help-13

[spare palm]

<@&286206848099549185>

[ancient delta]

lets start with question 3

how do you go about starting it

[spare palm]

Use distribution method

But it’s 0/0

[ancient delta]

yup

[spare palm]

So you use limit laws

[ancient delta]

since its 0/0 we factor top and bottom

[spare palm]

Factor?

Wym

[ancient delta]

are you familiar with GCF or X factor methods?

[spare palm]

No

I just learned about limit

So I’m new to all this

[ancient delta]

right so you're going to have to memorize all these methods and formulas soon ill help you

for the top youre gonna use a^2 - b^2 = (a-b)(a+b)

the top equation being t^2 - 9

[spare palm]

How would that work

I don’t understand

[ancient delta]

do you know how to square root?

[spare palm]

Yeah

But how would you use the equation t has no value

[ancient delta]

ok so square root t^2

[spare palm]

It’s t

[ancient delta]

we arent plugging anything in just yet

what were doing is simplifying the equation first

correct

square root 9

[spare palm]

3

We square root the bottom also?

[ancient delta]

so now we have t - 3 = (a-b)(a+b)

plug it in

[ancient delta]

no

we have to use a different method for that

[spare palm]

Wym plug it in

What do o plug in

I*

[ancient delta]

basically t = a

and 3 = b

[spare palm]

T-3=(t-3)(t+3)

[ancient delta]

yes correct

we leave out this part T-3

so just (t-3)(t+3)

[spare palm]

Ok

Ok

[ancient delta]

do you need any clarification before moving on or do you get it

[spare palm]

I get it

[ancient delta]

right

[spare palm]

We do the same for the bottom?

[ancient delta]

no

[spare palm]

What’s the next step?

[ancient delta]

right so for the bottom portion we have 2t^2 + 7t + 3

we have to also factor it

from the various methods this one we use X factor

[spare palm]

X factor?

[ancient delta]

https://www.youtube.com/watch?time_continue=65&v=70OyHPq5FqY&embeds_referring_euri=https%3A%2F%2Fwww.google.com%2F&source_ve_path=MjM4NTE&feature=emb_title

watch this video on how to do it

lmk if there is something you arent understanding and ill clarify

[spare palm]

Can you just go through the steps

I have 3 more assignments due in a hour

[ancient delta]

youre joking 😭

ight i got you

[spare palm]

Ty

[ancient delta]

so basically you got a piece of paper on you?

[spare palm]

Yeah

[ancient delta]

draw a X

[spare palm]

Ok

[ancient delta]

ok this is our equation 2t^2 + 7t + 3 we have a A B and C value

a = 2 b = 7 and c = 3

understand?

[spare palm]

Yeah

Where on the x do I put them

[ancient delta]

lemme draw it out for you gimme a min

[spare palm]

Ok

[ancient delta]

what we do is a * c gives us the top value

and b on its on is the bottom value

[spare palm]

6 on top

7 bottom

[ancient delta]

yup

this is going to sound confusing but on each side of the x what multiplies to the top being a but adds to get b

so what 2 values multiply to get 6 but add to get 7

[spare palm]

You can’t multiply to get 7?

[ancient delta]

i mixed up the numbers lol

youre right tho my mistake

[spare palm]

3*2 is 5

Is there anything else?

6*1?

It has to be 6 * 1

[ancient delta]

6 and 1 is right

so this is what we have

but if you notice the equation 2t^2 + 7t + 3

a has a 2

typically its just a 1

but since its a 2 we divide both of those values by it

[spare palm]

What values

[ancient delta]

these values

[spare palm]

So 3 and 1/2

[ancient delta]

correct

we cant have that 1/2 tho

were gonna multiply it by its common denominator

[spare palm]

Which is?

[ancient delta]

what the common denominator of 1/2?

[spare palm]

1/2

But it gets smaller

[ancient delta]

yes but we multiply it by its inverse

[white latch]

there you go.

2t^2 + 7t + 3

When we deal with coefficients larger than 1 there exists a product and sum method we can use to factor this. Remember the prime goal is to solve this algebraically and not just plugging in numbers close to the limit, which we could do, but would take far too long and is not efficient by any means.

What we are going to do to factorize this is using the procedural method where 2t^2 + 7t + 3

[spare palm]

Ok

How is the limit 1

We got 2 and 1

Nvm

[spare palm]

So limit 1 is does not exist

Or undefined

[white latch]

Yes, because for limits to be true the value that x approaches for f(x) must be approaching a certain value on both the left and right handside.

Chickendinner you can keep asking questions.

But until you start solving problems on your own doing the critical thinking for yourself its not gonna get any easier I tell you.

[spare palm]

I know but rn I just need to get it done

[white latch]

Alright.

[spare palm]

It’s due in 50 min

[white latch]

Got it.

You know what screw it. I'll help you finish this if you want me to.

But promise me you are going to learn the intuition behind the stuff after. I will assist you with solving these other hw problems if you like?

