help-23

[thin bridge]

is not 0

[boreal cypress]

must of entered it

wrong

can u graph

it

,w x^3+5x^2-7x+1

[flat frigate]

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[boreal cypress]

lol

idk how to do this

,w graph x^3+5x^2-7x+1

[flat frigate]

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Click here to refine your query online
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Requested by 69Doug#8205

[boreal cypress]

o.o

-6.00 something

[thin bridge]

after identifying one root,
you can proceed with

polynomial long division to factorise

[boreal cypress]

1/ poly?

lol

what

[thin bridge]

in which case you can approach it with stuff like
rational root theorem
in combination with polynomial/synthetic division
you responded with
i understand both now

[safe radish]

@boreal cypress Has your question been resolved?

[boreal cypress]

alright ramonov

you caught me

i dont know how to solve this

how do i solve it using those two things

[thin bridge]

you caught me
best policy is to not lie about what you do/don't know

did you actually look up polynomial long division

[boreal cypress]

omg

u can do that o.o?

and no i thought i knew them seperately

just not together?

very strange method

we were never taught this lol

isnt it better just to plug in 0

for x

x^3+5x^2-7x+1

into that ^

and hope for the best

[thin bridge]

well plugging in 0 for x gives you the point (0,1),
which helps in graphing

but you'd still want to determine the x-intercept(s)

you should first look up videos on factorising and graphing polynomials

[boreal cypress]

what about polynomial long division

l0l

[thin bridge]

that will come up in good videos

have you actually looked that up yet?

[boreal cypress]

i saw it

and immediately clsoed out

[thin bridge]

are you even searching what I'm recommending

[boreal cypress]

my brain is fried

[thin bridge]

so like I said, go to sleep

[boreal cypress]

and yes i have been

[thin bridge]

I'm not going to enable you anymore.

[boreal cypress]

just didnt roll up sleeves

[thin bridge]

have some rest and back later

with a clear refreshed mind

[boreal cypress]

if i did adderal

id be done with all my hw

in 1 day

id be caught up

on everything l0l

instead this is me

the entire time

https://tenor.com/view/normal-day-lame-tortoise-slow-motion-here-i-come-gif-17090395

pinned it

in a notepad

will review tomrrow

ty

.close

[safe radish]

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[safe radish]

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[tough leaf]

$$u_{n+1} = \frac{n}{2(n+1)} u_{n} + \frac{3(n+2)}{2(n+1)}$$

$$w_{n} = n(3 - u_{n})$$

I have to find the limit of (un) using (wn), i already proved that (un) is increasing and converges to 3.

[flat frigate]

TwisT

[tough leaf]

$$w_{n+1} = (n+1)(3-u_{n+1})$$

[flat frigate]

TwisT

[tough leaf]

$$w_{n+1} = (n+1)(3-(\frac{n}{2(n+1)} u_{n} + \frac{3(n+2)}{2(n+1)}))$$
i'm stuck at this stage

[flat frigate]

TwisT

[snow robin]

you mean as n goes to infinity?

[timid pasture]

How did you prove that un converges to 3, shouldn't it be 3/2 ?

[tough leaf]

yes the limit, it's 3 but i have to prove it using the definition of (wn)

[tough leaf]

Did induction

[timid pasture]

what is u0 or u1 like the starting?

[tough leaf]

u1 = -1

[timid pasture]

ah, my bad. 3 is correct, now you wanna find out the limit for wn?

[tough leaf]

Gotta find the limit of un using wn somehow

[timid pasture]

Oh, so you were supposed to find limit of un using wn

[tough leaf]

exactly

[timid pasture]

why not try wn is terms of un instead of what you did?

[tough leaf]

wdym by that ?

[timid pasture]

$$u_n = \frac{n-1}{2n} u_{n-1} + \frac{3(n+1)}{2n}$$

[flat frigate]

numbpy

[timid pasture]

Then, $$w_{n} = n(3-(\frac{n-1}{2n} u_{n-1} + \frac{3(n+1)}{2n}))$$

[flat frigate]

numbpy

[tough leaf]

still stuck with the un-1

[timid pasture]

Lemme try on my own

[tough leaf]

for sure trying on my own too

[timid pasture]

Well, I got a vague idea

basically this relies on the fact that limit of wn exists ie is finite

So, we calculate 2(wn - wn+1)

this will give an equation in un and un+1, use the original equation to substitute the value of un+1

Things will cancel and simplify a lot

[tough leaf]

how did you come up with that

[timid pasture]

well, I tried to calculate difference of wn and wn+1 cause in the limit both will go to the same number giving a zero

which we can use to equate with un, giving an equation in the limit of un

But then again, this is a weird way to do things

It's much faster to directly find out the limit of un instead of the wn shenanigans

[tough leaf]

i thought about getting the definition of wn with only n and same thing for un

[safe radish]

@tough leaf Has your question been resolved?

