help-10

[frigid hawk]

h=3? I'm confused

[robust raven]

h — высота равностороннего треугольника в основании этой пирамиды.

$h=\frac{a\sqrt{3}}{2}$

[warm shale]

Joanna Angel

[robust raven]

$h=\frac{4\sqrt{3}\cdot \sqrt{3}}{2}=6$

[warm shale]

Joanna Angel

[robust raven]

$MO^{2}+BO^{2}=BM^{2}$

[warm shale]

Joanna Angel

[robust raven]

$3^{2}+\left( \frac{2}{3}h \right)^{2}=BM^{2}$

[warm shale]

Joanna Angel

[robust raven]

plz read what i wrote for you,

[frigid hawk]

I understand that this needs to be solved using the Pythagorean theorem, which means MO + OB = BM. We know that MO equals 3, now we need to find OB. I'm not entirely sure how to find it; is it through the height, and what formula is needed for that?

thanks

[warm shale]

Besym

[robust raven]

is a regular tetrahedron

it is true

[warm shale]

Besym

[robust raven]

it is a regular tetrahedron, then the projection from the height to the base is the center of the circumscribed circle

[frigid hawk]

I don’t understand anything what to do next

[robust raven]

it is written in russian language

a is perpendicualr

[frigid hawk]

what should I do

10

in ukrainian school

MB= 12 + ??

[warm shale]

Besym

[frigid hawk]

Thank you very much for your help

do you want to help with one more task... it’s probably easier…?

yupiii thanks

one min

For a rectangular parallelepiped ABCDA1B1C1D1, a plane is drawn through segment DC1 and point B. Calculate BD^2 + DC^2 + BC^2 if a, b, c are the dimensions of the parallelepiped, with a = 3 cm, b = 4 cm, and c = 7 cm

ok

How is that

??

Yes, in a rectangular parallelepiped, each face is a rectangle. The term "rectangular parallelepiped" itself indicates that the six faces of the solid are parallelograms (specifically rectangles), and each pair of opposite faces are parallel.

yupiiii thank you very much

What do you think about this task?

oh really, thanks, the south doubted, thought 60

.close

[obtuse pebble]

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[white idol]

In a triangle ABC m<C is 36 degrees, m<B is 96 degrees, N and E are points in AC so that they are equal (AN=NE) M is midpoint of BC and CE=AB, what is m<MNC

[obtuse pebble]

@white idol Has your question been resolved?

[red ice]

have you tried drawing the diagram out?

[white idol]

yep

should be something like this

which, tbh I don't see anything other than drawing an isosceles by BC or try to draw a height from BN

[deep summit]

Proof of the absence of a limit sequence cos^2(n) via Cauchy negation

will you help me?

[red ice]

pls don't ask here

someone is still asking their question

[obtuse pebble]

@white idol Has your question been resolved?

[red ice]

https://math.stackexchange.com/questions/4814815/in-delta-abc-angle-c-36-circ-and-angle-b-96-circ-what-is/4814836#4814836

btw I brute-forced it using trig and coordinate geometry

couldn't find a better way

[obtuse pebble]

@white idol Has your question been resolved?

[obtuse pebble]

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[honest flicker]

Uhhh am I correct so far and idk how to do the last one

[shut lagoon]

It seems good to me. For the last one think of a formula you might've learned that gives P(A or B) in terms of P(A), P(B) and P(A and B).

[honest flicker]

Yo I didn't watch the videos

I'll watch them later fr🙏

[shut lagoon]

Search up inclusion exclusion principle.

[honest flicker]

Yeah I have no clue what I'm looking at

[shut lagoon]

Right so a naive way would be to say that P(dog or cat) is P(dog) + P(cat).

But this doesn't work. Why does it not work?

[honest flicker]

Cuz like it would euqal more than like

100%

Over

More

[shut lagoon]

Indeed, so you're double counting some people.

Let's think of it in terms of number of people.

If you want the total number of people that have a cat or a dog.

[honest flicker]

Idk not enough info😭 😭

[shut lagoon]

You do.

[honest flicker]

Idk

[shut lagoon]

So let's start with adding them together

We know that's too much

Who are we counting twice?

[honest flicker]

Uhhh the people who have both idk

IDK

[shut lagoon]

Spot on

[honest flicker]

Es

EZ

[shut lagoon]

So then you have to remove those people you double counted from the total

It's the same for probabilities.

$P(A or B) = P(A) + P(B) - P(A and B)$

[warm shale]

Azyrashacorki

[honest flicker]

Uhhh

230

[shut lagoon]

Yeah that would mean that there are 230 people with a cat or a dog, you can find the probability with that.

Or just use the formula above

[honest flicker]

uhhh

23/30

Ty

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[ripe hazel]

need help

[ripe hazel]

having trouble understanding the wording

would the equation be 4x + 2(2x+48) = 360?

