help-33

[marsh citrus]

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[finite pagoda]

question 1, am i being stupid how am i supposed to get x > -9 i only get less than

[finite pagoda]

no matter which method i use it’s just

less than

the other inequality x < -2 is easy

a shit there’s no fucking way

the graph shows that x is only greater than 3 when x is lower than -2 meaning x+2 is multiplying by a negative number, please tell me there is a better way to find that out before hands

[marsh citrus]

@finite pagoda Has your question been resolved?

[finite pagoda]

find range of y, the signs are supposed to be the other way around why?

[marsh citrus]

@finite pagoda Has your question been resolved?

[finite pagoda]

<@&286206848099549185> it has been an hour, i gotta sleep soon so uh what am i missing here in both questions

[raven olive]

Quickly skimming over it cause I’m in a rush but anytime you flip a negative to a positive you also have to flip the arrow

[finite pagoda]

yes i am aware

however i don’t do that anywhere

[raven olive]

You had (y-12)

That’s essentially -12

[finite pagoda]

??

y-12<0 is y < 12

no multiplication

the sign flips with negative multiplication

i might have to draw the graph and check if x + 3 is always negative

[raven olive]

Well there’s also the logic in how can y be less than 0 and greater than 12

[finite pagoda]

because it’s a function with asymptotes?

[raven olive]

That’s the part I didn’t process sorry but like I said I have to go soon so I’m rushing

[finite pagoda]

np

[raven olive]

Gtg hope some one else can answer this for you

[visual elbow]

mb im in the bus right now

[finite pagoda]

i should be on the bed rn, 1 am

[visual elbow]

Is this due tomorrow?

[finite pagoda]

it’s not due ever

i’m self studying further math

my own deadline is that i finish this ch by tomorrow to stay on tract but

it’s up to me in the end

and the next ch is summation of series which is arguably easier

[marsh citrus]

@finite pagoda Has your question been resolved?

[marsh citrus]

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[marsh citrus]

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[hasty flicker]

Is there any other way of solving this problem without a calculator?

[hasty flicker]

.close

[marsh citrus]

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[lyric bay]

?

[marsh citrus]

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[still temple]

how to expand?

[still temple]

i tried dots but it’s not working

[frank crypt]

what are dots

[still temple]

difference of two squares

[frank crypt]

oh

you just want to multiply both of them right

[still temple]

yes but there is supposed to be s special way

that is fast

[trim quest]

you could technically do difference of squares here but I'd consider that to be a lot more confusing than just distributing normally, and not really any faster if at all

if you really wanna do difference of squares, you could rearrange it as ((x^2+4) - 3x) ((x^2+4) + 3x)

then you have the form (a - b)(a + b)

[still temple]

wasnt it already difference of two squares?

with a being x^2 and b being 3x+4

[trim quest]

no, because x^2 - (3x+4) is not x^2 - 3x + 4

x^2 - (3x+4) = x^2 - 3x - 4

[still temple]

oh

[trim quest]

so if you did this,
a - b
x^2 - (3x + 4)
x^2 - 3x - 4

but x^2 - 3x - 4 is not what you have

[still temple]

another question

how to factor this?

i factor the first 3 but then can’t factor the last 3

[oblique burrow]

You have to explain it morrr

[still temple]

the only explanation is to factor

[trim quest]

see if you can rearrange the terms in a different order that allows you to factor both groups

[still temple]

the first 3 terms are a perfect square trinomial

[marsh citrus]

@still temple Has your question been resolved?

[trim quest]

@still temple
If you haven't made any progress here, I think what you want to do is think of it as if it's a polynomial of only one variable

for example you can express it as

x^2 + 6xy - x + 9y^2 - 3y - 42

x^2 + (6y - 1)x + (9y^2 - 3y - 42)

essentially, a quadratic in x with coefficients 1, (6y-1), and (9y^2 - 3y - 42)

[marsh citrus]

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[hushed crest]

For a,b,c>0, prove that

a/(a+2b)+b/(b+2c)+c/(c+2a)>=1

[hushed crest]

I’ve been stuck on this question for a while I don’t know what to do

The only thing I could really find is the condition of equality

[marsh citrus]

@hushed crest Has your question been resolved?

[marsh citrus]

@hushed crest Has your question been resolved?

[jade wedge]

Did you try plugging in fractions/ decimals in values of a, b, and c that are between 1 and 0

[hushed crest]

Yeah

That doesn’t help me solve it tho

[jade wedge]

a =3, b=1, c=1

[hushed crest]

I don’t get it, what are these values supposed to mean?

[jade wedge]

Did I write it in the wrong channel? Ignore that, did you try the Cauchy-Schwarz Inequality

[hushed crest]

it's alright

i tried to think about the cauchy-schwarz inequality in this context

[ancient slate]

Assume, without loss of generality, that a>b>c>0

[hushed crest]

but i couldn't find anything

[marsh citrus]

@hushed crest Has your question been resolved?