[tough leaf]

<@&286206848099549185>

.close

[safe radish]

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[safe radish]

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[buoyant dragon]

Find all possible positive values of the common ratio of a geometric progression consisting of five terms that can be rearranged to form an arithmetic progression.

[buoyant dragon]

anyone?

[lean otter]

is this the full question?

[buoyant dragon]

yes

[lean otter]

okay

let's solve this together : D

[buoyant dragon]

trying for past 20 mins

[lean otter]

what is the general form of gp

[buoyant dragon]

geometric progression

[lean otter]

nah nah I'm asking the general form

[buoyant dragon]

and i know it as i am not a first grader 🙂

[lean otter]

ik the full form of gp lmao

[buoyant dragon]

a, ar, arr, arrr...

[lean otter]

correct

[buoyant dragon]

i trid this out

[flat frigate]

Hack With Techno Boy

[lean otter]

hmmm

give me a second to think this out

[buoyant dragon]

but its giving answer 3

take your time

[fluid carbon]

I can help?

[lean otter]

sure sure

[fluid carbon]

So we need to solve this

[buoyant dragon]

:/ yes

[lean otter]

yup

[buoyant dragon]

my question exercise is just a nightmare ;-;

[lean otter]

ohh wait we need to find all possible terms of the common ratio !!

[buoyant dragon]

all possible positive* terms

[lean otter]

yee got it

[fluid carbon]

r >= 0

[flat frigate]

Hack With Techno Boy

[fluid carbon]

so

[lean otter]

yup

[fluid carbon]

I think when r = 0

And... 1?..no wait

Hm, lets me write it down

[buoyant dragon]

hm

[fluid carbon]

If we make it r = 0, and b1 = 0 then there would be a P.A of r = 0 and first term a1 = 0

so r = 0 is surely a answer

but Not sure if its the only one

[buoyant dragon]

can we take terms a/rr, a/r, a, ar, arr

[fluid carbon]

Wait, doing that will solve nothing

[fluid carbon]

then we will find a r that will decrease and ADD in a P.S

[buoyant dragon]

oh yea there is no product involved lol

[fluid carbon]

Ok ok

[buoyant dragon]

hm then r cant be equal to 0

[fluid carbon]

So we have a P.G

[buoyant dragon]

pg?

[fluid carbon]

Geometric Progression

[buoyant dragon]

gp...

[fluid carbon]

with a , a* r , ar^2 , ar^3, ar^4

[fluid carbon]

or GP yes

and to be a G.A then
ar^2 - ar = ar^3 - ar^2
ar^4 - ar^3 = ar^3 - ar^2

Because ar = a + d
and ar^2 = a + 2*d

so ar^2 - ar = a + 2d - a - d= d

or d as the difference between a1, a2 and a3 and a4 and a5 MUST be the same

so using
ar^2 - ar = ar^3 - ar^2
ar^4 - ar^3 = ar^3 - ar^2

[flat frigate]

Hack With Techno Boy

[fluid carbon]

Yes

[buoyant dragon]

but it is not satisfying 0 as we found earlier

[fluid carbon]

Now* simplify them

[fluid carbon]

Aa wait

[flat frigate]

Hack With Techno Boy

[fluid carbon]

Hm

[buoyant dragon]

again 0 not satisfying ;-;

[fluid carbon]

r(r^2 - 1) = 0

Solve this equation

[buoyant dragon]

+-1,0

[fluid carbon]

Yes and r must be positive so

The answer is r= {0,1}

[buoyant dragon]

but answers are three ;---;

[fluid carbon]

r >= 0 **

[buoyant dragon]

hm then zero eliminated

[fluid carbon]

0 is positive *

[buoyant dragon]

but in answer key it is giving there are three values of r

[fluid carbon]

3?

Maybe ait

[buoyant dragon]

yes

[fluid carbon]

wait*

ar^4 - ar^3 = ar^3 - ar^2
solve this also

[buoyant dragon]

hm wait

cancelled rr from both side

when r not eqal to 0

[flat frigate]

Hack With Techno Boy

[fluid carbon]

? the equation will be equal when r = 0

[buoyant dragon]

ik

[fluid carbon]

Not sure about 2?

[buoyant dragon]

but to solve quadratics we have to remove values where 1/r is not defined

as we divided by r

[fluid carbon]

Hm, 2 surely isnt a solution

[buoyant dragon]

as this we got 4 values

[fluid carbon]

wait what you did there?

[buoyant dragon]

no lol

my bad

[fluid carbon]

Oh ok

so x = {0 , 1 }? and maybe -1

[buoyant dragon]

um

1+sqrt5/2?

.close

[safe radish]

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[coral nimbus]

let's say i have a function $f(x) = Cx(\frac{\sqrt{x}}{3})$, but the value of C is different when x >= 10, how can I calculate the value when x = 15, in that case?

[flat frigate]

sabanigiri

[coral nimbus]

lets say when x < 10, then C = 0.2, otherwise C = 0.15.

