help-28

[exotic shoal]

AND THEN 240-5(16) WHICH GIVES ME 160

WHICH IS THE CORRECT ANSWER

I went to eat dinner sorry i took long

[noble horizon]

What did u get?

[exotic shoal]

but i finally did it

[noble horizon]

Yayyyyyyyy

[exotic shoal]

160 for the distance AC

[noble horizon]

Indeed

[exotic shoal]

but one problem i always have is assigning the s

so u assigned s to AC

cos we wanted to find it

[noble horizon]

Yea

[exotic shoal]

i thought we just sub it in from question

s =240

thats how i was confused

[noble horizon]

nah because youre considering the particles journey from A to C not A to B

[exotic shoal]

AH right ok

ok

thats good then

thank you very much good sir

when going in the opposite direction does the signs flip

just in general

[noble horizon]

Depends on the question

This one no

If it's asking about like velocity then yes

because velocity is a vector

[exotic shoal]

and acceleration?

[noble horizon]

acceleration goes negative when ur slowing down

[exotic shoal]

yes

so no ok

and displacement

[noble horizon]

yes

displacement is a vector

[exotic shoal]

wait i get weirded out by it

so it can be negative

[noble horizon]

yes

[exotic shoal]

as its a vector

but u see how much the particle has 'displaced' per say

and that tells u if its neg or pos

because u see relative to the start point

if its moved forward or backward

[noble horizon]

Ye

[exotic shoal]

ok thanks man

i appreciate ur help

Why is part b looking like that?

oh u just sketch the graphs of the functions

and thats it?

the positive quadrant

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[strong cliff]

How do I simplify this further?

[rocky saddle]

can you show me the original question?

[strong cliff]

2b. Which translates to simplify the equation

[rocky saddle]

so what is (sqrt(x) -1)^2 expanded?

[strong cliff]

x + 1

[rocky saddle]

no

[strong cliff]

Wdym

[rocky saddle]

we make things simpler

[strong cliff]

Oke explain further

[rocky saddle]

We have (a+b)^2

so we also can write it as (a+b)(a+b) right?

[strong cliff]

Ye siee

sure

Makes sense

[rocky saddle]

ok now you expand this

what does it become?

[strong cliff]

does expand mean calculatr

calculate

?

[rocky saddle]

no

you just make it so that there is no brackets left

[strong cliff]

Or like doing the x) thing in the corner

ooh

oke

like this right?

[rocky saddle]

yes

[strong cliff]

YEYYAYE

[rocky saddle]

and simplify (sqrt(x))^2

and the other things

[strong cliff]

oke and now I can prolly solve it

[rocky saddle]

ok

[strong cliff]

Ima ping you back if I fail :)

[rocky saddle]

ok

[strong cliff]

Oke I got it

x + 1

[rocky saddle]

yes

[strong cliff]

is the answer

Tyyy

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[dim compass]

Is y=x^2/x continuous function for its entire domain?

[dim compass]

I'm not sure but continuous for entire domain and just continuous seems different so I am asking this to clear up my confusion

[rough plaza]

this is an interesting question

[chilly stratus]

I’m a little confused by what your asking but y=x^2/x is a non continuous function I believe

[dim compass]

Yeah that's true

[chilly stratus]

I recommend plotting it in desmos

[dim compass]

,w graph y=x^2/x

[glossy valve]

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[dim compass]

They are showing x=0

Wow

[chilly stratus]

Pffff I thought you mean x^2/x

[dim compass]

Isn't that what I wrote

[rough plaza]

shouldn't x be undefined at x=0, and hence not continuous at x=0?

[dim compass]

Yes

But is it continuous if we see for its domain only

That was my question

[teal aurora]

it is continuous on its domain but not on R

[dim compass]

Ohh

Thanks for answering this question

So continuity definition varies depending on what's asked

[rough plaza]

I'll check domain

,w domain

[glossy valve]

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[dim compass]

Isn't domain x≠0

What's there to check

[rough plaza]

"for which a function is defined"

[rough plaza]

so yea

[dim compass]

Oh

I mean I know the definition of domain

[teal aurora]

the definition is the same its just 2 diferent questions

[rough plaza]

and i forgot

[dim compass]

Ohh I see

[dim compass]

Ah np

So, is y=1/x continuous for its domain?

[teal aurora]

yes

[dim compass]

Ohk

Tysm biscuit and kotar

💕

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[sturdy fulcrum]

https://www.toppr.com/ask/question/if-a-gp-having-2n1-terms-whose-most-middle-terms-is-m-then-product-of/

Can anyone explain the highlighted part please

[sleek bobcat]

this is a result of a sequence known as geometric progression

$b=\sqrt{a.c}$

[glossy valve]

[ɸ]=1.618033988749....

