help-33

[marsh citrus]

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[little geyser]

I’m doing an exercise from Axler and I need to know how to break these brackets. Any ideas?

[winter smelt]

proving associative property always feels too trivial, hence I'm not confident either. But I'm pretty sure you can just drop the [ ] around (a+c) + (b+d)i. Then do the same with alpha + (beta + lambda) and also drop with [ ], then say since both side are equal, done.

so it's like, (1+2)+3 = 1+2+3 = 1+(2+3), which is very trivial I know

[little geyser]

Respectfully, I’m gonna assume I can’t do that. That I “don’t know how to do that yet”

Do I add and subtract it because I know this:

What I mean is subtract everything inside the brackets by itself and then add it to the outside?

[winter smelt]

in my first year notes, we just assume that real addition and multiplication satisfy associativity, it's given/enforced as an axiom

so I guess to be more pathentic in your case, since alpha, beta and lambda are complex numbers, you write them in the form of x+iy like you did, then use real additive and multiplicative associativity to expand/re-bracket terms (for the ones with and without i separately)

[little geyser]

Ohhh

Okay

Thank you so much

[winter smelt]

you're welcome

[little geyser]

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[sweet flare]

help

[sweet flare]

how do i get help in dis

hello

i need help with this question

[lyric kelp]

which one-

[glass gazelle]

Yea, which one?

[sweet flare]

well

this is the whole question

i need to find the answers for the graph above

[lyric kelp]

well a) is pretty obvious at least no?

[glass gazelle]

↑

[sweet flare]

yep

already got that marked down

just need the others

[lyric kelp]

axis of symmetry is basically

when the parabola mirrors

at which x

so you can put x= ?

[sweet flare]

so 4?

x=4

[lyric kelp]

well i cant see the photo its too blurry but ill trust you

[lyric kelp]

vertex yk what it is?

[sweet flare]

im sending it rn internet is a bit slow

[sweet flare]

Not really.

[lyric kelp]

its the

[glass gazelle]

The apex

(h, k)

[lyric kelp]

max or minimum value or the parabola

[lyric kelp]

where it extrudes the most essentially

[sweet flare]

okay so i got the axis of symmetry down

[lyric kelp]

where do you think vertex is here

[sweet flare]

the top or lowest point of the graph right?

[lyric kelp]

yup

[sweet flare]

that’s what i’m struggling on finding the vertex

[glass gazelle]

Do you know what intercepts are?

[sweet flare]

nope

[lyric kelp]

well whats the max value of this parabola

[sweet flare]

where the line intercepts on the graph??

[lyric kelp]

in terms or y

[glass gazelle]

Yes

[lyric kelp]

like where is the y the biggest

[sweet flare]

4

[lyric kelp]

that x

i meant whats the biggest value of y

sorry

of this parabola

[glass gazelle]

Imagine you put a straight line. It will touch the parabola twice except for one point of the parabola

[sweet flare]

mmm okay

so lost rn

😭

sorry if i’m not the brightest

[lyric kelp]

vertex essentially just means where the max value or min value of y

so in this graph

you see that y is biggest at x=4 correct?

[sweet flare]

yepp

[lyric kelp]

so you got x established

(4, ?)

whats ?

[sweet flare]

4,-5

[glass gazelle]

Basically here, which line touch the parabola only once

[lyric kelp]

nope

[sweet flare]

awh

[lyric kelp]

whats y when x = 4

[sweet flare]

how do i find the other number then??

[lyric kelp]

well on your y axis

[glass gazelle]

Look at the graph

[sweet flare]

the line intercepts with the -5 tho right??

[glass gazelle]

There is a line crossing the other line

[sweet flare]

right here

[glass gazelle]

Here, where is the point?

[lyric kelp]

-5 would be here

aka no vertex

[sweet flare]

okay okay

So -5 is a no

[lyric kelp]

you want the coordinate of the max value of y

which you can visually see its here

right?

[sweet flare]

yep

[lyric kelp]

now you got x which is 4

looking at numbers on the horizontal line

[sweet flare]

(4,?)

[lyric kelp]

yup

now whats hte number on the vertical line

thats y

you gotta be more familiar with x and y line

[sweet flare]

Im familiar with them

is it perhaps -6?

[lyric kelp]

idk why youre moving down

do you think -1 would be a good fit

looking at the coordinate (4, -1) what do you find

[sweet flare]

because im looking at the vertical line?