[keen comet]

Are you just asking for
$$
f(x) = \begin{cases}C_{1}x^{3/2} & \text{if }x < 10 \ C_{2}x^{3/2} & \text{o.w.} \end{cases}
$$

[coral nimbus]

how would that factor into the equation i have?

[flat frigate]

草w

[coral nimbus]

hmm, not exactly. i want the value to accumulate.. if that makes sense. the curve should be continuous, but the rule just changes at x= 10.

[keen comet]

What is your use case of this question

Is this an assignment or game design

[coral nimbus]

i want the value to continue changing from where it left off of x = 10 from the previous rule.

but now with the new C value.

[keen comet]

If you want the functions such that $\lim_{x \to 10}f(x) = D$, you can't have $C_1 \ne C_2$ while only having a $x^{3/2}$ component

[flat frigate]

草w

[coral nimbus]

hmm, i don't think i am explaining this correctly. my bad.

let me create a desmos to better illustrate.

[keen comet]

Please do, and also please answer this question

[coral nimbus]

also i'm not sure i understand your answer. i'm not familiar with those terms (i'm a math pleb).

[keen comet]

That's fine, I can try to be clearer

I'm just asking first for purpose so you don't XY-problem out later

[coral nimbus]

it's for a prototype of a finance app i am working on, just in ideation phase. the use-case here is kind of complicated to explain, and the example is already super contrived.

[keen comet]

Ok, that's fine

So what you want is a piecewise function, defined on separate pieces. The requirement that the pieces agree on x=10 means they should be continuous at x=10

[coral nimbus]

yeah, that sounds right.

i almost want to shift the second curve up/down so that it aligns at x=10 with the previous fn (which used a different C value), but that process isn't clear to me.

[keen comet]

If both pieces are $Cx(\sqrt{x}/3)$, you can't have the constants be different yet agree at $x=10$

[flat frigate]

草w

[keen comet]

Ok, then this is a different function

[coral nimbus]

hmm, yeah.

yes, it would have to be then.

[keen comet]

I think that would look like
$$
f(x) = \begin{cases}C_{1}x^{3/2} & \text{if }x < 10 \ C_{2}x^{3/2} + C_{3} & \text{o.w.} \end{cases}
$$

[flat frigate]

草w

[keen comet]

I guess one question is how to make $C_3$ a function of $(C_1, C_2)$ to make the function continuous?

[flat frigate]

草w

[coral nimbus]

where did you get x^(3/2) here?

[keen comet]

$x\cdot \sqrt{x} = x^{3/2}$

[flat frigate]

草w

[keen comet]

Will this determine the generic growth of $f(x)$ as $x$ increases for your use case?

[flat frigate]

草w

[safe radish]

@coral nimbus Has your question been resolved?

[keen comet]

If you have something more ping me directly in #discussion

[safe radish]

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[safe radish]

@rugged trench Has your question been resolved?

[safe radish]

@rugged trench Has your question been resolved?

[safe radish]

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[buoyant shadow]

i don't understand what it's even asking

[safe radish]

@rugged trench Has your question been resolved?

[buoyant shadow]

i think you can draw 18 squares if the smalleer dots can't be used

my best guess

[woeful bramble]

count how many 2 by 2

4 by 4

6 by 6

but there is also squares 2sqrt2 by 2sqrt2

and just count all of these

[buoyant shadow]

this can;t be legal because there's 6 of those, so at least 24 total

[woeful bramble]

so i see 9 2by2 squares

4 4by4

1 6by6

4 2sqrt2by2sqrt2

so 18

[buoyant shadow]

yeah same

[woeful bramble]

i think its correct

[safe radish]

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[modern sparrow]

So, geometry. The problem goes as followed:
A parallelogram has an angle which has a cosine of -1/15. The face of the parallelogram is 4sqrt14 and the parameter is 16. Find the sides

[modern sparrow]

I have tried everything and I mean all the formulas I could find

I even created a triangle inside the parallelogram using diagonals

And converting cosine into sine using cosA = sin(90-A)

Nothing worked out for me. Help is much appreciated 🙏

[dusky sky]

im not a native english speaker so im bad english math terms but what is a parameter

[modern sparrow]

(a+b)2

The sum of the sides

[dusky sky]

oh ok

so a+b = 8

[modern sparrow]

Correct

[dusky sky]

i want to draw this but im in bed lmao

could you send a drawing if you have one

[modern sparrow]

Same😭😭

Okay gimme a sec

Its the best I could get rn 😭

[dusky sky]

its perfect

[modern sparrow]

Hahaha thanks

[dusky sky]

ok so

if cos d = -1/15

then sind =

sin²x = 1 - 1/225 = 224/225
sinx = 4sqrt(14)/15

what else is 4sqrt(14) ?

the mf surface

could you follow until here

[modern sparrow]

Wait how did u get sinx=4sqrt(14) 😭

[dusky sky]

sin²x = 1 - cos²x

i just did this

[modern sparrow]

