help-23

[hexed dune]

wait what

no

[lean otter]

thenwat

im not familiar with tangents being vertical

[hexed dune]

2y^2 = y^2 + 4 right?

[lean otter]

i fought it frmoa website, saying that the denominator has to be 0

[hexed dune]

so how does 2y^2 - y^2 become 3y^2

[lean otter]

xy = y^2 + 4

is the original equation

[hexed dune]

yes

[lean otter]

x = 2y

so

wait

okay im just mentally disabled

y^2 = 4

y = plus minus 2

[hexed dune]

yh

so now find out what x is

[lean otter]

so the coordinates

(2y,y)

so

(4,2)

and(-4,-2)

yay

.clsoe

.close

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[oblique idol]

Let φ : G → G′ be a homomorphism and H ⊆ G. Prove or disprove: If φ(H) is a
subgroup of G′
, then H is a subgroup of G

[oblique idol]

In general, I am more struggle with my starting point, I've found that in general I struggle with homomorphisms

Do I start with the subgroup test on G'?

I am unsure on how to use the given statement of φ (H)

[safe radish]

@oblique idol Has your question been resolved?

[oblique idol]

<@&286206848099549185> general advice would also be very helpful

[junior smelt]

In this case, it’s a “prove or disprove”

Nothing stops you from e.g. the trivial homomorphism that just sends you to the identity of the other group G’

[oblique idol]

would that then imply that φ (H) is simply the identity element of the group G' and that would mean that H is also a subgroup of G'? or am I misunderstanding

[junior smelt]

$\phi(H) = { e_{H} }$ no matter the choice of subset $H \subseteq G$, and clearly that’s the (trivial) subgroup of $G’$

[flat frigate]

@junior smelt

[oblique idol]

and can I then write that phi(H) = identity element of G' (for all h element in H)

[junior smelt]

See the statement I made though: no matter the choice of subset…

[oblique idol]

that actually makes a lot of sense

thank you

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[thorn chasm]

Doesn't matter you will probs just end up memorizing it if u work with it enough times but whatever way works for you

[lean otter]

unit circle for me.

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[lean otter]

can anyone help???

[ionic solstice]

are you sure that there is no other information in the question

[lean otter]

yes

[ionic solstice]

do you have a picture of the original question

[lean otter]

no

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@lean otter Has your question been resolved?

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[dreamy finch]

So I have a question about propositions. Can any term be simplified to n terms or less, where n is the number of unique letters in the proposition?

[dreamy finch]

for example:

this simplifies to just q. There are only 2 unique letters in the system, and q is one term

also I would define (q and p) as one term as well

please @ me if anyone responds

[broken yew]

Thinking about an example in sets gives you an example in props right?

In which case I think you fail for like symmetrical difference say

[dreamy finch]

I apologize for my feeble-mindedness, but i have no idea what you just said

[broken yew]

p and q

A intersect B

p or q

A union B

=====

not p

complement A

=====

I think these analogies work (because how the sets are formally defined)

In which case, consider the symmetric difference of sets

(A u B) - (A n B) = (A u B) n (A n B)'

[dreamy finch]

i don't think ive really been introduced to sets

Ive just been learning propositional statements

[broken yew]

ie. consider
(p or q) and not(p and q)

ok well thats where I got the inspiration from for this example

I dont think it simplifies to 2 or less

[dreamy finch]

oh okay, thank you!

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[peak crane]

How would u do 6

[thin bridge]

first express sqrt(M) in exponential form

[peak crane]

uhhh

wdym

how would u express the sqrt in exponential form

[thin bridge]

$\sqrt{M} = M^{?}$

[flat frigate]

ℝamonov

[peak crane]

oh 1/2

lol

ohhhh

alr i got it

thanks

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[floral pulsar]

Help. I don't know how to solve

[safe radish]

@floral pulsar Has your question been resolved?

[prisma haven]

I think what you wanna do is first find the area of the wire using 2pirh + 2pir^2. Once you got that you can multiply it by the charge density to find the total charge. Now having that total Charge, you can use kq/r^2. Where k is the electrostatic constant (8.99*10^9), q is the total charge, and r^2 is that distance squared.

correct me if im wrong though, cause im not amazing at electrostatics

make sure to convert units as well

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[summer lance]

hi

[safe radish]

Please don't occupy multiple help channels.

@summer lance Has your question been resolved?

