help-13

[upbeat lotus]

Ok

[bright sorrel]

Idk how to do this one

But Ik the formula is a square +b square =c square

But we gotta find b square

[kindred storm]

You already have that. The 15 is in square centimeters, so the side length is sqrt(15) centimeters and the square of that is 15 square centimeters.

[bright sorrel]

Idk how to

Do this

[cedar kiln]

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[cedar kiln]

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[cedar kiln]

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[dusky pond]

can someone call me

[dusky pond]

so i can screenshare my problems

[crimson delta]

ask a proper question. no one will call you if they dont even know what you need help with and if they can even help you

[dusky pond]

circle theorms mixed with some trig

[cedar kiln]

@dusky pond Has your question been resolved?

[cedar kiln]

@dusky pond Has your question been resolved?

[slow thicket]

just ask it

[dusky pond]

bro i cant

u have to like see the question

[slow thicket]

take a screenshot

[dusky pond]

oh yeaa

[slow thicket]

!status

[cedar kiln]

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

[dusky pond]

1

[slow thicket]

so you know the radius is from O to any point right

so say OB

and OB is also the same as OC

so you get a triangle

go from there

[dusky pond]

oooo lemme see

i j made a triangle

from O to C to B to O again

now what

[slow thicket]

what is the angle COB

[dusky pond]

90?

if not idk

[slow thicket]

look at the shape

why did you guess 90

[dusky pond]

because i cant figure out another way to get another angle and 90 looked about right

[slow thicket]

okay look

we know its a regular pentagon

because its in a circle

and since there are 5 sides there are 5 angles that share O as th ecenter

so 360/5 = 72 degrees

now just use the law of cosines

[dusky pond]

are we solving for a^2

or is it cos(A)

[slow thicket]

draw the triangle

and send a picture

[dusky pond]

okay]

[slow thicket]

label everything we know

and what we need to solve

[dusky pond]

okay

[slow thicket]

use numbers

[dusky pond]

i wasnt planning on using anything else

sorry had to

was that angle

90?

at

COB

[slow thicket]

no

360/5

[dusky pond]

why

oh

i get it

[slow thicket]

you also know the radius

= 12 cm

[dusky pond]

yes yes

so its

but how do we apply the law of cosines here then

[slow thicket]

do you know what the law of cosines is

write it out

[dusky pond]

a^2 = b^2 + c^2 -2bc cos(A)

[slow thicket]

yeah

now do it with the lengths and angles you know

[dusky pond]

okay

14.11?

[slow thicket]

idk i didnt do the math

what variable did you solve for

[dusky pond]

the side

a^2

[slow thicket]

okay

and what is a in context

which line segment

[dusky pond]

ehmm

BC

[slow thicket]

yeah

okay so now what

look back at the question

[dusky pond]

yes

m is the midoint

of

BC

so

BM =

7.055

hey quick question

how good are you maths and are you familiar with the edexcel/cie mathematics exam board for gcse

[slow thicket]

yep

[slow thicket]

good is subjective, and no

[dusky pond]

ahh okay

so how do i find BX

[slow thicket]

draw out the triangles

try to solve it for a few min before asking

the point is for you to be able to solve it on your own

[dusky pond]

u sound like my mom

but ur right

ty

can you give me a hint

[slow thicket]

no

what do you have so far

[dusky pond]

i know that OA is 12

BM = 7.055

other than that idk

[slow thicket]

draw the triangles!

use the white space you have in the problem

dont just draw on the existing diagram

[slow thicket]

draw on your white space

do you know what white space is

[dusky pond]

i doi

but like tf do i draw there

[slow thicket]

triangles

label your knowns and unknowns

[slow thicket]

omg

please use the white space

only draw what you need

OE is not helping

[dusky pond]

broooo idk what to draw on the white spcaes

well i ahve to go to bed

thank you for helping me though

i hope u have a great rest of your day

.close

[cedar kiln]

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[crimson sedge]

Help

[crimson sedge]

I don't understand how to do number 3

[cerulean sail]

Polynomial divide it, I would say

@summer kayak

[crimson sedge]

@cerulean sail can you guide me i really don't understand

[cerulean sail]

Erm, have you dealt with polynomial division before?

[crimson sedge]

Yes

Just pls tell me what to do

Lemme be done with this problem

@cerulean sail

[cerulean sail]

Then divide x^2- 3 by x + 2 and you'll get something easier to work with

If you know how to do it, then I'm sure you'll get the answer

,w (x^2 - 3)/(x+2)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by chartbit#3171

[cerulean sail]

See the second of the alternate forms, that's what you should get

From there, you should know how to integrate each and every of those terms

[cerulean sail]

Which rather helpfully Wolfie has given us here

I leave filling in the blanks to you

[crimson sedge]

ok thx

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[crimson sedge]

.closed

.reopen

[cedar kiln]

✅

[crimson sedge]

@cerulean sail

is this correct

.close

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[crimson sedge]

Is this how we use long division

[zenith sail]

Looks good to me

just don't forget it's a definite integral lol

@crimson sedge

[crimson sedge]

okay

ill try pls come back to check

Ok this is it

.close

[cedar kiln]

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[crimson sedge]

For 14 what is the definitive way to solve that

[crimson sedge]

Okay so I'm going to explain my thought process real quick here

so I'm not gonna redo the math but it is known that the longer-looking triangle is acute and the wider one is obtuse

I just have a feeling that K + L is greater than S and T but I just don't know the complete logic behind it

oh I think I solved this myself, even if the biggest angle was 89 degrees that would leave K + L to be 91 degrees which would be bigger than S and T since angle R is obtuse

okay I feel a bit stupid now

.close

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[crimson sedge]

how to solve this triangle?