[sleek bobcat]

known as geometric mean

[sturdy fulcrum]

oh yeah ik that

but why is an * a n+2 = (an + 1)^2

[sleek bobcat]

because n is defining the sequence here , you can just put this as $a_{n+1}=b$ , $a_{n}=a \ a_{n+2}=c$

[glossy valve]

[ɸ]=1.618033988749....

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[dreamy sable]

.ask

Part bi and bii of this question I have to idea how to do

[dreamy sable]

The values of a and b in part a is 1 and 1

But I’ve tried and don’t know how to approach the second part

[lofty island]

Start by writing a general equation of a cubic polynomial

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[supple sequoia]

in an isosceles triangle the sum of the base and the leg is 18 and the sine of the angle at the base is 2√6/5 Find the perimeter of the triangle

[supple sequoia]

so all I got is

c+a=18

[torn jolt]

you know that sin is perpendicular/hypotenuse right

use that

[supple sequoia]

sin is a/b

but if a=b

doesn tthat mean that sin=1

but sin is not 1

[supple sequoia]

Or am I wrong

[willow sedge]

I got an anwer but the method is way too long

Construct a perpendicular to base from top vertex

@supple sequoia

[willow sedge]

Yes

You can find length AC

[onyx glen]

note ABC is not a right triangle so sin(A) is not equal to a/b as written in this picture

[willow sedge]

then use pythagoras to find the length CD

Now CD/AC is the 2(sqrt(6)/5

[supple sequoia]

Abc is isosceles

I just realiesed that sin cos tg and cotg is only for right triangle

[supple sequoia]

So sin of the A angle would be CH/AH?

[onyx glen]

that's a very narrow view.

the trigonometric functions exist by themselves, not just "for" one type of triangle or another.

it is their definitions as sidelength ratios that are confined to right triangles.

[willow sedge]

Which vertex are you considering as H?

First of all it is given that AC+AB=18
Let AB=x so what is value of AC?

[supple sequoia]

Oh sec I forgot to add it to the picture

[supple sequoia]

Ac is 18-x

Ah is 18-x/2

[willow sedge]

Noo

AB is x

[supple sequoia]

Oh ye nvm

Ah is x/2

[willow sedge]

Yes

[supple sequoia]

And ac is 18-x

[willow sedge]

Now you can use sin

No wait

Find the length CH using pythagoreas theorem

[supple sequoia]

I cant if there is x

It would be jus smth plus or minus x

[willow sedge]

You can in terms of x

[supple sequoia]

Can I just

[willow sedge]

sqrt(AC^2-AH^2)

[supple sequoia]

Ok sec

[willow sedge]

oWAIT

[supple sequoia]

I used photomath to see if I shouldt even try

Im pretty sure its not that

[willow sedge]

I said wait

there's an easier method

[glossy valve]

B-eard

B-eard

[supple sequoia]

Oooh

I forgot abt it

[willow sedge]

so what do you get?

[supple sequoia]

I got cos=1

[willow sedge]

no

[supple sequoia]

Lemme try to calculate it again

[willow sedge]

show your process of finding the value of cos(theta)

[willow sedge]

Yes

Now take sqrt both sides

You get cos(theta)=1/5

But that is equal to AH/AC

and you have the values of AH and AC in terms of x

[supple sequoia]

I got 1/25

[willow sedge]

That is cos^2(theta)

[supple sequoia]

cos^2(theta) is 625

[willow sedge]

What

[willow sedge]

See the identity again

[glossy valve]

B-eard

[willow sedge]

Noo

check your process again

$\cos^{2}\left(\theta\right)=1-\frac{24}{25}⇒\cos^{2}\left(\theta\right)=\frac{25-24}{25}=\frac{1}{25}$

[glossy valve]

B-eard

[willow sedge]

<@&286206848099549185> I have guided him almost completely to the solution. Please someone guide him further as I gtg

[supple sequoia]

Wouldnt it need to go cos²/25 too

Oh nvm

I saw my mistake

So cos=1/5

[full forum]

@supple sequoia Has your question been resolved?

[willow sedge]

cos theta is equal to AH/HC

[supple sequoia]

so 1/5=ah/hc

[willow sedge]

yes

you have AC and HC in terms of x

[supple sequoia]

oooh

[supple sequoia]

uh I dont have HC

I have AC

the cos of the angle tho is ac/ah

[willow sedge]

so 1/5=(x/2)/(18-x)

Now solve for x

[supple sequoia]

what

also isnt the cos AC/AH

[willow sedge]

Once you solve for x

You can solve for the length of AB,AC and finally perimeter of the triangle

[supple sequoia]

I dont think its c/b

[willow sedge]

@supple sequoia

[supple sequoia]

yes

[hollow idol]

maybe I can help,where have you left with the problem?