[obtuse pebble]

@ripe hazel Has your question been resolved?

[ripe hazel]

<@&286206848099549185>

tf??

<@&286206848099549185>

[fresh copper]

@ripe hazel wait

[ripe hazel]

ok

[fresh copper]

do u know

the properties of an equilateral hexagon?

[ripe hazel]

ext. angles add up to 360, int. angles add up to 720

my question is with the wording tho

is it 4x + 2(x+48)?

[fresh copper]

yeah i think so

[fresh copper]

this equals 360

[ripe hazel]

yes

[fresh copper]

x = 44

then

but it cant be

[ripe hazel]

oh wait

[fresh copper]

because

its equilatreal

and therefore all exterior angles must be 60

which means ur problem is wrong

[ripe hazel]

yea this wasnt it either

[fresh copper]

and that it means its not an equalteral hexagon

so you can only assume

[ripe hazel]

i think its 4x + 2(x+48) + 2(x + 48)

[fresh copper]

44, 44, 44, 44, 92, 92

[ripe hazel]

this didnt work

[fresh copper]

then its this

21, 21, 21, 21, 138, 138

no

this is so wrong

[ripe hazel]

this worked

confusing ass problem

[fresh copper]

i have never seen a hexagon with

138 as an

exterior angle

☠️

amyways

.close

nvm

u have to doit

[ripe hazel]

.close

[obtuse pebble]

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[fresh copper]

have a good night

or dya

[ripe hazel]

u2

[obtuse pebble]

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[outer cargo]

halp

[frosty spoke]

are you aware that $\sqrt{7} = 7^{1/2}$?

[warm shale]

Saccharine

[outer cargo]

yes i am

the thing is

i cant put that in this

wait

ill try again

[frosty spoke]

can you simplify $7 \times 7^{1/2}$?

[warm shale]

Saccharine

[outer cargo]

but wouldnt that be 49 sqrt?

OH

OHHHHHHHHH

thank you kind stranger

.close

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[teal turret]

think about this logically first

[quiet plinth]

f(x)=g(x) ?

[teal turret]

how can you position 2 parabolas such that they only touch each other once

not u bro, the micklaren guy owns this channel

[ripe hazel]

their HUH

[quiet plinth]

one would open up the other would open down? im guessing f(x)=g(x), based on this i got 2x^2-14x+14=-k is that right?

idk where to go from there

[teal turret]

hmm

[hollow river]

Oh shit 💀😭

[teal turret]

well draw me a rough sketch of what u mean by opening up and down and how that would look

[hollow river]

I'm sorry Steph

[quiet plinth]

i know that one opens up another opens down since a is negative for one and a is positive for the other

[teal turret]

thats correct, but show me how they would touch

[quiet plinth]

ok 1 sec

Something like this

But only one point touches

Very rough sketch

[teal turret]

yep just flipped

alright lets go from here

[teal turret]

so lets do this first

what u got wasnt entirely correct

try doing it again

[quiet plinth]

so am i right for f(x)=g(x), meaning x^2-6x+14=-x^2-20x-k?

[teal turret]

yes

[quiet plinth]

2x^2+14x+14=-k?

[teal turret]

yes

but bring the k over

[quiet plinth]

2x^2+14x+14+k=0?

[teal turret]

yes

now

do u know what the discriminant is?

[quiet plinth]

oh so just 14^2-4(2)(k)?

[teal turret]

c isnt just k

theres another constant there

[quiet plinth]

14+k?

ohhh

[teal turret]

yes

and using the discriminant, how would we get exactly 1 solution? what must the discriminant be equal to?

[quiet plinth]

0

so i set d to 0

and solve for k

[teal turret]

exactly

once youve done that

put k back into the original equation

and then set f and g equal again and solve

[quiet plinth]

ok gimme a minute

so i got k=10.5

[teal turret]

,w 14^2-4(2)(14+k)= 0

[warm shale]

Results provided by WolframAlpha

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Requested by northsteve

[teal turret]

correct

[teal turret]

now just do this

[quiet plinth]

2x^2+14x+24.5=0?

[teal turret]

yea

[quiet plinth]

when u say solve do you mean use the quadratic formula?

[teal turret]

whatever method you use to find zeroes/roots of quadratic equations

can be quadratic formula

[quiet plinth]

ok 1 min

[quiet plinth]

x= 7.31 and 0.68 ?

but i got k is 10.5 thats enough right?

[teal turret]

lol when im graphing it, its not working out correctly

lemme see

wait it is

lol

[teal turret]

ye

[quiet plinth]

alright great

[quiet plinth]

thanks a lot for the help

have a good one

[obtuse pebble]

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[ancient knot]

How do you make that jump?