[crimson sedge]

ik that the last degree is gonna be 45

but idk what to do with that

[thin roost]

You need to find the legs AB and CB??

[crimson sedge]

how do i do that?

[thin roost]

Base angle are 45° that means it's a isosceles triangle

Does that help??

[crimson sedge]

sorta yeah ty, but this is the trig unit though, i think we're supposed to use the tan, sin, cosine ratios to find it if possible

[thin roost]

If that's that then

Use sin ratio to get AB, by using sin45=AB/CA, and use Cos ratio to find CB by using cos45=CB/CA

[crimson sedge]

aah okay tysm

[cedar kiln]

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[cobalt grotto]

This is sort of a CS/math question

[cobalt grotto]

Discrete structures/theory of computation

I guess my question is mostly, what happens if the automaton is at q2 and receives a c input, but has an empty stack?

As far as I can tell, the format is input, pop/push

My immediate guess is that this PDA defines language

$\L = { {a^x}{b^y}{c^z} | z = x + y }$

[wraith dagger]

Eyesonjune

[cedar kiln]

@cobalt grotto Has your question been resolved?

[lethal jackal]

I think if you have an empty stack in a PDA, it's a reject

[cedar kiln]

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[cobalt pulsar]

How do I do 12

[digital cliff]

what did you do after differentiating?

[cobalt pulsar]

Took quadratic

[lusty grotto]

what do you get when u differentiate velocity wrt time

[cobalt pulsar]

After differentiating we took the quadratic equation to find intercepts

[digital cliff]

but that would give you the time for max and min velocities, is that what the question wants?

[lusty grotto]

draw a rough graph of the quadratic in the interval 0 to 4

[cobalt pulsar]

Ya it want the minimum acceleration

[lusty grotto]

you could find the absolute minimum, and then see if it lies within the given range, if it doesnt, the minimum would be one of the boundary points

[cobalt pulsar]

Ok thanks that worked

.close

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[warm gate]

I'm doing a little bit of data analysis and I'm trying to figure out the chance of this dataset appearing naturally or if it's not significant.

[warm gate]

Additionally, this dataset will grow, and I'm trying to figure out a mathematical way to figure out the chance of this data appearing

[buoyant latch]

could you give a little more context of where this data is coming from?

[warm gate]

It's a sample from my robotics workshop, it's kinda stupid, but on my team, we have this theory that there are certain MBTI personality types that typically work there. Each column is a different type, Introvert, Intuitive, Feeling, and Judging

It's not the most scientific ways to do it like using the actual percentages from the test, but that's just what we're doing for now bc we thought it was strange all of us were intuitive when it's pretty uncommon worldwide (26%)

[buoyant latch]

what's the # of occurances

oh your team

[buoyant latch]

what is your null hypothesis and alternative hypothesis

[warm gate]

The test results, so for the first column for example, 5 of the 6 people who took the test were introverts

[buoyant latch]

if you want to look at inferential statistics and whether or not 2 data sets are significantly different

[warm gate]

yeah, I'm a little familiar with statical analysis but wasn't exactly sure how to apply it here

I'll look into inferential statistics, I never heard of that specifically

[buoyant latch]

i see, ok, so do you think there is a bias or there isn't?

[buoyant latch]

the thing you are missing here is what is the % of people worldwide that fit into each of those 4 columns

if that's what it means by world wide

i can tell you 6 people is not enough

you wont be able to make any useful conclusion

[warm gate]

oh I agree, we were planning on expanding it but idk how to do that math lol

[buoyant latch]

you can look at https://en.wikipedia.org/wiki/Checking_whether_a_coin_is_fair as a starting point

first start off by assuming you only have 2 types of people, and that they are equally likely to occur

(they are sides of a coin)

then from that you can try think about if a dice is biased, that'll be 6 supposedly equal outcomes

then just change their chances to be what you have as world wide

[warm gate]

That makes sense, I'll look into that

that's sorta where I got the 0.04% from, 0.267^6 since there are 6 consecutive occurrences when there's a 26.7% chance of one person having that attribute..

ofc I'm not sure if that's right, prob isn't, I'll read on it

ty

[buoyant latch]

so just because something has a small chance of happening does not mean it's biased

if i flipped a fair coin 5 times and it landed heads everytime, i only know it has a 3% chance of happening

but let's say the coin has a 55% chance to be heads, 45% chance to be tails

now this coin has a 5% chance for 5 heads to happen

inferential statistics help us analyse whether or not this 3% vs 5% difference is significant or not

[warm gate]

I see, that's a good point

[cedar kiln]

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[short blade]

is this math?