Yeah yeah but the

[dusky sky]

sqrt224 = 4sqrt14

do you see it or

[modern sparrow]

Got it

[dusky sky]

yes now

sinus area theorem

if you draw this

you get 2 equal triangles

[modern sparrow]

Yess

[dusky sky]

do you know the sinus area theorem

[modern sparrow]

absinGamma

[dusky sky]

yes so

wait btw

sind = 4sqrt14 / 15 not only 4sqrt14

lmao

i forgot the denominator

[modern sparrow]

I was literally abt to ask that

😭

[dusky sky]

ok then

since the whole area is 4sqrt14

one of the triangles is 2sqrt14

area = a.b.sin/2
2sqrt14 = (x(8-x).4sqrt(14)/15)/2

what do you get when you do this

im kinda tired

i think it's x(8-x) = 15 all things done

[modern sparrow]

Honestly dude past that point I am good to go. It's also really late and I gotta get up early. My mistakes are that I forgot to make the sides x and (8-x) and I couldn't figure out sin x

[dusky sky]

alr its really late here too 😂

i have to wake up in 4 hours

[modern sparrow]

I did the theorem and got 224/225 but I had no idea that it made 4sqrt(14)/15

[dusky sky]

just tried to divide it by 14 to see if anything happens

and found out on coincidence

lol

[modern sparrow]

Hahahaha it did all the work

[dusky sky]

yes

now you have a good night

[modern sparrow]

You have a good night too. Many many thanks for helping me out

You're great

[dusky sky]

😌

np

closing btw

[modern sparrow]

Yeah go ahead idk the command 😭😭

[dusky sky]

.close

ok u do that

[modern sparrow]

.close

[dusky sky]

cuz i cant

[safe radish]

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[lean otter]

One square is 70 m long and 50 m wide. If you increase the length by 10%, by what percentage does the area increase? What happens if you increase the width by 10% instead of the length?

[lean otter]

Can anyone help me its urgent

[split fulcrum]

Is this for an exam

Or test

[lean otter]

Nooo

[wheat cave]

I mean just take the new area that has 10% more lenght and compare to old area

[lean otter]

i got Inital area =3500 and

new area after 10% increase =3850\

by what percentage does the area increase?

do you guys know how to do this now

@wheat cave

[rich elm]

divide the difference by the original area

and take that as a percentage

[wheat cave]

maybe if you look at the formula you should find the answer faster

like its (a*1.1)*b=area

would that differ from a*(b*1.1)=area

please dont give answers

[rich elm]

mb

[lean otter]

.close

[safe radish]

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[scenic valley]

f'

[safe radish]

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[desert ginkgo]

hello

[desert ginkgo]

i need some help on finding the derivative using the limit definition for f(x) = 8/x

im getting stuck at 8/(x+h)-8/x/h

how would i go about simplifying that

[stray socket]

Turn the numerator into a single fraction

[desert ginkgo]

yea so would i multpily it by x(x+h)

?

[stray socket]

Mmhm

[desert ginkgo]

top and bottom correct?

[stray socket]

Well just combine the fractions

However method you do it

[desert ginkgo]

so

i get

wait my bad i need a little help on that part

[stray socket]

Gonna focus on the numerator here

$\frac 8{x+h} - \frac 8 x$

[flat frigate]

Umbraleviathan

[desert ginkgo]

ok

i know the lcd is x(x+h)

but i think the main problem i have is when distributing for some reason

[stray socket]

Multiply the left fraction by x/x and the other (x+h)/(x+h)

[desert ginkgo]

yep

so im left with

8x-8(x+h)/x(x+h)/h

oh bruh

u got to be kidding me

i was doing the math wrong

my bad

so would it be -8/x^2

[stray socket]

Yes

[desert ginkgo]

thanks

.close

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[bright oar]

Hello, I try to solve the integral of (1/√(1-x²) by using u-substitution but instead of define u as the whole thing inside the radical, I just define it with x² and got a different result (positif sign before ½). So, I just curious if there's a rule for u-substitution to work. Or maybe I have some careless mistake?

[unique bison]

Watch your mouth.

[stray socket]

The rule for u-sub is to realize a chain rule that would get the derivative of the primitive = the integrand

There's no "rule" to it and often you just gotta eye it

And not all u-subs are clear as day

[safe radish]

@bright oar Has your question been resolved?

[safe radish]

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[crisp nacelle]

How do I find the height?

[lapis shadow]

It's an isosceles triangle

[crisp nacelle]

So... how do I find it?

.close

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[lean otter]

How much would $1000000 turn into if it was 2% interest for every day for 2 years straight?

[safe radish]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[lean otter]

4

1.8972536e+12 can you translate this into a base number

;calc 1.8972536e+12

,calc 1.8972536e+12

[flat frigate]

Result:

1.8972536e+12

[lean otter]

bruh

[safe radish]

@lean otter Has your question been resolved?

