help-17

[solid hornet]

Sort of, but the calculator does it all

[bold scarab]

There’s this thing if that’s helpful ?

[solid hornet]

Unfortunately on the Ti-84 there is no way to get the calculator to get the scales for you and I suspect that might be the case with the Casio

But we can use other information from before

And make that the max and mins

So we can do it from here if you want

[bold scarab]

OH MT GOD

[solid hornet]

What

[bold scarab]

THAT WAS THE PROBOEM THE ENTIRE TIME??? I HAVE A GRAPH

[solid hornet]

Yeah that's what I thought.

[bold scarab]

Holy crap

I’ve been panicking

Thanks so much for the help

[solid hornet]

It's good that it is working now though

Okay

Now it's way easier to find the max and min

[bold scarab]

Yup 👍 I just pushed buttons to get the answer

Si I think that’s it

.close

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[solid hornet]

Nice Job

[vocal sleet]

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[sharp birch]

Assume that v(0)=0
Show that v(t)= for all t positive reals

[sharp birch]

Idk what i'm supposed to do

[warm path]

the problem might be a bit misleading

it should be
$$\frac{d}{dt}v(t) = -0.16v(t) + 9.81$$

[twin meteor]

spotify ads

[warm path]

to get that.

if not, you will get t^2 thingy

I think that should help you solve the problem

[sharp birch]

humm

[warm path]

or do you know how to solve that differential equation?

[sharp birch]

yeah but solve that equation didnt solve the problem

[warm path]

it actually is...

what do you have that leads to that conclusion?

[sharp birch]

yeahh I've found it

ok mb

Just need to simply solve the differntial equation find k and we got v(t)

[warm path]

yes

[sharp birch]

👍

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[lilac sluice]

for an angle-chord relationship (left image), why is it corresponding sides of CONGRUENT triangles while for a chord-angle relationship (right image), why is it corresponding angles of SIMILAR triangles?

[lilac sluice]

basically im asking why is one congruent and one similar

[novel ruin]

AB=CD in the right side?

[livid horizon]

Is any info given about the two angles?

[lilac sluice]

wth

[livid horizon]

Ignore

[lilac sluice]

for angle chord alpha = beta

and ur proving ab = cd

opposite for chord angle

[novel ruin]

hard to translate from english to my native language, but the only difference i see is that its given in the right image AB=CD

[lilac sluice]

yes

but

im asking why is that simliar

and the other is congruent

[novel ruin]

because similar means same angles

congurent means same triangle

[livid horizon]

And in the left one the two angles are the same?

Hmm

[lilac sluice]

yes

[livid horizon]

Both of em are congruent then

Left one by SAS and right one by SSS

[lilac sluice]

thats what i thought

but in my notes it's not

[livid horizon]

Where was it mentioned that they're similar btw?

[lilac sluice]

lemme show u

[livid horizon]

Kk

[lilac sluice]

right image

[livid horizon]

Oh ok

Similar is not the wrong term to use, but using the term congruent is more specific

But yes both of them are congruent

[lilac sluice]

so i could say corresponding angles of similar triangles?

sorry not similar

congruent

congruent triangles?

[livid horizon]

Yeah

[lilac sluice]

so why do they use similar in this case tho

[livid horizon]

All congruent triangles are similar

[lilac sluice]

doesnt congruent mean same size and shape

[livid horizon]

So in this case you can use them interchangably

But not everytime

[lilac sluice]

while similar is just same shape

[livid horizon]

It does, yes

[livid horizon]

No not quite

[lilac sluice]

oh fir enough

[lilac sluice]

they would have the same angles tho right?

just not the same lengths

[livid horizon]

Yes, same angles and the corresponding sides have the same ratio

[lilac sluice]

alr

[livid horizon]

In congruent triangles this ratio is 1

Since corresponding sides are equal

[lilac sluice]

oh yea

so in this case would it be more appropriate to use similar or congruent triangles as my reasoning?

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[tribal mulch]

On number 5 i got the question right, but im confused on how i got it right because i dont think my reasoning is correct

Is x greater than w because w isnt a right triangle?

wait

yeah that’s probably it nevermind

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[inner osprey]

specifically since it's acute

if the triangle were obtuse then x would be less than w

[tribal mulch]

wait

.reopen

[vocal sleet]

✅

[tribal mulch]

isn’t the first one also acute

because it’s a right triangle

[inner osprey]

a right triangle is classified as separate from an acute triangle

since an acute triangle is a triangle with three acute angles, and a right angle is not acute

[tribal mulch]

oh

wait i knew that I was just thinking about the angles in there

so the second one has all acute so they are all congruent right?

wait that’s for angles though im confused how that would help me find the outside part

would i use trig?