[summer lance]

no

[karmic hedge]

Where’s your question?

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[normal cradle]

If I have these 2 similar triangles and I’m trying to figure out the area of the bigger one, how does ratio affect the general area? I’m stuck on this question

[lean otter]

Whats the ratio of one side

4cm becomes 12 cm

Increased by 3 times

[normal cradle]

The information in the picture is all I have so the ratio is 1:3

[lean otter]

Yes

[normal cradle]

But I need to find the area of the bigger triangle

[lean otter]

Area is generally a multiplication of sides

Like a length square dimension

[normal cradle]

So the area would also increase by 3 times?

[lean otter]

Nope

[normal cradle]

Oh

[lean otter]

Let's take a square for example

What would be the answer

If the side increase by 3

Area would increase by?

[normal cradle]

Holdnup

Hold up

[lean otter]

Square area is sidexside

Ok

[normal cradle]

Yeah it’s l x w

So it would be 12 x 12?

[lean otter]

Yes how much did they increase by

Both sides got multiplied by 3

And the area got multiplied by?

[normal cradle]

Like over 10

[lean otter]

No

If each side got multiplied by 3

The area got multiplied by 3x3

9

[normal cradle]

Ohh

So it would be 90?

[lean otter]

What would be 90

The area would increase by 9 times

Since the side increased by 3 times

And u get area by multiplying two sides

[normal cradle]

If the area of the smaller triangle was 10 cm then the bigger triangle area would be 90? Increased 9 times

[lean otter]

Yes

[normal cradle]

Oh okay thanks

Wait is that only for squares

Or triangles too

[lean otter]

Everything

Everything increases by the same ratio

[normal cradle]

So if the ratio is 1:3 then the area would increase by 9x?

[lean otter]

Wjats the formula for calculating area of triangles

Yes

[normal cradle]

No idea isn’t it like base times height over 2?

[lean otter]

Yes

[normal cradle]

But I don’t have the base or the height

[lean otter]

Both base and height will increase by 3 times

So area will increase 9 times

U dont need cuz they gave the area of the small triangle

[normal cradle]

Ohhh

Yeah I got it thanks man 🙏

Appreciate it

[lean otter]

👍 np

[normal cradle]

So if it’s a rectangle with ratio 1:5 then the area would increase by x25?

Since length and width are both increasing by x5, then the total area would increase by x25?

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[high gate]

I need to prove that this series converges or diverges

[high gate]

I’ve already verified than the limit of (ln(n))/root(n) converges to 0

But I can’t figure out how to prove that it’s a decreasing function

[lean otter]

Yes

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[sly seal]

is this notation correct
$$\frac{d}{dx} (ln(x+1)) = (ln(x+1))' \times (x+1)' $$

[flat frigate]

xzino

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@sly seal Has your question been resolved?

[sly seal]

<@&286206848099549185>

[pseudo scroll]

It's correct

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[woven cloak]

any tips?

[woven cloak]

why is their math so complicated

how can i do this without doing their way

are they just cross multiplying?

or do i convert pounds to kg first

[eternal nova]

I can hardly read that 😭

[woven cloak]

same

lol

i dont understand what this line is and the pounds x 1 over 2.2

.close

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[eternal nova]

can somebody give me a question for rearranging formulas (Year 10 level), like questions where yiu make a variable in the question the main part of the question like, what does r =

[pseudo scroll]

What

[hexed dune]

he wants one of those "make x the subject of the formula" questions

ugh

i keep using he/him as default

sorry

habit

[quasi bison]

how many such questions do you want

[misty coral]

there are problem sheets online for that

[pseudo scroll]

I feel you

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@eternal nova Has your question been resolved?

[eternal nova]

oh shit sorry

I completely forgot I asked this

it's okay i don't want any

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[long jungle]

Help f

[long jungle]

The above one

F

You cant factorise it

How do I fo

Do

[lean otter]

you want to evaluate [
\lim_{x \to -2} \f{3}{x+2}]?

[long jungle]

Yes

[lean otter]

have you tried anything?

[long jungle]

Like you cant direct substitution

Also cannot factorise

Like how do I even

[lean otter]

okay the idea is that you will have something of the form 1/0 ultimately

[long jungle]

So its undefined

[lean otter]

it is similiar to, say, how you would you evaluate [
\lim_{x\to 0} \f 1x]

[lean otter]

yes it is indeed.

