help-42

[still marlin]

Then u can write H(t) (diff between height of ball from x axis and height of ground from x axis) in terms of time alone

So derive, set equal to 0, solve for time

then plug that t value back into H(t) to get max height

[shell spruce]

I don’t think there is time though?

[still marlin]

So I'll give u a freebie: height of ball is h(t) = - 1/2gt^2 + v_0sin(45)t

[still marlin]

there's always time in physics

[shell spruce]

True

[still marlin]

Now try to express x(t), which is the distance from the person of the ball in terms of time

Oops

I mean hoeizontal distance from the person

[shell spruce]

This is too hard for me 🥲 I’m so confused

[still marlin]

if it's not clear at first

Just write equations from the givens

that's what I did really

[shell spruce]

K

[still marlin]

I do wonder if there's a way to solve for things without ever bringing time into the equation, but I only know how to write trajectories in terms of time

[shell spruce]

I’M CONFUSION

[still marlin]

dw

U know ur 2D kinematics right

[shell spruce]

No

[still marlin]

oh

That's a much bigger problem outside the scope of this help channel then

go review that shtuff

[shell spruce]

It thought it was only algebra 2 😢

[still marlin]

interesting

[shell spruce]

And a tiny bit of trig

[still marlin]

ok hold on there's def an easier way then

[shell spruce]

XD

[still marlin]

ok

from y = ax^2 + x + c, plugging x = 0, clearly c = 0

then, let X' be where it hits the ground

y = -3/4x' based off the slope of the ground

Use Pythagorean theorem to get (9/16)x'^2 + x'^2 = 50^2

Solve for x'

then solve for a by plugging in for (x',y') into y = ax^2 + x + c

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[shell spruce]

@still marlin ty

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[fossil escarp]

how to do 5c

[calm coral]

@fossil escarp Has your question been resolved?

[untold compass]

if you go east and south, then to get back you have to go the negative of those distances

and bearing is arctan(y/x)

[calm coral]

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[onyx quiver]

I dont get how its 0-60t and not just 60t?

and why is it -45-45t

this is based off my teachers answers

i mean 45-4t

[calm coral]

@onyx quiver Has your question been resolved?

[clever ferry]

it's negative because it's travelling south

[onyx quiver]

but whys it gotta be 0-60t and not just -60t

[clever ferry]

because the station is at (0,0)

they added in the 0 to clarify that ig

and the other is 45 - 45t

negative because it's travelling west and the starting position is 45 because it reaches the station 1 hour after the other train's departure

[onyx quiver]

tysm but why is starting position 45 if its coming from the left wouldnt it be -45 ?

wait what

how did we even find the starting posiitin

[clever ferry]

it's coming from the right to the left

[onyx quiver]

Ohhhhhhhhhh

[clever ferry]

okay

so think of 10am as the starting point of the timeline

[onyx quiver]

ok

[clever ferry]

and each step is 1 hour

so 11am would be 1

we want d0 - 45(1) to equal zero

because it arrives at (0,0) at 11am

[onyx quiver]

45 - 45(1)

ohhhh

tyy

[strong igloo]

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[drifting seal]

.close

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[steel tide]

It should be one one and onto

Why they are giving only onto

[still marlin]

What do u think bijective means

[steel tide]

One one and onto

[still marlin]

Yup

[steel tide]

And this function is

Then why they are saying B

[still marlin]

oic

[steel tide]

Am I wrong?

[still marlin]

don't think so

[steel tide]

Okay

Tq

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[still marlin]

if x/(1 + |x|) = y/(1 + |y|) then the sign is wholly determined by the numerator, so x and y have same sign and thus denom are both 1 +x and 1 + y or 1-x and 1 - y respectively. From there it's p clear that it's injective

[steel tide]

.reopen

[calm coral]

✅

[steel tide]

Yeah

And it is covering the whole co domain

[still marlin]

yeah cus intermediate value theorem and taking limit as x goes to infinity/-infinity

[calm coral]

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[steel tide]

derivative of arctan(2sinhx)

[bronze adder]

chain rule

[steel tide]

But i am not getting what I wanted

Where is the mistake

,rotate

[steel tide]

@bronze adder

[bronze adder]

just multiply your answer with e^2x

the numerator and denominator

same thing

[ember trail]

$\frac{d}{dx}tan^{-1}(sinh(x))=\frac{cosh(x)}{sinh^2(x)+1}$
$=\frac{\frac{e^{2x}+e^{-x}}{2}}{(\frac{e^x-e^{-2x}}{4})+1}$

[potent lotus]

cheryy

[ember trail]

$=\frac{\frac{e^{2x}+e^{-x}}{2}}{\frac{e^x-e^{-2x}+4}{4}}$

[potent lotus]

cheryy

[ember trail]

$=\frac{2(e^{2x}+e^{-x})}{e^x-e^{-2x}+4}$

[potent lotus]

cheryy

[steel tide]

There is one edit in the question

.close

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[remote mural]

can someone tell me what's postulate and theorem in a simple way, I've been searching for it but I can't understand anything

[calm coral]

@remote mural Has your question been resolved?