[hushed crest]

<@&286206848099549185>

[hushed crest]

.close

[marsh citrus]

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[marsh citrus]

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[glad hearth]

is it possible to simply equations like “(2-4n)17” on a scientific calculator? It’s simply i know just want to know if it’s possible

[stoic saddle]

this isnt an equation but i doubt your avg scientific calc comes with a CAS

[wise jackal]

there may be programs if you can download stuff on it

[glad hearth]

yeah sorry i meant expression*

.close

[marsh citrus]

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[marsh citrus]

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[gray verge]

if 230.75 kilograms of juggery powder is to be packed equally in the packets each packet contain 2.5 lg of juggery powder find the number of required packets also find how much juggery powder will be there in 15 packets of mass kg (my statements questions are very poor please help)

[marsh citrus]

@gray verge Has your question been resolved?

[gray verge]

no

[night glade]

2.5kg right?

[gray verge]

yes

im really weak in statement questions

[night glade]

Uhhh I m not good at it too lol

[gray verge]

wer same then

[night glade]

Number of required packets is = 230.75/2.5

[gray verge]

so shall i divide them

or remove the decimal point

for 1 and take 0

[night glade]

Multiply 100 on both numerator and denominator

To remove the decimal

You will have 23075/250

The weird thing is the answer will still be in decimal

But again, the number of packets cannot be in decimal

[gray verge]

how shall i do that

are they getting multiplied or

added

[night glade]

You sure you wrote it correctly?

[gray verge]

i removed the decimal points

[night glade]

Not that, 230.75

[gray verge]

i got 2375/100 and 25/10

[night glade]

I'm talking about that

[gray verge]

what shall i do of these 2 now

[night glade]

(23075/100)*

You missed the 0

[gray verge]

how 0 comes here

oh yeah

uuhhh what now

[gray verge]

what now

[night glade]

,rotate

[night glade]

'92.3 packets' is not actually possible thats why I was asking about the 23075 part being correct or not

[gray verge]

by the way how did 10 got up

divition?

sorry dividion?

[night glade]

Dont you know flipping?

[gray verge]

yes

it comes after dividion

[gray verge]

and how did he got to division

i know this thank you but how did it get to dividion

[night glade]

This right?

[gray verge]

yup

[night glade]

You told me 230.75 can be written as 23075/100 and 2.5 as 25/100. So, 230.75/2.5 = (23075/100)/(25/10)

Do you get this or no?

[night glade]

Now after this, I flipped it

[gray verge]

sooo both of them were able to be divided

[night glade]

Yep but the main thing is

They asked for the number of packets

It cannot be in decimals

[gray verge]

i was going to ask that

[night glade]

We got 92.3 as the answer right?

[gray verge]

hmm

[night glade]

This is not possible.

[gray verge]

shall we divide again

[night glade]

The given value in the question is probably wrong

[night glade]

No. Its wrong

It has to be lol

[gray verge]

hmmm

92 whole 3/10

this is what i got

[night glade]

Yep

3/10 in decimal is 0.3

92+0.3 = 92.3

[gray verge]

soo

thats wrong

92.3 huh

lemme check it

[night glade]

The information you have given, the first question is solvable but not correct.

The second question can be solved

[gray verge]

if the first got rights

gots right

[night glade]

92.3?

Check

[gray verge]

theyre saying37.5

[night glade]

..

[gray verge]

93.3 packets = 93

but after taht

[night glade]

That's the answer to the second question

The 37.5

[gray verge]

they said to 37.5

and how it comes

[night glade]

Let's move on to the next question.
1 packet contain 2.5 kg powder
15 packets will contain (15*2.5) kg powder

Do you get this?

[gray verge]

15 2.5 or

how much is that

[night glade]

15 multiplied by 2.5

37.5

The answer you gave

[gray verge]

oh yeah

[night glade]

Is this written in the answers?

[gray verge]

but heres something else

from where 15 came

[night glade]

Or you just made it up

[night glade]

They literally asked how much powder will 15 packets contain

[gray verge]

well i got that myself and the answer is given in the end

[night glade]

1 packet = 2.5kg
15 packet = 15*2.5 kg

Multiplied both sides by 15

[gray verge]

oh yeah thank you for remindiing me

math is confusing

[night glade]

Not really

[gray verge]

and it makes you forget anytjingeasily

well not tha much

im the best in studies in class

but still the statements

are tiresome

[night glade]

Again im asking, is this written in the book?

[gray verge]

its 1 AM over here and i still got much to do

[night glade]

Or you just made it up

[gray verge]

the answer?

[night glade]

Yep

The 93

[gray verge]

well yes its in the end

but tht 93.3 is i got after dividing it

[night glade]

Yes

[gray verge]

the asnwer we got up

[night glade]

But the answer given is 93 right???