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[ocean pulsar]

I want to prove that f:]-1 , 1[ -> R with f(x)=$frac{2x}{1 - x^2}$ is continuous

[twin meteor]

Lukas

[peak matrix]

it's \frac

not frac

[ocean pulsar]

f(x):= $\frac{2x}{1 - x^2}$

[twin meteor]

Lukas

[ocean pulsar]

yeah, I'm just getting it typed down

my idea is to do $\lim_{x \to a} \frac{2x}{1 - x^2} = \frac{2a}{1 - a^2}$

[twin meteor]

Lukas

[ocean pulsar]

with a being an element of the interval ]-1 , 1[

on the interval ]-1 , 1 [

so far, I've taken an a from that interval and done the above.
The idea is that $\lim_{x \to a} f(x) = f(a)$

[twin meteor]

Lukas

[ocean pulsar]

I need to show that for every a ∈ ]-1 , 1 [ the above holds true

I'm not entirely sure what assumptions I am allwoed to make.

I have.

Just for clarity, how would I go about proving it with the definition?

The definition our professor uses is this: r ∈ N, D ⊂ R^r, a ∈ D and f : D → R
f is continuous in a if for every sequence (an) in D lim n→∞ an = a

$\lim_{n \to \infty} f(a_n ) = f(a)$

[twin meteor]

Lukas

[ocean pulsar]

Thank you! I'll have to spend a little more time grasping that definition, but it seems much more useful.

I'll just .close this for now

.close

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[magic lantern]

I don’t understand how in this solution they changed from this to this in red

[shadow raft]

is nothing more given?

[magic wasp]

It's the whole left hand side that changes, not just that red part

[stone gazelle]

They distributed the sin

[magic lantern]

I only don’t understand the red part

[magic lantern]

Yea

[magic lantern]

From where

Did they even get a sin to distribut

[stone gazelle]

-sin(x+y) (1+dy/dx)

Multiply the sin term with each term in the parentheses

[magic wasp]

That's a product

[magic lantern]

Then wouldn’t it be - sin(x + y) + - sin (x + y)dy/dx

So three times

[lime gorge]

Isn’t that what’s there

[magic lantern]

No

[stone gazelle]

Yeah thats what they have

[magic lantern]

No

[magic lantern]

It should have -sin three times

It only has it two times

[lime gorge]

Where would the third one come from

[lime gorge]

There’s no third one here

[magic lantern]

Oh

[stone gazelle]

There are only two terms in the parentheses

[magic lantern]

Nvm

Thanks

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[lime gorge]

coulda done this problem in 1 step smh 😭 calc1 gatekeeping the secrets to the kingdom fr

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[ornate cobalt]

Data set A consists of the heights of 75 buildings and
has a mean of 32 meters. Data set B consists of the
heights of 50 buildings and has a mean of 62 meters.
Data set C consists of the heights of the 125 buildings
from data sets A and B. What is the mean, in meters,
of data set C?

[shadow raft]

!status

[vocal sleet]

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

[ornate cobalt]

7

[shadow raft]

then what is it

[vocal sleet]

@ornate cobalt Has your question been resolved?

[ornate cobalt]

IM TAKING TO MY BOT

I DONT KNOW THE ANSWER

[ionic merlin]

Mean is the average.
You know average and size of A
You know average and size of B
How do you think you can find average of A + B?

[vocal sleet]

@ornate cobalt Has your question been resolved?

[glass grove]

I think you want to do this:

$\frac{(75 \cdot 32)(50 \cdot62)}{125}$

[twin meteor]

clonesolopros

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[keen pilot]

hi

[keen pilot]

ik this is a physics question but does anyone know how to find mass of an isotope without using unified atomic mass?

[shadow raft]

mass_proton*amount_of_protons+mass_neutron*amount_of_neutrons (+mass_electron*amount_of_electrons)

[vocal sleet]

@keen pilot Has your question been resolved?

[glass grove]

that is mostly true

[shadow raft]

whats missing?

[glass grove]

like a 0.0000000000000000001% or smth like that

[shadow raft]

from where

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[glass grove]

which comes from the strong nuclear force? idk

[shadow raft]

ah

strong nuclear force is cringe anyway

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[vast shale]

Trying to find the zero's for x^2 + 4x - 45 and I do grouping so I get 5 * -9 = -45 but then when I see the video I'm watching, the solution is (x + 9) and ( x - 5) which is not the same thing. How would I know which of either 9 or 5 is the negative please?

[novel ruin]

ask your self,
which numbers added are -4

[vast shale]

so sorry I understand now.

[glad python]

sum of solutions is the coefficent of x

[vast shale]

yep that.

.close

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[vast shale]

my apologies.

it just hit me as I waited for responses.

thanks anyway 🙏

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[trim lily]

is this correct

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[granite kettle]

hello I need help with mapping rule for transformed graph

[granite kettle]

i know the mapping rule is

let's say I needed to graph this function

my only difficulty is what to do with the k value since it's basically reversed than what you see in the equation

the k value is 1/3 and it means it's horizontally stretched by factor of 1/k which is 3

so does that mean I put 3 into the mapping rule or do I put 1/3 in the mapping rule

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[bright oracle]

Find from the definition the matrices of the given linear transformations in the indicated bases of the corresponding linear spaces.

[bright oracle]

Prove that the quadric (R,V,+,-), where
V ={(x,y,z) ∈ R3: x+2y +3z = 0} ⊂ R3
is a linear subspace of the space (R,R3,+,-).
verify that the vectors e1 = (-2,1,0) and e2 = (-3,0,1) belong to V, 2. verify that the vectors e1,e2 are linearly independent and form the base of the space V .

