help-23

[solar hazel]

it’s correct, but i’m not sure how much “answer” is expected or how much you just understood lol

like

do you also need to show why that N works?

[gusty glacier]

wdym with works?

oh how it works?

[solar hazel]

i mean do you need to explain why for any epsilon, -epsilon < h(x) < epsilon whenever x > 1/epsilon^2?

or can you just say let N = 1/epsilon^2 and that’s a complete solution

[gusty glacier]

um yes i have to explain lol, but is that not since as you mentioned before cos(x) lies between -1 and 1 "so multiplying 1/sqrt(x) by cos(x) only brings 1/sqrt(x) closer to 0" thereby we can only consider the 1/sqrt(x) part meaning we get the equation 1/sqrt(x) < epsilon which we solve for x and this gives us x > 1/epsilon^2 thus it can be replaced as N, i.e N = 1/epsilon^2

[solar hazel]

yea that’s roughly the idea

[gusty glacier]

ok Thank you! and sorry for being after the answer so much instead of trying to understanding it, its just i understand easy when i have the answer and work my way backwards(excuse....)

oh well

THANK YOU!

[solar hazel]

loll np ^-^

[gusty glacier]

.close

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[brazen parrot]

hallo

[brazen parrot]

so im trying to find the x intercepts of (x+2)^2

but its wrong?

[peak estuary]

who says it is?

[peak estuary]

also you really don't have to multiply this out

[brazen parrot]

the x ints are 4, -4

[brazen parrot]

what do u mean

[peak estuary]

https://i.imgur.com/PVqbBLl.png

how is that 4 or -4

if 0=(x+2)(x+2), then you don't have to multiply this out and then factor it again

[brazen parrot]

for the xints of x points

like the ones i need to graph the thing

[peak estuary]

you can just directly get x+2=0

the x-intercept is at x=-2

just like the graph shows

and like your math shows

[brazen parrot]

i cant explain it like the xints for the curvy bits

0,4

like this one

[peak estuary]

that is the y-intercept

cause it intercepts the y-axis

[brazen parrot]

and this

[peak estuary]

you can get it by plugging x=0 into your function

the other one you dont need

[brazen parrot]

like how did they get -4 and 0

those x intercepts

[peak estuary]

again, those are not x-intercepts

[brazen parrot]

what are they

[peak estuary]

(0,4) is the y-intercept

(-4, 4) is just a random point

[brazen parrot]

i need those to graph the curve tho

i forgot how i found them

wait let me think of an example

[peak estuary]

yes and you can uniquely graph the curve by knowing the x-intercept is at x=-2 and the y-intercept is at y=4

[brazen parrot]

like this one

it hits at -4 and -2

[peak estuary]

yes for that function the x-intercepts are at x=-4 and x=-2

and for your first function you only have the x-intercept at x=-2

[brazen parrot]

im confused

why doesnt it work for 1st one

[peak estuary]

because it's a double root? I don't understand the question

[brazen parrot]

wait so can u tell me how i can find the points

to graph it

[peak estuary]

you did find the points

the x-intercept is at x=-2. it's a single x-intercept

[brazen parrot]

wut

[peak estuary]

and the y-intercept is at y=4

and with that you can graph it

[brazen parrot]

whatttt

dont i need one on the left to be accurate

or do i count how far it is from the y axis

[peak estuary]

you have to use that it is a single x-intercept

that means the minimum of the parabola is also at that point

[brazen parrot]

ok so this is what i did

i counted how many points the point of symmetry was to 0,4 on the x axis

and it was 2 to the right

so i also went 2 to the left and then went up 4

would that work in all situations

where it has a single x int

[peak estuary]

yes

[brazen parrot]

ok thank you soo much

im not the best at math lol

[peak estuary]

if it has a single x-intercept, then at that point is the point of symmetry

[safe radish]

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[simple saffron]

i need help

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[quasi bison]

let f(x) = a_0 + a_1 x + ... + a_n x^n, then you are told int[0,1] f(x) dx = 0 and are asked to show f has a root in (0,1)

[main lynx]

I know that by the definition of rolles theorem , i should find a function which when differentiated i should get something similar to a0+a1x+.......+anxn=0

f(0) and f(1)=0

right?

[quasi bison]

not with f as i defined it

[main lynx]

yea

I do not understand this step

why f(x) is taken as this

[quasi bison]

that way f'(x) will be the left hand side of your equation

[main lynx]

Ig is it because when we differentiate it , for example a_1x^2 becomes 2a_1x and that 2 will be cancelled out right and we will eventually get that a_0+a_1.......=0

[main lynx]

Sorry I did not get it

[quasi bison]

f'(x) = a_0 + a_1 x + ... + a_n x^n

[main lynx]

yup yup got it I just could not understand why they took f(x) as this

can I do it in the way you suggested?

letting f(x)=a_0 + a_1 x + ... + a_n x^n

[quasi bison]

... sure, it'll only be a difference in notation

[main lynx]

Could you please explain?