[spare palm]

Ok

Ty bro

[white latch]

Np.

Lets get it.

How many questions do you have left till you gotta hand it in?

[spare palm]

Too much

[white latch]

Mk, well chickendinenr. 2 things. I expect you to be present at all times when assisting cus I'm not gonna wait for you to respond, unelss its solving problem. Secondly, is this homework or a test?

[spare palm]

It was homework before

Rn it’s a checkpoint

[white latch]

Alright. Show me how many questions there are.

Is it 10, 15?

[spare palm]

14

[white latch]

What happens if you don't get em in before 50 mins?

[spare palm]

Lose some points

[white latch]

Alright. Show me the 14 questions

send all of em.

[white latch]

Do you want me to show the process for each question and I prodd you analytical thinking. Or do you want me to solve them, I show you my work.

[spare palm]

Solve them

Pls

[white latch]

Alright fine. But you gotta promise me after ur gonna learn. I want you to do well, but you needa learn the stuff.

[spare palm]

Ok

[spare palm]

Ty

[spare palm]

Ty bro

[cedar kiln]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[white latch]

Don't worry I confirmed that with him, he is analyzing them analytically and solving them. Afterwards I shall be ensuring he properly understands the stuff.

[white latch]

Try doing that one. That one is fairly simple.

Show me an attempt of thought as you said you are.

[spare palm]

Ok

I got 10

You got the same?

[white latch]

ima try it

yeah.

also for the -1.5 basically for the graph f(x) it seems that the limit is -1.5 if I had to make a guess as guessing any other decimal numbers would lead to the possibility of numerous things which would be non sensical hence -1.5.

Okay, I double checked the stuff looks all good to me. Analyze the solutions and tell me if you are confused in the working out for any of em, but please make sure to read about how we know as to whether or not we can use the limit laws. I gave a good explanation for that.

[spare palm]

I’m confused on the one I’m doing rn

[white latch]

which?

[spare palm]

I got 1.66667

But I think it’s wrong

[white latch]

mk what was the fraction form?

[spare palm]

I tried direct substitution

Idk

How to do that on the calculator

[white latch]

alright ill take a look.

[spare palm]

I got

5/3

That’s correct?

I got stuck on this one

Direct substitution doesn’t work

Nvm

I did it

It’s 4

[white latch]

yep.

Good job! And here the reason I used the limit laws is because I could infer from beforehand that if it was evaluated the limit is a real number, and not infinity or undefined, hence the limit laws I applied here assuming that the limit is a real number.

[spare palm]

I’m stuck on this one rn

[white latch]

Uhhhh I think this is more than 14 questions lol what the heck?

[spare palm]

Some questions had many parts

[white latch]

Oh okay.

1/27

We had to use the remainder theorem to factor t^3

[spare palm]

Man ty

But I gtg

Sleep

[white latch]

Np, just promise me your going to analyze it and understand why as you said you would. Read about the explanation I gave for limit laws and try your best to understand.

[spare palm]

Ok

I understood some of it

But I still have some difficulty

[white latch]

Well that is cause your asking for help a lot, but not actually struggling to think about the process. The struggle is what is going to make or break you. Take good notes, and don't just solve questions learn the intuition behind solving problems.

[spare palm]

Ok

[white latch]

K pce.

[cedar kiln]

@spare palm Has your question been resolved?

[cedar kiln]

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[cedar kiln]

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[ebon scaffold]

Hey, pleae could someone help me, please. I don't know what im supposed to do when attempting this reverse percentage question. Tysm

[ebon scaffold]

At first I tried doing 4500 * 1.20 because I thought that 20% would be the multiplier but when I put the answer that I thought (5400) it was wrong

[dense socket]

Do you know the formula for percentage?

[ebon scaffold]

hmm I don't think so

[dense socket]

The percentage amount is equal to the percentage Times the original value

Youre looking for the original value, you know the percentage value

[ebon scaffold]

yeah

[dense socket]

And you know that its 20% less than the og value

So the New value is how much percent of the og value ?

?*

[ebon scaffold]

hmm let me think

[dense socket]

Og value is 100%

[ebon scaffold]

So the percentage amount is 4500 right?

[dense socket]

This is 20% less...

[dense socket]

Yes

[ebon scaffold]

oh so 4500 = 20 * original value ?

[dense socket]

Thats the common trap

The original value is reduced by 20% but you arent calculating 20% of the og value, which would be the amount for which the value has reduced

Youre calculating the new value after the og value has been reduced by 20%

[ebon scaffold]

I dont really understand.

[dense socket]

Okay lemme give u a similar example

A ball Costs 100 dollars but is on a 10% sale

The new price is 90 dollars

Is that 10% of 100?

[ebon scaffold]

well it costs 110 before the sale because 100 +10% (*1.1) = 110

[ebon scaffold]

10% of 100 is 10

Is this correct @dense socket thanks

[odd flower]

no...

