help-17

[safe sedge]

it might be tbh

[spiral inlet]

180 isn't even a factor of a if that's really 33

I'm guessing it's supposed to say 3^3

[safe sedge]

yeah i was thinking

ill try 3^3

[spiral inlet]

do you know how to approach this then?

[safe sedge]

if its 3^3 then yes

[spiral inlet]

cool 😎

[safe sedge]

.close

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[exotic delta]

i need help with my discrete math. Using the replacement rule, show that each of these conditional statements is a tautology. i cant get my head around the logical equivalences (laws)
a. [~p ∧ (p ∨ q)] → q
b. (p → ~q) ∨ (~r → p)

[nocturne spade]

Can you give a list of the exact laws you are allowed to use including the replacement law?

[nocturne spade]

How were implications introduced to you?

[vocal sleet]

@exotic delta Has your question been resolved?

[exotic delta]

for the most part we use it to simplify forms or to establish logical equivalences between different expressions

[nocturne spade]

hm

We need to proof something with them.

if we do not know how they relate to the other objects then I don't know what to do.

One can define "a -> b" to be equivalent to "~a or b"

We could use that but if your course did something else, then that might not be what they are looking for here.

[exotic delta]

oh u mean that,sorry . its a → b is equivalent to ~a ∨ b

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[exotic delta]

.reopen

[vocal sleet]

✅

[nocturne spade]

ah nice

then I can start think about how to solve it lol

We actually want to prove

~(~p ∧ (p ∨ q)) ∨ q

I suggest trying de morgans law a bunch of times

@exotic delta

As a general pointer

we are trying to transform the problem using equivalences to something that we know to be true.

[exotic delta]

alright ill try that

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[vivid sapphire]

hi

[lilac plaza]

🤦

[vivid sapphire]

I need help with this question, I understand functions like plugging in 5-x^2 into what though

[vivid sapphire]

whatsup

[lilac plaza]

I told you

How to solve

What have you tried so far

[vivid sapphire]

I really didnt understand bro Im sorry

[lilac plaza]

Tell me

What do you not understand

I'm here for you

[vivid sapphire]

I tried to plug into 5-x^2 into the thing in the right

but for what

[vivid sapphire]

appreciate it a lot

[lilac plaza]

What did you plug in?

[vivid sapphire]

into the x

and then I wrote g(5-x^2 +h)

and then the rest

its most likely wrong

[nocturne spade]

!noclopen

[vocal sleet]

Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem, and is confusing for helpers, making it more difficult for them to answer your question. We ask you to please be patient, even if your channel has not received much attention. If you are having a problem with a helper, please report it to <@&833154869451292722> rather than closing the channel and attempting to seek out another helper.

[vivid sapphire]

I am unsure of what to do with the g(x+h)

[lilac plaza]

Why did the h not get squared?

[vivid sapphire]

I wasnt sure what do with the h

if there was no h I would be able to do it

[lilac plaza]

You're subbing x + h into x^2

So it should be (x + h)^2, no?

[vivid sapphire]

is that what this whole thing is

what do u do with -g(x) then

where does that go

[lilac plaza]

Nothing

It's just x in this case

[vivid sapphire]

g(x+h)−g(x)/h — so I take the x+h from this part of the question and plug it into the g(x+h)=5-(x+h)^2

?

[vivid sapphire]

?

[lilac plaza]

Just sub whatever is in the (parentheses) into g(x) in x

x + h -> x

x -> x

[vivid sapphire]

But

theres 2 bracket

[lilac plaza]

Which is basically no difference

[vivid sapphire]

here

on the right one remember

which one do u look at

or if U can tell me what the topic of this question is called I can maybe watch a video and understand it a bit betterbecause its hard to type all this out

[vivid sapphire]

.

[lilac plaza]

https://www.youtube.com/watch?v=-aTLjoDT1GQ

This might be hard to understand

Just ignore all the derivative parts

I have to leave for a while

[vivid sapphire]

oh ok thanks bro

I appreciate ur help and finding me this video

[vivid sapphire]

I have a question for u though, why do u answer peoples questions, are u getting paid for this or what

[vivid sapphire]

thank u so much I finallu understand

[autumn peak]

Can someone help me with this problem

What should be my first step?

[lilac plaza]

#❓how-to-get-help

[lilac plaza]

I help other people while I get help myself

Helping others improve your memory and skill

So you don't forget concepts

[vivid sapphire]

very true

thanks a lot man

[lilac plaza]

No problem

[vivid sapphire]

is this the right answer

5- (x+h)^2 - (5-x^2) /h

[vivid sapphire]

🙏

[mild flower]

i have learned to see problems a new way from helping people here

and i just like making people happy :)

[vocal sleet]

@vivid sapphire Has your question been resolved?