[quasi bison]

the solution will look a little bit different but it will essentially be the same as with their choice of f

the idea will be the same

or do you want me to write out in full what it will look like if you take f as i suggested

[main lynx]

yea please write out

could you?

[quasi bison]

let F be an antiderivative of f. then we know F(1)-F(0)=0, therefore F(0)=F(1), therefore by rolle's theorem F' has a zero in [0,1]

F' = f

[main lynx]

yes i understand what you said

so I should find the anti derivative of f(x)=a_0+a_1 x+.....

and then how do we know that F(1)-F(0)=0

is that a result

?

@quasi bison

[quasi bison]

see here

[main lynx]

.close

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[lean otter]

hey there

[lean otter]

needed help with this question

$x^3+\frac{2}{x^3} =0$

[flat frigate]

LordFoogThe2st

[lean otter]

i am getting a negative root as the answer

$x=i\sqrt[6]2$

[flat frigate]

LordFoogThe2st

[lean otter]

$x \notin R$ I believe

[flat frigate]

♡LexQa♡

[lean otter]

For this function at 0

gotcha

thanks

i was thinking of the same thing

but my book has a different answer for it

have a nice day btw @lean otter

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[lean otter]

Have a nice day too

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[safe radish]

Please don't occupy multiple help channels.

[simple saffron]

<@&286206848099549185>

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[vocal portal]

multiply by 8 both sides

[safe radish]

@simple saffron Has your question been resolved?

[simple saffron]

huh

[vocal portal]

y > -8

end result

[safe radish]

@simple saffron Has your question been resolved?

[simple saffron]

@vocal portal

[safe radish]

@simple saffron Has your question been resolved?

[safe radish]

@simple saffron Has your question been resolved?

[safe radish]

@simple saffron Has your question been resolved?

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[ashen totem]

If f(x) = -2x + 12, find f(6). Type only the number. ****

[urban dock]

Just plug in. Use your calculator or something.

[ashen totem]

i dont have one

[urban dock]

You can just plug in 6 for x

f(6)=-2+12

[ashen totem]

oo ur smart

so thats the answer?

[plucky elk]

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions

[safe radish]

@ashen totem Has your question been resolved?

[safe radish]

@ashen totem Has your question been resolved?

[lean otter]

F(6) is basically asking for the output that corresponds the input value of 6 or the y-coordinate of a point on the Cartesian plane, (6,y). To solve for the output, whenever you see an x, substitute it with a 6 because x=6. The left side of the equation will give you the final answer after you manipulate the numbers together in the correct order f(6)=-2(6)+12

[safe radish]

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[lean otter]

Can I use this app for this question

[acoustic wolf]

idk

u can do this w/o it tho

[lean otter]

i gotta solve the equation on papaer?

[acoustic wolf]

A = P(1+r)^n

[lean otter]

how u know to us this equation over another

[acoustic wolf]

this is the compound interest formula

[lean otter]

oh ok

its ez with the app tho

[acoustic wolf]

$A = 98000(1+\frac{0.041}{12})^{35*12}$

[flat frigate]

WhyWouldYouKap

[lean otter]

hard

no actually ez

ty for helping me

[acoustic wolf]

all good mate

A = 410559.80

[acoustic wolf]

sorry i misread the question

[lean otter]

ok

[acoustic wolf]

98000 is the amount not the principle

your answer is correct

[lean otter]

its ok

ty for teaching me

[acoustic wolf]

all good

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[acoustic wolf]

.close

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[fresh widget]

im confused how d(df) is proportional to $dx^2$ shouldnt it be proportional to $2dx$? because it took 2 steps to the right

[flat frigate]

LichBaw_GT

[fresh widget]

is there anyway to prove that d(df) is proportional to dx^2?

[sand minnow]

$df_1+df_2$ is proportional to $2dx$ but they are doing the derivative first $\dv{x}f(x)$ twice, so $$\dv{x}\left(\dv{x}f(x)\right)$$ so imagine that this is equal to some constant $a$ $$\dv{x}\left(\dv{x}f(x)\right)=a$$multiplying both sides by $dx^2$ and you get $d(df)=a dx^2$ honestly though this is kind of where the slope/graph arguments start to somewhat fail. in generally you want to think about $\dv{x}$ as an operator, aka the differential operator wrt $x$. treating it as a fraction start causing issues

[flat frigate]

Duh Hello

[safe radish]

@fresh widget Has your question been resolved?

[safe radish]

@fresh widget Has your question been resolved?

