help-0

[woeful pulsar]

yeah

can you use the same idea to get n?

[young oriole]

so 15 in A ig

[woeful pulsar]

15 elements in S

[young oriole]

since 30 sets of A in union = n sets of B in Union

so 3n/9?

[alpine sable]

it's wednesday because 4 R 2 the R2 plus Monday would be wednesday idk if im right

[young oriole]

idk not sure

[woeful pulsar]

yeah

[woeful pulsar]

erm, what is 3n/9 supposed to be here?

[young oriole]

the elements in B

unique

elements

[young oriole]

each set of B has 3 elements and there are n sets and 9 elements of B belong to S i suppose (repeated?)

[woeful pulsar]

so what should 3n/9 be equal to?

from there you should be able to solve for n

[young oriole]

15 and S?

[alpine sable]

I can't solve number 14 :((

[woeful pulsar]

yeah 3n/9=15

[alpine sable]

200/6 = 33 R 2

[young oriole]

yeah got it

n = 45

[woeful pulsar]

first part or second part?

[alpine sable]

2nd

[woeful pulsar]

yeah

[woeful pulsar]

yeah

[young oriole]

!thanks!

[vagrant jetty]

Given the following x-factor. What would go in a and b?

nvm i know the answer

[alpine sable]

cool

what is it?

[vagrant jetty]

hold on

[sharp sail]

This eq. has 6 real solutions, but I only got 4

How come I find the remaining ones

[vagrant jetty]

nvm idk lol

[sharp sail]

I did the following cases exponent is 0 and the base is 1

[indigo jetty]

have you considered the case 1^1?

[sharp sail]

Yea

Wait

I got it

I missed the case
-1^even number

:)

Lol I solved myself

[indigo jetty]

👍

[vagrant jetty]

can someone help me now

Given the following x-factor. What would go in a and b?

[sharp sail]

what's this

[unborn ingot]

I think he is just doing the diamond method

to factor

wait I can do it

[tepid otter]

https://i.imgur.com/W9utFcU.png

this should be B right?

[alpine sable]

does anyone know how to do this?

[vagrant jetty]

shouldnt it be flipped to the right

[unborn ingot]

yeah just flip it

same stuff tho

[vagrant jetty]

ok

thx

[unborn ingot]

np

[wispy swan]

@night geyser !

I might have another problem

my hero

[fading jay]

(x+2)^2+(y-5)^2=R^2=74,R=len between (-2,5) and (3,2)

[wispy swan]

@fading jay am i typing it wrong? I appreciate the help!

[gray isle]

wheres 74 coming from?

[wispy swan]

im not sure tbh, i just typed in what he stated above

[gray isle]

apply the distance formula for those two points yourself

[wispy swan]

ok

[woeful pulsar]

wait erm

yeah it's leq

because absolute value there

[eternal herald]

https://i.imgur.com/8FEsc7Z.png the answer i got is 9, is it correct?

[hidden horizon]

yes @eternal herald it is correct

[candid dagger]

ye you could do this one in many ways

[hidden horizon]

u can use pythagoras , trignometry , similarity also

[candid dagger]

yeah, i used euclid's

[eternal herald]

oop

I used, 5.20*5.20/3

[alpine sable]

Can anyone help

Onky the d and e

Only*

Actually nvm

I got it

[eternal herald]

good job

https://i.imgur.com/UitAYGc.png does it want me to use 4/3pir^3 ?

thanks.. then its none of the above.

sorry if my questions are dumb

WHAT

but it gives me a full diameter not the radius, the radius should be R=25/2

am i wrong?

[woeful pulsar]

yeah you are right about that

[eternal herald]

so which answer is correct?

none of the above

?

[woeful pulsar]

you need to round to the nearest cubic cm

[eternal herald]

i got 8177.083

oh..

[woeful pulsar]

,calc (4/3)pi12.5^3

[ocean seal]

Result:

8181.2308687234

[eternal herald]

i didnt use pi i used 3.14 and got 8177

[woeful pulsar]

i guess it's fine

[alpine sable]

,calc 2+2

[ocean seal]

Result:

4

[alpine sable]

Thanks calc

,help

[ocean seal]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[stone remnant]

,calc y=x^(2)sin (2x)

[ocean seal]

The following error occured while calculating:
Error: Undefined symbol x

[stone remnant]

ok I need help lol

[alpine sable]

,time

[ocean seal]

You haven't set your timezone! Set it using the interactive timezone picker with ,ti --set.

[alpine sable]

,ti --set 08:03

[woeful pulsar]

hmm, what are you trying to do here?

[stone remnant]

what's the derivative of y=x^(2) * sin (2x)

do I use the product or chain rule?

[woeful pulsar]

yes

[ocean seal]

Your timezone has been set to Etc/GMT+11!
Your current time is 08:04 PM (-11) on Thu, 27/05/2021.
Note that due to the POSIX standard, the timezone Etc/GMT+11 represents the time in GMT+11.
If your time is incorrect, consider setting your timezone to Etc/GMT+11, where the time is currently 08:04 PM (-11) on Thu, 27/05/2021.
You can read more about the standard at https://en.wikipedia.org/wiki/Tz_database#Area.

[stone remnant]

yes to product or yes to chain xD

[eternal herald]

if i put pi in the calculator it shows 8181

[alpine sable]

,time @eternal herald

[ocean seal]

This user hasn't set their timezone! Ask them to set it using ,ti --set.

[woeful pulsar]

you can use both

[eternal herald]

should i use 3.14 or pi?

they both gave different answers

[alpine sable]

,avatar @eternal herald

[ocean seal]

DevilAzz#0666's Avatar

Click here to view the image.

[eternal herald]

alright thnx..

[stone remnant]

x^2 * 2*cos2x + 2x * sin2x@woeful pulsar?