[vivid sapphire]

very nice of u 🙂

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[vast shale]

answer key is 30 idk how

i got 45

what i did

[split wind]

4 sides equal doesn't mean 4 angles the same

[vast shale]

how so?

[split wind]

i.e. OPQR is not a square

[vast shale]

wait wht

idk how

[split wind]

if 4 angles are equal, OPQR will be a square

which clearly isn't

[vast shale]

oh i see

[split wind]

have you learnt concyclic quadrilaterals?

[vast shale]

no

never learned that

[split wind]

what is this chapter about?

[vast shale]

im just preparing for the sat and someone sent me this questrion

its geometry related stuff

[split wind]

i see

you can draw a line on OQ

and find equilateral triangles

to find angles

[vast shale]

ohh i see why its 30 now

i get it

.close

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[undone aurora]

I dont really understand this

[undone aurora]

for context this was example 1.1.2

is the relative frequency just (amount of times the event occured)/(amount of times the dice was rolled)

I dont understand the last line in the first image

why do we associate B with a number p that is close to the relative frequency for B

is it just saying that the chances of an event from B to occur is p = 0.15?

[late ingot]

it doesnt say you are assigning 0.15 to p, but a number "close to" it.

its implying 0.15 is close to what p actually is.

in other words, 0.15 is a good estimate of the true probability of event B

[undone aurora]

ah so we arent sure if its exactly 0.15

so the relative frequency is just an estimate

[late ingot]

right, but as far as the results of the random experiment go, the relative frequency was 0.15

[undone aurora]

wait what im confused now

why should we assign a number close to 0.15 then

if we know it is 0.15

why not j assign 0.15

[late ingot]

idk, the wording says "might"

[undone aurora]

mhm

can I ask another question

I dont understand this at all

p =2/5 for A would mean the chances of A occuring is 2/5 correct

now where did they get p/(1-p) from

wth is that

[late ingot]

probability it happens / probability it doesn't happen

1 - p is the opposite event's probability.

[undone aurora]

oh so

why do we divide them

[late ingot]

ratio of success

[undone aurora]

like what does dividing them give us

[undone aurora]

what does that mean i dont get it sorry

probability it happens \neq ratio of success ?

[late ingot]

success % / loss % = odds

[undone aurora]

and what about when they say

either side of bet "win 3 units if A occures and lose 2 if it does not occur"

how did they conclude that

from that formula

[late ingot]

2/3 represents "two to three" odds

[undone aurora]

but how did they find the value for winnin units and losing units

like if the numerator = units they will lose if it doesnt occur

[late ingot]

for every 2 wins, there are 3 losses on "average." or the inverse, for every 3 wins, there are 2 losses on "average".

[undone aurora]

and denominator = units they will win if it does

[undone aurora]

oh

so lets say we had 5/7 then that would mean for every 7 wins theres 5 losses

[late ingot]

reverse the conclusion

for every 5 wins there are 7 losses

[undone aurora]

oh so the top is wins and bottom is losses

[late ingot]

because p (chance of winning) is the top side of the ratio

[undone aurora]

ye right

bet

tysm

[late ingot]

when they talk about "two sides" of the bet, they mean betting "against" p when it is inverted.

[undone aurora]

so the other side would be for every 7 wins theres 5 losses?

[late ingot]

right, and it offers lower odds, you bet 7 units, you win 5 units

[undone aurora]

ooo

alr I think I understand it now

tysm

[late ingot]

dont go to a casino whatever you do lmao

[undone aurora]

😭

.close

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[distant umbra]

Btw I don't have the textbook so I can't see example 4

[flat whale]

Khan academy is good for learning how to plot

[distant umbra]

I don't understand what I'm supposed to do

We learned power functions but never learned this and it's homework

[flat whale]

Which part don't you understand?

Plotting?

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:standard-form-quadratic/v/graphing-a-parabola-using-roots-and-vertex

[distant umbra]

5.a and 6.a

[distant umbra]

Thanks but I'm supposed to graph 0 and 10?

[flat whale]

Yes that's not as hard

r is the x axis

A(r) will be the y-axis

So for example one point on your graph will be (0,0)

And another will be (1,pi)

Keep getting points until you figure out the graph

And don't go beyond r=10

[distant umbra]

Ok I'll try thanks

Also idk how to use pi like that yet we didn't learn it

.close

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[trim acorn]

I’m unable to solve this problem. I understand it up to the final step where it goes to 93 fives but idk why it goes to 93 fives and not 93 sixes

[mild flower]

what's 1000 - 444?