[supple sequoia]

I have found cos

1/5

Ab+AC=18

And sin A is there

[hollow idol]

okkk

so the perimeter

As I can see you've found that AH = AB/ = X/2

[supple sequoia]

what

for ah

I havent found anything

[hollow idol]

what cos have you found?

of what angle

[supple sequoia]

oh nvm

nvm

yes

So

[hollow idol]

you can make a equation using that cos CAH = sin ACH because cos CAH = sin ( 90 degrees - CAH )

[supple sequoia]

AB+AC=18
AC=18-x (if ab is x)

[hollow idol]

after you found that cos CAH = sin ACH
sin ACH = ( 2 rad 6 ) /5
that means if sin ACH = AH / AC ==> sin ACH= X / 2 / 18 -X ( 2 rad 6) / 5

I make in paint

if uwant

[supple sequoia]

cos is AC/AH and sin is CH/AH

that would mean AC=CH

which is not true

[hollow idol]

No,I meant sin of ACH,not sin CAH

srry

you can show that cos CAH = sin ACH

but nvm ,you can also do it with cos ,but you need to arrive at
X/2/18 - X = 2 rad 6 /5

[supple sequoia]

can u draw it in paint if u can

[hollow idol]

yeah

now

[supple sequoia]

but

isnt

cos from a ac/ah

not ah/ac

[hollow idol]

from the formula of cos it s AH/AC

[supple sequoia]

do you mean the cos of ach?

[hollow idol]

no,cos CAH,because you have the cos of the angle CAH

the cos of ACH would be CH/AC and you don t need this

[supple sequoia]

but cos is the side thats like next to it / the one that is like the base

[hollow idol]

yeah,cos is the side thats like next to it ,but the side is the cathetus

[supple sequoia]

whaat

[hollow idol]

no,you are in a right-angle triangle
the base is the hypotenuse

[supple sequoia]

ooooooooh

[hollow idol]

but you need some algebra calculus now

after you did this with X/2/18-X =2 rad 6 /5

[supple sequoia]

I wanted to see if it would work so I used photomath but I dint think this is the answer

[hollow idol]

let me see

[supple sequoia]

ok'

[hollow idol]

I need to verify the calculus \

I need to verify the calculus cuz you will get X = 72 rad 6 / ( 5 + 4 rad 6 )

as I can see it gives me the same calculus

the same result*

[supple sequoia]

is rad radius

[hollow idol]

radical,but I make an abbrevation

abbreviation *

now I try to see if working with those values it would give the perimeter

[willow sedge]

What are ya'll evenh doing

[supple sequoia]

trying to slove it 😭

[willow sedge]

,w solve 1/5=(x/2)/(18-x)

[glossy valve]

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[supple sequoia]

but what is 1/5

[willow sedge]

cos(theta)

[supple sequoia]

so ac would be 18-(36/7)?

[willow sedge]

Yes

[supple sequoia]

90/7

[willow sedge]

Yes

[supple sequoia]

ah would be 18/7

[willow sedge]

we don't need that value anymore

Just find AB

[supple sequoia]

AB is 2 times AH

[willow sedge]

and BC

[supple sequoia]

so its 216/7

the perimeter

[willow sedge]

Yes

[supple sequoia]

thx

[willow sedge]

welcomme

[supple sequoia]

I also have a quick question

nvm

thx

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[severe basin]

Is this allowed? (image deleted)

[severe basin]

This is the first time I am seeing something like this.

[spice orchid]

Yes, determinant is linear in each column of a matrix

[severe basin]

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[tribal gust]

I cant make intuitive sense of the multiplication theorem of probability. P(A∩B) = P(A|B) . P(B). I do however have an intuitive understanding of the definition of conditional probability of an event A given an event B occured and i can see that i can algebraicly manipulate the equation to get the multiplication theorem. it still doesnt click tho

[tribal gust]

Could someone provide some extra info or maybe an example or something to help me understand?

I also dont understand how if the events A and B have no set theoretical intersection and so their intersection is the empty set has a non zero probability of occuring. P(A∩B) = P(A|B) . P(B) = P(A).P(B) =/ 0?

Or does this conditional probability equation only hold for dependent events?

[median cedar]

wait i have something might be helpful

for example, P(D|A) is not equal to P(A|D)
if you wanna find P(A|D) ("probability of an event A given an event D occured")

P(A|D) = P(A∩D)/P(D)

[tribal gust]

Oh but i get P(A|D) = P(A∩D)/P(D) i just dont get P(A∩D) = P(A|D).P(D)

I understand that you can get that equation through algebraic manipulation but it doesnt click intuitivaly

For example what if the intersection of A and D is the empty set? The probability given by this equation would give a non zero result no?

