help-17

[astral apex]

correct?

[sly sierra]

,rotate

[astral apex]

found this online

practicing right now

and a friend said

its wrong

or looks wrong idk

wanna make sire

[sly sierra]

according to the normal rules of operator priority, tan 2x - 4 tan x means tan(2x) - 4tan(x), not tan(2x-4) tan(x)

[astral apex]

so is it wrong

wait what

[astral apex]

i dont get this

[sly sierra]

the first line is already wrong, so if the answer is right it's a total coincidence

[sly sierra]

what don't you get?

[astral apex]

ohhh

ok

ill try solving myself

[sly sierra]

ok

[astral apex]

and let you guys know my answer

[sly sierra]

sure

[astral apex]

thanks alot

[sly sierra]

happy to check your work if you want

[astral apex]

im gonna close ticket for now

.close

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[compact eagle]

when graphing sin/cos, how do i determine the points on the x axis from the center point to the period?

[compact eagle]

say i have a period of 3pi

and a scale of 3pi/4

what do i do to determine the numbers between?

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[twin rampart]

Could anyone help me?

[twin rampart]

One moment, I'll translate for you

Have to choose the function, when for each x of its domain f(-x) = -f(x)

[heavy yoke]

for each of the functions you have to find f(-x) and -f(x) and see if they're the same

[twin rampart]

But there's not functions like that

[desert hornet]

yes there are

they are called odd functions

[twin rampart]

2/x ?

[desert hornet]

yeah

[twin rampart]

But if f(-x) = 2/-(-2) = 1

[foggy aspen]

or actually 2/(-x)

will give -(2/x)

means -f(x)

[vocal sleet]

@twin rampart Has your question been resolved?

[twin rampart]

But if we plug -2 in -(2/x), it's still 1

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[exotic pebble]

is 5/6π the radiant of 150°?

[midnight rapids]

Radian, yes

[exotic pebble]

so it's right?

[floral seal]

Change $\pi$ to $180^o$

[twin meteor]

MochaOhwelp

[exotic pebble]

so i should write it 2/6180?

[floral seal]

$150^o \cdot \frac{\pi}{180^o}=?$

[twin meteor]

MochaOhwelp

[floral seal]

Should be this one

[exotic pebble]

thanks

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[native mantle]

No. 4 and 5 only

[outer warren]

supposedly this question is linked to a diagram

[native mantle]

Yep

This is the trianhle

[outer warren]

can you post the full question

you're cutting off important information linked to the diagram

[native mantle]

Its actually just "Given AI= 3x - 2 and MC = 9x - 13

Just that nothing else

[outer warren]

the information about the diagram

[native mantle]

Ahhh

[outer warren]

did you do Q1?

[native mantle]

Already did 1-3

Just need 4-5

[outer warren]

consider your answer to

How did you solve for MC

and apply that here

[native mantle]

Multiply AI by 2

Ooohhhhh

so 2AI = MC right?

aight I get it now. Thanks @outer warren

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[azure horizon]

Still can’t get q5

[azure horizon]

Cant find the point P

[fleet ember]

express the equation of the tangent in a general manner, such that when you use the info that (1, 0) belongs to it, you get the only tangent solution (and then deduce P)

y = f'(a)(x-a) + f(a)
= (2a-3)(x-a) + a² -3a + 18

that's what the tangents looks like

which ones goes through (1, 0) ?

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[ruby barn]

I have a question regarding standard deviation and measurement uncertainty

[ruby barn]

I know of these 2 formulas for calculating standard deviation for a sample or population experiment

but in our physics labs we're told to use this

I am unable to find any resources about it in english

In Polish they call it "niepewność standardowa średniej" which translates to "the standard uncertainty of the mean"

I was also wondering why this way to calculate standard deviation isn't available in excel

or at least I can't find it

[urban edge]

It should be STDEV for standard deviation i think

[ruby barn]

that calculates it for a sample

so it only divides by n-1

whilee stdev.p calculates for the population and divides it only by n

I know I could calculate it by calculating stdev.s and then dividing it by sqrt(n)

but my question is whether somebody knows where I can find information about this

and whether excel has a built in function for it

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@ruby barn Has your question been resolved?

[ruby barn]

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[graceful ember]

how do you know how many stationary points there r

[south token]

The highest power of the equation should help

[graceful ember]

but the first one i found 2

x=1

[south token]

To find and classify you need to differentiate first and then again to find if it’s minimum or maximum

[graceful ember]

ye i did

[south token]

For the first one?

[graceful ember]

ye wait

i differeient it again and i put what i got for x

[south token]

To classify yes

[graceful ember]

so it = 0 which means its inflection point right

[south token]

Yes so you need to do the first derivative test

[graceful ember]

ye gg i got that

for the second one

why does x = + or - 1 though

would it not just be 1

[south token]

Because the power on the x term is even so there’s two solutions

[graceful ember]

is that always the case then

[south token]

If the power is even yes

[graceful ember]

and if its odd is der one solution?