[remote mural]

<@&286206848099549185>

[remote mural]

Postulates are the same thing as axioms. They're statements that cannot be proven or disproven, and are true by default on which the mathematics is built.

A theorem is a statement that can be proved via a chain of logical reasonings using the axioms

I have seen the word postulate being used in geometry more

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[remote mural]

Is it solved what about the other 4 ?

[calm coral]

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[remote mural]

Nope

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[jolly crest]

how am i supposed to do this question

[white atlas]

,,\sqrt{6 + \color{red}\sqrt{6 + \sqrt{6 + \ldots}}} = x

[potent lotus]

kanna

[white atlas]

the red thing could be x too?

[jolly crest]

ohh

yeah right on

[dusky flax]

after this it's an easy quadratic

[jolly crest]

yeah

gotcha

thanks a bunch

[winter elbow]

Good one

[jolly crest]

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[jovial dove]

b

[calm coral]

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[chrome plume]

Michat practices basketball. Average from the free throw line to the basket
8 times for 10 throws. The referee awarded three free throws for Michat.
Calculate the probability of Michael getting into the basket:
a) at least once.

[chrome plume]

Is it okay to do 1-(1/5)^3?

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[cursive moth]

Why is the yellow part added? In my opinion it is quite unnecessary?

[glass heart]

exactly two books

[cursive moth]

ah oke vhm lol

thanks

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[blazing coyote]

So to start, there are 27 elements in X

is that right

[brisk pelican]

Yea

[gloomy ibex]

yes you would be right

[blazing coyote]

now obviously the vector wherin all elements are 0 wont consist of perpendicualr vectors

so Y is a subset of X

now then, for 3 vectors to be mutally perpendicular, their dot product, taken two at a time should be zero

either that or

$V_1 \cdot v_2 \cross v_3=0$

[potent lotus]

Why am. I here

[blazing coyote]

is that right

thought I don't see that helping very much

[gloomy ibex]

can you elaborate?

[blazing coyote]

let $v_1=0i$

[potent lotus]

Why am. I here

[blazing coyote]

$v_2=0j$

[potent lotus]

Why am. I here

[blazing coyote]

$v_3=0k$

[potent lotus]

Why am. I here

[blazing coyote]

these vectors aren't perpendicular

oh

right

null vectors are perpendicualr

[gloomy ibex]

by saying v1 = 0i you are setting the other two components to be 0, which makes it a null vector

[blazing coyote]

so the answer is 27?

[gloomy ibex]

we probably shouldnt be jumping to conclusions, because there is nothing that says v1 v2 and v3 are distinct vectors

[blazing coyote]

ah

right

so the answer would be 24 in that case, wouldn't it?

wait, wouldn't it be less than that?

What am I doing wrong

[gloomy ibex]

the total number of relations in AxAxA would be 27 ^3, of which Y can be any proportion of, so concluding that Y would be a subset of X doesn't seem right

[blazing coyote]

oh

right

hmm

[gloomy ibex]

to summarize what we have to do:
we have some 27 vectors, we have to find how many 3 vectors are mutually perpendicular
we also know all the vectors

step 1 would be to list out all possibilities

which is tedious, and time consuming

before approaching this problem, let us clean up some things

say v1 v2 and v3 are perpendicular,
this implies that (v1 v2 v3) is in Y

but, we can rearrange this ordered pair in 6 ways, and still all of the vectors will be mutually perpendicular ( given v1 v2 and v3 are distinct)

[blazing coyote]

hmm

actually sorry gtg now

[gloomy ibex]

sure

[blazing coyote]

I'm really sorry

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[flint wasp]

Any idea on what happened here?

I moved that inverse part down as a fraction

[calm coral]

@flint wasp Has your question been resolved?

[calm coral]

@flint wasp Has your question been resolved?

[calm coral]

@flint wasp Has your question been resolved?