For example the probability of the event of getting heads AND tails in a coinflip is given by P(A).P(D) which for a fair coin is 0.25 while intuitively i feel like the answer should be zero

so im going wrong somewhere

[median cedar]

maybe i can try to answer this one in arabic

[tribal gust]

My arabic is bad srry

[median cedar]

look at this pic, if i wanna find P(D)
what would it be?

[tribal gust]

I honestly dont get that picture at all 😅

[tribal gust]

<@&286206848099549185>

[median cedar]

why do you feel like the answer should be zero?

[tribal gust]

Well we're calculating the probability of the event "A and B" . Since A and B are disjoint their intersection is the empty set and the event "A and B" is an impossible event so P(A∩B) = 0

Okey wait i think im confusing mutually exclusive events with independant events

Imma gonna review that and i'll be back in a few min

Okey i definitely confused the two concepts for a bit there. When two events are independent we can write the

yk what im gonna stop worrying about it and just accept the theorem for what it is. My exam is too soon to care about understanding atm haha

ty for the help tho!

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[errant axle]

what is a problem like this called?

I want to search online how to do it

[north echo]

https://m.youtube.com/watch?v=kEcbxiLeGTc

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@errant axle Has your question been resolved?

[errant axle]

thx

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[torn jolt]

कुल तरीकों की संख्या जिसमें छह व्यक्ति 4 कुर्सियों पर बैठ सकते हैं

[torn jolt]

help

help

help

help

help

help

help

help

help

help

help

help

help

help

help

help

help

help

help

please help

कुल तरीकों की संख्या जिसमें छह व्यक्ति 4 कुर्सियों पर बैठ सकते हैं

[tranquil vault]

360

[torn jolt]

how

[tranquil vault]

6P4

if you care about order

[north echo]

6 choose 4

[tranquil vault]

6C4 if you don't

6C4 is 15

so 15 if you don't care about order

360 if you do

[torn jolt]

the 1rd person has 4 choice nd the 2rd has 3 choice nd the 3rd has 2 choice and 1st person only 1

so why not ans 432*1

[tranquil vault]

put a \ before every * for discord to ignore it

[torn jolt]

4 * 3 * 2 * 1

ok i don't know sorry

[pine badger]

It wouldn't be 4 factorial because there are six people

[tranquil vault]

yea

[torn jolt]

why my logic wrong but

[pine badger]

If there were 4 people and 4 chairs there would be 4! different combinations

[tranquil vault]

you have six people, and the first four can choose and the last two don't. so theres different possible combinations of who chooses and who doesn't

6C4 and 6P4 acount for these extra combinations

[torn jolt]

oh ty a lot

rip u also ty

[tranquil vault]

no problem

[torn jolt]

now u can close this

[robust slate]

.close

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[harsh elk]

help?

[wide sundial]

What are some characteristics of a quadratic being negative

You’re not the OP

You’re not the OP, and even if it was correct I want to help the OP understand how one could get to that conclusion

Alright, I didn’t know

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[harsh elk]

no

how is this wrong

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[harsh elk]

how is this wrong

[wide sundial]

The inequalities

[simple totem]

what happens if you plug in -6

[wide sundial]

x < -7 or x < -5 just means x < -5

[harsh elk]

this is

a

negative

so downward parabola

[simple totem]

ok

[harsh elk]

so the vertex is greater

[wide sundial]

Look at this

[simple totem]

did you read what i said

[harsh elk]

so this is a 2 piece

graph

[harsh elk]

ohh yea

so what do i do?

[wide sundial]

Why did you answer with x < -7 or x < -5

[harsh elk]

idk

im confused with this

this is a 2 piece

inequality

[wide sundial]

Guessing is never the way to go in maths

[harsh elk]

u right

[wide sundial]

So you know it’s a downwards parabola

[harsh elk]

wait

it cant be -6

so it cant be x>-5

damn

[wide sundial]

Which means the negative zones should be x< something or x > something

[harsh elk]

but it cant be -5

[wide sundial]

What happens at -5

[harsh elk]

it becomes -6

which cant be true

because -6 is an inc

not dec

[full forum]

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[cedar monolith]

yo

[cedar monolith]

f continuous

g(x)=f(x)-x

is it obvious that g(x)=0 has at least one root?

is that even true

[simple totem]

not necessarily

[cedar monolith]

so i did'nt understand the assignment

[cedar monolith]

when is this true?

[simple totem]

what would it mean for g(x) to have a root?