[cedar kiln]

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[crimson sedge]

how do i find the area of dis

[zenith sail]

it's a triangle, so bh/2

[crimson sedge]

ok but

thats gonna

give me the entire

area

i dont want the

shaded part

[zenith sail]

oh, I think the 15 is the base of just the shaded part

The part on the outside is just to show you that the 9 is perpendicular to the 15

[crimson sedge]

ohh ok

that makes more sense

so then 9 times 15 divided by 2 works

right?

[zenith sail]

yeah

[crimson sedge]

bet thx

i thought it was the entire

length

so i was

stuck

[zenith sail]

I don't think so, doesn't seem like there's enough information if that's what they meant

[crimson sedge]

ye

thx

.close

[cedar kiln]

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[crimson sedge]

how would i find this shaded part

does 8 times 20 work or no

for the second

[cedar kiln]

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[crimson sedge]

What would be a good text to study fractals

[crimson sedge]

and what field of math do fractals come under ?

I basically want to know which Fractals can be represented as a graph

[obsidian coral]

Ask this in #discussion

[crimson sedge]

Like sierpinski triangle

[obsidian coral]

It's more suited there

[crimson sedge]

guy told me to use ChatGPT

alright I guess

!close

.close

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[pseudo merlin]

hi

[pseudo merlin]

why is my answer wrong?

[valid yacht]

a will be $\sqrt 5 (x+6)$

[wraith dagger]

n11

[pseudo merlin]

???

[valid yacht]

but what are you actually trying to do here

whats the question

[pseudo merlin]

factorise

[valid yacht]

what rule did you apply

[pseudo merlin]

difference of perfect squares

[obsidian coral]

I suggest expanding (x + 6)^2 first

Then factoring

[pseudo merlin]

but then i cant use difference of perfect squares

[valid yacht]

while writing $5(x-6)^2 - 90$ as a difference of perfect square, the $a^2$ term will be $5(x-6)^2$

[wraith dagger]

n11

[pseudo merlin]

yes

[obsidian coral]

Are you required to use this?

[valid yacht]

so a will be $\sqrt 5 (x-6)$ while you didn't write it that way

[wraith dagger]

n11

[pseudo merlin]

yeah the question in my test will ask use DOPS to factorise

oh true

[obsidian coral]

From above, it looks like you misread $5(x+6)^2 - 90$ as $5((x+6)^2 - 90)$ instead of $(5(x+6)^2) - 90$

[wraith dagger]

dldh06

[pseudo merlin]

wat

[obsidian coral]

Original problem: $5(x+6)^2 - 90$

[wraith dagger]

dldh06

[obsidian coral]

What you read it as: $5((x+6)^2 - 90)$

[wraith dagger]

dldh06

[obsidian coral]

What it meant to be: $(5(x+6)^2) - 90$

[wraith dagger]

dldh06

[pseudo merlin]

so how am i supposed to use dops to factorise

[obsidian coral]

Same process you did above except you need to include the 5

[pseudo merlin]

how

[obsidian coral]

You need to sqrt everything, including the 5

[pseudo merlin]

Is this correct

[pseudo merlin]

I got the same wrong answer

[obsidian coral]

Because you are confusing yourself by not using enough parentheses

[pseudo merlin]

Can u show me with enough parentheses

[obsidian coral]

The sqrt(5) is with the (x+6)

You kept separating it

[pseudo merlin]

In the answers its not 3sqrt10 its 3sqrt2

[obsidian coral]

What's the answer say?

[obsidian coral]

Then what happened was it factor out sqrt(5) from the second line

[pseudo merlin]

Wat

[obsidian coral]

Second line here

Factor out sqrt(5)

[pseudo merlin]

How?

[obsidian coral]

Factoring by gcf

[pseudo merlin]

I dont understand

[obsidian coral]

If you had 2x + 4, could you factor out the gcf?

[pseudo merlin]

2(x+2)

[obsidian coral]

Same process, except the gcf is sqrt(5)

[obsidian coral]

And I was mistaken, you want to factor out sqrt(5) from each set, on the third line

So factor out sqrt(5) from sqrt(5)(x + 6) - 3sqrt(10) and sqrt(5)(x + 6) + 3sqrt(10)

[cedar kiln]

@pseudo merlin Has your question been resolved?

[cedar kiln]

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[crimson sedge]

Can you help me with number 2

[crimson sedge]

<@&286206848099549185>

[solid juniper]

x+2 = (sqrt(x-3))^2 + 5

[crimson sedge]

Then?

@solid juniper

[solid juniper]

use that to rewrite the integral with u's only haha

[crimson sedge]

Huh can you show on like paper

I have been waiting since yesterday for someone to help

@solid juniper

[solid juniper]

just like

substitute the stuff

[solid juniper]

this says x+2 = u^2 + 5

[crimson sedge]

Okay then

@solid juniper

<@&286206848099549185>

what do I do next

[solid juniper]

sorry i don't really have time to continue this :c

[crimson sedge]

pls

<@&286206848099549185> its due in like five minutes

just tell me what to

or write it on a paper

@solid juniper

[cedar kiln]

@crimson sedge Has your question been resolved?