[south token]

Yes

[graceful ember]

legend ty !

[south token]

No problem! :))

[graceful ember]

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[twin rampart]

Anyone help me pleaee

[maiden iron]

[twin rampart]

(sqrt(9 + 4sqrt(5))) * (sqrt(9 - 4sqrt(5)))

How to solve it?

[maiden iron]

solve what

[twin rampart]

I just dont get how to multiple

[twin rampart]

That

[maiden iron]

calculate or solve

[twin rampart]

No, I'm not supposed to use calc

Another way

[maiden iron]

Simplify

[twin rampart]

How?

That's what I've got

[maiden iron]

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

[twin rampart]

Look at the picture

[maiden iron]

i dont understand what you wrote

can u write clearly ?

[twin rampart]

18 - 2 * (sqrt(9 + 4sqrt(5))) * (sqrt(9 - 4sqrt(5)))

[maiden iron]

$\left(\sqrt{9+4\sqrt{5}} - \sqrt{9-4\sqrt{5}}\right)^2 = 9+4\sqrt{5} - 2\sqrt{81 - 80} + 9 -4\sqrt{5}$

[twin meteor]

Herels

[twin rampart]

How did you multiply?

[maiden iron]

I just used (a-b)^2 = a^2 - 2ab + b^2

[twin rampart]

No, I mean

How did you multiply (sqrt(9 + 4sqrt(5))) * (sqrt(9 - 4sqrt(5)))?

[maiden iron]

$\sqrt{9 + 4\sqrt{5}} \sqrt{9 - 4\sqrt{5}} = \sqrt{(9+4\sqrt{5})(9-4\sqrt{5})}$

[twin meteor]

Herels

[twin rampart]

🙄

[maiden iron]

I think I did something wrong

[twin rampart]

OMG, I haven't seen that )

[twin rampart]

Why?

[twin rampart]

You did alright in here )

[maiden iron]

not here

[twin rampart]

But where?

[maiden iron]

oh well I did nothing wrong I checked

[twin rampart]

Thank you very much!

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[dusty oyster]

Hi

[dusty oyster]

Can you guys help me with this

I prepared my matrix with my equations and I put it all in the other matrix

I don't know what's the next

Step

Help

Please

Can someone

Hello

😦

[elfin blaze]

lol

[dusty oyster]

What

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[mossy hound]

Is the difference between a hyperbole and a eclipse just the subtraction sign (equation)

[lime gorge]

||🌞🌎🌚||

Yea

For the equations

[formal pond]

Looks like it

[loud heath]

The hyperbola is the wrong way round

[mossy hound]

How do you tell if it’s horizontal/vertical?

[loud heath]

Substitute 0 for one of the coordinates

Or whatever factor it's shifted by

[mossy hound]

👍

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[zenith sentinel]

okay guys so this is a 100% serious inquiry
is there any way for me to discover a new mathematical constant (like pi) in a reasonable amount of time with litle to no knowledge

[vast shale]

Why

[zenith sentinel]

it would be really funny to be able to give it like a common name

[worthy citrus]

You can take any number you like and call it whatever you like, but its unlikely people will 1) care about your number 2) listen to you

[zenith sentinel]

no but i seriously want to make something that hasnt been discovered and give it a name that will stick around

[floral seal]

First you need to be good at math

[worthy citrus]

Okay first get a PhD in maths

[zenith sentinel]

okay

[floral seal]

Better to study engineering also

[zenith sentinel]

then

[worthy citrus]

Then come back and ask again

[zenith sentinel]

you do not need to be so condescending towards my idea

[worthy citrus]

Again, people will only care the number is useful or interesting and even then probably only care if you're somewhat of an established mathematician

Anyone can "discover" a constant

[zenith sentinel]

well then how do i get to that point without being established

[worthy citrus]

You don't

If it was this easy everyone would be doing it

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@zenith sentinel Has your question been resolved?

[zenith sentinel]

i will prove you wrong. just you wait.

[worthy citrus]

Please do

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[onyx karma]

can someone double check this for me

[rugged vortex]

It looks like you're trying to find a function such that its gradient is the field

Is that what a potential function means?

[rugged vortex]

Looks fine with me if that's what a potential function is

Just make sure your 5xz doesn't look like a 6xz

[onyx karma]

thanks

.close

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[hollow forge]

A motorist fills the tank of her car with unleaded petrol, which costs $1.57 per litre. Her tank can hold a maximum of 60 litres of petrol. When she started filling the tank, there was already 7 litres in it.
Let c be the cost of adding v litres of petrol to the tank.
a Write down a linear model in terms of c and v to represent this situation.
b Sketch the graph of showing the coordinates of the intercept and it send point.
c Use the model to predict the cost of filling the tank of her car with petrol.