[native inlet]

just like they said: comparing coefficients

[ancient knot]

I’m an idiot lmao

Thanks

Have a good day!

[native inlet]

you too boss!

[obtuse pebble]

@ancient knot Has your question been resolved?

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[obsidian scarab]

Need help proving for that a dfa that accepts a binary string who's decimal value is greater than or equal to 6, the minimal number of states is 5.

[obsidian scarab]

This is what I've done so far but I do not know how to proceed: Suppose there exists a DFA D = (Q, Σ, δ,s, F) that accepts L and has fewer than four states. Consider the four strings w0 = ϵ, w1 = 1, w2 = 11, and w3 = 111. By the Pigeonhole Principle, two of these strings reach the same state in D from the initial state. I would like to solve by contradiction/php since I am not allowed to use any other method like myhill nerode.

this refers to part 3 of this specifically

[obtuse pebble]

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[marsh walrus]

You should consider the expansion of k.sin(x+a) anda apply an identity, so you'll get your equalities.

[obtuse pebble]

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[thin stream]

😭

[obtuse pebble]

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[weak tinsel]

can someone just give me an explanation on how this works

[tardy epoch]

https://tutorial.math.lamar.edu/Classes/CalcI/OneSidedLimits.aspx

[weak tinsel]

ok thank you

@tardy epoch

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[deep harness]

i'm having trouble coming up with the descriptions in an eloquent way for 72

[deep harness]

Like for (a) I realize that the graph of g is just the graph of f but the x-coordinate of each point is shifted to the left by 2

but is there a better way to say it?

Is that equivalent to the whole graph being shifted to the left by 2 units?

[empty cypress]

its going to the right, is it not

[deep harness]

is it?

how would it be going to the right

[empty cypress]

https://www.desmos.com/calculator/bserg4gnex

[deep harness]

hmm ok this feels counterintuitive

but i see

i guess i'm just not convinced that this holds when it's a function of 2 variables?

because, for the sake of an example, in 71(a) g is f shifted upwards by 2 units

but i feel like we'd say the same thing if g(x, y) = f(x, y-2)

so is it true that f(x, y) + 2 = f(x, y-2) ?

<@&286206848099549185> not sure if anyone would be able to offer some further elaboration or help

[deep harness]

where is the z direction coming into play?

ok

im not sure what that is supposed to explain

but i don't have anything to graph in 3 dimensions

i don't see how any of this is relevant to my example

[obtuse pebble]

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[obtuse pebble]

@lost ocean Has your question been resolved?

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[maiden cloud]

help with graphing composite functions

[maiden cloud]

no clue on how to even start these

[obtuse pebble]

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[daring cairn]

what's the difference between these symbols and A and B?

[latent walrus]

theyre greek letters

[violet sentinel]

alpha and beta here represent two angles.

[daring cairn]

how would i prove that 2A = cosA^2 - sinA^2

don't rly understand

[latent walrus]

you mean cos(2A)?

[daring cairn]

oh mb yeah

[latent walrus]

take the cos(a+b) formula, and set both a and b to A
then you have cos(A+A)=...=cos(2A)

[obtuse pebble]

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[grand thunder]

i'm stuck on (e)

btw partial A = boundary A

i WTS b A subset eq b b A and b b A subset eq b A

but i'm struggling with the former

[obtuse pebble]

@grand thunder Has your question been resolved?

[final thunder]

Omg it’s gkn1

[grand thunder]

hey

HELP ME

[final thunder]

It’s all in the definition my guy

[grand thunder]

do we apply (d) twice to LHS

[final thunder]

Each neighbourhood contains at least one point in A and one not in A and that

Closure and that

But like

,ti

[warm shale]

The current time for pure1144 is 03:55 AM (GMT) on Mon, 27/11/2023.

[final thunder]

U see

[grand thunder]

but ive sketched a metric space where it looks like (e) doesnt hold

[final thunder]

I gtg sleep

[grand thunder]

OK gn

[grand thunder]

(Pure dont look)

this is A subset X

dark shading = subset A, light shgading = not subset A

solid line = boundary subset A

dotted line = boundary not subset A

[final thunder]

This cannot be the case because the boundary of the set is closed. Del del A cannot contain new points not already in del A because the boundary points of A is already the limit points. In actual topological representation the dots should coincide with the black solid line.

[obtuse pebble]

@grand thunder Has your question been resolved?

[grand thunder]

but i think Del del A could be a proper subset of del A

in some cases

[grand thunder]

.close

[obtuse pebble]

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[modern onyx]

How should i approach this?

[neon eagle]

what have you tried

[modern onyx]

tried breaking up sin and cos

[hollow river]

1-sin²x formula?

[modern onyx]

No

i broke down sin^5 into like sin^4xsin and cos into cos^2xcos

[hollow river]

Then substitution?

Did that work?