[vocal sleet]

@trim acorn Has your question been resolved?

[paper depot]

,rccw

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[trim acorn]

God damnit I had to go and it closed again

I’m unable to solve this problem. I understand it up to the final step where it goes to 93 fives but idk why it goes to 93 fives and not 93 sixes

[trim acorn]

Hi yeah I’m available for awhile now so I won’t vanish this time

[mild flower]

what is 1000 - 444?

[paper depot]

,rccw

[paper depot]

@trim acorn yeah, i'm with hayley here, what's 1000 - 444?

[vocal sleet]

@trim acorn Has your question been resolved?

[paper depot]

so much for "won't vanish"!

[mild flower]

[paper depot]

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[reef veldt]

.close

.help

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Commands:
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[reef veldt]

hi

[reef veldt]

how do i do this

The answer is 81:100 but idk how

hello?

[merry python]

are both the pentagons regular?

[reef veldt]

uhm no it doesnt say we are supposed to use this formula

[merry python]

oh okay

so what is the given information?

[reef veldt]

"In each part below the figures are similar. Find the ratio of a side on the smaller figure to the matching side on the larger ,then find the pro numeral

[merry python]

so in the question side lengths of both pentagons have beem given?

[reef veldt]

yeah smaller one is 4.4 cm and larger is 6.875 cm

[merry python]

wait, is that the area or side?

[reef veldt]

I'm so sorry thats the area the side of the smaller is 2 and for the larger is y

[merry python]

,w sqrt(6.875)/sqrt(4.4)=y/2

[twin meteor]

Results provided by WolframAlpha

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

Requested by beard420

[merry python]

well, indeed y=2.5

are you sure the answer is 81:100?

[reef veldt]

I'm sorry this textbook is so confusing it's driving me insane. its 4:5

[paper depot]

what does "pronumeral" mean here

[reef veldt]

y

where it says length is y cm

[merry python]

well yeah.
2:2.5 is just 4:5

[paper depot]

lmao why not just say "find y"

[reef veldt]

OH wait I get it now THANKS SO MUCH

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[hybrid totem]

I think the question is wrong

[hybrid totem]

For a.)
At the top of the swing, diam is 2r so circumference is 2πr,
Half of that is πr which is how much the string is shortened by

Never minddd

Its shortened by 1/4 of the circumference

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[austere creek]

Hi, How can i multiply (x+1)? xd

[vast shale]

what is happening in there

explain and provide context please?

[austere creek]

it’s about algebra

[vast shale]

again what are u doing

[fathom drum]

it says to multiply (x+1) and (2x-4)

[vast shale]

your picture is extremely vague

[austere creek]

oohh, I thought that’s a 2 sorry, thanks for answering though

how can i cloose this?

close*

[fathom drum]

type “.close”

[austere creek]

.close

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[slender stone]

wt does it mean by trasnforamtion?

[fathom drum]

,tex .transformation rules

[twin meteor]

rti

[slender stone]

so will it move horixontally

[fathom drum]

Yes

And vertically

[slender stone]

does it stretch

@fathom drum

[fathom drum]

check the table I sent

[slender stone]

i did

[fathom drum]

look for the entries that say “stretch”

do you see these forms in the equation?

[slender stone]

yep

[fathom drum]

where

[slender stone]

af(x)

[fathom drum]

do you see these forms here?

[slender stone]

forms for y=(x-1_^3+2 or the transformation

[fathom drum]

for the first one

[slender stone]

no i cant find anything that has the power of 3 in it

[fathom drum]

so, is it a stretch?

[slender stone]

nno

[fathom drum]

so it doesn’t

[slender stone]

yep

[fathom drum]

so, can you graph it

[slender stone]

no

[fathom drum]

Why not

[slender stone]

cuase there are no transformations that relate to the on in the question

[fathom drum]

There are

[fathom drum]

see

[slender stone]

so we only doing it for inside the bracket?

[fathom drum]

What do you mean

[slender stone]

(x-1)

[fathom drum]

I think so

[fathom drum]

But can you state that in a full sentence

[fathom drum]

doing what for what inside the parentheses?

[slender stone]

no

[fathom drum]

Well then I can’t help you

[slender stone]

wait do i move horizontally by 1 unit

[fathom drum]

Yes

[slender stone]

i didnt know wt u were saying

[fathom drum]

And I didn’t know how much you understood

[slender stone]

should i graph it first then do hte transformation?

hello

@fathom drum

[fathom drum]

Ok

[fathom drum]

This is already the graph you need

[slender stone]

so wt unit in the equation to i move horizontally by 1?