[ebon scaffold]

oh wait

[ebon scaffold]

its 90 because 100 * .9 = 90?

Am I right?

[odd flower]

yea

[ebon scaffold]

@odd flower Am I doing smth wrong?

[odd flower]

no, he's asking "if the product is 10% sale, is the new price is 10% of the original price?"

[ebon scaffold]

ohk

So what do i do after?

@odd flower

@dense socket ghosted me 💀 , was i being dumb

[odd flower]

back to the original qs

[odd flower]

what the qs give u?

[ebon scaffold]

But I dont understand what I did wrong. I did 4500 (sale amt) * 1.2 but i got 5400 but its apparently wrong

[odd flower]

that's not how u do it

[ebon scaffold]

then?

[dense socket]

Sorry i was busy

[odd flower]

(new price)=(the percentage)*(original value)

[ebon scaffold]

oh np : )

[odd flower]

What u wanna do here is put what the qs gives u

[dense socket]

The new ball price is 90 % and the discount is 10% hence 90 = 90% *100

[ebon scaffold]

is the %amt = 20?

oh so 20 = 80% * 100?

[dense socket]

So the price reduced by 10 % making the new price 90% of the original

Here price reduced by 20% making 4500 how much % of the original?

4500 Being the new price

[ebon scaffold]

hm

[dense socket]

Any guesses?

[ebon scaffold]

so reduced is 20% so its 80% of orig. So isn't it 4500 = 80%*orig value

[odd flower]

exactly

That's it

[dense socket]

Yeah now just calculate it

[ebon scaffold]

i dont know how to do it

though

[dense socket]

Well, thats a whole different problem

Do you know how to write 80% as a fraction or a decimal?

[ebon scaffold]

0.8

[dense socket]

Okay so you have 4500=0.8x

Can you solve that?

[ebon scaffold]

x = 4500/0.8 = 5625

Is that right

[odd flower]

yea, it's correct

[ebon scaffold]

yay corr

for this how would i do

im a bit confused abt the method now cos we tried so many lmao

would i make it into decimal

so like 0.8x

126 = 0.8x

and then solve?

[odd flower]

oh this is a brand new one

the "126" can be seperate to "the original price" and "the VAT"

[ebon scaffold]

i dont get it

[odd flower]

ok so when u buy food or anything at the supermarket

U have to pay a bit more amount of money than the original price that supplier wants

[ebon scaffold]

yeah

[odd flower]

That's VAT

its a tax

[ebon scaffold]

sorry i dont get it

[odd flower]

hmmmm

i think u don't know what "VAT" is

go have a search on wikipedia

[ebon scaffold]

pl

ok

its a added tax

[odd flower]

yea

back to the qs

Is the "126 pound" price only include the price of hotel?

[ebon scaffold]

no

theres also vat

[odd flower]

so the original price is 100%
what is the "included tax" price percentage?

[ebon scaffold]

uhh

20% is vat

so 80% is the hotel

[odd flower]

no

the tax is a add-on to the original one

[ebon scaffold]

smh I really am strugglign to understand

I think ill just do this later to be honest and try and figure it out with my teacher

im so sorry for wasting your time :/

[odd flower]

it's fine tho, im not goin to play valorant today =))

[ebon scaffold]

cool u play valorant? what rank are you

btw tysm for ur help

[odd flower]

iron lol

[odd flower]

no problem

[ebon scaffold]

cool u in asia if so after i solve this and finish all my work i can help you cos im silver lmao

[odd flower]

yea, we can try some if we have free time tho

btw, cya

[ebon scaffold]

aight see u

[cedar kiln]

@ebon scaffold Has your question been resolved?

[cedar kiln]

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[next spruce]

the x intercept is 0 and y intercept is 2?

[livid hound]

why do you think the x-int is 0

[next spruce]

oh wait there is no x intercept since it didn't pass through 0

is that right?

[next spruce]

I assumed since the arrow on the left is nearing 0

thanks!!!

.close

[cedar kiln]

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[dusk finch]

well every x intercept has y-coord 0

so it still shouldnt mean that x intercept is 0

when you are describing x-intercept, you describe it by x-coordinate since y-coordinate of x-intercept is always 0

[cedar kiln]

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[honest frigate]

can i get help on this problem

[honest frigate]

do i turn tan into sin/cos

or do i factor

[junior dome]

try to get this to tanx/x form

[honest frigate]

so do i multiply by y-4

[junior dome]

why would you do that

hint : y^2 - 4 = (y+2)(y-2)

[honest frigate]

then i would have to get rid of th ey-2

[junior dome]

.