[long jungle]

O

So like there is no other way

So it only can become undefine?

[lean otter]

what even are you asking?

you want to define the limit another way

?

[long jungle]

No

But

The answer is infinity though

[lean otter]

it is wrong then

[wintry condor]

,w plot y=3/(x+2)

[flat frigate]

Results provided by WolframAlpha

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

Requested by jay.#3594

[supple shore]

We don't know if the -2 comes to the right or left

[wintry condor]

You can see that the left hand limit is -inf and the right hand limit is +inf

Left hand limit and right hand limit are not the same so it should be undefined

[long jungle]

Ah I see

Because I thought a limit answer cannot be undefined

Alright tq everyone

.close

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[neat kiln]

integrate 1/sqrt(1+x^2)

[neat kiln]

trig sub not working

[hexed dune]

because the integral to this is known

this is something you have to work in reverse

[pseudo scroll]

$\int \frac{\dd{x}}{\sqrt{1 + x^2}}$

[flat frigate]

NEONPerseus

[pseudo scroll]

What did you sub

[hexed dune]

wait, im thinking of 1/(1+x^2)

not 1/sqrt(1+x^2)

[pseudo scroll]

It should still work though, trig sub with that

[neat kiln]

x = tan theta?

[balmy sky]

tan theta should work

[pseudo scroll]

And what did that lend you

Yes it should

$\int \sec \theta \dd{\theta}$

[flat frigate]

NEONPerseus

[pseudo scroll]

You should've ended up with this right

[neat kiln]

yeah I got there

[balmy sky]

thats wrong

[neat kiln]

what I do now?

[pseudo scroll]

And you're unaware of how to integrate secant?

[winged cloak]

no

[balmy sky]

you have to change the dx too

[winged cloak]

it is / sec O dO

[pseudo scroll]

Multiply and divide by sec tan

[pseudo scroll]

I did?

[balmy sky]

OH WAIT SORRY

[pseudo scroll]

[balmy sky]

lol

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@neat kiln Has your question been resolved?

[neat kiln]

yeah got it after some painful steps

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[lean otter]

2x^3+9x^2=x+3

[neat kiln]

bring everything to one side

see if you can factor by grouping

[lean otter]

wait

but when i do that

i get

x^2(2x+9)-1(x+3)

@neat kiln

[neat kiln]

try 2x^3 -x and +9x^2 -3

[lean otter]

wait u can do that

i never knew

[neat kiln]

a+b+c = a +c + b

so you can move stuff

[lean otter]

it still dont work

i gor

x(2x^2-1)3(3x^2-1)

@neat kiln

[neat kiln]

I see

use rational zero theorem then

[lean otter]

how do u do that

[neat kiln]

https://www.youtube.com/watch?v=Iaq7z7reznM&ab_channel=TheOrganicChemistryTutor

[lean otter]

bruh

so u dnt know

.close

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[lean otter]

how do i approach solving

[split ether]

Consider substituting for 1 + e^(2x)

[lean otter]

so u sub?

[deep depot]

Yes

[lean otter]

wait doesnt that become integration by parts

[split ether]

Nope

Just do u = 1 + e^(2x)

[lean otter]

but then its like e^2x/u

so then e^2x(u^-1)

[deep depot]

u=1+e^(2x)
Now find du to replace dx

[lean otter]

ohh

wait i think i see-

[deep depot]

Then what will you do?

[lean otter]

so its lim t --> infinity (1/2 intergral from t to 2 of ln(1+e^2x))

im just confused about how infinity can be the lower bound

[deep depot]

It is possible to have infinity in the lower bound until the upper bound is a finite value

[lean otter]

uh but then how do i evaluate it

[deep depot]

You already have did the half process you have to change the bound to move on

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@lean otter Has your question been resolved?

[safe radish]

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[wicked horizon]

Can anyone help me with integrals

[wicked horizon]

I got this as my answer

I just wanna know if my answer is correct or not

[frank glen]

Hmm

Separable

tan(x) + c = -e^{-y}

y = ln(1/(tan(x) + c))

Yeah

Correct

You can further check if your answer is correct

By visiting

https://www.integral-calculator.com

And you can check it by also differentiating your function and seeing if it gives you the same thing as you started with

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[safe radish]

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[safe radish]

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[covert berry]

how to do with binary exponentiation?