(-2,1,0) = k (-3,0,1)
Yh
-2 = -3k?
1 = 0k
0 = k
no value of k so they are linearly independent

idk how to show the latter

Same thing

[brisk cloak]

well V spans R3, so we know that the dimension of V is 3 right

we already have 2 vectors of V, all we need is a 3rd which is linearly independed to the other 2

[bright oracle]

How do I gyo about finding it

and

are you sure

Doesn't the above assert that the basis is formed of just two vectors?

[brisk cloak]

yeah ur right my bad, said a dum dum

since the 2 vectors we have are linearly independent we actually already know that they form a basis of V

but if you havent talked about that in class yet then we can go about proving it if you want to

are u familiar with the equivelancy there?

[bright oracle]

What? I have to prove it

[bright oracle]

How thlo

[brisk cloak]

if not, then just assume a vector u = (x,y,z) in the linear subspace V. therefore, the vector satisfies the equation x+2y+3z=0
now lets try describing that vector u using e1 and e2:
u= a * e1 + b * e2
(x,y,z) = (-2a, a, 0) + (-3b, 0, b)
therefore:
x=-2a-3b
y=a
z=b

substituting that in the equation x+2y+3z=0 we get:
-2a-3b+2a+3b=0 or 0=0, which of course is always true. so every single vector u that belongs in V can be written as the linear combination of e1 and e2

thats how we go about proving it

[bright oracle]

ok ty

Now let's solve this

Do I just write 4 equations here?

-2 = x - 5y
4 = x + y ->
2x + y = 7 -> 8 - 2y + y = 7 -> 2y = -y = -1 -> y = 1
x + y = 4 -> x = 4 - y

<@&286206848099549185> @brisk cloak

[tender moat]

wth is this

i have calc next year

this is acc terrifying

[bright oracle]

linear algebra

[bright oracle]

Those are the coordinates of v in V, I geuss?

and basis vectors aie figured out from
(x−5y,x+y,2x+y,x+y)=x(1,1,2,1)+y(−5,1,1,1)

i.e., they're (1, 1, 2, 1) and (-5, 1, 1, 1)

Yeah ok I solved this

Determine the kernels, images, their bases and give the dimensions of the kernels and images of the following linear transformations:

<@&286206848099549185>

[stone gazelle]

Start by finding the matrix that corresponds to each linear transformation

[bright oracle]

How

[stone gazelle]

L(v) = v’ means when the linear transformation/map is applied to some vector v, the result is v’

In matrix form, this would look like:
Lv = v’ where L is the matrix

[ L \begin{bmatrix} x \ y \ z \end{bmatrix} = \begin{bmatrix} x+y \ y+z \end{bmatrix} ]

[twin meteor]

shsgd

[stone gazelle]

If you are familiar with matrix multiplication, you should be able to find L by observation

[bright oracle]

?

[stone gazelle]

How comfortable are you with matrix multiplication?

[bright oracle]

Wut

Normally

If I have m * n and n * p matrices

a and b

then the resulting matrix
c_ij = sum from k to n of a_ik * bj

[stone gazelle]

Right, so what dimensions would L have

[bright oracle]

DImension is a number of linearly independent vectors

I would say that x + y and y + z are linearly dependant

since they both have y

if that's what yohu're referring ot

[stone gazelle]

No, sorry I mean structurally

So m*n what would m and n be for L

[bright oracle]

Dimensions

[stone gazelle]

But in the case of this equation

[bright oracle]

IDK what you'hre erferring to

pelase stop being vague

m is a number of rows, n is a number of columns

Here I guess you have two rows and one column

[stone gazelle]

the vector (x,y,z) is left multiplied by L.
The vector is a matrix with dimensions 3x1 which means L must have dimensions m x 3

The result (vector on right hand side) is a matrix with dimensions 2x1 thus m = 2

So you have
[ \bmqty{ a & b & c \ d & e & f } \bmqty{ x \ y \ z } = \bmqty{x+y \ y+z} ]

[twin meteor]

shsgd

[stone gazelle]

Can you see what L would be now?

[bright oracle]

1 1 0
0 1 1

[stone gazelle]

Yeah

That is the matrix that corresponds to the linear transformation L(x,y,z)

Now you can just use definitions of image, kernel etc

[bright oracle]

Alrig'ht ty

I'm tierd so I'll do it after waking up tho

ty

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[vagrant sable]

Ok weird question

[vagrant sable]

Why do we learn quotient rule

We have product rule already

F(x)/g(x) = f(x) * 1/g(x)

[vagrant sable]

This is faster

Since both need the name stuff

(F(x)g’(x) - f’(x)g(x))/g(x)^2

[tawny hollow]

It’s just preference

[vagrant sable]

Yall know product rule needs the same numerator (but its a + instead of a -)

[tawny hollow]

I remember having the same opinion, but I ended up doing the quotient rule anyways lmao

[regal bane]

Honestly because quotients are easy to spot. When the derivative gets complicated, I absolutely love reaching for a formula that works with the current form.

