help-28

[wispy bay]

didn't continue since I knew the answer is wrong

[mighty crescent]

What’s e

[wispy bay]

that's d

[mighty crescent]

Why 8

[wispy bay]

since 8 is my 3rd term

and my 17th term being 43

I tried substituting 8 for the nth term and 3 for the n and ended up with 2

but I don't think an even number can get 43

[mighty crescent]

In the second line, the 8 and the 3 look the same

[mighty crescent]

What do you mean

[wispy bay]

sorry for the confusion

[wispy bay]

in this, I tried substituting the nth term with 8 and the n with 8

[wispy bay]

but in here, I started another computation but replaced the n term with 3

[mighty crescent]

if you’d substituted the index of the term with 3, then it would be right

[mighty crescent]

yes, this is right

[wispy bay]

oh

but then, how did the 17th term be 43

[mighty crescent]

Why can’t it

[mighty crescent]

Can you show how you got 2

[wispy bay]

sure

oh wait

it wasn't two

four, rather

my apologies

,rotate

[wispy bay]

is the computation correct

[mighty crescent]

Why did you scribble out the d

It should be there

[wispy bay]

oh

alrighty

but if there were the d, where would it go?

[mighty crescent]

and here, on the second line, where did the plus go

could you write it without scribblings out?

[wispy bay]

sure sure

wait, so if there was the d

it would ba 8 = a sub 1 + (2)d

[wispy bay]

I already subtracted 3 to 1 here

wouldn't the next step be multiplying 2 to d?

[mossy wagon]

wait

first tell me you already have 2 eqns right?

you have 3rd and 17th term right?

[wispy bay]

yes

[mighty crescent]

I think so

[mighty crescent]

but you still have 2 variables here

[opaque imp]

Hi

[wispy bay]

exactly

it confuses me

[mossy wagon]

d will get reduced

[mighty crescent]

you can get another equation involving these two variables using the 17th term

[mossy wagon]

first tell the 2 eqns you got

[mighty crescent]

can you let me finish

[wispy bay]

what's eqns

equations?

[mighty crescent]

short for equations, yes

[opaque imp]

What was the question?

[mighty crescent]

It’s pinned

[wispy bay]

there's been only one equation so far

the arithmetic equation

[mighty crescent]

Can you use the 17th term to get a similar equation?

[wispy bay]

if I use the 17th term..

[wispy bay]

the d will just go away?

[mossy wagon]

no first form the 2nd equation

then i will tell

[wispy bay]

,rotate

[wispy bay]

if I use the 17th term in which is 43

I get this

I stopped after multiplying 16 to d since I don't know what comes next

[mossy wagon]

good

now subtract equation 2 by 1

[mighty crescent]

after that, you can solve them simultaneously

[mighty crescent]

do you know how to solve 2 equations simultaneously?

[wispy bay]

I'll subtract this to the one I just did right now?

[wispy bay]

hehe

[mighty crescent]

Yes

[mossy wagon]

You know?

[mighty crescent]

And that should give you d

[wispy bay]

sadly I cannot

[wispy bay]

but I'll get the common difference (d)

if I do that

[mossy wagon]

yes

[wispy bay]

I'm looking for the 1st term

of the sequence

[mighty crescent]

And then you can substitute it back in

To find the first term

[wispy bay]

ohhh okayy

[mossy wagon]

you will get it

[mighty crescent]

Can you complete it from here?

[wispy bay]

it hit me now

how do you compute 2 eqns simultaneously tho..

I think I've never encountered that in school

[mighty crescent]

It just means the process that I described

[mighty crescent]

you can google “solve 2 linear equations in 2 variables” if you want to learn more

[mossy wagon]

or you can subract directly by putting the equations together
subtract right side of '=' and left side simultaneously of both equation

left side of equation 1 will subtract to left side of equation 2

[wispy bay]

all of that just to get the 1st term of an arithmetic sequence?

[mossy wagon]

no

to get d

then you can put it in any equation you got
you will get a

[mighty crescent]

there’s another way to think of it

that doesn’t involve solving 2 linear equations

[wispy bay]

what is it?

[mighty crescent]

here, there are 14 terms between the 3rd term and the 17th term

or 14 “jumps”

[mighty crescent]

(well, because of fencepost issues, there are 13 terms between the 3rd and 17th term, but that isn’t the point)

[mighty crescent]

so, between them, you add d 14 times

or, in other words, add 14 times d

so then 8 + 14d = 43

and then you get d

after that, you can jump back by 2 times d, to get the first term

[wispy bay]

how do I get d from that

do I transpose 8 to 43?