[gray verge]

i divided it to whole number

so i got 93.3

[night glade]

92..

[gray verge]

yup

92

[night glade]

They rounded up to the nearest number

[gray verge]

yes

[night glade]

92.3 -> 92

[gray verge]

thats a strange amthematic

[night glade]

Well you get it right?

The first and second one

[gray verge]

yes the asnwer is right

[night glade]

The first one was weird but yeah

[gray verge]

i have 2 more

dang

[night glade]

Alright

You can send

[gray verge]

but im soo sleepy

really

[night glade]

Where do you live?

[gray verge]

pakistan

i hate my country

people here are cruel bad

and they dont even care about health and studies

[night glade]

Uh this is maths channel. Avoid talking about your country ...

💀

[gray verge]

oh yeah thanks for reminding

[night glade]

You can send

[gray verge]

im sllepy and a little depressed

[night glade]

Or close the channel if you are done for today

[gray verge]

ok

[night glade]

I'm not a therapist but i sure can do maths

[gray verge]

zeeshan wants to fill 137.5 litres of petrol find the number of bottles if 1: the capacity of each bottle is 5.5 litres 2: the capacity of each bottle is 6.25 litres 3: also tell how much petrol will be there in 18 bottles of 6.25 litres each

there are 3 in 1 m

[gray verge]

soo can you help me

[night glade]

Aight now this is ok

[gray verge]

this ones looks easy

[night glade]

You remember what i did in the previous question

The first question

Apply that here

Same shit

[gray verge]

but the bottles

need to find the bottles

dang this means seperation of petrol into parts

[night glade]

No

[gray verge]

soo

my eyes are like stones

🤣

gotta hurry

[gray verge]

need to wake up at 5 AM again

[night glade]

,rotate

[night glade]

The first one

Shitttt

[gray verge]

can you tell me how division comes

[night glade]

It will be 'capacity of bottle'

😭

[night glade]

Ok

[gray verge]

how did you got these numbers

and in division

can i know please

[night glade]

Literally written in the problem

[gray verge]

137.5 i cant take it to that number

how have you done it

its pretty confusing

trying my best to understand

[night glade]

Ok let's take an example.
I have 100 candies and there are 10 students.

How many candies will one student get?

[gray verge]

10

[night glade]

Exactly

Same thing applies there too

[gray verge]

sorry i was thinking about my friend

[night glade]

Just divide

[gray verge]

but

how i dont know which numbers have you divided with them

nor i can end them after division

[night glade]

CROSS MULTIPLICATION

[gray verge]

well my cross multiplication occurs between 2 fractions whic type is this

😵‍💫

😭

why i cant understand

im such a fool

what about the decimal points

im gonna leave this question

[gray verge]

i wont waste your time

goodbye friend thank you very much for your help

[night glade]

Yo

[gray verge]

yes

[night glade]

Come back tmr I'm sleepy too

[gray verge]

can i ask something

[night glade]

Yea

[gray verge]

what is lifting up 1 day later

[night glade]

Eh

[gray verge]

i got banned from an aoo

app

[night glade]

How

[gray verge]

and he says lifting up 1 day later

well

there were 2 guys a girl wanted to argue with me

[night glade]

Oh

[gray verge]

she wanted to make me angry

[night glade]

Ban will be lifted after 1 day later

[gray verge]

but she didnt knew im a troll

[night glade]

You will be unbanned

[gray verge]

im not a pure troll

but i know how to annoy people badly

so i annopyed her soo much that she pissed off

[night glade]

Aight. This is not the place to talk about all this.

[gray verge]

now that other guy was also

ok

please accept my friend request

[night glade]

Close the channel using the command .close if you are done. You can dm me the problem, I'll look at it later.

Bet

[gray verge]

thank you very much for your help

wish you have great day tomorrow

goodnight

bye

[night glade]

Gn

[marsh citrus]

@gray verge Has your question been resolved?

[marsh citrus]

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[past falcon]

how do i go about calculating csc

[past falcon]

its the opposite of sin right

[spark otter]

yes, csc(x) = 1/sin(x)

[past falcon]

oh should i calculate with sin first then do 1/sin

for csc

[spark otter]

that's a good idea

[past falcon]

wait so I wouldn't input it in the same way I would input it like tan on a calc would i

like 270sin(68)

i did 1/sin(250) and ended up with a negative

wait this is cos not csc

270cos(68

[marsh citrus]

@past falcon Has your question been resolved?

[past falcon]

.close

[marsh citrus]

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[dire verge]

hyelp

[dire verge]

image loading

[marble glacier]

assuming each section is the same area/ probability

how many sections are there in total

and how many are labelled A

[dire verge]

2

3 of B 3 of C

[marble glacier]

Ok

[dire verge]

8 in total

[marble glacier]

Yea

So whats the probability if there are 2 A sections it could land on but 8 sections in total

[dire verge]

it cannot be fractions either btw

[marble glacier]

Thats fine, we can convert

[dire verge]

idk

[marble glacier]

If you roll a dice, what are the odds of getting a 6

[dire verge]

1

[marble glacier]

1? that would mean that you will always get a 6

is this true?

