar goblet]

show your work

[sleek bough]

I let log_2 x = a

I got sqrt((a+1)^2)+sqrt((a-3)^2)=4

And I am stuck on the step of inequalities and intervals

[restive river]

you need to consider |a+1|+|a-3|=4
intervals would be a<-1, -1<=a<3, a>=3

[tough cove]

there is an easier way to solve this equation if you know the graph

its basically a pot

[tough cove]

its a formal way and more acceptable

[sleek bough]

when a<-1. I solve that a=-1, contradiction?

when -1<=a<3, I solve that 4=4 which is wierd

[sleek bough]

I don't know the graph

[sleek bough]

?

the log_2 (x) is like the inverse of the exponential function right?

[restive river]

yes

[restive river]

whenever there's a contradiction it means the value isn't valid

[sleek bough]

yup. And I solved that when a>=3, a=3, and x is 8

x increase when the a increase

wait:
here is the list of interval
a<-1, invalid
a=-1,valid,x is 0.5
-1<a<3, the expression is always 4 regardless of x
a=3, x is 8
a>3,a=3, invalid again

so x_max is 8, and x_min is 0.5, is my thought correct?

Hmm, is the answer an interval of X?

Oh the solution is indeed 0.5~8

Thanks guys

.close

[devout snow]

Channel closed

Closed by @sleek bough

Use .reopen if this was a mistake.

[devout snow]

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.

[bright juniper]

Need to find every value of a so the equation has an answer

[pastel pasture]

what do you know about exponentials

in particular, about their range?

[bright juniper]

Mhh not sure

[devout snow]

@bright juniper Has your question been resolved?

[bright juniper]

.close

[devout snow]

Channel closed

Closed by @bright juniper

Use .reopen if this was a mistake.

[devout snow]

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.

[restive river]

i am not sure on what the minimum spanning tree is or how much the branc

Weighs

I asked this wuestion earlier waited about 2 hours and no one helped guyz 🙏

[devout snow]

@restive river Has your question been resolved?

[restive river]

<@&286206848099549185>

[devout snow]

@restive river Has your question been resolved?

[tame palm]

Did you find the minimum spanning tree?

[restive river]

I told u im not sure

If i can

Its alot more dofficult then anything ive ever done

[tame palm]

Does this help?

And do you understand how Prim's Algorithm works?

You are told to start at vertex A so you add vertex A to the spanning tree. Prim's Algorithm states that you assess the weight of all the edges currently connected to the spanning tree and choose the edge with the smallest weight that does not create a cycle, meaning an edge that does not connect back to the spanning tree.

[tame palm]

Between those two edges, which weight is smaller?

[tame palm]

How do you expect to get any help if you aren't paying attention to somebody who is trying to help you?

[devout snow]

@restive river Has your question been resolved?

[restive river]

you werent @ me

sry

[tame palm]

Do you understand what the algorithm is asking you to do so far?

@restive river

[restive river]

hold on i will look

now

hmm

yes i know what its asking me to do

[restive river]

uhh61

@tame palm come back my friend!!!!!!

[tame palm]

Ok

[restive river]

hi

[tame palm]

Prim's Algorithm says to add the vertex connected to that edge to the spanning tree. You then consider all of the edges connected to the updated spanning tree.

[restive river]

why is b to g one of them

i thought making a cycle wasnt allowed

[tame palm]

Because it is an edge connected to the spanning tree.

The purple are candidate edges.

Green is the current spanning tree.

[restive river]

right

[tame palm]

BG is an edge specified in the adjacency matrix given by the problem.

[restive river]

so

the minimum weight is then 61+18?

i thought the tree would have looked like this 😭

[tame palm]

No, you need to connect all of the vertices to find the minimum spanning tree. Prim's Algorithm gives you a methodical method to find that minimum spanning tree that has edges with the smallest weight.

[restive river]

so you are saying it would be like this?

or do i need to connect the top right part too?

sorry i am very new to this topic

and my worksheet i dont know if im stupid or its just not very clear

[tame palm]

No.

[restive river]

oh

[tame palm]

You determined that AB is the lighter edge so you add B to the spanning tree connected to A.