[delicate mason]

Yeah, quotient rule can be derived from product rule + chain rule, so it's not its own unique thing but rather a useful combination

[regal bane]

Plus all being over the same denominator is nice, usually saves a step

[vagrant sable]

Maybe its like complicated adult stuff bc-for example, (x+1)/(x-1) is faster with product bc you dont need g(x)^2

[tawny hollow]

Also I could play the same game by saying that in multivariable calculus, you realize one can even derive the product rule from the chain rule and etc.

[vagrant sable]

Yes that too but i feel like doing product instead of chain will make things harder

But i also felt like doing product is easier than quotient

Ok ig. Ty yall

[tawny hollow]

That’s perfectly valid!

[vagrant sable]

Ig ill see the importance of quotient when i advance in calculus? We’ll see

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[bright patrol]

dont rlly know how to start this problem

[red spruce]

you have to use Euclid's theorem to solve this problem

[inner osprey]

identify similar triangles and set up an equation involving ratios

[red spruce]

or that

[inner osprey]

pardon?

[mellow oyster]

there's three right triangles here, set up three equations using pythagorean theorem for each of them

[inner osprey]

no

that's the long way

[mellow oyster]

oh there's a faster way?

[inner osprey]

just said it

[mellow oyster]

oh i interpreted that as the same thing but i see what you mean

[bright patrol]

um how do i set uo that equation

[red spruce]

it's the same as finding the similar triangles and writing the ratios

[inner osprey]

yeah ok

"euclid's theorem" usually means something else

[bright patrol]

how do i set up the equation??

[inner osprey]

do you know what similar triangles are?

[bright patrol]

yes

same shape

diff size

[inner osprey]

yeah ok

[inner osprey]

first, it's good to know that all 3 triangles in this diagram are similar to each other

do you see why?

[bright patrol]

yea

they all salene too

scalene

so what do i do next

[inner osprey]

the ratios of corresponding side lengths in similar triangles are the same

you can use this fact to pick two of those similar triangles up there and set up an equation using the variable y

[bright patrol]

what if i choose that small triangle on the left

and the other ttriangle

[inner osprey]

the two triangles you want to pick should have y as a side length

[bright patrol]

so that small triangle

and the triangle that the 2 smaller triangles make up

[proper dock]

what is the question

[bright patrol]

^

[proper dock]

right

so x^2 = 12*3

so x = 6

[bright patrol]

i need y

and z

[proper dock]

yeha

use pythag theorem

and tell me what u get

[bright patrol]

how do i use pythag for this?

[proper dock]

x = 6

do you get it

[bright patrol]

yea

[proper dock]

so there is a right triangle

with hypotenuse

y

with legs of lenght 3 and 6

and another one

with legs of length 6 and 12

with hypotenuse z

[bright patrol]

if legs are 6 and 3

i gt 6.71

13.42 if legs are 6 and 12

[proper dock]

lemme use calculator rq

yes

so y = 6.71

it only asks for y

[bright patrol]

what does it mean by round ur answer to one decimal place

[proper dock]

nearest tenth

i think

so 6.7

[bright patrol]

ok

in the same assingmnet

it also asks for z

[proper dock]

then

13.4

[bright patrol]

X

i meant

x

x =6

[proper dock]

x is 6

[bright patrol]

?

yea ok

[proper dock]

yes

[bright patrol]

ok tysm

u helped me a lot

[proper dock]

yeah no prob but do you get why x =6?

[bright patrol]

yea

3/x=x/12

i think

[proper dock]

yes, but i nthe future remember the theorem

that the two parts of the hypotenuse cut by the altitude multiplied by eachother is the square of the altitude

[bright patrol]

oh ok

thanks

[proper dock]

np

[bright patrol]

.lose

.close

[vocal sleet]

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[inner osprey]

that's correct but better way to do this problem is to directly solve for y

not get x first, then y

if u use similar triangles on y, you have y/3 = 15/y

so y^2 = 45 and then you just find decimal

[bright patrol]

oh

alr

thaks

[vocal sleet]

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[simple quarry]

Posted it before in another server but
If I have an empty set and I add something to it such that there is no longer an empty set, could it be said that empty sets are temporal or does the definition by itself disallows that? Maybe in a practical way?
Sorry my math knowledge is really bad I just read a bit of the Wikipedia page and I became interested

[simple quarry]

For example, in coding most arrays begin as empty sets but you can easily add elements to it

[shadow raft]

if you have an empty set, and add an item to it, its no longer an empty set

[vocal sleet]

@simple quarry Has your question been resolved?

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[pulsar bridge]

Ive started doing the sat course on Khan and Ive encountered this explanation for a Equation, the second line confuses me. I can understand the first half with multiplying (3x) and (1)by 2 but the second half is very confusing, where do the two* -1 come from and why is it allowed. I dont really get how the solution can remain the same with such a big shift.

[vast shale]

The -1 is implied by the subtraction sign

-(9-2x)=-1(9-2x)

They just distributed the -1 to both the terms

@pulsar bridge

[pulsar bridge]

okay

[vast shale]

Good luck preparing for the SAT

[pulsar bridge]

thanks

.close

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[steel lance]

Hello, I'm not sure where to ask this but if anyone has any ideas on how to solve my problem it would be greatly appreciated.