[honest frigate]

tan(y-2)(y+2)/y+2

[junior dome]

yes

now you want a y-2 too in the denominator

[honest frigate]

so mult by 1/(y-2)

[junior dome]

correct

[honest frigate]

which cancels the numerator

and the newly multiplied one

so its would end up being tan(y+2)/y+2

[junior dome]

what?

you cant cancel the inside of argument

what I meant was to multiply and divide by y-2

[honest frigate]

then it would be

tan(y-2)(y+2)/(y+2)(y-2)

[junior dome]

missing a y-2 in the numerator

[honest frigate]

multiplay again

[wraith dagger]

Dyssrupt

[honest frigate]

tan(y+2)(y-2)(y-2)/(y+2)(y-2)

[junior dome]

but the y-2 is not inside tan

you are mixing it with the argument of tan

[honest frigate]

where would i tbe

[junior dome]

i just wrote it out for you

[honest frigate]

oh

then wat woul di do

tan((y+2)(y-2))(y-2)/(y+2)(y-2)

[junior dome]

you now have tanx/x form

[honest frigate]

Like this

[junior dome]

,rotate

[junior dome]

yeah

[honest frigate]

now wat

or is that it

[cedar kiln]

@honest frigate Has your question been resolved?

[junior dome]

finished

tanx/x is 1

whats left is y-2

sub in the limit

[honest frigate]

ohh

tysm :D

.close

[cedar kiln]

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[cedar kiln]

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[echo sedge]

Hi

[echo sedge]

I had to choose 5 equations where the implication can be replaced by a biimplication

I dont know how I messed up here?

4 is wrong ?

[high coyote]

No, who said so?

[echo sedge]

test said

[high coyote]

Well

[echo sedge]

lemme send you

[high coyote]

$$x^2+y^2=(x+iy)(x-iy)$$

[wraith dagger]

Categorist

[high coyote]

I don't understand this format. Are you using a Computer Assessment System?

[echo sedge]

I think so

[high coyote]

Choice 1 is false. I mean, $x=-1$ and $y=3$ you have that $-3<0$ but -$1+3\neq 0$

[wraith dagger]

Categorist

[high coyote]

I think I'm understanding what are you actually gicen

given

[echo sedge]

Yeah im given a few different ones

its so hard for met o explain, sorry, because i cant see the original options

[cedar kiln]

@echo sedge Has your question been resolved?

[cedar kiln]

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[solid dragon]

,rotate

[sour vapor]

whyyy

[solid dragon]

? yes pochie

let x = 98799, y = 98126, z = 673

,rotate

[solid dragon]

this is my working

[cedar kiln]

@solid dragon Has your question been resolved?

[solid dragon]

<@&286206848099549185>

[solid dragon]

im going to sleep, don't close this channel in case someone knows how to solve it

[cedar kiln]

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[prisma gull]

Is there an example of a set S, a binary operation on S, and two different elements $e_1,e_2 \in S$ such that for all a $\in S, e_1a=a$ and $ae_2=a$?. Prove if there is not one.

[wraith dagger]

.doc

[prisma gull]

I attempted a proof, I need to help with my proof writing, ie coming up with correct arguments

My idea is just one liner, e1*e2=e2 (since e1 is left identity)

also e1*e2=e1 ( e2 is right identity)

thus e1*e2 is equal to different element which aren't same, it sort of cannot happen

how do I write this more formally?

it's a proof by contradiction ?

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[broken sable]

I'm trying to solve an integer: (x/(x+1)(x^2+4))dx. From here I do this: x/(x+1)(x^2+4) = A/x+1 + (Bx+C)/x^2+4 and then it becomes x=A(x^+2+4)+(Bx+C)(x+1) and from here I do different substituions with number to try to find A,B,C so I can solve it but I keep getting the wrong numbers.

[agile plume]

wait

can u send photo?

of ur work

[broken sable]

Ok hold on

[agile plume]

x+1=?

for x=-1

y*(x+1)=?

for x=-1

[broken sable]

My apologies, I'm having difficulties understanding how you got to that conclusion

[agile plume]

just 1-1=?

[broken sable]

?

[agile plume]

what is the result of this action

1-1

[broken sable]

0

[agile plume]

good

1 s

for x=-1

-1= a(1+4?)+0

cus (bx+c)*0

there is x^2+4?

[broken sable]

yes

[agile plume]

so -1=a(1+4)

[broken sable]

So it's A=-1/5

[agile plume]

yup

[broken sable]

Hold on, we have x=-1 -> -1= A+B+-B-C+4A+C and what I've written there is wrong cuz I overlooked (-1)^2 = 1, and from here we get -1=0

[agile plume]

i looked for first line , wait

[agile plume]

idk cus u have -c ,

if u took (-1)^2 =-1 there stiill no c

[broken sable]

Right, there is a -c, I accidentally crossed the A with -C. So we actually get -1=A-C, is that right?

[agile plume]

here u just took (-1)^2=-1

here?

[broken sable]

Yes

No

[agile plume]

blue?