[calm coral]

@flint wasp Has your question been resolved?

[regal bolt]

They're essentially just writing the rows of V as vectors v_i and using that Sigma is a diagonal matrix

lemme see i'll try to be more explicit

[flint wasp]

I'm in bed sleeping now, I will read in morning can I dm if I have a question?

[regal bolt]

Ye sure

I'll try to write some stuff down already

[flint wasp]

Tyty

[regal bolt]

nite

$\Sigma$ is diagonal (since it comes from a SVD, as i understand), so inverting $(\Sigma^2 + \lambda^2 I)$ is easy, you just take the inverse of the diagonal elements, and it is itself again a diagonal element. So matrix multiplication is easy:

$(V \cdot (\Sigma^2 + \lambda^2 I)^{-1}){ij} = V{ij} \frac{1}{\sigma_j^2 + \lambda^2}$, where $\sigma_j = \Sigma_{jj}$ is the $j$-th singular value.

[potent lotus]

Lartomato

[regal bolt]

So the rest of the matrix multiplication in the expression is easy: Looking just at the $i$-th component of the resulting vector, we find:

$(V \cdot (\Sigma^2 + \lambda^2 I)^{-1}) \Sigma U^T b){i} = \sum_k V{ik} \frac{1}{\sigma_k^2 + \lambda^2} (\Sigma U^T b){k} =
\sum_k V{ik} \frac{1}{\sigma_k^2 + \lambda^2} \sigma_k (U^Tb)_{k}$

[potent lotus]

Lartomato

[regal bolt]

Now we get the expression that you see in the paper if we define the vectors $v_k$ with components $(v_k)i := V{ik}$ and $u_k$ with components $(u_k)i := U{ik}$

[potent lotus]

Lartomato

[regal bolt]

To see that, note that $(U^T b)k = \sum_r U{rk} b_r = \sum_r (u_k)_r b_r = u_k^T b$, hence

$(V \cdot (\Sigma^2 + \lambda^2 I)^{-1}) \Sigma U^T b){i} = \sum_k (v_k){i} \frac{1}{\sigma_k^2 + \lambda^2} \sigma_k u_k^T b$

[potent lotus]

Lartomato

[regal bolt]

Now, dividing by one more factor of \sigma_k within the expression gives you exactly what they wrote. Have fun!

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[solid seal]

Integral of 1/x^2-x+2 dx, I am getting arctan((2x-1)/sqrt 7) and not (2 arctan ((2x-1))/sqrt7) )/ sqrt7

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[latent zinc]

I need help with this

The extrema are found either in the stationary points, in on the edge or in non-differentiable points (there are none)

i checked the stationary points and found that its outside of B

so whats left is the edge of B

from this I get a minimum of -5 and max of -3, but when I brute-force with numpy to see the possibilites where x >= 0 and x^2+y^2 <= 1, I get a new maximum and minimum

so Im rather confused

[calm coral]

@latent zinc Has your question been resolved?

[marsh valley]

What method did you use to find the -5 and -3 extrema?

You've found that the interior of f is free of extrema, so it's true it remains to check the boundary. One would usually use some tool like the Lagrange multipliers to find extrema on the boundary.

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[latent zinc]

how do I do that?

.reopen

[calm coral]

✅

[latent zinc]

I havent heard of Lagrange multipliers

[latent zinc]

just took the end points of the circle

but its not really extrema

[marsh valley]

Yeah no. If you can't find extrema inside the domain, then you check the boundary, and the boundary of this domain is a half circle with its diameter

[latent zinc]

exactly

And so I wrote a script to bruteforce it, but ofc this isnt 100% accurate

The question is whether I can solve an equation to find these max and min points

@marsh valley Is there a way through either parametrisation or something else that I can solve for these points?

I dont think lagrange applies for something like this, I just looked it up

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[mighty dagger]

lim infinity/infinity = 1 ?

[sinful pasture]

No

[potent smelt]

It can be any value or no value at all

[sinful pasture]

2x/x when x --> inf for example

[potent smelt]

It's called an "indeterminate form"

[sinful pasture]

Dear god

[mighty dagger]

why here at the end he said 1^infinity

[sinful pasture]

Good luck

[mighty dagger]

lmfao

[sinful pasture]

Is not 1^inf originally I would guess

[potent smelt]

This turn into a 1^inf form

[sinful pasture]

Original post ?

[mighty dagger]

how

[potent smelt]

If you ignore the 1^inf stuff that seems to have been written in?