[cedar monolith]

g(x)=0

[simple totem]

plug in the definition of g(x) in there

[cedar monolith]

g(x)=f(x)-x=0

[simple totem]

move the x over

[cedar monolith]

f(x)=x

[simple totem]

that’s a necessary and sufficient condition for g(x) to have a root

f(x) = x for some x

[cedar monolith]

and is that true for every f on that interval when f continuous

it doesnt sound right

[simple totem]

no

[cedar monolith]

f(x)=2 is continuous

yeah

[simple totem]

oh

yes it is

[cedar monolith]

so why am i asked to prove this

[simple totem]

it may not be obvious but it is actually true

[simple totem]

it is true

g(x) has at least one root

[cedar monolith]

ok

[cedar monolith]

so a<= g(x) <= b

[simple totem]

not necessarily

[cedar monolith]

oh wait ye

srry

[cedar monolith]

where do i start

[simple totem]

have you proved the intermediate value theorem?

[cedar monolith]

yes

[simple totem]

that’s your first hint. use IVT

[cedar monolith]

i need to find a value where g(x) is negative and positive, a-b <= f(x)-x <= b - a

so a-b neg and b-a positive so it's like that?

@simple totem

[simple totem]

let’s take a step back

we want to show g(x) is positive at one point and negative at another

what can you say about g(a)

[cedar monolith]

nothing much?

[simple totem]

well

what can you say about f(x) in general, with regards to a and b

[cedar monolith]

continuous

and bounded by them

[simple totem]

a <= f(x) <= b yes

so specifically

f(a) >= a

and so f(a) - a is what

[cedar monolith]

positive or zero

[simple totem]

yes

so g(a) >= 0

now let’s assume > 0, since if g(a) = 0 we’re done

can you make a similar statement for g(b)?

[cedar monolith]

g(b)<0

[simple totem]

can you explain to me why

[cedar monolith]

it's exacly the same thing as above but the inequality is reverse

so when g(b) is not 0 and g(a) is not 0; they would at least be with opposite sign so there's at least one point where g(x)=0?

[simple totem]

by the IVT yes, but only if g(x) is continuous

is g(x) continuous?

[cedar monolith]

yes

because f(x) is and x

[simple totem]

i will assume you understand why

if so that’s the whole proof

[cedar monolith]

wait no, the difference between two continuous functions is not always continuous

so i was wrong

[simple totem]

it is

the sum of continuous functions is continuous, and -1 * a continuous function is also continuous

[cedar monolith]

but why is 1/(x+1) - 1/(x+2) not continuous then

[simple totem]

they have different domains

[cedar monolith]

ah

so they need to have the same domain

[simple totem]

to talk about the sum of two functions yeah kind of

[cedar monolith]

ok thanks

[cedar monolith]

and this one

f still continuous

and when x different from y that inequality is always true

[simple totem]

what about it

[cedar monolith]

prove that g(x)=0 has exactly one solution

[simple totem]

well what did we just prove above

[cedar monolith]

that it has at least one solution

[simple totem]

so now we just want to show uniqueness

[cedar monolith]

yes

[simple totem]

so assume g(x) = g(y) = 0

maybe it’s worth asking if you know how to show uniqueness

[cedar monolith]

i need to show that g(x)=g(y) implies x=y

[simple totem]

only for g(x)=g(y)=0

[cedar monolith]

yes

so f(x)-x=f(y)-y=0

[simple totem]

mhm

[cedar monolith]

f(x)-f(y)=x-y=0

[simple totem]

so whats the conclusion

[cedar monolith]

x=y

[simple totem]

yes

[cedar monolith]

mmmh

isnt there something weird?

[simple totem]

what’s weird

[cedar monolith]

we just proved that g(x) could have multiple roots in the begining but now we proved that there's only one

[simple totem]

what

when did we prove it could have multiple

[cedar monolith]

without using the statement in the second function

[cedar monolith]

i mean the first question

[simple totem]

let’s go back to this

[cedar monolith]

ok

[simple totem]

this line is actually wrong

f(x) - f(y) = x - y

is correct

but saying this is 0 is not valid yet

[cedar monolith]

true

[simple totem]

but we had a constraint on the function

what was it

[cedar monolith]

here

[simple totem]

so do you see why x = y?

[cedar monolith]

the constraint is not respected if g(x) has 2 roots

[simple totem]

yes

[cedar monolith]

ok thanks

wait, so we should also show that it's not true when g(x) has more than 2 roots

f(x)-f(y)-f(z)=x-y+z

if g(x)=g(y)=g(z)

@simple totem

what is that

no actaully

unecessary sorry

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[severe basin]

Find the difference between the angle of the triangle, one angle lying on the x axis and another on the y axis, whose coordinates are (3,4), (5, 0), (-5, 0).

[severe basin]

there is no angle lying on the y-axis?

[full forum]

@severe basin Has your question been resolved?

