help-17

[opal dragon]

great

so x = 27/4

[sly sierra]

yep

[opal dragon]

I have another question

[sly sierra]

sure

[opal dragon]

I think i can do it actually

So the triangles are similar

[sly sierra]

yea those are similar as well

so you can use the same technique

[opal dragon]

How do i know theyr esimilar

[sly sierra]

well the angles where they meet are the same by some theorem or another

and then the lower left angle of the bottom triangle equals the upper right angle of the top triangle

by another theorem

i forget the names of these theorems haha

[opal dragon]

I see. So. The base of the small one is 20mm and the base of the big one is 36mm, it's asking us to find the side of the bigger triangle

[sly sierra]

yep, and the 20 and 36 tell you the scale factor

[opal dragon]

so if it's an esf

esf = 20/36 = 5/9

5/9 * 15 = 75/9

x = 75/9

[sly sierra]

x should be bigger than 15 no?

[opal dragon]

Yeah i just realized that

let me see where i went wrong

Yeah so an esf is big over small

[sly sierra]

you're almost right, you just need the reciprocal

[opal dragon]

36/20 = 9/5

9/5 * 15 = 27

x = 27

[sly sierra]

yes

correct

[opal dragon]

Nice

Alright, I'm going to post a question with my working and can you correct it

[sly sierra]

sure

[opal dragon]

Area (Small Field) = 117m²
ESF = 25/15 = 5/3
ASF = (SF)² = (5/3)² = 25/9
25/9 * 117 = 325
Answer = 325m²

[sly sierra]

yes this is correct

[opal dragon]

👍

This one says find the gradient and y intercept of the equation

2y + 7x - 1 = 0
2y = -7x + 1
y = -7x/2 + 1/2
Gradient = -7x/2
Y-intercept = (0,1)

[sly sierra]

gradient should just be a number

the x doesn't belong there

[opal dragon]

ah yeah you only put the x if you ae writing the equation

[sly sierra]

right

the y intercept is wrong also

[opal dragon]

9x - 4y + 3 = 0
-4y = -9x - 3
4y = 9x + 3
y =9x/4 + 3/4
Gradient = 9/4
Intercept = (0,3)

[opal dragon]

Please tell

[sly sierra]

what do you get for y when you plug x=0 into y = -7x/2 + 1/2 ?

[opal dragon]

My mistake, the y intercept is (0,0.5)

[sly sierra]

gradient is correct, y intercept is wrong

[sly sierra]

yes

[opal dragon]

For the other one the gradient is (0,0.75)

intercept*

[sly sierra]

yes

[opal dragon]

A straight line is defined by the equation 3y – 4x = 7.
Find the line’s gradient and the coordinates of the point where it crosses the
y-axis.

3y - 4x = 7
3y = 4x +7
y = 4x/3 + 7/3
Gradient = 4/3
Y intercept = (0,3.5)

[sly sierra]

7/3 is not 3.5

[opal dragon]

i keep mixing up

Is it permissible to leave the intercept as (0,7/3)

[sly sierra]

sure, unless the problem (or your instructor) wants it in decimal form

[opal dragon]

One more for today

A sector of a circle has a radius of 13.2m and an angle of 181° at its centre.
Calculate
a. The sector’s area.
b. (i) The arc length
(ii) The perimeter of the sector.

(a) Sector Area = 181/360 * pi * 13.2^2
= 275.216082825m^2

(b) Arc Length = 181/360 * pi * 26.4
= 41.6994064886m

(ii) p = Arc Length + 2r
p = 41.6994064886 + 2 * 13.2
p = 41.6994064886 + 26.4
p = 68.0994064886

This might be a pain to mark

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[inner lake]

is this like supposed to be a number or a function of something? im confused

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[pliant eagle]

What's the domain of f(g(x))?

[pliant eagle]

Ik f(x)'s domain is [-2,2] and range is [-5,3]

And g(x) donain is [-2, 4] and range is [-2, 3]

<@&286206848099549185>

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[cyan shadow]

1. What can g(x) take?
2. Out of what g(x) can take, how much of it maps into things f(x) can take?

g(x) takes -2 to 4, so it cant be more than that

f(x) seems to take -2 to 2, so which of g(x) from -2 to 4 have outputs in that range?

answer: ||until about 3 looks like||

[pliant eagle]

Right si we have to go back to g(x) and determine the correct rangen

I got it

[cyan shadow]

sounds good

close if you have no other questions

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[vast shale]

I want to re-write sin function which has period between 0 and 180 only so only positive range is included in function.It's graph will look like valleys lined up one after the other. Can i do it with fourier series maybe?

[vast shale]

graph will be like this ig

[dapper condor]

This might be very simplistic, but couldn’t you do this with absolute values

[vast shale]

It might be f(x)=|sinx| too but i want to find a way to write it without absolute values

[dapper condor]

Ah okay

[vast shale]

can you write it like sum of two periodic function so you can get what i want or something

[mild flower]

not with those sharp corners

,w plot (1+sin(1/2 x))/2

[twin meteor]

Results provided by WolframAlpha

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Requested by kitten.in.a.teacup

[vast shale]

Is this graph a slightly higher located version of the original graph?