[woeful pulsar]

looks reasonable

,w differentiate x^2*sin(2x)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Element118#2437

[stone remnant]

do I crossmultiply now maybe?

[woeful pulsar]

yeah wolfram agrees

[stone remnant]

but I had x^2

[woeful pulsar]

why do you need to crossmultiply

[stone remnant]

wait oh

okayyy thanks!!!

[alpine sable]

can someone help me for D?

[alpine sable]

<@&286206848099549185>

can someone help

[wicked steeple]

What is the formula

and what is it telling you

[alpine sable]

y=6191(0.94)^x

[wicked steeple]

$y=6191(0.94)^{x}$

right

[ocean seal]

Alpaka

[wicked steeple]

what does this tell us

[fair rapids]

can smoeone help me how to solve this

[wicked steeple]

this channel is being used

[fair rapids]

ok sory

ry

[wicked steeple]

put it in a different one and I'll help you after this questtion

[alpine sable]

tells us the population?

[wicked steeple]

right

what variable there tells us the population

[alpine sable]

y?

[wicked steeple]

right

and d is asking us to find when the population is going to be 2500

so how can you use the equation for this

[alpine sable]

umm put 2500 for y

or X

[wicked steeple]

y or x?

[alpine sable]

y? idk

[wicked steeple]

y, yes

so

$2500=6191(0.94)^{x}$

[ocean seal]

Alpaka

[wicked steeple]

that's now our equation

can you solve for x?

[alpine sable]

yeha i can try

[wicked steeple]

alright

[alpine sable]

i got 3319.54

or is that competently wrong

[wicked steeple]

not quite

show your work

[alpine sable]

i just put it in the calculator is it 14.655

[wicked steeple]

Yeah

[alpine sable]

so thats the answer?

[wicked steeple]

units?

[alpine sable]

ill take 14 years?

[wicked steeple]

14.655 years yeah

[alpine sable]

oh okay

thank you so much

have a good night

[wicked steeple]

np

you too

[atomic bane]

since we're talking in time you should round up, so 14.6653 round up to 14.666 round up all the way to 15

[outer crane]

YOU MUST FIND A THREE-DIGIT CODE.

682 A DIGIT IS IN THE RIGHT PLACE

615 A ​​DIGIT IS CORRECT IN THE WRONG PLACE

206 TWO DIGITS ARE CORRECT IN THE WRONG PLACE

738 ALL NUMBERS ARE WRONG

308 A NUMBER IS CORRECT IN THE WRONG PLACE Whats the code?

[bronze birch]

Does anyone know how to find the exact value of a trig function when given a number other than the well known ones like 4pi/3 or 11pi/6

I have to find 7pi/12 which is 105 degrees I believe

Cos 7pi/12*

[woeful pulsar]

Well you can check every code from 000 to 999 to see if they satisfy the criteria

[upper ember]

here u will have to use some identities and do some manipulation

[bronze birch]

Ah shoot

I was hoping you could do it graphically

[upper ember]

well u can

[bronze birch]

It would be hard tho right?

[upper ember]

but it would be somewhat tedious i believe

[bronze birch]

yea and I don't think it would be "exact"

[upper ember]

coz u will get an answer, that u will have to approximate

[upper ember]

yea

[bronze birch]

What identify would I have to use for something like this?

[upper ember]

well there are a lot that u can use

[bronze birch]

Isn't there 3?

[upper ember]

the one i would recommend is

[bronze birch]

For cosine

[upper ember]

there are 4 for cos(2x)

but here i would say to use $\cos(\frac{x}{2})=\pm \sqrt{\frac{1+\cos(x)}{2}}$

[ocean seal]

Shashwat

[bronze birch]

I wasn't taught that one

I thought you were talking about 2x identities

not 1/2

[upper ember]

Well u can derive it

[upper ember]

we can use them to get this actually

like u know of an identity

cos(2x)=2cos^2x-1

replace the x by x/2

[upper ember]

and manipulate a little, to get this one

[bronze birch]

I'm a bit lost lol

I'm not able to do that level of mental math with formulas yet

[upper ember]

no need to do it mentally

write it down

or i can show u the process in latex

[bronze birch]

Nah it's fine

[bronze birch]

So I'd just use one of the double angle identifies to find this exact measure?

[upper ember]

yea

also

we need to a little thing before we actually get to calculating this

[bronze birch]

alright

[upper ember]

now, Cos(7pi/12)=Cos[(7pi/6)*(1/2)]

[bronze birch]

Are you able to do one of the identities that don't involve halves of x?

[upper ember]

so we need to evaluate $\pm \sqrt{\frac{1+\cos(\frac{7\pi}{6})}{2}}$

[bronze birch]

I was never taught any of those

[ocean seal]

Shashwat

[bronze birch]

So I don't really understand it

[upper ember]

yea we can ig

wait lemme see if i can find some identity to do this straight away

[bronze birch]

Thanks, I appreciate it a lot

[upper ember]

Ok so do you know the identity for the addition of cosine?

Cos(A+B)

[bronze birch]

Yeah

[upper ember]

nice

so what we do is

we write cos(7pi/12) as cos(4pi/12 +cos 3pi/12)

which is equal to cos(pi/3+pi/4)

now apply the identity and u get the answer

[bronze birch]

One sec lemmie write this down so I can follow along and make the connections a little better

[upper ember]

Sure

[bronze birch]

Wait so why is A: 4pi/12 And why is B: cos 3pi/12

Do you just split them up as evenly as you can to a whole number?

[upper ember]

we can split them up in many ways, but yes we want to split them in a way that they give us nice or known values

[bronze birch]

I missed my zoom meeting for the one day we went over sum identities so I'm a little behind on this concept

[upper ember]

like we know the trig function values for pi/3 and pi/4

[upper ember]

no worries

basically in trig, if we have any opportunity to get some thing known, we will take it

[bronze birch]

Could you do it the other way around if you wanted?

