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[devout snow]

@next tinsel Has your question been resolved?

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[raven leaf]

heya, what does the set $\mathbb{C}^*$ mean

[woven radish]

Xetrov

[faint zinc]

@raven leaf that's C union ∞

[raven leaf]

oh

extension

[faint zinc]

I.e. the Riemann sphere

[raven leaf]

cheers

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[faint zinc]

@raven leaf it can also mean C - {0}

Depends on context

So be sure to verify

[raven leaf]

.reopen

[devout snow]

✅

[raven leaf]

I need to prove that it's an open subset of C

so presumably it's that then

[faint zinc]

Oh, then yes C - {0} is what you want

[raven leaf]

ok

thanks a lot

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[serene inlet]

Is this correct?

I am so confused because I thought the derivative of a constant is always 0

[stone stump]

well you seem to accept that the derivative of 2x is 2, even though the derivative of 2 is 0

same idea

multiplicative constants are just "ignored" for the purpose of differentiating

[serene inlet]

Won't the a turn into 0 in the first derivative though?

[stone stump]

derivative of number*function = number*derivative of function

[serene inlet]

What about this?

[thin basin]

If a is constant then a' = 0

So you are left with x' • a

[thin basin]

This is correct

[serene inlet]

So the a does become 0 but comes back?

[thin basin]

a' = 0

a can be any number

[devout snow]

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[void knot]

how to disprove the -> direction? ( →👉direction)

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[brave plaza]

I have to prove that if a system of equations has a unique solution in all of Zp, then it has a solution in the integers. So my outline of a prove goes like this, assume that it has no solution in integers, therefore we must get some contradiction say 0=k, where k is non-zero, now taking this equation modulo any prime p that doesnt divide k, we get a contradiction mod p, implying that this system has no solutions in Zp. Im not sure whether this proof is correct for fields, in the proof I assume that the operations done in Z are well defined in Zp, can I assume that?, is this proof valid?

[brave plaza]

I mean that we must get some contradiction trying to solve the matrix of equations using the Gauss elimination algorithm

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[brave plaza]

<@&286206848099549185>

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[lament schooner]

whats the j here

btw this is just F=ma

but idk what the j variable represents

[uncut crow]

[lament schooner]

hiii

[uncut crow]

hiii

[clever frigate]

i think that its just shows you that m*g which represents the weight only exists in the Y axis

because j usually represents the unit vector of the Y axis

[lament schooner]

oh okty

[clever frigate]

np

[lament schooner]

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[heavy current]

[devout snow]

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[restive river]

I do not know where to start, I thought I could use the last few equations sub in others and whatnot but I'm not getting anywhere w it

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@restive river Has your question been resolved?

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[gloomy sonnet]

How would you solve this using factoring

[cloud turret]

Hi

Somone can help me in this exercise

Preferiblemente en español

[crystal obsidian]

cant get perfect squares right?

should factorise by completing square

[gloomy sonnet]

@crystal obsidian

This is where I’m stuck

What’s the gcf in the right side

[crystal obsidian]

did u got it?

i tried writing sin^2x as 1-cos2x/2

[gloomy sonnet]

No not yet 😭😭

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[devout snow]

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[hollow patrol]

Please help me with the next step of this

[hollow patrol]

I am simplifying

[timber pebble]

you have a good start

I'm not sure that you did the last root correctly though

does it maybe help to write it as $\qty( x^{10} y^{15} )^{\frac 14 }$

[woven radish]

jan Niku

[timber pebble]

oh, i guess you did do it correctly

my mistake

I would go a step further, and get everything as either x or y, to some power

even if that power is fraction

so for $\sqrt[4]{x^2 y^3}$, maybe we want to write it like $x^{\frac 12} \cdot y^{\frac 34}$

[woven radish]

jan Niku

[timber pebble]

good on that rewrite?

[hollow patrol]

Oh yeah

[timber pebble]

once you do this, its easier i think

you know the steps through the rest of it?

rearrange, group, rewrite, etc

[hollow patrol]

Okay so we can rewrite it like that because its the same inside the radicand as it is outside?

x^2y^3

[timber pebble]

we can use associativity

which allows us to put parantheses wherever we want

as long as were only talking about multiplication

so something like $\sqrt[3]{x^2 y^4} = \qty( x^2 y^4 ) ^\frac 13 = \qty( x^2) ^\frac 13 \cdot (y^4) ^\frac 13$

[woven radish]

jan Niku

[timber pebble]

you can think about the steps from here as commutativity of multiplication; we can multiply in any order we want, as long as its just multiplication

so $\qty( x^2 ) ^\frac 13$ may become $x^\frac 23$

[woven radish]

jan Niku

[hollow patrol]

Im sorry I'm confused

[timber pebble]

its enough to just recognize properties of exponents

sorry i got too into the underlying stuff

[timber pebble]

do you understand that its legal to do this move

[timber pebble]

the goal is to get to $$y^3 y^\frac 54 x^2 y^3 x^\frac 23 y^\frac 34$

[woven radish]

jan Niku
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[hollow patrol]

well I don't understand why the radicand power changes from 4 to 3

[timber pebble]

from 4 to 3?