[mighty dagger]

then its infinity/infinity

(infinity/infinity)^infinity

since i have inf/inf

that already makes me go another way

[potent smelt]

[

\lim_{x \rightarrow \infty} {\qty(\frac{3x-1}{3x+2})}^{3x-1}

]

[potent lotus]

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

[sinful pasture]

No. If 1^inf came from a previous step, it means approaching 1 and approaching inf. It's not a perfect 1

Because it's a limit, it's not the same number by itself. For example, (0.99999999)^1000000000000000000000000000000000000000

That won't approach 1 so 1^inf is not 1

[potent smelt]

So take the log of both sides

You'll get a 0 * inf indeterminate form

Which you can turn into a 0/0 one easily

And apply L'hopitals

Or inf/inf might be better actually?

[mighty dagger]

i dont wanna use here lhopitals

im not allowed to

[potent smelt]

Ok, what are you allowed to use then?

[mighty dagger]

no it just says i cant use this

well at the begin we have the formula too

[potent smelt]

Ah

[mighty dagger]

the thing beside a/x is accident

the line

[potent smelt]

That's useful

[mighty dagger]

ye

[potent smelt]

Well use that then

[mighty dagger]

well i figured it out

i made the -1 = 2-3

but like

[potent smelt]

Yup

[mighty dagger]

i was just wondering why he did 1^inf

not inf/inf

[potent smelt]

As you take the limit

The fraction does inf/inf sure

But it's an easy one to figure out

It just goes to 1

And the exponent goes to inf

So it is 1^inf

[mighty dagger]

ah ok

but does that help me in any way ?

other than 0/0 and inf/inf

[potent smelt]

Nope, it's a red herring

You were given the formula to use

[mighty dagger]

ye but like in general if i get 1^inf or inf/0 or whatever

does this help me in anything

or it doesnt

[sinful pasture]

Inf/0 yes

That one is not undetermined

[mighty dagger]

lmfao alright

ill take that as a yes

but anyways u got the point do they help knowing

or not

[sinful pasture]

1^inf no

[potent smelt]

It helps you to know how to use L'hopitals rule

[mighty dagger]

ye but other than that nth right ?

[sinful pasture]

Can you show all steps of the image you sent previously?

The one that contains 1^inf

[sinful pasture]

.

[mighty dagger]

oh

[sinful pasture]

Oh yes. What Omnipotent said. It is 1^inf undeterminated from the beginning

And those undeterminated forms are not useful except knowing they are not useful

Inf/inf, 0/0 1^inf

Inf^inf, 0^0

[mighty dagger]

oh ok tysm

appreciate it

.close

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[potent smelt]

These not indeterminate lol

Wait

Inf^inf isn't

0^0 of course is

I was thinking 0^inf which surprisingly isn't.

[sinful pasture]

Yeah idk why I wrote inf ^ inf

My bad

[potent smelt]

I turned around and made an equally bad blunder, except I did it while attempting to play the pedant, which is obviously worse

It's all good

[calm coral]

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[mighty dagger]

another question

[mighty dagger]

why cant i just put the 1/4 down on the second ()

and it be like

(...)^((1/4)-1)

[alpine gust]

why? when u finsh whats inside the big (), it will be 4x^2

raised to (1/4), it will be x^2

[mighty dagger]

ye right

[alpine gust]

and whats about the first ()

[mighty dagger]

oh ye gotcha cuz

itll be then 4x^2 + 1/4

[alpine gust]

yes

[mighty dagger]

ah

ok

[alpine gust]

exponents rules

[mighty dagger]

ok ty ty

and one more thing

[alpine gust]

yep

[mighty dagger]

how do you solve equation with power of 2

like

x^2 + 3x + 2 for example

now i want to do it like

(x+smth)^2 + 2 or whatever the missing number

how do u make it like that

[alpine gust]

u mean solving a quadratic equation?