[buoyant shadow]

it's 1897253602776

or ...777

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[granite cobalt]

hi

[granite cobalt]

the solutions for this is wrong right?

the initial term can't be 11/4

wiat nvm

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[ember stratus]

Hi! I was watching a video tutorial on a question and the uploader solved an integral in the problem by taking the partial derivative of a constant. Is this valid (i.e., can you take partial derivatives of constants?)

[hot thistle]

sure

as in you can

[ember stratus]

I'm a bit confused as to why we can

[stoic dune]

λ is not a constant, with respect to λ

In other words, as you change λ, then λ changes

[ember stratus]

So it's a constant outside the integral and a variable inside the integral?

[ember stratus]

nvm I think I understand

thanks!

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[white apex]

Can someone help me with the highlighted one?

[white apex]

its e

[light shoal]

is the rocket accelerating?

[white apex]

yes

but its not constant

its acceleartating linearly

accelerating

[light shoal]

if it's accelerating at all, then the velocity is not constant, right?

[white apex]

yes

[light shoal]

so that could explain why simply multiplying velocity times time doesn't give you the correct answer, yes?

[white apex]

Yes, but how do I find the correct answe?

[light shoal]

what correct answer?

it's asking you to provide an explanation

[white apex]

How many feet does the rocket actually travel during the
second between t=10 seconds and t = 20 seconds?

I have to asnwer that

[light shoal]

you have a table

[white apex]

1520 - 390?

[white apex]

?

[light shoal]

aye

[white apex]

But on the graph I have

it's like

when v(20) it should be around 150

[white apex]

im confused

[light shoal]

1520 - 390 = 1130 yes?

[white apex]

yes

[light shoal]

so that tells you the average velocity between t=10 and t=20 is what?

[white apex]

do I do that divided by 10?

113?

[light shoal]

yea

and 113 is not 77 yes?

[white apex]

Lol true

[light shoal]

so 77 is a poor estimate of the average velocity over the interval

so is any other random velocity that you choose from that interval

no reason to assume that it will correctly predict the change in position during that interval

[white apex]

so I should be good with just 113

[light shoal]

well 113 correctly predicts the change in height, but only because you calculated it from the change in height

[white apex]

And thats what they asked for

[light shoal]

"explain why the change is not 770 feet"

glib answer: because that's not what we measured

[white apex]

yeah ill just be like

[light shoal]

physics answer: because the velocity of 77 at the start of the interval did not hold constant throughout the entire interval

i.e. the velocity changed, as evidenced by the fact that it didn't travel 770 feet in 10 seconds

[white apex]

While you're here can u check this

:3

[light shoal]

which part is the actual question

[white apex]

evaluating the limit

its b

[misty bay]

so basically when they ask you to make a table

[white apex]

i feel like its right

[misty bay]

they're just asking you to try some values close to 3

same with a graph honestly

[light shoal]

from the graph i can't tell, because the x axis has no labels

so i don't know where x=3 is

but by plugging in numbers close to 3, your answer looks more or less right

[white apex]

when i put it into symbolab

it says its right

[light shoal]

yea

[white apex]

so im feeling pretty confident

okay i submitted it so if you guys think its wrong dont tell me anymore

[light shoal]

you can use calculus to find the actual limit but you'll still need to plug it into calculator/software

no the number is fine

[white apex]

awesome sauce.

[safe radish]

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[lean otter]

Where does this u+y come from?

[mossy ruin]

see the steps

[lean otter]

I get up to the part where u = sqrt(x)-y and taking derivative of u on both sides, we get du = 1/(2sqrt(x)), but where does the (u+y) come from in the next step?

Okay

$\begin{aligned}du=\dfrac{1}{2\sqrt{x}}dx;dx=2\sqrt{x}du\ u+y=\sqrt{x}-y+y=\sqrt{x}\ dx=2\left( u+y\right)du \end{aligned}$

[pseudo scroll]

$\dd{u}$

[flat frigate]

NEONPerseus

[lean otter]

right dx=2(u+y)du my mistake

[flat frigate]

Zamarus

[lean otter]

okay, i understand the first line, but i'm still not understanding the 2nd line: u+y = sqrt(x-y+y = sqrt(x) part

look at the value for u and add y

u=sqrt(x)-y so if you add y it's sqrt(x)

may i ask if there's a reason why we can add y specifically?

No it's more like you have sqrt(x) and you notice that if you add y you can write it in terms of u and y

got it

that makes sense thank you

wlc

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[prime cobalt]

ji

[prime cobalt]

hi

for cartesian equation can we leave it in the form x=

or is it y=

[hexed dune]

@prime cobalt pretty vague but yh

Why not

What other form would you have it in

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[edgy cape]

Idk where start

[faint seal]

do you know trigonometry?

[edgy cape]

Barely

[faint seal]

ah

are you allowed to use a calculator?

[edgy cape]

Yeah

[faint seal]

ahh

so do you know what $cos(\theta)$ is?