[hollow forge]

pls help

the linear equation i made was c = 7 + 1.57v

but when i go to the answers it is wrong 🤨

[karmic imp]

Do you know what the answer is?

[hollow forge]

yes

it say it is c = 1.57v

but idk why they didnt count the 7

[karmic imp]

Because at that time, there was just 7 liters

What if the motorist had 2 liters?

Or 5? Or 25

There's not a set starting value, it's just asking for the equation that relates volume and cost

[hollow forge]

i dont rlly get it

it literally says there was 7liters already in it, would this be the starting value

[karmic imp]

Let c be the cost of adding v litres of petrol to the tank.

You're creating a general equation

[hollow forge]

wouldnt it be c = 2+fjefefu

[heavy yoke]

it's asking for the cost of adding a certain amount to the tank, not the cost of filling it to a certain level

[karmic imp]

For just the cost

[karmic imp]

That's just for that specific case

The question is generic

Meaning in general, what would be the cost of gas based on the volume

[hollow forge]

mm ok

[karmic imp]

The problem gave 7 liters and a max of 60 liter tank because that means overall, the motorist can only fill 60 - 7 liters, or 53 liters of fuel

[hollow forge]

yh ok

and also

i dont understand what this means

0<t<53

<or equal to

[karmic imp]

That's the interval

She can fill 0 liters and up to 53

As mentioned

the motorist can only fill 60 - 7 liters, or 53 liters of fuel

[hollow forge]

yh

[karmic imp]

She already has an existing 7 liters

And her tank can only hold 60 liters

Could she fill 100 liters of gas?

[hollow forge]

ofc not

[karmic imp]

What about 54 liters? Could she fill that much?

[hollow forge]

no?

[karmic imp]

She has 7 liters already, if she adds 54 liters, will her tank hold that much?

[hollow forge]

An empty 20 L cylindrical beer keg is to be filled with beer at a constant rate of 5 litres per minute.
Let V be the volume of beer in the keg after t minutes.
a The beer keg is filled in 4 minutes; write down a linear model in terms of V and t to represent this situation.
b Sketch the graph showing the coordinates of the intercept and its endpoint.
c Use the model to predict the volume of beer in the keg after 3.2 minutes.

ok

for this question

what would the 0<t< thing be?

wouldnt it be 20L because that is the max?

[karmic imp]

Yes

[hollow forge]

? im confused lol

[karmic imp]

Because you were asking about the volume

The beer keg is filled in 4 minutes

The max volume is 20 L

The graph is t vs volume

Meaning t is on the x axis

So the most the time can go to is 4 min

[hollow forge]

ohhhhh ok

prob last question

will the 0<t< thing always be t?

like will it always be (x)

[karmic imp]

Normally

[hollow forge]

mm ok thanks

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[bold bluff]

,rotate

[timber orchid]

Which question we takin' a look at?

[bold bluff]

We have to use synthetic division but I wasn’t sure how to set it up

16 mainly but hopefully understand so I can do both

[timber orchid]

Synthetic division starts w guessing a root x = a

[bold bluff]

Wdym guessing

[timber orchid]

The way you set up synthetic division involves having a root to test

So you can check if the remainder is 0

[bold bluff]

Just plug until remainder is 0

[timber orchid]

Ye

[bold bluff]

-1

[timber orchid]

Nice

So x + 1 is a factor

Of the polynomial

[bold bluff]

X+1?

[timber orchid]

Yes

[bold bluff]

What do I do with it

[timber orchid]

Well you have the coefficients of the quotient of (given polynomial) / (x + 1)

given f(x) = (x+1)(2x^2 - 7x - 4)

[bold bluff]

X+1 is one of the answers

[timber orchid]

Yes

This graph confirms everything we've found so far

[bold bluff]

What do I do to get the rest of the answers

[timber orchid]

You can factor the remaining quadratic

Factor this:

[bold bluff]

Yea I ended up getting that

[timber orchid]

👍

[bold bluff]

Then what

[timber orchid]

You can factor it

[bold bluff]

..

That the x/2(a)^2 thing?