I'm not sure I follow

[timber pebble]

my example has 3 yours has 4

im just illustrating the property

[hollow patrol]

oh

okay i didn't know that

[hollow patrol]

ah yes the exponent rules

[timber pebble]

so your goal is to use various rules

[timber pebble]

to get to something like this

just a bunch of x's and y's, alone

raised to some power

then we wanna move all the x's together, and all the y's together

[timber pebble]

and use the product rule, to combine all the exponents together

like $x^3 y^2 x y^\frac 12 = x^3 x y^2 y^\frac 12 = x^{3+1} y^{2+\frac 12} = x^4 y^\frac52$

[woven radish]

jan Niku

[hollow patrol]

oh

isee

okay i think i can figure this out

so the rule you were using is the fractional exponent

to change it from a radical to a fractional exponent

[timber pebble]

yea

since this makes it easier to add

[hollow patrol]

with the one that is

do i use the fractional exponent rule as well

[timber pebble]

yea

so youll have y^1

and then 4th root of y becomes ...

[hollow patrol]

y^1/4

[timber pebble]

so $y^{1} \cdot y^\frac 14$

[woven radish]

jan Niku

[timber pebble]

now you have another root to take care of

[hollow patrol]

y^3

so that would be y^ 3 + 1

[timber pebble]

👀

I'm not sure exactly what youre working on

[hollow patrol]

okay i have a y^3 and a y^1 if i use the product rule

i can combine them and get y^3 + 1?

[timber pebble]

to get y^(3+1), yes

[hollow patrol]

then would i do the product rule again?

[timber pebble]

I'm not sure what youre working on

[hollow patrol]

so y^(3+1) and x^(1/2)y^(1/3)

so it's y^(3+1+1/3)x^(1/3)

[timber pebble]

yea

[hollow patrol]

ty

:3

[timber pebble]

sure

you can use uhhh

well, its a little not friendly to use

i think symbolab has a nice simplification tool

or, desmos, just plotting your answer and question

anyways, np

[hollow patrol]

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[restive river]

bernoulli differential equation, question and my solution is attached but idk where i went wrong

[jade warren]

Strictly doing limit comparison test on this series and unsure how to continue

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[desert surge]

Hello I was wondering if I were to represent $cos(x)=Re(e^{ix})$ and wanted to display a phase shift of +90 degree, all I would have to do is multiply $i*Re(e^{ix})=-sin(x)$

[woven radish]

yoga545

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[upbeat marten]

what am i doing wrong

im the blue

[prime egret]

It’s arccsc not 1/csc

[upbeat marten]

oh gosh

i did NOT wanna begin that

lemme try and gather my notes

[prime egret]

[restive river]

you have to use the identity then i don't think there's any around it

the one on the right looks good

alr cya i need to sleep

good luck

[prime egret]

You can derive it from setting
[\wrb{y=\csc^{-1}(x)==>\csc y=x}]
And go from there

[woven radish]

𓂧 𓅱𓂋𓀮 - 𓈖𓋹

[desert maple]

you struggling with calc ab too? 😭

test tmrw and i dont wanna study :(

[devout snow]

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[upbeat marten]

say swear

say swear

i have a test tommrow

aswell

by chance are you from californioa

[devout snow]

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[desert maple]

nope texas

[desert maple]

oops

.close

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@void knot Has your question been resolved?

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[winged hornet]

map length = actual length/scale
if l = 9.7cm, you take it as cm because the scale is 1cm:2500cm

9.7 = actual/2500
actual = 24250cm = 242.5m

same thing for the breadth
l = 6cm
actual = 6 * 2500 = 15000cm = 150m

answer would be off indeed cause you're multiplying mm with a scale in cm

can't be too off it's a straight line which they have already drawn for you

hm then I think you either measured the line wrong

or

the tb is smoking something

hm the textbook wants it to be 62mm

hm true yea so the tb is on something

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[keen latch]

If all the six digit numbers x1 x2 x3 x4 x5 x6 with 0 < x1 < x2 < x3 < x4 < x5 < x6 are arranged in the increasing order, then the sum of the digits in the 72th number

[junior chasm]

start with x1 = 1

so x2 = 2 etc

[hollow ice]

can you write a formula for how many such numbers are there?