[dire verge]

1/6

[marble glacier]

Yea

1/6

because there is only one 1, and there are 6 total

now back to our example

there are 2'A and 8 in total

so whats the probability

its the same thing you did

[dire verge]

2/8

[marble glacier]

Perfect

now whats 2/8 simplified

like simplify the fraction

[dire verge]

I forgor how to simplify

[marble glacier]

thats fine

[dire verge]

.25

[marble glacier]

So basically to simplify a fraction you find the biggest factor in both the top and bottom, and divide the top and bottom by that

wtf

didnt even need me

but yes

2/8 = 1/4 = 0.25

[dire verge]

the calculator was faster than reading

[marble glacier]

xD

[dire verge]

this is the second question

image loading

well

whats the denominator

I already know the numerator is 3

[sly zephyr]

how many balls do you have ?

[dire verge]

2

[sly zephyr]

in total

[dire verge]

I have 2 balls

like every other male

oh shi you meant the problem

uh

14

[sly zephyr]

so ?

[dire verge]

so what

oh

thaats the denominator

[sly zephyr]

ye

[dire verge]

wb this

[sly zephyr]

what's the numbers of C's and the numbers of part on the wheel ?

[dire verge]

8 wheel parts

3 cs

[sly zephyr]

so ?

[dire verge]

so what

3/8

[sly zephyr]

ye

[dire verge]

.375

as a decimal

[sly zephyr]

and in % ?

[dire verge]

idk

37.5

[sly zephyr]

multiplie .375 by 100

[marsh citrus]

@dire verge Has your question been resolved?

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[civic dove]

mmm kinda lost

i got all the way to 9(sec(x)-1)/2

[shell granite]

how did you get there?

[civic dove]

i turned cot into 1/tan(x)

so 1/ 1/2

so 2 at the bottom

than i took out the 9 at the top

[shell granite]

you should be left with sqrt(9(sec^2x-1)) then

[civic dove]

the sqaure root and sqaure don't cancel out?

[shell granite]

it cancels out if the whole thing is squared not just one of the terms

[civic dove]

mmm ok

[shell granite]

you should use trigonometric identities to get the numerator in terms of tan

[civic dove]

so sqrt 9(sec^2(x)-1 / 2

[shell granite]

yea

[civic dove]

does sec^2(x)-1 = tan(x)???

[shell granite]

tan^2 (x)

[civic dove]

mmm ok

so sqrt9(tan^2(x) /2

would it become (1/2)^2

[shell granite]

not really no

how did you get there?

[civic dove]

hmm

i just assummed

[shell granite]

that step is right tho

[civic dove]

because tan(x) = 1/2 is given

[shell granite]

yea so it's sqrt (9.(1/2)^2)/2

[civic dove]

mmm

can i just square the 9 right now?

[shell granite]

yes

[civic dove]

3*1/4

3/4 / 2

[shell granite]

you should square both the 9 and the (1/2)^2

[civic dove]

wait it can't just go way

since now its squaring a number

[shell granite]

you mean the (1/2)^2?

why wouldn't it?

[civic dove]

i got it i think

3/4

.close

[marsh citrus]

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[mellow basalt]

kinda lost don't really know how to do

drew the graph but is there any easier ways to solve it

[marsh citrus]

@mellow basalt Has your question been resolved?

[mellow basalt]

<@&286206848099549185>

[marsh citrus]

@mellow basalt Has your question been resolved?

[marsh citrus]

@mellow basalt Has your question been resolved?

[mellow basalt]

<@&286206848099549185>

[hasty ruin]

wym drew the graph, the graph of both the original and its transform are given

[hasty ruin]

oh ig you meant you drew (1/2)f(-x)

the answer is not really, following those steps and doing it this way is about as concrete and simplified as it gets until you get familiar with transformations enough to do them in your head (at which point you’re still doing the same thing just saves some writing)

i guess one tip is to only look at “interesting” points (endpoints of straight line segments)

(also you unfortunately drew (1/2)f(-x) wrong by a little bit)

[mellow basalt]

ive calculated the bit and found out that a= 1/2, b=-1, h=2, k=-6

im not sure if theyre correct tho

[hasty ruin]

now it is

[mellow basalt]

may I know is this correct??

[marsh citrus]

@mellow basalt Has your question been resolved?

[marsh citrus]

@mellow basalt Has your question been resolved?

[remote barn]

it gets reflected from the middle, and it's translating down to the SAME place, not the highest point of g(x) to the lowest of f(x)

[marsh citrus]

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[karmic fulcrum]

How do I find the derivative of this question:

[karmic fulcrum]

This is what I’ve done so far:

[undone bane]

you mixed quotient rule and product rule here.