[peak estuary]

do you know eulers theorem

[covert berry]

Yes a^prime number of n = 1 (mod n)

[peak estuary]

I assume you mean a^phi(n)=1 mod n

but that is really not what phi(n) means

[covert berry]

Oh, I meant a^prime factors of n = 1 mod n

[peak estuary]

well ok still wrong

[covert berry]

a^ amount of prime factors that are the same prime factor of n = 1 mod n

[peak estuary]

still no

[covert berry]

a^ number of relatively prime numbers of n = 1 mod n

[peak estuary]

there we go

well at least somewhat

still technically wrong

[covert berry]

a^phi(n) = 1 mod n

[peak estuary]

good so we arrived at what I wrote

now what

[safe radish]

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[main belfry]

like how do a inverse composite function jawn

[safe radish]

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[viscid pike]

Need help with 49

[viscid pike]

How do I prove the piece wise function is continuous at 0,0

[trim swan]

,rotate

[shut inlet]

you still need to use LH since it's 0/0

not 1/0

2^0 = 1

there is an easier method without using the LH

[flat frigate]

Mehdi_Moulati

Mehdi_Moulati

[safe radish]

@viscid pike Has your question been resolved?

[viscid pike]

I’ll try that thanks

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[atomic oak]

Need help please

[worthy hemlock]

What exactly are you stuck on?

[atomic oak]

What to do after

[lean otter]

-2-4 != 6

and is the 2nd point meant to be (5,-2)?

[atomic oak]

Yeah

[worthy hemlock]

Also, your value for slope is wrong

-2 - -4

[atomic oak]

Ah that’s where I went wrong cus I was thinking the double negative would make it positive so I did the reciprocal

Thank you

And I still don’t understand how I keep ending with the wrong answer

[lean otter]

working out?

[lean otter]

5 - (-3)

[atomic oak]

2/8?

[lean otter]

yh

[atomic oak]

I’m still confused

[safe radish]

@atomic oak Has your question been resolved?

[pure agate]

What are you confused about?

[safe radish]

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[maiden holly]

i missed this calculus unit and the class notes weren't very helpful. this is the problem im given and any help how to get started is appreciated. for the first question, is the answer because e^x dominates the function 1+x?? thanks

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@maiden holly Has your question been resolved?

[maiden holly]

<@&286206848099549185>

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@maiden holly Has your question been resolved?

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@maiden holly Has your question been resolved?

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[mossy holly]

help?

[mossy holly]

ok i did it is it correct??

[flint prawn]

yes 👍🏻

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[mossy holly]

thanks

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[safe radish]

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[lean otter]

The radiation y from an antenna on a cell phone mast is described by the function y = C/(x^2), where x is the distance to the mast and C is a constant. Measurements show that the permitted limit value for the radiation is reached at a distance of 3 m from the antenna.

What percentage of the limit value is reached 10 m from the antenna?
Answer with whole percent.

[lean otter]

I have only understood that x is both 3 and 10

like this

But what do I do after?

[thin bridge]

its a good idea to state what each expression / calculations represent

max permitted radiation = C/9
radiation at 10m = C/100

then express
(radiation at 10m)/(max permitted radiation)
as a percentage

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

oh okay thank you, I got 9% and it was right

[safe radish]

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[pliant sonnet]

Might be very dumb, but I need help understanding this, why lambda = 0 is easy result?

[lean otter]

Depends what they're trying to achieve

[pliant sonnet]

proofing that darboux integral are linear

[lean otter]

Oh, I see

Well, if lambda=0, then lambda*f=0

And lambda*the integral=0

And it should be clear than integrating over f(x)=0 will give you 0 no matter the range

[pliant sonnet]

and the defined integral of 0 is still 0 right?

[lean otter]

Yep

[pliant sonnet]

aha, yeah think i get it actually

yeah, thanks

.close

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[worn yacht]

!close

[quasi bison]

it's .close

[swift lily]

LMFAO

[oak wraith]

.close

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[zinc token]

.close

is this bugged

[zinc token]

.close

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[zinc token]

woah

[swift lily]

XD

[shut inlet]

[shut inlet]

too slow

[zinc token]

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[lean otter]

Did not understand the chapter ''Powers and Exponents'' at all. Can i have a brief summary of the topic?