[upper ember]

this is a thing thats true in most part of maths

[upper ember]

what do u mean other way around?

[bronze birch]

Like 3pi/12 for A instead of B

[upper ember]

oh yeah yea

we can take either of them as A or B

[bronze birch]

Ok good to know

[upper ember]

it doesnt matter we choose as A or B here

[upper ember]

now, can you try to calculate this?

[bronze birch]

So as long as the values add up correctly it's fine?

it's just prefferable to have them a certain way

[bronze birch]

I will try my best lol

[upper ember]

sure

[upper ember]

yes it is

makes our lives easier u know

[bronze birch]

is pi/3 and pi/4 just simplified?

[upper ember]

yes

adding them together gives 7pi/12

[bronze birch]

Alr give me 5 minutes and I'll see what I can do

I'll try to remember as much as I can from memory

[tacit breach]

That answer gonna be 1.68×10^5

[bronze birch]

Alright so for the cosine side I have 1/2 x sqrt2/sqrt2

@upper ember

[upper ember]

Cosine side?

[bronze birch]

Left of the +

For the expanded equation

I'll send a pic

Am I doing this right so far?

[upper ember]

its not a plus in the middle

its a minus

[bronze birch]

I thought this was a sum identity

[upper ember]

yes it is

[bronze birch]

wait

Why is it called a sum identity if there is a minus sign lol

[upper ember]

Cos(A+B)=CosA*SinB-CosB*SinA

[upper ember]

coz its the identity of the cos of the sum of 2 angles

its kinda weird ik

[bronze birch]

It's in my notebook as the equation I have down rn

So either my teacher taught me wrong or I wrote it down incorrectly

Oh wait no it's not

I'm just a moron

LOL

I read it wrong

Ok, so apart from that little hiccup am I doing this correctly?

[upper ember]

yes u are

[bronze birch]

Alright wonderful, now for the multiplication and rationalization

I'm terrible at rationalizing

[upper ember]

[upper ember]

lol u dont need to rationalize here

[bronze birch]

no?

Why not

There is a sqrt in the denominator of the sin side

Oh jesus I read that wrong too

wow

[upper ember]

lol

exactly

u wrote it wrong

[bronze birch]

I must have dyslexia lmfao

[upper ember]

thats all

[upper ember]

happens

when first doing trig its weird

[bronze birch]

I guess I should've wrote my trig cheat sheet table down a little more neatly

The teacher was rushing through it tho

[upper ember]

u can find those cheat sheet stuffs online

write em down once or twice

it helps

[bronze birch]

Alright sooo

Correct?

Oh I forgot the little funnel arrow on the right side

[upper ember]

and this is correct!

[bronze birch]

Wonderful

[upper ember]

good job

[bronze birch]

Thanks for being so patient with me 😂

[upper ember]

no worries lol

it didnt take that long

[bronze birch]

I might have a couple other questions later if you're still on bc I'm studying a bunch tonight. But anyway, I appreciate it

[proud burrow]

@bronze birch do you have any more question than i can help

[bronze birch]

Hm?

[rich basin]

I'm extremely confused with the following statement

[upper ember]

if i am online, i will try to help

[rich basin]

What i'm not clear with this is for this negation to persist as true is for if there lays a non blue ball

but wouldn't if there be no balls to hence make the negation to be true

because no balls can necessarily mean their to be no blue balls

[noble sinew]

what are you asking? The negation of the statement is indeed what they wrote

[rich basin]

what i am asking is why the negation is incorrect

But the only way this negation can be true is for there actually to be a nonblue ball in the bowl. And there is not! Hence the negation is false, and so the statement is true “by default.”

[noble sinew]

There exists a ball in the bowl that is not blue is the negation?

what are you asking

[rich basin]

that is the negation of "All the balls in the bowl are blue."

[noble sinew]

yes

[rich basin]

I'm not sure how this necessarily implies the statement to be true by default of the statement "All the balls in the bowl are blue."

Wouldn't negation mean for such a statement to be false

and if you were to apply the same logic to the first statement. It will be focus, hence a negation

[noble sinew]

Its some truth table stuff - can google truth table if you want. We have a statement "..." which is the same as "not ..." is false

[rich basin]

yeah

[noble sinew]

Its a P implies Q statement in disguise

[rich basin]

I know that

We were taught about the negation of quantifiers

but not sure of why is it that a negation can be wrong when it is false when placed into original statement

[noble sinew]

what

[rich basin]

so if you were to put the case of that "there are no balls in the bowl" in the statement "All the balls in the bowl are blue

Wouldn't that statement be false

why is it that because of the negation is false, therefore the original statement is true by default. When i could reason, how it is false for the original statement

[noble sinew]

lets write it as for all balls x in the bowl we have the ball is blue

So for all x -> x blue

[rich basin]

yes

[noble sinew]

since we have no x we have from truth table it doesn't matter truth of the following

(Not P) implies Q - or (Not P) implies not Q are both true

[rich basin]

what exactly makes it true

[noble sinew]

definition of implies

[rich basin]

o

i'm confused of how they are both the same

[noble sinew]

every man that has 100 legs is a world leader is also true

since no man has 100 legs

[rich basin]

yeah

wouldn't that be a inverse error (Not P) implies not Q

if we make it for x -> x blue be p implies q

Sorry can you please take it to another channel

[noble sinew]

All we are saying is if a is divisible by 4 then a is divisible by 2

[rich basin]

yeah

[noble sinew]

bad example

if a>3 then a^2>9

if a is -4 for example a^2 is still greater than 9

if a is 2 for example a^2>9 is not greater than 9

[rich basin]

then the negation for that would be a <= 3

[noble sinew]

notice how it doesn't matter the truth of the following

if the first statement isn't fullfilled

[rich basin]

yeah

[noble sinew]

if it doesn't make sense just remember this table for now probably

[rich basin]

I can't see the table

I only could see it in text format

[noble sinew]

?

