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[tidal grove]

Hey

[tidal grove]

I get minimal distance as 19 using prims method

But prof got 21 so unsure

He did it using linear programing, have i made an error?

[floral dew]

Hey, let me try to help you

Could it be that your professor searched for a cycle instead of a path?

I believe the TSP is often used in both of these ways, so either where the salesman has to visit each city once and that's it, or that the salesman has to visit each city once and end at the city they started at

It could maybe be that the confusion arose due to that

[topaz sinew]

@tidal grove Has your question been resolved?

[tidal grove]

Hmm @floral dew im not sure

If my application of Prims algorithm is correct

Then i dont mind having a different answer

Do you think you can verify this for me

Lets say if the sales man had to go back to A im not sure that would be represented by a distance of 2 anyways

[floral dew]

I am not entitely sure how you came to your solution, I did have a go at it myself and found a possible path E-A-B-C-D of length 14

[tidal grove]

Hmm

Why method is

To start at A

Cross row out

Number colum A as 1

Find smallest number in row

And circle that in the A column

Then see which row Letter than number corresponds to

And then my next column

Write 2

Above it

Then cross out that row

Find smallest in that row

And circle in the column i numbered 2

And repeat

[floral dew]

I see

[tidal grove]

Whilst making sure i never go back to a row

[floral dew]

While I unfortunately can't tell you exactly why, I'm pretty certain that method does run into some problems. I don't think you made a mistake using that method

[tidal grove]

Its oversimplified

Yes i understand

[floral dew]

Is there anything else I could help you with now?

[tidal grove]

You got any tips for optimisation

Linear programming?

[floral dew]

For linear programs I'd generally advice anyone to have a look at a couple of these programs and really make sure you understand what is happening and what kinds of techniques are being used. You will quickly start recognizing those same techniques in all kinds of linear programs.

[tidal grove]

Ahhh cool

Yeah i agree with this

Mathworks have a quite a few examples

Quite scary at a first glance

[floral dew]

Haha yeah I can imagine

Btw, to get back to your original question. Your professor solved the problem for the cycle variant. I just came to the same solution of 21.

[tidal grove]

Ahh can u explain how you did this ?

Did u do it by hand or program?

[floral dew]

For this specific instance I did it by hand, mostly by trial and error.

I could tell you my reasoning, but it's not a great methodology by any means

[tidal grove]

No i get u

Brute force methods do work but are tedious

Maybe hearing it i can know how to make it better

[floral dew]

Sure, in this case I just started with some cycle that looked kinds short (A-B-C-D-E-A)

[tidal grove]

Oh okayyy

[floral dew]

then DE has weight 10, which is quite high and I tried to somehow get rid of it, in this case by picking BD and CE instead of CD and DE

you then have (A-B-D-C-E-A) which coincidentally got me to 21

But in general (especially as the size of the graph increases) these problems are very hard to solve by hand. That's for a great part what motivated the field of Discrete Mathematics & Optimization.

[tidal grove]

Oh so this is discrete maths

Interesting

[floral dew]

I hope I have been able to answer your question more or less :D

[tidal grove]

You have been great

Thanks a bunch

[floral dew]

No worries!

[topaz sinew]

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[slender sonnet]

In a ABCD ractangle there is a AC diagnal is ABC angles bisector and it corosses the diagnal in point M the distance from M point to BC is 10 and to AD is 4 i need to find the AC diagnal

[slender sonnet]

Since its the bisector the right trialgles sides would both be 10 and the hyp is sqrt200 i have found that so far

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

Can someone help

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[molten vine]

to find the total amount of heat i do a double integral right ?

[thorny flame]

Adam Chebil

[molten vine]

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[frank narwhal]

How am I supposed to solve problems like this?