[supple shore]

something like this ? like the rule how does it works

[lean otter]

Very basic ones

I am not sure if the name is correct but an example is

it has all numbers

and you know how there are numbers that are squared

instead of only 2

there are other numbers

example

4 rays to the power of 3

is 64 right

I dont get how you calculate that

[supple shore]

yes

[lean otter]

its that

[supple shore]

so it's $444$

[flat frigate]

phoestaclies

[lean otter]

its 4 with a 3 on top

of it

[supple shore]

repear 3 times

[lean otter]

4x4x4?

[supple shore]

yes is equal to 64

[lean otter]

I dont get how to multiply thrice

example 5 rays to power of 3

idk what the answer is

as i dont know how to multiply 3 times

[supple shore]

it's $555$ so it's the same as $5²5$ or $255$

[flat frigate]

phoestaclies

[lean otter]

so 6 rays to power of 3 is 6x6 x 6 which is 36 x 6?

[supple shore]

yes

[lean otter]

and then 36x6 is the answer

[supple shore]

yes

[lean otter]

oh is that all in it?

[supple shore]

yes

[lean otter]

wait what about adding them

example when we add 7 rays to the power of 4 to 9 rays to the power of 8

[supple shore]

you can't add because they don't have any factor in common, your final result will be $7^{4}*9^{8}$

[flat frigate]

phoestaclies

[supple shore]

look at this rules

[lean otter]

I dont get a single thing

[supple shore]

oh ok sorry, so what do you want to know also ?

do you have some exercise to work in

[lean otter]

how do we get the exponential form of numbers

example getting the exponential form of 1 milllion

[supple shore]

? if I understand well you want to make a number in form $a^{b}$

[flat frigate]

phoestaclies

[lean otter]

yes

getting that form out of big numbers

[supple shore]

so some number can't be express like that

[lean otter]

like i want to get 4 raised to the power of 3 from 64

I need to name the exponential form of numbers

[supple shore]

like 7 can't be express like that or maybe $7^{1}$ which is 7 so we don't write like that

[flat frigate]

phoestaclies

[supple shore]

yo have his exponent you need to decompose in factor the number

[lean otter]

yes but it will always be large numbers

[supple shore]

and see if multiples terms repeat but there is only them

[lean otter]

that i will have to get exponential form of

they will always be at least 2 digit

numbers

[supple shore]

to have the power of 1 million is easy, we have 1 with 6 zéro so $1101010101010$ so we can write $10^{6}$

[flat frigate]

phoestaclies

[supple shore]

because 10 repeats 6 times

[lean otter]

what about other numbers

[supple shore]

no for example try to make exponent at 9

you will have $3²$

[flat frigate]

phoestaclies

[lean otter]

yes

exponent for 5 is only 5 power to 1

also can we have a decimal form for exponents?

[supple shore]

yes so you don't write it just 5

yes sure

like do you know square root

[lean otter]

Yes

[supple shore]

so $\sqrt a = a^{0.5}$

[flat frigate]

phoestaclies

[lean otter]

oh

so square root of 16

16 rays to the power or 0.5

[supple shore]

yes

[lean otter]

= 4?

[supple shore]

yes

[lean otter]

what if the decimal is more than 1

1.1 and onwards

and exponent is like 3

[supple shore]

we write $a^{\frac{m}{n}} = \sqrt[n]{a^{m}}$

[flat frigate]

phoestaclies

[lean otter]

?

[oak wraith]

it might be easier to learn $a^{\frac{\text{power}}{\text{root}} = \sqrt[\text{root}]{a^{\text{power}}}$

using words

FUCK, I hate latex

[supple shore]

me too

[flat frigate]

Juke | ping me if no response
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[supple shore]

[oak wraith]

u get the point tho

[lean otter]

uh

no

[oak wraith]

that's the relationship between exponent and roots

all roots can be expressed as an fractional exponent

vice versa

[lean otter]

I dont understand

[oak wraith]

What part specifically?

[lean otter]

What you just said

[oak wraith]

all roots can be expressed as an fractional exponent?

[lean otter]

the relationship between exponent and roots

[flat frigate]

Juke | ping me if no response
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[lean otter]

and this too

[lean otter]

ik

ik what roots are

ik square roots

[oak wraith]

and so when we right this, it really means $a^{\frac{1}{2}}$

[flat frigate]

Juke | ping me if no response

[oak wraith]

a to the exponent of 1/2 is the same as the square root of a

[lean otter]

i thought a to the power of 1/2 is the same as the square root of a

[oak wraith]

that's what I am saying

oh I had a typo above and didn't type the a inside the sqrt, my bad

[flat frigate]

Juke | ping me if no response

Juke | ping me if no response

[lean otter]

I really dont understand what power/root is

[oak wraith]

the exponent

[lean otter]

a to the exponent?