[elfin berry]

Dyssrupt

[marsh peak]

Were you trying to use this? (u/v)' = (u'v - uv')/v^2

[karmic fulcrum]

I’m trying to use quotient rule

For this question

[undone bane]

if you wanna go with quotient rule, the functions are x^2 and sqrt(x+1)

[marsh peak]

Then you should let v = (x + 1)^(1/2)

Rather than (x + 1)^(-1/2)

[karmic fulcrum]

But shouldn’t 1/2 be negative since it’s on the bottom denominator?

[marsh peak]

v is the denominator in u/v, right?

[karmic fulcrum]

Yes

OHHHHHHHHH

SO IT SHOULD BE POSITIVE OHHHH

[marsh peak]

Indeed

[karmic fulcrum]

This is what I ended up getting

How do you factorise it out?

[marsh peak]

Yeah, you can factor x out but I would first multiply top and bottom by (x + 1)^(1/2) before that

[karmic fulcrum]

Hmm okay

Ohhhhhh

Okay thank you so much!!

Ok I can understand the rest to answer the question… thank you :))

.close

[marsh citrus]

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[warm scroll]

Certainly, here's a more polite version of your message:

"Hello, I've been working on this problem for quite some time and could use a little assistance, please. Here are the patterns I've noticed:

2 ☆ 3 = 9
5 ☆ 3 = 18
6 ☆ 4 = 30

Now, I'm trying to figure out the next step: 7 ☆ 4 = ? Your guidance would be greatly appreciated. Thank you!"

[random palm]

either 35 or 32?

[late geode]

many arbitrary rules that you could make up

one of them may match the one the author thought of

try random things, see if they work for the first three equations

[warm scroll]

I believe that the simplest option would align with the author's intended meaning.

[late geode]

that's impossible unless you have supernatural abilities and are able to read their mind

[warm scroll]

I attempted to use the operation a☆b = a*b+b, but unfortunately, it did not yield the expected result when applied to 6 ☆ 4, which should ideally equal 30.

[late geode]

you could make a small adjustment where you add any multiples of 3 present

[warm scroll]

I'm not entirely certain about this. Could you please provide me with some hints or guidance?

[late geode]

which of 2,3 are multiples of 3

[warm scroll]

it's 3

[late geode]

yes

and adding that to the product gives 9

which of 3,5 are muliples of 3

[warm scroll]

also 3

[late geode]

and adding that to the product gives 18

which of 6,4 are multiples of 3

[warm scroll]

it's 6

[late geode]

and adding that to the product gives 30

[warm scroll]

Ah, I believe I'm starting to grasp the concept.

[late geode]

that rule seems to work for the first three equations

and can be applied to the last

to get a justifiable result

whether its the same as what the author intneded is a different story

[warm scroll]

I don't observe that either 4 or 7 can be expressed as a product of 3.

😥

[late geode]

yeh, so you don't add anything

[warm scroll]

OK

May I suggest that we explore the possibilities of using multiplication, division, or perhaps subtraction to address this matter?

[late geode]

how so

there's too much to go through / compute

[warm scroll]

oh ok I see

[late geode]

infinitely many combinations

fluke one that works

[quaint elm]

three points define a plane so this should be possible with a linear constraint

[stoic saddle]

did you GPT this

[warm scroll]

What is GPT?

.close

[marsh citrus]

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[warm scroll]

bye! imma leave

[stoic saddle]

bye lol

not even waiting for an answer to your own question

[marsh citrus]

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[stark field]

guys is this truth?

[runic temple]

Indeed

[stark field]

hmmm

werid because

this is derivation of average costs

it would mean its diseconomy of scale

but i previously got its conomy of scale

but you donno

🇮🇱🍺 Israel beer for you GarlicB

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[runic temple]

,w derivative of 2/(y^1/3)

[elfin berry]

Results provided by WolframAlpha

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

Requested by garlicbredfries

[stark field]

fr

yo

but maybe if y rises, then it increases?

is this rising function ?

woah

woah!

not rly?

[marsh citrus]

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[still temple]

Hi, we're going through complex numbers and arithmetic operations with complex numbers, and i'm completely stuck with my homework. Can someone help me solve this one and explain step-by-step how you do it?

[next raft]

what does the question ask you to do?

[still temple]

to calculate the solution

[distant peak]

and what should be the solution

🤔

hint : ||rationalize the denominator||

[still temple]

i've honestly got no clue

doesn't rationalising the denominator require a square in the problem?

[next raft]

rationalising the denominator means to get rid of the imaginary part

(a+bi) (a-bi) =a^2+b^2

just multiply the numerator and the denominator by the conjugate of the denominator.

[still temple]

Ahh

I see it now

Yeah, I think i got it. Thank you!