[hollow comet]

Hi, it's a double u sub
First let u = sqrt(x-3)
Then square both sides to
u^2 = x - 3
Next add 5 to both sides so you get
u^2 + 5 = x + 2
Then sub this second one in so you are doing the integral of

$\int \frac{u}{u^2 + 5}du$

Then do a second u sub, let the new variable be called r.
Let r = u^2 + 5
Then

$dr = u du$

[wraith dagger]

Umm, Who?

[hollow comet]

Which is perfect because that takes care of the top part.
So essentially it just boils down to finding the integral of

$\int \frac{2}{r}dr$

[wraith dagger]

Umm, Who?

[hollow comet]

(Sorry forgot the 2 in my dr sub)

Hope that helps @crimson sedge

[wraith dagger]

Umm, Who?

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

@hollow comet are you still three

I just need you to double check

[hollow comet]

Sure

Quickly though.

I'm supposed to be sleep.lol

[crimson sedge]

@hollow comet

@hollow comet I'm trying to upload the pic

?

[hollow comet]

No problem @crimson sedge you're doing really well and getting really close. You're just missing the key part of the last steps.
Once you have

$\int \frac{u}{u^2 + 5}du$

[wraith dagger]

Umm, Who?

[hollow comet]

You now need to do another "u sub". This time, just to avoid confusion, I'm going to use the variable r so it's clear.
Let

$r = u^2 + 5$

[wraith dagger]

Umm, Who?

[hollow comet]

Then

$dr = 2udu$

[wraith dagger]

Umm, Who?

[hollow comet]

Or
$dr/2 = udu$

[wraith dagger]

Umm, Who?

[hollow comet]

Thus putting this back into my integral gives the final integral in terms of r

[crimson sedge]

Okay

Lemme try

[hollow comet]

$\frac{1}{2}\int \frac{1}{r}dr$

[wraith dagger]

Umm, Who?

[crimson sedge]

What is next

@hollow comet

[hollow comet]

Good so far. Now you need to get to this integral:

[hollow comet]

This one

[crimson sedge]

How

[hollow comet]

So now that you've set r = u^2 + 5

You take the derivative wrt u, but notice that you also have a u on the top

[crimson sedge]

Yeah?

[hollow comet]

in the numerator of your integral already.

Usually this is problematic BUT in this case it works out nicely because again, taking derivative of r wrt u gives

[hollow comet]

This

Subbing that into integral leads to this new integral:

[hollow comet]

This new integral

But that's an easy one to take the antiderivative of

[crimson sedge]

I feel like i skipped a step

[hollow comet]

It's just ln|x|

[crimson sedge]

U have paper

Pls write and show

[hollow comet]

Um yeah you're not writing out the integral as you do the substitution

Here

I'll write it out quickly

Oops sorry I made a slight error but don't worry it's easily correctable

[crimson sedge]

Okay pls send the working

R u done

@hollow comet

[hollow comet]

Nearly

You have to use polynomial division

[crimson sedge]

Okay

Hurry pls

@hollow comet

[hollow comet]

Here

Don't forget the +C in the last step

[cedar kiln]

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[hollow comet]

@crimson sedge did that help?

[cedar kiln]

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[untold charm]

(-2)^n = (-1)^n *2^n

[untold charm]

for n=> 1, is this correct?

[tropic oxide]

it's correct for all n ∈ Z.

[untold charm]

okay

[wind pewter]

(ab)^n = a^n b^n

[untold charm]

i got an alternating series that involved the (-2)^n and I tried proving divergence with n'th term but I ran into a problem involving log(-2) which is undefined

Can I take the absolute value of the series before applying the nth term divergence test and the result will hold?

[wind pewter]

no idea what your series is or whether there is divergence

[untold charm]

i suppose my questions was more general that if the absolute value of a series term is not zero when n approaches infinity, is the series divergent

which makes sense to me

this is the series in question

[wind pewter]

that doesn't converge yea

[cedar kiln]

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[main jetty]

When we solve questions like, “determine when this matrix has a unique solution, infinite solutions, and no solutions”, what exactly does Infinite solutions and unique solutions and no solutions mean?

[main jetty]

I know if 2 vectors are linearly independent, any vector on the plane they span can only be written by a unique linear combination

Therefore, how can a vector have infinite solutions?

And I assume that no solutions mean they’re linearly dependent?

[wind pewter]

https://chbe241.github.io/Module-0-Introduction/MATH-152/Unique Solution, No Solution, or Infinite Solutions.html

[main jetty]

Awesome thank you. Does the latex work on computer? It’s not on my phone

Nvm it works now

Thank you 🙏🏽

.close

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[wind pewter]

yw

[cedar kiln]

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[visual basin]

My brain stopped working
Could someone please help me out with these 4 questions?