[fresh widget]

alr thanks

i thought as it as a small difference in y over a small difference in x

i guess i can try treating it as a differential operator wrt x

.close

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[safe radish]

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[lean otter]

Hello. Can someone help me out? I'm trying to understand point and line symmetry

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[lean otter]

.reopen

[safe radish]

✅

[lean otter]

<@&286206848099549185>

[unkempt perch]

i'd need more information to know how to help

do you have a sample problem that you're working on?

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

yeah for sure

there are essentially these 2 types of formulas

f(x)=f(-x)

and then there's a second one

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[celest plinth]

Hey I have a question

[celest plinth]

I was wondering how to, from a data set, create a set of rates to be used in a differential equation

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[frigid nebula]

why

[frigid nebula]

Why i cannot find the right value

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[lean otter]

hi i need help to give the derivative function from these functions

[warm stirrup]

use quotient rule and chain rule

[lean otter]

okay

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[sleek elk]

In automoata theory how do I tell if my NFA model is correct?

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[lean otter]

Solve for integer values: 23x + 29y = 7

[plucky elk]

euclidean algorithm

[lean otter]

im sorry i dont exactly know how to use it

hello?

[plucky elk]

https://www.khanacademy.org/computing/computer-science/cryptography/modarithmetic/a/the-euclidean-algorithm

whole lesson there

[lean otter]

ok

hope i get it

ty

.close

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[slender crypt]

How do I master simpluifying algebraic expressions?

[slender crypt]

y=3(x+5)(x-2)

[fossil turret]

practice

u want me to help u with that

[slender crypt]

indeed

[fossil turret]

so firstly u want to expand the first bracket 3(x+5) = 3x + 15

[slender crypt]

ok

[fossil turret]

so we now have (3x + 15)(x-2)

[slender crypt]

yes

[fossil turret]

the use foil to get a quadratic

so 3x^2 + 9x - 30

[slender crypt]

Thanks fo much dude

[fossil turret]

np

anytime

[slender crypt]

can you explain in anymore detail?

if that's possible.

[fossil turret]

um

sure i guess

y=3(x+5)(x-2)

so we want to expand this to eliminate these brackets

there are two ways of tackling this, either expanding the two brackets and then multiplying the result of that by 3

which i can show u that method

so with (x+5)(x-2)

u times x by 5 to get 5x

then times x by -2 to get -2x

then time -2 by 5 to get -10

then x times x = x squared which is x^2

add that together to get x^2 + 3x -10

and dont forget we have a 3 outside the bracket

so 3(x^2 + 3x -10)

which gives 3x^2 + 9x - 30

there you go

[slender crypt]

thx

i see i where i fucked up at dude thx forreal

[fossil turret]

np

[slender crypt]

thx

but one more

question

are you using foil in the second method

[fossil turret]

yes

[slender crypt]

ok thanks

[fossil turret]

u do the 3 last instead of first

btw -1x is -x

[slender crypt]

ok haha

[fossil turret]

lol

[slender crypt]

thx i got it

[fossil turret]

k

[slender crypt]

u were really helpful

[fossil turret]

good to hear

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@slender crypt Has your question been resolved?

[safe radish]

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[small rover]

Binomial coefficient

🙂

[warped heart]

can you please explain?

I don't really understand Binomial coefficient

[small rover]

occurrence of this number is in combinatorics, where it gives the number of ways, disregarding order, that k objects can be chosen from among n objects; more formally, the number of k-element subsets (or k-combinations) of an n-element set

That the formal definition

Here you have 6 person that you want to put by group of 2

[warped heart]

that formula?

[small rover]

yes

I think here n is 6 and k is 2

so if it's right the result will be 15

[warped heart]

ohhh, okay, thank you

.close

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[timid solstice]

5 + 8 + 11 + . . . + (3n + 2) = n(3n + 7)/2

[timid solstice]

I need help with this induction

I the first two steps wasily but then when I have to do n+1 I get lost

so its induction but with three steps the first 2 are eassy asf for me but the last is where I get lost

[plucky elk]

Show your work

[timid solstice]

can I just get the written solution

just for the n+1 part

I've been studying for 4 hours i can't write anything else

[lean otter]

#❓how-to-get-help

[timid solstice]

I'm discussing tho

[proud belfry]

ok

what are u struggling with

@timid solstice

[timid solstice]

So the 3 steps

I get the first two easily always

[proud belfry]

what 3 steps

[timid solstice]

So 1st step is to calculate is the first elemen equal to the other side

For n=1

[proud belfry]

yes

base case

[timid solstice]

Yes

[proud belfry]

what is step 2

[timid solstice]

Then the assumption

Which is just rewritten start

[proud belfry]

ok

what are you struggling with

[plucky elk]

helpers dont' give solutions. follow server rules

[proud belfry]

what is step 3

[timid solstice]