[sweet flare]

yea i think it’s good

-1

[lyric kelp]

yeha

idk where you got the -6 from

[sweet flare]

okay now

i need to find the intercepts

for x and y

[lyric kelp]

yeah so you said youre familiar with x and y line correct?

does the parabola at any point touch the x line

[sweet flare]

yeppp

[lyric kelp]

where

[sweet flare]

nope

[lyric kelp]

ok good

[sweet flare]

it only touches the 4

not the actual line

but the line touches the y axis

[lyric kelp]

right so it doesnt touch x axis

[sweet flare]

yep

[lyric kelp]

and on y axis where does it touch?

[sweet flare]

it touches the -5

i’m pretty sure

[lyric kelp]

yup

so thats your y intercept

[sweet flare]

okay

do i need another number ??

or is it

0,-5

[lyric kelp]

yup thats good

[sweet flare]

alright

wait it told me d is incorrect

[lyric kelp]

which

btw i cant see photo for 4) its a bit too blurry

[sweet flare]

hold up pic is loading to send

there ya go

[lyric kelp]

what about the a) and b)

[sweet flare]

they are correct

just d)

[lyric kelp]

i might be on crack but

could be it bc of this they assumed you put 2 coords

try just -5

[sweet flare]

soo??

[lyric kelp]

tell me if that works

[sweet flare]

thank you!!

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[marsh citrus]

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[jaunty vault]

how do i draw this

[marsh citrus]

@jaunty vault Has your question been resolved?

[jaunty vault]

no

[marsh citrus]

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[spring oracle]

can you guys help me how those cancelations and simplifications happened? appreciate it

[fervent rampart]

the 1 + 1/n is from (n+1)/n

the rest are combining exponents

[spring oracle]

i am confused

what step is that

i know that when you divide powers you subtract them

[fervent rampart]

,, \frac{3^{n+1}}{3^{n+2}} = 3^{(n+1)-(n+2)} = 3^{-1} = \frac 13

[elfin berry]

pnoןɔ

[fervent rampart]

and similar for the x + 2 term

[spring oracle]

oooohh

yah

appreciate it mate!

[marsh citrus]

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[true bluff]

for this question i got this far but im so lost is -90 is correct for x

[marsh citrus]

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[eternal schooner]

,calc logBASE(9,3^{1/5})

[elfin berry]

The following error occured while calculating:
Error: Symbol or string expected as object key (char 14)

[sleek topaz]

is the q 9^t = ⁵√3?

[tranquil elbow]

ye

[marsh citrus]

@tranquil elbow Has your question been resolved?

[errant garnet]

you wanna take log base 9 of both sides and that should be the final answer

[tranquil elbow]

whats log base

I'm not american

I'm pretty sure my first step is right

just dont know how to proceed with the 2nd par

[errant garnet]

i suppose you could do that too

so the right hand side is just 3^(1/5)

so you can solve for 2t = 1/5

[tranquil elbow]

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[errant garnet]

Do you know how to setup the system of eqns for Lagrange multipliers?

[still temple]

Yes

I got lambda equals +/-sqrt(1/9)

[errant garnet]

I think the setup was wrong then. If you look at their solution they solve the gradient for {1,1,1,1} because the other variables can be considered constants in f(x,y,z,t) when doing the partial derivatives

[still temple]

i can send a picture of my work

one sec

[still temple]

sent a picture

[errant garnet]

I’m struggling to find the mistake tbh but symmetry simplifies the problem a lot. In the solution on webassign you can see that they solve for lambda first and they are able to show x=y=z=t which you could also do with your method, then you can just say 4x^2=9 then simplify

[still temple]

okk

[errant garnet]

I think you would be able to get it if we substituted at the end of the problem

[still temple]

Oh rlly?

Let me try that real quick

[errant garnet]

You could end up with 1/9=1/4x^2 which is basically just 4x^2 = 9 giving the right solution

Then the easy part of evaluating the function with the + or - for min and max values

[still temple]

wait is x lambda in this

[errant garnet]

Well earlier you established lambda=1/2x right

So if you plug 1/2x back into lambda when we have lambda^2=1/9

Then you get that

[still temple]

No that was x = 1/2lambda

[errant garnet]

Wait

Yeah I think honestly your math is correct it’s just that you took a path that made it more complicated. Because now we’d need to do a lot of extra algebra to get the lambda to be 1/2lambda

[still temple]

Oh wait

if lambda equals +/- 1/3

then x,y,z,and t = 3/2

[errant garnet]

Oh right lmao

I hated those problems but it was better than solving for absolute min/max along the boundary

[still temple]

Oops 😀

[errant garnet]

Yeah I do that stuff all the time lol

[still temple]

yeah im trying to cram for a test i have in less than 12 hrs

and doing that tedious work was NOT fun

lmao

[errant garnet]

Our webassigns for calc 3 had answers that were like so long it was terrible

[still temple]

I still have to cover the assignments for double integrals and iterated integrals over polar regions

wish me luck

😭

Thank you so much though!