[modern onyx]

Oh wait

i made a mistake in my work

mb

[hollow river]

Cheers

[modern onyx]

.close

[obtuse pebble]

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[tough flax]

can someone help me with this question pls

[jagged dirge]

What dont you understand?

[tough flax]

i know that these triangles r isosceles

so angle abc would be (180-x)/2

right?

[jagged dirge]

Try using the info provided in the question to first fill out the known values?

[obtuse pebble]

@tough flax Has your question been resolved?

[tough flax]

then angle bpc would also be (180-x)/2, cuz they r isosceles

angle bcp = 180 - PBC - BPC

BCP = 180 - ((180-x)/2) - ((180-x)/2)

@jagged dirge

[tough flax]

<@&286206848099549185>

[obtuse pebble]

@tough flax Has your question been resolved?

[obtuse pebble]

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[vivid creek]

Am I supposed to limit 3d since a is negative

[glossy basalt]

isn't the bounds for x just -a to a?

[vivid creek]

I’m not sure

Don’t I have to do lim -a = t?

[glossy basalt]

i wonder why would you need to take limit 🤔

[vivid creek]

Isn’t it cus sech can’t take in a negative

[glossy basalt]

sech(x) , x can be negative

[vivid creek]

Oh

So I didn’t even need to do that

Ok thanks

.close

[obtuse pebble]

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[rare sparrow]

hey

[rare sparrow]

can someone help w this

ignore whats written in blue

[runic void]

@rare sparrow

put x=-1 and see if you can get a constant

[rare sparrow]

where

[runic void]

you are trying to figure out A, B, C right?

$x^2+5=A(x+1)(x-2)+B(x-2)+c(x+1)$

[warm shale]

.doc

[runic void]

so put x=-1, first and last term will disappear

$(-1)^2 +5=B(-1-2)$

[rare sparrow]

play

[warm shale]

.doc

[rare sparrow]

that’s all B

?*

[runic void]

what do you get for B?

[rare sparrow]

idk 😭

[runic void]

solve this

you wll get the value for B

[runic void]

notice, we have have an equality, so it should work for all value of x right?

for any x, they should be the same

i just choose x=-1 and found B

[obtuse pebble]

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[obtuse pebble]

@rare sparrow Has your question been resolved?

[obtuse pebble]

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[umbral cave]

could anybody advise if i use the wrong formula? i can’t get the right answer

[obtuse pebble]

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@umbral cave Has your question been resolved?

[umbral cave]

<@&286206848099549185>

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[steel locust]

hello

[steel locust]

can someone tutor me with speed maths and some tricks

[obtuse pebble]

@steel locust Has your question been resolved?

[empty cypress]

this is not a tutor request server, we can help with specific questions

if you dont have one, close (both of) your channels

[tardy epoch]

.close

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[fluid patio]

How can I prove that 1/x is unbounded over the interval (0,infinity) using the definition of a unbounded function.

[shut lagoon]

Right, so you want that for any given value M>0, you can find x such that 1/x > M right?

[fluid patio]

yeah

[shut lagoon]

Can you do a bit of manipulation on that last equation to find some restriction on x?

[fluid patio]

restriction?

[shut lagoon]

Like x < something or x > something.

[fluid patio]

divide bothe sides by 1

so x> 1/M

[shut lagoon]

Hmm

[fluid patio]

something like that

[shut lagoon]

It's almost that, but you have to be careful with the direction of the inequality.

[fluid patio]

x < 1/M

[shut lagoon]

doing 1/ both sides makes it flip in a way

So now, if you pick x such that 0 < x < 1/M, does it work?

[fluid patio]

yeah that makes sense

[shut lagoon]

Good

[fluid patio]

thats it?

[shut lagoon]

Hmm yes. This x exists right because you can always find something between 0 and 1/M.

And then if you put it together, you have 1/x > ...

[fluid patio]

yeahhhhhh

alright

i get it

bye

.close

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@nimble dove Has your question been resolved?

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[formal turtle]

could someone help pls

[obtuse pebble]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

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[tired nacelle]

xRy <=> x<=y

Show anti semantic:
Their is x,y / ∀x, y ∈ IR,((xRy)∧(yRx)) ⇔ ((x ≤ y)∧(y ≤ x)) ⇒
x = y

xRy <=> x <= y
yRx <=> y >= x
=> y = x

[tired nacelle]

True?

[tired nacelle]

I try to do

yRx <=> y <= x
But it's illogical since it's opposite of First one

I can also say directly from first one that y = x but what about yRx?

[obtuse pebble]

@tired nacelle Has your question been resolved?