[slender stone]

nvmd i got it thx

.close

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[indigo copper]

sorry my question closed earlier and i couldnt figure out how to reopen:

what is the difference between combinations with repetition and stars and bars or are they the same. If so, what situation would each be used for?

[hybrid flicker]

Sorry if I'm a bit unfamiliar with "stars and bars"

[indigo copper]

the technique where u have a bar divide a group

[gaunt sparrow]

Stars and bars problems usually have a very recognizable pattern. By solving some you'll get the hand of it, but whenever you're trying to divide things into bins is where you'd use that.

I think they're the same as combinations with repetition also

[indigo copper]

would u use this is a different type of q?

or the same

[gaunt sparrow]

No I'm pretty sure they come down to the same problems

[indigo copper]

is there a way to tell when to use?

as sometimes questions want you to assume its indistinguishable and i find myself unable to that often 😅

[gaunt sparrow]

I wouldn't say there's a clear cut definition of when you'd use them, but as I said, these problems are solvable this way because they have a very recognizable pattern that you can build intuition on picking up by solving a couple of them.

[indigo copper]

yup thank u so much!!

[gaunt sparrow]

No worries, there should be plenty of examples online that will help you through that, and perhaps even tricks I can't think of now

[indigo copper]

.close

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[lilac plaza]

I'm trying find the center of this equation

What did I do wrong?

[obtuse sierra]

44y sus

[lilac plaza]

Why not?

[obtuse sierra]

whats 4*44?

is it 8?

[lilac plaza]

Oh

My

My brain

Thanks

.close

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[lilac plaza]

.reopen

[obtuse sierra]

lol

[lilac plaza]

tf

[vocal sleet]

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[true vapor]

Hello

[true vapor]

Can I ask if 4(y-2)²-9 =0 is able to be factored

I've been stuck on this question for like an hour now I've been trying ways to factor it

[stoic drift]

My guy, difference of squares.

(2(y-2))^2-3^2

[true vapor]

I'll try to search it up since I don't know that yet or maybe I do I just forgot 💀 it seems familiar tho

[stoic drift]

a^2-b^2=(a+b)(a-b)
Do you know this?

[fathom drum]

do you need to factor it, or do you just need to solve it

[stoic drift]

Either way, factoring will lead to the answer.

[true vapor]

Solve it

[true vapor]

Nope I don't think so

Let me see

[fathom drum]

Then you can add 9 to both sides and take square roots

[fathom drum]

oh

[stoic drift]

I see. This is a pretty common and powerful identity. You should be aware of this.

[true vapor]

Do I turn it into like standard form or something I'm genuinely confused as to what to do

Idk if I'm just bad at listening in class or I just don't comprehend everything that's said to me

[stoic drift]

Basically if you have a quadratic that's of the form a^2-b^2 you can write it as (a+b)*(a-b)

[true vapor]

I made it into this if this is right?

[stoic drift]

For example:
x^2-4=x^2-2^2=(x+2)(x-2)

[stoic drift]

That's the long way to do this. You can do this in three steps.

[true vapor]

What's a and b in 4(y-2)²-9?
Sorry might be getting in your nerves lol

[true vapor]

Oh

[stoic drift]

a^2=4(y-2)^2
b^2=9

To find a and b you can take the positive square root.

Once you get it in the form, apply the formula/identity.

[true vapor]

Ohh

[stoic drift]

Also I'm pretty patient, it's alright.

[true vapor]

Is there any explanation as to why 9 is separate? Is it because of the parenthesis?

[stoic drift]

That's just how the question was given right? Actually this form of quadratic equations are called vertex forms.

[stoic drift]

But it's mostly to hint you at using the identity.

[true vapor]

This one?

[stoic drift]

Yeah. Don't worry about it if your teacher hasn't taught you this.

It's just how the question was given.

[true vapor]

I'm still confused about the difference of squares thing, it seems like I've already watched a video of it, I rewatched it again but it doesn't have the same like layout or something.
Their examples go like
x² - 9 where both terms are perfect squares but I don't really see it in 4(y-2)² - 9
Yes 4 and 9 are perfect squares but where does the (y-2)² go?
Also is this equation solvable or just factorable?

[stoic drift]

Both.

[stoic drift]

(y-2)^2 is a square right?

[true vapor]

Oh ye right...

Where does it go tho

Can u like write it on paper if u can (if u don't want to it's alright) I just have a hard time understanding thru chat

[stoic drift]

It's not possible atm. I'll write it in latex and show you.

[true vapor]

Thank you so much

[stoic drift]

,tex $4\left(y-2\right)^{2}-9=0$
\newline $\left(2\left(y-2\right)\right)^{2}-3^{2}=0$

[twin meteor]

ℝage-EMILY

[stoic drift]

,tex Where you can take a as $2(y-2)$ and b as 3.