[rich basin]

Even my own image has its own problems

[noble sinew]

google "truth table" (like I also said earlier) then

[rich basin]

I think i kind of get it. Is it because the statement original is already contradicted when provided in different cases

and the contradiction gets carried out as well into the negation

[alpine sable]

can anyone help with these?

[gaunt bramble]

Yes

Where are you stuck in this question?

[hasty bough]

1. According to Ohm's Law : E = I ( R + r ) , you can get current got lower when r is higher
   2.Resistors in series will divide the voltage
   3.Same thing as no.2

[alpine sable]

what do u mean in ur explanation for 2? do u mean that the resistors distribute the voltage drop, so they both share the same load, or does one reduce the voltage then the other one compounds that of the previous one and adds on to it

[gaunt bramble]

Remember how current flowing through series resistances is equal. So all you need to do is assume two resistances and apply Ohm's law to get the answer.
The answer is 6V.

[alpine sable]

so then, that would mean that 3 is impossible right?

[gaunt bramble]

What are you referring to here?

[alpine sable]

oh sorry, if u scroll up a little ull see question 3 in the image I sent

thats what im wondering about

[gaunt bramble]

Oh okay.
Actually if you solve the second question algebraically you will arrive at a relationship that the second resistance is two times the first resistor.
Hence, you have made the wrong choice in the third question. Two resistors can have the same voltage drop provided the value of their resistance is same. So second option is correct.

[alpine sable]

ohhh okay, yeah thats my fault for just being lazy, I solved it through, and your right thank you so much I really appreciate your help physics is beating me up rn

[ember island]

okay, so basically i have a problem with an exam i am preparing for.
on the previous years, there was an exercised included that was the following:
A snail was going up a post. The upwards path was 6 metres, but after that, the snail went downwords for 5 metres. The whole journey took 14 hours. When the snail was going up, it's speed was 2m/h slower than when it was going down. How long did the snail go up? how long did the snail go down?
So far I've gotten to a point where I have made an equation but it never seems to work out.
x will describe the snail's speed upwards.
(6/x)+(5/(x+2))=14
It always ends as an irrational number for me. Perhaps I am doing something wrong. Could anyone help out?

[strong furnace]

are you sure about the answer being irrational , I got a rational answer the number inside was a perfect square

[ember island]

oh, could you please share your process as to how you got that answer?
What I did was multiply fraction with the other's denominator.
From that I got: (6(x+2)+5x)/(x(x+2))=14
Then I crossed off both (x+2)s since they were identical and a part of multiplication sequences.
Then I ended up with ((6+5x)/x)=14
From this point on I generally got confused because I forgot what you are supposed to do, I usually ended up bringing the 14 to the other wise, resulting in: ((5x-8)/x)=0
Then I multiplied the whole equation with x. That way I got 5x-8=0
Then I ended up with x=1.6

While it doesn't always end up irrational, it usually ends up not fit as the answer.

[strong furnace]

are you sure thats how brackets/fractions work?

all the operations that you have done on the initial expression are incorrect

[ember island]

In regards to the denominators?

[strong furnace]

first step crossing off x-2 from denominator

you need to have an associated/ common (x-2) in the sum in numerator to be able to cross them off

[ember island]

Alrighty, so that means, due to the sum sequence in the numerator, I cannot cross of both (x+2)s, correct?

[strong furnace]

you could say that

[ember island]

I am unsure what to do further on then, since I end up with ((11x+12)/(x(x+2))=14

Do I multiply the whole equation by x(x+2)?

That way I end up with a quadratic equation

[strong furnace]

yes

[ember island]

One of the roots ends up being 0.5.
Inserting the value in place of the x, I end up with 6/0.5, 5/2.5, and that indeed does result in 14.

Or, wait, that is incorrect.

Nevermind, eveything is correct. Thank you , @strong furnace

[untold pulsar]

Hey babe

Ops

Wrong server

Sorry

[bronze birch]

LMAO

[cinder sundial]

Am I right

[alpine sable]

Of course that's the same

[glad swift]

is the inverse of If a^4⩽b^4 then a≠b, If a^4>b^4 then a=b ?

[cinder sundial]

Thank you

[glass lichen]

yes

[alpine sable]

someone please

[glass lichen]

$P\implies Q$ has an inverse of $\neg P \implies \neg Q$

[ocean seal]

Mosh

[alpine sable]

can you help me with that one

[alpine sable]

theas one

es

[ebon ether]

I am so confusing, can anybody please help solving quadratic relation equation form (standart form) with the vertex (3.5,3.5) and y-intercept (0,1). Formula for this are y=ax^2+bx+c

[indigo jetty]

You can start to solve for c first, then complete the square

[ember island]

do you still need it?

[alpine sable]

yes please

[ember island]

do you also need the algorithm of gaining the volume and surface area?

[alpine sable]

yes

please

[severe sphinx]

Can some one help with this word prblem Iodine-123 is a radioactive element used in medical imaging. It decays to 1/4or 2^2 of its original mass after 26 hours. Determine the remaining mass of 20g after a) 26 hours b)104 hours

[ember island]

The first figure is called a prism, I believe so at least, I am not familiar with english terminology in regards to maths, but it seems to be a right triangle prism. It has 5 faces, 6 edges, I guess 6 vertices, unsure of what that is.
To calculate the surface area of the prism, you must calculate the surface area for each figure in the prism.
Both of the triangles in the prism are identical, since they are opposite of each other, the lines connecting them are parallel and such. The formula for calculating the surface area of a ''right'' triangle is (leg*leg)/2, where the leg is the side next to the 90 degree angle. If we put the formula to use, we get: (6 multiplied by 8)/2=48/2=24 cm^2.
Now we must calculate each rectangle's surface area. The front rectangle's (the one that connets hypotenuse) surface area is 15 multiplied by 10=150 cm^2. The bottom panel rectangle's surface area is 8 multiplied by 15=120 cm^2. The last rectangle's, which could be considered the back-end one, surface area is 6 multiplied by 15=90 cm^2
The total surface area of the prism is the sum of all of the afromentioned surface areas. That would be 24 multiplied by 2 (because there are 2 identical triangles)+150+120+90=408 cm^2.
The volume of a prism is calculated by the surface area of the base multiplied by the height of the prism. In this case, the base's surface area is the same 24 cm^2 and the height is 15 cm, so the volume is 24 multiplied by 15=360 cm^3.