[visual basin]

I have a rough idea about 8
So I'm fine with that one
No idea what to do for 9 and 10
I'll figure out 11 and 12 eventually

So maybe just 9 and 10, please

[cedar kiln]

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[ionic rock]

The growth rate of grass in every square meter in a grass field is the same at a constant rate. 48 sheep can eat all the grass in a 10 square meter grass field in 18 days, and 21 cows can eat all the grass in a 30 square meter grass field in 36 days. How many sheep are needed to eat all the grass in a 60 square meter grass field in 10 days if a cow can eat 4 times more than a sheep and the speed of eating of both animals remains constant?

[ionic rock]

this is my answer but my teacher said it was incorrect

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@ionic rock Has your question been resolved?

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[steady jewel]

x
2

[steady jewel]

what is f(3)

stıpo

sotp

.close

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[rare patrol]

I wanna know if there is any possibility I can calculate the slope of the graph between observation 6th and 7th for all 3 years?

[rare patrol]

Idk if this is an excel matter, anybody can help with, but I would appreciate it if somebody could help.

[cedar kiln]

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[storm loom]

hey i want a small help with the following question:
A girl as only Rs. 1 coins and Rs. 2 coins with her. If the total number of coins that she has is 50 and the amount of money she has is rs.75 the find the number of rs.1 and rs.2 coins are respectively. (the "rs" denotes ruppees, and its only the currency has nothing to do with the question.)

I'm able to frame one equation that is
let thenumber of rs. 1 coins be x and number of rs. 2 coins be y
so,
x+y=50 --(1)

i need help to frame the second equation...
thanks for the help

[livid hound]

the second equation would represent how much money she has from all her coins

given that she has x number of $1 coins,
how many dollars/monies does she have from those? (in terms of x)

[crimson sedge]

how much money u have in total if u got 3 rs 50 notes and 1 rs 100 note

@storm loom

[storm loom]

ohh

i got it

@livid hound @crimson sedge thanks mates

.close

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[normal turtle]

38th one

[cerulean sail]

,rccw

[cerulean sail]

Maybe start with the identities for tan^2 and cot^2?

[normal turtle]

Ok

[vague rapids]

You just need 2 identities

$sec^2θ-tan^2θ=1$
$cosec^2θ-cot^2θ=1$

[wraith dagger]

B-eard

[vague rapids]

These two will do the job

Just manipulate these identities

Notice $1+tan^2θ=sec^2θ$ and $1+cot^2θ=cosec^2θ$

[wraith dagger]

B-eard

[vague rapids]

and just two very simples ones
$tanθ=sinθ/cosθ$ and $cotθ=cosθ/sinθ$

[wraith dagger]

B-eard

[cerulean sail]

and that these are derivable from the wonderful $\sin^{2}(\theta) + \cos^{2}(\theta) \equiv 1$

[wraith dagger]

@cerulean sail

[cerulean sail]

[hint]

[vague rapids]

yess

[vague rapids]

off topic but I am sure you are in 10th and preparing for boards

[cedar kiln]

@normal turtle Has your question been resolved?

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[severe elbow]

can someone pls help me pls TT

[cerulean sail]

You can e.g. try simplifying both sides separately and notice you get the same thing

[cedar kiln]

@severe elbow Has your question been resolved?

[severe elbow]

wait

so like

u can work on both side at once?

[cerulean sail]

It's perfectly valid to do so! if you show that both sides equal the same thing, that's the same as showing they're equal

[vague rapids]

Pretty easy just use two identities
$sec^2θ-tan^2θ=1$ and $cosec^2θ-cot^2θ=1$

[wraith dagger]

B-eard

[severe elbow]

okk tyy

[cedar kiln]

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[stoic pagoda]

Hi Im dealing with abstract algebra.
I have binary operation as so:
x ° y = xy + x + y
Im finding neutral element.
I know that x ° e = x
So how would I find it in my operation ?

[stoic pagoda]

xe + x + e = ?

From this x ° e = x, we know that it should be equal to first variable, thats being x.
But in my case I have three variables. xe, x and e

should it be equal to xe ?

[gilded elm]

neutral meaning inverse?

ok

firstly, which of the operations does it form a group under

is it (G, +) or is it (G, *)

where * is your circ thingy

[stoic pagoda]

not inverse. identity element.

We are talking in real numbers

[gilded elm]

x, y are real?