[oak wraith]

yup

[lean otter]

so the exponent is the thing that goes above the number

or the power?

[oak wraith]

we read that as "a to the exponent of ..." or "a to the power of ..."

but the connection I am trying to show is that when we have the left side with a raised to something, we can write it as a fraction where the numerator is the power that a is raised to when inside the radical with that root, from the denominator

[lean otter]

exponents and powers are the same thing or exponents and bases are the same thing?

[oak wraith]

exponents and powers are the same thing

[lean otter]

I can only understand a little but it is my bad

[oak wraith]

https://youtu.be/-rzQQExcXoY

maybe this video help

[lean otter]

but

I was shown

this

that they look different to me

[oak wraith]

this is what it should be

but when people say something raised to something, they interpret power and exponent as the same

most ppl don't say "5 raised to the exponent of 3"

u say "5 raised to the power of 3"

[lean otter]

which is 125

what if they say

as you said above

the exponent

of it

[oak wraith]

or "5 with exponent 3"

[lean otter]

oh so 5 with exponent of 3 is same as 5 with power of 3

ohh

[oak wraith]

sure, I mean, if u tell somebody this they will understand it as $5^3$

[flat frigate]

Juke | ping me if no response

[oak wraith]

u almost always get the same interpretation if u switch the words power and exponent

[lean otter]

in exercises in my school they add and multiply these

[oak wraith]

since that's how we talk

[oak wraith]

yeah u can

[lean otter]

5 rays to power of 3 x 4 raised to power of 3

do i add the results

or multiply them

[oak wraith]

I assume they want it in the order in which it's read

so u start with "5 rays to power of 3"

so

5^3 so far

okay now what?

x 4

okay so 5^3 x 4

[lean otter]

no

[oak wraith]

wym

[lean otter]

the result of 5 raised to the power of 3

x result of 4 raised to power of 3

[oak wraith]

this is the same as what I wrote

[lean otter]

oh so that is how you do it

i thought use 64

not 4

[oak wraith]

how would u get 64

[lean otter]

4 raised to power of 3?

[oak wraith]

^

when translating from english to math, we always did it in the order in which we read

[lean otter]

well my bad sorry

[oak wraith]

so for "5 raised to power of 3 x 4 raised to power of 3", there are a few main parts:

5 raised to power of 3
x4
raised to the power of 3

so we get 5^3 then this times 4 which is 5^3 x 4 and then this raised to the power of 3 so (5^3 x 4)^3

[lean otter]

(5^3 x 4)^3
5^3 x 4 ^3
125x4 ^3
500^3

Is that how it is?

oh wait

[oak wraith]

,calc 125 * 4

[flat frigate]

Result:

500

[oak wraith]

,calc 500^3

[flat frigate]

Result:

1.25e+8

[oak wraith]

125 000 000

[lean otter]

oh

So it is supposed to be calculated like that

[oak wraith]

don't take off the ()

[lean otter]

oh that is how I do it in school

[oak wraith]

we kept the () on purpose bc PEMDAS

(5^3 x 4)^3 and 5^3 x 4 ^3 are not the same

the left evaluates to 125,000,000 and the right one evaluates to 125 x 64 which is uhh..

,calc 125 * 64

[flat frigate]

Result:

8000

[oak wraith]

8000

[lean otter]

like we have another one: 2^2x3^4x2^5/2^4x9

[oak wraith]

very different numbers

[oak wraith]

is this exactly how it's written?

[lean otter]

It is written like this

I am supposed to simplify it

[oak wraith]

okay so this one u can notice that 9=3^2 and so with 3^4/3^2 u get 3^2 on the numerator only

and then 2^2 * 2^5 is just 2^7

and so 2^7/2^4 is 2^3

so the final answer would be 2^3 x 3^2

[lean otter]

8x9

72

[oak wraith]

yup

[lean otter]

simplified tho

is 2^3x3^2

i dont even need the answer

[oak wraith]

sure

[lean otter]

just that simplified

[oak wraith]

I mean 72 is the simplest

[oak wraith]

but if u need the bases then keep it as this...?