[ebon ether]

what do you mean?

[indigo jetty]

you have the y-intercept, use it to get the value of c

then complete the square for ax^2+bx+c, where you already obtained the value of c

[ember island]

The second figure is a cylinder. It has 3 (I think so at least) faces, I believe 0 edges, and 0 vertices.
The surface area of both circles are radius^2 multiplied by ''pi''. So the total surface area, including both circles, is (4^2 multiplied by 3.14) multiplied by the total number of identical circles, which is 2. The result is 100,48 cm^2.
The surface area of the side is the circumference aka length of the circle multiplied by the height. The circumference is the radius multiplied by ''pi'', multiplied by 2. Putting that formula into effect, we get 4 times 3.14 times 2=25.12 cm. Using that value we can calculate the surface area of the side, which is 25.12 multiplied by 12=301.44 cm^2
The volume of the figure is the surface area of the circle multiplied by the height. So we have 100,48 multiplied by 12=1205,86 cm^3.

@alpine sable Hope I was of help.

[alpine sable]

thanks very much

[glad swift]

When performing induction. If we have stated that P(n) or any function holds for that matter

Do we use n+1 on top of sigma when showing working out

and replace all 2 variables with n+1

or the other variable j+!

[ebon ether]

but how?

is this 1?

like y= 1

[indigo jetty]

sub x = 0 and y = 1 into the equation

[ebon ether]

?

[indigo jetty]

the point (0,1) satisfies the equation y = ax^2 + bx + c, so you sub x = 0 and y =1 into the equation

[ebon ether]

what does b represent?

[indigo jetty]

just a constant coefficient

we will find that later

[ebon ether]

oh right

so it's a(x)^2+bx+1?

[indigo jetty]

so after subbing in the values, what do you get for c?

yes

c = 1

[ebon ether]

so i get something like that

[indigo jetty]

how did u get those values?

[ebon ether]

what?

oh wait

is that right?

[indigo jetty]

um, did the original question come with the value 10/49?

[ebon ether]

it's vertex

[indigo jetty]

oh so you already completed the square

[ebon ether]

yes, and i need the another 3 forms

[indigo jetty]

what other forms needed?

[ebon ether]

like i need vertex, standart and factored form

three different one to complete

[indigo jetty]

ok since u started with the vertex form, solve for k first

[ebon ether]

hm?

[indigo jetty]

so vertex is at (3.5, 3.5)

[ebon ether]

yes

[indigo jetty]

so what is k?

[ebon ether]

i don't know how to find the k one

that's the point

[indigo jetty]

notice your h is 3.5

so when you sub x = 3.5, notice that y = k

[ebon ether]

so 3.5 = k?

[indigo jetty]

because the whole square happens to be 0

yes

now with this, just expand the vertex form and simplify it to get your standard form

[ebon ether]

is that right?

[indigo jetty]

no

so you have y = -10/49 * (x - 3.5)^2 + 3.5

expand out the brackets, then simplify the expression

[ebon ether]

something like that ?

[indigo jetty]

yes, but expand the brackets

[ebon ether]

wdym?

[indigo jetty]

as in expand (x-3.5)^2

[ebon ether]

x^2-7x+12.25?

i really don't get that

[indigo jetty]

yes

so now you have -10/49 * (x^2 - 7x + 12.25) + 3.5

expand again, then simplify

you want it to be simplified to the form ax^2 + bx + c

[indigo jetty]

let me write in latex

$y = -\frac{10}{49}(x^2 - 7x + \frac{49}{4}) + \frac{7}{2}$

[ebon ether]

that's what calculator get

[ocean seal]

Ken G

[indigo jetty]

i converted the decimals into fractions for easier simplification

[ebon ether]

so what's next?

[indigo jetty]

so expand out the brackets, and simplify, what do you get?

just leave your coefficients in fraction form rather than decimal

[ebon ether]

something wrong

[indigo jetty]

$y = -\frac{10}{49}x^2 + \frac{10}{7}x - \frac{10}{4} + \frac{7}{2}$

[ocean seal]

Ken G

[indigo jetty]

this is after you expand out the brackets

[ebon ether]

wait nvm

[indigo jetty]

now you simplify -10/4 + 7/2

you will end up with the standard form

$y = -\frac{10}{49}x^2 + \frac{10}{7}x + 1$

[ocean seal]

Ken G

[ebon ether]

I really appreciate for your help

[indigo jetty]

i'll leave it to you to do the factorised form

2 ways of doing it

find the factors using the cross rule or whatever you learnt before

or use the quadratic formula to get the roots of the equation, then use it to form the factorised form

tbh this equation doesn't look nice, so i'd rather save time by using the quadratic formula

[ebon ether]

Aha, I get it. Thank you

[indigo jetty]

👍

[ebon ether]

wait

what is the formula for this

[indigo jetty]

this is just a by-product of expanding the vertex form

we normally do not use this particular form

we expand it out and simplify to get the more familiar standard form

[ebon ether]

can you please send that formula

i cannot find it

for expanding

[indigo jetty]

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

[ocean seal]

Ken G

[indigo jetty]

or the other variant

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

[ocean seal]

Ken G

[ebon ether]

but you uses another one

did you not?