Step 3 is you have to test it for n+1

[proud belfry]

okay

[timid solstice]

You add +1 to the every n in the induction

[proud belfry]

what?

ok

so

do you have experience

with induction proofs

[timid solstice]

Yes

There were some that I got correct

But idk why I get confused with some like these

Which seem so easy

[proud belfry]

ok

try to go from one integer to another

so we have the sum of all.. whatevers + 3(n+1)+2

[timid solstice]

When I add +1 would that be 3n+5

Soo that what you wrote

[proud belfry]

so that is $\frac{n\left(3n+7\right)}{2}$+$3n+5$

[timid solstice]

Isn't it 3n+5

[flat frigate]

hired

[proud belfry]

yes

it is

anyway

[timid solstice]

That is equal to (n+1)(3n+10)/2

[proud belfry]

now we have $\frac{\left(3n^2+7n\right)}{2}+3n+5)$

[flat frigate]

hired

[proud belfry]

then you add the other terms

factor it

and you get that

so

gj

so

what was your problem

[timid solstice]

Proving that left side is equal to fhe right side

[proud belfry]

that

what

[timid solstice]

Now you have to like

Do math

And conversions

So that one side is the same as the other one

[safe radish]

@timid solstice Has your question been resolved?

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[lean otter]

How did it become fd

[proud belfry]

is f(x) a linear function

[lean otter]

No

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

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[forest obsidian]

I would like help factoring a quadratic equation

[compact egret]

What have you tried

[forest obsidian]

well, i haven’t i’m not rlly sure where to start

i believe i’m suppose to find the common factor between the given numbers

[obtuse plover]

Do u know the ac method

[forest obsidian]

i do not

[obtuse plover]

so our standard form is ax^2 + bx + c

U wanna find factors of ac that add to b

So what would ac be here

[forest obsidian]

1 and 24?

or 2

[obtuse plover]

well

ax^2 + bx + c

x^2 - 5x - 24

a = 1, b = -5, c = -24

[forest obsidian]

yes

[obtuse plover]

So what’s ac

[forest obsidian]

1 and 24

25?

[obtuse plover]

ac = -24. a = 1, c = -24. ac = a * c = 1 * -24 = -24

[forest obsidian]

i don’t get that

[obtuse plover]

Don’t get what?

[forest obsidian]

this

why’s it -24

[obtuse plover]

Do u get that a = 1

[forest obsidian]

yes

[obtuse plover]

Do u get that c = -24

[forest obsidian]

yes

[obtuse plover]

So what’s a * c

[forest obsidian]

OHHHH

-24

😅

[obtuse plover]

Yea

So

What are factors of -24 that add to -5

[forest obsidian]

1 and 5

[obtuse plover]

So 1 * 5 = -24 ?

[forest obsidian]

oh

2 and 12

but they don’t add to -5

[obtuse plover]

Right, and they don’t multiply to -24

Don’t forget the minus sign

But if you did include it, it still wouldn’t work

[forest obsidian]

hmmm

so it has to multiply and get -24 and add to get -5

[obtuse plover]

Yes

[forest obsidian]

-4 and -6

wait

nvm

[obtuse plover]

Ur so close lol

[forest obsidian]

i honestly have no idea

is there an easier way to figure it out

[deft tartan]

what 2 numbers do u multiple to get a negative number

[deft tartan]

this is probably the easiest, imo

[forest obsidian]

-1*1

[deft tartan]

yes

so u need a negative and a positive

that adds up to -5 and multiple to 24

[forest obsidian]

-4 * 6 will give me the -24

[deft tartan]

anyways, gtg, in school

[forest obsidian]

but not the -5

[obtuse plover]

Right

U went from 2 and 12 to 4 and 6

What about in between?

[forest obsidian]

OHHH

-3 and 8

[obtuse plover]

So they multiply to -24 but what do they add to?

[forest obsidian]

5

[obtuse plover]

Right, and we want -5

What’s an easy fix we can do

Using the negative sign

[forest obsidian]

3 and -8

[obtuse plover]

Corrrectttt

So 3 and -8 multiply to -24 and add to -5

[forest obsidian]

yes

[obtuse plover]

So our two values we got are +3 and -8. To factor them, we just put them in parentheses and put an x in front of each of them

So it becomes (x+3)(x-8)

Do u get how we did that

[forest obsidian]

yes

[obtuse plover]

Cool

[forest obsidian]

oh is that it

[obtuse plover]

Yea

[forest obsidian]

thank you

.close

[safe radish]

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[iron glacier]

If you take the derivative of something and then factor it out, would the derivative of the factored form be equal to the derivative of the non factored form?
ex.
f(x) = x^3 -3x^2 + 4
f'(x) = 3x^2 -6x
3x(x-2)
If you differentiate again, would the derivative of 3x^2 -6x be equal to the derivative of 3x(x-2)

[alpine tiger]

yes it woudl

like the derivative of 6x + 6 and 6(x+1) is the same.

a) 6
b) 0 * (x+1) + (6 * 1) = 6

just using an easier example

same principles

[iron glacier]

so whichever you decide to differentiate is up to you?