[mild flower]

higher, shorter, stretched

[dapper condor]

I know absolutely nothing about the Fourier series but I found this on the internet

The second last one seems to be the thing you’re looking for

[vast shale]

yeah it is i will check that

but is there literally no way to write in different form?

i mean without absolute values

or infinite series

[mild flower]

to make it exact? no

,w plot 2/π - 4/π sum[1 to 4] (1/(2n+1)sin(2n+1)x)

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[vast shale]

im actually interested to just integrate |sinx|

so i thought maybe it would be done using some fourier stuff but i guess it was bad idea

|sinx| don't have indefinite integral answer right?

[dapper condor]

You could try some cases for it

[vast shale]

i want to integrate it between 2018 and 0

[dapper condor]

Oh that changes things

Before we tackle that

https://math.stackexchange.com/questions/3274401/integral-of-textabs-sinx-explanation

This is an interesting forum on the sign changing idea I was taking about with the cases

There does seem to be an indefinite integral

[vast shale]

what does that "sgn" mean

[dapper condor]

Read on

There’s a link that explains it

[vast shale]

this one actually made sense to me

i didnt get it why do they say it must be wrong

what does absolutely continuous mean

[dapper condor]

Means that it is continuous at every point

So basically the wolfram alpha answer is wrong

Use the answer below it

That’s seems to be right

Because it is continuous and differentiable at every point

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[karmic dagger]

Hi I am taking Math 232 right now and I am stuck on this question. I understand that the vector p and d are on the same line because vector p is a scaler of the vector d but I am confused by the part of proving.Thanks

[mild flower]

prove it one way then the other

like first assume that p is a scalar multiple of d, and show that the line passes through the origin

and then assume it passes through the origin and show that p has to be a scalar multiple of d

[karmic dagger]

so does it mean I can prove it by graphing?

[dapper condor]

Proof by graphing is always a very iffy thing to do

It’s not very rigorous at all

So I would recommend to avoid that

Do it in a more algebraic way

[karmic dagger]

so I can set a value for p and d then show that the origin is in the line?

[dapper condor]

If you have a line with no fixed vector then it must pass through the origin

[karmic dagger]

sry but I am still kinda confused. How will you approach this question ? Thx

[dapper condor]

So define coordinates for d and p

And format it such that the line equation has no fixed vector

[karmic dagger]

ah i get it now thanks

.close

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[vast shale]

Hi, I am super confused. Could anyone please tell me how to go about this question? Identify all closed sets in a Discrete metric space.

Aren't all sets closed in a Discrete metric space? So, do I say whole R?

[paper depot]

you say all sets

not "whole R"

but rather "all subsets of the space"

[vast shale]

Oh okay, makes sense, thank you so much!

[paper depot]

!occupied

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[vast shale]

.close

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[vast shale]

can help

do not know what im wrong

for the last mark

[languid pier]

Did you solve it

[vast shale]

no

i got it never mind

.close

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[full turret]

hello! i was just wondering if i answered this question correctly but the answer and working should be simple!

[vast shale]

??

[merry python]

The change from step 2 to step 3 is pretty sus

What was your reasoning behind it?

[vast shale]

if you multiply both sides by 4 you dont get that

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[coarse gust]

what hv I done wrong?

[coarse gust]

Using this calculation the answer is 64.4 (1sf). But it should be 85.7

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[coarse gust]

<@&286206848099549185>

<@&286206848099549185>

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

[delicate stirrup]

But he waited lol

[outer warren]

once

anyway, work seems alright

who's saying it should be 85.7

[coarse gust]

The answer sheet

[coarse gust]

Yea lol

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[somber portal]

the problem is ambiguous. where does it say that C is due east from A?

[coarse gust]

From C 40m east of A

I'm so confused with this one too

I can do the cos rule but have no idea how to show that

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[urban token]

Can anyone help with q4

[vast shale]

,rotate

[chrome raptor]

What have you tried?

Do you at least calculated the power series of e^x and cos(x)?

[urban token]

I have got this

[native spindle]

huh

[urban token]

Do i multiply the first 2 terms of each sequence

It might be wrong

[native spindle]

can you just type it?

[mild flower]

multiply them like you would any other polynomials

[urban token]

The first 2 terms of each?

Because i only need up to x^3

[mild flower]

any combination of terms that give you a power ≤ 3

[urban token]

Okay thanks

Is that all i need to do for this q

[mild flower]

ye

[urban token]

Ok thanks alot

Also what is the maclaurin series for tanx

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[strong comet]

Don't even know how to set this one up

[proven garden]

#❓how-to-get-help

[proven garden]

let y=mx+b

and use the properties of tangent line

[strong comet]

3=m(1+b)? I'm sorry, I'm confused on which values to use

Oh wait, I think I might get it now lol

sorry I guess I'm still lost, how am I finding either the slope or b with only one set of points for the tangent line?

h' is a point on the tangent line correct?

since h'(1) = 3, that means the slope of the tangent line is 3, and I use the points for f(x) to fill in my values for y=mx+b, ergo 3=1(1+b)?