[hollow ice]

why? x2 can be 0

[junior chasm]

it says 0 <x1 <x2

[hollow ice]

Oh...

[dry geyser]

Is there context missing to this post? What 72nd number?

[hollow ice]

72nd smallest number of the set

[dry geyser]

Ah

[devout snow]

@keen latch Has your question been resolved?

[junior chasm]

shit i forgot to continue

[junior chasm]

because it says its in increasing order

so 1 2 _ _ _ _ -> how many choices here? 7C4 = 35 (you have 7 digits left to choose from: {1,2,3,4,5,6,7,8,9} because of the constraint)

then with 1 3 _ _ _ _ , now u have 6 digits left to choose from to 6C4 = 15

continue this till you reach 72nd digit

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[hazy birch]

Hi does anyone know how to solve these four questions?

[hazy birch]

Maybe 79 a. will do. I will try to solve the rest without any help

[devout snow]

@hazy birch Has your question been resolved?

[lilac patio]

you can transform the limit so that it becomes f(x)

[hazy birch]

How can i do that?

I cant apply the quotient rule of limit since the denominator approaches zero right

[lilac patio]

to illustrate a most basic example, if $\lim_{x\to a} \frac{f(x)}{x} = L$ then you could say $\lim_{x\to a} \frac{f(x)}{x} \cdot \lim_{x\to a} x = \lim_{x\to a} (\frac{f(x)}{x} \cdot x) = \lim_{x\to a} f(x)$

[woven radish]

hskthca

[lilac patio]

but you know $\lim_{x\to a} \frac{f(x)}{x} = L$ and $\lim_{x\to a} x = a$ so you would know the value of the final limit

[woven radish]

hskthca

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[thick schooner]

what does angle subtended by a chord on a major arc mean?

[thick schooner]

if EF is the chord then is the triangle it?

[hushed wraith]

The major arc is the bigger arc

[thick schooner]

yes

so what does angle subtended mean

this right?

[hushed wraith]

So ECF is an angle subtended by the chord EF on the major arc

[hushed wraith]

Yes that too

For any point on the major arc

[thick schooner]

Okay

[thick schooner]

while we’re at it

any of this angle will be less than 90 right?

suppose i choose a third point ahead of the black line

[hushed wraith]

Angles subtended on the major arc are all less than 90. Angles subtended on the minor arc are all greater than 90.
Angles subtended on a semicircle are all exactly 90

[hushed wraith]

I suppose

[thick schooner]

so any point on green connecting to EF < 90 degrees?

[thick schooner]

oh, can you prove it?

[hushed wraith]

Yes. The green part can extend to meet E and F and that would still be true

[thick schooner]

right that’s what it looks like

how do we prove it though?

[hushed wraith]

You can

The angle subtended by a chord at the center is twice the angle it subtends on the arc

You can use that fact

[hushed wraith]

Which again is provable

[thick schooner]

Let’s call the center O

Then if EOF = 180 which means blue becomes black then the subtended angle would be half that so 90

[hushed wraith]

Yes

[thick schooner]

since EOF < 180 then the angle subtended on the major half is < 90

[hushed wraith]

Yes

[thick schooner]

okay but what about minor arc

wait i got it

[hushed wraith]

The same theorem applies. Or else it's just 360 minus something

[thick schooner]

hmm actually no i don’t get it

i mean i get arc the major arc > 180 and the minor arc < 180

maybe i’m tired but so what?

[thick schooner]

how does the same theorem apply?

cuz like it’s in reverse

oh i’ve never seen that before lol

the green one

weird

[hushed wraith]

U got it?

[thick schooner]

not with this

[thick schooner]

with this yeah but the green thing is weird

never seen it apply in reverse lol

[devout snow]

@thick schooner Has your question been resolved?

[hushed wraith]

Hey sorry, I'm a bit busy rn. Hopefully somebody else will answer, or I'll answer when I'm back

[thick schooner]

uh okay

[devout snow]

@thick schooner Has your question been resolved?

[small jackal]

What is the question

[devout snow]

@thick schooner Has your question been resolved?