I have a list of 100 random points on a 2D plane (each have a random x and y value). The goal is to sort them into a 10x10 grid where each grid cell is occupied by only one of these points, based on their random x and y position. The result would therefor be the original 100 points evenly spaced out from each other.

[sly sierra]

what do you mean by sort?
what's the end goal, to have each point randomly located in its own cell?

[steel lance]

the goal is to have all the points be evenly spaced out from each other on a 10x10 grid, from the original random arrangement of 100 points

kind of like how particles of water will space out to fill a container, but each point needs to snap to a point on a 10x10 grid

the first thought I had would be to iterate through each point on the 10x10 grid and find the nearest point to it, but when there are clusters, some points get ignored until the very end

[vocal sleet]

@steel lance Has your question been resolved?

[steel lance]

.close

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[vagrant sable]

Ehm ehm

[vagrant sable]

A parallelogram

Its base is a square

Its length is x

Its height is y

Its volume is 80

[scenic ravine]

volume?

[vagrant sable]

Whats dy/dx when x=4

[vagrant sable]

Ah- حجم

Translate

[scenic ravine]

area?

[vagrant sable]

No its a 3d shape

Wait

Cuboid

Not parallelogram

Cuboid

A cuboid

Its volume is 80

Base is a square

Length is x

Height is y

Whats dy/dx

So

The volume of a cuboid is height times base times length

So… whats the base?

Is it x?

[vagrant sable]

(I meant cuboid)

[scenic ravine]

not sure, sorry

so volume is $V=x^2y$

[twin meteor]

ƒ(Why am. I here)=I don't know

[scenic ravine]

differentiate that

[vagrant sable]

So y=80/x^2

A sec

[vagrant sable]

-(80 *2x)/x^2

?

-40 when you plug in x=4

Its wrong

The question is a choose question

And none of the answers is -40

[scenic ravine]

what's the question?

[vagrant sable]

A cuboid

Its base is a square

Its length is x

Its height is y

Its volume is 80

Whats dy/dx

[vagrant sable]

[bitter pilot]

is that your derivative?

[vagrant sable]

Y=80/x^2

Yes

[bitter pilot]

that your function

now differentiate it

,,y = \frac{80}{x^2} = 80x^{-2}

[twin meteor]

𝔸dωn𝓲²s

[vagrant sable]

I mean… here?

[bitter pilot]

use power rule to differentiate

[vagrant sable]

Oh

Ok

5/2

[bitter pilot]

If we apply d/dx on both sides

[vagrant sable]

Yes

But what was wrong with my quotient rule

[bitter pilot]

,,\frac{\dd y}{\dd x} = \frac{\dd}{\dd x} (80x^{-2})

[twin meteor]

𝔸dωn𝓲²s

[bitter pilot]

that's too overkill

[vagrant sable]

Yes its 5/2 when x=4

[vagrant sable]

Idk im dumb

But like

Still

Can you show

The steps

But with quotient

[bitter pilot]

but quotient rule would be $$\frac{\dd y}{\dd x} = \frac{(80)' \cdot x^2 - 80 \cdot (x^2)'}{(x^2)^2}= \frac{0 \cdot x^2 - 80 \cdot 2x}{x^4}$$

[vagrant sable]

Bc idk what i did erong

X^4

.

🤦‍♂️

Sorry

I didnt square the bottom

[twin meteor]

𝔸dωn𝓲²s

[vagrant sable]

Ok ty ig

[bitter pilot]

np

[vagrant sable]

.close

[vocal sleet]

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[vocal sleet]

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[balmy mica]

hey in quadratic equation -6x2-6x+12=0
do i need to simplify it to slove it or i can procced with it
like solution i saw did this 6(-x2-x+2)=0
-x2-x+2=0

[balmy mica]

like if i dont simplifiiy it i can still get the correct answer right

[fallow igloo]

you can get it but the calculation will be heavier

[balmy mica]

i got it but wrong

Wait

i got the signs flipped

its 1 and -2

as correct ans

[unborn linden]

wait let me confirm

is this the q

[balmy mica]

yes

[unborn linden]

$\frac{4}{x} - 3 = \frac{5}{2x+3}$

[twin meteor]

poudel

[unborn linden]

??

[balmy mica]

ye

[unborn linden]

yeah aigh

yk how u have $-6x^2 - 6x + 12 = 0$

[twin meteor]

poudel

[unborn linden]

divide both sides by -6

and it should be chill

[balmy mica]

ye

[unborn linden]

i dont see anything wrong w ur working out

[balmy mica]

but my ans had signed flipped

[unborn linden]

$x^2 + x - 2 = 0$
\ $(x + 2)(x-1) = 0$

[balmy mica]

the coorect is 1 and -2

for the roots

i got -1 and 2

[twin meteor]

poudel

[balmy mica]

cant locate the error

[unborn linden]

you just solved ur quadratic weong

[balmy mica]

idk where tho

[unborn linden]

icl i can barely see qhat u did

i ur mistake nvm

i gotchu

[fallow igloo]

is that -5 on RHS

[unborn linden]

u incorrected said that $-6x$ is the same as $12x - 6x$

@balmy mica

[twin meteor]

poudel

[balmy mica]

no

[unborn linden]

look at the very last line u wrote on the left hand column

[balmy mica]

wait lemme see

[unborn linden]

basically $-6x^2 -6x + 12 \neq -6x^2 -6x + 12x + 12$

which is just straight wrong

[twin meteor]

poudel

[unborn linden]

it should be

[balmy mica]

i split it wrong

[unborn linden]