[alpine tiger]

yuh

do whichever is more convienient

i cant spell sorry

my hands are freezing

[iron glacier]

aight tysm

[alpine tiger]

like for this, i would differentiate the non factored form

cuz i want to avoid the product rule at all costs

[iron glacier]

.close

[safe radish]

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[old grove]

Having trouble finding the Range

[safe radish]

@old grove Has your question been resolved?

[old grove]

Can someone help me with this one

[lapis rose]

It should be -1 <= y < 6 , I think?

[old grove]

You sure?

[lapis rose]

Yeah

[old grove]

How do you do it in [

[,]

[lapis rose]

[-1, 6)

[old grove]

Got it right thank you so much ❤️

I was right I know it was that

But I was just making sure

[lapis rose]

All good, but goodjob!

[old grove]

.close

[safe radish]

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[limber pine]

yo

[safe radish]

Please don't occupy multiple help channels.

[limber pine]

4x+5/4 - 9+2x/3 > 0
i tried solving this, and i got 20x > -21
but the texbook answer says x:x > 5.25
i have no idea
why is there even a ratio
<@&286206848099549185>

[dim smelt]

x:x = 1 unless x = 0

so x:x > 5.25 does not make sense

[limber pine]

it doesnt make sense to me either

also, how'd you solve it?

can you tell me the steps?

[dim smelt]

I would get rid of the fractions by multiplying by a common multiple

then solve for x as usual

[limber pine]

i found the solution

turns out it was indeed 5.25

its bc i did >-21 instead of positive

and i didnt divide it by 4

[dim smelt]

yes that's good

[safe radish]

@limber pine Has your question been resolved?

[limber pine]

kurt my g

ima have to ask u for 1 more question 🗿

i understand the concept now but

in the question 3(x-2)/2 - x-3/4 > 4

i got x>1.57 as my answer

but thats way off 💀

the text book answer says it's x : x > 5

how?

in the first step, i distributed the 3 in the paranthesis

[dim smelt]

are you distributing the - sign in the second fraction?

the textbook answer is correct

[dim smelt]

this is ok to do

[limber pine]

yeah

lemme type my steps

[limber pine]

3x - 6/2 - x - 3 /4 > 4

4(3x-6)/2 - 4(-x-3/4) > 4

2(3x - 6) - 1(-x - 3) > 4

6x-12 + x + 3 > 4

7x-9 > 4

7x > -5

x > 1.57

[dim smelt]

here

the x shouldn't be negative

[safe radish]

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[dim smelt]

like this $-4 \frac{x-3}{4}$

[limber pine]

OHHHHHHHHHHHH

[dim smelt]

wait actually this is more readable $-4 \frac{(x-3)}{4}$

[flat frigate]

Kurt

[limber pine]

the minus threw me off

[safe radish]

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[delicate bobcat]

You should integrate velocity to get distance

But if you need only do distance traveled in 10 seconds

You can also do s(10) - s(0)

[coarse kelp]

what?

but we aren't there yet

we are at absolute extrema

[delicate bobcat]

Then you just have to do s(10) - s(0)

If you integrated velocity it would be the same thing

[coarse kelp]

why what does that do?

[coarse kelp]

what are we essentially doing here?

[delicate bobcat]

you take position at time 10

Minus initial position

[coarse kelp]

isn't that displacement?

[delicate bobcat]

That gives you change in position in the first 10 seconds

Which is distance traveled

Unless it's going back and forth on the line

[coarse kelp]

hmm

[safe radish]

@coarse kelp Has your question been resolved?

[coarse kelp]

do extremas indicate change in direction?

[safe radish]

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[tawdry shard]

Hello

[tawdry shard]

How can I fix this?

[grizzled fossil]

Fix what?

[tawdry shard]

Accumulation, I like to make it a bit more readable

[grizzled fossil]

What? And this sounds like you asking how do I do this on x software (so not a math question)

And probably a good idea to say what you are using then don’t you think?

[tawdry shard]

Sorry, internet crashed

I use python, though it seemed to me a more mathematical problem to create a function distribute the instances more evenly

[grizzled fossil]

your question is very unclear

[swift hedge]

Maybe change the point size. I am going to bed now plus I have not used Python enough to solve your problem

[silk violet]

hi

can someone help after u are done?