.close

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[waxen heron]

I have tried this problem, I am not sure if I did it right

$P_w = 0.6\
P_l = 1 - P_w = 1 - 0.6\
P(losing all the matches) = P_l1 * P_l2 * \dots * P_{15}\
=(1 - P_w)^{15}\
P(Winning at least one)=1-(1-0.6)^{15}$

[elfin berry]

13wrc

[waxen heron]

can someone please help?

<@&286206848099549185>

[marsh citrus]

@waxen heron Has your question been resolved?

[main idol]

sounds right

[unborn condor]

it is correct, if you're allowed to not use a distribution.

[waxen heron]

hi

[waxen heron]

but the question here asks for a distribution

I have not reached that topic yet

[waxen heron]

okay thnks

[unborn condor]

look into binomial distribution

[waxen heron]

thanks

[waxen heron]

could you please give me an idea how I should go about solving this with the help of binomial distribution?

[unborn condor]

Binomial distribution cares about something that you do repeatedly, and only care if it happens or not.
For example, tossing a coin, and seeing if it lands on heads.
You got a number of trials, a constant probability of success on each trial, and the number of successes that you're asking for.
The binomial distribution gives you the probability of getting exactly that many successes in that many trials.

[marsh citrus]

@waxen heron Has your question been resolved?

[main idol]

The name of the one you used is called Bernoulli distribution

[marsh citrus]

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[thorn wharf]

Can someone pls help me out with this idk how I would do step 3

[desert dirge]

assuming its true for n=k, i.e. u_k=4*2^k +2, you can use the recurrence relation:
u_(k+1)=2(u_k)-2

try see what you can do from there

[thorn wharf]

Well I know the value of k is 4 * 2^k +2

So I could write u(k+1) = 2 * (4.2^k +2) -2

But I doont know what I'd do next

[desert dirge]

expand the bracket

[thorn wharf]

U(k+1) = 8.4^k +2

[desert dirge]

remember a*a^n=a^(n+1)

[thorn wharf]

🤔

[desert dirge]

$2\cdot 2^k = 2^{k+1}$

[elfin berry]

AℤØ

[thorn wharf]

Don't see how I would use that to expand

OHHH

Nvmm I wrote 4.2 instead of 4*2

Gonna try again now

Like this?

[desert dirge]

not quite

on the second line, you cant have both 4 and 2^k multiplied by 2

that would imply a multiplication of 4

and you still want the 4 there to have your induction complete

[thorn wharf]

Hmm

So I need to manipulate this in order to get 4 * 2^k+1 + 2?

I don't get how I can make 4 stay 😭

[desert dirge]

$2(ab)\neq(2\cdot a \cdot 2 \cdot b)$

[elfin berry]

AℤØ

[desert dirge]

thats the issue with your second line

you multiplied both the 4 and the 2^k by 2 each

$2(4\cdot 2^k)=4\cdot 2 \cdot 2^k$

[elfin berry]

AℤØ

[thorn wharf]

I think I got itt

Does this look correct?

[desert dirge]

its a bit contrived with the converting 4 to 2^2 and making it 2^k+3 but logically yeah its fine

[thorn wharf]

Still want to try understand what youre saying

[thorn wharf]

Ookayy

Is this better?

[desert dirge]

much better

perfect

[thorn wharf]

Yayy thank uu so much

[desert dirge]

np

[thorn wharf]

.close

[marsh citrus]

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[junior robin]

Doing a little review, and I have no clue where I am going wrong here. First term turns into 2x, second term has product rule done to it, third term turns into 2y(dy/dx), and 5 turns into 0.

[junior robin]

There’s another problem which is the exact same except for 5 being 9, and I get the same thing.

Mind the bad handwriting

Maybe I'm missing a step and y' != dy/dx?

<@&286206848099549185>

[marsh citrus]

@junior robin Has your question been resolved?

[marsh citrus]

@junior robin Has your question been resolved?

[junior robin]

Is my question really that trivial? 😂

<@&286206848099549185>

[violet falcon]

I am trying to solve the question mentioned below. Based on my calculation, I am getting 2,239,444.68 as Chi-Square value and Degree of Freedom as 5. Based on the Chi-Square Calculator, I am getting P-value of 0.0000 but the correct **P-value **of the below quiz question is mentioned as 0.32. Could you please provide solution for this Chi-Squared Goodness of Fit Test?

[junior robin]

I found my issue. It is supposed to be x, not xy in the denominator.

.close

[marsh citrus]

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[pliant yacht]

how to simplify square roots- eg simplify square root of 48?

[south smelt]

You want to find the biggest square multiple of 48

biggest multiple of 48 that's a square*

[cobalt sentinel]

U mean factor?

[still temple]

biggest square factor

haha

[south smelt]

I did. Tired

[cobalt sentinel]

I feel u bro

[foggy shoal]

Find the biggest squared factor

Ie 4 9 16 25… etc

[pliant yacht]

How do I do that

[foggy shoal]

For example I could simplify sqrt27 by saying it was equal to sqrt9 x sqrt3

Which would become 3sqrt3

[pliant yacht]

right

oaky

[foggy shoal]

So what would you say the biggest square multiple of 48 is

[pliant yacht]

8?