[mighty crescent]

You don’t have to transpose anything

Subtract 8 from both sides

Then divide both sides by 14

[wispy bay]

this doesn't involve using 2 equations right

[onyx glen]

in fact i'd go so far as to say that even using the word "transpose" is icky in this context.

[wispy bay]

I'm just a 10th grader that sucks at math 😢

[wispy bay]

then I'll be able to get d, then eventually, the first term?

[mighty crescent]

Yes

[wispy bay]

alrighty, thanks!

I can go from here now on

thank you very much

[mighty crescent]

You’re welcome!

[wispy bay]

thankies

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[tidal depot]

Where did I go wrong

[mortal sigil]

I don't think you can separate the cos or smth

Where'd sin(x/2)cos(x/3) come from

[glossy valve]

Dyssrupt

[narrow helm]

also your method wont work

[tidal depot]

Shoot

Chain rule

[tidal depot]

Y not

By parts is wrong?

[narrow helm]

this will just result in endless cycle ig

[tidal depot]

Ok

[tidal depot]

Ill try again with this

Is that possible

[narrow helm]

i just pointed out a mistake, so no dont need to work on that

[glossy valve]

Dyssrupt

[tidal depot]

Hmm okay

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[hoary tendon]

should i draw the line first?

[fast peak]

the line?

there at least 5 lines you can draw for this problem

[hoary tendon]

ohhhh

nvm

i just need to put the number on F

8.25 = 20

its right

is it A?

[fast peak]

8*2.5 but well who cares about correct notation

[fast peak]

does the point satisfy all constraints?

[hoary tendon]

wait

yes

its satisfy all contraints

[fast peak]

what about the next point

[hoary tendon]

this one is a

too

its satisfy all contraints

[fast peak]

but is that the minimum

you dont just have to check whether it fits the constraints

it also has to give the smallest value among all those points which satisfy the constraints

[hoary tendon]

hmm

ur right

0,0 also fits all contraints

i dont know what to do

helo

@fast peak

[fast peak]

and it has a smaller value

so it definitely cant be A

but maybe one of C-E

you have to check all of them

[hoary tendon]

oh

is it D

it have the lowest number

this same as before?

is this is the same as before

its E

@fast peak what should i do for this one

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[mint leaf]

.close

[naive river]

hi guys

how do i solve it

[glacial pasture]

youll have to find the inverse function for f, if that doesnt get the answer then its d by elimination

[naive river]

put x as -x?

[glacial pasture]

unless you can choose more than one answer, in which case you should probably check d anyway

[naive river]

answer is a ;-;

[narrow helm]

yes it is

[naive river]

ye how

[narrow helm]

find the inverse

[naive river]

put x as -x?

[narrow helm]

no

[naive river]

then

how

[narrow helm]

let f(x) = y for easier notation

express x in terms of y

at last interchange x and y

[naive river]

k

[narrow helm]

and you'll get inverse

[naive river]

wait ill solve

ye sorry for the delay

@narrow helm

,tex x= $\frac{3y+2}{5y-3}$

after this?

[glossy valve]

gamefly

[naive river]

after this

[narrow helm]

.

[naive river]

im not understanding hoe

how

,tex y= $\frac{3y+2}{5y-3}$

[glossy valve]

gamefly

[naive river]

like this?

@narrow helm

pls bro

i dont have much time

@narrow helm

<@&286206848099549185>

[kindred oriole]

now change the y's in the fraction to x

[naive river]

ok

one moment

[naive river]

in this eq or

[naive river]

this

@kindred oriole

[kindred oriole]

this one

[naive river]

k

[kindred oriole]

you have got x = y which is the inverse function. You then change the x to be y and vice versa (literally drag 'n drop) to make it look nicer and for graphing reasons etc

[naive river]

,tex y= $\frac{3x+2}{5x-3}$

[glossy valve]

gamefly

[naive river]

is this correct

[kindred oriole]

ye

[naive river]

k

thx

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[eternal yoke]

I have no idea how to do this

[mint veldt]

can anyone solve this @glossy sandal

[rapid rain]

If f is differentiable everywhere, then f has to be differentiable at 0

[rapid rain]

#❓how-to-get-help this channel is unavailable

[mint veldt]

k

[eternal yoke]

Why at 0 though

Is that like a definition

[rapid rain]

It's implied

[eternal yoke]

Is it because of the value x≥0

So x can equal 0 in this instance

But only for ax+b

[rapid rain]

You already know that f is differentiable at any point that is either x>0 or x<0

Because 9cos(x) is differentiable and ax+b is differentiable

[eternal yoke]

I understand this part

[rapid rain]

The problem comes at x = 0, where to the left of 0 we have 9cos(x) and to the right we have ax+b

The left and right derivatives might be different

[eternal yoke]

So maybe this a left sided right sided limit problem?