[frank narwhal]

i know sin^2x + cos^2x = 1 but im not sure why or how to get there

[dense cairn]

thats the answer to the first question

other ones are just basic, you can turn the tan^2 x into sin^2x/cos^2x

and then go from there

[torpid sparrow]

Use this to prove it

[frank narwhal]

i dont really see how i can use that to solve it

[torpid sparrow]

Do sin^2x+cos^2x using that

[frank narwhal]

well yah i just dont know what to do with that information

[frank narwhal]

wouldnt 2. be 2 since itd be 1 + 1

or no nvm

[torpid sparrow]

$\cos^2(\alpha) + \sin^2(\alpha)
= \left(\frac{a}{h}\right)^2 + \left(\frac{b}{h}\right)^2
= \frac{a^2}{h^2} + \frac{b^2}{h^2}
= \frac{1}{h^2}(a^2 + b^2)$

[thorny flame]

Samuel

[torpid sparrow]

Now, how much is a^2+b^2?

$a^2 + b^2 = h^2$

[thorny flame]

Samuel

[torpid sparrow]

$\frac{h^2}{h^2}
= 1$

[thorny flame]

Samuel

[frank narwhal]

so how do you get a^2 and b^2 together like that in the last part

oh just adding them i assume

[torpid sparrow]

you take 1/h^2 common factor

[frank narwhal]

ohh okay

tyty that helped a lot

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[slim sparrow]

how do I do the derivative of tan^-1 (x+1)

[slim sparrow]

its chain rule right?

1/((x+1) + 1) * 1/(2sqrt(x+1))

[void crow]

you sure its chain rule?

$tan^-1(x+1)$

[thorny flame]

sin

[void crow]

which is basically

$cot(x+1)$

[thorny flame]

sin

[void crow]

wait ooh

this is interesting

[slim sparrow]

So i use the quotient

?

1/tan(x+1)

[void crow]

whats the derivative of $cotf(x)$

[thorny flame]

sin

[gleaming reef]

it's the function inverse not multiplicative inverse p sure

so we are talking about arctan(x)

[void crow]

you can take arctan or cot

and essentially yes, its chain rule

that was my mistake, i thought i saw tan x 😭

[slim sparrow]

• cosec^2 (f(x))?

1/sin^2 f(x)

why cant it be 1/(x+1)^2 + 1

[void crow]

look again

[void crow]

you have to derive the arctan/cot too, remember?

[slim sparrow]

isnt tan^-1 (x) equivalent to 1/(x^2'+1)

[void crow]

how did you get that

:0

[slim sparrow]

Sorry I forgot to add ^2

cant we do tan^-1(u) where u = x+1

so its 1/((x+1)^2 + 1)

[void crow]

its

derivative

yes

it is

[void crow]

correct

[slim sparrow]

how would I do this derivative with tan^-1(sqrt(x+1))

sqrt(x) = square root of x

[void crow]

hmm

[slim sparrow]

i replace square root of x+1 with u right?

[void crow]

fundamentally, yes

[slim sparrow]

arctan(u)

[void crow]

,w derive tan^-1(sqrt(x+1))

[thorny flame]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by waitara

[slim sparrow]

I need to get the derivative of tangent u

which is sec^2(u)

so

because

its 1/sec^2(u)

and sec = 1/cos

does it become cos^2(u)

because its technically 1/(1/cos^2(u))

so then

[void crow]

im not quite sure 😭

this is a new subject for me too LMAOA

[slim sparrow]

same

Well, not really new, I learnt it a week ago and fell off cause i didnt revise it at all

[slim sparrow]

Partially revised it I guess but not to this extent

[slim sparrow]

wait

derivative of tan^-1 u is just 1/u^2 + 1

what the hell was I thinking

1/x+2

one thing thats confusing me is how someone online got this

from deriving this:

i found a trick to do integration by parts easily

https://www.youtube.com/watch?v=V8uZYdd4Jnk

But the problem is in 4:28

where he gets 1/(x+2) MULTIPLIED BY 1/2(sqrt(x+1))

it seemed simple enough until i saw this

Nevermind, im such an idiot :.(

I forgot what this is all based on

integration by parts

(x+z) X (1/(x+2)) X du

i replaced X with * because * putting stuff inbetween asterisk puts them in italics form*

[slim sparrow]

Oh now it doesnt work :/

ty

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[neon iron]

find the equation of the parabola whose latus-rectus is 4 units and axis is the line 3x+4y-4=0 and the tangent at the vertex is the line 4x-3y+7=0

[neon iron]

how do i do this

i was think of choosing a arbitary point on the parabola and write the expressions for perpendicular distances of (x,y) on both the lines

but i am stuck after that

[topaz sinew]

@neon iron Has your question been resolved?