[twin meteor]

ℝage-EMILY

[true vapor]

OHHHH

I think I understand it now

Thank you so much

You've been a very big helper 😭

[stoic drift]

Glad to help.

,tex You will end up at this after applying the identity, try doing this part yourself.
\newline $\left(2y-7\right)\left(2y-1\right)=0$

[twin meteor]

ℝage-EMILY

[true vapor]

1 more questionnn
2(y-2)-3 is this the final answer or do I have to do another step that I definitely do not know of?

[stoic drift]

,tex You should be getting $\left(2\left(y-2\right)-3\right)\left(\left(2\left(y-2\right)+3\right)\right)=0$

[twin meteor]

ℝage-EMILY

[stoic drift]

After this, distribute the 2.

[true vapor]

Ohhh I got it so it's not just (a-b) but it's both (a-b) (a+b)

[stoic drift]

Yep.

You can check for yourself by multiplying (a+b)(a-b)

[true vapor]

Alright

Thank you for enlightening me lol the fog has finally cleared up

I COULD NOT sleep without solving this one

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[raven mauve]

I need help with the c part no matter how many bracket i put in different ways they always ends up at 22-8=14

[split heart]

You have to do the division first

[vast shale]

Nope that's wrong

[split heart]

sign of that 2 is negative

[vast shale]

Before I answer, may I see your working to point out where you are making a mistake

[final latch]

My bad

[raven mauve]

Oh wait sorry its not c part its supoosed to be (b) part made a mistake.

[split heart]

[raven mauve]

C part i did like this

I tried the b part in pencil somewhere and erased it

[split heart]

Am I high or what

[paper depot]

it's this one we're doing, right?

[raven mauve]

Yep

[paper depot]

you're parenthesizing it in ways already implied by the order of operations.

which result do you want to go for first

[raven mauve]

6

[paper depot]

right

i mean ok this is all just guess and check basically there isnt much logic to it

but 6 + (4^2 - 16) / 2

[raven mauve]

But how

[paper depot]

how what

[raven mauve]

Im getting three

Ur correct

How did u like get fhe answer 6

[paper depot]

you're calculating 6 + (4^2 - 16) / 2 and getting 3?

show your work.

[paper depot]

6 + 0 / 2 is not 6 / 2

division has higher priority

[raven mauve]

Oh then how do u ddo it

Ohhh wait

Is that how u do it?

[paper depot]

formally correct but way too complicated

did you not see that 0/2 is literally just 0

[raven mauve]

Ohhhh howd i miss that

Damn oki thank u again

. close

[paper depot]

.close

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[vast shale]

,rotate

[vast shale]

How would I start to do number 19?

Can someone walk me through it please

Is it just asking if L is increasing

[grand ledge]

in a function where the derivative is positive, it means its increasing yea

[vocal sleet]

@vast shale Has your question been resolved?

[vast shale]

👍

What about the ones that don’t say increasing or decreasing?

[grand ledge]

if its not increasing or decreasing it usually means the derivate is 0, meaning its flat

[vast shale]

So it’s basically constant there?

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[vast shale]

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[royal talon]

it is 14 if there is not any phranteses

[wraith parrot]

But te task is to put phranteses to get the values

[royal talon]

I didnt see any pranteses in orginal question

[wraith parrot]

The taks is to write pharenteses in the equations so it gives the values 6, 3 and 92

[royal talon]

how you found 92 bro

[wraith parrot]

On the picture

[royal talon]

iii is a option or isnt it ?

[wraith parrot]

Read the question

[royal talon]

I readed already

it wants to the answer

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[river minnow]

You have a mistake there, 2 + 2x - 4 is not 2x - 4

[hot lark]

May i ask why you use epsilon delta here?

Owh owkay

So look at whete you take the limit

Where*

You might understand that the answer is clear as day

[river minnow]

No that makes 1/|x - 2| > 1/2 which doesn't help

|x - 1| < 1/2
-1/2 < x - 1 < 1/2
-3/2 < x - 2 < -1/2
|x - 2| > 1/2
1/|x - 2| < 2

Looks like letting delta <= 1/2 helps

Yeah but |x - 2| > 1/2 is also implied

In fact you have 3/2 > |x - 2| > 1/2 from that double inequality

And I took the second part of that

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@gentle bane Has your question been resolved?

[vast shale]

yup?

tell me the qn

so where are you stuck

?

[nocturne spade]

!status

[vocal sleet]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[vocal sleet]

@gentle bane Has your question been resolved?