[rapid rain]

And left and right limits as well

[rapid rain]

Yep

First, since f is differentiable :

• f is continuous at 0
• f is left-differentiable and right-differentiable at 0 and both derivatives have the same value

Since f is continuous, what does this imply on a and b?

[eternal yoke]

This what I did

[rapid rain]

Yep

And since f is continuous, what do those left and right limits tell us?

[eternal yoke]

The limit exists?

Because i know for a limit both sides have to equal the same value

But b is just a variable

[rapid rain]

Yes, this exactly

So the left limit is 9

And the right limit is b

[rapid rain]

Since you told me this

What can we say about b?

[eternal yoke]

b is equal to 9

[rapid rain]

Yes

[eternal yoke]

Would finding a be a different approach

The only thing I can think of is taking the derivative of the function to get rid of that b

I think like this

So wouldn't that imply a is 0

[rapid rain]

Yes

[eternal yoke]

It makes alot more sense now. Thanks for the help

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[charred escarp]

p(x-1) + 2(3x+k) ≡ 4(x+2) where p and k are integers, work out the values of p and k

[fast peak]

and what is x?

why did you write congruent instead of equal?

[charred escarp]

It's an identity

Idk what x is, I just saw someone online answer the question but I don't understand how they've done it

[fast peak]

what type of thing is x

[onyx glen]

||i think the ≡ is supposed to mean this is true for all x||

[onyx glen]

genuine or socratic?

[fast peak]

well I dont like guessing

[charred escarp]

I'm not sure, the question is from a further maths gcse paper

[onyx glen]

was asking dena

anyway

[charred escarp]

My bad

[onyx glen]

this thing being an identity means its true for all real values of x

[charred escarp]

Oh okay

[onyx glen]

and you can for example expand, collect like terms and equate coefficients

which imo is the least headache-y thing to do here

[charred escarp]

px − p + 6x + 2k = 4x + 8

But where do I go from here?

[spiral vigil]

combine all of the x terms together, and combine all of the non-x terms together

[onyx glen]

collect like terms ^

[charred escarp]

px + 6x = 4x
-p + 2k = 8

Like this?

[fast peak]

yes

[charred escarp]

How can I work out values of p and k if I have an x in there?

[fast peak]

on the left you can factor out an x

to get (p+6)x = 4x

now you can compare the cofficients

an equation like that is only true for all possible values of x if the things infront of the x are the same

[charred escarp]

Okay that makes sense

So p = -2

[fast peak]

yes

[charred escarp]

So what can I sub that in for the other part to work out k to be 4?

[fast peak]

k is not 4

but yes you can plug it into the other equation

[charred escarp]

Oh I meant 3

[fast peak]

yup

[charred escarp]

Thanks

[fast peak]

youre welcome

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[obsidian tulip]

How many prime numbers p are there st. p+2, p+4 also are prime are there?

[obsidian tulip]

The solution is only 3,5,7

But I don’t know how to prove it

I dont know if the distribution of primes is a valid argument, probably not.

[spiral vigil]

distribution/density wouldn't be a valid argument because that's average density

[gritty rose]

Yea it's a lot easier than this

One of p, p+2, p+4 is always divisible by some small integer

[spice orchid]

1!

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[sturdy summit]

Can I simplify this further?

[sturdy summit]

,rotate

[torn jolt]

,w solve 3x² + 5x - 7

[glossy valve]

Results provided by WolframAlpha

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

Requested by eragon._._.