[flat frigate]

kheerii

[pseudo scroll]

$\cos$

[flat frigate]

NEONPerseus

[hexed dune]

$cosine$

[flat frigate]

doctor99268

[safe radish]

@edgy cape Has your question been resolved?

[ancient narwhal]

Use cos^-1(Adjacent/Hypotenuse)

To get the degree

In this case, arccos(5/7)

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[viral leaf]

how to do part c)(i)

i did the first 2

i got b as (1-2k)pi/5

i got a as 16

[faint seal]

how did you do b?

[viral leaf]

pi/5-2kpi/5

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@viral leaf Has your question been resolved?

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[potent bay]

maybe this satisfies your curiosity

https://www.mathsisfun.com/sets/injective-surjective-bijective.html

[mint olive]

.close

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[visual socket]

explain please

[safe radish]

@visual socket Has your question been resolved?

[visual socket]

no

[safe radish]

@visual socket Has your question been resolved?

[visual socket]

still no

[visual socket]

<@&286206848099549185>

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@visual socket Has your question been resolved?

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[polar birch]

If the "pac-mans" on each side are approaching opposite infinities, this would be called,

[polar birch]

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[obtuse plover]

https://tenor.com/view/pacman-reaction-information-my-reaction-to-that-information-my-reaction-to-that-information-meme-gif-25863475

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[kindred jolt]

I need help with geometry and im not sure how to do this type of work, i have missed previous years and i am in severe need of help

[deep depot]

You can use
1)Thales theorem
2) similiar triangle property

[kindred jolt]

Im not sure what those are-

[deep depot]

Oh

They you should learn about it first

[kindred jolt]

Oh.. uh...

How do i do that?

[deep depot]

https://youtu.be/8h-BeLqfa3E

[timid pasture]

Khan Academy maybe

[deep depot]

YT

[kindred jolt]

Ok i'll try thanks ig

I understand whats going on in the video but i dont understand how that corresponds to the issue i am currently having

There is only 1 triangle in my problem

@deep depot

[timid pasture]

We use similarity to prove the thales theorem

[plucky elk]

There's 2

[jagged widget]

small triangle inside the bigger one

[kindred jolt]

Where?

There is only 1 triangle

This isnt helping me, thanks anyway though....

[tardy mango]

[timid pasture]

KPQ and KJK ???

[deep depot]

This triangle

And this ∆ too

And notice that both triangles are similar

They have same angles

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[faint seal]

!status

[safe radish]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[ripe frost]

number 3

[faint seal]

what did you get?

and how

[ripe frost]

i thought the maximum was 8

because that's the highest point of the graph

[faint seal]

well

have you learnt derivatives?

[ripe frost]

yeah i have

oh i didn't know you had to use it

[faint seal]

you dont really have to

tbh

[ripe frost]

i haven't used it in a while so i've forgetten a bit

[bold ferry]

do you know how to find the derivative or are you unsure what to do after finding it?

[ripe frost]

how to find the derivativ

[bold ferry]

true, you could figure it out if yk how the square root graph works

but anyway

like do you know the power rule

[ripe frost]

kinda

[bold ferry]

maybe you should brush up on that

technically chain rule is needed for this

[ripe frost]

can we use the non calculus method though since this work doesn't include this topic\

[bold ferry]

or you could know the derivative of sqrt(x) is 1 / 2sqrt(x)

[bold ferry]

hm

well

when we expand it out

$-2\sqrt{x-9} - 16$

[flat frigate]

Kihei

[bold ferry]

so it’s shifted 9 to the right and down 16

and it’s a negative squareroot function

[faint seal]

since there's a negative number in front of the bracket, the expression inside the bracket must be minimum for the overall expression to be maximum

meaning

root(x-9) must be minimum

minimum value of root(x) = 0

thus

-2*8

=-16

[bold ferry]

yeah pretty much what I was gonna say

[ripe frost]

ohhh thanks i get it now thanks

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[heavy path]

would I be correct?

[obtuse plover]

No

[heavy path]

hmm

out of those is there any that I got correct

[obtuse plover]

No

[heavy path]

ok : (

Then I am confused

it always confuses me on which line we are talking about when doing this

for example on the first one if we are saying as x goes to -4 from the left down it would just be that f(x) is going to - infinity ?

[lean otter]

yes that would be going to negative infinity

[heavy path]

does that mean that as it goes from the right to left it also goes to - infinity or would it get closer to 2

[lean otter]

when it says x approaches -4 (-) side, it's referring to the lower one

and when x approach -4 (+), it's referencing the upper one

[heavy path]

ohh

I thought It indicated from left to right or right to left

[lean otter]

and when x approaches positive infinity, as the number goes up ex: x=10, x=100, x=1000, what number does the curve get closer and closer to?

[heavy path]

infinity

or sorry

it goes up to infinity

but it gets closer to 2

[lean otter]

no.

as the value of x goes to infinity, where does the curve get closer and closer to

[heavy path]

-4 ?