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[thick shore]

sorry for the small handwriting

[thick shore]

I’m using a formula to calculate the present value of annuity

I keep getting a diff answer each time I do 😭

[topaz sinew]

@thick shore Has your question been resolved?

[thick shore]

<@&286206848099549185>

[topaz sinew]

@thick shore Has your question been resolved?

[thick shore]

<@&286206848099549185> pls help me I’ve been struggling for an hour and a half 😭

[feral escarp]

Your ans is correct

638,...

[thick shore]

wait it’s supposed to be 638,000 or something? I tried that (using Desmos) and it’s wrong apparently :(

[thick shore]

please elaborate on this

[feral escarp]

I'm assuming the down payment is made before calculating the interest? So the Maximum cost you can afford is 785,480

[thick shore]

Tried that, it’s still incorrect for some reason. ChatGPT’D it numerous times, all wrong too
I wanna say it’s Desmos that’s wrong bc of all of this. I tried all the formulas I learned today too so 💀

[thick shore]

Thanks for ur input tho, I’ve been using mortgage calculators and they’ve all been getting that

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[tepid gazelle]

ok so i have a maths problem based on trig applications for ib sl analysis

[tepid gazelle]

it's for this one teacher who has a history of being harder than he needs to be

this problem was given to me by a sr to prepare for one of his tests

this is not a calculus question, just to confirm that

this is a purely trigonometric problem

@knotty finch sorry to bother but pls i really want to go sleep

[topaz sinew]

@tepid gazelle Has your question been resolved?

[topaz sinew]

@tepid gazelle Has your question been resolved?

[rare lagoon]

maybe if ic ould read that I could sove it but currently your best bet is to make the question moire visible or write it digitally

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[twin pollen]

What is a rational expression

[twin pollen]

Does this have a rational expressy

Expression

[fallow igloo]

!status

[topaz sinew]

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

[twin pollen]

Its just a question

In case it comes up on the test

Its a yes or no question

Cause it says rational expression have polynomial in numerator and denominator

I dont see it

So is it no?

?

[abstract wadi]

Expressions don't have equality.

Equations have equality.

[twin pollen]

But does that pic have expressions

I thought it had to have polynomial in denominator and numberator someone

Somewhere

[abstract wadi]

Does the image have an equality?

[twin pollen]

Yes

[abstract wadi]

Then it's an equation.

[twin pollen]

But my teacher said a rational equation is one that has a rational expression

[abstract wadi]

This is a rational equation, yes.

[twin pollen]

Where is the rational expression

[abstract wadi]

As a whole this is an equation, not an expression.

[twin pollen]

So there is no expresy

Expression

What does this mean then

[abstract wadi]

On either side of the equality what you have is an expression.

[twin pollen]

What is a rational expression can u define it?

[abstract wadi]

A rational expression has rational terms.

[twin pollen]

What are rational terms

[abstract wadi]

By rational terms I mean numerator and denominators are polynomials.

Terms are usually separated by +- operations.

So for example,

3x + 5

Is an expression.

3x + 5 = 2x^2 - 3 is an equation

[twin pollen]

Is it a rational expression?

[abstract wadi]

Yes it is a rational expression.

[twin pollen]

How

[abstract wadi]

3x+5 that is.

[twin pollen]

How

[abstract wadi]

3x+5 is the same as (3x+5)/1

Both the numerator and denominator are polynomials.