Should be $-6x^2 -6x + 12 = -6x^2 +6x -12x + 12$

yeah

lmao

im just practising my math type while we're here

[twin meteor]

poudel

[unborn linden]

yeah but

key take away would be simplifying the coeff as much as possible

[balmy mica]

i meant to write -6x2-(6-12)x+12

[unborn linden]

before u solve

like if u just divided by -6 on both sides

i doubt u wouldve made that mistake

[balmy mica]

so i just wrote the correct one on the next line

[unborn linden]

wdym

r u saying yhat ur method is still correct

and that u only messed that line up

[balmy mica]

no

wait

[unborn linden]

or u chillin now cause yk what u did wrong

[balmy mica]

it was correct till -6x2-6x+12=0 right

[unborn linden]

no

thats also correct

it was correct until

-6x^2 -6x + 12x + 12 = 0

u made this mistaking when u tried splitting the -6x

[balmy mica]

oh

[unborn linden]

do u get what im saying or nah

[balmy mica]

wait how

[unborn linden]

$12 - 6 = 6 \neq -6$

[twin meteor]

poudel

[unborn linden]

this is basically the mistake u made

[balmy mica]

-6x(x+1)=-6x2-6x

oh the other side

[unborn linden]

that isnt the mistake im saying u made

lmaoo

i meant left column very last line

[balmy mica]

ye so there the second last line is inccorect

[unborn linden]

yeah

i gtg now bro but yh thats the mistake

gl

[balmy mica]

ohk

thanks for the help

[unborn linden]

nws

[charred anvil]

I'll take it from here

[balmy mica]

so

he said it was the last line

but if u would see the line before i gave a=-6

its -6x2-6x+12=0
and i broke it into
-6x2-(-6+12)x+12
which iis wrong

wait

oh

i just thought i had to break -6 forgetting the minus sign would be outside the bracket

well

thx

[charred anvil]

At least give me the final answer you get

I'm having a bit of a stroke reading your sentences but no worries

[balmy mica]

well the final answer is -1 and 2

my old ans had flipped signs

[balmy mica]

yea i get that a lot

[charred anvil]

Isn't that your old answer

[balmy mica]

my old one was 1 and -2

wait a sec

it was -1 and 2

[charred anvil]

[balmy mica]

wait my brain broke

ye final is -2 and 1

[charred anvil]

Man I'm starting to get confused too

[balmy mica]

brain not functioning man

[charred anvil]

Lemme recheck

[balmy mica]

but frfr its -2 and 1

[charred anvil]

Ye ye you're right

I want to know why you approach this path tho

[balmy mica]

now im gonna try solving it with quadratic equation cuz for some reason dude wants that

[charred anvil]

The last line in left column I mean

[balmy mica]

huh

[balmy mica]

the old one?

oh i thought i did it wrong

[charred anvil]

Well what's your current equation

If you were to correct that line

[balmy mica]

like i assumed that i had to split -6

but i then went and put bracket around 6

like
-(6)

so i was spliting 6 now

so when i try added it made 6 at the place of -6 forgetting i left minus outside the bracket

so i flipped the sign to make it -6 in last line

understandble?

[charred anvil]

Ohhh I see now

[balmy mica]

its even my 2nd times in 2 days for this same type or mistake

so ye

anyway

[balmy mica]

now

[charred anvil]

Alright

[balmy mica]

i gotta melt my brain again

[charred anvil]

You know how to do it right?

[balmy mica]

i always hate underoot

[balmy mica]

well ik the formula so i will jjust put the values and try solving

but thats the place where i always mess up

so cant say confidently

[charred anvil]

Honestly using the formula for this is very bothersome

[balmy mica]

ye right

[charred anvil]

But it's what he wants so lmao

[balmy mica]

fr man

[charred anvil]

Alright try the equation

[balmy mica]

ok

and thankyou for the help

[charred anvil]

Are you going to do it now or later

[balmy mica]

now

[charred anvil]

I want to sit you through the whole thing

[balmy mica]

but this might close

[charred anvil]

In case your brain deactivate lmao

[balmy mica]

ok then

i am on it

[charred anvil]

Alright take your time, dont rush

You could also divide the equation by -6 like the last guy said

-6x2-6x+12=0 This part I mean

Making the equation as simple and low as possible will make things easier

[balmy mica]

so x2+x-2?

[charred anvil]

yep

The value of a b c will be lower and easier to calculate

[balmy mica]

oh so thats why the solution did it

i was like why is he doing it and why am i getting wrong answer

[charred anvil]

You dont necessary have to do it, it just make thing easier

You will still get the same answer just maybe slower

[balmy mica]

well i got -1 (plus minus) 3/root2

how do i deal with plus minus symbol?