[spice orchid]

you are correct there is no angle "lying on the y axis"

[severe basin]

So, is the question wrong?

[topaz valley]

i cant even understand what this question is asking

[teal aurora]

are you sure those are the coordinates

[severe basin]

Yes

[teal aurora]

💀

[topaz valley]

you're gonna need a better question

[severe basin]

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[dry perch]

heyo guys

[dry perch]

i have a quetsion

related to expansion of ln (1+X)

is this applicable to ALL x belonging to R ?

[wise wyvern]

It is not.

[onyx glen]

no, only x ∈ (-1, 1).

[dry perch]

what is the range

oha

[onyx glen]

that's the interval of convergence for 1/(1+x), the derivative of log(1+x)

[dry perch]

i want to ask , how did they find out that ln (1+x) expands to this , same question for sin x cos x
can i do it ?(obviously not)

we can prove that the reverse

[onyx glen]

missing parentheses

you definitely meant ln(1+x) and not ln 1 + x

[dry perch]

that the expansion equals ln(1 +x)

[onyx glen]

missing parentheses

by some accounts, these taylor series are simply the definitions of exp, sin and cos.

they can also be derived relatively easily from the definition of exp as the unique function that satisfies exp' = exp and exp(0) = 1

and of sin and cos which satisfy sin' = cos, cos' = -sin, sin(0) = 0, cos(0) = 1

[dry perch]

oh yes! so we can think of some expansion which satisfies this

[wise wyvern]

You don't have to "think" of it.
You can obtain it using expansion of any arbitrary function f(x)

,w f(x) expansion

[glossy valve]

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[wise wyvern]

The denominators are 0!, 1!, 2!, 3!... And so on if you didn't notice.

[dry perch]

oh so you did use this series tho ... i want to ask what was Prof.Brook Taylor was doing when he discovered this series

like how did he find out about this

[wise wyvern]

I wouldn't know. Probably some heavy analysis based work.

[dry perch]

i just realised something , if any fx can be represented as a sum of its various deriavtive , then wont we be able to integrate any fx ? since we can differntiate everything yet some of the functions are there that literally can NOT be integrated

[wise wyvern]

Every function can NOT be differentiated.

[dry perch]

for example?

[wise wyvern]

|x| at x = 0

That's one.

There's plenty others.

[dry perch]

i know now

thank you

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[smoky shuttle]

i need help with a physics prblem

[smoky shuttle]

typically you would add both the x1 and x2 and y1 and y2 together but for this they subtract y1 by x1 and add x2 by y2

it doesnt make any sense to me

[pure sandal]

assuming that the earth is flat lmao

i would start by drawing it out

[smoky shuttle]

i drew it like 3 times it makes no sense to me

this physics is mind bogglingly hard

[pure sandal]

it’s not physics it’s vectors

!show

[full forum]

Show your work, and if possible, explain where you are stuck.

[smoky shuttle]

Typically it’s x1 + x2 and y1+ y2 but here they’re subtracting opposite signs

[pure sandal]

have you heard of the cosine rule

[smoky shuttle]

No

[pure sandal]

oh

well that is how i would solve it

there must be a way without it though

so you want to use trig to find x1, x2 y1 and y2?

[smoky shuttle]

Yeah that’s what my professor wants us to do

[pure sandal]

ok

do it

[smoky shuttle]

in the textbook the way to solve is much different than the other

here they add both cos and both sin

in the first i showed they subtract x1 and y2 and that confuses me why

[pure sandal]

why have you written x1-y2

[smoky shuttle]

There are the values

[pure sandal]

okay

[smoky shuttle]

any idea

kill me

[onyx charm]

xd

[pure sandal]

oh

to get the distance, use pythag

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[stark geyser]

$$ \lim_{x \to 0} \left( \frac{1}{arctan^2(x)}-\frac{1}{tan^2(x)} \right) $$

[glossy valve]

『Marius』

[stark geyser]

as much as i did is this

excuse my writing

idk what the next step should be or if i even went in the right direction

[nova island]

What class is this for?

[stark geyser]

this was on an exam for getting into computer science idk

12 grade

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[vernal ermine]

Can someone help me solve this

[warm carbon]

hi

[vernal ermine]

,,(x+6)(x+6)

[glossy valve]

Mr.PP

[vernal ermine]

hi

[onyx glen]

what's the question?

,w evaluate (x+6)(x+6) at x = 42069

[glossy valve]

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[wintry fulcrum]

x^2+12x+36

[onyx glen]

!nosols

[full forum]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[onyx glen]

also don't absolve OP of the responsibility to post the full question

[wintry fulcrum]

im simply just solving it 🤷‍♀️

[dark shore]

The rules are simple. Don't solve.