[errant garnet]

Yeah, np. Gl!

[still temple]

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[still temple]

Dumb question but for adjoint matrices does it matter if we conjugate before we transpose or transpose before we conjugate? So I am basically trying to see if [
A^* = \overline{\trans A} = \trans{\overline A}
]

[fiery harbor]

its correct

[still temple]

this is not the inverse though

[fiery harbor]

yeah it still doesnt matter I suppose

[still temple]

ok

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[jovial bear]

how to prove 7^n - 1 is divisible by 3 using the fact that sum of digits must be divisible by 3

[devout mauve]

why do you want to do it that way

that seems pretty much impossible

[jovial bear]

gotta prove 7^n - 1 is divisible by 6 but im not allowed to use induction

[devout mauve]

7=6+1 and binomial theorem

[jovial bear]

so i said it gotta be divisible by 2 and 3

[devout mauve]

assuming you are allowed to use binomial theorem I guess

or modulo if you know that

[jovial bear]

yes i can use binomial theorem

but idk how to apply it here

[devout mauve]

7^n=(6+1)^n

[jovial bear]

mhm

[devout mauve]

it might help to write it out explicitly for n=2,3,4

[jovial bear]

wait so the method ur doing

proves its divisible by 6? or by 3

[devout mauve]

6

[jovial bear]

oh

wait does this way work?

i used the summation formula

subbing x = 6 and y = 1

i get (n k) * 6^(n-k) * 1^k

6^(n-k) will always be divisible by 3

oh but then idk what to do with the -1

[marsh citrus]

@jovial bear Has your question been resolved?

[jovial bear]

<@&286206848099549185>

[spark otter]

when k = n,

you get 1 from the sum

so - 1...

and only when k is not equal to n, that term is divisible by 6

[jovial bear]

sorry im confused

so your saying itll be x^0 right

which is 1

[jovial bear]

OH I GOT IT

thanks

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[tranquil elbow]

not sure if correct

[marsh citrus]

@tranquil elbow Has your question been resolved?

[tranquil elbow]

<@&286206848099549185>

[still temple]

U need help on letter c, right?

[tranquil elbow]

yea

[still temple]

Explain upper bound and lower bound to me

And give me an example

(Im knowledge-checking you)

[tranquil elbow]

ranges ig?

45 minutes to the nearest minute would be 44.5 - 45.5

[still temple]

What are your answers for a and b?

[tranquil elbow]

a) lower 44.5min upper 45.5min

b) lower 245l upper 255l

[still temple]

Have you checked those answers if they are correct?

@tranquil elbow

[tranquil elbow]

There's no marking scheme sadly

but I'm 99.99% sure they're

unless I got it mixed up

[still temple]

Have you done something similar and got them right in the past?

[tranquil elbow]

yea

just not sure if I did c correctly

[still temple]

There are constraints on determining upper and lower bound numbers. The statement from the above sure looks simple and does not seem to tell if there’s any constraints, so we can safely assume that the answers you provided are correct as I also think the same to them.

Last knowledge-check, explain to me the meaning of “three significant figures” and give me two examples.

@tranquil elbow

We are going through this together!

[tranquil elbow]

3 significant numbers

then rounding if needed

[still temple]

You have to tell me more than that

[tranquil elbow]

idk how to explain it

12379124015

1.28346129234

[still temple]

You should know lol

Take ur time

[tranquil elbow]

I do know i j don't know how to say it in words

[still temple]

If u cant say your thoughts, then you can have trouble finding solutions to your problems

Have you read something about it?

@tranquil elbow your answer 5.51 litres/min, provided that:

The rate is 5.5555555(inf) or 5.56. And the lower bound for that is just a simple -0.05 from the 5.56 which equals to 5.51. Hence, the correct answer could be 5.51 litres/minute.

Im only 99.9% sure that this is the answer just in case we missed something.

Check your mates answer for that if thats allowed.

[marsh citrus]

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[patent vine]

do you think my teacher forgot about x=3?

or is x=3 'not' a vertical asymptote?

<@&286206848099549185>

also i have one more question

how do you know if this part is going upward

couldn't it be also going downward?

[upper obsidian]

oh yeah they did

[patent vine]

it's not specified enough

[patent vine]

also could you also help me with this

i feel like the rightmost arrow it not necessarily going upward

at least it's not specified

imo

[upper obsidian]

you're right it can go down too

also on the left part

in -7

that part can go up

[patent vine]

-7?