[twin pollen]

1 is a polynomial?

[abstract wadi]

Sure.

[twin pollen]

I thought polynomials have variable

[abstract wadi]

A polynomial needs to have whole number powers of the variable.

1 = x^0

[twin pollen]

Is 5 a polynomial?

[abstract wadi]

Sure.

[twin pollen]

How

[abstract wadi]

5x^0

[twin pollen]

O rlly so everything is a polynomial

[abstract wadi]

Not really, polynomials are very specific.

[twin pollen]

What is not a polynomial

[thorny flame]

! What the hell am I doing here?

! What the hell am I doing here?

[twin pollen]

Wait why

Both these not

[abstract wadi]

What's the exponent of x here?

[twin pollen]

1

[abstract wadi]

No.

[abstract wadi]

This is -1

[abstract wadi]

This is 1/2

[twin pollen]

Ooo ya

But how is that not a polynomial

[abstract wadi]

Because polynomials have whole number exponents of the variable.

Neither of these numbers are whole numbers. (-1 or 1/2)

[twin pollen]

How do I classify a polynomial then

I didnt learn this

[abstract wadi]

A polynomial is an algebraic expression with variables and coefficients, such that the exponent of the variable is only whole numbers throughout.

If you haven't studied this, you can refer this definition and use this to solve problems.

If there's a lot more you don't know, such as an expression or equality or terms or coefficients, then revise basic algebraic terminology. I'm sure you have something if not everything in your textbook.

[topaz sinew]

@twin pollen Has your question been resolved?

[topaz sinew]

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[rare citrus]

Can someone pls help with question a?

[flat kindle]

you forgot to change the bounds

[rare citrus]

how would I do that?

[flat kindle]

you start with x=0 to x=3

[rare citrus]

radians or degrees

[flat kindle]

find theta

[rare citrus]

OHHHH

SHIT

x = 6sintheta

[flat kindle]

in calculus you always use radians

[rare citrus]

3 = 6sintheta

alright that makes sense

[rare citrus]

so the upper bound is pi/6 and the lower bound is 0

[flat kindle]

ya

[rare citrus]

yep its correct

thanks for explaining that to me

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[exotic saddle]

Pls help

[ruby mural]

Which question?

And

[topaz sinew]

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

[exotic saddle]

both

i dont know what it means

[ruby mural]

Look at the options, they want you to write one variable in terms of the other

For example in the first one, try isolating y

On one side

[exotic saddle]

so ill isolate the y in 4x - 2y = 10?

[ruby mural]

Yeah

[exotic saddle]

alr wait

y = -2x + 5

@ruby mural

[ruby mural]

That matches with one of the options

Also no wait

[exotic saddle]

Yeah, a. now what?

[ruby mural]

It should be the negative of what u got

[exotic saddle]

wdym?

[ruby mural]

I mean that it should be y=2x-5

[exotic saddle]

oh yeah mb

so after this, what do i do?

[ruby mural]

Tick the correct option and move on?

[exotic saddle]

what does in terms of x mean tho

[ruby mural]

They want you to find a way in which you can relate y with x in some way

[exotic saddle]

what 😭

[ruby mural]

I mean

Uh

Ig all they wanted you to do was isolate y on one side

And write it in terms of x

[exotic saddle]

ahh alright tyy

.done

[ruby mural]

Np

[exotic saddle]

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[shadow nymph]

hoy :D
(0,6x - 0,45)/(0,6x - 0.75) = 0.45/0.75 ?

[flat kindle]

no

[shadow nymph]

Then what should I do if I want to get a number wihout x ?