[restive river]

yes

[tame palm]

From there, you examine all of the edges connected to the updated spanning tree (green).

[restive river]

oh

[tame palm]

Which edge has the lightest weight amongst the candidate edges (purple)?

[restive river]

18

[tame palm]

Ok, and that edge is connect to vertex G so you add that vertex to the spanning tree.

[restive river]

so

is this the total tree

[tame palm]

Now consider all of the candidate edges connected to the updated spanning tree.

[restive river]

8!!!

[tame palm]

Good.

[restive river]

oh

do i take 29?

[tame palm]

Check all of the edges. There is one that is less than 29.

[restive river]

oh

28

g toc

[restive river]

now its 29

[tame palm]

Correct.

[restive river]

33?

i rthought i couldnt make loopsss

[tame palm]

You can't.

[restive river]

oh okay

then 51

[tame palm]

EF is not a valid connection to make in the minimu spanning tree.

Correct.

There. Now all of the vertices are connected and you have a minimu spanning tree.

[restive river]

so this is the tree!!!!!

[tame palm]

Now all you need to do is add the weights of the green edges to calculate the weight of the minimum spanning tree.

[restive river]

so the mimimum weigh is 195

[tame palm]

Yes.

[restive river]

yesssss

thank you so much bro

[tame palm]

yw

[restive river]

genuinely u helped make it so much more clear

[tame palm]

Do you understand how the algorithm works now?

[restive river]

yesss

[restive river]

i have one more question

if that is okay with you

[tame palm]

Ask away.

[restive river]

it is

my worksheet does not mention any of those

so i dont really know what they mean

and whatever this is

i asked my mom and she said google but google isnt

understanding me

[tame palm]

Do you know what a Eularian Graph is?

[restive river]

well

only from what i have googled

lol

its a graph that has a connection to every verticie

i think?

[tame palm]

No. A Eularian Graph consists of vertices that are an even degree. The degree of a vertex is the number of edges connected to it, that includes looping edges.

[restive river]

doesnt it always have to be even

[tame palm]

In the above graph, vertex B has two edges connected to it so it is an even degree.

Yes, a Eularian Graph can only have vertices of even degrees.

[restive river]

well

d doesnt have even

or a

[tame palm]

A Semi-Eularian Graph can only have two odd vertices.

So is the graph above a Eularian Graph?

[restive river]

no

only a and d

so it is semi

[tame palm]

👍

[restive river]

so if it had more then

2 odd ones

it would be neither?

[tame palm]

Correct.

[restive river]

okay i see

ty very much

[tame palm]

yw

[restive river]

can i know the website you were using to helkp me

[tame palm]

I'm not using one.

[restive river]

oh

you were just drawing lines haha

[tame palm]

I made the graph using Geogebra.

[restive river]

if i follow these instructions for this question

will i get it right

[tame palm]

https://www.geogebra.org/classic/uuhxmutv

That's a link to the Geogebra file I made the Minimum Spanning Tree in.

[restive river]

isee

ty

[tame palm]

I don't see why not.

[restive river]

is there an easier way

[tame palm]

Probably not. If you do find one, you should share it with the world. 😉

[restive river]

okay

i am working on it

[restive river]

FOR d to h

why is it 0

oh

its not

lol

its 2?

[tame palm]

The edge connecting D to H? It has weight of 2.

[restive river]

yah okay

if i follow these instructions for this question

oops

[tame palm]

You forgot EH.

[restive river]

sorry im making the things

pop up on my page

[restive river]

oh yes

what does it mean by all possible pairings

[tame palm]

Any edges that connect two odd vertices.

[restive river]

theres none

directly

oh pairings

so two

or 4

umm

cause there is no 2

this better not be a 2 paths thing

where has my king gone

[devout snow]

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.

[steady onyx]

how do I determine the coefficent of a³b²c² in the development of (a+b+c)^7

[fervent sundial]

do you know the multinomial theorem?