[tawdry shard]

Majestic solution, doubt it will work tho, there are 184 thousand of them, have a good sleep

[tawdry shard]

you can claim available channels, you don't have to wait

#help-3 @silk violet

[silk violet]

ok

thanks

[safe radish]

@tawdry shard Has your question been resolved?

[tawdry shard]

.close

[safe radish]

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[raw narwhal]

Hello i would like to ask how to draw the Line of best fit by hand

[raw narwhal]

Knowing all the values

So at the moment i have y = 211.4 - 7/5 (x)

[lean otter]

are u asking to draw the best line?

[raw narwhal]

I believe that 200 the y intercept is the value of y when x is at 0

[lean otter]

as in, the actual thing?

[raw narwhal]

But how do i plot the slope which is negative 7/5?

[raw narwhal]

Im not sure i understood ur wuestion. I u derstand the numerical equation and formula

But i dont know how to plot the slope on graph :/

[lean otter]

oh okay i thought we were talking plotting and research graphing when u said that

okay

thats fine

[raw narwhal]

These r my values btw

[lean otter]

tbh just like, choose 3-4 points

[lean otter]

like take x = 0, x= 1, x =2

oh u already have them nice

well just connect them

but afterwards, just keep the line going at the same gradient your points indicate

like, do u have a graph with u rn? @raw narwhal

to draw it

[raw narwhal]

Hmm theyre not linear tho

Yes

[warm drum]

is this linear regression?

[lean otter]

oh wait is it a 1/x function or a linear function?

[raw narwhal]

It looks like this and the red line is the best fit one

[lean otter]

this changes things a bit

[raw narwhal]

Sorry what is a 1/x function? Xd

Its not linear, this is a line of best fit trend for some scattered data

I understand how it works numericallt

[lean otter]

okay i am just gonna guess this is $y = \frac{-7}{5}x +211.4$ right?

[flat frigate]

♡LexQa♡

[raw narwhal]

Yes!

[lean otter]

it should be linear

[raw narwhal]

Yeah the line is linear

[lean otter]

okay so, what is the problem you are encountering

[lean otter]

i think it looks... about right

[raw narwhal]

Yeah i didnt draw it the professor did

[lean otter]

actually nvm

[raw narwhal]

I dont u derstand how to plot the slope

On graph

[lean otter]

ur slope needs to be more downwards

[raw narwhal]

So the -7/5

Yeah its not exact

How do u draw the slope?

[lean otter]

okay so lets do this step by step okay? @raw narwhal

[raw narwhal]

Yeah

[lean otter]

i want u to take out a graph paper or something

or draw up a graph

[raw narwhal]

Yeah

[lean otter]

okay, now i want u to have a calculator with u for ease of calculation

[raw narwhal]

Yes

[lean otter]

okay, so now, can u tell me what -7(0)/5 +211.4 is going to be?

[raw narwhal]

When x is at 0?

[lean otter]

yes

[raw narwhal]

The y would be 211.4

[lean otter]

okay, i want u to take ur pencil and draw a circle over the point (0,211.4)

just plot that point

[raw narwhal]

Sorry btw! In this case i believe 0= 1? Because it is a trend line for 5 periods 1 - 5

This was the line for 8 periods

And it starts from 1 as the base period so

[lean otter]

okay thats fine

take x = 1 then

instead

and tell me what that gives u

[raw narwhal]

So like this?

[lean otter]

yeah it is gonna be like 210

[raw narwhal]

Yeah

[lean otter]

anyways, take x = 2 now

[raw narwhal]

Cuz not exact when drawn by hand right

Okay

[lean otter]

yeah i mean ur scaling is like accurate to the second digit more or less

[raw narwhal]

Yeah

[lean otter]

so we are approximating, but u can do it properly

[raw narwhal]

So i plot in 2 in the x of

211.4 - 7/5 (x)?

[lean otter]

yes

[raw narwhal]

To find the spot

[lean otter]

exactly

[raw narwhal]

Or would it be 1?

[lean otter]

its gonna be like 208?

[raw narwhal]

Because in the previous case 0 = 1

So now 1 = 2?

[lean otter]

nah

just keep them the same values

take x = 1 exactly the same on x =1

or else your line would be different

[raw narwhal]

So yeah 208

Ag

Ah

And then u just connect it straight?

The 2 dots i mean from previous and now

[safe radish]

@raw narwhal Has your question been resolved?

[safe radish]

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[edgy coral]

helps pls

[lean otter]

Yeah don't know what to tell you but

Scale and add?

[safe flower]

^

[edgy coral]

heh? i wasn't paying attention in class

[lean otter]

You see v has two components?

Same with u

[edgy coral]

yes

[lean otter]

Okay, now it says 2v

When you multiply a vector with a scalar, you just multiply every component of that vector with that scalar

So, multiply both of v's Components with 2

[edgy coral]

so itll become 4 over 12?