[indigo jetty]

$(x - 3.5)^2 = x^2 - 2(3.5)x + 3.5^2 = x^2 - 7x + 12.25$

[ocean seal]

Ken G

[indigo jetty]

basically the (a-b)^2 formula

just take note 12.25 = 49/4

[ebon ether]

aha thanks

[severe sphinx]

i want to chk my answer is this correct ? y = 3 (x - 5)^2 + 4 Compression of factor 3, shift up by 4 units, shift right by 5 units

[indigo jetty]

you started from y = x^2?

[ebon ether]

how to make vertex form working as the quadratic graph

[indigo jetty]

wydm to make it working?

as in how to plot the graph given the vertex form?

[ebon ether]

nevermind, i did it

[runic pendant]

I need help

[proud burrow]

@runic pendant use trigonometry

Tan of unknown angel

[runic pendant]

I don’t know how to do any of that

[ebon ether]

@indigo jetty is this right?

[indigo jetty]

i didn't try it out, but if your values of (3.5, 3.5) and (0, 1) satisfies the equation, it should be correct

[ebon ether]

how to find r and s in equation way

like is this possible without graphic

[indigo jetty]

use the quadratic formula (you will need your standard form for this)

[ebon ether]

this?

[indigo jetty]

yes

the values u get will form your r and s

[novel edge]

is x 43.5180?

[ebon ether]

Thanks Ken

[proud burrow]

@novel edge use the same method used in previous method

[novel edge]

I did do I use it for both X and Y

for X I got 43.5180 is that right

[proud burrow]

@novel edge let me see

[sand lichen]

someone pls ik its easy but i forgot how to do it

[proud burrow]

@novel edge which trigonometry function did you used this time

[novel edge]

the same one

[proud burrow]

No this time we don't know both x and y and here tan52=x/y

So use sin52=x/34

[novel edge]

and for y do I do

[proud burrow]

Use cos52=y/34

@novel edge I think you don't know trigonometry

[glad aspen]

should be a simple question for most of you

for sqrt(x^2+2x+3)/x when x tends towards infinity

to find the asymptotes

[rigid smelt]

Just factor out the highest degree term

Of the numerator and denominator

[glad aspen]

is it 2x+3 are negligible therefore we get x/x = 1

[proud burrow]

No it's sqrt(1+2/x+3/x^2)

@glad aspen yes answer is 1

[glad aspen]

because I know that when x tends towards infinity you just keep the highest degree

but if we remove 2x + 3, then I would also remove the denominator x

I guess the fact that its squareroot changes that though

[rigid smelt]

No you dont remove the x i nthe denominator

Because x is the highest degree i nthe denominator

You only look at the numerator and denominator seperately, not as a whole

[glad aspen]

alright thanks guys

[mild wren]

Let P(0,2) be a point that belongs to the function y = x² + 2x + 4m - 2, what is the image set of this function?
(a) Im (f) = { y ∈R |y ≥1}
(b) Im (f) = { y ∈R |y ≤1}
(c) Im (f) = { y ∈R |y ≥0}
(d) Im (f) = { y ∈R |y ≤0}
(e) Im (f) = { y ∈R |y ≥4}

My teacher didn't teach me this subjects. Me and the others students are angry with the math teacher

Pls i need help

I have to send this questions in 50 minutes

[glass lichen]

solve for m then find the range

[carmine heart]

k h a n a c a d e m y

[brazen harness]

I always hated that thing

but it does help

[mild wren]

Thanks

[mild wren]

Is this an app?

[mild wren]

How?

[mild wren]

How do i do this?

[glass lichen]

dont ping me twice

once is sufficient

but anyway... use the point to solve m, then complete the square to find the vertex

[mild wren]

Ok...I will try...

Thanks for all

[glass lichen]

good idea..

[alpine sable]

Hello I am stuck with this problem can anyone tell how to approach it

Interesting

[alpine sable]

I don't know how to do it. All I know is that you can show (1,2,3) is a solution. But it's also asking you to show that there is no other solution

A proof of contradiction of some sort needed

[fresh parcel]

is this a math olympiad question

[alpine sable]

hmm idk

[fresh parcel]

this problem is actually quite odd

let me think

[alpine sable]

you have to use identities

And find solution

(A+B+C)2 = A2+B2+C2 +2AB + 2BC+ 2CA

[sly mantle]

@alpine sable @alpine sable it's asking to prove uniqueness of an object

[alpine sable]

A3+B3+C3=(a+b+c)(a2+b2+c2+ab+bc+ca)+3abc

[sly mantle]

generally to prove there exists a unique object satisfying a property, we first show there exists such an object. then let x & y be such objects and show x=y

applied to this problem, we let (x,y,z) & (a,b,c) be solutions to the system then show (x,y,z)=(a,b,c)

[alpine sable]

Ah right

Square the 1st equation

interesting

[fresh parcel]

but then you just end up with a whole bunch of stuff

that you cant do anything about

wait

shoot i just ended up when i started

[alpine sable]

idk what that means but it is telling to prove that only a pair of solution satisfies the system of equations

[fresh parcel]

i got something possibly helpful

[alpine sable]

who knows this LOL

[fresh parcel]

pi

wait what

i dont know

[alpine sable]

hmm

Hey guys

Where do I ask my questions?

[fresh parcel]

x^2 x y^2 + x^2 x z^2 + y^2 x z^2 = 49

[alpine sable]

I have a question based on multiple regression statistics

[fresh parcel]

in a channel that isnt occupied

i dont know what that is

[ocean seal]

Πολλά άτομα είναι

[alpine sable]

@alpine sable

^

ye

[alpine sable]

use this for the Wave Period

T = Wave period, f = frequency, lambda (λ) = wavelength, v = velocity

[alpine sable]

the period of function is difference in x or distance after when it gives same value

Why Physics in Maths

[severe sphinx]

Determine the equation of the parabola in factoredForm.