[steady onyx]

i believe so

it is just tricky doing it with the three terms instead of two

[fervent sundial]

I mean you can read off the coefficient if you know the multinomial theorem lol

the coefficient of a^3 b^3 c^2 is just

,, {n \choose {3,2,2}} = {7 \choose {3,2,2}} = \frac{7!}{3! \cdot 2! \cdot 2!}

[steady onyx]

so

[woven radish]

kanna

[steady onyx]

yeah

[fervent sundial]

yeah so it's just 210

[woven radish]

Result:

210

[steady onyx]

would this correspond with the multinomial theorem?

[fervent sundial]

no that's the binomial theorem

bi = 2 things

[steady onyx]

oh

[fervent sundial]

multi = more than 2 things

,, (x_1 + x_2 + x_3)^n = \sum_{k_1 +k_2+ k_3; k_1,k_2,k_3 \geq 0} {n \choose k_1, k_2,k_3} \prod_{l=1}^mx_l^{k_l}

[woven radish]

kanna

[steady onyx]

then i havent done that yet

could you find the answer using binomial theorem?

[fervent sundial]

I mean binomial theorem is for binomials (sum of two terms)

a + b + c is the sum of three terms

[steady onyx]

true

however i have been asked this question in the context of a binomial theorem chapter

[fervent sundial]

well i guess you can treat a+b as one term and c as another

[steady onyx]

hmm

i will have a go at that

thank you

.close

[devout snow]

Channel closed

Closed by @steady onyx

Use .reopen if this was a mistake.

[steady onyx]

.reopen

[devout snow]

✅

[steady onyx]

I have had an issue with that

where i get (a^(7-i))*(b^i+c^i) = a³b²c²

.close

[devout snow]

Channel closed

Closed by @steady onyx

Use .reopen if this was a mistake.

[fervent sundial]

did you still need?

U didn't ping me so i didn't see lol

[steady onyx]

yeah

[fervent sundial]

you should probably reopen your channel first

[steady onyx]

.reopen

[devout snow]

✅

[fervent sundial]

,, (a+b+c)^7 = \sum_{k=0}^7 {7 \choose k} a^{7-k} (b + c)^k

[woven radish]

kanna

[fervent sundial]

we had the splitting into two terms thing i mentioned prior right?

[steady onyx]

yeah

[steady onyx]

what i tried here

[fervent sundial]

we want the coefficient of a to be 4

so 7 - k = 4

k = 3

[steady onyx]

yeah

[fervent sundial]

actually wait

we want the coefficient of a to be 3 not 4

so k = 4

[steady onyx]

mhm

[fervent sundial]

so we have ${7 \choose 4} \cdot a^3(b + c)^4$

finally we want b^2 c^2

,, (b+c)^4 = b^4 + 4b^3c + {\color{red}6}b^2 c^2 + \ldots

[woven radish]

kanna

[fervent sundial]

so the coefficient of b^2 c^2 is 6

[woven radish]

kanna

[steady onyx]

you're quick

gimme a sec

[fervent sundial]

LOL

okay okay

[steady onyx]

okay i get it

[fervent sundial]

yeah so it's just ${7 \choose 4} a^3 \cdot (b^4 + 4b^3 + {\color{red} 6b^2 c^2} + \ldots)$

[woven radish]

kanna

[fervent sundial]

the coefficient is then just 7C4 * 6

[steady onyx]

which alligns with the multinomial

[fervent sundial]

since technically you just have ${7 \choose 4} a^3 6b^2 c^2 = {7 \choose 4} \cdot 6 a^3 b^2 c^2$

[woven radish]

kanna

[fervent sundial]

yeah it should

,w (7 choose 4) * 6

[woven radish]

Results provided by WolframAlpha

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

Requested by kannaaaaaaaaaaaaaaaaaaaaaaa

[fervent sundial]

anyway yeah multinomial was probably quicker lol

[steady onyx]

i guess

[steady onyx]

but how would you get 7 choose 6 * 6 from this?