I know the answer is y = 3x - 1 but not sure if my methodology is correct here

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[woven rivet]

Can I get help with both questions

[woven rivet]

Solve for v 5/9+w=z

[floral pike]

What would you have to do to get the term with v in it by itself

[woven rivet]

Divide

Right?

@floral pike

<@&286206848099549185>

[solemn cape]

!15min

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

[woven rivet]

Ok

[honest ridge]

As Disorganized said, you have two variables on the left, try getting rid of the w .

[woven rivet]

Oh I got that answer already

I just need help with the other one

[honest ridge]

7. ?

[woven rivet]

Yes

[honest ridge]

btw I guess we see each other again

[woven rivet]

Solve for b ab+5/4= C

And yeah, I guess

But there are so many math helpers on here.

[honest ridge]

that's why I am amazed

[woven rivet]

I like ur username

[honest ridge]

thanks 😀

but going back to the problem
( ab+5) /4= c
try getting rid of the denominator

[woven rivet]

So do I divide it by both sides?

[honest ridge]

I'd myself multiply by 4

because you can throw the 4 away from the denominator on the lhs

[woven rivet]

So would it be ab+5=4c?

[honest ridge]

exactly.

What do we do now?

[woven rivet]

Do we get rid of the 5?

[honest ridge]

indeed

[woven rivet]

By subtracting?

[honest ridge]

yes, we need to subtract

[woven rivet]

Then do we divide ab?

I meant a

[honest ridge]

First of all, what did you get from the previous step?

[woven rivet]

Ab=4c-5

[honest ridge]

Now you need to get rid of the b to have a by itself

[woven rivet]

Do I divide?

[honest ridge]

exactly
because a * b / b = a * 1 = a

[woven rivet]

I have a=4c-5

[honest ridge]

You forgot about the RHS

It still has to be divided by a

[woven rivet]

Would it be a=4c-5b

[honest ridge]

Why though? I thought we were dividing

[woven rivet]

Would it be b=4c-5/a?

[honest ridge]

exactly,
now I've noticed a mistake of mine, I thought we were solving for a

[woven rivet]

It’s chill

[honest ridge]

but anyways your solution is correct

[honest ridge]

😆

[woven rivet]

I need help with 3

Lol

[honest ridge]

let me write it in tex, brb

[woven rivet]

Don’t mind my hieroglyphics at the bottom

[honest ridge]

$$\frac{1}{3}+2m=m-\frac{2}{3}$$
Here we need to get the exact value of m since there ane no other variables

[twin meteor]

themathboi #2137

[woven rivet]

Ok

[honest ridge]

Notice we have m on both sides here, it's kinda not what we want

[woven rivet]

Do we move one M to the other side?

[honest ridge]

Yes, just subtract it from both sides

[woven rivet]

Ok

1/3+1m=-3/2

[honest ridge]

exactly, now there's the unnecessary 1/3 on the LHS

[woven rivet]

So we cancel that out and bring it to the other side?

[honest ridge]

also, it should be -2/3 not -3/2

[honest ridge]

indeed

[woven rivet]

So what after that

[honest ridge]

What did you get?

[woven rivet]

I have 3/6+1M

[honest ridge]

something went wrong here, I need to explain something

[woven rivet]

I have a feeling that isn’t right

[twin meteor]

themathboi #2137

[honest ridge]

this is what we begun with

[woven rivet]

Yes

[honest ridge]

$$\frac{1}{3}+m-\frac{1}{3}=-\frac{2}{3}-\frac{1}{3}$$
subtracting 1/3 from both sides

[twin meteor]

themathboi #2137

[woven rivet]

Oh, I thought we brought -2/3 over

Ok

[honest ridge]

You technically could, but calculations get a bit harder

now simplifying:

$$m=-\frac{3}{3}$$
$$m = -1$$

[twin meteor]

themathboi #2137

[woven rivet]

So is it M = 1/2?

[honest ridge]

Why though?

[woven rivet]

Is it 1/3+M=3/6?

Wait

[honest ridge]

I'm all ears

[woven rivet]

Is it M-1/3=-3/6?

[honest ridge]

It was equal to 2/3

[honest ridge]

and why subtracting anything from pure m?

[woven rivet]

So was it Is it 1/3+M=3/6? Then

[honest ridge]

why 3/6 though? It's equal to 1/2

[woven rivet]

I’m not getting it

[honest ridge]

which step are you struggling with?

[woven rivet]

themathboi #2137

1/3 subtracting from both sides

[honest ridge]

I have an idea, aybe this will help

$\frac{a}{x}+\frac{b}{x}=\frac{a+b}{x}:not:\frac{a+b}{x+x}$

[twin meteor]

themathboi #2137

[honest ridge]

the same goes for subtraction

[woven rivet]

Ok

[honest ridge]

whoops, I guess bbl

[woven rivet]

Ok

I have to go soon thanks for the hel

Help

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[elfin moon]

It will be 31 right?