[broken sable]

You don't see it because I wrote it after I took the pic

Let me write it again

[agile plume]

blue line is better to solve than black

cus u see easy that x=-1 delete bx+c

and u have only a

[broken sable]

I corrected my mistake I made previously and I got to here

[agile plume]

how u got $-1&=1-c-2c+2-c?$

[wraith dagger]

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

[broken sable]

I used the substitutions I already had for A and B

[agile plume]

but a and b wrong

[broken sable]

Is it because I used the same expression?

[agile plume]

maybe

[broken sable]

Can you show me where to go from here?

[agile plume]

from here

[agile plume]

its hard, if you counted wrong earlier

[broken sable]

I have no doubt

[agile plume]

start here by correcting the calculations

[cedar kiln]

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[cedar kiln]

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[junior timber]

could someone double check for me?

I think I’m doing it right but I also think I’m doing it wrong

[tropic oxide]

you cut almost the entire problem off

[cedar kiln]

@junior timber Has your question been resolved?

[junior timber]

OH SHOOT

[tropic oxide]

right

a, b, c are correct. d is wrong.

[junior timber]

is it 23.3 repeating?

for d?

[cedar kiln]

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[crimson sedge]

is anyone here good at trigonometry lmao 😭

[vagrant elbow]

I know a thing or two

[dry temple]

what's a trigonometry

best website https://dontasktoask.com/

[crimson sedge]

1- post your question, don't ask to ask
2- don't open up multiple help channels
3- don't ask your question in occupied help channels that are opened by other people

[cedar kiln]

@crimson sedge Has your question been resolved?

[dry temple]

Not actually asking the question leads to you confusing everyone, you're asking someone to take responsibility of answering your question, which may be a lot to ask depending on the question. You're slowing down the process of actually getting an answer because you have to wait for a round of "are you there" "yes i'm there" "ok" ... waiting (posts question), that's like 4 back and forth-s before actually even starting the work on the problem. In addition, the process of formulating and asking a good question may many times help you realize what you missed because it forces you to review, I've had many times where I wanted to ask a question but when formulating the question I realized I did not even need to. Also, as for why taking responsibility can be bad, the math asked here can vary a lot in difficulty. There could be some competitive math question on trig that are far beyond a normal person's capabilities, or a trig problem that can be solved by someone has horrible at trig as me

I can usually solve most high school level trig problems but asking me to take responsibility for a potentially ridiculously hard problem is asking for too much and you may be simply ignored by many people

And now this is probably the most confusing behavior I have ever seen, opens 2 channels obviously trying very hard to get people's attention

Proceeding to literally ghost your own channels

wtf are you trying to do

[jaunty mural]

alright lets chill a tad. ping mods if they do it again

@crimson sedge see above^ on why not to do this

[crimson sedge]

yeah no need for that much lmao

stuff happens maybe they got busy irl

[dry temple]

Oops went on a bit of a tangent

[vestal bear]

realest thing to ever be said on this server

[cedar kiln]

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[cedar kiln]

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[crimson sedge]

Someone help me understand trig equations, please

[crimson sedge]

I know the identities but I don't know how to use them

How do I solve this, for example

okay what does sec(x) represent in terms of cos(x)

1/cosx

also btw are you working with degrees or radians

Radians

and also are you asked to find a general solution or did they give you an interval to work with

[0,2pi]

like did they ask to find the solutions in the interval [0,2pi] or not

okay great

Yeah

Sorry slow typing I'm panicking lol

[crimson sedge]

\dm
alright so you have [
2 \map \cos x + \f1{\map \cos x} = 3
]
Try to simplify this by adding the fractions

[crimson sedge]

no worries take it easy. No stress

Like this?

yes great

\dm
now you can also bring that 3 over to the left side too so that [
\f{2\map{\cos^2}x +1}{\map \cos x} -3 = 0
]
Can you simplify this as well?

Wait how does that happen?

Sorry

well like

How did you get the 3 in the numerator

That's what I'm asking

[untold torrent]

Should be 2

also hi

[crimson sedge]

oh yeah just a typo

sowi

hello red

[crimson sedge]

there ya go

Like that?

yes great!

okay now does this like

ring a bell to you

it oddly looks like a good ol' quadratic doesn't it

OH

IT FACTORS

to see it better. How about we make a substitution of t = cos(x)

yep!!

exactly

yaaaas

and then cosx is either ,5 or 1

yes

Ohhhh that makes sense

should be straightforward then for you

Yeah thank you I kept trying to shove a trig identity in there

you can try writing the general solution too for funsies if you want to practice too btw

Nah I just need to get the general knowledge of how to simplify them

Thank you for your help 🤍

fair enough

aight good luck

have a good one

.close

[cedar kiln]

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[rotund night]

is this key wrong? and if it isn't, can someone explain to me how this works?