[south smelt]

you can find a bigger one

[foggy shoal]

So 8 isn’t a square multiple

[pliant yacht]

uhhh

[foggy shoal]

Like 2 x 2 = 4 3*3 = 9

So what out of the perfect square numbers go into 48

[pliant yacht]

how do I find square multiples

[foggy shoal]

Square 2

What’s the answer

[pliant yacht]

4

[foggy shoal]

Square 3?

[pliant yacht]

soo???

[foggy shoal]

And so on for every whole number

Why don’t you write out all the factors for 48 and send us a photo

[foggy shoal]

Okay this isn’t wrong but do it for just 48 specifically

[pliant yacht]

that's prime factors

oops

[foggy shoal]

Yes ok

So now out of all the numbers which ones are perfect squares of a whole number

Like 2x2 and 3x3 and 4x4

[pliant yacht]

none??

I am confused

none of them are x themselves

[foggy shoal]

2x2 = 4

4 x 4 = 16

[pliant yacht]

OH

Uhhh

16?

[foggy shoal]

So 4 is there and 16 is there

But we are trying to get the highest one

So we pick 16

[pliant yacht]

so 4x4 = 16

[foggy shoal]

Yes

Perfect square multiple

[pliant yacht]

so how does that turn into simplifying the square number

[foggy shoal]

Ok so 16 x 3 = 48 yes

So therefore we can rewrite 48 as 16 x 3

Or square root of 48 = sqrt 3 x square root 16

[pliant yacht]

so 16x3 is the simplified sqr48

[foggy shoal]

No not necessarily

It’s the first step

[pliant yacht]

what comes next

[foggy shoal]

I’m not going to tell you exactly, I’m trying to get you to figure out on your own

So if 48 can be written as 16 x 3 what do you think you can rewrite your square root as?

[pliant yacht]

sqr16 x sqr3?

i honestly have no idea

[foggy shoal]

Yes that’s right

[pliant yacht]

can you explain why

or is there no why

[foggy shoal]

Ignore the square root, 48 has factors like you presented earlier

1,48 2,24 etc

Whilst you could rewrite 48 as any multiple of these factors, only a couple of them help us simplify

In this question, because there is a square root, we are looking for numbers that breakdown into a whole number when square rooted

ie numbers that are themselves squared

Hence why we picked 16 and 3.

Make sense?

[pliant yacht]

I think so

so simplifying

√63 would be √7 x √9?

[foggy shoal]

Yes

But what is that square root 9 become?

[pliant yacht]

3x3

?

[foggy shoal]

Well no

9 = 3 x 3

[pliant yacht]

so √9 is 3

?

[foggy shoal]

So sqrt9 is essentially asking what times by itself is equal to 9

[pliant yacht]

so 3

[foggy shoal]

Yes

So now you can rewrite it like this

[pliant yacht]

rewrite it like what

im so sorry maths is not my strong suit

[foggy shoal]

Sqrt63 = 3 x sqrt7

[pliant yacht]

is that simplified

[foggy shoal]

Yes

That is sqrt 63 simplified

And so for 48 it would be

[pliant yacht]

why is that like that but the other question wasnt?

[foggy shoal]

What do you mean the other question wasn’t

[pliant yacht]

oh

Well you didnt say the other question was meant to be written like that

[foggy shoal]

Well we never finished it you asked a different question

But we got to sqrt16 x sqrt3 if you recall

[pliant yacht]

I thought it was finished

[foggy shoal]

Nah not just yet

So 16 = 4x4 so sqrt16 = 4

Hence why it’s 4 x sqrt3

Understand?

I’ll give you an example and you send me your working

Simplify sqrt50

[pliant yacht]

i dont really understand why it is like it is but I understand how we get to that]

[foggy shoal]

Just laws of maths, it’s how square roots work,

Consider revising square numbers and such

Write out a simplification for square root 50 and I’ll tell you how you go

[foggy shoal]

Perfect

As you get better you’ll be able to do these things in your head

[pliant yacht]

okay cool

so if im adding 2 square roots and simplifying

Then I just do x√y + a√b

?

[foggy shoal]

Send me an example

Not quite sure what you.mena

[pliant yacht]

so √12 + √27

[foggy shoal]

Ah ok

Simplify first

So sqrt12 would be?

[pliant yacht]

2√3

?

[foggy shoal]

Yes

Now sqrt27

[pliant yacht]

3√3

[foggy shoal]

Correct

Now “collect like terms”

So In an algebraic sense

2x + x = 3x

So 2sqrt3 + 3sqrt3 = ??