[mighty dagger]

ye but a one that u cant do a(x+b)(x+c)

u need to do this way that i said up

[alpine gust]

this way is called completing a square, cuz u have to make it (smth) raised to a square like u typed it

[mighty dagger]

oh ok thanks

ill look it up on google

[alpine gust]

lets say u have an eq. like this
x^2 + bx + c

then u add and subtract (b/2)^2

to be like this
x^2 + bx + (b/2)^2 + c - (b/2)^2

[mighty dagger]

oh

what if i have a beside the x^2

[alpine gust]

u divide by this

[alpine gust]

to make it 1, just to simplify things

[mighty dagger]

oh ok gotcha

tysm for the example and for the explaination

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[mighty dagger]

i got a question

[mighty dagger]

i have rn (1/x^3)/(1/x^4)

can i make it x^3/x^4

[potent smelt]

No

You can make it x^4/x^3

[mighty dagger]

oh whats that rule or formula or theory called

[potent smelt]

It's just how reciprocals and fractions work

[remote mural]

its called basic algebra

[potent smelt]

a/b = a * 1/b

Set a = (1/x^3) and b = (1/x^4)

And 1/(1/c) = c (if c ≠ 0)

[mighty dagger]

oh ok gotcha

tysm

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[steel tide]

I am confused in A and D

[pallid halo]

the wording is terrible and vague

D seems the most suspicious to me

it's easy to find two discontinuous functions f and g such that f+g is continuous, for example

but i don't know if that's what they mean by "decompose"

[calm coral]

@steel tide Has your question been resolved?

[steel tide]

So D is the wrong one?@bungo.the.original

[buoyant patrol]

D is the answer for the Question

i think

say a point is not included on a line in the graph of a function

when u decompose the function into smaller pieces

u MAY automatically omit the end points of the smaller functions as when u put limit x-->a where a is the point which was not included in the function the smaller function will be defined BUT the point "a" was not included but the limit still holds as x-->a

[steel tide]

So when we decomposition we are getting many holes?@buoyant patrol

[buoyant patrol]

yes

not neccesarily

but when there are holes, they can get away with being one and the fact that the smaller ones were continuos but the bigger was not..

due to limits

its like the goverment , when there is no problem they are happy, but when there is a problem the still figure out a way to be happy , by ignoring the problems

did you get it?😭

[steel tide]

You set a greate xample

[buoyant patrol]

Thanku

[exotic falcon]

@steel tide do you still have a doubt?

[steel tide]

Yes

I was waiting for your response 🤣

.close

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[wild tree]

help

[calm coral]

Please don't occupy multiple help channels.

@wild tree Has your question been resolved?

[calm coral]

@wild tree Has your question been resolved?

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[steady citrus]

why is the product rule used in the second example but not the first

[glacial inlet]

that’s because we don’t have a product of two functions in the first one when partial differentiating with respect to x

the y’s are treated as constants

but for the second, we are instead treating x as the constant

so we do have a product of two functions

[calm coral]

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[vast parcel]

If someone can help me...

[quaint sphinx]

try to construct the function, starting from inputs f(1), f(2), etc

[calm coral]

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[thick fog]

Where did i go wrong? When i use a integral calculator to check my ans it shows 65/3

[blazing coyote]

I'm pretty sure that's floor(x+1)

[thick fog]

ah i didnt see that

but how does that affect the way i did it tho ?

am i supposed to do something else

[blazing coyote]

recall teh defn of floor(x)

and try again

[thick fog]

is it just rounding down ?

[solar spruce]

yes

[thick fog]

do i round down after subbing in the values 3 and -2 ?

[solar spruce]

i would suggest you write the definition of that floor function using symbols

it is a piecewise function

it would also probably be helpful to think of this in terms of areas

[calm coral]

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[vast parcel]

. reopen

[latent zinc]

Need help with C

Im not sure about what minimal or maximal error constitutes and I don't know how to proceed

[calm coral]

@latent zinc Has your question been resolved?

[calm coral]

@latent zinc Has your question been resolved?

[latent zinc]

<@&286206848099549185>

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[vale flame]

for part d

how do u know t is 1 day

i thought it would be zero

[rustic osprey]

$\log_{10} T=0 \implies T=10^0=1$

[potent lotus]

Civil Service Pigeon

[vale flame]

ohhh ok thank u

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[remote mural]

i need some help

[remote mural]

it's a physics question basically but the math part is kinda confusing me rn

[cloud nexus]

Ask away

[remote mural]

that green line is a fixed surface, there's a ball projected at it, initial and final velocity vectors are given

and e which is coefficient of restitution here

this is how my teacher has solved

using this logic smh

[cloud nexus]

Idk what the coefficient of restitution is but id go about finding the magnitude of vi and vf and plugging them into the formula

[remote mural]

ok but we don't know n cap

it's ok if you don't know thanks for turning in still

n cap is a unit vector given to us in the direction of the normal the ball is gonna be having with the surface btw

[cloud nexus]

Wait so you need to calculate that normal vector?

[remote mural]

no we have to find e

which also requires us finding n cap

[cloud nexus]

So you do have to find that normal vector

[remote mural]

yea

[polar jetty]

What is the issue that you are facing?