.close

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[vast shale]

In the fifth grade classroom, the teacher organizes his 24 students into 8 groups so that each one can create a model. In how many ways can you form the groups?

[vast shale]

Is my answer correct?

[fleet ember]

I don't think so, what you're doing is picking 8 students among the 24

You're not counting groups

[potent quest]

no its wrong

[fleet ember]

The answer should be way larger

like 10^13, around that

[vast shale]

Mm first, why it isn't combinatory

?

Combinatory is for when the order doesn't matter

like in this case

they want groups

not lines

the order is irrelevant

[fleet ember]

it is combinatorics, but you can't just pick 8 students among 24 and say that it has to be how to build 8 groups

just because there is a formula to count how to pick 8 students doesn't mean the exercise is about counting how to pick students

you want to construct groups

a group is 3 students

[vast shale]

Ohh now I get it

is not a group of 8

Is 8 groups

with 3 students each

[fleet ember]

yeah, presumably of 3 each

[vast shale]

I didn't read well

mm so I could use the same formula to find the ways to form one group of 3, and then I would have to eliminate 24 - 3, and calculate it for that one, and so on, until it's 0
And finally I would have to multiply them?

[fleet ember]

yeah but be careful

if you do that, you count several times the same group

and you have to account for it

[vast shale]

m why?
I would be doing 24-3 and so on to eliminate the already existing group

[fleet ember]

if you have 6 peoples A, B, C, D, E, F
then {{A, B, C}, {D, E, F}} and {{D, E, F}, {A, B, C}} are the same building of groups

but you count it twice if you just take 6 choose 3 * 3 choose 3

because you count the 2

you're counting each construction as many times as there are permutations of the 8 groups

[vast shale]

mm right
so I would have to divide by 8?
or maybe divide by 2 the second time, then by 3 then third time and so on until 8??
or maybe divide by 2 the second time, then by 2, and so on

[fleet ember]

8!

there are 8! permutations of 8 groups

not 8

[vast shale]

yes, there are 8! possible group configurations

[fleet ember]

you're dividing by 8! because you count each construction 8! times

[vast shale]

mm yes, so the final answer I would divide it by 8!

like after multiplying each case

[fleet ember]

yes

[vast shale]

m ok, I'll do it now

[fleet ember]

result should be close to 10^13

[vast shale]

mm ok, I'll check that also

[vivid cape]

Can anyone help me with this
I have to further convert it into normal form. And is the rank correct?

[delicate stirrup]

#❓how-to-get-help

[vast shale]

Yes

now is it correct?

[vast shale]

mm something that worries me is that it says: In how many ways can you form the groups?

@fleet ember

[fleet ember]

seems about right

[vast shale]

but I guess it refers to what we did

It makes more sense

[vast shale]

thanks a lot for the help (:
can I ask you one more question

[fleet ember]

yes

[vast shale]

If I had read correctly I would have done the multiplications, but I think I would have missed the fact that you need to divide it by 8!

How can I study to perceive these kind of things

In order to learn this, did you practiced and reflected about the problems?

or maybe you did another things

[fleet ember]

my method is "always think 3 times" and "check what you counted"
when I count how to form the group I go by
"ok, I choose 3 among 24 for the first group, 3 among 21 for the second..."
and at the end I ask myself, what did I count ? so I check with an example
and I realize that I counted all permutations of a specific "building of groups", and I obviously did the same for every "building of groups"
and since I counted each 8! times, I divide by 8!

it's not really about anticipating it, it's more about being careful and knowing that this kind of mistake is possible

so that you'll always need to double check yourself in some way

[vast shale]

Oh okay, from now on I will check this possible error and evaluate it methodically using similar situations like you did
Thanks (:

.close

[vocal sleet]

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[lilac plaza]

Hi, not sure where to start

[split heart]

draw

best place to start here

[lilac plaza]

Here

[obtuse sierra]

what's the displacement in the y-direction?

[lilac plaza]

8

[obtuse sierra]

correct

and in the same time, what is the displacement in the x direction?

[lilac plaza]

18

[obtuse sierra]

is there any external force in x direction?

[lilac plaza]

wdym external force?

[obtuse sierra]

like gravitational force

[lilac plaza]

Only g

[obtuse sierra]

in x direction?

[lilac plaza]

No

[obtuse sierra]

btw g is not the force but the acceleration due to it

[lilac plaza]

Okay

[obtuse sierra]

so velocity is constant in x direction

[lilac plaza]

Yes

[obtuse sierra]

how can you write the displacement in x direction then?

[lilac plaza]

Multiplied by two

But subtracted by the amount before it hits the building

[obtuse sierra]

no

i asked x direction only

[lilac plaza]

Displacement was 18m though

What you talking about?

[obtuse sierra]

in terms of time and velocity?

[lilac plaza]

Not sure..

[obtuse sierra]

is there any acceleration?

no, right?