[untold torrent]

It's correct

Basically, you look at the limit in 2 ways:

As x approaches 5 from the right

and as x approaches 5 from the left

In both cases, the denominator will approach 0 (but from above, meaning as x gets closer to 5, the denominator will become a very small positive number)

And the numerator approaches 5

So intuitively you have 5/(a very small number)

which goes to infinity

[rotund night]

okay but if i plugged in 4.999 as a test value to see from the left, wouldn't it be a negative value

and don't both sides have to be positive for it to be labeled as positive infinity

[untold torrent]

Oh wait

it will

Yeah I'm dumb

So it's incorrect

[rotund night]

alr thanks

no worries man, my math teacher trips eveyrone up with these random errors in keys

[untold torrent]

Yeah sometimes I make stupid mistakes

[cedar kiln]

@rotund night Has your question been resolved?

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[wild cypress]

help on this question please

[cedar kiln]

@wild cypress Has your question been resolved?

[cedar kiln]

@wild cypress Has your question been resolved?

[cedar kiln]

@wild cypress Has your question been resolved?

[tiny marten]

what have you tried and what are you stuck at

[cedar kiln]

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[gentle sail]

Sorry, I already asked a question before but could someone help me again?

[gentle sail]

Don’t know where to go from here

[dire geode]

You got the formula variables wrong

Should be either a or h, not both

[gentle sail]

ur right.

ok I changed that

[dire geode]

The rest is algebra

Factoring, etc

[gentle sail]

how could I approach factoring the top

because for the terms with the x factoring out something doesn’t make sense

because they have a different leading number

same for the a I guess

[dire geode]

Not factoring that way

Factor out x-a

[gentle sail]

ohhh ok

@dire geode

[cedar kiln]

@gentle sail Has your question been resolved?

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[ancient delta]

confused on getting T_1

i know T_3 = 50N, W=mg

T_2 = 70.7N, T_2 sin 45 = 50N

[drifting fable]

the block is not moving, correct?

sorry, the point in the middle is not moving, correct?

[ancient delta]

correct

[drifting fable]

the entire system is in static equilibrium, right

ok

so if the point in the middle is not moving

then the net force acting on the middle must be zero, right?

[ancient delta]

yes

[drifting fable]

ok, so T1+T2+T3=0?

i am referring to the vectors

if the point in the middle is not moving, the net force along the x axis must be zero, right?

[ancient delta]

no idea but from your work it is

nope

much appreciated yeah its seems most logical

[cedar kiln]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[ancient delta]

i already knew T2 was 70.7 though..

[ancient delta]

.

[ancient delta]

idk why they gave you that warning

using this T_1 is 50N

ok then thank you

.close

[cedar kiln]

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[cedar kiln]

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[main oak]

What is force constant

I thought there is only something called spring constant

and it is physics btw

tbh i figured it out by myself

.close

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[icy holly]

What exactly does perpendicular bisector mean in that instance?
If that means that VU perpendicular to BE, then why is it drawn like that?

[brave tree]

perpendicular bisector is applicable for a line ryt

wdym perpedicular bisector of an angle

that doesnt make sense does it

[icy holly]

Thats the whole point

[brave tree]

wrong question then

[icy holly]

Though the wikipedia states that it has to be perpendicular to the opposing line

[cedar kiln]

@icy holly Has your question been resolved?

[cedar kiln]

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[brave tree]

no spoonfeeding here

[sour canyon]

how i ca do the C* v,:

[brave tree]

show work

[sour canyon]

@brave tree

I can do the 2th case?

on thatt

is factoring

<@&286206848099549185>

[dim tiger]

what is the question exactly

[sour canyon]

with what case i can continue that

[dim tiger]

cases of what and what are you trying to do

[wind lily]

ik this is a very easy question for you guys, but can you guys still help me with this question-

[dim tiger]

please open your own channel

#❓how-to-get-help

[dim tiger]

you want to factorize??

[sour canyon]

yes

[dim tiger]

ok

i will give you a hint

[sour canyon]

alr

[dim tiger]

try to group 2 tems together and the other 2 together

then take a common factor from each and observe

is my hint clear or my wording is bad

[sour canyon]

( 6a²x - 3axz ) * ( 2ay + 1yz )?

some like that

?

what i can do with the extra letters as they are?

idk how do this :,vv

[dim tiger]

,w factor 30a^4x-15a^3xz-10a^3y+5a^2yz

[wraith dagger]

Results provided by WolframAlpha

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

Requested by calculus is fun#0096

[sour canyon]

oh

is that?

[dim tiger]

thats the factorization

[dim tiger]

how did you get this

what are each 2 terms that you grouped together

[dim tiger]

,rotate

[sour canyon]

i first do common factor and after do common factor but with groups

[dim tiger]

your mistake is from 2nd to 3rd step

the first step is like this

observe that the power of a in the first term is 1 more than that in the second term

[sour canyon]

what

wait what

[dim tiger]

what is the power of a in the first term

[sour canyon]

ill do again that

but cleaned

i can do the 4th case on that??