[upper obsidian]

-3 sorry

[patent vine]

lol allg

[upper obsidian]

in fact there are infintely many ways you can draw this

take for example a segment (0,1)

you can draw it like this

point is

it doesn't matter if it's not specified

any answer that satisfies those conditions is correct

[patent vine]

gotcha!

that exactly answers my question

much appreciated

:)

[upper obsidian]

you're welcome :)

[patent vine]

have a good one!

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[chilly mulch]

Need help with n

I feel there is just one thing I am missing

[astral night]

Is answer 0

[chilly mulch]

No

I think it should be 6/5

[chilly mulch]

By the way hello

[astral night]

Hi
I just solved it and got numerator 0. I'll just check in calculator once

[chilly mulch]

For n?

[chilly mulch]

Did you solve it using co-functions and reductions?

[astral night]

Right it isn't 0. It's 6/5 correct

[chilly mulch]

Could you show me how you got your answer please

[marsh citrus]

@chilly mulch Has your question been resolved?

[chilly mulch]

<@&286206848099549185>

[chilly mulch]

<@&286206848099549185>

[marsh citrus]

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[barren abyss]

so as x approaches 1 from the right side (basically right to left) the limit is positive infinity?

[winter smelt]

yes

[valid cape]

yes

[barren abyss]

thx

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[wooden grotto]

can someone please help me with this problem?

[marsh citrus]

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[robust notch]

How do I find the equation for B

[tranquil osprey]

Can someone pleasd explain the part i circled

[winter smelt]

from what you circled, I see $\sqrt{2i} = \sqrt{2} (\frac{\sqrt{2}}{2} + i\frac{\sqrt{2}}{2})$

[elfin berry]

lgkoo

[tranquil osprey]

yeah

[winter smelt]

is that your question?

[tranquil osprey]

yeah

its ok i found

the explanation

on the page

thank u .ck

.close

[winter smelt]

[robust notch]

Did I just get cucked in my own room

.close

[marsh citrus]

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[marsh citrus]

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[young helm]

by this do they want me to state in between the functions so between 2.8 and 0.5

[young helm]

I'm a little confused on that specific part

[glacial python]

when its increasing, doesnt it mean positive gradient?

[young helm]

yeah just wanted to confirm also how would I solve this?

I have part a

but i"m very confused with part b

I have f(x) = k x(x-3)^2 so far

[glacial python]

damn i took this last year in school, ill try to help you

[young helm]

please do

I'm very stuck rn

I tried plugging in the y coordinates and I couldn't figure out where I went wrong

I also need help for this question

so 2 questions rn

[silk sable]

Do you understand the relationship between linear factors of a polynomial equation and where it equals zero?

[glacial python]

i thhink u just get the gradient at x=1

i didnt take finding the equation for a graph with that many turns so ill leave someone else to help u sadghe

[young helm]

yes I do I got 0 for k so that's why I was confused

[young helm]

do you think you could help me with the instantaneous question too pleaese

[young helm]

yes I do understand that part

[glacial python]

sure ill try

[silk sable]

What equation did you get for the graph in 5b?

[young helm]

for the graph so far I have f(x) = x^2(x-3)^2

sorry

I meant

x(x-3)^2

[silk sable]

The former was almost correct.

[young helm]

oh I switch the 2 around and get x^2(x-3)

[silk sable]

There is also an unknown constant, k, which fine tunes the vertical stretch of the graph.

[young helm]

how can I solve for K in this situation?

[silk sable]

Are you learning about derivatives?

[young helm]

no I have not learnt about derivitives yet no

do you think it's fine to assume k is 1 or how would I do it

I graphed it on desmos and it looks like 0.5

or 2

I can't sub 0 in for anything s I am very confused right now

[silk sable]

So you have the equation

f(x) = k \* x^2 \* (x-3)^2

[young helm]

also if it says Factor x^3-9x fully do I do x(x+3)(x-3)? Or do I have to give the roots of x= 0 x = -3 x = 3

[glacial python]

how would u find rate of change if u dont know derivatives tho?

[young helm]

we use newtons law thingy

lemme find it

[silk sable]

So you are in Calculus 1?

[glacial python]

newtons?!

[young helm]

Newtons quotient

[young helm]

No advanced functions

[glacial python]

ohh the f(x+h)

[young helm]

yeah

[glacial python]

didnt know that was newton's ngl

alr sure ill use it to help ya

[silk sable]

Well, the usual option would be to pick a given x value from the graph that has an obvious corresponding y value and solve for k that way.

[young helm]

ok ty

[young helm]

wait but everything is 0

that means the other side would have to equal 0

[silk sable]

Look at the graph where x = 4.