[tired nacelle]

<@&286206848099549185>

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[pulsar quarry]

can anyone just check this rq

[pulsar quarry]

if this is right

.close

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[cunning skiff]

how do i do 10b

i tried using tan^-1 and stuff but i didn't get the right answer i got stuff like 70° or smth

the answer key says it's 1.89, 5.03

<@&286206848099549185>

i need some explaining

i got the answer but i don get why we have to subtract 360 and 180 from the degree

[obtuse pebble]

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[autumn spear]

When two triangles are congruent do all three triangle congruency criterions need to be meet? (S.S.S, S.A.S, A.S.A). You can also interpret this question as vice-versa logic, take for instance S.S.S, If S.S.S is not met, then, are the triangles not congruent?

[candid rock]

...yes, they are all equivalent

SSS means SAS means ASA means SSS

just because you aren't given SSS doesn't mean it doesn't hold

[autumn spear]

I dont understand

So when two triangles are congruent the three criterions need to be met right?

[candid rock]

yes

[autumn spear]

Ignoring if we have all data

Just as a fact

[candid rock]

one of them being met (for both triangles) means all 3 are met

[autumn spear]

Thank you

[candid rock]

proving one is not met = proving none of them are met

[autumn spear]

.close

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[sour granite]

Without the axiom of choice, does a union of infinitely (uncountably) many countable sets even exist?

[candid rock]

why wouldn't it?

[glacial obsidian]

Yes. A union of a set of sets always exists

[candid rock]

union of uncountably many empty sets

[glacial obsidian]

It is a different axiom

[sour granite]

Each set is countably infinite though

[candid rock]

union of uncountably many copies of N

[sour granite]

and if they're disjoint?

[glacial obsidian]

https://en.wikipedia.org/wiki/Axiom_of_union here it is described

[sour granite]

Ah ok i'll have a look

Cool i think it makes sense, thanks!

So basically for an uncountable set $$S = {A \mid A \text{ are countably infinite and disjoint}}$$ i can assign $B=\bigcup_{A\in S} A$

[warm shale]

π=√g

[glacial obsidian]

Yes

S must be a set, that is important

[obtuse pebble]

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[tidal nymph]

How am i supposed to know AH if i only have these measurements?

[tidal nymph]

yes

BAC and AHC are right triangles

[obtuse pebble]

@tidal nymph Has your question been resolved?

[obtuse pebble]

@tidal nymph Has your question been resolved?

[warped pier]

Let AH be a
Triangle AHC and ABH are similar triangles. Let k be the ratio of the size of AHC and ABH
k(1) = a
k(a) = x
x= a^2
AH = sqrt(x)

Rotate ABH by 90 degrees clockwise and let it rest within AHC

[obtuse pebble]

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[ember frost]

lets say a multiple choice test has 10 questions. each question has 4 options and only one answer is correct. lets say i truly choose the options randomly, whats the chance i get x or more questions correct

[final thunder]

binomeow

[ember frost]

for 10 i can easily see its $(\frac14)^{10}$

but im not sure with anything below 10

[warm shale]

FungusDesu

[wispy wadi]

by doing sums, P(X >= x) = P(X = x) + P(X = x+1)+...
and P(X = k) = (10 choose k)*(1/4)^k * (3/4)^(10-k)

what pure meant by binomeow is to use binomial law

your number of success follows a binomial law of parameters 10 and 1/4

[ember frost]

what is P?

[wispy wadi]

probability of

[ember frost]

my region's notation is different

[wispy wadi]

P(X >= x) is probability of X >= x

[final thunder]

have you done named probability distribution

ie. binomial geometric exponential poissson blah blah

[ember frost]

we dont study distribution

[final thunder]

[ember frost]

for us i believe its for uni or for math honor class

[final thunder]

maybe...

draw a tree diagram

for smaller number of questions, say 3 or 4 and see if you can find a pattern

or just look up binomial distribution on google

[obtuse pebble]

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[worn kelp]

need help with area questions involving polar coordinates

[obtuse pebble]

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@worn kelp Has your question been resolved?

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[wind oar]

heres the problem for reference:

[wind oar]

how do i write "if x > 60, subtract $1,50 from the cost and redo it every 10 people that enter" algebraically

[narrow vault]

some ugly piecewise function involving floor functions

but you do have work arounds that make it better but makes you solve a slightly different problem temporarily

[wind oar]

involving whaat...

i dont think ive gotten that far yet

[narrow vault]

floor function, the concept is simple enough: round everything down to a whole number

so floor(1)=1, floor(1.5)=1, floor(1.999999999)=1, floor(2)=2

what the question probably wants you do is to ignore the whole $1.5/10 people thing and just treat it as “every person past 60 makes the price $0.15 cheaper”

you can even allow for decimal numbers of people and it will still let you figure out the correct answer (however showing this is not the easiest)

[wind oar]

huh ok

seems interesting

ill revamp what i have to fit

so the statement changes to "if x > 60, subtract $0.15 from every extra person that enters"

yes?

if so, how do i put that in algebraic form

[narrow vault]

write an expression with a condition

[wind oar]

well i have an expression

r (revenue) = (30)(x) (x = amount of people)

i just dont know how to put the condition into algebraic form

[narrow vault]

that’s not the correct expression since your price per person isn’t changing

so modify the 30

[wind oar]

hm ok

uh..

hm

r = (30)(x) except when 60 > x, turns into 30-0.15 and keeps adding

[narrow vault]

close enough, but you want to keep track of the number of people above 60. so if x = 61, you’d want 1, right?

so what function f(x) do you want to use such that when x=61, f(x)=1, when x =62, f(x)=2, … etc?