[fervent sundial]

what do you mean?

it's 7 choose 4 btw

[steady onyx]

o yeah

[fervent sundial]

well to recap we wrote out the binomial formula

https://cdn.discordapp.com/attachments/903486480075354182/1217232987238699131/687632422212468806.png?ex=6603478f&is=65f0d28f&hm=f6ff0a254c29dfb2d316c0d63f726c2fbcc741505634cc218f95f090ade85e6d&

[steady onyx]

indeed

[fervent sundial]

we want the exponent of a to be 3 but now it's at 7-k

7-k = 3 gives k = 4 for which we'd have a^3

so now we sub the value k = 4 into this part:

so we get:

7C4 * a^3 * (b+c)^4

our goal is to get b^2 c^2 from the (b+c)^4 term

[steady onyx]

from what it was in the original form

[fervent sundial]

(b+c)^4 = b^4 + 4b^3 c + 6b^2 c^2 + .... so the coefficient with the b^2 c^2 is 6

[fervent sundial]

so this just boils down to 7C4 * a^3 * 6b^2 c^2

the coefficient of a^3 b^2 c^2 is then just 7C4 * 6

are you still confused or do you get it now? Lol

[steady onyx]

how is it that you can elect 6b^2 c^2 if that isnt (b+c)^4 full form

or am i just not thinking straight

[fervent sundial]

,, {7 \choose 4} a^3 (b^4 + 4b^3 c + 6b^2 c^2 + ...)

[woven radish]

kanna

[fervent sundial]

but do you notice that you multiply 7C4 * a^3 to every term?

[steady onyx]

yes

[fervent sundial]

,, {7 \choose 4} a^3 (b^4 + 4b^3 c + 6b^2 c^2 + ...) = {7 \choose 4}a^3 b^4 + {7 \choose 4}a^3 \cdot 4 b^3 c + {\color{red}{7 \choose 4}a^3 \cdot 6 b^2 c^2} + \ldots

we're only concerned about the red term

[steady onyx]

okay

[woven radish]

kanna

[fervent sundial]

i'm just expanding the left hand side btw if that wasn't apparent

since u said i "elected"

i elected cuz the red thing is the only thing that matters

but i think it should be fairly obvious now that i expanded things out

[steady onyx]

yes i think so too

i might be a bit tired actually

because you have given plenty of explanation

i will review it tomorrow and it should probably click then

[fervent sundial]

I mean you can come back to it later

yeah

[steady onyx]

okay

well i appreciate your help very much

and you patience even more

[fervent sundial]

sure, no worries lol

hopefully you get it the second time around

[steady onyx]

okay, thanks a bunch

.close

[devout snow]

Channel closed

Closed by @steady onyx

Use .reopen if this was a mistake.

[devout snow]

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.

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.

[devout snow]

The original post of this help channel has been deleted, and it will abruptly close and possibly lock. (This is irreversible.) Please claim a new channel, and don't delete the first message of any future channel you claim.

[prime narwhal]

(didnt mean to)

i sent it again

[dense jay]

the channel is going to lock

[prime narwhal]

bruh

ill open a new one

.close

[eager nova]

Just open a new one

[devout snow]

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 sigil]

i need help with calculus

dinner with kanye

lmfao

[devout snow]

@sturdy sigil Has your question been resolved?

[devout snow]

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.

[ember notch]

can someone explain? teacher barely went over it

[mortal vale]

looks right to me

[ember notch]

OH I FORGOT THE DEGREE SYMBOL

wow

[devout snow]

@ember notch Has your question been resolved?

Channel closed

Closed by @ember notch

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.

[restive river]

Hey, is finding the rate of change of a given function $f$ at point $P$ in the direction of unit vector $\vec{u}$ exactly the same as computing $D_{\vec{u}} f(P) = \nabla f(P) \cdot \vec{u}$?

[woven radish]

00

[timber pebble]

maybe this answers your question? https://tutorial.math.lamar.edu/classes/calciii/directionalderiv.aspx

i believe you have the form though

[restive river]

I'm unable to open the link

I was just wondering if the directional derivative gave the rate of change of f at a certain point

[timber pebble]

it gives you the rate of change in a certain direction

for a 2 variable function it doesnt make sense to say "the rate of change" as in a number

you have to say in some direction

or generalize to the gradient

[timber pebble]

again i think you got it right

[restive river]

Yep, thank you for confirming

Have a good one

.close

[devout snow]

Channel closed

Closed by @finite fulcrum

Use .reopen if this was a mistake.