[devout snow]

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[zenith cairn]

\int \frac{4x^2}{4x^2+1}

[zenith cairn]

$\int \frac{4x^2}{4x^2+1}$

[woven radish]

s a g e

[zenith cairn]

can someone help pls

i used u sub of 4x^2

[wary crescent]

4x^2 = 4x^2+1-1

[zenith cairn]

oh

[misty crest]

then split the integral

[zenith cairn]

yea

[wary crescent]

After that it's easy

[zenith cairn]

how do u integrate 1/4x^2 + 1

u need it to be in the form 1/x^2 + a^2

i cant take a factor of 1/4 out

[misty crest]

arctan

[wary crescent]

Let u=2x

[zenith cairn]

oh bro

alr i got it now

ty

.close

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[devout snow]

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[foggy iron]

im not sure how to do this question, so far i found the area of the lawn which is 2x^2

[foggy iron]

.close

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[spare sphinx]

When a f(x) is continuos and is derivable in a interval [a,b] tryng to understand th of rolle,l'agrange and de l'hospital

[supple knot]

do problems and see

[spare sphinx]

You right now i try in case i come back

.close

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[floral blaze]

Show that $( \sqrt{11 + 6\sqrt{2}} = 3 + \sqrt{2} )$
i need help with the first step

[woven radish]

✨StillTyping✨

[supple knot]

did you try squaring both sides

[floral blaze]

no..

[limpid basin]

why in ()

[floral blaze]

ok so im left with 11 plus 6sqrt 2 = 11

[floral blaze]

typo

lol

$\sqrt{11 + 6\sqrt{2}} = 3 + \sqrt{2} $

[supple knot]

the right side looks wrong

[floral blaze]

hm?

[supple knot]

$(3 + \sqrt{2})^2 = 9 + 2 + .... $

pain

[floral blaze]

ohhh

lol

forgot abt that

ty ill do that n ill tell u what i got

woah thats genious

11 plus 6sqrt2 = 11 plus 6sqrt2

eliminate 6sqrt2

11=11

TYY

[floral blaze]

✨

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[devout snow]

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[timid peak]

for e^z you can split it up like e^(x+iy)=e^xe^(iy)=e^x(cosy+isiny)

[timid peak]

but is there a way to split e^(iz)? where its not in the form cos(z)+isin(z)

[wise storm]

you can write z = Re(z) + i Im(z) which is basically the same idea

[timid peak]

I’m trying to graph sinz

I’ll play around with the equations for a bit more

I dont want anyone to tell me the answer, some hints would be nice, but only after I try some ideas

[wise storm]

gotcha sounds good

[timid peak]

yup!

like I want to graph two graphs, one w domain, other w range

so its just a transformation of z=x+iy into sin(z)

I was also thinking maybe I can pick some values of x and it would be the angle to rotate

[wise storm]

yeah that sounds like the right idea

[devout snow]

@timid peak Has your question been resolved?

[wise storm]

you probably already know desmos has complex numbers now. I worked out what the real and imaginary parts of sin(z) would be and graphed them on top of each other, but not graphed like how you're wanting.

but if you drag around the blue point along the x axis you can see that rotation happening, don't look at what I put on the left cause it's spoilers I guess haha

https://www.desmos.com/calculator/8jowfwgcmq

[timid peak]

i dont like the 2i as the denominator... cause then for e^(iz)/2i I can't have an imaginary length of rotation

[timid peak]

ok so I was trying to match the form at the top, where I still have a length/scale of rotation, but the rotation is weird

Im gonna put this other term in the same form and see if I can do smth w that

[timid peak]

ok so my idea is I could try and bring i in to change (cos(x)-isin(x)) into (sin(x)-icos(x) and try and cancel it out or smth

with this

if I could get it in the form sin^2x+cos^2x that would cancel out to be 1

which would be nice

honestly I havae no idea

i keep getting distracted

😂 arhaihuddaidsjsjjj

omg im lost

ahh wait

I can also split sinz in a diff way

[timid peak]

from desmos, the shape makes out to be something like this

[wise storm]

yeah good, those are actually hyperbolas

much like $$e^{ix} = \cos x + i \sin x$$ we also have the similar, $$e^x = \cosh(x) + \sinh(x)$$

[woven radish]

Merosity

[wise storm]

worth noting the first can be thought of as on a unit circle x^2+y^2=1 while the second can be thought of as on a hyperbola x^2-y^2=1

definitely more to say about all thi

but that might help get a better idea of the relationships going on there

[timid peak]

ok im gonna leave and come back

in a bit

[devout snow]

@timid peak Has your question been resolved?

[devout snow]

@timid peak Has your question been resolved?

[timid peak]

ok so I ended up selecting good ranges for this first case, x in (0,pi/2) and x in (-pi/2,0)

Im not sure about the 'distinctive' intervals for hyperbolic trig...

im trying to apply the same method for case 2.

im gonna try to find some graphs lol

I guess I can split into (-inf, 0) and (0, inf)

[timid peak]

wait this is so weird and cool

when z=x, sin(z) will 'bounce' back and forth between -1 and 1

[timid peak]

ok I just realized what I just said is pretty self explanatory

how do you graph it when y in (0, inf) and y in (-inf, 0)?