[stoic pagoda]

yes

[gilded elm]

Uh

Can you post the original questiion

I am highly unconvinced that the identity exists

[stoic pagoda]

Ok, How would you try find identity/neutral element in operation:
x ° y = xy + x + y

[gilded elm]

I meant

take a picture of your original question

[stoic pagoda]

xDDDDDDDDDDDDDDDDDDDDDDDD

[crimson delta]

if e exists, then it has to satisfy x°e=x for all x. so you can also plug in specific x. like x=0 or x=1

[stoic pagoda]

jk jk

[gilded elm]

if you're going to do that I'm not going to help you anymore

[stoic pagoda]

sorry, I had to

[gilded elm]

might as well go to sleep

[stoic pagoda]

ok

good night

[gilded elm]

take a picture of your homework

[stoic pagoda]

Its in diff. language so Im a paste a translation

Verify that the specified prescription is a binary operation. Explore its properties. Edit the definition scope (specify "{?}" ) so that for each x there is an inverse element.
a) x ° y = xy + x + y, on the set ℝ \ {?}

[gilded elm]

oh you removed 0

[stoic pagoda]

I didnt remove anything yet

[gilded elm]

well not 0

you need to remove something such that the inverse exists

[stoic pagoda]

Yes, But first I should find identity element so I can play with inverse

[gilded elm]

if e is the inverse then e ° x = x ° e = x

use this property and expand

[stoic pagoda]

Yes, my question is How to apply this property on my operation

if
x ° e = x
then
xe + x + e = ?

[slim jasper]

Small drive-by hint: write xy+x+y as (x+1)(y+1) - 1 instead.

[cedar kiln]

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[runic garnet]

Try drawing this out

[supple fox]

so it is supposed that I have to search for the perimeter of a semi circle right?

[cloud saddle]

10 + perimeter_of_circle(5 km radius)/2

oops

[supple fox]

damm

lol

yeah but I got it

so just to be sure

the perimeter of the semicircle is 5000 pi m

[cloud saddle]

semi circle?

[supple fox]

oh sorry semi circle

[cloud saddle]

(5000*pi + 1000) meters I think

[supple fox]

the next step right?

yeah yeah I think also it's like that

do i have to multiply first 5000*pi right?

and then add 1000

15.707,96 m

[supple fox]

would be the final result right?

[livid hound]

not 1000

[supple fox]

well @cloud saddle told me that I had to add up 1000 m

but not sure

[livid hound]

what's the radius in metres

[supple fox]

5000 m

[livid hound]

hence what's the length of the diameter and the straight part?

[supple fox]

1000 m

the diameter

[livid hound]

how are you getting 1000m

whats the relation between radius and diameter

[supple fox]

cause when I found the perimeter of the semicricle which is 5000 pi m

i had to then add to those 1000 m

I would get the final perimeter

(5000*pi + 1000)

[livid hound]

but wheres 1000m coming from, and don't say because the other guy said

whats the relation between radius and diameter

[supple fox]

if 5 km it's the radius, the diameter it's 10 km

but as I had to convert it or I'm using meters

[livid hound]

yes and how would you convert that to metres

[supple fox]

oh hold

I made a mistake

10 km = 10000 m

my mistake bro

apologises

25707.96 m

would the final perimeter

already resolved

I think

if you can close ticket

@livid hound

@cedar kiln close ticket

[cedar kiln]

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[summer kayak]

Why do I get a different answer when I take the integral of a symmetric function depending on I used it's symmetric properties or if I just integrated

[lyric narwhal]

what?

[summer kayak]

I will post the question

wait sec

[tropic oxide]

you may or may not have fucked up at least once.

[summer kayak]

Determine the area of the bounded region enclosed by the curve f(x) = $\frac1{1+4x^2}$ and $y=\frac12$

they intersect at -1/2 and 1/2 the integral is $\int_{-1/2}^{1/2} \frac1{1+4x^4} - \frac{1}{2} dx = [arctan(2x) - \frac{x}2]$

[lyric narwhal]

are you sure?

they do not intersect at -1/2 and 1/2

[summer kayak]

they do tho

[lyric narwhal]

no

and

your integral is wrong

[wraith dagger]

afeAlway

[tropic oxide]

,w 1/(1+4x^4) = 1/2

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Ann#0413

[lyric narwhal]

,w integral of 1/(1+4x^4)

[tropic oxide]

1/(1+4x^4) or 1/(1+4x^2)?

[summer kayak]

wait I accidentally soemthing wrong, let me fix it realy quick

[lyric narwhal]

oh

yea

i didnt notice

[wraith dagger]

afeAlway

[summer kayak]

It is x^2

[lyric narwhal]

ya

[summer kayak]

So anyways the funciton is symmetric so we can use $\int_{0}^{1/2}$ instead of $\int_{-1/2}^{1/2}$

[wraith dagger]

afeAlway

[lyric narwhal]

again

your values are

wrong

the two functions do NOT intersect at 1/2 and -1/2

[summer kayak]

But I did it the hard way and got $\frac{\pi + 1}2$ whilst in the answers they got $\frac{\pi - 2}2$

[wraith dagger]

afeAlway

[lyric narwhal]

are you listening to me?

[summer kayak]

$\frac12 = \frac1{1+4x^2} <=> 2 = 1 + 4x^2 <=> 1 = 4x^2 <=> x^2 = frac14 <=> x = \frac12 - \frac12$

[lyric narwhal]

oh

wait

mb

[wraith dagger]

afeAlway

[lyric narwhal]

i thought it was x^4

like you originally wrote

[lyric narwhal]

how did you get pi + 1 /2?

[summer kayak]

I used $\int_{-1/2}^{1/2}$

[lyric narwhal]

what?