Also, "help me solve this" is not the same as "solve it for me".

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[vernal ermine]

wont it be (x+6)^2

[odd fox]

Ye

[vernal ermine]

so (x+6)^2 is eual to x^2+12x+36?

[onyx glen]

you still haven't told us what the question actually asks of you

like yes sure (x+6)^2 is equal to x^2 + 12x + 36 but you were obviously looking for the value of this expression at x = 42069

[odd fox]

Yes

[vernal ermine]

just find the product

like simplify it

[vernal ermine]

i dont understand how

can someone explain

<@&286206848099549185>

[faint iron]

sub in x = 42069

(42069 + 6)^2

shoudl be answer

[vernal ermine]

the question is just to simplify the expxresion

[onyx glen]

and you are only telling us this now lol

[vernal ermine]

sorry

[dark shore]

That's a product, you have to expand.

[royal pebble]

does anybody know Business Math?

[vernal ermine]

but my question was that how can (x+6)^ = x^2+12x+36

[vernal ermine]

but why

cant you just simplify to (x+6)^2

[dark shore]

Your original question says (x+6) * (x+6), do you know how to multiply?

[dark shore]

That's true, x^2+12+36 is expanding.

[vernal ermine]

multiply x to x and x to 6 and 6 to x and 6 to 6

so x^2 +6x +6x + 36

[dark shore]

yes

[vernal ermine]

=x^2 + 12x + 36

but my question is that it can also be written as

[dark shore]

When you expand it, you're simplifying it.

[vernal ermine]

(x+6)^2

we can write it as that also>

?

[dark shore]

That's also simplified.

[vernal ermine]

so (x+6)^2 = x^2 + 6^2 right

[hot herald]

if you['re starting with
(x+6)(x+6)
the instruction to "simplify" is vague

so (x+6)^2 = x^2 + 6^2 right
np

[dark shore]

no

[hot herald]

$\fdream$

[glossy valve]

ℝamonov

[vernal ermine]

what

g7uys i dont understand

im in 8th

can you pls try to make it a bit more clear

[vernal ermine]

huh

[vernal ermine]

is says find the product but how does that matter

[hot herald]

can you type the exact wording? (word for word)
is it asking you to find the product?

to simplify?

a combination of both?

or something else

[vernal ermine]

what is this

[vernal ermine]

thats write

it says find the prodcuts of the following expressions

but how does it really mattter?

[hot herald]

instructions need to be clear to know what they actually want

the above is freshmans dream

[vernal ermine]

simplification will also get us (x+6)^2
and so will multiplication
which gets us to
(x+6)^2 = x^2 + 6^2

[hot herald]

raising a sum to a power is not the same as summing the powers of the individual terms

[vernal ermine]

oh that law is applicable only to multiplication

[hot herald]

using a simple example with numbers
(1+1)^2 isn't the same as 1^2 + 1^2

[vernal ermine]

so
,,(a+b)^2 is NOT EQUAL TO (a^2+b^2)

but (ab)^2 = a^2b^2

[hot herald]

yes

[vernal ermine]

Omg im such a baka

i forgot simple exponental laws

im so sorry for wasting your time here

[hot herald]

as for expanding
(x+6)(x+6)
apply distributive property or binomial theorem

[vernal ermine]

yes i get that

thanks a million

again sorry

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[dim compass]

Is derivative of f(-x) = -f'(x)?

[dim compass]

By chain rule

[torn jolt]

wouldn't it be
-f'(-x)

f'(g(x))g'(x)

[dim compass]

Oh

What you said makes sense!

Or maybe it doesn't

I'm confused, why would it be this

No I actually realised your correct

👍

[torn jolt]

g(x) = -x

[dim compass]

Yes

So

I want to prove that if f(x) is a even function and is differentiable at x=0 then f'(0)=0

I tried differentiating on both sides of f(x)=f(-x)

It would be f'(x)=-f'(-x)

I think it I solved the actual question now 😀

Thank you @torn jolt

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[jolly bane]

This isn’t school work it’s actually for a game 😂 but I’m just having trouble.

I’m trying to figure out a basic formula to help my life just a little bit

Product takes times to make
How much time until I reach 140

Right now I’m doing one on axes
1 axe takes 21 seconds how much time until 140 axes
But later in I need to do it with bigger sums of time
1 hammer = 2h 10m
I’ve always been bad with time related math but I’m assuming with a formula I can maybe lessen my brain

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[jolly bane]

Bro what

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[balmy sierra]

hello. i need help

[keen olive]

with what part

[balmy sierra]

start from scratch

in finding EA

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[uncut glade]

Can anyone please tell me if i have performed this quick sort correct as i have done one pass and already got the numbers into decending order

[uncut glade]

,rccw

[uncut glade]

<@&286206848099549185>

[peak night]

what to answer

[uncut glade]

i just want to know if that quick sort is right

its to decending order

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@uncut glade Has your question been resolved?