[timber orchid]

Yes I believe

[bold bluff]

Ok i undertaking the factored answers, what about the roots

Ik one of them is -1

[timber orchid]

,rotate

[timber orchid]

Now solve

For the last 2 roots

[bold bluff]

Oh yea u right

,rotate

What about this one it seems different

I have the first root and factored form

But there’s 5 numbers now not 4 to factor

4 not 3*

[timber orchid]

,rotate

[timber orchid]

Well here your polynomial is x^3 + x^2 - 8x - 12

[bold bluff]

How did you get that

[timber orchid]

You can check your result by graphing

(original polynomial)

and

(factor you just found) * (resulting polynomial)

These are the coefficients of the new polynomial

[bold bluff]

The x^2 at least

How did you get that part

x^2

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[zenith crescent]

find the derivative of the following

[zenith crescent]

I have tried this but I do not know what to do next

[fluid obsidian]

is that plus or multiplication in between where you used chain rule?

[zenith crescent]

it is multiplication, I accidenatlly wrote plus

[fluid obsidian]

yes it's multiplication

[zenith crescent]

after this part what do I do next?

[timber orchid]

Pretty much just simplify once you've done your power rule, chain rule, quotient rule

[zenith crescent]

okay okay ill try

[zenith crescent]

So like tis?

[fluid obsidian]

what is in the denominator?

[zenith crescent]

(2x + 1)^2

[fluid obsidian]

this may be right

[timber orchid]

Yes this looks good, althought you'll want the ^(1/2) on the set of parentheses you see there

You can check w a derivative calculator

[zenith crescent]

ah the one on the right?

[fluid obsidian]

,w differentiate sqrt((1+3x^2)/(2x+1))

[timber orchid]

Yes

[timber orchid]

I always forget this command

[zenith crescent]

ahh yeah

[twin meteor]

Results provided by WolframAlpha

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

Requested by yes sam#5028

[zenith crescent]

ohhhh

[timber orchid]

And that's essentially what you have 🙂

[zenith crescent]

ohhhhh! Okay I got it now, thanks you both!!

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[fluid obsidian]

now you won't

[timber orchid]

Eh, we'll see about that 🙂

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[lofty oyster]

Hi, I’m a little stuck on 5c here. I understand most of the problem but I’m having trouble understanding why the answer key says “when 0 = x(t) = tcos(pit) we have t = 0, t = 1/2, or t = 3/2”. The question states that I’m supposed to find the tan line to the path when the particle crosses the negative y-axis, but I’m unsure how this ties in. Why do you set x(t) equal to 0?

[hushed willow]

Because the y axis is located at x = 0

[lofty oyster]

Alright, thanks 🙂

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[dim crypt]

Here is a vector resolution question. The teachers working is also attached. I get why the answer is C (as they resoluted with respect the the plane) , but I did it with respect to the i-cap and j-cap vectors. My working is attached. Obvious since the question is multiple choice I need to make sure its in the same form, but why does my answer give different values when I assume a m, g, F and theta value?

[vocal sleet]

@dim crypt Has your question been resolved?

[dim crypt]

<@&286206848099549185>

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@dim crypt Has your question been resolved?

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@dim crypt Has your question been resolved?

[left crest]

Have you tried finding the component of force along the incline and perpendicular to the incline

[vocal sleet]

@dim crypt Has your question been resolved?

[warm nest]

have you tried his advice @dim crypt

[vocal sleet]

@dim crypt Has your question been resolved?

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[formal sinew]

https://i.imgur.com/RfHSHys.png how do I know that there is a horizontal shift of a cosine function here?

[formal sinew]

I guess my mistake is doing (pi/2)x = 1.3 seconds

I ended up with pi/2.6

obviously they provide the period of 3

but if they didn't, would I be able to find what kind of a function it is?

let's go with that still, please, thanks

[vocal sleet]

@formal sinew Has your question been resolved?

[half imp]

It doesn't need to be a cosine function in particular

sine and cosine functions are horizontal shifts of each other

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[royal grove]

Is this notation correct

[civic pendant]

is 7 in the interval (6,8)?

Yes

If $a =7$, then $a \in (6,8)$.

[twin meteor]

Cain

[civic pendant]

$\in$ means in

[twin meteor]

Cain

[royal grove]

thanks for your help

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[vast shale]

i am very confused about what the chain rule is in probability

[flat whale]

do problems or watch lectures or read a book

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[thin vale]

, rotate

[vocal sleet]

@dreamy turret Has your question been resolved?

[dreamy turret]

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[clear sundial]

im confused about what this question is asking for

i expanded out and used summation rules but my answer was incorrect

[pale perch]

could you show your working

[clear sundial]

this is what i have so far

but idk how to go fruther

[pale perch]

i believe your general formula for the k^2 is wrong

its [n(n+1)(2n+1)]/6

[pale perch]

there would certainly be a n^3 term if you expanded it correctly

n(2n^2+3n+1)=2n^3+3n^2+n

[clear sundial]

like this?

first foil n(2n+1)

then using the result of that foil with (n+1)

[pale perch]

yeah, write your brackets in on the first line though

if you fix that in your original answer it should be right

[clear sundial]

ah yep got it

i was just doing the algebra wrong

need to practice it a bit mroe

ty!