[wraith dagger]

afeAlway

[lyric narwhal]

yea

but

what did you get for your antiderivative

[summer kayak]

$[arctan(2x) - \frac{x}2]$

[wraith dagger]

afeAlway

[lyric narwhal]

nope

[summer kayak]

y?

[lyric narwhal]

how did you get the arctan(2x)?

[summer kayak]

4x^2 = (2x)^2

[lyric narwhal]

yes

so?

what would you do next

[summer kayak]

the derivative of arctan x is $\frac1{1+x^2}$

[wraith dagger]

afeAlway

[lyric narwhal]

yes

[summer kayak]

so you just put 2x instead of x

[lyric narwhal]

no

not how it works

when you differentiate arctan(2x), what would you get?

[summer kayak]

wait

I knew something was wrong there

[lyric narwhal]

chain rule

always gets you

one easy way to prevent that mistake is

doing u substitution

[summer kayak]

but the funniest thing is in the answers they also just got arctan2x tho? So I didn't care to check anything

[lyric narwhal]

that doesn't make sense

[summer kayak]

let me send a screenshot

[lyric narwhal]

it will be arctan(2x)/2

[lyric narwhal]

yes

[summer kayak]

I know it is wrong now that you said it but

[lyric narwhal]

see

they did arctan(2x)/2 as well

[summer kayak]

Im BLIND

[summer kayak]

yeah now my answer makes a SENSE

Thanks for the help I really appreciate it!

[lyric narwhal]

no worries

[summer kayak]

.close

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[lyric narwhal]

what is the question?

[marsh pond]

I thought that subtraction was not commutative?

[tropic oxide]

subtraction is indeed not commutative, but what has this got to do with the expression you posted?

[marsh pond]

but in this case it could also be written
(2y - x^2)/(y^2 - 2x)

[tropic oxide]

yeah, sure.

by means of multiplying numerator and denominator by -1.

a - b = -(b-a).

[marsh pond]

so it kind of gives the illusion of commutativity, but it's not?

[tropic oxide]

do not overthink it. it is not so deep.

[wraith dagger]

MathIsAlwaysRight

[tropic oxide]

a - b = -(b-a).

reversing the order of operands in a subtraction flips the result.

all properties in which such switches appear to happen follow from that.

[lyric narwhal]

you are overcomplicating it wayyy too much

[vagrant elbow]

is this blackpenredpen lol

[dusk finch]

those are all correct

but why are you doing it?

[marsh pond]

math is complicated sometimes. how is this not useful to see this?

gotta train to get stronger 💪

[lyric narwhal]

what exactly did you see?

[crimson sedge]

this feels like some XY problem, what is your original problem?

[marsh pond]

whenever i see "complicating it way too much", which seems to be a common occurrence here on Discord, I sometimes feel like it's the equivalent of saying "I'm too lazy to think about it this way.. what a waste of time"

[lyric narwhal]

no, it means that you are wasting both your own as well as our time

[dusk finch]

Well so do you have any other questions?

[marsh pond]

no more questions, but I really don't see it as a waste of time to know this stuff

it's very useful

[lyric narwhal]

what "stuff" are you talking about

you just proved that -(a-b) = b-a

[marsh pond]

this stuff

[lyric narwhal]

i don't get what this is even supposed to prove

what are you trying to do here?

[marsh pond]

it's may appear to you like it is just mental masturbation, getting nowhere, but the idea is to get more comfortable with it. to see all of this is equal

[lyric narwhal]

if it helps you visualise it better, then sure

do you have any other questions?

if not, please close this channel

[marsh pond]

yes it does, i don't know why so many ppl are so quick to judge

i will close it now

thank you all

.close

[cedar kiln]

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[bronze briar]

so aside from the fact that there are different numbers, aren't all of these essentially the same question?

[bronze briar]

or is there a difference between question 1 and question 2?

[kindred storm]

The second part requires that you use a particular method to get the GCD.

Other than that, they're the same.

So, you can use a cheaper method than the extended Euclidean algorithm on part 1.

[bronze briar]

oh. On part 1 i used the extended euclidean algorithm, do you think that would be okay?

[kindred storm]

Yes, it allows any method.

[bronze briar]

also, im a little confused by what it means by ax+by. I know the gcd on 1.1 is 1, so do i just write it as 13(2) + 5(-5) = 1?

[kindred storm]

Yes, that's right.

[bronze briar]

awesome, thank you so much!

[kindred storm]

You're welcome.

[bronze briar]

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[jaunty mural]

what you are seeing follows from it being anticommutative

or maybe thats the wrong word lemme check

[marsh pond]

what's anticommutative?

like anticommunist?

[jaunty mural]

but a - b = -(b - a)

[cedar kiln]

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[marsh pond]

oh it's a real thing, wow

https://en.wikipedia.org/wiki/Anticommutative_property

[cedar kiln]

Please don't occupy multiple help channels.