[devout snow]

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.

[worthy oxide]

hi i need help understanding how to tell if a function is convergent or divergent using the comparision theorem

i have watched a few videos about it but i cannot seem to grasp it

i know that this function is convergent but it would be helpful to see the work and thought process behind it

thank you any help is appreciated

[eternal tree]

well $\frac{1}{x+e^{2x}} < \frac{1}{e^{2x}}$ for $x > 1$

[woven radish]

Waffloid

[worthy oxide]

yea that makes sense

[eternal tree]

but then, we can explicitly evaluate $\int_1^N e^{-2x}$

[woven radish]

Waffloid

[worthy oxide]

what is N?

[eternal tree]

just some dummy variable that we'll take to infinity after we evaluate the integral

technically u could just directly go and calculate $\int_1^\infty e^{-2x}$, depends how formal u wanna be

[woven radish]

Waffloid

[worthy oxide]

oh ok why do we want to calculate that integral?

[eternal tree]

this inequality tells us that it should be strictly bigger

so if the bigger integral converges, then the smaller one does too

ie we apply the comparison test

[worthy oxide]

bigger out of 1/e^2x and 1/x ?

why are we only taking one part out of the integral if that makes sense?

[eternal tree]

okay ill explain my thinking

we want to show that $\int_1^\infty \frac{1}{x+e^{2x}}$ converges

[woven radish]

Waffloid

[eternal tree]

the way id want to do this would be to just calculate it direclty and be like "this is equal to some number C so it converges!"

but instead we arent so lucky and we cant calculate it direclty

so instead, we want to find an integral, that should be strictly larger, that we can calculate the value of directly

[eternal tree]

because if this thing is smaller than some finite number, then it must also converge

thats why i compare it against $\int_{1}^\infty \frac{1}{e^{2x}}$

[woven radish]

Waffloid

[eternal tree]

dropping the x term gives me a smaller denominator, so overall a larger function

and thus overall a larger integral

[worthy oxide]

would'nt 1/x be bigger?

[eternal tree]

well yea

but thats way too much bigger

roughly speaking i chose this one coz its a better estimate for 1/(x+e^2x)

the integral $\int_1^\infty 1/x$ doesn't even converge

[woven radish]

Waffloid

[eternal tree]

so while indeed you could try to compare against this, it doesnt tell u anything

[worthy oxide]

ok i think i got it btw the problem is asking if it is convergent or divergent not necassarily trying to prove convergence

[eternal tree]

sure

[worthy oxide]

alright so we evaluate1/e^2x

as an integral?

[eternal tree]

yea

we're saying that $\int_1^\infty \frac{1}{x+e^{2x}} < \int_1^\infty \frac{1}{e^{2x}}$

[woven radish]

Waffloid

[eternal tree]

so ye

you can just plug in the integral of e^-2x and put the bounds in

should give you $e^{-2}/2$ overall

[woven radish]

Waffloid

[worthy oxide]

-2 what about the x

?

oh ok

yea i got

[eternal tree]

we calculate the indefinite integral of $e^{-2x}$ as $-\frac{1}{2}e^{-2x}$

[worthy oxide]

it

[eternal tree]

then we sub it in

yeah

sure

[worthy oxide]

yea that makes sense

ok well

[woven radish]

Waffloid

[eternal tree]

okay cool

[worthy oxide]

so if it was convergent it would be infinity right?

or sorry

[eternal tree]

?

[worthy oxide]

divergent

[eternal tree]

yes, but be careful

you can't conclude from an upper bound estimate that your integral is divergent

[worthy oxide]

?

[eternal tree]

eg if you said $\int_1^\infty\frac{1}{x+e^{2x}} \leq \int_1^\infty \frac{1}{x} = \infty$

you cant conclude from this that the integral is divergent

[worthy oxide]

because that would be false rightt?

[eternal tree]

well this is true

[worthy oxide]

or because you jsut cant use the upeer bound

[eternal tree]

its just that this doesnt tell us anything

[woven radish]

Waffloid

[eternal tree]

yeah lol

the comparison test doesnt apply here

[worthy oxide]

how would that be true tho?