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[soft flame]

I need help. I tried working through the problem but now I am stuck.

[soft flame]

here is my work. What do I do now.

[karmic imp]

I don't suggest factoring

[vast salmon]

The second last step

[karmic imp]

Group the r^2

[soft flame]

oh so would it be 2r^2?

[karmic imp]

Aka make the equation equal to 0

[soft flame]

oh wait

yeah subtract

thank you. Let me try that.

@karmic imp thank you. I got 9 and it was right.

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[solar rock]

how do u graph this

[vocal sleet]

Please don't occupy multiple help channels.

[solar rock]

if anyone has a good video that explains id id be thankful

[shrewd pollen]

then find it in yt

[shrewd pollen]

use desmos

[solar rock]

couldnt find a good one idk

[shrewd pollen]

ok, let me draw for u

[solar rock]

i wanna graph it myself

[shrewd pollen]

go to desmos.com and then write the equation

if u cant see anything then check if the graph icon is enabled

but if you still cant see anything then maybe desmos is crashing

[solar rock]

what

[shrewd pollen]

what what

[solar rock]

uhhh

[shrewd pollen]

i think this is crashing

[solar rock]

damn

[formal pond]

he doesnt have a y=

[formal pond]

put y= infrton of the equation

you simply stating that doesnt mean anything

[solar rock]

oh lol

[shrewd pollen]

oh yeah lol

[vast shale]

try using geogebra

[formal pond]

geogebra yucky

[shrewd pollen]

no ithink desmos í best

[vast shale]

😠

[shrewd pollen]

is

[formal pond]

if your on windows, clcik on caluclator and change to graphcial

[vast shale]

true

[formal pond]

put in your formula and click the little lightening

and it gives you all the info you need about the graph

maxima and minimas roots periods ect

[solar rock]

wait it still doesnt show

ugh

[vast shale]

I have just learned today that the windows calculator can do a lot of things

[solar rock]

yk what ill just skip that one

is this correct?

[vast shale]

can someone help me with #help-29 I am a dum dum

[shrewd pollen]

okay

[formal pond]

graphing

[formal pond]

Well yes and no

[solar rock]

how

[solar rock]

plslsss explain

[formal pond]

it just depends at what level your taught at

by the question at the start my guess is you would assume yes

and btw

your function

is weird

[solar rock]

how is that

the - right?

[formal pond]

yea

[solar rock]

ive never seen one like that its so weird

[formal pond]

its like

x^x

[solar rock]

idk how to deal w it

[formal pond]

Well

You see

your thing

isnt really a function

DOnt quote me on this as im not a maths student

but

make if x was 0.5

'y' would be complex

as the sqrt of a negative number

is complex

but lets say we re-write 0.5 as 2/4

than this is psosible

as we square the number and than 4th root it

which is possible as squaring a negative number makes it positive

you see

and since 2/4 = 1/2

your function is not a function

as a function defines as 1 input 1 output, not 1 input multiple outputs

[solar rock]

kinda makes sense tbh

can we graph it as two functions?

[formal pond]

Like i said

function would yield complex numbers

and i have no clue where you would plot these

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[brave ruin]

Anyone see the my mistake?

[hidden kelp]

@brave ruin I think it's because you wrote du = 7, wich isn't true, du = 7dx

then you can divide by 7 and get dx on its own

[brave ruin]

Oh okay

Honestly I don't fully understand the substitution for dx or du

[hidden kelp]

What don't you understand? Anything specific or the whole process?

[brave ruin]

Well

[brave ruin]

Why isn't du = 7 not true

Oh wait

Uhhh

[hidden kelp]

hm?

[brave ruin]

Nvm

I'll try it again

Would that even change anything though?

[hidden kelp]

yes, you would end up with 1/7 in front of your integral

[brave ruin]

In (4)??

Oh I see whatnyoure saying I think

So

Instead of just du

It would be 1/7 du

Right?

[hidden kelp]

yup

[dim crypt]

.reopen

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[amber hound]

Help

[vocal sleet]

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[bold compass]

Hi,
I had a question about using Horner's Method. Is it true that for any degree d polynomial, Horner's Method will evaluate the polynomial to have exactly d multiplications and d addition/subtractions? And if so, would the polynomial below have 3 addition/subtractions and 3 multiplications?