[torn jolt]

Uhh no

No more simplification

Maybe make the numerator (x+2)²

But no more

[sturdy summit]

I tried removing the 3 by 3(x² + 5/3x -7/3)

Cant reverse foil this out

[torn jolt]

Yeah but unless youre gonna work on that more i dont see a need

Idk what reverse foil is

[sturdy summit]

This equation is the function; (m/g)(x)

[torn jolt]

error 42: user doesnt know all that

[sturdy summit]

Damn

[torn jolt]

basic simplification, the things you get till 11th grade, cancelling out factors of x, nah no more

anything more than thatz nah idk

[sturdy summit]

This is 11th grade

Well goodluck for me

[torn jolt]

Then what is reverse foil

Ohhh okay

Splitting the middle term

No , no reverse foil

Cuz you get -21 and addition of +5 when 21 is just 7*3 so no , no reverser foil

[sturdy summit]

(x² + 4x + 4) ≈ (x+2)(x+2) = reverse foil method

[torn jolt]

Yeah

Splitting the middle term

Differnt names same shi-

No more simplifications

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[torn jolt]

Hey , how can I know if my waveform is complex exponential Fourier series ?

[torn jolt]

Πλάτος stands for amplitude and φάση means phase

[severe linden]

What exactly do you mean by being "complex expoenential Fourer Series"?

[torn jolt]

exponential Fourier series

[severe linden]

What exactly does the graph represent?

[torn jolt]

Fourier series can represent as trigonometric functions and exponential

[severe linden]

You can write a periodic function that has exactly those frequencies if that is what you are asking?

[torn jolt]

That’s what I’m asking how can I guess if it’s in exponential Fourier function.

[torn jolt]

No , how can I guess if this particular graph is an exponential Fourier series or trigonometric Fourier series.

[severe linden]

❓

Trignometirc and expoentnial fourer series are extremely related, they are just slightly rewirrten.

If you have one, you can easily also construct the other.

[torn jolt]

Yes but which Fourier series are they representing ?

[severe linden]

It doesn't make much of a difference.

$4 + 10\exp(4 \pi i t + \pi) + 6\exp(6 \pi i t + \pi/2) + 4\exp(10 \pi i t - \pi/3)$

If you consider only the real part or the iamginary part

it is the same but just cos(...) or sin(...) instead exp(i...).

[glossy valve]

M8732

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[torn jolt]

!status

[full forum]

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

[torn jolt]

3

[torn jolt]

A physics question but , Isn't 2 correct ??

Dimensionally

ping me for answer

[near storm]

@torn jolt
hi
as far as I know when we are talking about periodic motion general formula is in this form
a_max sin(ωt) or a_max cos(ωt)

[torn jolt]

Umm idk
The question is on dimensional analysis
Dimension of LHS should be equal to the Dimension of RHS

Its a uh physics Question

[near storm]

sorry mb I got it wrong

[torn jolt]

Yeah np

[torn jolt]

<@&286206848099549185>

Forget it

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[somber mountain]

How do you calculate 3c-c/3 ?

[elfin stump]

are you swedish or danish?

[torn jolt]

take denominator common

[elfin stump]

just seeing if i have to use laymans terms

C can be anything, any variable, therefore assume c-c is 0 and c* c = c ^2
From there you should be able to catch the big C

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[summer mist]

I need a explanation on how to do this

[thorn harbor]

Multiply 3(x-1) first because pemdas rule or something (idk in english cuz i learn in french)

u multiply 3 with each factor in ()

so its 3x-3

5+3x-3

and just 5-3 to simply the same factors

so its 2+3x if im not wrong

[summer mist]

Wait so when you say multiply 3(x-1) is it just -1x - 3?

[frail needle]

No u distribute it

3 x x and 3 x -1

[thorn harbor]

no u multiply 3 with x which equals 3x and then u multiply 3 with -1 which equals -3

put it toghether its 3x-3

[summer mist]

Ok then jus add 5 to the answer of that

[thorn harbor]

yes

[summer mist]

Then I got my answer

Or is there more steps

[thorn harbor]

no thats it

[summer mist]

Ok Thanks for the help rlly needed it for my quiz

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[elder cape]

I think this is a geometric series with a = 4 and r = 0.3

So would the sum be 4/(1-0.3)

therefore, 4/0.7 ?

[tulip beacon]

hm

Did u skip out 4(0.3) and 4(0.3)^3

[elder cape]

yeah

[tulip beacon]

Than yea

seems good

[ivory cairn]

that formula is for the infinite sum of a geometric series that has all it's terms.

[elder cape]

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[trail stump]

how to find the slope of the tangent line to the graph of a function at a point

[tulip beacon]

well lets you have a function f(x)

[trail stump]

ok

[tulip beacon]

you would just do f'(x) (differentiate)

[trail stump]

yeah

[tulip beacon]

and than plug in the x cord

[trail stump]

what does it mean to differenciate? and relevance?

this is more like a concepts question

x cord?