[eternal tree]

well whats wrong?

[worthy oxide]

1 over infinity would be 0 right

?

wiat

never

mind

its an integral

[eternal tree]

yep

the integral is ln

[worthy oxide]

ok so you would use lower bound for divergence?

[eternal tree]

exactly

[worthy oxide]

if you did not know before hand if it was divergent or convergent how would you start then?

or would you just use both

[eternal tree]

you develop an intuition for whether an integral is divergent or convergent

theres some rules of thumb

eg, if we had $\int_1^\infty \frac{1}{3x^2 + x}$

[woven radish]

Waffloid

[eternal tree]

i know that this is "basically" the integral of $\1/x^2$, which i know converges in this interval

[woven radish]

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

[eternal tree]

to make this precise, id give an upper bound of 1/3x^2 and note that this converges

in general, the behaviour of convergence/divergence is roughly determined by the most powerful term, so u can ignore the smaller things and just look at how that behaves

this is prolly quite vague without context tho, so feel free to send a few more examples and i can be more concrete

[worthy oxide]

what would be the lower bound in this problem

ok i will send one more

thank you for your help

btw

i really appreciate it

[eternal tree]

no worries :)

[eternal tree]

interesting

hmm

thats a lot less obvious

my first thoughts are

as x is small, sin(x) is roughly x

and i think(? will have to double check) that the integral of 1/x^2 diverges if its in an interval 0 to something positive

which would mean this diverges

yeah i think this works

[worthy oxide]

ok

so

let me think for a minute

where did you get x^2

?

[eternal tree]

intuitively, sin(x) and x are almost the same for small x

eg look at the graph;

so i thought about whether it converges if i replace sin(x) with x, since as they are so similar they should have the same answer

[worthy oxide]

ok but doesn't sinx go up and down while x would just go up forever?

[eternal tree]

true, but look at the bounds we are integrating over

0 to pi/2

[worthy oxide]

ohohohohoho

oyeoyoayroeuo

yea

yea

okokok yea

ur right

[worthy oxide]

ok yea that makes sense

but why would it be divergent would'nt 2/(pi/2)^2 be a number ?

[eternal tree]

wdym?

[worthy oxide]

like when you intgerate 2/x^2

wait

[eternal tree]

yeah but try evaluate that at 0

[worthy oxide]

yea at 0 it would be 0

[eternal tree]

uhh

you'd be doing 1/x and x = 0

[worthy oxide]

but then it would be - the pi 2 right

so does the first part being non existent completly negate the other part

[eternal tree]

i dont follow

[worthy oxide]

like it is for sure divergent if it is ever divided by 0?

like any time 1/0 or 3/0

subrtact by the other plug in during the function

it would always be divergent?

[eternal tree]

i think so

[worthy oxide]

ok

yea that makes

sense

[eternal tree]

like, the way id justify it is

say the integral of f(x) is F(x), and i want to calculate, say, the integral of f between 1 and 0, which is F(1) - F(0)

if calculating F(0) is given by 1/0

then close to 0, we have stuff blowing up to infinity

eg

F(0.01) would be like 1/0.01 = 100

F(0.0001) = 1/0.00001 = 100000

so when we see a 1/0, its pointing at the fact we have this blowup happening

[worthy oxide]

ok i think i get it

yea

ok

alright i have one more question if that is alright

[eternal tree]

sure

[worthy oxide]

wait

actually i think this exsplanation answered

the question

[eternal tree]

great

[worthy oxide]

but let me make sure

[eternal tree]

go for it

[eternal tree]

fun

[worthy oxide]

so this would be divergent because it would be ln(1/0 +tan()) right?

[eternal tree]

hmmm

maybe, ill walk u through what im thinking

sorry thats nonsense LOL

hmm

looks pretty divergent

[eternal tree]

but this alone isnt a proof

u can turn it into one though along the lines of what i was saying though yes

personally id consider smth like

$\int_0^x 5\sec(x)$

[woven radish]

Waffloid

[eternal tree]

plug in ur integral for this

and then note that taking x to pi sends the value to infinity

[worthy oxide]

ln(sec+tan)?