<@&286206848099549185>

its going to be sin(x)(positive constant)+icos(positive constant)

but Im not sure how to graph it.. I know its going to be ellipses..

oh so just e^(ix) where angle rotates counter clockwise

and I guess its stretched by some constant

wait no

e^(ix) is cosx+isin(x)

[supple knot]

Can you summarize what your question is

[timid peak]

ok in a bit!

ok, so for the 2nd case, where I have z=x+iy, x in all reals, and y is a specific value, I want to graph the portions where y <0 and y>0

thought that it would rotate counterclockwise because it was in the form cos(x)+isin(x), but I read it wrong, its in the form sin(x)+icos(x)

so Im not sure how I should graph the ellipse

[timid peak]

ok I’m gonna sleep soon

ill wait for a bit

but i’ll close the chat soon

okkk

byeeeeee

.close

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[devout snow]

Please don't occupy multiple help channels.

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[devout snow]

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[junior whale]

Hi, I just have a quick question regards finite automata conversion. I'm converting an epsilon NFA to an NFA, and I noticed that some of the original states are no longer reachable. Is it fine to remove those unused states when defining the new machine?

[devout snow]

@junior whale Has your question been resolved?

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@junior whale Has your question been resolved?

[devout snow]

@junior whale Has your question been resolved?

[dry geyser]

Could you post exactly what you’ve done?

[devout snow]

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[junior whale]

.reopen

[devout snow]

✅

[junior whale]

sure

Epsilon NFA (Old machine)

NFA (New machine)

As you can see, states 2 and 3 is not reachable in the new machine.

[junior whale]

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[lethal shard]

helb

[lethal shard]

I need to derive this function

I used the power rule

but when simplifing i seem to be doing something wrong

[delicate fossil]

you need to use product rule too

[lethal shard]

simplifying*

The product rule?

[delicate fossil]

yes

[lethal shard]

I am not really sure of the names of the rules but after deriving everything I reached

(2x^4-6x^2+3x) + (3x^4)

[delicate fossil]

show your work

[lethal shard]

Alright one sec

Discord isn't really helping me rn

its loading

[delicate fossil]

okay

[delicate fossil]

Do you know this formula/rule?

$\frac{\mathrm{d}}{\dd{x}}\left(f(x)g(x)\right)=\frac{\mathrm{d}}{\dd{x}}f(x)\cdot g(x)+f(x)\cdot\frac{\mathrm{d}}{\dd{x}}g(x)$

[woven radish]

@delicate fossil

[lethal shard]

whaaa

I don't think i do

[delicate fossil]

why did you add f(x) to itself?

[lethal shard]

hmm

I think I understand what has went wrong with my solving

[delicate fossil]

u have two things multiplied

[delicate fossil]

to differentiate this you have to do this

[lethal shard]

yeah

After I differentiate both of them I just leave them like this?

[delicate fossil]

noo

[lethal shard]

🤦

[delicate fossil]

okay you don't know the product rule

soo

lets do a simpler version

$\frac{\dd{}}{\dd{x}}x(x+1)$

[snow raptor]

would be better if you just multiply

[delicate fossil]

oh

lol

true

[snow raptor]

if there was (x+3)^4 * (2x-5)^8 smth like that

you could use product rule

[delicate fossil]

,w simplify (x^2+3)(x^3-3x+1)

[woven radish]

Results provided by WolframAlpha

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

Requested by shr1han

[delicate fossil]

the first one here is something you can derive

usng power rules

[devout snow]

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[devout snow]

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[foggy iron]

Im not sure how to not make the denominator a surd for this question

[foggy iron]

so far i've solved it until this point

but im not sure how to make the denominator not to be surd

[delicate fossil]

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

[woven radish]

@delicate fossil

[foggy iron]

ohh

[foggy iron]

so is p = x-y and q = 6x-3/2?

[cinder nova]

yup

[foggy iron]

tysm!

.close

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[lost laurel]

Let $V= \R^2$ and $W_1 = {(a_1,0) : a_1 \in \R}$. Give. examples of two different subspaces $W_2$ and $W_2'$ such that $V = W_1 \oplus W_2$ and $V=W_1 \oplus W_2'$

[woven radish]

A dense set

[lost laurel]

$W_2={(0,a_2) \mid a_2 \in \R}$

[woven radish]

A dense set

[lost laurel]

$W_2'={(0,a^3) \mid a_2 \in \R}$

[woven radish]

A dense set

[lost laurel]

This better?

Hmm

${W_2' = {(x,y) \mid x=y , x,y \in \R}$

[woven radish]

A dense set

[lost laurel]

[vocal cypress]

why dont you just write it as (y,y) or smth?

[upper schooner]

(hence the additional sadcatthumbsup!)

[lost laurel]

Me likes overcomplicating stuff

Thanks!

.close

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[dull kiln]

please help! Wtf am I doing!