[charred anvil]

Why did you get 3 root 2?

[balmy mica]

well i got -1 (+-)root(9/2)

so i changed it into that

[charred anvil]

9/2?

The eqution is b^2 - 4ac right?

[charred anvil]

ahhhh

You see your root

The root is only for the numerator

(the top part)

[balmy mica]

ohhhhh

makes sense actually

[charred anvil]

Yeah try to write your equation clearly

[balmy mica]

well question still remains

[charred anvil]

Yourself and others sometimes get confused if you write something wrong

[balmy mica]

how do i deal with +- sign

[balmy mica]

yea i see now

[charred anvil]

+- means that there will be 2 answer

[balmy mica]

?

[charred anvil]

one using + and the other using -

[balmy mica]

oh

ok

dude i got the answers as 1/2 and -5/2

[charred anvil]

Huh

what's your final equation before dealing with +-

[balmy mica]

which as far as i can recall isnt =1 and -2

-1+-(3/2)

[charred anvil]

ah I see

[balmy mica]

wait is 2 under -1 aswell

[charred anvil]

Fyi this is the full formula

[balmy mica]

no way right

[charred anvil]

I dont know how to use the bot lmao

[balmy mica]

bruh

either i was drunk when i wrote it or its the place i copied it from's mistake

[charred anvil]

Eh, sometimes you just remember it wrong

[balmy mica]

how did i not take -b under underoot but took 2a

[charred anvil]

Dont worry, youll get used to it as you use it more

[balmy mica]

well lets see now

well got the ans

now i have 40 minutes of lecture to watch to understand rest of the chapter

[charred anvil]

Haha gl

Generally you dont use this formula unless you cant factor it at all

[balmy mica]

well the dudes a devil

[charred anvil]

Fr

Or just bad example of question

Also one thing

[balmy mica]

yea

[charred anvil]

How do you seperate x^2 + x - 2 = 0 ?

Seeing the way you do it, it's a bit different from what I do and Im curious

[balmy mica]

a=1,b=1,c=-2

[charred anvil]

Like how do you turn it to (x-1)(x+2)

[balmy mica]

1*-2=-2

[charred anvil]

Ah so it's not different then

[balmy mica]

x2+(-1+2)x-2

[balmy mica]

what did u thought

[charred anvil]

I make a mental math like this

1 2
x
1 -1

x is a cross btw

Left column is from seperating (1)x^2

Right is from -2

[balmy mica]

man im confused

[charred anvil]

When you cross multiply and add it together it should equal the middle value

so 1x2 + 1x-1 = 2+ (-1) = 1

[balmy mica]

it doesnt feel like u speaking the same language anymore

[charred anvil]

It's hard to explain like this but if you understand it, it's very quick mental math

Don't be concerned about it, I think your teach would want you to "show your work" anyway

[balmy mica]

well thats factz

well i should start watching the lecture

[charred anvil]

Yeah Gl

[balmy mica]

this chapter is taking longer than it should have

thanks

[vocal sleet]

@balmy mica Has your question been resolved?

[weak topaz]

g

[vocal sleet]

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[vocal sleet]

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[surreal marten]

can anyone help me with the 4 th question

[scenic ravine]

!status

[vocal sleet]

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

[astral pilot]

make cases

[scenic ravine]

|x|= x when x>0

and |x|=-x when x<0

[surreal marten]

i know that but for some reason i m just getting stuck midway

[scenic ravine]

then show us your work

please

[surreal marten]

ok

see the red box part i dont know where i am goin wrong

[scenic ravine]

,rotate

[scenic ravine]

so x=5 is a valid solution

but NOT x=5/3

why?

[surreal marten]

tht is my doubt why is x=5/3 is not a solution

[astral pilot]

bcz x<0

[scenic ravine]

because you define x<0 when solving it

[surreal marten]

oh my 😞

bad

sry for such a stupid doubt

.close

[vocal sleet]

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[vocal sleet]

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[thorn coral]

guys i need some help for this question

.reopen

[orchid wren]

Hi

you know binomial distribution ?

@thorn coral ?

[vocal sleet]

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[orchid wren]

See np = 5
npq = 4
So dividing , q = 4/5
So p = 1/5
n = 25

[orchid wren]

.close

[vocal sleet]

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[fallen hawk]

that was some quick help

[thorn coral]

ooo silly me, i miscalculated n to be 5 for some reason lol

thanks for the help

[vocal sleet]

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[paper sierra]

help urgent pls

[vocal sleet]

Please don't occupy multiple help channels.

[fallen hawk]

oh you're in an exam arent you

[paper sierra]

im sorry for the disturbance i still dont get it

[paper sierra]

how am i in an exam if im taking a picture of my workings bro

im just getting triggered

[fallen hawk]

i've done it in the past...