[alpine sable]

not physics related

it's math

trig waves

[severe sphinx]

can someone help

[glass lichen]

channel is in use

[severe sphinx]

oh

my bad

[thorn kindle]

Given two fractions with natural number arguments: x1/x2, y1/y2. prove that there must be a fraction z1/z2 that is greater than X and less than Y

[uncut oak]

hi guys I need help, What is the equation of a quadratic relation that is congruent to y = 3x^2, is reflected in the x- axis, and has a vertex (2,5)?

[alpine sable]

Unironically

[uncut oak]

please ty

[glass lichen]

what's X and Y?

[alpine sable]

Draw a picture

[alpine sable]

this channel is occupied move to another one

[thorn kindle]

x1/x2 and y1/y2

[uncut oak]

ok ty

[thorn kindle]

Im working through peano axioms

[alpine sable]

Draw a picture on the number line

[thorn kindle]

We have not defined the reals yet

[alpine sable]

You know that the sum and product of two rationals is a rational though don’t you

[thorn kindle]

Sure

[alpine sable]

Draw a picture on the number line

[glass lichen]

they dont have access to R

they're doing it axiomatically

[alpine sable]

Draw a picture on Q

Just please

Draw a picture

You will see

What the number you should pick is

I’m not saying to use the picture as a proof

But this will tell you what number to pick

[alpine sable]

Hint!!!

[thorn kindle]

I guess you could take the average of the numbers

[lethal wolf]

my homework is due in 15 min

can someone help me

there is one question i cant solve

[glass lichen]

why did you put it off then?

[thorn kindle]

Not sure if division is allowed though

[lethal wolf]

last week of school

[alpine sable]

No need to be rude

[lethal wolf]

got lazy

now i have an 88 in math

[alpine sable]

Draw a rectangle

[glass lichen]

what's the length in terms of the width?

[lethal wolf]

ok

[alpine sable]

Now what can you fill on the rectangles sides

[lethal wolf]

14 cm

[alpine sable]

14 cm what though

[lethal wolf]

i dont get it

width?

[alpine sable]

You are probably going to need an x somewhere yeah?

X is an unknown

[lethal wolf]

yeah

[alpine sable]

So either the length or the width

[lethal wolf]

length is the x

[alpine sable]

Okay you can do that

Might be easier pick the width to be x

[hidden horizon]

let width be x
therefore length = (x-14)
solve nd ur done dude

[lethal wolf]

what

damn

[alpine sable]

I don’t think you are meant to do the homework for them

[hidden horizon]

thts why i didnt tell answer dude ,chill

[alpine sable]

But you did the important part

I am chill

[hidden horizon]

ok

[hidden horizon]

kinda

[alpine sable]

No you did the important part

Not kinda

This question is about learning how to set up equations

[pearl vessel]

can anybody solve this

[alpine sable]

Draw a picture

[scenic stone]

Please Help I am noob

Studying for my ged

What am I doing wrong

[hidden horizon]

where is n next to -5 in first step nd second

i think dats the mistake

[obsidian lantern]

Yeah it is

[wary stream]

Yeah, you're missing an "n"

It's -5n

[scenic stone]

Oops

Answer should be 0 but I'm getting fractions

[obsidian lantern]

you forgot the n again

Remember it’s 5n

[hidden horizon]

lol u forgot n in 2nd step xD , again

[wary stream]

What are you adding -5n to 8?

[obsidian lantern]

it is like terms with +56n

so therefore you add to -8+51n

now you add 8 to both sides you get zero on the other side

what times 51 gives you zero

[scenic stone]

0

I see

[livid owl]

is the answer -25^4?

[scenic stone]

Thanks guys

I'll rewrite it again with the ns

[wary stream]

You forgot an x

[livid owl]

mb the x after the -25

[wary stream]

But yes

[livid owl]

so for this one would it be

[wary stream]

Apply power rule

[livid owl]

45x*4+12x^3+9x^2-14x

[wary stream]

Yes

[livid owl]

thank you

[wary stream]

But write it properly on paper

You made some typos typing it out

[livid owl]

ok thank you

no typos

?

[wary stream]

Yes

[livid owl]

mhm thank you

[brazen sleet]

hello

uhm

i am

brain dead

now

[alpine sable]

what is inflection point?

[brazen sleet]

a point where it changes direction but curved

concave up & down

right?

@alpine sable

[alpine sable]

yes

this is occupied move to another channel

[brazen sleet]

Ahh

[alpine sable]

at inflection piont f''(X) becomes 0 right?

[brazen sleet]

yes

those would give me the point where they change

[scenic trench]

i don’t know how to do this

and i don’t know what the stuff in the equation represents

[alpine sable]

when you would solve for f''(X)=0 that would be a quadratic equation

[brazen sleet]

Hm so what does that tell me since it is a quadratic equation

[glass lichen]

find the roots of the quadratic

[alpine sable]

there must be two inflection point so there must be two roots of that equation

[atomic solar]

a d f?

[scenic trench]

how

[glass lichen]

like any other quadratic...

[brazen sleet]

what can i do with the roots?

[scenic trench]

but i don’t know how to do that

[alpine sable]

the question ask you that there must be 2 inflection point so there must be 2 roots for the equation

so discriminant must be >0

[wary stream]

Use the quadratic formula, factor, something to find the solutions to your quadratic

[scenic trench]

oh okay

[drowsy dagger]

only need C

[wary stream]

That's a special right triangle

[austere osprey]

alr

[alpine sable]

No. A and E

[drowsy dagger]

Sum of all angles is 180, and you already have 90, meaning the other two angles add up to 90 as well

[austere osprey]

but its asking for R and S which are both 45 so waht would T equal?

[wary stream]

No need for this info

[alpine sable]

What is option F?