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[tame flower]

Explain how I'd do this using the x-1 key

[tame flower]

To get 0.08, I've gotten 0.8 but that isn't the answer

Also as far as my understanding goes 1/1/5 =1/5

[upbeat chasm]

the expression 1/1/5 is vague

(1/5)/5 == 1/(1/5)

in either case its not 1/5

anyway, not sure what you mean by x-1 key

[tame flower]

Inverse key

[upbeat chasm]

oh right

[tame flower]

1/x or x-1 depending on ur calculator

[upbeat chasm]

so what are you putting in your calculator

[tame flower]

(10 ^-1 +( 5 ^ -1 + 5^-1)^-1)^-1

Not all at once

But you get the gist of it

[upbeat chasm]

i agree with most of it

except 5^-1 + 5^-1 isnt 10^-1

[tame flower]

Yea I figured

I've been at this for 20 minutes

Imma try doing it all at once

[upbeat chasm]

you're completely right without that mistake though

[tame flower]

I get 2.9 without inversing one time

0.344 when I do

I did it like this now

(5^-1+5^-1+(5^-1+5^-1)^-1)^-1

[upbeat chasm]

oh wait

you can just put (5 + 5 + (5^-1+5^-1)^-1)^-1

the denominator is 5 + 5 + (5^-1+5^-1)^-1

[tame flower]

12.5

Which is correct

[upbeat chasm]

definitely isnt

[tame flower]

It is

Because the answer wS 1/0.08

Was trying to figure out how to get 0.08 under

But how does it work?

[upbeat chasm]

ohh okay

[tame flower]

Bro that calculator would've saved me so much time

[upbeat chasm]

lol

also works

[vocal sleet]

@tame flower Has your question been resolved?

[vocal sleet]

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[zenith crag]

Can you help me solve this one

[fluid obsidian]

who "you"?

[zenith crag]

idk

I don't get how to organize it in a triangle and answer the questions

[fluid obsidian]

make 3 points and label them as balls and write their lenghts

[west raptor]

hint:use the laws of cosine with a=18, b=14 and c=12

[zenith crag]

It might be a little bit more like this

[outer warren]

you aren't told nor should you assume that you have a right triangle here
5,14,18 isn't a pythagorean triple so you dont

[ornate ember]

this looks correct. Use the law of cosines:

[vocal sleet]

@zenith crag Has your question been resolved?

[zenith crag]

Still working on it

how can I find the angle that the cue ball makes with the 8 ball and the 5 ball with that?

<@&286206848099549185>

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[river kettle]

Derive the equation of the circle with its centre (-4,2) and a line 3x+4y-16=0 tangent to the circle

[river kettle]

this one is really confusing me

im not sure how to start

[paper depot]

do you know in general what info you need to write down the equation of a circle?

[river kettle]

I think so

$\frac{\left|ax_{0}+by_{0}+c\right|}{\sqrt{a^{2}+b^{2}}}$

[twin meteor]

waterr beam

[paper depot]

bad.

does not answer my question!

what info do you need, in general, to write down the equation of a circle?

[river kettle]

centre

radius

[paper depot]

great

which of these (if any) do you already have? which of these (if any) do you not yet have?

[drifting bane]

CAN I ANSWER THAT PLEASE

[paper depot]

no

[drifting bane]

[river kettle]

well we have (-4,2) as the centre of the circle

and we dont have radius

[paper depot]

indeed.

we do, however, have that the line 3x+4y-16=0 is tangent to the circle

[river kettle]

yes

[river kettle]

what next

[paper depot]

the distance from (-4, 2) to the line equals the distance from (-4, 2) to the point of contact

and therefore the radius

[vocal sleet]

@river kettle Has your question been resolved?

[paper depot]

👻

[vocal sleet]

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[left crest]

Could you send your working?

!status

[vocal sleet]

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

[surreal lotus]

i found the gradient of ab which was 2

then i did dy/dx = 3x-12x^-2

then i set dy/dx =2 but i dont know what to do now

[left crest]

Ok, what did you get after differentiation

[surreal lotus]

my dy/dx value is 3-12x^-2

[left crest]

$3-\frac{12}{x^{2}}=\frac{dy}{dx}=2$

[twin meteor]

Try_hard

[left crest]

Now, you can find the value of x which satisfy the above equation.

[surreal lotus]

yeah im not sure what to do after this though

[surreal lotus]

oh

dont i need 2 x values though

[left crest]

Well, have find coordinate of C and D, hence you will need two values of x

Can you simplify to this step $1=\frac{12}{x^{2}}$

[twin meteor]

Try_hard

[surreal lotus]

yeah i just take 2 from both sides

[gaunt oyster]

its plus and minus sq.root of 12

[left crest]

Yes, after you got, the answer then you can substitute the answer in the original equation and find the y coordinates of the points

[surreal lotus]

oh ok thank u guys!

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[tame zephyr]

(Number 10) I seem to have conflicting notes, which one is the right method for finding PR²?