[tulip beacon]

x co-ordinate

[trail stump]

yeah

[tulip beacon]

Wow

[trail stump]

yea thats how to find it

what does it mean to differenciate

[tulip beacon]

honestly i have no idea how to even answer thisd

[trail stump]

ok

i need help for this though

[tulip beacon]

I would say

differetiate is to find the rate of change of something

[trail stump]

yea...

is it?

[tulip beacon]

Yea

when you dffierentiate at a certain point your basically asking for the rate of change at that point

[trail stump]

yea

after you plug in the value in the differenciated function, you get the slope of the tan line

right?

[tulip beacon]

Yea you will

[trail stump]

ok

i guess

just a bit lost on the parts

thanks though

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[pliant lagoon]

i just keep getting more and more confused

i got 1/cos on the right

and i have no idea on the left side

[hollow ridge]

Pythagorean Identity
$$1 + \tan^2{\theta} = \sec^2(\theta)$$

[glossy valve]

Rmoney

[pliant lagoon]

hmm

but i have $$tan^2(x) + 2 * 1/cos(x)$$

[glossy valve]

puckmyseen

[hollow ridge]

Subtract 1 from both sides of the Pyth. identity

[pliant lagoon]

i don't see

i don't get it

[hollow ridge]

Pythagorean Identity \begin{align*}
\tan^2{\theta} &= \sec^2(\theta) - 1 \
\tan^2{\theta} &= a^2 - 1
\end{align*}

[pliant lagoon]

yes

[glossy valve]

Rmoney

[pliant lagoon]

so would it be $$tan^2(x) -1 + 2 * 1/cos(x) $$

[glossy valve]

puckmyseen

[hollow ridge]

No, since tan^2 is equal to a^2 - 1, you can substitute it with a^2 - 1

[pliant lagoon]

$$a^2 - 1 + 2 *1/cos(x)$$

[glossy valve]

puckmyseen

[hollow ridge]

Yes

[pliant lagoon]

ok

[hollow ridge]

1/cos(x) can be rewritten using reciprocal identity

[pliant lagoon]

$$a^2 + 1 *1/cos(x)$$

[glossy valve]

puckmyseen

[hollow ridge]

No, illegal move

[pliant lagoon]

lol

hmmm

ohh 1 /cos = sec

[hollow ridge]

Remember that your goal is just to end up with an expression containing only a’s, b’s and numbers

Yep!

[pliant lagoon]

yess

a^2 + 1 + b

yikes

i dont think so

[hollow ridge]

Almost, but you have to revert the illegal move you did

[pliant lagoon]

did i mess up in the middle based off the answer choice

[hollow ridge]

You were still good here

[pliant lagoon]

hmm

but 1/cos = sec

or do you want me to revert back to the origirinal origrinal

ohhh

a^2+2ab+1

correct?

wait

no

a^2 +1 +2b tan

[hollow ridge]

Start from $$a^2 - 1 + 2 *1/cos(x)$$

[pliant lagoon]

is where im at

[glossy valve]

Rmoney

[pliant lagoon]

i reverted it

1/cos to csc and tax

tan

[hollow ridge]

$$a^2 - 1 + (2 *\frac{1}{\cos(x)})$$

[pliant lagoon]

hmp

[glossy valve]

Rmoney

[pliant lagoon]

yea

2*sec(x)

2(b)

no?

[hollow ridge]

sec(x) = a from the Problem statement

[pliant lagoon]

$$a^2+2b-1$$

?

[glossy valve]

puckmyseen

[pliant lagoon]

oh a

$$a^2+2a-1$$

[glossy valve]

puckmyseen

[hollow ridge]

Yes

[pliant lagoon]

oh ok

thank you

[hollow ridge]

Np!

[pliant lagoon]

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[earnest pebble]

Can anyone help solve this problem?

[earnest pebble]

I got 11 for the first answer, but it showed as incorrect

anybody?

help?

[primal forge]

ok

use log properties

[earnest pebble]

i havent learnt logs

thats why i need help

[primal forge]

ok so basically this is all log rules

like these

[earnest pebble]

idk how to use logs im in 7th grade

what rules would you even use

[primal forge]

well id take the ln of both sides

[earnest pebble]

like i said i have no idea what natural logarithms are

im pretty sure you use e though

wait nvm i solved

i realized

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[spark field]

Quick trig question. I have this problem:

The angle of elevation from a rowboat moored 75 feet from a cliff is 37.8 degrees. Find the height of the cliff to the nearest foot.