[uncut glade]

<@&286206848099549185>

[hoary zinc]

It's correct

[uncut glade]

Thanks

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[drowsy glen]

Construct the missing vertices of triangle ABC with the hypotenuse ta=ASa, the hypotenuse on side b=AC of length tb and the length cc of side c=AB. If there are more than one such triangle, construct any of the possible solutions.
This is the starting position. You know the lenghts at the top left corner, and yo also know A and As.

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@drowsy glen Has your question been resolved?

[drowsy glen]

Guys?

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@drowsy glen Has your question been resolved?

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@drowsy glen Has your question been resolved?

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[lime blaze]

hi

[lime blaze]

Hi, just quickly I need help with the equation below - idk what ive done wrong

[dusk nest]

it has to be out of 70

[lime blaze]

yes but it wants it simplified, hence I got 22/35

[dusk nest]

oh nvm

i got 1/2

[lime blaze]

how

i did it again and got 7/15

[dusk nest]

well it says piano OR violin so u dont want the middle of the two

so piano i got 8+15 and violin i got 10+2

and put those added together over 70

[lime blaze]

lets try it then

wrong...

dw tho thanks

[dusk nest]

sorry ;-;

[lime blaze]

na na allg wasnt a test so its fine

.close

[full forum]

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[dusk nest]

the answer is 9/14, the numbers confused me lol i didnt read it properly

[full forum]

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[karmic smelt]

https://www.behance.net/gallery/162774625/2022/modules/918498609

[karmic smelt]

What shape is this making? 👀

Looks like a weird distorted donut but I’m sure there’s a proper name to it

[dusky locust]

Torus?

[shrewd hamlet]

That’s the chandelier I saw at the thrift store the other day

You can thank me later

[karmic smelt]

Thanks :)

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[torn jolt]

hi, what 3.12 * 1.5 to significant figures would be?

[torn jolt]

while its 4.68g to be exact

but since we need two significant didgits

[onyx glen]

to significant figures

to how many significant figures?

[torn jolt]

2

it just says that

[onyx glen]

,calc 3.12 * 1.5

[glossy valve]

Result:

4.68

[onyx glen]

ok yeah

so round this to two sig figs

what's the problem

[torn jolt]

4.7?

[torn jolt]

it didnt match the answers that were given on various sites

[onyx glen]

you could have said this at the beginning

[torn jolt]

they are just writing it out as 4.68

[onyx glen]

er wait ok

so you're going to websites and not looking at your teacher's answer key

[torn jolt]

sorry

[onyx glen]

are you sure you are not confusing dp and sf

because you might be

[torn jolt]

there is none to refer to

should i post the original question

If the density of a solution is 3.12 g mL^–1, the mass of 1.5 mL solution in
significant figures is...

[onyx glen]

"in significant figures"?

not "to 2 significant figures"?

[torn jolt]

but isnt that a rule that the number of significant digits in the product is the number of significant digits in the multipicant with the least number of significant figures?

Here’s a reference from my book

[onyx glen]

right ok

so like

by all accounts it would appear that the correct answer to your problem is 4.7, except you went to one or more websites and entered the problem into it and got something else

[torn jolt]

Also, the options are 4.7g, 4680 * 10^(-3)g, 4.680g and 46.80g

Is there a particular difference between the second and third?

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[north beacon]

Hi can anyone help with this:

[blissful vine]

I gotchu bro

[north beacon]

I used:
1/2(r^2)theta = 11
and
2r+r(theta)=4r(theta)

[north beacon]

ty bro 🙏

[blissful vine]

np

gimme a sec

[north beacon]

👍

[blissful vine]

ahh

[hot herald]

did you do anything after that

[blissful vine]

ok

here we go

[north beacon]

tried to solve but didn't really know anything and was all random

[hot herald]

show your full attempt

[north beacon]

2r+r(theta)=4r(theta)

2r/rθ + 1 = 4
2r/rθ = 3
2r = 3rθ

I don't think the math is mathing here tho

[blissful vine]

lemme show u my method

so

if AB = x

4x = 2r + x

right?

[north beacon]

yeah

[blissful vine]

so 3x = 2r

now we solve for x in terms of r

[north beacon]

x=2r/3

[blissful vine]

ok?

[north beacon]

right?

[blissful vine]

yes

wait

hold on

gimme a sec

[hot herald]

from

2r = 3rθ
theta = ?

[blissful vine]

yea

we can use the area = 11

to solve for theta

[hot herald]

easier to solve for theta from the equation you're already working with