[wind oar]

i got no clue

i dont even know functions really

all i know is that when f(x) equals something it usually means y

in what ive learned

[narrow vault]

eh, y gets used because it saves some ink over f(x), but the idea is much the same

[narrow vault]

your price decreases by 0.15 per person over 60, so algebraically:
price = 30 - 0.15 * (number of attendees over 60), yes?

now try to think how you might express “number of attendees over 60” as an expression”

(to make it easier, you might want to allow it be negative anyway)

[wind oar]

yes

to the first

[obtuse pebble]

@wind oar Has your question been resolved?

[wind oar]

x+60?

i dunno

[narrow vault]

close but not quite
if you kept x = number of attendees, x=61 then x+60=121, not 1 like you would want

[wind oar]

ahm

hmm

x+1 and than add one each time

something like that..

[narrow vault]

if you go back to say 7th grade functions and write

x |y
————
61|1
62|2
63|3
64|4
….

where x = number of attendees and
y = number of attendees over 60

you can probably tell it’s a straight line. now figure out y as an expression

[wind oar]

right

y=x+1

wait no

y=x-60

[narrow vault]

yup, you got there
now continue with the question

[wind oar]

so p = 30-0.15*y=x-60

[narrow vault]

you’ll want to replace y with the expression in terms of x so that you only have 1 unknown

[wind oar]

so you want me to remove y and replace it with x-60?

or is it somethign else im not getting

[narrow vault]

ye just replace

[wind oar]

so p = 30-0.15*x-60-x-60?

[narrow vault]

missing some brackets
also why do you have x-60 twice?

[wind oar]

you said replace y with x-60

no?

[narrow vault]

yes, but didn’t we get
p=30-0.15*(numbers of attendees over 60)

or

p=30-0.15*y

?

[wind oar]

oh wait

aah

i see

so its p=30-0.15*y

but how do you get x..?

[narrow vault]

once you get your r as a function of x you can then try finding the maximum of r

[wind oar]

yeah this is funky

i dont think i can do math anymore now

its 12:16 am

thanks for the help tho @narrow vault

i appreciate it

.close

[obtuse pebble]

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[strong arrow]

So I have the derivative dI/dt = 0.00001SI - 1/14I
And I have that S = S(t), I = I(t). And the original values: S(0) = 45400 and I(0) = 2100.
I have to know the maximum of the original function. So I have to equal the equation above to 0, then integrate the derivative and then plug in the function in the equation that resulted from the integral. However, don't know exactly how can I solve 0 = 0.00001SI-1/14I.

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[shut obsidian]

<@&286206848099549185>

[shut lagoon]

This is geometric, isn't it?

[obtuse pebble]

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[cinder junco]

I need help with this question

[obtuse pebble]

@cinder junco Has your question been resolved?

[cinder junco]

I just don't know how to set it up in terms of cylindrical or spherical

[viscid gull]

Set up in terms of polar

[cinder junco]

Then how does y = x^2 map on to x-z plane in polar?

[viscid gull]

rsin(theta) = r^2cos^2(theta), solve for r

Bound for angle is w/e keeps it in the first octant

[cinder junco]

Thank you

.close

[obtuse pebble]

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[timid silo]

how did we simplify to get rid of x^6 here?

[crystal notch]

The x^6 goes inside the parenthesis, and becomes x^2 since (x^2)^3 = x^6
Then, you simply divide every term

[timid silo]

oh wait right lmao

.close

[obtuse pebble]

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[pulsar charm]

Help with this problem on functions.

[civic briar]

replace x with 1 - x

you'll have linear equations in f(x) and f(1-x)

then solve for f(x)

[pulsar charm]

I didn't get that...

[glossy basalt]

what jewels! mean is that replace all the x's to (1-x)'s in the equation:
2f(x) + f(1-x) = x²
and with the modified equation together with the original one, you can solve for f(x)

[obtuse pebble]

@pulsar charm Has your question been resolved?

[livid glade]

what did you try

oh wait channel in use, use another chanel please

[glossy basalt]

true

[tiny oar]

what chanel i don't understand?