[lilac plaza]

Yea

[obtuse sierra]

so the velocity is constant, right?

[lilac plaza]

Yes

[obtuse sierra]

dont you think velocity can be written as just displacement/time here?

since there's nothing that is increasing/decreasing the velocity

[lilac plaza]

18/t

Since we don't know t

[obtuse sierra]

correct

and in the exact same time, the body has a displacement of h in the y direction

which equation of motion do you think we should apply in y direction?

[lilac plaza]

V_osin(x)?

[obtuse sierra]

i asked the equation

not the velocity in y

[lilac plaza]

h = v_o^2/2g

This?

[obtuse sierra]

nah

h is not the maximum height

[lilac plaza]

I really don't know...

v_o^2sin(x)^2/2g

[lilac plaza]

Gimme a hint pls

[obtuse sierra]

the second equation of motion?

[lilac plaza]

Among the big five equations?

[obtuse sierra]

there are 3, no?

whatever

the second one

[lilac plaza]

Are you talking about v_o*t - 1/2gt^2?

[obtuse sierra]

yeah

[lilac plaza]

Why are we using this?

[obtuse sierra]

you have the displacement

[lilac plaza]

Can I have like a visual representation pls

[obtuse sierra]

the velocity

the acceleration

the only unknown is time

these 3 equations are the basics

always try to use these first

the others are derived from these

[lilac plaza]

Okay

[obtuse sierra]

so use it what do you get

[lilac plaza]

h = v_o*t - 1/2(10)t^2

Everything else we don't know?

[obtuse sierra]

where vo is?

[lilac plaza]

v_o isn't given

[obtuse sierra]

wdym

[lilac plaza]

Are we supposed to use sin(x) for v_o

I have like a solution here

[obtuse sierra]

yeah

[lilac plaza]

But I don't know why it does like that

[obtuse sierra]

remove it

[lilac plaza]

?

[obtuse sierra]

the same solution I am showing you

dont read it if its confusing you

[obtuse sierra]

we are applying this for the y direction

[lilac plaza]

I'm trying not to

[lilac plaza]

Yes

[obtuse sierra]

so everything is gonna be for the y direction there

the h

[lilac plaza]

Yes

[obtuse sierra]

the velocity

the acceleration

[lilac plaza]

Ohhh

[obtuse sierra]

so sub the values

[lilac plaza]

So

I have to change

v_o

[obtuse sierra]

yeah

[lilac plaza]

to v_o sin(x)

Ahh

I see

[obtuse sierra]

this seems like an emoji

[lilac plaza]

I STARTED IT

I have the authority

I get credit

lmao

Anyways

[obtuse sierra]

v_o

[lilac plaza]

v_v

Uhhh

So

How do I get t

[obtuse sierra]

first form the equation

[lilac plaza]

Of?

[obtuse sierra]

.

[lilac plaza]

Sub what values 😢

[split heart]

What's the progress here

[obtuse sierra]

going good

[lilac plaza]

Uhhh

[obtuse sierra]

about to finish

[split heart]

Duality of man lol

[lilac plaza]

Really?

[obtuse sierra]

the h, the v

[lilac plaza]

Oh okay

Hold up

h = v_osin(x)*t - 1.2gt^2

Like this?

[obtuse sierra]

yeah yeah

[lilac plaza]

Yay

What next

[obtuse sierra]

we'll sub the values later

now, time

[lilac plaza]

Okay

How do I get time

Money can't buy time

[obtuse sierra]

what did you get from the x direction?

[lilac plaza]

x = v_o*cos(x)t

[obtuse sierra]

yep

you have the x and the v

[lilac plaza]

Yeah

[obtuse sierra]

and t is same for both the equations

right?

[lilac plaza]

Yeah

But hold on

[lilac plaza]

Why is it v_o?

Shouldn't it be just v?

[obtuse sierra]

wdym

[split heart]

good lord why would they put "x" as multiplication so randomly lol

[lilac plaza]

lmao

"AP" Physics

[obtuse sierra]

[lilac plaza]

So like look at equation 4

It's not v inital

[obtuse sierra]

um hm

[lilac plaza]

It's v final

[obtuse sierra]

oh really?

[lilac plaza]

But I wrote my equation as minus

[lilac plaza]

Yea?

[obtuse sierra]

no

equation 4's v_o is intial velocity

[lilac plaza]

Where's v_o?

That's just v

Shouldn't we be using equation 3 then?

[obtuse sierra]

yeah whatever, v

its initial

[lilac plaza]

The minus and plus are different

I'm confused though

[obtuse sierra]

bruh who tf gave you those equations

[lilac plaza]

"AP" Physics

lol

[obtuse sierra]

the only ones you need are 2nd, 3rd and 5th

delete the other

they stupid

[lilac plaza]

It's a picture

But okay

[lilac plaza]

So using equation 3 here

I should change the minus to plus, right?

[obtuse sierra]

is g + or -?

[lilac plaza]

Ohhhhhhhhhhhhhh

That makes sense

So h = vt - 1/2(10)t^2

[obtuse sierra]

yeah

and v is?