@remote mural

[remote mural]

yea sorry i was geting the ss

this part

i dont get how he wrote this

[polar jetty]

Well, to understand that, first, we need to ensure that you understand what is meant by the coefficient of restitution. Are you aware of its definition?

[remote mural]

yes sir

relative velocity of seperation

/ " " approach

[polar jetty]

Ah. Great.

So, you understand that velocity of approach is the component of initial velocity along the n cap vector. Right?

[remote mural]

yes

[polar jetty]

n cap vector is just a unit vector perpendicular to the given surface.

Similarly, velocity of separation is also the component of final velocity along the n cap vector.

Makes sense?

[remote mural]

yes

yea

[polar jetty]

Also, both the initial velocity and final velocity have a component parallel to the surface(perpendicular to n cap vector) which remains unchanged.

[remote mural]

yes

[polar jetty]

If you are not sure why, think Newton's second law.

[remote mural]

they remain same cus no force acting on that direction

[polar jetty]

Great. Moving on.

[remote mural]

no impulse more like

[remote mural]

sure yea

[polar jetty]

So, now if you write Vf - Vi, the components parallel to the surface will get cancelled. Remaining components are along the n cap vectors so their difference will also be along n cap vector.

Now, you just divide by magnitude of |Vf- Vi| to ensure that magnitude is 1 and you get n cap vector.

[remote mural]

sharing this just to let you know that i have knowledge of these things so you can provide a better help ig

[polar jetty]

I think you must already be getting it. Anything which didn't make sense in last two texts?

[remote mural]

just give me some time

@polar jetty i get it!

thank you so much for your help

[polar jetty]

Happy to help.

[remote mural]

bye

have a nice day

.close

[calm coral]

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[calm coral]

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[austere topaz]

Factoring trinomials question, whats my first step?

[remote mural]

not really a trinomial

but

ok

so

what do you think you should do there

[fathom shuttle]

it is a trinomial

[austere topaz]

get factors

[fathom shuttle]

factors of what?

[austere topaz]

numbers

[fathom shuttle]

what number

[austere topaz]

90

[fathom shuttle]

not 90, its -90

[austere topaz]

-90 yea

no

we factor

[torn hinge]

Guess you guys have this one الحمد لله

[austere topaz]

then we do big - small

we factor the number

wait no, calculate ac

then get there factors

then we do big - small and big plus small

theres no x

theres m

[torn hinge]

Did you learn any method such as "complete the square" ?

[austere topaz]

no

[torn hinge]

m is just x in a costume

Same logic though!

[austere topaz]

yea

i forgot how to fully do it

its a good method tho

90m2

-90

yea thats what i did

1x90

2x45

3x30

i dont know the rest

but im sure one of those work

6x15

[torn hinge]

6 x 15 is though

[austere topaz]

yea thats what i meant

[torn hinge]

All good, arithmetic can be a pain

[austere topaz]

yea school is a pain

i got a 36% rn

in math

im doin good in gym tho

ap gym student

[torn hinge]

There should be 18*5 as well

[austere topaz]

my teacher doesnt use negatives

[torn hinge]

Though it's not the solution

[austere topaz]

we ignore them for now

for those specific reasons

[torn hinge]

Absolute unit lol

[austere topaz]

amen

[torn hinge]

If I'm intruding I can leave you fellas be

[austere topaz]

no stay

i like you

yes

now what

wait wait

[torn hinge]

Ayt the trick is to see that the coefficient next to m is just 1 (which is the +m term) so your two factors should add up to +1

[austere topaz]

i just noticed

no negatives

here should me

big + small or big - small

therefore 15-9

or 15+9

therefore 24

for big

and 6 for small

or smt

ok let me try

i think its 9x10

cuz if u subtarct

u get 1

[torn hinge]

Great rationale

Keep in mind the product is -90 so one of them has to be negative

[austere topaz]

ye

10-9

we never do small - big

allways big number

uh

ok

where do i put it

uh

yea

(m-9) (m+10)

fianl answer

im so cooked

thats for your help

ima become a gym teacher

.close

[calm coral]

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[coral dew]

How?

[coral dew]

And this

How do I tell ?

[kindred estuary]

You can apply zero product property which states that if A * B = 0 then A = 0 or B = 0

[coral dew]

Ohh ok

So -3 and -7?

and same for the other one right

I solve for x

[kindred estuary]

Yes

[coral dew]

Ok it’s 14 and -9?