[outer warren]

do you have a clear pic

[tame zephyr]

Let me rewrite the one written in pencil, wait a min

[tame zephyr]

Here is a pic with both methods

[outer warren]

diagram is still a bit blurry also what are

[tame zephyr]

The angle at point R and the angle at point Q

[outer warren]

that first line isn't a correct representation of the sine rule/law

you can't ditch the sin there

which was present in the following line

looking at the rest now, gimme a min

[tame zephyr]

Here is a better pic of the diagram, if it helps

[outer warren]

this issue is that the original diagram doesn't make sense

the interior sum of that triangle is somehow 110°

the given pairs of angles and sides don't satisfy the sine law/rule either

IF the values in the question are valid,
provided that there's sufficient info, both sine and cosine rule/law would be valid approaches
however since the diagram/question is invalid, it all turns to crap

wait

is that a 45 or 115

[tame zephyr]

It's a 115

[outer warren]

ok,

,w 30/sin(115deg)

[twin meteor]

Results provided by WolframAlpha

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

Requested by ramonov#0921

[outer warren]

,w 25/sin(52 deg)

[twin meteor]

Results provided by WolframAlpha

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

Requested by ramonov#0921

[outer warren]

that's quite off

the relation isn't valid, so depending on the method used (which ignores certain aspects)
there'll be a different result

[tame zephyr]

Hmmm, my calculator produces a different result though

[silk comet]

52 radians ≠ 52 degrees

[outer warren]

calc in in radians

[tame zephyr]

So that was the problem...

[outer warren]

that's part of the problem

either way the value from each method will be different

in this case differs by around 0.5

[tame zephyr]

Thanks, I checked it on a different problem and it seems that both methods work

.close

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[formal kraken]

hello. the problem is:

"A coffee vending machine is designed to dispense 180 ml of coffee but its owner suspects that it is dispensing more than what is designed for. He took a random sample of 40 and found out that the mean is 192 ml with a standard deviation of 4 ml. Do you think the owner is right about his suspicion? Test at 0.05 level of significance."

I used the formula for Z-test to look for the Z-score given that sample size is > 30. But the answer I get is 18.97. Am i wrong or should I use a different formula?

[sharp lynx]

You're probably not wrong

The z-score looks like it should be very big

[vocal sleet]

@formal kraken Has your question been resolved?

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@formal kraken Has your question been resolved?

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[next arrow]

Suppose a researcher investigates the performances of randomly selected teachers in 4 schools. The variance of their performance rating is shown below.

School A - 3.1
School B - 4.9
School C - 1.7
School D - 3.2

Which set of data probably has the points closest to the mean? Why?

a.
School D because the value of the variance is 5, which is very close to the mean performance rating of all schools.

b.
School A because the value of the variance is 3.1, which is very close to the mean performance rating of all schools.

c.
School B because the variance is the highest. The higher the variance, the closer the set of data points to the mean.

d.
School C because the variance is the smallest. The smaller the variance, the closer the set of data points to the mean.

[floral seal]

prop d

i guess

this is how standard deviation is calculated

where variance is square of sd

[hushed willow]

thats for sample, population is with just n

[floral seal]

i randomly chose from internet

im sorry

didnt notice that

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[open cave]

How do I solve this?

[open cave]

when I expand and subtract, i just get a linear equation

[pastel cedar]

I haven't written it out myself, but if you have a linear equation relating x and y, can't you just substitute y out of one of the original equations and solve the resulting quadratic?

[open cave]

one second i will expand

[wicked sierra]

yes you should get a linear because second power values of x have equal coefficients

when u get a linear you can find a relationship between x and y and use that to solve the problem

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[trail sinew]

Let $f:X\rightarrow Y$ be a continuous function. Let $E\subseteq X$. ($E\neq \varnothing $). Let $y\in \overline{f(E)}$. Let $(y_n){n\in\mathbb{N}}\in f(E)^{\mathbb{N}}$ such that $\lim{n\rightarrow \infty } y_n = y$.
Show that there is a convergent sequence $(x_n)_{n\in\mathbb{N}}\in E^{\mathbb{N}}$ such that $f(x_n) = y_n \forall n \in \mathbb{N}$.

[twin meteor]

Casiel368

[trail sinew]

The part of finding a sequence such that f of that sequence is y_n is easy. But I have to be a bit more careful with that because if I choose any sequence it might not be convergent when f is not injective

Take $y_n = 1-\frac{1}{n}, x_n = (-1)^n - \frac{(-1)^{n}}{n}$ with $X = Y = \mathbb{R}$ and $f = |x|$

[twin meteor]

Casiel368

[trail sinew]

ignore the +1 in the (-1)^n+1

@reef grove

<@&286206848099549185> (Sorry for the mistaken ping)

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[vast shale]

hi

[open cave]

you have 7 days

[vast shale]

What is the probability

[open cave]

oh nvm

[vast shale]

that six dice

will roll out for a total of six points

?