What does y equal at x = 4?

[young helm]

y= 12

I got k = 4/3 but I'm unsure if that would be correct

is it?

[silk sable]

No. I checked. The graph doesn't line up at y=8.

[young helm]

nvm it is I just graphed it

and one more question regarding this I was confused on part C for thsi question since it didn't make sense to me

[silk sable]

The graph doesn't line up finding k in this manner which likely means the power of one or both linear factors is not correct.

[young helm]

wait so is f(x) = 4/3 x^2(x-3) wrong??

[silk sable]

If you notice in the graph given to you by the problem, it has a "vertex" at y=-8.

[young helm]

so that means it has to be 2

which is what I didn't get

[glacial python]

just to make sure, at the end, i should assume h is so small, its just 0 right?

[young helm]

i belive so

[glacial python]

I hope i didnt make any mistakes

[young helm]

wait so are you certain the answer is 2?

like if we were to use the derivitive rules the answer would be 2??

[glacial python]

i mean i did it with d/dx and got 2 the first time, just took a big longer with this method

[young helm]

oh so you got 2 with both

[glacial python]

Yeah

[young helm]

I got -14997 which is why I knew I was wrong for sure

[glacial python]

no matter the value for x, f'(x) is always 2

[glacial python]

xd

[young helm]

so would it be better to use derivitives ehre

or to just learn them

and when it says x^3-9x factor it out completely

do I have to list the x coordinates

[young helm]

if you can do you think you could pls show me how to do this with product rule

[silk sable]

You know what. I think f(x) = k * x^2 * (x-3)^2 would probably be enough.

[glacial python]

sorry no clue what that is

[young helm]

like do you think you could pls show ur work with derivitives so I can try it out

[young helm]

ok I'll write that down for now instead

[glacial python]

hmm i got x+1 this time

[young helm]

how can it be x+1 though?

[glacial python]

sorry i probably did something wrong in the f(x+h)

[young helm]

can you plss solve it rq I'll try learning it through seeing you do the derivitive

I know basic ones so far

[silk sable]

I wonder who made this problem, because they did not make it easy even with derivatives. 🙂

[glacial python]

oh the answer has been 2 the whole time

[young helm]

my teacher sent this link to us

[young helm]

yeah

[glacial python]

but i tried to do it using the f(x+h) way

[young helm]

I think it's 2

I got 15k once

this is what I was given

for online notes

also no ones answered my question about when factoring completely what happens

[glacial python]

?

[young helm]

do I have to give the x values

so like x^3-9x

is x(x+3)(x-3)

do I have to say x = 0 x = -3 x = 3

[glacial python]

if they want the x intercept i guess yeah

[young helm]

it just says factor comopletely though

so ig I won't add x intercept in?

[glacial python]

i mean idk what the question wants so idk

[young helm]

it's this

[glacial python]

ig just leave it in the x(x+3)(x-3) format

[young helm]

ok tyty do you think I could dm you with questions?

[glacial python]

sure idm

[young helm]

ok ty

.close

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[marsh citrus]

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[young helm]

how would I answer C here?

[young helm]

<@&286206848099549185>

[slim spire]

I think you need more information to get the exact value?

you're just looking for the steepest slope that looks like /

[young helm]

so would I just say -1.4

because it looks like that's what would be the steepest in this case

[slim spire]

oh what are the numbers on the grid axes I can't read them

[young helm]

it starts reducing at -1.5 and goes to 1,0 on the x axis

so the very peak to the x-intercept

[slim spire]

oh if it's that short range I guess 1.5 then

since for the rest of the function it's going concave downwards, getting lower and lower steepness

[young helm]

but it says largest positive rate of change

none of it is positive

unless that doesn't matter

[slim spire]

is -3/2 < x < 1 this range?

[young helm]

yes it isthat range

would I just put down -1.499

[slim spire]

uhhhh yea the question makes it hard to say the value

I'd just put -1.5 anyways but it's up to you

[young helm]

ok ty

.clsoe

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[pseudo aspen]

How could I put $\int_1^2 ! \frac{1}{x}dx$ into a Riemann equation?

[elfin berry]

Someone

[marsh citrus]

@pseudo aspen Has your question been resolved?

[glass silo]

As in like a Riemann sum?

[pseudo aspen]

Yeah

[glass silo]

Well, I guess, "the usual way" do you want to use any particular endpoints?