[kindred estuary]

Yes

[coral dew]

Thx!

Wait guys

What about this

Do I do same thing?

[kindred estuary]

Same process as before

[coral dew]

-5/2 and 4/3 I got

[kindred estuary]

Yes

[coral dew]

For this one should I use quadratic equation thing?

[kindred estuary]

You can

[coral dew]

I forgot the other ways

Are they easier?

[kindred estuary]

You can factor in general, like the other problems

[coral dew]

There was like perfecting the square or something

[kindred estuary]

But if you are just finding the solutions to that, quadratic formula is the quickest since it just gives you the solutions after applying it

[coral dew]

Ohh ok

What are the other ways tho?

[kindred estuary]

Factoring, completing the square

The tedious method is just plugging in each answer choice and see what results in 0

[coral dew]

Oh ok

Are the other ways important to know

[kindred estuary]

They are methods in solving quadratics, just depends on what you prefer

All the methods are valid methods

[coral dew]

If I can use one I don’t need the others right?

For future courses

[kindred estuary]

It just depends on the situation

Sometimes factoring isn't possible so you can complete the square to find the solutions

Quadratic formula is normally the last resort since it can be tedious to apply

[coral dew]

I have notes but they aren’t labeled which method I used

How to do perfecting square?

[kindred estuary]

If you have trouble with certain methods, googling them can be useful

[coral dew]

Ohh ok I will

[kindred estuary]

There are tons of resources/videos that goes through the process well

[calm coral]

@coral dew Has your question been resolved?

[coral dew]

Thxxx

Btw guys what’s this method called..? Just factoring ?

I think I did it wrong too

Why is it wrong

Ohhh

25

Yeah

It’s normal factoring right?

Not completing the square

Sorry weird question but -1^2 is 1 right?

Oh I don’t know

It was for this

Oh ok

That’s so weird

So this whole problem is messed up because the 1 isn’t negative?

,rotate

[coral dew]

I did +1 instead of -1

It’s completing the square

The 13 would have been 11

If I did -1

But I did +1

So is that wrong?

Because -1^2 is actually -1

[calm coral]

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).

[sleek phoenix]

Don care

[coral dew]

Oh ok

[sleek phoenix]

Alr sry

[coral dew]

Oh

We weren’t taught that

Idk identity

Only quadratic

Nope

Not yet

But what I did is still correct right?

Okay awesome

Oh yeah probably

In what case would it be -(1)^2?

Oh ok

[coral dew]

.close

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[dusky brook]

can anyone do this?

[calm coral]

Please don't occupy multiple help channels.

[pure kayak]

probably, do you have any idea though

[thick sinew]

consider the term within the root

[dusky brook]

yes i did the conjugate and loptial rule

[dusky brook]

i got here

[thick sinew]

argue via the relevance of 3x instead

regardless of what your limit will be, in the term 4x²+3x, the 3x is irrelevant in its contribution to the limit

because 4x² grows faster as x tends towards inf. or -inf.

thereby we can reduce the limit to:

sqrt(4x²)+2x

-> |2x|+2x

since x is negative

-> 0

@dusky brook

[dusky brook]

this is the original; problem

online calcul,ators are saying 3/4

[thick sinew]

ah ryt made a mistake

[dusky brook]

ok if you can do this I wqould be super grateful

I have these 3 probl;ems in my textbook that are bery similar but I dont know how to do them

[thick sinew]

hm am currently unsure

[dusky brook]

.close

[calm coral]

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[thick sinew]

sry came back late, but your initial approach would work

conjugate, then factor out x

gives you 3/(-sqrt(4-3/x)-2)

which tends towards -3/4

[runic rune]

do conjugate then divide everything by x

[calm coral]

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[normal wasp]

A train was moving but it suddenly stopped for 12 minutes after continuing to move the trains driver increased the trains speed by 20km/h and he made up for the 12 minutes stoppage over 99km what speed was the train moving before the stop

[pearl dune]

!status

[calm coral]

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

@normal wasp Has your question been resolved?

[normal wasp]

Idk where to start i mean ik i need to make a equation or a system but idk

[calm coral]

@normal wasp Has your question been resolved?

[calm coral]

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[undone gull]

I need help with this question

[drifting seal]

integrate

[midnight current]

you use an integral

[undone gull]

What about from x 0 to 2

[midnight current]

to find the area under a function you use a defined integral

[midnight current]

in this case the bounds would be 0 and 2

are you familiar with them?