[obtuse pebble]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[iron juniper]

Assume x=1-u
Then 2f(1-u)+f(u)=(1-2u+u²)
f is the same function in any case, so we might as well set u=x
2f(1-x)+f(x)=1-2x+x²

Then solve the two equations

[obtuse pebble]

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[livid glade]

each angle? ,

like thats the whole question?

[unreal minnow]

yeah

do you do cose inverse on -1/1.375

[livid glade]

what "each angle" context of the question?

[unreal minnow]

its asking how many angles can there be where theta is greater than or equal or zero

and less than or equal to 720

given csc=1.375

you can draw a sketch of it though

i think in Q1 and Q4 of the chart

[livid glade]

csc c is 1.375 where is the theta parameter here

can you check if that really is the entirety of the question and this question is not based on a prev question

[unreal minnow]

yeah its separate

[unreal minnow]

the parameter is that theta is greater than or equal or zero

and less than or equal to 720

[livid glade]

is there any relation between c and theta?

the questions feels like something is missing

[obtuse pebble]

@unreal minnow Has your question been resolved?

[obtuse pebble]

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[tribal abyss]

In the opposite figure, a circular disc weighing 4 Newtons resting on a vertical wall and a horizontal ground with the same coefficient of friction was applied to it by a horizontal force tangential to the disc of 15 Newtons until the disc was about to rotate in the direction of the force, so the coefficient of friction = ? (Note that the vertical reaction to the ground is twice the vertical reaction to the wall)

[tribal abyss]

How to solve it

[livid glade]

can you check the question langauge again?

did you translate it or something?

[tribal abyss]

Yeah

[tribal abyss]

What's wrong

[obtuse pebble]

@tribal abyss Has your question been resolved?

[tribal abyss]

<@&286206848099549185>

It's something like that question

[tribal abyss]

I want this question please

[tribal abyss]

<@&286206848099549185>

[obtuse pebble]

@tribal abyss Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[neat rock]

Hi, just a little confused about something basic.

(root2)^2 = 2 because powers cancel out
(roo2)^3 = 2Root2 << im confused about this
(root2)^4 = 4 cuz 2^2

[fossil crag]

(Root2)³ = (root2)² × root2

[neat rock]

oh yeah

haha

[indigo steeple]

Hey

[neat rock]

thanks

[neat rock]

hi

[indigo steeple]

How are you?

[neat rock]

good, you?

(3RootA)(3RootA) = 9a right?

[high lily]

=9A

math is case sensitive

[neat rock]

true

((9A)(3rootA)(A))/3rootA = 27A^(13/6)

apparently

[neat rock]

why do i get 9A^2

huh?

Ohhhh

It’s cuz

It’s cuberoot a

thats confsued me even more

[obtuse pebble]

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[copper tusk]

hello, does someone understand french for help me?

[livid glade]

!da2a

[obtuse pebble]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[polar fossil]

we have some French speakers yeah

[copper tusk]

cuz i do homeschool and i don't have anyone to help me

and i m a kid so

[polar fossil]

ok well est-ce que tu as lu il question?

[copper tusk]

oui je l'ai lu

[polar fossil]

ok so combien de tours tourne il moteur en 3 minutes? combien de tours en 6 minutes?

[copper tusk]

en six minutes il fait 2 fois ce qu'il fesait en 3 min

[polar fossil]

oui

[copper tusk]

oui mais comment on sait combien il fait de tours en 2min30

ah merci j'ai compris

[polar fossil]

well il tourne 3540 tours en 3 minutes oui? et combien en 1 minute?

ah ok

[copper tusk]

désolé j'était pas assez councentrer

[polar fossil]

pas de problème

[obtuse pebble]

@copper tusk Has your question been resolved?

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[random portal]

hey can i get some help with a couple problems

[random portal]

please and thanks to anybody who can help me

and honestly im just looking for somebody to solve at least one of these for me its nearly 2 am and im sleepy

@lyric snow

[obtuse pebble]

@random portal Has your question been resolved?

[obtuse pebble]

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[oak axle]

How do I solve this by divison

[final thunder]

use rational root thm

[obtuse pebble]

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[strange oyster]

Why isn't anyone using something like infinity.number.fractional?
For example ∞+2+0.51=1.(0)2.51, 2*∞+972+0.013=2.(0)972.013, ∞:2+9.5=0.5(0)9.5? I hope you understand what I meant

[obtuse pebble]

@strange oyster Has your question been resolved?

[final thunder]

What?

[copper tusk]

chat gpt

[strange oyster]

∞+2+0.5=1.(0)2.5
1 it's a ∞ and 2 i's 2, 5 it's 0.5

∞+2.5=1.(0)2.5

infinity.normal number.fractional

Exaple ∞ it's 1.0.0

2 it's 0.2.0

And 0.4 it's 0.0.4

If you add it you get 1.(0)2.4

[obtuse pebble]

@strange oyster Has your question been resolved?