Would the correct formula be: tan(37.8°) * 75

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[prisma bane]

why isn't this right?

[prisma bane]

isnt that an example of a level surface

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[twilit leaf]

x^2+y^2>=0 is already satisfied by default on the real numbers

[stuck skiff]

i found this on another forum online

[fathom saddle]

If that were true, then these values should work:
x = 1, y = 1, z = -3

[stuck skiff]

oh i get it now thanks

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✅

[stuck skiff]

wait i tried z>0, z^2>x^2+y^2 and it didn't work. is my brain just not functioning today

[spiral vigil]

it's a inside that ln

z

not z²

[stuck skiff]

what do you mean?

[spiral vigil]

wait no that's fine

wait yeah

what if z was like -1000

and x and y were 1

[stuck skiff]

z - sqrt(x^+y^2) > 0, and since sqrt(x^2+y^2) >= 0, z > 0 right?

[spiral vigil]

yes

[stuck skiff]

so what am i missing?

[spiral vigil]

well

the point is that your constraints allow that

[stuck skiff]

it doesn't though, i have a constraint saying z>0

[spiral vigil]

where

[stuck skiff]

this is when i retried it

[spiral vigil]

oh

oh you said that oooops

[cosmic canopy]

wait why is it not as simple as $z>\sqrt{x^2+y^2}$

[glossy valve]

ed

[stuck skiff]

i mean i guess that would be right, but that doesn't make mine wrong either?

[forest widget]

parsing correct answers is hard

[stuck skiff]

i just want to make sure my answer is correct, so i can try email my teacher and see if he'll give me the marks

[forest widget]

your answer is fine, complain about the software :p

[stuck skiff]

ok thanks

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[brittle patio]

calamuclus

[brittle patio]

i think i got it this time

i just need to check my work

so basically its 0/0 so apply the hospital

and you get

$\frac{1}{x^2}$

[glossy valve]

dabbingpotato

[brittle patio]

so just 1/1

so 1

[narrow helm]

nani

[gritty rose]

,w plot log(x^2)/(x^2-1) for 0.5 < x < 1.5

Looks right

Orrrre

[brittle patio]

lets go

[glossy valve]

Results provided by WolframAlpha

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

Requested by rie.mann

[brittle patio]

does anyone know why there is an n in this problem

[narrow helm]

n is an arbitary constant

[brittle patio]

okay thx

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[turbid bluff]

What I've tried:

[mighty crescent]

What is the word next to the up-pointing arrow?

[turbid bluff]

Normal

[limber flicker]

is that drawn normal to the ramp ?

[turbid bluff]

Hm?

[limber flicker]

the vector you've labelled 'normal' is not very normal

to the ramp

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[low scarab]

3x^2-16x+3=0

[low scarab]

I need help with this

[hot herald]

what issue do you have with this

[low scarab]

I don't understand how to solve this

I knew how to,but i forgot everything within summer

[hot herald]

that's conflicting

how do you know something if you forgot it

well this is a quadratic equation
math names can be uncreative, quadratic formula would be applicable here

[low scarab]

Wdym?

[low scarab]

Wdym?

[low scarab]

I see that this is quadratic equation

Quadratic formula?

Sorry I don't know how these formulas called in english

[hot herald]

google quadratic formula

other places may call it abc formula

or the alternate variant, pq formula

[low scarab]

I tried quadratic formula,it doesn't work here,There is no square root of 220

[hot herald]

doesn't mean the formula doesn't work

sqrt(220) is a number too,
don't discriminate against non-integers

[low scarab]

I told you I tried.It doesn't

You may try

I may be dumb

[hot herald]

and i'm saying it doesn't really matter what ends up being under the root

not all quadratic equations are guarenteed to have nice solutions

just because you don't get a nice perfect square under the radical
doesn't mean that you did something wrong, or the fomula doesn't work

[low scarab]

I told you I tried.It doesn't

[hot herald]

wdym by doesn't work

the formula doesn't work or the answer you're submitting into a system

or the value you reached doesn't match a solution

the issue isn't with the application of the fomula
but rather sqrt(220) can be simplified

[low scarab]

I tried to solve it even with weird square root

[hot herald]

did you simplify the sqrt(220)

[low scarab]

Idk how

[hot herald]

apply
sqrt(ab) = sqrt(a) * sqrt(b)
and look for perfect square factors of 220

[low scarab]

I hate math

That's too smart for me

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[dense edge]

0x + 0y = (h-2)/3
therefor, wouldn't h have to equal 2? in order to get 0 + 0 = 0

[spiral vigil]

last step

[dense edge]

oh.. it's (h+2)/3 isn't it

i messed up the sign I think

[spiral vigil]

yep

[dense edge]

i answered this too quickly by just looking at how each could be divided by 4

but maybe i should have tried -2 instead of 2?

since the signs are opposite for each column

did i distribute this 2 correctly? lol

feels weird..