[restive river]

,rotate

[restive river]

,rotate

[fossil locust]

you have $y = a \cdot b^x$

[woven radish]

south's secret twin brother

[fossil locust]

now sub in those (x, y) in and you get two equations

note also that $\ln y = \ln a + b \ln x$ so you get simultaneous equations in $\ln y, \ln x$

[woven radish]

south's secret twin brother

[dull kiln]

give me a second to comprehend thay

ok

@fossil locust ?

[fossil locust]

cool that's correct

[dull kiln]

how do i turn these into the function

[fossil locust]

ah then I overthought it

$\frac{54}{3} = \frac{ab^6}{ab^4}$

[woven radish]

south's secret twin brother

[fossil locust]

gives you b^2 directly

[dull kiln]

18 = ab^2?

wait no

18 = b^2

[fossil locust]

yep!

actually for exponential functions we need b > 0 by definition
there are problems when you raise negative numbers to non-integer powers: you get complex numbers

and then sub in b into 3 = ab^4, to find a

[dull kiln]

would it change the fact that v= square root 18

b8

B****

b is square root of 18

[fossil locust]

yeah so we can't have -sqrt(18) is what I mean

b = sqrt(18) only

[dull kiln]

oki see

then i plyg in

54 = a(4.2426^6)

[fossil locust]

cool

[dull kiln]

but i feel like this is wrong

[fossil locust]

yeah alternative since b^2 = 18, (b^2)^2 = b^4 = 18^2

[dull kiln]

this answer gives me .009259….. and i do bot think this is correct

[fossil locust]

,calc 3/18^2

[woven radish]

Result:

0.0092592592592593

[dull kiln]

oh

the equation just looks very long

[fossil locust]

,calc 54/4.2426^6

[woven radish]

Result:

0.009259792057475

[dull kiln]

y= .0093(4.2426)^x

[fossil locust]

https://www.desmos.com/calculator/c5dyxf7vlq

[fossil locust]

well welcome to maths where the answers aren't neat

[dull kiln]

LOL

ok i see

thank you much for your gelp 😁

[fossil locust]

stupid textbook authors like to make sure their answers are always fractions or whole numbers (rational numbers)

[dull kiln]

yes im used to seeing those nice numbers

[fossil locust]

so like how to check your answer is right is by making a sketch, or use Desmos to graph

or making sure your answer makes sense in a ballpark way

so if we have a > 3 that must be wrong

cause y = ab^x: if you put in x = 0, you get y = a and the function is increasing

so if a = 3, we would have f(0) = 3 and that's off

[devout snow]

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[feral bobcat]

shouldnt it be - inf , -3/7

why onyl -3/7

[supple knot]

what even is the question

[acoustic leaf]

note it says that a quantity in absolute value is less than or equal to 0

[twin thunder]

use definition of absolute value function and solve

[feral bobcat]

it should be 0< 7x+3 < 0

right?

oh i think i get it

but why they didnt use []

[twin thunder]

cuz there is only one value

[knotty sage]

the brackets are used for interval notations like
[1,3) means from 1 to 3 including 1
but because we have 1 element in our set we can’t express it as an interval between 2 values

[twin thunder]

and that is used for intervals

[restive river]

guys can you help me Im doing the junior math challenge

[twin thunder]

open your own channel

[restive river]

ok

[twin thunder]

on the math help available channels

[restive river]

how

[twin thunder]

#help-16

[devout snow]

@feral bobcat Has your question been resolved?

[devout snow]

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[plush grail]

im supposed to use cylinderical coordinates here

how am i supposed to know that

and how am i supposed to know the bounds of each integral

well mainly the first one

[devout snow]

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[strange dune]

i return

[strange dune]

i figured out a)

i need help with b) decide the possibilites of X being an odd number

im confused

is it the value of 5,15 and 25 then? so it would be what 3/5 or 60%?

[stable wraith]

ja

[strange dune]

ah alr

good good

on esec i need help with another one

jeg forstår ikke b

C:

[stable wraith]

a eller b

[strange dune]

b

[stable wraith]

what have you tried

[strange dune]

Well i tried adding it all together so like -10* 0,5+2* 0,25+10* 0,15...

but idk the numbers didnt make sense

so i dont rlly know what to do

i did an earlier task that was kinda similar

but yeah idunno

[stable wraith]

its a good start

you will just have to set up an equation

[strange dune]

oh so like

(−10) * 0.5+2 * 0.25+10 * 0.15+x * 0.10 =4?

wait so that gives:
-5+0.5+1.5+0.10x=4

but

1.5+0.10x=4
-4+1.6=x

so its -2.4?

or is it x=4-1.6=2.4

[devout snow]

@strange dune Has your question been resolved?