[nocturne spade]

wrong

2 + 2x - 4 = 2x - 2

maybe that will solve the entire issue.

then, where are we stuck now?

Estimate |x-1| <= delta and 1/(x-2) <= 1/1.5 if delta < 0.5

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[cinder oyster]

For question a

I had this on my test today and didnt know how to do it 😭

i show how i start

I know to rationalize denominator u multipky denominator on the top and bottom but here idk if its right my steps

Plz and thnx

[west raptor]

That's right if you're dealing with square roots, but here you're dealing with cube roots, so you multiply the numer and denomin by the square of the denomin

[vast ferry]

hey man this is how I solved it

@cinder oyster

You can solve it in 2 steps I just over simplified it in case you got lost in any step

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[last grail]

how do i find the inverse

[dull maple]

!status

[vocal sleet]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
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6. None of the above

[last grail]

!status

[vocal sleet]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[last grail]

!1

1

[dull maple]

So, i take it that you don't know at all how to find inverse in general?

[last grail]

swap x and y

[dull maple]

Yes. Okay, that's something.

After that?

[last grail]

for the first one it would be x=y^5

i forgot after that

[dull maple]

After that you try to manipulate the equation so as to bring it into the form y = <something>.

[last grail]

would i square root?

[dull maple]

Will that get you y?

[last grail]

no

well i know if its the inverse like the first equation it would be 1/5

[dull maple]

Yes. So, you have to raise both the sides to the power of 1/5.

[last grail]

okay

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[dusky willow]

what have u tried

[frosty tundra]

what do you not get

[dusky willow]

substitute in the values

A = pi(radius^2)

you get the area formula right?

if you had a given radius

you know how to find the area of a circle

right?

ok

lets say you had a circle with radius 5

you plug it into the formula A = pi(radius^2)

you would get A = pi(5^2)

simplifies to A = 25pi

which simplifies to 550/7

@vast shale do you get that

what has your teacher taught you

[karmic imp]

Do you have notes?

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[tacit raven]

How should I solve question 9 guys?

Thank you

[vocal sleet]

@tacit raven Has your question been resolved?

[tacit raven]

<@&286206848099549185>

[devout trellis]

what have you tried?

[tacit raven]

only this

sorry for blurry pic

[devout trellis]

ok so you drew a picture

nice

[tacit raven]

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[vast shale]

Does unbounded and DNE mean the same thing?

[thin vale]

Unbounded referring to what

Can you use it in a sentence please

[vast shale]

because according to khan academy unbounded means when a limit from both sides approaches infinity

but in this case they use DNE or the limit from the lhs does not exist

idk why

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[night barn]

What do square brackets mean here? I understand {...} is a set, but what is [...]?

[dreamy viper]

closed interval

[waxen portal]

[[1, 2] = {x \in \mathbb{R} \mid 1 \le x \le 2}]
[[1, 2) = {x \in \mathbb{R} \mid 1 \le x < 2}]

[twin meteor]

Watson

[night barn]

@dreamy viper@waxen portalthanks

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@vast shale Has your question been resolved?

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@vast shale Has your question been resolved?

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[halcyon marlin]

are these correct?

[paper depot]

#7 has a sign error

[vast shale]

7. is wrong

[paper depot]

everything else is correct

[vast shale]

it's not a sign error

[halcyon marlin]

then?

[vast shale]

oh nevermind you just switched the places of the terms

[paper depot]

ok then you can take over

[vast shale]

yes it is indeed a sign error

[halcyon marlin]

so plus sign?

[vast shale]

wdym plus sign

be more specific

[halcyon marlin]

like do i have to change the sign

[vast shale]

16. is wrong I believe

[vast shale]

yeah you do

distribute again and see what you get

7 and 16 are wrong, everything else is correct, i believe

yeah I concur

[halcyon marlin]

im still getting the same ans

[vast shale]

show your work and explain your thinking process

[vast shale]

Show your work

[halcyon marlin]

-v x -4v + -v x 4v²

[vast shale]

right

what do you get

[halcyon marlin]

4v^2 + 4v^3

[vast shale]

no

-v*4v^2 is negative times positive

negative times positive is what?

[halcyon marlin]

negtive

[vast shale]

yeah u wrote +4v^3

[halcyon marlin]

ohh

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[regal spindle]

what is pythagorean theorem how to solve it heree

[vocal sleet]

@regal spindle Has your question been resolved?

[floral pike]

Pythagorean Theorem is probably the most prolific theorem in Mathematics

The Distance Formula is another form of the Pythagorean Theorem.

@regal spindle do you understand this coordinate system?

The graph

[regal spindle]

no

[floral pike]

The points have positions written like (x,y)

[regal spindle]

yes ik that

[floral pike]

Where x is how far left or right from the center, and y is how far up or down.