[undone gull]

Oh

Yeah ty

My brain wasn't working ig

Sorry

Ty tho

[midnight current]

don't be sorry it's a help channel

[undone gull]

.close

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[blazing coyote]

so to start, I'm eliminating sphere as it has the lowest surface area to volume ratio

wait

they have equal masses, not volumes

hmm

but the rate of cooling by newton's law is area independent

which kind of cooling do I assume here

at the same time, assuming the cooling doesn;t follow newton's law

it should be the cube

it has the highest surface area to volume ratio

I feel I'm missing something simple

they. have equal masses, and density

oh, so their volumes are equal

<@&286206848099549185>

which kind of cooling do I assume

and if not the simplest form of newton's law, is it cube?

.close

[calm coral]

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[austere topaz]

i dont understand my teachers instructions

[austere topaz]

here are the steps

so my factor is 2.15

[astral mural]

I would recommend using the cross method

What can 6 be divided by?

[austere topaz]

i am not learning a new method

i got the quiz tmr

and its late

[astral mural]

I doubt there is an easier method than this

[austere topaz]

wym

ur method or this method

[short wedge]

yeah

[austere topaz]

yea i didnt get that middle term split

i wanna do it

the way my teacher did

or does

whatever u wanna call it

[austere topaz]

y is there a fraction

[astral mural]

It's an underline

[austere topaz]

oh

[astral mural]

4 + 6 = 10

[austere topaz]

what

[astral mural]

All my friends use this method in university

[austere topaz]

i aint in university

im ap psyed

100% in my class

yea

axc

[astral mural]

We can't tell you how to do this method without knowing the context

[austere topaz]

let me get an example

also does this count

i dont think i can use this

cuz its apparently to easy

but is this for when its 1 or not

heres a example tho

ac is 30

no factoring negatives

exponets

varibles

[astral mural]

You have cases where this method works and doesn't

[austere topaz]

well

u know what

teach me the other method

then

i got time

3+10

i think its better

to use a diff method

then whatever my teacher came up with

i dont like it

or i just dont like math

sure

or that switchy switchy method

that other person talked about

[austere topaz]

this

i liked this

come back pls

lets here your method tho

ye

-30

[astral mural]

Wait

Hold on

Where are you at rn

[austere topaz]

[astral mural]

Let's just start from the start

For example, we have a function like (3x^2 + 14x + 8)

[austere topaz]

ye

[astral mural]

What can 3 be factored by?

3 and 1, right?

[austere topaz]

1

ye

[astral mural]

Now, try for 8

[austere topaz]

1.8

[astral mural]

What are the possibilities?

[austere topaz]

2.4

[astral mural]

Nice nice

You want to multiply the two factors and the addition of the results should equal the middle coefficient of the function

[austere topaz]

so 3.1 is just 3

[astral mural]

3 * 2 = 6

[austere topaz]

and the 2.4 and 1.8 is

huh

[astral mural]

1 * 4 = 4

But if you add 6 and 4

[austere topaz]

wait are you crossing

[astral mural]

You don't get 14

[austere topaz]

both factors

[astral mural]

Yes

[austere topaz]

ooh

how do you know to factor 4 and 2

and not 1 and 8

or u just trail an error

or use ur head

[astral mural]

Yes

Trial and error

There isn't many possibilities, so it should be easy

[austere topaz]

yea

ok so continue

so u wanna get 14

right

[astral mural]

Yes

So multiply different factored numbers

What are they?

[austere topaz]

3.1 is 3 8.1 is 8

adding them up

gives 11

wait

what number should be first

big right

[astral mural]

That also doesn't work

Last chance

Or rather last possibility

[austere topaz]

what else can i do

3.1 is the only factor

8 has 1 and 2.4

oh

thats exactly it

[astral mural]

Yes

Good job

[austere topaz]

but what number goes first

or it dont matter

[astral mural]

wdym

[austere topaz]

like for factor of 8

2.4

[astral mural]

It does matter

[austere topaz]

so big number

or small number

or whatever works

[astral mural]

You have to do the calculation

Yes

If the coeff for x^2 is negative

Be sure to put a negative value for one of the factored number

Or if the coeff for x^2 is positive, both factored numbers can be negative

Because negative times negative is positive, right?

[austere topaz]

uh

yea ok

do me a favor if you could

could you write the steps down

you dont need to be super specific

just so i can have a look

let me answer the number in the mean time

4.3 1.2

which is 14

which is correct

well 3.4 but yea

and then what

[astral mural]

For what?

[austere topaz]

just like steps