[lean otter]

Yes

These are all the types of questions and i know there are different methods for solving each

questions like these

will also show up in the exam

but I think i got it done

.close

[safe radish]

Channel closed

Closed by @simple adder

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[oak wraith]

okay, so- oop nvm, bye!

[safe radish]

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[solid bolt]

Can someone please tell me how to get the area of PQF

[blazing kindle]

did you tried it

?

[safe radish]

@solid bolt Has your question been resolved?

[solid bolt]

Yes

I’ve been trying it and asking for help for 4 hour straight

I cant sleep without thinking about this god damn problem

Now I cant sleep

Please someone help me get some sleep

[blazing kindle]

well

i am thinking

for it

i can't promise

that i can solve

but i will try my best

[solid bolt]

Yes thanks

[blazing kindle]

well

we nonly need to think

about

pq

and pf

because they are unknow

we know qf

qf=2cm

[woven swan]

yea get all the side lengths with pythagoras then deduce from there

[solid bolt]

We know Pf too

[solid bolt]

Idk how to get PQ though

[woven swan]

3d pythagoras

https://media.discordapp.net/attachments/438760008033763354/1076225091609829406/image0.jpg

[blazing kindle]

bro

its not cuboid

[woven swan]

wait

[blazing kindle]

its

prism

[woven swan]

oh ye oof

not right angles

sorry

[blazing kindle]

np

:),

[blazing kindle]

hey

do we know CF

?

yes

[solid bolt]

Yeah

[blazing kindle]

CF=4

then we can find pf

yeahh

PF

[solid bolt]

Yeah

17root

[blazing kindle]

IS pf

ROOT(17)

yes

same

[blazing kindle]

yes

now we only have to find PQ

i think i found a way

to find PQ

lemme send you

[solid bolt]

Yeah thanks

[blazing kindle]

we can join

the midpoint

lemme label it

[solid bolt]

Alr thanks!

[blazing kindle]

we know GQ

[solid bolt]

Yeah

4

[blazing kindle]

we can draw one more thing

[solid bolt]

Mhh

Can we solve it with Pythagorean theorem

[blazing kindle]

well

[woven swan]

i found a really good way which uses pythagoras only

well i think

[blazing kindle]

i am thinking

[woven swan]

it works

[blazing kindle]

sure

intrer

tell us

[woven swan]

say M’ is the midpoint of BC, basically move the point P so that it’s on the line AM’ (but still 2/3 of the way up), this doesn’t change the area

then it’s a right angled triangle in Q, and finding PQ is fairly easy

[blazing kindle]

but

do u have proof

it willl not change th area

after moving to AM

[woven swan]

QF, the base, is parallel to CM’ and if we say P’ is the new point where P sits, then P’P is parallel to CM’ meaning P’P is parallel to QF

[blazing kindle]

cuz it will become a right angled triangled after that so it maybe area will change

[woven swan]

since P’P is parallel to QF (the base of the triangle), we can move P to any point on P’P without affecting the area, including to P’

[blazing kindle]

@solid bolt are you on

??

[solid bolt]

Yes

I’m trying to ask my teacher for help

[blazing kindle]

well

i found

a way

but

it

need 3d model

to

explain

it

[solid bolt]

Oh

This question is too hard

[blazing kindle]

no

[blazing kindle]

its not

i can give you solution though

[solid bolt]

Yes that’ll be helpful

[blazing kindle]

ok

will you

wait

a bit

i need to time to write

sol

[solid bolt]

Yeah

[blazing kindle]

i will just take 10 min

ok

can i use concept of similiarity

?

[solid bolt]

Yeah

[blazing kindle]

ok

see this

[solid bolt]

Yeah

[blazing kindle]

we can find

PL

from it

by applying pythagoras

[solid bolt]

Wow

[blazing kindle]

PF^2 = PL^2+LF^2

17=PL^2+1

PL=root(16)

PL=4

pl=4cm

we know pl

now we can find

PQ

we will get PQ as root(17)

so its isosceles

triangle

we can find the are of it

@solid bolt are you ONLIne

[round yoke]

what is the final answer of ∆PQF you get

I'm curious

to explore this question

[safe radish]

@solid bolt Has your question been resolved?

[round yoke]

ans is 4?

[safe radish]

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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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[silent rain]

i know this is an easy one that can be solved threw looking of the function is odd or even but i am not sure oh what is the result when its odd and what if its even

[lean otter]

Use partial fractions if you are not sure

[silent rain]

how exacly ?