Do you know what a right triangle is?

@regal spindle

I'm going to bed @regal spindle

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[fathom drum]

What is Xe

so, $$x \in $$?

[twin meteor]

rti

[fathom drum]

It is decreasing on that interval

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[minor gorge]

what is the math notation for saying "let c be a non-negative real number"

[river minnow]

Let $c \ge 0$ be a real number or let $c \in \bR_{\ge0}$

[twin meteor]

A Lonely Bean

[minor gorge]

.close

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[open turtle]

Is the proof I’ve written valid?

[hard atlas]

yes

[open turtle]

Ok perfect thanks

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[hazy heath]

my teacher is letting us use one side of an index card as notes for a test. should I make a mobius strip to have more notes?

[sudden gulch]

Not really

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[cosmic orbit]

yes

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[brazen tree]

help

[brazen tree]

how to find height

i h vae brain cancer now

[austere ore]

what grade are you

[brazen tree]

8

[austere ore]

oh

im younger ig

also what is that , i mean is your drawing

[brazen tree]

wdym

[austere ore]

te

the

[austere ore]

this

wait i kinda have the same lesson

wait

[brazen tree]

can you also help with this

i also need to find the height

wait can you send in dms cause its my bed time now

i gtg

[austere ore]

alr just write it down when you wake up

sleep well

gn

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[brisk moss]

@cobalt crypt

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[hard atlas]

what is the index of the Z?

maybe before you find the order of the element, how many elements does the factor group have

[azure rose]

Can someone explain this to me? I understand the Emperical rule but can’t apply it when I get values over M+ 3Sigma

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[lament linden]

How many tangent lines to the curve$$ y = \frac{x}{x+1} $$pass
through the point s$$(1,2)$$? At which points do these tangent lines
touch the curve?

[twin meteor]

neither

[lament linden]

how do i solve this

do i just take derivative and set it equal to the slope formula and solve it

tbh idk but it seems messy

ii found the equation

u just set the derivative to the slope formula at that point but idk how to solve this

i already plugged it in to a calculator and know it works but dunno how to issolate x

[pale perch]

you should end up with a quadratic you can solve

just requires some work to get to it

you could start by multiplying both sides by x+1

[mild flower]

and then do it again lol

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[lament linden]

k i did it but pretty annoying

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[keen bane]

is this correct

for this question

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[mellow rampart]

dumb question

[mellow rampart]

Is f(x) + g(x) = (f+g)(x)?

Just from a calculus pov

[calm hinge]

As far as I know f(x) + g(x) = (f + g)(x) by definition

[mellow rampart]

By definition?

[calm hinge]

Yeah, that's just how (f + g)(x) is defined (what it means)

[mellow rampart]

I see

right I think Im overthinking

thank you

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[leaden geode]

Hii. Need help in this question

[leaden geode]

I got it wrong, again. Where am I going wrong? I feel like it has to do with the limit of t/5. I will post my working out in a second.

<@&286206848099549185>

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@leaden geode Has your question been resolved?

[hollow bone]

@leaden geode This problem is easily solved. first you should try and determind what type of differential equation this is

is it linear? is it separable? homogenous?

from there you can make an educated guess as to what might be the best way forward with solving it

you should try to solve this as a homogenous equation. what you have did is incorrect, and very difficult

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[fervent tulip]

Hi, can anyone explain to me how to find the order, linearity, and if its an ode or pde for an equation such as this:

[fervent tulip]

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[opal fog]

Hello i have problem with my homework idk where did i mess up X_X. This is a question and my calculations:
There are 2 urn with balls where 1st urn have 4 BLACK balls and 6 WHITE, and 2nd urn have 5 WHITE balls and 7 BLACK balls. We toss a six-sided dice if we get Prime numbers we draw from 1st urn else if we get composite number we draw from 2nd urn else we dont draw any ball. Count probability of drawing 2 white balls we toss dice at the beggining (sry for my english its not my first language)

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<@&286206848099549185>

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[vast shale]

for integrals,

[vast shale]

when dealing with + C, and you do something like divide the side + C is on by 2 or multiply it by 3 or square root it, do you include the C into all of that?

i assume so

[round plover]

yes, but it's just an arbitrary constant

so it you divide it by 2, it's still an arbitrary constant, so sometimes you continue to just write +C instead of +C/2

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@vast shale Has your question been resolved?

[vast shale]

hmm but what if you are supposed to find a C after making the equation?

would it work itself out?