[lean otter]

Don't say over 12 as if it is a fraction

But yes

[edgy coral]

so just add up both components ?

[lean otter]

Now, it says to add the 2v vector with the vector of u. Again, when you add vectors, you only need to add their components together

So do that

[edgy coral]

so it will become 12,10? or 12 over 10

[lean otter]

Yes...

[edgy coral]

oh just like thhat final answer?

[lean otter]

Yes

[edgy coral]

thanks mate, appreciate it.

[lean otter]

Of course, have a nice time

[edgy coral]

no nut november

[lean otter]

[edgy coral]

.end

huh

how to end

[lean otter]

It's .close

[edgy coral]

thanks again

.close

[safe radish]

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[solid epoch]

Hey, I’m a bit struggling with linear algebra, we have a couple of exercises that I can’t solve… in the first one I found that it is a subspace and we know that p(x)=a0 + a1x + a2x^2 and p(0)=0 => that a0 needs to be 0 and therefore any polynomial from this subspace can be written as p(x)=a1x + a2x^2 but can’t move after this step…
For the second I’m not sure at all how to proceed…
For the third I came to solution that it could be {(-B/A, B,0), (-C/A, 0, C)} but I’m not sure as I couldn’t prove that it spans…

[safe radish]

@solid epoch Has your question been resolved?

[solid epoch]

<@&286206848099549185>

[ashen spruce]

hi sir

idk what that is

:(

[trail ridge]

NNN
Sorry, couldn't resist this joke

[safe radish]

@solid epoch Has your question been resolved?

[solid epoch]

@safe radish no

[safe radish]

@solid epoch Has your question been resolved?

[safe radish]

@solid epoch Has your question been resolved?

[safe radish]

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[outer violet]

Hoe is this solved

[safe radish]

@outer violet Has your question been resolved?

[safe radish]

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[tawdry fox]

show sin(1) + sin(2) + ... + sin(n) is bounded for all natural n

[ornate creek]

you can use the exponantial form of sin(k)

and you know the explicit formula of the sums of x^k

then you find something bounded times something bounded

thus it's bounded

do you know all of these notations?

like the imaginary part of e^(ik)

[tawdry fox]

yeah im just trying to figure out how the new sum is bounded

[ornate creek]

you have to do the helf angle technique

idk if it's called like that in english

I'll show you on a paint

@tawdry fox

I might'have made a mistake somewhere becasue I did it quickly

but you got the idea

try it yourself and see how it goes

[tawdry fox]

ok

[ornate creek]

@tawdry fox did it work for you?

[tawdry fox]

the steps made sense im just having trouble seeing the motivation

nvm it makes sense

.close

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[lean otter]

replace f(x) with y and then solve for x

than replace x with f inverse x and y with x

that will be your answer

[safe radish]

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[tawdry hornet]

.reopen

[safe radish]

✅

[tawdry hornet]

I did this and got x=(2(1+y))/(y-1)

[lean otter]

check your calculation
3rd option is correct

[tawdry hornet]

Ok. Thanks!

.close

[safe radish]

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[gentle valley]

An arithmetic progression has first 1.71 and common difference 0.02. A geometric progression has first term 250 and common ratio r. The sum to infinity of the geometric progression is equal to the sum of the first 80 terms of the arithmetic progression. Find the value of r.

[gentle valley]

I solved it and got an answer just wanted to double check

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[flat frigate]

physmo

[safe radish]

@silver blade Has your question been resolved?

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[humble bluff]

Helpp mee
Determine the value of 𝑎 that satisfies a linear agreement system with many solutions, no
has a solution and or one solution by using Elementary Row Operations
that's just one question

[humble bluff]

<@&286206848099549185>

[humble bluff]

idk how to find a value

<@&286206848099549185>

[safe radish]

@humble bluff Has your question been resolved?

[humble bluff]

<@&286206848099549185>

[dim smelt]

try using gauss elimination, then calculate rank of the resulting matrix

[humble bluff]

What's mean calculate rank of resulting matrix?

I don't undertand the way to find "a" value

[dim smelt]

count the number of linearly independent rows

in this case rank = 3 would mean 1 or no solution

[humble bluff]

Can you give me example

[dim smelt]

rank < 3 would mean infinite solutions

[humble bluff]

How did you to the rank is 3??

3 variables?

[dim smelt]

hmm if you don't know rank yet, first convert the system to row echelon form

[humble bluff]

Hmmm ik now

I'm still confused how to find a

[dim smelt]

you get a after converting to row echelon

first do that and send the result you get

[humble bluff]

Did you mean like this

[humble bluff]

And then

[dim smelt]

now apply elementary row operations until you get the echelon form of that matrix

[humble bluff]

The a d f is equal to 1?