[lilac plaza]

sin(x)

[obtuse sierra]

vsin(x) yeah

so now from x direction we had?

[lilac plaza]

d = vcos(x)t?

[lilac plaza]

What x direction?

[obtuse sierra]

yeah

[lilac plaza]

Kay

Good

[obtuse sierra]

now take that t, and sub it in the y direction equation

because t is same for both

[lilac plaza]

Ayyy

[obtuse sierra]

yup correct

sub the values and get the answer

no wait

you yeeted the 't' again

[lilac plaza]

Shit

Hold up

Thereee we go

[obtuse sierra]

replace the t ._.

[lilac plaza]

Oh

I like to yeet t

Like fr

There we go

[obtuse sierra]

the last t is squared

[lilac plaza]

AHHHHHH

[opal dragon]

still no answer

[lilac plaza]

Too late man

[opal dragon]

wym

[lilac plaza]

Squared it

[opal dragon]

dont use that phrase again

[vast shale]

Do u need help

[lilac plaza]

?

[vocal sleet]

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).

[obtuse sierra]

you are done.

[opal dragon]

i wus just looking to see if my answer got marked

[lilac plaza]

Bro, you asked a question yesterday

You expect it to be open for an entire day

[obtuse sierra]

this channel is occupied!

[opal dragon]

clearly no one answered the question i asked in this channel

so cool

bye

[lilac plaza]

Maybe no one knew how to answer it?

[opal dragon]

it was 14 yo work

[obtuse sierra]

ignore it

[opal dragon]

Butbye

[lilac plaza]

sighs

[obtuse sierra]

got the answer?

[opal dragon]

nah nah nah dont use sigh as a text actually say it man

[lilac plaza]

But wait

[opal dragon]

Now bye

[obtuse sierra]

can you just go?

[lilac plaza]

I can change it to tan right?

[opal dragon]

Your so annoying

[lilac plaza]

*you're

[obtuse sierra]

yeah you can

you have the values

[opal dragon]

ok last time i checked it was an math server not english now bye for real im gone

[lilac plaza]

Ohhh

[obtuse sierra]

you can just sub them

[lilac plaza]

Got it

[obtuse sierra]

<@&268886789983436800> really being annoying

[opal dragon]

IM LEAVINGg

BYE

[lilac plaza]

Just don't reply to them

[obtuse sierra]

also their bio

[lilac plaza]

They seek attention

Attention seekers

[opal dragon]

bio??

what about my bio

sorry for distrupting

but if you have an issue with my bio take it to dms

[blissful sentinel]

@opal dragon this is no longer your channel

!occupied

[vocal sleet]

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).

[opal dragon]

yes yes im aware and i apologise

goodbye

[obtuse sierra]

already did that eric

[lilac plaza]

Eric's omnipotent

[obtuse sierra]

so .close?

[lilac plaza]

Yep

[obtuse sierra]

wait

[lilac plaza]

Just checked the answer

Ye?

[obtuse sierra]

eric's here

[lilac plaza]

Hi Eric

[obtuse sierra]

or he left

[blissful sentinel]

has your question been answered

[lilac plaza]

Yes

Thanks Dyssrupt

As always

[blissful sentinel]

okay yea go ahead and close it

[lilac plaza]

.close

[vocal sleet]

Channel closed

Closed by @lilac plaza

Use .reopen if this was a mistake.

[opal dragon]

!help

[vocal sleet]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

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[gritty geyser]

I’ve been trying to solve this problem. I know the answer is -1/2 but I can’t figure out how to actually get there. Nothing seems to cancel and I can’t substitute for in 2 for x yet because then I end up dividing by zero. I’m really lost. Any help would be much appreciated!

[delicate stirrup]

,rotate

[delicate stirrup]

get the derivative of $sqrt(2x-1)$ as shown above

[twin meteor]

TimK

[delicate stirrup]

then substitude 25

[gritty geyser]

oh sorry I should've clarified. It's #2. I haven't started #3 yet because I wanna figure out where I'm going wrong in #2.

[delicate stirrup]

oh

isn't it lim x->2 -1/sqrt(2-x)?

[gritty geyser]

for what? the answer?

[delicate stirrup]

yes

[gritty geyser]

where did you get a -1 from?

[delicate stirrup]

x-2 = -(2-x)

[gritty geyser]

hm. but then you're dividing by zero when you substitute 2 in for x

I mean. idk. I'm like 95% sure the answer is -1/2 because it's just a practice problem I got from class that I'm trying to figure out why I got wrong.

[vocal sleet]

@gritty geyser Has your question been resolved?

[vocal sleet]

@gritty geyser Has your question been resolved?

[vocal sleet]

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• Show your work, and if possible, explain where you are stuck.
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[grand ledge]

Im trying to solve this $$x-11\sqrt(x)+24=0$$

[twin meteor]

Totalani

[grand ledge]

Im getting x=8, I checked wolfram and it says x=9

What I did was I turned the sqrtx into t, so $$t^2-11\sqrt{t}+24=0$$

[twin meteor]

Totalani

[grand ledge]

and then solved it

how do you edit?