[pseudo aspen]

Uhhh, not really

just not really sure how to plug it into this when there's a fraction

[glass silo]

Well, mostly just using appropriate should do really, and then if you really really want to, then you could try "doing algebra" to make it nicer

In this case you have f(x) = 1/x so f(a + (b - a)k/n) is just 1/(a + (b - a)k/n)

[elfin berry]

Someone

[pseudo aspen]

so like that?

$\frac{1}{(1 + \frac{2-1}{n}i)}$

[elfin berry]

Someone

[pseudo aspen]

$\frac{1}{(1 + \frac{i}{n})}$

[elfin berry]

Someone

[glass silo]

Yep pretty much

[pseudo aspen]

got it, I guess I was just confused with the 1

but that makes a lot more sense

thank you!

.solved

[marsh citrus]

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[kind remnant]

can someone explain to me how to do this

[desert dirge]

would you be able to tell me what 3u and 4v are

[kind remnant]

1 minute

[kind remnant]

3u = -6i + 9j , 4v = 24i - 4j

[desert dirge]

good
how about 4v-w then

with the fact (ai+bj)+(ci+dj)=(a+c)i+(b+d)j as one may expect

[kind remnant]

i got -33i - 5j

[desert dirge]

for the whole thing?

[kind remnant]

ya like 3u - (4v - w)

[desert dirge]

youve made a minor issue with regards to w

[kind remnant]

oh whoops u said whats the 4v - w

[desert dirge]

youve subtracted w from 3u-4v

when you should add it

3u-(4v-w)=3u-4v+w

[kind remnant]

oh, i subtracted w from 4v first

[desert dirge]

oh?

[kind remnant]

then subtracted that result from 3u

i wasn't supposed to?

[desert dirge]

you can, what did you get at 4v-w?

oh wait im silly

the j term is still off though

9-(-4+0)

[kind remnant]

for 4v - w , i got 27i - 4j

[desert dirge]

si

[kind remnant]

is that just the solution to the problem or i gotta do sum else

[desert dirge]

-33i+5j isnt right, the 5 is wrong

[kind remnant]

did u get (27 i - 4 j) for the 4v -w?

[desert dirge]

that is correct

[kind remnant]

cuz then i subtracted that from 3u

(-6 i - 27 i) - (9 j - 4 j)

[desert dirge]

uh

+(9j-(-4j))

[kind remnant]

oh so -33 i + 13 j

[desert dirge]

oui

[kind remnant]

do i have to do more? or is that the whole vector

[desert dirge]

tis all

[kind remnant]

thank you my dude

[desert dirge]

no worries

[marsh citrus]

@kind remnant Has your question been resolved?

[marsh citrus]

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[void shoal]

can anyone help me with part a and b?

[marsh citrus]

Please don't occupy multiple help channels.

[frail hinge]

what is the problem you’re facing?

[void shoal]

im just not sure what im supposed to do to find the value of lambda

[frail hinge]

normal vector addition

[void shoal]

can u specify?

[frail hinge]

have you learnt vector addition?

[void shoal]

i have but how can i use it to figure out lamdba?

[frail hinge]

find the AC vector and then apply modulus AC = 17

then you can find for lambda

do you understand?

[void shoal]

yes yes im sure of how to do part a

i just dont know how to do b or c

[frail hinge]

you asked b and a here

[frail hinge]

for b part they should be collinear

[void shoal]

oh sorry i meant b and c

[void shoal]

so i can solve it by doing AB = k AC?

[frail hinge]

yes AB should be parallel (collinear) with AC or BC

[void shoal]

alr ty

how about c?

[frail hinge]

for c if i’m taking B as the right angle then BA and BC should be perpendicular

have you done scalar product?

[void shoal]

oh no i havnt

but is it still possible without it?

[frail hinge]

okay, let me think of a way without it

[void shoal]

ok ty

[frail hinge]

pythagoras theorem

but scalar product is an easier way to go

[void shoal]

how so?

could u do AB x BC = -1?

[frail hinge]

there is nothing like “slope(gradient)” in vectors

[void shoal]

ok makes sense but how could i use pythagoras theorem?

[frail hinge]

(AC)^2 + (BC)^2 = (AB)^2

we know the length of AB , just need to find lambda

[void shoal]

oh okk

tysm

[void shoal]

btw ur considering C to be the point of right angle right?

[frail hinge]

yes

[void shoal]

would i still work if i used B as the right ngle isntead of C?

[frail hinge]

yeah i think it should work

[void shoal]

kk

ty

.close

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[zenith dirge]

Find compount interst on Rs. 6250 at 16% p.a. for 3 years, compound anually

.reopen

[marsh citrus]

@midnight tusk Has your question been resolved?