[obtuse pebble]

@strange oyster Has your question been resolved?

[kind hawk]

well its not used because its not useful

[strange oyster]

ok

[obtuse pebble]

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[shy hawk]

Hi, can anyone help me with this. I was wondering if it was viable to divide both sides by (1+x^2), because i tried and it gives me a dodgy answers

[fierce vale]

what did u get ?

[shy hawk]

y(1+x^2)=(x+x^3)/3 + c

[obtuse pebble]

@shy hawk Has your question been resolved?

[obtuse pebble]

@shy hawk Has your question been resolved?

[obtuse pebble]

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[astral hound]

how would i solve -3x +3y = 4 and -x + y = 3

[latent walrus]

you dont

[astral hound]

wdym

im not saying for the answer

[latent walrus]

it has no solution

[astral hound]

huh???

run me through it

whats the work

[latent walrus]

multiply the right one by 3

youd end up that somehow 4=9

actually no (i retract this no)

[astral hound]

i need coordinates

[latent walrus]

that 0=5 or 0=-5

[astral hound]

i need to solve by substitution and the answer needs to be coordinates

[latent walrus]

you cant

theres no answer

[astral hound]

alright

[latent walrus]

you can try

but you wont get anything from it

[astral hound]

alright

.close

[obtuse pebble]

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[slate agate]

can someone explain to me exactly what one two and three are supposed to represent in these indices?

[slate agate]

i have no idea what they correspond to

[tardy epoch]

They're the index of the coordinate

1 could be x, 2 could be y, 3 could be z e.g.

[slate agate]

is is just up the me to decide which index stands for x y or z or is there some convention of which i am ignorant?

For example, this is a quantum mechanics problme which works with the spin operators and their commutator relations

im confused as to how the levi civitia is applied here

i understand that s_k must be whicever index is not used (x and z here)

but the ordering of value of i j and k confuse me here

i think i might see it

if x = i = one, y = j = three z = k = two

then the ordering in the levi civtia is one three two, so that's negative one

for this one

if y = i = one, and z = j = two, z = k = three, then our ordering is two three one, so it's a positive one value

no instead i can just assign the same numbers and it works out....because two three one is a positive

if that's the case, then Sx, Sy must be.. one three two negative sz

no

one two three

so positive Sz

ok i figured it out

.close

[obtuse pebble]

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[vagrant kite]

How do I do this

[worn yoke]

i would start by rearranging them into slope-intercept form

[vagrant kite]

Oh yeah your right

Ok ill do that right now thanks

[vagrant kite]

I did that and for the question number 2 the equations I got were:
y = -2x - 7
y = 2x - 4
y = 4x - 5

[worn yoke]

so now we compare the slopes

[vagrant kite]

to find if theyre perpendicular u just see if any of their slopes are negative opposites right

oh ye

so none of them are perpendicular

im not sure how to find if they're parralel though

[worn yoke]

parallel means same slope

[vagrant kite]

ohh

ok thanks so none of them are parallel or perpendicular

ok thanks, I appreciate the help a lot

.close

[obtuse pebble]

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[worn yoke]

looking at this set of equations, i don't think you did the second one right

[obtuse pebble]

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[scenic yacht]

yes

what else is f(t) equal to?

if we want to find doubling time

not exactly

its not 2 * f(t)

but 2 * ?

okay

so we have

f(t) = i * e^rt

where i is the intial amount

we are interested in the doubling time

what is f(t) equal to once its doubled?

okay a better question

whats the intial amount

whats the amount when its doubled

yes

so whats an equation

you can form

and which variable are we solving for

no

read the question

what are we looking to show

yes

no

im asking what variable we are interested in

ignore the equations

we want to show that "doubling time is (ln2)/(r)"

so what variable is that?

yes

but what variable represents that

tell me what each variable is/means

yes

we want to find the doubling time

so what variable is that

doubling time

your variables are

t, i, r

which of the three

yes

so we have

f(t) = i * e^rt
where i is the intial amount

and we want to rewrite it in terms of t

when f(t) also equals 2i

so whats the equation

yes

and solve for t

np

its ok

huh?

yes

$2i = i \cdot e^{rt}$

[warm shale]

Abyss

[scenic yacht]

$2i = i \cdot e^{rt} \arrow 2 = e^{rt} \arrow ...$

yes

yes

okay u did it correct

[obtuse pebble]

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[rotund vector]

Could someone help me out with this?

[rotund vector]

here is my working

[obtuse pebble]

@rotund vector Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[pure epoch]

how do i find this using algebra of limits

wow nvm divide by n

what a fool i am

.close

[obtuse pebble]

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[green echo]

Perimeter of Gray area

Help pls