[marsh pond]

oops

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[jaunty mural]

yeah anticommutative is the right word

a - b = -(b - a)

So when you reverse it on the numerator

and on the denominator

it cancels out

because -1 * -1 = 1

[marsh pond]

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[vagrant elbow]

$\sum_{r = 0}^{\infty} \frac{r}{4^r}$

[wraith dagger]

NEONPerseus

[vagrant elbow]

Now I know there's the perfect method of multiplying by 4

And subtracting

Like yes

Very nice

BUT

There has to be something cooler

Lix

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[velvet ferry]

i got 3^n for a not sure about b

[tropic oxide]

isn't part b similar to a just with more steps

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[lavish olive]

Can anyone help?

[dull oxide]

what have you tried

[cedar kiln]

@lavish olive Has your question been resolved?

[lavish olive]

I just got to it

And I forgot how to do translations

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[azure citrus]

i believe im supposed to solve this via integration by parts but that causes me to integrate tan x which is not optimal

[azure citrus]

or i just dont know what to do with it

or maybe im supposed to integrate by parts twice one second

[crimson sedge]

no it doesn't

the integral of sec^2(x) is tan(x)

[violet night]

integrating tanx isnt as painful as you think

[crimson sedge]

and the integral of tan(x) is something you'll be forced to remember at some point

use the ILATE rule - Inverse, Logarithmic, Algebraic, Trigonometric, Exponential

[azure citrus]

the what

[crimson sedge]

dv = sec^2(x)

u = x

and then apply $\int u\dd{v} = uv - \int v \dd{u}$

[wraith dagger]

Nika

[azure citrus]

huh

yeah im not following that

[azure citrus]

nd i havent seen it last semester im not sure why i would see it in the future

well near future

sorry

this is on a circuit and all the answers are fractional but i have absolutely no clue how to do this without a calculator

you end with xtan x - log|sec x| i think

and i dont know at all how to manipulate that with the definite integral to make it possible without a calculator

[cedar kiln]

@azure citrus Has your question been resolved?

[azure citrus]

no bud

[crimson sedge]

what's confusing you still?

$\int x\sec^2{x} = x\tan{x} \dd{x} - \int \tan{x} \dd{x}$

[wraith dagger]

Nika

[crimson sedge]

notice that $\int \tan{x} \dd{x} = \int \frac{\sin{x}}{\cos{x}} \dd{x}$

[wraith dagger]

Nika

[azure citrus]

yeah im past that i tried to figure out how to integrate tan x and i gave up

it doesnt make sense its not something i can do

the problem is i have a bunch of potential answers to this question and none of them line up with the one im getting which is pi/4

oh nevermind thats wrong nevermind

[crimson sedge]

No

Use u-substitution

[azure citrus]

nevermind im overexaggerating

use usub for wht

[crimson sedge]

u = cos(x)

du = -sin(x) dx

[azure citrus]

doesnt that just become -1??

[crimson sedge]

does it?

I think I've helped u enough

[azure citrus]

why is it log and not ln???

is it ln or log???

i guess it doesnt matter

thatnk jhm,

thanks

.closr

.c;oeyrfuioghj

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[regal vessel]

A rectangular schoolroom floor can be covered by 2400 square tiles. If the tiles are 5cm longer and 5cm wider, 1350 tiles are needed.
If none of the tiles are cut, what is the area of the floor in m2?

[regal vessel]

Any ideas how to move on from this point?

It meant to be lower case l instead of L in (l+5)

[digital cliff]

i dont think you really need to have the length and width of the room. You can say the smaller square tiles have side length x, so area x^2 and the larger tiles have length x+5 so area (x+5)^2

which is kinda what youre doing but you dont need seperate variables for length and width

[regal vessel]

Yes

I see what you mean

2400(x^2)

Instead of lw

[digital cliff]

anyway, just set these bottom two equal to eachother while keeping in mind that l=w so just replace them with a single variable

[digital cliff]

yeah

[regal vessel]

I can remove x^2 from both equations right?

[digital cliff]

No

you have 2400x^2=1350(x^2+10x+25)

those x^2 dont cancel out

[regal vessel]

I multiply out first

I have it i think

[digital cliff]

what did you get

[regal vessel]

15

[digital cliff]

thats x yeah (in cm)

[regal vessel]

Yup

[digital cliff]

so now just get the area and convert it into the correct units

[regal vessel]

That seems wrong

[digital cliff]

it is

225cm^2 isnt 2.25m^2

1m^2=10000cm^2

[regal vessel]

I thought when i did 0.15x0.15 .0225 was too small

[digital cliff]

its what the maths brings us to

the area of the room comes to 54m^2 which is relatively believable

5400m^2 is huge for a room

[regal vessel]

Appreciate the help

[digital cliff]

np

[regal vessel]

Cya

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[warm elm]

How do I turn the first part to the other

[cedar kiln]

@warm elm Has your question been resolved?

[ancient lodge]

,w expand (6y-x^2-y^2)(6yx-2y^3)

[wraith dagger]

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[ancient lodge]

Pretty sure you can't tbh

[warm elm]

🥶

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[pastel sinew]

.help

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Commands:
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[ancient lodge]

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