[paper sierra]

on why

[midnight stone]

lol

[paper sierra]

well here u cant take a pic mid exam

[fallen hawk]

also, youcan clearly see in the picture that the graph is not continuous at 0

[paper sierra]

not even cheat

[fallen hawk]

which one do you think it is

[astral pilot]

Umm, so derivative is defined based on limits, now, if you see, when 0 is approached from both sides then you will get different answers, so limit does not exist

[paper sierra]

hm

yeah

okay

oh so its because of the definition of derivative

i suppose

[shadow raft]

for the derivative to exist, the left and right limits at that point need to be equal

[paper sierra]

yeah i got it i think

[astral pilot]

we call that the function is not differentiable at x = 0

[paper sierra]

got it

[vocal sleet]

@paper sierra Has your question been resolved?

[vocal sleet]

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[cedar linden]

$f(x, y) = \ln^5(x^y + x^2 + 2^y)$ \newline
calculate $\frac{\partial , \f}{\partial , y}, \frac{\partial , \f}{\partial , x}$

[twin meteor]

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

[cedar linden]

dont know anything

i know basics derivatives things

but i dont know this topic

[shadow raft]

do you know what it means to take a partial derivative?

[astral pilot]

treat other variables as constants

chain rule

[cedar linden]

aight

i dont think i will solve this problem

but

is this topic hard_

? or easy to learn

[astral pilot]

easy

[shadow raft]

if you can do normal derivatives

[cedar linden]

aight ❤️

[shadow raft]

partial derivatives shouldnt be much of a problem

[cedar linden]

yes i can, i also can do integrals

thanks guys ❤️ for nothing

.close

[vocal sleet]

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[astral pilot]

💀 :

[vocal sleet]

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[undone crane]

I can't figure out how to completely solve this, I can't wrap my head around it

[undone crane]

I did x = -y and x = y

[scenic ravine]

good , use that now

[astral pilot]

system of equations?

[undone crane]

and I got -(y^3) + (-y)*y = 0 which I didn't know what to do with

[astral pilot]

factorise

there are exactly 3 solutions to this

[astral pilot]

or atleast one which i could find

[undone crane]

I'm aware of that, I don't know how to get solutions other than (0,0)

[undone crane]

what is there to factorise

[astral pilot]

-y^3 - y^2 =0

[undone crane]

I guess my factorising game is pretty weak

[astral pilot]

-y^2(y+1) = 0

-y^2 = 0 or y+1 = 0

y=0 or y=-1

did you get this?

yo?

[undone crane]

yea sorry I also tried factoring it myself

is (y^2)(-1-y) also a viable way to factor?

[astral pilot]

yes

that is also right

[undone crane]

from that I get y = 0 or y=-1

[astral pilot]

yes

[stone gazelle]

@undone crane i’d say its easier to sub in for y

[astral pilot]

ok if y = 0 then x^2 = 0, so x = 0

if y = -1 ??? then what?

[undone crane]

then x = 1

[astral pilot]

and?

[undone crane]

also -1 because x=y

[astral pilot]

yes

so there are your three point

[undone crane]

(0,0)
(-1,-1)
(1,-1)

that was a lot simpler than I thought lol

[astral pilot]

yes

lol

[undone crane]

I have a hard time noticing opportunities to factor

do I always factor whenever I have the opportunity or is it something I have to see?

[astral pilot]

depends on the question, generally when something = 0 is good time to factorise

[undone crane]

what about when simplifying equations

[astral pilot]

yeah that's what simplifying means

[undone crane]

I've really struggled with simplifying this one for example because I think I missed an opportunity to factorise

I always reach something weird like 3/((x^2)+2x)

[vocal sleet]

@undone crane Has your question been resolved?

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[odd willow]

Please help me guys

[astral pilot]

cross multiplication

[odd willow]

?

Pls help

[odd willow]

I know what cross multiplication is but uow would it help here

Can you help me

[astral pilot]

try adding both fractions

[north frost]

Rationalisation

[lethal bison]

how bro

haah

[vocal sleet]

@odd willow Has your question been resolved?

[lethal bison]

idk guys ur all just typing 1 word every 10 mins i cant get it to work

[astral pilot]

wdym bro, this isn't your channel

[north frost]

Oh I see

I thought you asked the question 😆

[vocal sleet]

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[brisk idol]

test

[jade anvil]

test

[brisk idol]

hello i need help with this math problem

im dumb i tried using the math calculators like wolfram etc. but i cant understand how to get the answer

[astral pilot]

I see many problems, which one do need help with?

[brisk idol]

can you help me with no 7 first

[lethal bison]

val players

[brisk idol]

i got the a0 but i dont know if it is right

[wicked shard]

???

[brisk idol]

i searched youtube for the tutorial

im stuck in finding an and ab

like i dont know how to do the integral

I don't know what else to do

From the tutorial i need to insert n=1, 2 etc

[orchid wren]

,rotate

[brisk idol]

i got a0 is 10,25

[orchid wren]

Which one is question?

[brisk idol]

but im not sure if the T is right either 3/6

[brisk idol]

no 7 here

any clues?

i have a chat gpt generated answer but idk if it is correct

or maybe anyone can help with other questions?

<@&286206848099549185>

or maybe help with differential equation?

[noble tiger]

What is question 7 asking

[brisk idol]

question 7 is fourier series

i resend the picture

or can anyone help with partial derivative?

number 1 through 4 maybe?

maybe tomorrow someone can lend a hand

[gilded osprey]

What did you start