[midnight tusk]

.close

[marsh citrus]

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[worthy halo]

im lost

[full orchid]

are you familiar with the cross product of 2 vectors

[worthy halo]

yes

i am

[full orchid]

do you know the formula | u x v | = |u||v| sin theta

[worthy halo]

no

but now i do

[full orchid]

ah

are you good with the problem now?

[worthy halo]

um well

so it wud be

sqrt 2/3 = sin theta

wut do u do from there

like how wud i turn sin into cos

[still temple]

Cos²x+sin²x=1

Sinx=√(2/3)

[worthy halo]

ohhhhh

[full orchid]

i didnt even think of that thats smart

[worthy halo]

what was ur approach

[full orchid]

i was still in the process of thinking of an approach 😭

[worthy halo]

😭

ok well thanks guys

.close

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[still temple]

I did tell this last time

To the same person

[worthy halo]

gj

[marsh citrus]

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[alpine tendon]

Okay so to start with I only had the line on the graph in [0,9]. For getting (t, 9t) I understand the y= 9-x for the y coordinate being the equation of the line in f(x,y) but for the x why is it t?

[lone hare]

i honestly dont know what you mean by t

it could be any variable if im understanding correctly

[alpine tendon]

yeah it could be any variable its just stated as for t in [0,9]

[amber birch]

They use the letter t because it normally means you have a parametric function

So here x and y are both functions of t

x(t) = t
y(t) = 9 - t

And the line is given by (x(t), y(t))

[alpine tendon]

how does x(t)=t though?

@amber birch

[amber birch]

It's just one choice of x(t)

It's probably the easiest choice

But you can also have x(t) = t^2, y(t) = 9 - t^2

But then you would need to have -3 <= t <= 3

[alpine tendon]

i'm still kind of confused

[amber birch]

You can choose x(t) to be anything

You could have x(t) = e^t + sin(t) + tanh(t)

And y(t) = 9 - e^t - sin(t) - tanh(t)

And x(t) + y(t) = 9 for all t

So it works out

Good luck figuring out the domain for t though

[alpine tendon]

oh okay

.close

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[valid hinge]

Can anyone explain this solution?

[marsh citrus]

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[shy barn]

I know that I have to turn all the bottom ones into a(a-2)(a+2), but I have no idea what to do with 2^2 - a^2 in order to get to it

because 2^2 - a^2 is not (a-2)(a+2) right?

[placid hound]

yes it is

a^2 - b^2 = (a-b)(a+b)

oh sry

[shy barn]

why? (a-2)(a+2) = a^2 - 4, which is different

[placid hound]

i read it the other way

[shy barn]

6-4 is not 4-6 for example

[placid hound]

yea you're right

[shy barn]

what can I do to turn it into (a-2)(a+2)?

[placid hound]

maybe multiply by -1, so you have -(a-2)(a+2)

but I don't really understand what the exercice is exactly

[shy barn]

I have to simplify it

[placid hound]

the expression on the first line?

[shy barn]

yeah

the little arrows with hebrew text are explanations for every step I'm doing, as I have to explain each step to get a full mark on this

[placid hound]

ok, well by multiplying by -1 could work to then get the fractions with the same denominator

[shy barn]

I think you're right, thanks

[marsh citrus]

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[bleak quartz]

How does this work?

[sterile rock]

need more context

[sterile rock]

what is v?

is this showing displacement in terms of acceleration or smth

and time

[bleak quartz]

v velocity
t time
y is displacement

I have the top equation and am trying to solve it for v

[sterile rock]

alright, so this looks like chain rule

basically

oh

so ur given

acceleration = g-kv^2

$test$

[elfin berry]

UsingApp

[sterile rock]

ok that works

search up chain rule

basically

khan academy

idt i will explain well

[bleak quartz]

I get the chain rule part but just not the final part with the 1/2

[copper raven]

it's a product rule thing

[sterile rock]

oh wait yeah

[copper raven]

d(v^2)/dy = v dv/dy + dv/dy v = 2 v dv/dy

[sterile rock]

i think i mixed them up

oops

[bleak quartz]

ah ok thanks

[marsh citrus]

@bleak quartz Has your question been resolved?

[marsh citrus]

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[brittle sun]

for part C , how do i know the integral bouns?!

[marsh citrus]

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[brittle sun]

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[sage gate]

I can't figure out the other two

[cyan parcel]

The general formula of a line is y = ax + b

U have 3 line

Why there's an a term there?

[sage gate]

https://www.youtube.com/watch?v=eWo8tWuaGfU

[cyan parcel]

I will guide u

[sage gate]

okay

[cyan parcel]

First pick 2 random point in 1 lines

For this line pick 2 random points

[sage gate]

-3,-5?