I ment to write 11t

[full arch]

so you got t=8 as a solution to that equation

and you made the sub x=t^2

[grand ledge]

one of the solution I got as t=8 yea

[full arch]

and the other one?

[grand ledge]

and the other solution would be 64 since its t^2

but wolfram says x=9 and x=64

just not sure why it says 9

[full arch]

yes because you're forgetting your 'other' solution

[full arch]

because it has two solutions

[grand ledge]

yea, 8 and 64?

[full arch]

no

what did you get for both your t values, as solutions for f(t)

[grand ledge]

why 9? 9*9 is 81

so I got $$t=5.5\pm2.5$$

[twin meteor]

Totalani

[full arch]

which is

either

[grand ledge]

8 and 3

oh

[full arch]

meaning??

[grand ledge]

so you are supose to quadric both?

[full arch]

what do you mean

[grand ledge]

3^2=9

[full arch]

the goal is to find the solution to the equation you have made the substitution to f(t), then go back and correct the value for x, and test it holds true

[grand ledge]

right

[eager elbow]

you can do (x-11sqrt(x)+24)^2=0

[grand ledge]

which I tried

64 is correct, it gives me 0

[full arch]

so you found both 3,8 as solutions to f(t)=0, meaning x=9,64 (potentially for f(x)=0), and we go back and check for f(x) for f(9) and f(64) and see they both = 0 , so we can say x=9,64 are solutions for f(x)=0

[grand ledge]

ah yea, i forgot to change the 9 into 3 in the sqrt

urgh

thank you !

.close

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[snow raptor]

a bit confused about this part

[snow raptor]

dont we convert sinx cosx to =1/2 sin2x

and then it should be t^2/[1+t^2]

wait

im stupid.

MY BAD.

I was correct.

then we just use the substitute t=tan x/2

and then sinx= 2t/[1+t^2]

.close

[vocal sleet]

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[vocal sleet]

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[elder geyser]

any shortcut trick for this

options

oops

💀

[vocal sleet]

Channel closed

Closed due to the original message being deleted

[elder geyser]

.close

IT WONT COOSE

CLOSE

,close

.close

[solemn cape]

It will close don’t worry

[vocal sleet]

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[haughty garden]

<@&286206848099549185> (calculus) im trying to prove that there exist infinite solutions to a^a=b^b for a≠b. i tried taking the ln of both sides but nothing

[rancid blaze]

maybe try looking at the graph of xln(x)

[vocal sleet]

@haughty garden Has your question been resolved?

[haughty garden]

and then what

[rancid blaze]

have you looked at it?

[haughty garden]

yes

[rancid blaze]

you want to find points where a ln(a) = b ln (b)

for a neq b

so what would taht look like on the graph

[haughty garden]

oh so can i just say since its not 1 to 1 on the interval (0, 1]

then there exist infinite solutions

since for every point a there is a point b such that

[rancid blaze]

might need a bit more since thats just saying theres some solution in (0,1]

[haughty garden]

f(a) = f(b)

[rancid blaze]

yeah

second bit

[haughty garden]

but how caj i prove prove that rigorously

[haughty garden]

does there exist a way to do so

[rancid blaze]

uh

maybe something like if you can show its not injective in any sufficiently small neighbourhood of the minimum

then one solution exists and then you can think of the smaller neightbourhood that excludes that solution

edited sry

and u can do that infinitely many times

actually maybe you can explicitly say for any a on the left hand side of the minimum what the b on the right hand side would be so that aln(a) = bln(b)

that sounds easier

[vocal sleet]

@haughty garden Has your question been resolved?

[haughty garden]

okay bet ty

[vocal sleet]

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[vast shale]

so i derived it alr, i just need help for part B

do i just plug in 1 into derived equation for slope and 1 into normal equation for y int

then simplify into y=mx+b?

[deft mortar]

yeah

[outer warren]

subbing 1 into the original equation doesn't give you the y-intercept

[deft mortar]

but you will need b

[vast shale]

gives u y1?

[deft mortar]

just clear b

[vast shale]

wdym clear b

here let me write it out rq

[deft mortar]

solve for b from the equation u got

[deft mortar]

this is true

but not interception

just Y

you have Y = mx but less b

b = y - m(1)

[vast shale]

alr so im left with this

[deft mortar]

and b is the Y intersection

[vast shale]

m =4, y1 = 8 if i put it in y-y1 equation?

[outer warren]

if by y-y1 equation you mean point slope form equation, yes.
don't forget your x_1

[vast shale]

yeah, then u can simplify into slope form, right?

[outer warren]

slope intercept form, yes

[deft mortar]

it would be easier if you do: b = 8 - 4(1)

[vast shale]

x1 would would 1 since x=1 is given

is this good

[vast shale]

yeah thats what i did

subtracted 8 from both sides

[deft mortar]

r?

or y or x?