[wary stream]

It's a 45 -45 - 90 right triangle

[austere osprey]

check DM

[drowsy dagger]

said the same exact thing and tells me theres no need for this info

[alpine sable]

Bisect t. Line from Centre of right angle. T/2 both sides at the bottom.

[drowsy dagger]

anyways to find T its the hypotenuse so use the formula to find that

[austere osprey]

so what would be the answer

[alpine sable]

45

Both

[austere osprey]

for t?

i alr got mR and mS

[alpine sable]

Sqrt (98)

[drowsy dagger]

^

[austere osprey]

so t = 9 8

[alpine sable]

Bruh

[austere osprey]

bro im not good at math

[drowsy dagger]

it would be the square root of 98

[austere osprey]

ok

[drowsy dagger]

u can leave it at that or you can actually square it, but youll need to round

[alpine sable]

9.899

[drowsy dagger]

((ugly number))

[alpine sable]

Yes. High school math is cringe

[austere osprey]

wouldnt 9.899 rounded be 9.9?

nvm

no need

[wary stream]

I mean it's easy to know it's a 45 -45 -90 special right triangle because the legs are the same

[alpine sable]

Depends on how many decimal places you need to round to.

[austere osprey]

can someone get on a call w me and help me out w this stupid geometry PLZ

[alpine sable]

T = √(7²+7²)=√(2x49)=7√2

=9.899...

[wary stream]

Use trig ratios

SOH CAH TOA

[austere osprey]

i am bad at solving or understanding math, can I just get the answer

[alpine sable]

500/sin(16°)

[wary stream]

Nope

We don't give answers

[alpine sable]

=1813.977...

[wary stream]

Please stop giving answers

Let the person figure it out themselves

You can teach them the concept

[alpine sable]

Yes Sir!

Sorry, No worries

[spark ibex]

can someone verify my work and answer?

[rain cape]

can someone help me with this

[spark ibex]

<@&286206848099549185>

[cedar wave]

Looks right to me!

[cedar wave]

PTS and QTR are vertical angles, which are two angles on opposite sides of where two lines cross. So the argument for saying those are equal is that vertical angles are congruent.

[cunning sigil]

does someone know how to do this

[spark ibex]

@cedar wave so for the profit where i got 1264, someone said they got 1610

im so confused how they got that

this is my friends work

i literally have the same work but they got 1610 for the profit

am i trippin or they trippin?

[cedar wave]

Your friends formula is right but they must have made a mistake in calculating the answer, yours is right

[spark ibex]

ok i was boutta say

i put it in my calculator like 20 times but kept getting 1264

[random crypt]

Can someone help me?

[spark ibex]

are my explanations on what they represent correct?

[cedar wave]

Yes!

Though you are explaining the revenue by saying 'this is the weekly revenue', which may not be the most clear

[spark ibex]

how should i say it

[cedar wave]

It may be a more clear explanation to say something like 'the revenue is the total amount of money that comes in in the week' and 'the profit is the money that is left over after subtracting all costs from the revenue'

[spark ibex]

ok

so just replace it represents... for both the profit and revenue and say what you said

but keep that first part for both

[cedar wave]

Yes, I think that would be good. You got the first part right

[spark ibex]

cool thank you!

[cedar wave]

no problem

[chrome plinth]

when ur finding the slope, how do you determine which y and x coordinates will be squared?

[sour lynx]

i need to find the value of x and its special angle pair relation ship

i know its a vertical angle

but i dont know how to find out what x it

is*

[gray isle]

what do you know about vertical angles

[sour lynx]

that they are 2 angles that cross over eachother

[gray isle]

what else

also vague wording

the angles with measures of 2x° and 155° are vertical angles

[sour lynx]

mhm

[gray isle]

what information does that tell you?

[sour lynx]

that 2x + 155 has to equal 180 or something

[gray isle]

no

[sour lynx]

ok

[gray isle]

do quick search on vert angles

[sour lynx]

each of the pairs of opposite angles made by two intersecting lines.

[gray isle]

keep reading past that

notes should tell you something very specific about them

[sour lynx]

they are congruent angles

[gray isle]

yes

[sour lynx]

and what do i do with that information

[gray isle]

apply the definition of congruent and set up an equation

[sour lynx]

wdym by apply the definition of congruend

congruent*

[gray isle]

what does it mean for angles to be congruent

[sour lynx]

to be equal

[gray isle]

yes

and use that to set up an equation

[alpine sable]

can someone help me

how is there even a correct one

it's just in different orders

how would I know which order is right

[gray isle]

identify the corresponding vertices

[alpine sable]

I got VMS ~ CPS

but that's not a choice

[gray isle]

only the respective positions need to be the same

[alpine sable]

i got num 3

[gray isle]

e.g V corresponds to C
but the statement would still be valid if in your triangle label, they were written in the second or third positions

num3 is incorrect

[alpine sable]

whaaat hmm

let's see

[gray isle]

V corresponds to C right
M to P and
S to S

[sour lynx]

@gray isle is it 2x=155

[alpine sable]

nevermind it's 4

[gray isle]

yes

and then solve for x

[sour lynx]

ok

thanks

[alpine sable]

it's num 4

[gray isle]

yes

[alpine sable]

This is the same,right?

I got 3

[sour lynx]

now i need help on something else

[gray isle]

its the best option available

[gray isle]

but technically its supposed to be insufficient info to justify congruence

[alpine sable]

okay

[covert solar]

z

[alpine sable]

I don't understand

This 2

Look

It's "Not drawn to scale"

so how would I know if it's not rotation

[gray isle]

its a bad question

[alpine sable]

this?

[wary stream]

If you rotated the shape, it would look different

[gray isle]

i guess assume the respective rations are still the same

[alpine sable]

OHh

So it's translation

[gray isle]

well if its not drawn to scale

dilation would also be applicable and probs more appropriate (if its really not drawn to scale)

[wary stream]

Plus the labels would be different if you rotated