[lean otter]

did you figure out if its odd or even or neither?

[silent rain]

(x-4)(x+4) ?

[silent rain]

not yet

[quasi bison]

no, the denominator does not factor as (x-4)(x+4)

[silent rain]

i also meant if its even then whats the naswer and if odd what is the answer ?

[lean otter]

if its odd then 0

[silent rain]

oh (x-2)(x+2)

[silent rain]

and if even ?

[lean otter]

2* integral from 0 to 1

[silent rain]

tyvm

.close

[safe radish]

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[formal cove]

can some one please help me with this question

[raven sleet]

seems like an answer of a problem, what part are you stuck at?

[formal cove]

i dont know why E[x] =np

[raven sleet]

I'm assuming X is a binomial random variable, that's one of the properties of the RV

[formal cove]

RV?

[raven sleet]

random variable

for a binomial random variable X, it will have n "trials", each trial with a p probability of success

the expected number of successes is np

[formal cove]

so mean of a bionomial random is np?

[raven sleet]

https://www.khanacademy.org/math/statistics-probability/random-variables-stats-library/binomial-random-variables/v/binomial-distribution
khan academy video on binomial distributions

yes

[formal cove]

ty

[formal cove]

i still dont quite understand

why is the mean of a binomial random variable pn

[raven sleet]

https://proofwiki.org/wiki/Expectation_of_Binomial_Distribution

bunch of proofs online, basically you just use the expectation formula with the pmf of binomial distribution

mostly grunt work

[formal cove]

ok ty

[raven sleet]

though intuitively,

flipping a coin is the easiest example. if you have a 50/50 chance of getting heads (p= 1/2), say if you flip a coin 100 times (n = 100), you'd expect to get 50 heads (on average)

np = 100 * (1/2) = 50

if you have some trial where you have a p chance of success, out of n trials, you'd expect p proportion of n trials to be successful

so np

[safe radish]

@formal cove Has your question been resolved?

[formal cove]

.close

[safe radish]

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[formal cove]

can some one please help me with this queston?

[formal cove]

this is the answer but i am having some trouble following it

[plucky elk]

where do you first get lost

[formal cove]

This is what I think it should be

so a couple of thigs

alpha x n-n*p

why is it that?

using the formula in front of me it should be just alpha x n

the numerator on the right side of the equality should np(1-p)

because that is the variance of the bionomial

and then the denom on the right side of the equality also doesnt make sense

at least to me

[formal cove]

Hello?

[plucky elk]

why what

[formal cove]

like if i compare my answer to the answer

i feel i am right but apparently not

so what am i missing?

[plucky elk]

nowhere are you even calculating $\pr(X \ge \alpha n)$

[flat frigate]

riemann

[plucky elk]

That should be your starting point

not this

[formal cove]

.close

[safe radish]

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[safe radish]

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[timid goblet]

Don’t know how to start or begin

[safe radish]

@timid goblet Has your question been resolved?

[timid goblet]

<@&286206848099549185>

Waht

I Need help

This question I don’t understand at all

<@&286206848099549185>

[frosty skiff]

It asks at which point is the curve P(x) defined by R(x)-C(x) was the highest and lowest in the interval [2;16] if i understand well

[timid goblet]

Yea but I don’t know how to solve

Nor begin

[frosty skiff]

1. draw the curve of P(x) in the interval [2;16]
2. find the highest point and lowest of the curve and write them down

[timid goblet]

How do I draw it

Where do I find it

And for 2

How????

[frosty skiff]

You have two functions R(x) and C(x) wrote down

R(x) is the revenue
C(x) is the cost

[timid goblet]

Mhm

Wait so can I plug it into my calculator

Y=?

To graph

Or draw the thing

Is that what u want me to do

[frosty skiff]

Y = R(x)-C(x)

In your calculator

[timid goblet]

How do I type R and c

Alpha R and Alpha C?

[frosty skiff]

In graph it will ask for a function and you write down the function that they gave you

[timid goblet]

What do you mean?

Where do I click to get R and C

Like alpha “x” to get R?

[frosty skiff]

In the exercise they define a function called R(x) and C(x) you see them?

[timid goblet]

Yea

R(x)= Revenue
C(X)= Costs

[frosty skiff]

Yes now they ask you to draw with a calculator the function P(x) wich is equal to R(x)-C(x)

[timid goblet]

Sorry I’m a bit slow wdym?