[dim smelt]

it could be equal to 1

the important thing is that everything below the main diagonal is 0

it's just gauss elimination method

[humble bluff]

Ohh wait i try this

May i know what the result of
-1 x 1 + -a ?

Is it still -a?

[dim smelt]

is the x here multiplication?

[humble bluff]

Yes

Then how about 1 + a? Is the result is "1a" or "a"?

[dim smelt]

using pemdas this is just - 1 - a

1 + a is just 1 + a, you can't reduce it any further

you don't need to reduce it further yet either, don't worry about it

[humble bluff]

How bout this?

[humble bluff]

Using gauss echelon form

[dim smelt]

give me a min

let me check

[humble bluff]

Okay

[dim smelt]

first two rows are ok

the last row is wrong

you might want to check it again

[humble bluff]

Where the wrong ans

The formula or the ans ?

[dim smelt]

I don't understand your question

try doing last row again

[humble bluff]

I still didn't understand which part that i did doing wrong

The "a"?

[dim smelt]

yeah, you are doing row3 - row1 right?

[humble bluff]

Yep

R3= -1R1 + R3

[dim smelt]

yes

you get 0 0 -a-1 a-2

[humble bluff]

I still dont understand

Ohh

[dim smelt]

like this

[humble bluff]

Okay why it can be -a-1 a-2?

[dim smelt]

it is just the way it is

you can't simplify those expressions further

[humble bluff]

Ohh okay then what's the next part?

[dim smelt]

okay now your question is asking to find a such that it has

• many solutions
• no solutions
• one solution

you have to find different values of a

now what would happen if you have 3 pivots in this system?

[humble bluff]

Hmmm

I'm still confused

[dim smelt]

do you know what a pivot is?

[humble bluff]

Not really

[dim smelt]

the pivots are the first non 0 value of every row

in this case

1

-6

-1-a

[humble bluff]

Why a-2 is not a pivot?

[dim smelt]

because pivots can only exist inside the system matrix

this

not in the extended one

[humble bluff]

Ohh ik

Then what should i do now

[dim smelt]

okay nice, now what happens if you have 3 pivots?

a pivot in every row

[humble bluff]

Change it to 1?

[dim smelt]

no

the number of pivots are related to the number of solutions of the system

if you have a pivot in every row your system would have a unique solution

if you don't have a pivot in every row your system would have infinite solutions or no solution at all

that's how you get the a's

[humble bluff]

So this is unique solution?

[dim smelt]

you have to find an a for each of these cases

[humble bluff]

Hmm i still don't understand to find an "a" in this cases

[dim smelt]

what happens here if a = -1

how many pivots would you have?

[humble bluff]

-a-1 = 0

[dim smelt]

exactly

and you would only have 2 pivots

[humble bluff]

So

Make 1 and -6 to zero?

[dim smelt]

no don't worry about the other values

try to write the matrix in the case where a=-1

and see if it has solutions

[dim smelt]

exactly

does that system have a solution?

[humble bluff]

I think no

[dim smelt]

exactly it doesn't

because if a=-1 you eliminate the pivot

[humble bluff]

0≠-3

[dim smelt]

yes

[dim smelt]

this is the important part

if you don't have a pivot in every row then there are infinite solutions or no solution

that's the rule

[humble bluff]

Owhh okay

The answer just like that?

[dim smelt]

what happens if a is any other number apart from -1

[dim smelt]

we'll get to that

[humble bluff]

Maybe it has solution

[dim smelt]

yes

you would have a pivot on every row

which means there is a unique solution

[humble bluff]

Ohhh ik

How about infinite solution

[dim smelt]

in these case we can't pick a such that it has infinite solutions

because we already ccovered all possible values of a

and we noticed it's either unique solution or no solution

[dim smelt]

that's why there is an or here

[humble bluff]

Oww so just pick 1 solution in this case?

So i should not find for infinite and unique solution right

[dim smelt]

your answer should look something like \

• unique solution: for all $a \neq -1$ \
• no solution: $a = -1$

[flat frigate]

Kurt

[humble bluff]

Owwhh okay

[dim smelt]

for next time remember number of solutions is directly related to number of pivots

[humble bluff]

Okay , Thank you for your help

[dim smelt]

you're welcome!

[safe radish]

@humble bluff Has your question been resolved?

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[safe radish]

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[livid sparrow]

Could someone explain the last two lines here? I dont understand why you divide all the terms by 2

2+2x(2(3x+2)+2)
2+2x(6x+4+2)
2+2x(6x+6)
2+(12x^2+12x)
12^x/2 + 12x/2 + 2/2
6x^2 + 1

[swift palm]

What is the question. Is it to simplify?