[fluid obsidian]

You have 7 days

[vast shale]

Why do I have seven days

[fluid obsidian]

What are the conditions?

[vast shale]

You can only roll once

[fluid obsidian]

What's the actual question?

[vast shale]

What's the probability that 6 dice will roll out for a total of 6 points?

[fluid obsidian]

There are 6 dice?

[vast shale]

Yes

[fluid obsidian]

Or 6 faced die

[vast shale]

no 6 die

[fluid obsidian]

Since we get atleast 1 point for each die there is only one case here

1,1,1,1,1,1

[vast shale]

Ok

I get it now

.close

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[fluid obsidian]

What's the anser

[vast shale]

0.00002143347

Also I meant there are no conditions

Sorry I don't know why I said there was any

[fluid obsidian]

,w 1/6⁶

[twin meteor]

Results provided by WolframAlpha

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

Requested by yes sam#5028

[vast shale]

What is this

[fluid obsidian]

Probability

[vast shale]

So I was right

0.00002143347

Now I get it

.close

.close

uhhhhh

.CLOSE

,close

uh

[fluid obsidian]

It's already

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[lyric crane]

help

[lyric crane]

Ik how to find linear regression using y = a + bx , but when there is only one x column with one y column, now i have 3 y columns how do i solve this now

using this formula for a

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<@&286206848099549185>

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[sudden lantern]

need help with laurent series

[upper iron]

The Laurent expansion of the function like this is kinda impossible

You first need to simplify it

Do its partial fraction decomposition

Make it two fractions

[tall patio]

yes

[upper iron]

A/(z+1) + B/(z+3)

And then do the Laurent expansion of each and sum them

That should do it!

[soft walrus]

@upper iron how tf are you an undergrad, sorry kinda off topic ;-;

[flat whale]

#discussion or #chill please

[flat whale]

Do Luna's suggestion

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[mellow rapids]

hello, I need help finding a basis of the kernel of this matrix
every video about it that i find seems to solve it through linear systems, but the second row is null in row echelon form, so I'm not sure on how to do it

[tall patio]

so you found a row echelon form

nice

so you know the dimension of the kernel right?

use the rank nullity theorem

[mellow rapids]

i'm not sure tbh, is it the number of non-null rows?

[tall patio]

so do you know what is the rank of a matrix?

[mellow rapids]

yes (i'm having sort of a language barrier here, sorry)

[tall patio]

which language?

[mellow rapids]

portuguese

[tall patio]

yeah ok forget it

[mellow rapids]

lmao

so the rank is 1, right?

[tall patio]

so this would be true for a square matrix

the rank is the dimension of the image

and the nullity is the dimension of the kernel

as the image in this case of dimension 2 at most*

because the output of a matrix product is of dimension 2

at most*

the rank is read

by the number of non zero rows

in echelon form

because the dimension of the image is at most the number of rows

so here rank =1 right

[mellow rapids]

yes

[tall patio]

and using rank nullity theorem

you can find the dimension of the kernel (the nullity)

the theorem is

rank + nullity = dim(E)

where E is the starting space

or equivalently

dim(E) = number of columns

so here nullity = ?

[mellow rapids]

2?

[tall patio]

yes

so we need for our basis of the kernel

only 2 vectors

non linearly depend

ant

so lets find (x,y,z)

such that M(x,y,z)^T = (0,0)^T

so as in the videos

find solutions of the system

[mellow rapids]

does ^T mean transposed?

[tall patio]

yeah

idk how to make vertical vectors

[mellow rapids]

do I transpose the original matrix or the echelon form?

[tall patio]

you dont transpose the matrix

this is on the (x,y,z) vector

so that (x,y,z)^T

is vertical

[mellow rapids]

oh i see

like this?

[tall patio]

no

the whole form

the matrix itself

[mellow rapids]

the problem is that i'm not sure on how to go on from here, as there seems to be no independent variable

[tall patio]

solve it by sub

as you would for any such system

x = y +4/3 z

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@mellow rapids Has your question been resolved?

[upper iron]

What seems to be the problem here?

The question

[upper iron]

How to solve this?

[mellow rapids]

what do I do after reaching 0 = 0?

[mellow rapids]

it was this

finding a basis of the kernel for this matrix

[tall patio]

you shouldnt reach 0 = 0 really

oh im stupid

you cant solve it any further than this

my bad

so just chose two values for x and y

and z is given

by the first equation

then chose two other values (such that the vector wont be linearly dependant)

and z is given and you have your second vector

for example x=1, y =0

and x=0, y=1

find the z for each

and you have two vectors v1 v2 such that

Mv1 = 0

and Mv2=0

[upper iron]

Guys guys, the first equation and the second equation are the same

Notice that the second is just the first scaled by (-3)

[tall patio]

i know