[lean otter]

what happens to the y value as the x values approaches -4 from the right side

[heavy path]

it gets closer to -4

[lean otter]

the y value

[heavy path]

umm in my mind it just sitting at 2 but I know that wrong

[lean otter]

look at the y value

what happens as x goes to -4

from the right

[heavy path]

it increases

[lean otter]

yes

to what?

[heavy path]

so it would increase to infinity

[lean otter]

yes

[heavy path]

ahhh'

[lean otter]

lim from the right approaches infinity

[heavy path]

so would the + also indicate that it goes right to left

[lean otter]

yes

[heavy path]

gotcha

so that would mean that as x goes to infinity f(x) gets closer to 23

2

[lean otter]

what

where did the 2 come from

oh

infinity

yes

thats correct

[heavy path]

gotcha

you scared me for a second lol

[lean otter]

whats the limit as x approaches -4?

using ur answer for (1) and (2)

[heavy path]

ummm for positive 4?

or -

[lean otter]

-4*

[heavy path]

ah okay it would be -4

sorry

[lean otter]

no

[heavy path]

wait

[lean otter]

lim from the left is -inf, lim from the right is inf

whats the lim as x-> -4

[heavy path]

• inf?

[lean otter]

If the left and right limit are different the limit DNE

[heavy path]

what does DNE mean

[lean otter]

doesnt exist

does not exist.

[heavy path]

gotcha

understood

I appreciate it guys

[lean otter]

👍

[heavy path]

imna try working some more practice problems to nail it down

.close

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[lean otter]

do you know how to tell between which curve

[heavy path]

.reopen

[safe radish]

✅

[lean otter]

when to use the left curve or when to use the right curve?

[heavy path]

from the + or - right

[lean otter]

yes

[heavy path]

fs fs

[lean otter]

and now you understand what x approach infinity means right

or - infinity

[heavy path]

correct ive kinda got the hang of it

I am just going to do some more practice problems to prepare for my test tomorrow

[lean otter]

got it. if you need more help don't be afraid to drop them here ^^

[heavy path]

Will do!

Thank you

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[safe radish]

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[woven cloak]

hi for some reason they keep getting 320

[potent bay]

if you just type 320 without the decimal?

or you guessed the 30?

what does "for some reason they keep getting 320" mean?

[woven cloak]

i dont know how they keep getting 320

[potent bay]

who are they

[woven cloak]

im getting 0.75x divided by 144

which isnt 320

[woven cloak]

the college/math website

[potent bay]

originally they have 72 g

[woven cloak]

following that math

and not getting 320

something must be wrong

[potent bay]

and in the end we need 216

so the added 144 comes from the change

which has to be a part of the 60% solution

[woven cloak]

what is 216?

[potent bay]

thats 45% more than the original

[potent bay]

480*0.45

[woven cloak]

tbh id idnt get nothing

im just curious how they get 320 what to do with that number I got

0.75 and 144

[potent bay]

so this surplus is part of the more dense solution, so if we change x ml we have x*0.45 extra dextrose 144=0.45x , solve it

[woven cloak]

now i got 320

[potent bay]

in your paper too

-0.15 +0.6

is not 0.75

[woven cloak]

thats what i got

0.15+0.60=0.75

oops i didnt put negative

sorry

thank you

.close

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[exotic jackal]

Could someone help me understand this? The prof never showed implicit differentiation with exponential functions, especially with e^y. I know e^x derivative is just e^x, is e^y the same?

I don't find their explanation helpful. How do they get the dy/dx on the third step of the first line?

[plucky elk]

Use chain rule to differentiate e^y

you can check your answer for y=x^2

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[wind siren]

i get to check p-a.s we have to check the probability of X \neq Y but how does that integral exactly appear and what changes if the function f was another function?

[safe radish]

@wind siren Has your question been resolved?

[wind siren]

@sonic wadi

[peak estuary]

well its the density of the measure

to find the probability of a set, you integrate the density over that set

[wind siren]

can you elaborate on what is the density of the measure?

[wind siren]

and why are we not integrating x,y

[safe radish]

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[stray socket]

1 sig fig

[tawdry plover]

woah neat handwriting

you're subtracting them, yes? @cold pumice

i am also getting 0.856

oh

i see where you went wrong

the 0.10000 is indeed 5 sigfigs

not 1

when you have zeros trailing post decimal point after a non-zero number, those are significant figures

its similar to 25.00

the 2 zeroes after the 5 and decimal point are considered significant

similarly, the 4 zeroes after the 1 and the decimal point are considered significant

yeah lol

sigfig rules are terrible its okay

they are easy, but sometimes gets to be unintuitive like this

thats why its much better to write things in scientific notation

like

$0.10000 = 1.0000 \times 10^{-1}$

[flat frigate]

blanket

[tawdry plover]

unambiguously (also easier to see) that its 5 sigfigs

but wtv

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[keen marsh]

.close

[safe radish]

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[woven hare]

Can someone help me w this

[woven hare]

<@&286206848099549185>

[safe radish]

@woven hare Has your question been resolved?