[eternal tree]

which is basically the same as what u said

[eternal tree]

yea

tan(pi) = 0 but sec(x) -> infinity as x -> pi

informally sec(pi) = infinity

so ln(sec(pi)+tan(pi)) =ln(infinity)= infinity so it diverges

to make this "formal" though we talk about limits

the level of detail ur argument needs depends on ur teacher tho ig

but u were right all along anyway

soz for dragging it out a bit, seems you understood my point better than i did...

[worthy oxide]

Ok

My computer just died btw

On my phone now

But yea

I think i got it for the most part

Have a great day

[eternal tree]

wonderful

[worthy oxide]

.close

[eternal tree]

thanks you too

[devout snow]

Channel closed

Closed by @worthy oxide

Use .reopen if this was a mistake.

[devout snow]

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.

[polar cargo]

Pls help me.

[polar cargo]

Algebra 1

I’m not sure what 8 is asking on part b and c. The 9 is just confusing

[steady forge]

can you show the top of the page

[steady forge]

,rotate

[steady forge]

could you explain which part is confusing

[polar cargo]

Where it says to find the distance I’m not sure how to do it. Am I supposed to add the or that part C. Or add them?

[steady forge]

well its just asking the distance between the points

[polar cargo]

Do I add it

[steady forge]

well how would you get the distance here

[polar cargo]

Adding 5

[steady forge]

could you explain what you mean

[polar cargo]

No you add 10 oops. Cause you add 5 to get to zero then add 5 to get to five

[thin pagoda]

Man just use chat gpt

[steady forge]

yes

so 5-(-5)

[steady forge]

go ahead and get your answers wrong

not really my problem

[thin pagoda]

Help me

5. b

[steady forge]

this is not your channel

open your own

[thin pagoda]

Why

[steady forge]

open your own.

[thin pagoda]

Why though

Will you help

[steady forge]

because it's rude and it's not that hard

open your own channel

[steady forge]

do you think you can try figure out c?

[polar cargo]

I’ll try then let you know if I got it

Got 75. I put zeros for the x’s

[steady forge]

well, it's asking for the width of both arches, not how high the arch is

[polar cargo]

Not 15 a 10 and 19

10

20

Answer=20

[steady forge]

yes

[polar cargo]

For 9. Am I just plugging in the 3 for t?

[steady forge]

yep

also for your factored form

factored form of a quadratic is just y=a(x-x1)(x-x2) where x1 and x2 are the zeroes of the function

so you don't have to solve

recheck your factoring though

[polar cargo]

Opps I wrote 8

[devout snow]

@polar cargo Has your question been resolved?

Channel closed

Closed by @polar cargo

Use .reopen if this was a mistake.

[devout snow]

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.

[manic osprey]

Can someone explain how they got 5 to the power of 2 like is there a rule or something

[weak cove]

yes, ln(a^b)=bln(a)

[manic osprey]

Is there any reasoning behind it, also do u by chance know where I can drink find all the rules

[weak cove]

of course there is a reason, I suggest you search something like "properties of logarithms" on youtube or khan academy

[manic osprey]

Oh it’s in my notes lol

Wait

I don’t get this

[weak cove]

What do you not understand?

[manic osprey]

How does it turn into In10

[weak cove]

they swapped the direction of the equality

[manic osprey]

Damn😿

[weak cove]

It's just a question so I can help

take the first line

swap it around

10=e^(5-3x)

then take the ln of both sides

ln(10)=ln(e^(5-3x))

[manic osprey]

Why

[weak cove]

and another log property for you

ln(e^(a))=a

so that is why

[manic osprey]

How do u know to take In of both sides

[weak cove]

because you want to solve for x

and it's up in the power of e

so you want to get it down

you want to undo the exponentiation

ln is the inverse of exponentiation

just like multiplication inverts division

if you have 5x=10

you divide

because you want to undo the multiplication by 5

to solve for x

so when you have y=e^x

you take the natural log

to undo the e^...

ln(y)=x

Does that help you understand?