[vast shale]

u mean under the 8?

if so, thats an 8, my handwriting is just rlly bad bro 😭

[outer warren]

looks fine

[deft mortar]

oh thats number 8

[vast shale]

yeah 🤣

[deft mortar]

XD

[vast shale]

tysm guys

.close

[vocal sleet]

Channel closed

Closed by @willow jetty

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[vocal sleet]

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Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[keen ocean]

if you can take any square number, can you always construct a rectangle with the same area as the square, where both length and width are prime? is this the same as asking if all square numbers have two prime factors?

[prime mulch]

quite sure it's the same

just asking if you can factor a perfect square into two prime numbers

[keen ocean]

yeah you're right it was have to be (p * q) + k^2, k < n. to match the area of the n^2

[prime mulch]

perfect squares only have 3 factors

[brisk moss]

sorry ignore what i just typed

[prime mulch]

1, x, x^2

so no you can't

because x^2 isn't prime

and you (probably) can't use x again

[keen ocean]

.close

[vocal sleet]

Channel closed

Closed by @keen ocean

Use .reopen if this was a mistake.

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[vast shale]

Please help

[vast shale]

I got no clues

[formal gazelle]

m isnt given so idk how u find n

[spiral inlet]

Have you tried expanding the expression at the top and combining the like terms?

like terms in terms of x, I should say

[vocal sleet]

@vast shale Has your question been resolved?

[vast shale]

Thats what yo get

idk if that helps

[spiral inlet]

so look at your x^3 terms and your x^2 terms

you can still gather like terms, treating m as a constant

[vast shale]

But the value of the exponent is different

how can you add them?

[spiral inlet]

well x^3 and x^2 separately

like your x^3 terms are

2mx^3 + x^3

= (2m+1)x^3

[vast shale]

Ohh

so wait are you gonna make 8mx^2 then to (8m+1)x^2

[spiral inlet]

no, that doesn't match what you have for x^2

8mx^2 - 4x^2

if you combine those, the coefficient is not 8m+1

[vast shale]

OHHHHHH

I see what your doing

so it becomes (8m-4)x^2

[spiral inlet]

yeah

[vast shale]

so then you have (2m+1)x^3+(8m-4)x^2

[spiral inlet]

yes exactly

and that's supposed to be equivalent to nx^3

[vast shale]

yes but that aint my options

😭

[spiral inlet]

well, we haven't answered the question yet

the question is what's the value of n

so, we basically have two polynomials
(2m+1)x^3 + (8m-4)x^2
and
nx^3

keep in mind, only x is a variable here, m and n are constants

which means these two polynomials are equivalent ONLY IF the x^3 terms are equal, and the x^2 terms are equal

am I making any sense?

[vast shale]

So are you gonna make the (2m+1)x^3 = nx^3?

[spiral inlet]

Yep!

the x^3 part just kinda disappears

[vast shale]

Oh

Yeah

[spiral inlet]

the important thing is that the coefficients are equal

[vast shale]

so n is equal to 2m+1

[spiral inlet]

yep

and what about 8m-4? 🤔

[vast shale]

Throw it in a hole and forget about it

[spiral inlet]

Lol

I dunno about that

[spiral inlet]

here you said n=2m+1

but that's not very useful without knowing the value of m

which is where the x^2 terms come in

[vast shale]

WAIT

Oh

I THINK

I KNOW

no

i dont

wait

i wanted to say you could say that 8m-4 is like 4n but there is the stupid subtraction sign

[spiral inlet]

nah, look at your two polynomials one more time

(2m+1)x^3 + (8m-4)x^2
and
nx^3

the first one's x^2 coefficient is 8m-4

what about the second one?

don't overthink it too much lol

[vast shale]

I am

😭

[spiral inlet]

The second one has an x^2 coefficient of 0

since there is no x^2 term

after all, 0x^2 is equal to 0, so we don't usually write that term if the coefficient is 0

[vast shale]

Wait would one term be 8mx^2 and the other be -4x^2

im confused

[spiral inlet]

nah

[spiral inlet]

so like from here

we matched up the x^3 terms right? and said

2m+1 = n

[vast shale]

yeah

[spiral inlet]

and now we do the same for the x^2 terms

8m-4 = 0

[vast shale]

Oh

i see

So the answer is two

So you can 8m-4=0 so you can just find the solution?

[spiral inlet]

yeah well

2 is correct for n but it doesn't sound like you got all the way there

you solve 8m-4 = 0 for m

then substitute it in 2m+1 = n to find n

[vast shale]

so 8m=4

m=1/2

2(1/2)+1=2

Bam

[spiral inlet]

yep 👍

[vast shale]

I want to love math

but math hates me

[spiral inlet]

This one was kinda tricky, especially with the way it was worded

[vast shale]

Its my stupid SAT prep class

[spiral inlet]

they called m and n constants but should have emphasized that x was the variable of the polynomial

oh

[vast shale]

i cant wait to take the test and be done with it

[spiral inlet]

tbh this is harder than most of what you'll see on the sat

[vast shale]

Thats good news

What grade you in?

assuming college?