[pliant yacht]

im so confused

[foggy shoal]

Here let me write it out

[pliant yacht]

2√3 + 3√3

[foggy shoal]

Yes

[pliant yacht]

where do I start

[foggy shoal]

Have you done basic algebra?

[pliant yacht]

yeah

im not good at it lmao

[foggy shoal]

That’s ok

But if I wrote 2x + 3x

What would you say the answer is?

[pliant yacht]

6x

or 5x

i don't remember

[foggy shoal]

5x yes

It’s plus not times

Make sense?

[pliant yacht]

yes

[foggy shoal]

Okay so now imagine that x = sqrt3

And redo 2x + 3x

[pliant yacht]

so its 5x

[foggy shoal]

Orrr

[pliant yacht]

but idk what the sqr 3 becomes

it adds

together

[foggy shoal]

it becomes x

[pliant yacht]

is it six or 9

[foggy shoal]

So 5sqrt3

[pliant yacht]

so it stays the same?

[foggy shoal]

Sorry I probably confused you

The x is just a variable that has some value

It’s not times

[pliant yacht]

im gonna go to sleep cuz its 3am but thank you so much for your help

[foggy shoal]

All good man

Have a look when you wake up it might just clock for you

[marsh citrus]

@pliant yacht Has your question been resolved?

[marsh citrus]

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[marsh citrus]

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[low comet]

Can someone explain to me what we did

Where I underlined in black please

[hard gull]

u added and subtracted 1

in the denominator

[low comet]

yes but during the video session he said it should be +1

so it became sqrt (4)

[still temple]

br

bro

you just took out the 4 common lol

no addition or subtraction

[low comet]

but why divided by two

because we have power 2?

[still temple]

yea

[low comet]

calculus is becoming really tricky

gotta start practicing iguess

[marsh citrus]

@low comet Has your question been resolved?

[marsh citrus]

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[native tapir]

Missed last two math periods, i don't know what the question means by period and why it is 360 for the example. Please teach me how to work it out for 1 of the 9 questions

[marsh citrus]

@native tapir Has your question been resolved?

[native tapir]

<@&286206848099549185>

Nevermind

.close

[marsh citrus]

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[woeful dawn]

.reopen

hey

[marsh citrus]

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[gray shale]

I have doubt about what I've done

[main idol]

what's the question

@gray shale

[gray shale]

study the sequance

but here i'm just tryna get something more comfortable

[main idol]

why is this a log(sin) here?

,tex .log rules

[elfin berry]

riemann

[main idol]

use power rule there

[sullen ice]

I assume if you were given the sequence it's already in its "comfortable" state

[gray shale]

ye no ln, i fucked up

[gray shale]

not really

also i have a doubt about the 1/2

[main idol]

that's not a real question ?

doesn't tell you what to find

[gray shale]

ln(1^y * 2^y * ... * n^y) = y^n * (ln(1) + ln(2) + ... + ln(n))
am i right?

[gray shale]

generally what it means is finding if it converge if yes then what's the limit stuff like that

[gentle ledge]

false

[gray shale]

then what's the answer

[gentle ledge]

it's just ln(1^y * 2^y * ... * n^y) = y* (ln(1) + ln(2) + ... + ln(n))

[gray shale]

fair

I think it must be right

[scarlet hinge]

no

[scarlet hinge]

yes

However

pls put brackets after sin

it is very ambigious otherwise

[gray shale]

ye forgot

[scarlet hinge]

[gray shale]

i'd like to use rieman to find the equivalent of the sum

so with b=1 and a=0

but i don't have 1/n before the sum, do i put *n on the right side?

no it's fucked up a=1

[scarlet hinge]

yes

[scarlet hinge]

yes

n/n

[gray shale]

a must be equal to 1

[scarlet hinge]

however

[gray shale]

because i have 1 + k/n

[scarlet hinge]

you have 1 + k(b-a)/n

b=1 and a=0 best

[gray shale]

so b-a=1
a=1

[scarlet hinge]

no

compute

b=1

a=0

then

b-a=1-0=1

so good

[gray shale]

then it's the sum of k/n

[scarlet hinge]

oh

[gray shale]

not 1+k/n

[scarlet hinge]

you want to put f=ln?

[gray shale]

ye

why?

i can f differrent?

[scarlet hinge]

I would put f(x)=ln(x+1)

[gray shale]

oh f(x) = len(1+x)$

[scarlet hinge]

yeah

[gray shale]

ye didn't thought about it

[scarlet hinge]

a=1, b=2 would work too though.

You need to also do something with sin.

[scarlet hinge]

What does ~ mean?

[gray shale]

equivalent of, because i don't care about the limit itself

[scarlet hinge]

😬

I don't like this notion, I think this allows for mistakes.

you sometimes cannot compute parts of limits individually and put together.

[gray shale]

of what i remember the first time i heard about riemann was qith equivalent and not limit

[scarlet hinge]

😬

It's just a lmit.

[gray shale]

fine anyway

[young owl]

hmmm