I still think you should go watch some videos

[manic osprey]

Ok so

e^y like e^5-3x and it equals x like 10 then Inx = y so In10 = 5-3x

Then isolate x

[manic osprey]

Ye

any suggestions

[weak cove]

https://youtu.be/LRbi_pMX1DM?si=jzcJh4moQsWrBfSz

[manic osprey]

Thank you

[devout snow]

@manic osprey Has your question been resolved?

Channel closed

Closed by @manic osprey

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.

[rain bluff]

The bee population in a certain area is declining at an uninhibited rate of 36.5% per year. How long will it take for that population to be one-fourth of the initial population?

[topaz axle]

do you know what logarithms are?

[rain bluff]

mhm

essentially yes

[topaz axle]

they are just saying that 0.635^x = 1/4

so x = log_0.635(1/4)

[rain bluff]

wait wait wait

hold on i need small steps

[topaz axle]

i didn;t say any steps

i think

[rain bluff]

you didnt im just saying i need a slow roll lol

[topaz axle]

after one year the population becomes 0.635 of whatever it was

[rain bluff]

like baby steps

why is that?

[topaz axle]

because it loses 0.365

so the first step is you read 36.5% as 0.365

then 1 − 0.365 = 0.635

that's how much is left after one year

[rain bluff]

oh

hm

thats not one of the options

[topaz axle]

why would it be one of the options

i'm surprised that i'm not surprised

[rain bluff]

sorry no not that i tried to fully solve it

[topaz axle]

ah my bad

[rain bluff]

that being your calculation of how much was left after 1 year

no no thats on me and my talking to myself

[topaz axle]

you probably need to know this formula to solve it this way

you use x = e

so the calculator has a button for this

[rain bluff]

mmmm symbolab time

[topaz axle]

b = 0.635
a = 1/4

what are the options?

maybe i also didn;t get any of them

[rain bluff]

probably not, i was doing it a weird way lol

11.3 and 3.8

[topaz axle]

what, 2 options?

[rain bluff]

yep

weird right

[topaz axle]

well it's not any of them, so i need to start from scratch

[thin pagoda]

Use chat got

[rain bluff]

lmao

worst advice possible

chatgpt is somehow dumber than me

[thin pagoda]

Snapchat AI?

[rain bluff]

[topaz axle]

ok 3.8 is waht they want

[rain bluff]

how did we get there?

[topaz axle]

i can't explain it though

it's not 36.5% per year, it's a fake number

[rain bluff]

??

fake number

<@&286206848099549185> second opinions?

[rain bluff]

this is a weird ass problem considering it has just 2 options

[topaz axle]

0.365 is the rate constant

[rain bluff]

ok

[topaz axle]

,calc exp(-0.365)

[woven radish]

Result:

0.69419665087798

[topaz axle]

so this is the actual "what's left", instead of 0.635

then it works out to 3.8

so it works on an arbitrary rule, and they phrased it in a way like they meant a sensible rule

[rain bluff]

oh

this is weird

thank you for sticking with it tho!

[rain bluff]

this is how you got there right

[topaz axle]

i didn't, i don't know that much calculus

they just give the solution right afterwards https://en.wikipedia.org/wiki/Exponential_decay

[rain bluff]

interesting..

this isnt calc however

this is alg2

[topaz axle]

then they give the formula

[rain bluff]

there must be a more reasonable way to get this one

[topaz axle]

at some point in some way

nope

[rain bluff]

strange stuff

thanks frownyfrog!

.close

[devout snow]

Channel closed

Closed by @rain bluff

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.

[fallen condor]

How do you use QR factorization of a matrix to find its orthonormal basis?

[fallen condor]

I was under the impression that you need to know the orthnormal basis to find its QR factorizatoin

[wicked turtle]

isn't this essentially gram-schmidt?

[devout snow]

@fallen condor Has your question been resolved?

[dawn cairn]

yes

[devout snow]

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.

[restive river]

Why is the equation of wave not y = Asin(omega(t) - kx)

[wicked turtle]

it's probably looking at one fixed value of x

[restive river]

They didn’t specify

So I’m confused

[wicked turtle]

hard to say without any context

[restive river]

He just wanted to explain beats. So he considered these two waves to explain their interference

That was the first step

Wait this is a screenshot of the pdf he provided