[woven hare]

How do y do this without the function given?

[raw veldt]

You need to convert each of these integrals into the 3 different types of functions for each problem

[woven hare]

0 to 40 40 to 70 70 to 90 90 to 100?

I don’t get it

[raw veldt]

Its 4 subintervals right?

[woven hare]

Yea

[raw veldt]

So the distance between each variable must be the same

So its 0 to 25 26 to 50 50 to 75 76 to 100

[woven hare]

Oh

[raw veldt]

With the numbers you have given there you need to solve the approximate g(x) at those variables

So find g(x) at 25, 50, 75, and you already have 100

[woven hare]

Don’t you need to know the g(x) at 25

[raw veldt]

Yes

[woven hare]

Idk the equation

[raw veldt]

You have to find the variables there by finding average slopes between the given g(x)s

[woven hare]

Is that derivative

[raw veldt]

It doesn’t matter what the function is, just find the average g(x) and the answer will be a given riemann subinterval

[woven hare]

As in add the interval together and divide by 2?

From 0 to 40 it’s 165 average g(x) but the x is 20

I’m lost

[raw veldt]

Then fine the average from 20 to 40

Thats 30

Then the average from 20 to 30

Which is 25

[woven hare]

Oh

What about 40 n 70

That would be 55

Then 55 to 40 is 47.5

47.5 to 55 is 51.25

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[safe radish]

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[deep dune]

can anyone

[deep dune]

help me understand this

[worthy hemlock]

You're given the coordinates, and coordinates are in the form of (x, y). Plug that into the inequality and see if it's true

For example, let's take (1, 3) and the inequality you have $y \leq 6 - x$. Plug in 1 and 3, so you have $ 3 \leq 6 - 1$, simplify and you get $3 \leq 5$ and that's true so (1, 3) is a solution to that inequality

[flat frigate]

dldh06

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[heady sable]

am i doing this correct

[heady sable]

i feel like there is smth wrong

[junior smelt]

For (i), did you simplify it?

[heady sable]

no

is it correct now

[junior smelt]

,rccw

[heady sable]

am i supposed to find the value for n

[junior smelt]

You are [supposed to find the value of n] yes

[heady sable]

oh

i thought im wrong

okay thank you

oh

[junior smelt]

Wait for the expansion what did you do?

[heady sable]

i did the binomial theorem thing

[junior smelt]

The line you wrote to begin with was fine here

But, for example, you know $\binom{n}{1} = n$ and $\binom{n}{2} = \frac{n(n-1)}{2}$

[flat frigate]

@junior smelt

[heady sable]

yea

[junior smelt]

And of course you know how to work with, say, $\pqty{-\frac{x}{3}}^{2}$ so that you can write it as some coefficient for $x^{2}$

[heady sable]

i think so

[flat frigate]

@junior smelt

[heady sable]

is it correct now

[junior smelt]

Hmm, why do you have terms like these?

[heady sable]

2xn-2

[junior smelt]

From here, you said that you have
[
(1)^n + \binom{n}{1} (1)^{n-1} \pqty{-\frac{x}{3}} + \binom{n}{2} (1)^{n-2} \pqty{-\frac{x}{3}}^{2} + \ldots \
]

[flat frigate]

@junior smelt

[heady sable]

yea

[junior smelt]

From here we can replace the n choose 1 and the n choose 2

[heady sable]

yes

[junior smelt]

And we can also square the brackets here to get that x^2 coefficient

[heady sable]

yes

[junior smelt]

All we need to do is replace those terms, and of course 1 to any power is still 1

So then, e.g. replacing the binomial coefficents and the powers of 1 would give that
[
1 + n\pqty{-\frac{x}{3}} + \frac{n(n-1)}{2} \pqty{-\frac{x}{3}}^{2} + \ldots
]

[flat frigate]

@junior smelt

[heady sable]

huh

[junior smelt]

And then you can simplify that a bit more of course

[heady sable]

huh

what about the 1^ n-2

they will be one so we dont add them in the equation?

[junior smelt]

$1^{n-2} = 1$ and anything multiplied by 1 is just the same thing

[flat frigate]

@junior smelt

[heady sable]

okayy

[junior smelt]

Similarly for 1^{n-1} = 1 and you're just multiplying that by something

[heady sable]

ouh

cirrect?

[junior smelt]

But anyways, if you simplify that, then you should get that you have
[
1 - \frac{n}{3} x + \frac{n(n-1)}{18} x^{2} + \ldots
]
Do you agree?

[flat frigate]

@junior smelt

[heady sable]

yes

oh.

OHH

okay

i got it

thanks

I have to go now

bye

[junior smelt]

See ya later!

[safe radish]

@heady sable Has your question been resolved?

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