[spiral vigil]

yes

[dense edge]

x = 2s + h + 4/3

is this at all helping for solving?

[spiral vigil]

dunno what s is

[dense edge]

the free variable for y

[spiral vigil]

what

[dense edge]

there is no pivot on y, only x

so doesn't that mean y is free variable?

[spiral vigil]

uh
i thought you just needed to find h that made it consistent

[dense edge]

well, i found out what x is, but i don't know if that helps

i don't know what it's asking for if the answer to this question is not h = -2

[spiral vigil]

pretty sure it is

[dense edge]

i'm just guessing based on pattern

i don't know how to solve for h using theory

like the steps involved to show my work

h = -2 is correct, but why is it correct?

[spiral vigil]

because you get a row of 000

[dense edge]

how did you get a row of 0?

using REF?

but aside from pattern matching, how did you get h = -2 to begin with

like let's say it's something tricky with fractions for each entry, and i can't easily use pattern matching to solve for h

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@dense edge Has your question been resolved?

[spiral vigil]

RREF yeah

[dense edge]

so this should tell me right away that h = -2?

[spiral vigil]

p much yeah

[dense edge]

i don't see it, even after I did all that work to find x=

[spiral vigil]

(h+2)/3 = 0

or else the system has no slns

[dense edge]

ohh

so i didn't need to find x

i needed to find how 0 + 0 = 0

[spiral vigil]

no

i was very confused why you were doing that lol

[dense edge]

if the question asked for inconsistent, i would say h does not equal -2?

[spiral vigil]

yeah

[dense edge]

OK

and what if it was (h+2)/0 instead of (h+2)/3?

just curious how it could be solved, if at all

you would still say inconsistent? or undefined, it would throw an error

[spiral vigil]

not sure how you'd end up with that

[dense edge]

theoretically lol

[spiral vigil]

no i mean like

you'd have to divide by 0 at some point to get there

which is, you know, not allowes

[dense edge]

so it would never be asked to begin with, beacuse this is not a matrix anymore

it's something else

when you divide by 0, wormholes start appearing

[spiral vigil]

it's meaningless

[dense edge]

OK

ty!

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[pseudo cape]

With Bolzano's theorem (a special case of the mean value theorem), we can find the zeros of a function approximately

[pseudo cape]

If we want to find a zero correctly up to 2 decimals, how would we know when we can stop?

[dusky locust]

Are you using the bisection method?

[pseudo cape]

(if we know the zeros are in the interval [a, b], then try f((a+b)/2), if it's less than 0, set it equal to a, if it's greater than 0, set it equal to b, repeat)

[dusky locust]

If you know the root is interval [a,b], then guess r = (a+b)/2. The margin of error is less than the size of the interval

[pseudo cape]

Ah

[pseudo cape]

So we should make a and b agree up to 2 decimal places, right?

Well three if we want to round

Yeah, thanks

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[thick crystal]

How does the second to last line follow

how do they go from cos n theta - i sin n theta / r^n(cos^2 n theta + sin^2 n theta) to r^-n (cos n theta - i sin n theta)

More specifically how do they simplify the cos and sins, I understand how r^n goes to r^-n

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[thick crystal]

.reopn

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✅

[raven yacht]

pythagoras

[severe linden]

^

sin²+cos²=1

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[limber socket]

How do I find a quadratic function of this graph?

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[molten wadi]

does someone know how I would solve this, Ive tried using the Bisection method but I dont see a function to use it on.

[eternal leaf]

If it has only one real zero or (root), and is continuous (i.e. it has a valid value for each x if x is a real number), then it will only change sign once (flip from positive to negative or vice versa)

therefore it must be in between -8 and -1

[molten wadi]

Thank you

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[mystic harness]

I need help

<@&286206848099549185>

[torn jolt]

send a closer pic

of the graphs

[mystic harness]

Ok

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[wild ermine]

f(x) = 4x^3 - 3x - 1

[primal forge]

!status

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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

[wild ermine]

I'm supposed to be finding the x-intercepts

1

I wasn't sure how to proceed with it, we did a bit on q/p but not much

[light sonnet]

You mean rational root theorem?