[devout snow]

@strange dune Has your question been resolved?

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[versed island]

i just cant solve this lol...someone told me the way to solve it on this server but that didnt help...can any of u pls try this

[devout snow]

@versed island Has your question been resolved?

[versed island]

<@&286206848099549185>

[heavy swift]

something like that i suppose...

what do you think?

[versed island]

hmm i tried this but by this i am getting 1as my answer which isnt exactly the case i dont know ?

ig this is what i wrote similar to what u suggested ... sorry for my handwriting

basically what the prob is by using this we are getting f(X) = 1 which if true doesnt meet the initial constraint

here is what i mean

[devout snow]

@versed island Has your question been resolved?

[devout snow]

@versed island Has your question been resolved?

[versed island]

.close

[devout snow]

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[restive river]

Hello! is this channel available?

[trail eagle]

If you write in a channel with the green message above (available) , it'll claim it as your own.

So you're good

[restive river]

Okay! i have a question

its algebra 2

functions

[restive river]

huh

well

look

i have to find the range of this and i have NO idea how to ive alreagy gotten it wrong

<@&286206848099549185>

[bright cliff]

is range like domain for Y?, if so then should be [1,-infinity

[restive river]

yes

[lament thicket]

Should be y ≤ 1

Sorry

1

[bright cliff]

is range the same as codomain?

[restive river]

no its still wrong

[lament thicket]

Well because you put 1, inf

1 is your y not your x

-inf, 1

[restive river]

THANK YOU SO MUCH

i have an idea on how to do the rest of the problems!

[lament thicket]

Yes yes of course

[restive river]

i lack math skills are you helped me alot

bye bye!

.close

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[vivid estuary]

where does the highlighted part come from

[vivid estuary]

I've never seen that and they listed like it was common knowledge without showing why we can say that

or if someone knows a source that can explain it for me

not sure what this trick is called

[dense jay]

the good old adding 0

adding (a-a)

[vivid estuary]

oh it is

😭

didnt even see that

I thought it was some magical formula that they derived from something

thanks for the help

[devout snow]

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[wheat river]

Can somebody check this because the x coords don’t correlate

Please I’m desperate

[near stone]

hi again :)

[wheat river]

Wdym again 😭

[near stone]

I'm getting confused on which question are you referring to

[near stone]

different server

[wheat river]

Homework help?

prob that one

[near stone]

you asked for transformation rules cheat sheet

[wheat river]

YOOO Ontarionian

[near stone]

yeah

[wheat river]

uh the g(x)

I plugged a point on the graph into a but when I go to check it it doesn’t work

[near stone]

this step is wrong

[wheat river]

I got square root four which I just made 2

a

[near stone]

ah right

I checked

does the question asking you to find the a?

from what I can see it looks correct

[wheat river]

she said only a values finding equation from graphs questions will be on test

[near stone]

yeah so a

[wheat river]

same but when I plug into my calc it spits out a diff values

I’ll show u

[near stone]

also show the full original of the question

[wheat river]

Oh kk

[near stone]

was it a blank graph?

or has points

[wheat river]

I graphed parent function but g of x was already there

[near stone]

it looks like you drew it

!occupied

[devout snow]

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).

[wheat river]

Ohhh second last line I did -2 + 8 but kept it 8

it should’ve been @=3

A equal 3 I think

[near stone]

ye also stop using someone's channel

[wheat river]

Let me plug it in

[near stone]

open your own

[near stone]

the question a is asking you find the equation but I don't see any original given from there

[wheat river]

IT WORKS

Let’s go

[near stone]

#❓how-to-get-help pics helps at least

[wheat river]

wdym? The original would be sqrt parent function

[near stone]

I know

but where are you getting the points

[wheat river]

Ohhh

looking at g of x

I plugged a point that would be a perfect square for x+7

[near stone]

not sure where are you getting this from

was this already given or did you drew both?

[wheat river]

Look at( -3,8) g(x)

I used that

[wheat river]

Parent drawn g of x given

[near stone]

I know what parent of sqrt is

[wheat river]

The line on g of x going the other way is smtg else de about that

[near stone]

but I assume you're making an equation on your own

[near stone]

gimme a sec

and answer me

[wheat river]

Yeah I am

I’m using the y = a f k(x-d)^2 + c formula

Not formula but that thingy

[near stone]

which one was already given?