[dim tiger]

no need for brackets

what is the 4th case

you reached the factored form

you are done like that

[sour canyon]

ah

[sour canyon]

so is done??

ah yes

tysm @dim tiger

.close

.close

:,V

can u close?@dim tiger

[cedar kiln]

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[dim tiger]

np have a nice day

[cedar kiln]

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[lofty mantle]

someone help me with this quadratic formula, 3x2 - 48 = 0 ( 2 is an exponent )

[gray blade]

What have have tried

[lofty mantle]

• 3x2 - 48 + 48 = 0 + 48
• 3x2 = 48
• ?? idk how to solve for 3x2

[gray blade]

well you want to isolate x^2 now

[tropic oxide]

did you mean 3x^2 - 48 = 0?

[lofty mantle]

yes

[tropic oxide]

i think you misunderstand what "solve for ___" means

because if your goal was to "solve for 3x^2" in the literal meaning of that, then you've already done so.

but you probably want to solve for x.

[lofty mantle]

like remove 3?

[lofty mantle]

ye

[tropic oxide]

you want to divide both sides by 3, yes.

[lofty mantle]

oh ok ty

[cedar kiln]

@lofty mantle Has your question been resolved?

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[wet fossil]

How many lists (x,y,z) of three integers are there with 0 \leq x \leq y \leq z \leq 100 ?
So (0,1,2) would be such a list while (4,2,3) not. there are (101)^3 total lists, but how many of these lists are such that the integers in the list are in increasing order from left to right ?

[crimson delta]

lets ignore the equality cases for a second

if you have three numbers x,y,z all distinct

how many tuples do they form

how many of those are allowed

[wet fossil]

101.100.99

[crimson delta]

no

[wet fossil]

All three distinct would form 101×100×99 lists no?

[crimson delta]

x,y,z are fixed

lets say you have the three numbers 18, 27, 91. how many tuples can you make with these

how many of those are allowed

[wet fossil]

Ohh 3!

[crimson delta]

yes

[wet fossil]

only 1 is allowed

[crimson delta]

yes

so you can just calculate the number of all tuples and divide by 6

and then something similar if eg x=y

[wet fossil]

hmm (101×100×99)/6?

So for each tuple (x,y,z) there are 3! lists (or permutations) and only 1 of them obey the inequality

[crimson delta]

yes

[wet fossil]

hmm okay and now just add the cases when x=y , y=z and x=y=z ignoring the case when x=z \neq y (because it will obey the inequality)

Alright thanks

.close

[cedar kiln]

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[nova snow]

Why would there be a total of only 2 solutions for (sinx-1)(tanx+2) = 0

[nova snow]

wouldnt it be 3 solutions

because there are 2 solutions to tanx = -2

right

and one solution for sinx = 1

so thats 3 in total

(the question asks for the total amount of solutions that exist between 0 and 2pi)

this is the provided answer

[fading summit]

pi/2 isn't a solution because, like it says, tan(pi/2) is undefined.

[nova snow]

how did we get pi/2 in the first place thats what im confused

because arctan(-2) = some nasty looking angle

but pi/2 i dont know where you get that from

[livid hound]

read the stuff before that

[fading summit]

Sin(pi/2)=1

[nova snow]

yeah i understand the solution for sin

[fading summit]

so it would be a solution if not for the tanx term in the equation

[nova snow]

wait so are we combining them or something

i thought we were looking at them separately

[livid hound]

you initially consider them separately
however you must also ensure that all expressions will defined at those values

[nova snow]

hmmm

wait so the goal of tanx = -2

you are trying to find solutions where tan is negative right

and tan is negative in Q2 and Q4

[livid hound]

you don't explicitly need to get the solutions
just recognise from the properties of the tan fucntion / unit circle that there'll be two solutions to tan(x) = - 2in the specified interval

[nova snow]

do we need to get sinx = -2 then?

[livid hound]

no

the initial step was just zero product property / null factor
something you are definitely already familiar with

[nova snow]

so how come we consider tan pi/2 from the sin solution but we dont consider the sin -2?

[nova snow]

yeah i get that part

[livid hound]

however you must also ensure that all expressions will defined at those values

[nova snow]

is sin -2 defined?

[livid hound]

yes, but we don't care about that

what happens when you try putting $x=\frac{\pi}{2}$ into
$$(\sin(x) - 1)(\red{\tan(x)} + 2)$$

[wraith dagger]

ℝam()n()v

[livid hound]

specifially what happens to that red component

[nova snow]

i get 0.24... putting into the calculator

but I think i see why pi/2 is undefined not from this but from intuition that theres an asymptote at pi/2 intervals?

[livid hound]

tan(x) has asymptotes at odd multiples of pi/2

you can consider tan(x)= sin(x)/cos(x)

which is clearly undefined at values where cos(x) = 0

[nova snow]

hm mkay

wait wait wait wait

so we get 2 solutions from tanx = -2 right?