[cyan parcel]

Can u provide a better graph

It hurts my eyes

[sage gate]

like that

[cyan parcel]

Do u know what a point look like?

[sage gate]

idk what you mean

[cyan parcel]

let select this red point

whats its value?

[sage gate]

-3

[cyan parcel]

Nope

[sage gate]

-2

[cyan parcel]

A point is present as (x,y)

So?

[sage gate]

(-2,-3)

[cyan parcel]

Why did u remove the ()

[sage gate]

ummm added lol

[cyan parcel]

Good

Pink?

[sage gate]

(-6,-1)

[cyan parcel]

Good

[sage gate]

okay

[cyan parcel]

Here's how u get a

Remember the 2 point

Let call red the first point; pink the 2rd point

Then red is (x1, y1)

pink is (x2, y2)

plug it in

to find a

[sage gate]

1/2

[cyan parcel]

Is it?

Always double check

[sage gate]

-1/2

[cyan parcel]

good

Now

Whats we need to find then?

[sage gate]

not sure

[cyan parcel]

we have a already

[sage gate]

okay

[cyan parcel]

Whats the other value that we dont know?

[sage gate]

b

[cyan parcel]

Good

The way we get b is use the random point we select from the step 1

Choose 1 point

[sage gate]

-3

[cyan parcel]

What do u choose?

[cyan parcel]

What did I teach u about point?

[sage gate]

oh you want both?

(-2,-3)

[cyan parcel]

Remember

A point is ALWAYS defined as (x,y)

Now

Whats the line formula we got so far?

[cyan parcel]

plug a in here

[sage gate]

-1/2x?

[cyan parcel]

Where the y term and b?

Why are u always removing important part? 💀

[sage gate]

idk what you mean

[cyan parcel]

y = -1/2 * x +b

[sage gate]

your telling me enter something idk

[cyan parcel]

bruh

Plug in doesnt mean entering a value

[sage gate]

idk what you mean or what you are saying

[cyan parcel]

See

y = ax +b

we know a = -1/2

We plug a in

so we got y = -1/2 *x +b

Understood this part?

[sage gate]

yes

[cyan parcel]

Now

[quaint valley]

plug means substitute btw

[cyan parcel]

Since we have a point that this line must go through

[sage gate]

okay

[cyan parcel]

And u choose this point

We subs x and y (of the point) into the line equation (x and y term) to find b

Whats b =.... ?

[sage gate]

-3=-1/2(-2)+b

[sage gate]

idk

[cyan parcel]

U have this

Whats b? (treat b as x in algebra)

[quaint valley]

Use Algebra to solve for b.

[sage gate]

-2

[cyan parcel]

try again

[sage gate]

-4

[cyan parcel]

Good

then plug both a and b to the general formula of the line

[cyan parcel]

.

Thats ur answer

Good job!

[sage gate]

-3=-1/2(-2)-4

like that?

[cyan parcel]

Nope

x and y term stays

just a and b get subs

Whats ur final answer?

[sage gate]

y=-1/2x-4

[cyan parcel]

Good job

btw

@sage gate

convert that -1/2 to -0.5

[cyan parcel]

some people might confused it as -1/(2x)

[sage gate]

okay

this is showing me what the final answer is

[cyan parcel]

if u expand it out

You should see the given solution should match yours

[sage gate]

how so

[cyan parcel]

-0.5 * (x + 2) - 4 +1
=> -0.5 x - 1 - 4 +1
=> -0.5 x -4

thus match ur answer

[cyan parcel]

.

The teacher just hide the "y =" .... term

[sage gate]

oh I see now

[cyan parcel]

Do this line urself

[sage gate]

alright ]

[cyan parcel]

Give me the answer (ping)

[sage gate]

is that point (6,2.5)??

[cyan parcel]

Why choose that point?

Choose this

Any point on the line works

[cyan parcel]

a should be 5/2

b should be -25/2

[sage gate]

wiat how

(3,5) (0,5)

[cyan parcel]

@sage gate

Its not (3,5)

Its (3,-5)

[sage gate]

oh right that's what I have

[cyan parcel]

And its not (0,5)

[sage gate]

gives me 0/3

[cyan parcel]

Its (5,0)

[sage gate]

0/5.

[cyan parcel]

2 points should be (3,-5) and (5,0)

a = (-5 -5)/(3-5) = -10/-2 = 5 /2

bruh

[sage gate]

bruh I asked

[cyan parcel]

asked?

[sage gate]

nvm

[marsh citrus]

@sage gate Has your question been resolved?

Channel closed

Closed by @sage gate

Use .reopen if this was a mistake.