[wild ermine]

Yeah, that, I keep forgetting the name 😭

[light sonnet]

Do you understand the rational root theorem?

[wild ermine]

Somewhat, I forget which one goes first

[light sonnet]

Google is useful fyi

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[thick heart]

Help

[thick heart]

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[thick heart]

Mb

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[sharp nebula]

x-inter I got is
( (-2/3)^{3/5} , 0 )

Is the y-inter
(0, 0)
?

[glacial pasture]

x cant be 0

[sharp nebula]

Hi again haha

[sharp nebula]

That holds true for 2/x

What abt the front part

[glacial pasture]

doesnt matter, its defined due to the presence of 2/x that x can not be x

for the entire function

[sharp nebula]

So no matter how absurdly long the function is, if there's a 2/x, x=/ 0 ?

[glacial pasture]

yeah

its excluded from the domain

[sharp nebula]

Aight
I'll be back maybe

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[chrome dock]

i get 40

using

Power=E/t

Energy = mgh

but the answer is 100

i dont understand please help

[simple ridge]

wdym by energy

[simple ridge]

here

[chrome dock]

potential energy

gravitational

[simple ridge]

so what did you get for E

[chrome dock]

20 times 10 times 10

so 2000

divided by 25

which is 40

[simple ridge]

it is 80

[chrome dock]

oh yeah sorry

80

but thats still isnt correct

it supposed to be 100

[simple ridge]

how are you sure that it is 100 answer key?

[chrome dock]

it says it on the markscheme

[simple ridge]

whats that

[chrome dock]

like

where all the answers are

[full forum]

@chrome dock Has your question been resolved?

[full forum]

@chrome dock Has your question been resolved?

[chrome dock]

wait i found a solution online but i dont really understand it

"You've got the right idea, but power is really an instantaneous measure
P = dE/dt
The potential energy gained is proportional (mg) to the height increase.
The graph is basically linear apart from the start and end tails. So if you did the calculation in the mid part, you'd get a gradient (velocity) of
dh/dt = 0.5
where h is the height and a power (force*velocity) of 100W."

nvm i got it

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[turbid thunder]

Can somebody help me solve this problem? I am supposed to solve using integration by parts. Can someone help me identify where I messed up?

[gritty rose]

$\cot^{-1}(x) \neq \frac{1}{\cot(x)}$

[glossy valve]

riemann

[torn jolt]

what's the problem?

[gritty rose]

which one is your problem asking

[gritty rose]

the left side or the right side here

[gritty rose]

yea it's not $\int tan(x)dx$

[turbid thunder]

wait is it arccotangent?

[glossy valve]

riemann

[torn jolt]

ye

[turbid thunder]

ooohh ok that makes wayyyy more sense

thank you! ill give it another try now

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[supple jay]

guys this is truth?

or i miserably failed?

in the the math war ⚔️

[potent vine]

false

[supple jay]

woah

.

howcometh?

[potent vine]

$4^{1/3 }$ is different from 4

[supple jay]

hmmm

so then i jut

just

[glossy valve]

exophades

[supple jay]

hmmm no?

[potent vine]

there is no simplification left, you can write it though as $100 \cdot p^{1/3} \cdot 4^{2/3}$

[glossy valve]

exophades

[supple jay]

i can do just like this?

turnt up

?

or literaly

do nothing?

[potent vine]

yes but you can rewrite 400 as 4*100

[supple jay]

turnt up 5000%

just do nothing

[potent vine]

depends on what they're asking you to do

[supple jay]

its function of market supply of all 400 producers

which is 400 * (function of supply of 1 firm)

yo

@potent vine mister

if I have like this, and like divide all by p^-1

[quaint prawn]

⚔️ math war 🗡️

[supple jay]

will it actually be +1 on the p^1/3

on the exponent

war

battle of stalingrad right now

p^-1 battle

autisn withhold his troops

because he deems this battle not worth fighting

but deep inside he is actualy scared of the enemy

and wants to prevent heavy casualties

[potent vine]

bro what

[quaint prawn]

Notice that “dividing by p^-1” is just the same thing as multiply by p

[potent vine]

how did you get 9

[supple jay]

oh

its like not connected with the previous

this is looking for market price

but i need isolate p = ..

ok so

divide all by p^-1