[livid hound]

yes

[nova snow]

and because the sin solution for pi/2 is invalid that doesnt count

so its just 2 then

[livid hound]

yes

[nova snow]

okayyyy

i seeee

cool cool

thanks

.closr

.close

[cedar kiln]

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[static crystal]

Hey do you know why this equals to positive infinity but not negative infinity?

[crystal raptor]

is 1/(x+1)^2 ever negative?

[static crystal]

wdym?

[junior dome]

is square of something ever negative?

[static crystal]

no?

[junior dome]

then how will this tend to negative infinity?

[static crystal]

ah thats true

wait then

some questions like lim(x->2^-1) 1/x-2 = negative infinity

[crystal raptor]

btw i think you mean $2^{-}$, as in, from the left, and not $2^{-1}$ as in, $\frac12$

[wraith dagger]

ΣΑCu

[static crystal]

oh so if its coming from the left does it go down to negative infinity opposed to the right which is going to pos infinity?

[crystal raptor]

well not necessarily, you have to look at the expression

$\frac{1}{x-2}$

[wraith dagger]

ΣΑCu

[crystal raptor]

and x is approaching 2 from the left, so is x bigger than or less than 2?

[static crystal]

less?

[crystal raptor]

right, so is x-2 positive or negative?

[static crystal]

negative??

[crystal raptor]

yes

[static crystal]

sorry i dont have a very good understanding of this topic yet

[crystal raptor]

so as we approach 2 from the left we are always negative, but getting more and more negative

so tending to -inf

[static crystal]

so its kinda like when limx->1 1/(x-1)^2 = infinity because x is approaching 0 infinitely?

[crystal raptor]

x is approaching 1, not 0

[static crystal]

mb

[crystal raptor]

in this case, it doesnt matter which side we approach from, we are always positive and getting bigger and bigger

[static crystal]

yeah im just having some trouble whether if the equation is neg or pos

like in limx->2^+ 1/x-2 = positive infinity but limx->2^- 1/x-2 = negative infinity

[crystal raptor]

we just did the 2^- case

you can do the same analysis for the 2^+ case

[static crystal]

so x is bigger than 2 so it goes positive?

leading to positive infinity

[crystal raptor]

yeah x is bigger than 2 so x-2 is bigger than 0

[static crystal]

and for this case

x is bigger than -1 so the left hand side goes positive?

oh kinda like x->-1, (x+1)^2 ->0?

ok i understand a bit more now

thanks for the help

.close

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@jade tangle Has your question been resolved?

[crystal raptor]

why dont you write out the definition of symmetric difference

[cedar kiln]

@jade tangle Has your question been resolved?

[crystal raptor]

if you don't know, check your notes or look it up

[cedar kiln]

@jade tangle Has your question been resolved?

[cedar kiln]

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[pearl spoke]

so im on 7 ii) and am completely clueless every attempt is wrong pls help

[sullen wharf]

what concept we using here?

[pearl spoke]

product rule for counting

using like factorials

[cedar kiln]

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[ancient galleon]

how do i write this in interval notation

[jaunty mural]

you know (a, b) means 'doesnt include the ends' right

if you dont include an end, you can write infinity or -infinity in it.

[ancient galleon]

so infinity less then 5?

[jaunty mural]

write what u think it is?

[ancient galleon]

idk how the brackets and parenthesis work

[jaunty mural]

(-infinity, 5)

means -infinity < x < 5 (informally writing)

its just a convention of notation

[ancient galleon]

hmmm

ok i think i get it

[jaunty mural]

no?

[ancient galleon]

😭

[jaunty mural]

But yes good point, x is an element of is what you should write

[tepid crest]

Oh my bad

[jaunty mural]

x ∈ your interval

[tepid crest]

So sorry

[obsidian coral]

Did you turn your paper sideways and write an 8 as infinity?

[tepid crest]

I thought it's x>5 😭

[ancient galleon]

maybe

[tepid crest]

New ans-
x ∈ (-infinity, 5)

[ancient galleon]

idk how to draw a infinity sign

so does the less then sign fit in there at all?

nvm i got it

thank you

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[stark kiln]

this is a statistics question i was confused on

[stark kiln]

I think I don't fully get what a simple random sample is

i thought it's when you just take random members of the population

why wouldn't it be 350 republicans, 400 democrats, 250 independents? if those numbers represent the actual percentages of the population and you are taking random members

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[vernal shell]

Hello. I think the problem here is that they went to each group and picked a certain number of them

I mean they picked group by group

If it was a simple random sample, then they would pick 1000 people from all registered votes in the state

[vernal shell]

This is probably called stratified sample (? I'm not sure

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[brave nacelle]

Need help on rational functions

[brave nacelle]

1.(x³+2x²+7)/(3x+2)
2.5/9x4

Rational or not rational

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[vast cedar]

how does this turn into rad 3?

[fair mortar]

what

[ancient valley]

what do you mean by rad 3?

do you mean sqrt(3) by chance?

[vast cedar]

wait i thikn i worded that wrong

YES LMFAOO