[wheat river]

Red line

[near stone]

okay

[wheat river]

The thingy on the back is useless it was only for y axis reflection

[near stone]

the blue function is the parent of sqrt

[wheat river]

Yeah

[near stone]

so you want only to write equation of red

[wheat river]

Yeah

[near stone]

did you check desmos

or wolfram

make sure it looks correct

[wheat river]

Yeah it looks the same with same points and stuff

[near stone]

great you got it

for part a

let's look for part b

and c

it is only domain and range but your work looks correct

[wheat river]

Wait question 10?

oh Yeah

I got that part correct I think

[near stone]

is there another part

[wheat river]

Nope that’s it

[near stone]

then you're good

but from what I can see again that the red line looks a parabola not a sqrt

I believe it is a typo of drawing

[wheat river]

Maybe but I spent way to long on this question so I’m done 😭

[near stone]

no worries

do .close if you are done

[wheat river]

.close

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[blissful gorge]

can someone explain why this is incorrect?

[misty crest]

well what did you do to find it

[blissful gorge]

synthetic division

[misty crest]

use long division

i’m pretty sure synthetic division fails here

it has to be of the form x-k

[blissful gorge]

we havent done long divison for about a year, plus its not what the teacher reccomends

i could try but then i gotta look it up

[misty crest]

it’s essentially the same process?

[blissful gorge]

is it

i am unsure as i said its been a while

[misty crest]

watch a short khan academy video it’ll come back quick

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[hot quiver]

Would this be a good proof? Or should I be adding more stuff like a sentence or something

i haven't really done proofs before

[torn bane]

yeah that's probably sufficient

it's pretty much a direct computation

[hot quiver]

ok bet thank you

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[pearl fractal]

could someone explain the reasoning behind this?'

[supple knot]

Just the definition of derivative

[pearl fractal]

ohh nvm

ty

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[sick basin]

Hi. p1 = 0.8, p2 = 0.7, p3 = 0.9

P(A) = 1 - q1q2q3 = 1 - 0.2 * 0.3 * 0.1 = 0.994

that way we found probability of any event happening. What formula do i need to use to know the probability of 1 event, 2 or 3 events? I have that one:

P1=p1⋅q2⋅q3+q1⋅p2⋅q3+q1⋅q2⋅p3
P2=p1⋅p2⋅q3+p1⋅q2⋅p3+q1⋅p2⋅p3

but its a bit crazy, what if i have a lot of events? No way ppl use that, is there other formulas? (sry if stpd)

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[uncut crow]

[thick schooner]

AB + BM > AM and AC + MC > AM

[thick schooner]

hi lol

thus 2AM < AB + AC + BM + CM = AB + AC + BC

hmmm

what next?

here's the triangle

oh it's just AM + MB > AB and AM + MC > AC

so 2AM + BC > AB + AC and hence AM > (AB + AC - BC)/2

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[tacit sparrow]

How todo 7 and 8

[devout snow]

@tacit sparrow Has your question been resolved?

[tacit sparrow]

?

can someone help

<@&286206848099549185>

[twilit shale]

hello

[tacit sparrow]

hey can I get help with 7-8

How to find domain?

[winged oracle]

@tacit sparrow

[winter torrent]

we don't need you to post output from chatgpt here, and it is against the rules of the server. doing so again will see you ejected.

[tacit sparrow]

yes

[tacit sparrow]

😦

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[viscid kettle]

Point e

Need to simplify

Dont know how to

Anticipated thanks )

[dapper fable]

I feel like It should be cube root of b^2 but I’m not sure

[devout snow]

@viscid kettle Has your question been resolved?

[viscid kettle]

So if without that which rezult u get

I will compare it with the book response

[dapper fable]

if this just factorize the denominator using a^3 + b^3

[viscid kettle]

So which rezult u get ?

I will just compare it to the book rezult and then i will start digging in the procces of rezolving

[devout snow]

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[spark hound]

Am I tweaking

How is 4(1/2) not 2?

Is it just cause it has a percentage that we read it as a 4.5?

[visual hazel]

usually if it doesnt have brackets its read as 4 and one half

[dapper fable]

I think that’s a fraction

[spark hound]

Dayum

All my life I just been reading it as 4(1/2)

...

Explains alot

Thanks guy

Guys

.solved

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[mild bronze]

how'd you do that

[rare merlin]

left * 4/4 right * x/x

[mild bronze]

so 2 * 4 = x * 3?

@rare merlin

@rare merlin

@rare merlin

[rare merlin]

2+3x/4 = 0

[mild bronze]

so its at the end 2 2/3?

@rare merlin

@rare merlin

answer

<@&286206848099549185>

EEEEEEEEEE.

[restive river]

Hi I suppose you’re trying to solve for x?

[mild bronze]

RAAAAAARRRRRWWWW.

[mild bronze]

YES!!!!!!!!

[restive river]

You should

1. Subtract 3/4 from both sides
2. Multiply each side with x
3. Divide each side with -3/4

you should have isolated x if you do these things

[mild bronze]

is it 2 2/3