[round plover]

if you're finding a value for the constant, it'll be the same overall

as in, if you write +C, then compared to writing +C/2, your C value would just be half as big

and you'd end up adding the same thing in the end

it's the same as doing a variable substitution; the thing you're adding overall is the same

[vast shale]

ty ty

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[ember carbon]

hello i was wondering why for this equation to pull the rope you do (x) * 1/2 instead of (50 - x) * 1/2

[ember carbon]

https://cdn.discordapp.com/attachments/980726766140276777/1151303658198269953/image.png

A uniform cable 30 feet long and weighing 60 pounds hands vertically from a pulley system at the top of a building. A steel beam that weighs 500 pounds is attached to the end of the capble

these two problems have you pull a rope up but one is x while the other is (30 - x)

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[vast shale]

The answer is 25

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[vocal sleet]

@vast shale Has your question been resolved?

[vast shale]

No

Use

Vertex form

$a(x-h)^2 + k$

[twin meteor]

Replaced by new brandon H

[vast shale]

then solve for a using (2,12)

It told you what h and k were

re read the question

[sudden gulch]

That's for 6b

6a is system of equations

although we do know one value of the x-intercept

[vast shale]

for both

yes

then you solve for a

[sudden gulch]

I don't see how that works, though, it's not my problem

[vast shale]

it's asking for a quadratic equation

it gives you both h & k then a point you can use to solve for a

after expanding you have (not that a)x^2 + bx + c

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[quick pewter]

Is flipping ab/b=sinAsinB/sinB to b/ab=sinB/sinAsinB valid?

[livid tapir]

yeah

Wait actually

Did you sinB/sinAsinB or sinB/(sinAsinB)

Mean

[quick pewter]

Can I just send a pic of my work

[livid tapir]

And similarly b/ab or b/(ab)

yeha sure

[quick pewter]

I’m trying to use law of sines to prove the equation on the top and idk if I’m doing it correct so far

[quick estuary]

cancel out the sin b?

[quick pewter]

The original equation I need to make sure is true has sinB on top and bottom

So I’m just gonna leave it there

But I’m so close to the solution, but idk if just flipping both sides of the equal sign would still be viable

[livid tapir]

Uh your work is wrong but not the part that you mentioned originally

[quick estuary]

wait what

how did you write

a/b+b/b

as ab/b

[quick pewter]

Damn, the answer key said I was on the right track, except it randomly flips both sides so idk if I should just flip or if there is steps in between

Both have common denominators

[livid tapir]

Mainly a/b + b/b isn't ab/b and also sinA/sinB +sinB/sinB isn't sinAsinB/sinB

[quick estuary]

yeah

[quick pewter]

I assume that they could add

[quick estuary]

they add

you multiplied

it would be

a+b/b

[quick pewter]

Oh damn

[quick estuary]

ohh

so you just componendo dividendo for this question

a/sina =b/sinb

a/b=sina/sinb

a+b/b=sina +sinb/sin b

that was the original eq iirc

and then invertando

b/a+b=sin b/sina +sin b

[livid tapir]

Original equation you wrote is wrong unless there's supposed to be a + in the denominator

[quick pewter]

That’s what they key says so I was just following it loosely but I now see what y’all are talking about

[livid tapir]

OK yeah

[quick estuary]

see

[livid tapir]

So there is

[quick estuary]

exactly what i did

the +1 step

is called componendo

[quick pewter]

Yeah I did that, or atleast how I thought it was supposed to be done

[livid tapir]

it is?

[quick estuary]

you got everything right

[livid tapir]

I honestly never knew it had a name lol

[quick estuary]

but you wrote it wrong

[quick pewter]

Mb

But yeah I meant to put a + between the a and b and sines

[livid tapir]

kool

[quick pewter]

But thank you guys for the help

[tidal umbra]

welcome

[quick pewter]

Who r u?

[tidal umbra]

LMAO

[quick pewter]

😂

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[rancid ibex]

can someone explain to me how to shift this to the right

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[vast shale]

,rotate

[vast shale]

How would I do part C for 6?

First I got the total displacement

Which is 12

Then divided that by 37.8 because 10/72 in the first part is 0.13 hr then multiply that by 60 I get 7.8 minutes

Add that to 30

37.8

12/37.8 = 19.2

[delicate stirrup]

Yeah

That's right

[vast shale]

Ok was just making sure because chatgpt said 31km/hr for some reason

[delicate stirrup]

Use wolfram alpha mb?

[vast shale]

?

[vast shale]

chatgpt is terrible at math trust me i tried lol

What is that

[delicate stirrup]

Google it

[vast shale]

www.wolframalpha.com

[vast shale]

if u have premium use the wolfram plugin it makes it slightly better

https://www.wolframalpha.com

Is it like chatgpt

But math