My exercice want to prove that a sequence is géometrical

let me a moment

[ruby mural]

! original

[topaz sinew]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[shadow nymph]

translatedish

I'm blocked in 3.a

[shadow nymph]

Alr thanks u I will keep it in mind

[flat kindle]

where's the first part

[shadow nymph]

The 1st part is about probability

I did perfect on these

[flat kindle]

well

[shadow nymph]

sry

[shadow nymph]

I did good in 2 but I'm always blocked when it come to 3.a

I had the same situation Twice which kinda make me down in a exam

I belive I don't have good base in fraction but with x or any variable it make more confusing

[shadow nymph]

When I just pass this question I do fine but it's always this one who fuk me up

[flat kindle]

you want to show that u_n = c*u_n-1 for some contant c

you can do it by altering the equation u_n=p_n-0.75

by substitute p_n = 0.6p_n-1 + 0.3

[shadow nymph]

Hm hm

Wait

u can do that (never learned from) ?

I thought the only way to show if a sequence is geometrical is
Un+1/Un = Number

[flat kindle]

umm

[shadow nymph]

it work with Un/Un-1 ?

[flat kindle]

Un/Un-1 = number is the same as Un = Un-1 * number

[shadow nymph]

oooh

i'm still confused

[flat kindle]

what do you get after substituting

[shadow nymph]

How it's possible to do this ? I remplace p_n with p_n+1. it all the data I got ?

[flat kindle]

hmm

[shadow nymph]

how u justify the need of u_n-1 ?

[flat kindle]

p_n+1 also works

ok let's use p_n+1

what do you get

[shadow nymph]

u_n+1 = 0.6p_n - 0.45

[shadow nymph]

p_n+1 = 0.6pn + 0.3 (the exam gave us p_n+1)

[shadow nymph]

while
u_n = pn - 0.75

[flat kindle]

ok

now calculate u_n+1/u_n

[shadow nymph]

alr

[shadow nymph]

Hm I'm blocked here

[flat kindle]

you can factor and cancel

[shadow nymph]

factor by pn ?

[flat kindle]

no

[shadow nymph]

hmmm

[flat kindle]

it's decimal so it's hard to see

[shadow nymph]

should I convert these decimal to fraction ?

[flat kindle]

yeah try doing that

[shadow nymph]

i suck or wut ? I don't see it ;-;

I used 10 because it's the easiest to convert to

[flat kindle]

um

[shadow nymph]

the goal is to find (pn-0.75)(something) = 0.6pn + 0.3

right ?

[flat kindle]

yes

actually you just need to factor 0.6

[shadow nymph]

let me try

I feel like I'm going nowhere

[shadow nymph]

Btw what's the general method to find the "something"

[shadow nymph]

Here ?

Maybe it's what I miss rn

[flat kindle]

wait

you copied

wrong

[flat kindle]

should be 0.6pn-0.45 / pn-0.75

[shadow nymph]

oh

[shadow nymph]

Un+1 = 0.6pn-0.45 ?

OH yeah !

[flat kindle]

ya

[shadow nymph]

my bad

always got issue with this

being too fast each time

thanks u

[shadow nymph]

so i apply the facotrisation of 0.6 right ?

[flat kindle]

yes

you should be able to cancel pn out

[shadow nymph]

Hm factor again ?

[flat kindle]

no

you only need to factor the 0.6 on numerator

[shadow nymph]

hmmmmm ?

okay ?

OH

sigh I hate this factor/fraction exercices

[flat kindle]

yay finally

[shadow nymph]

Alr Today I learned that facotring the numerator only can help killing this factor bar

[shadow nymph]

Thanks u ! I really need to recheck the base of facotrisation ;-;

[flat kindle]

no problem

[shadow nymph]

I never though it was that easy

In my exam it was like this

Man I'm going to kill my phone somehow

Anyway just heavy calculation

The problem is that I didn't find the factor and got something like
(Un²+2un+number)/(same thing but proportional) = constant

I just jumped into the conclusion since I got no time ,-,

[shadow nymph]

Thanks u I wish u a really nice day

.close

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[topaz sinew]

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[tawny prairie]

Henlo c: I could use some help with this task

An employee works in a team with 3 other colleagues on the realization of a customer order. The price the customer pays to the company for the successful completion of the order is 1.5 million euros. The management has promised the team a reward for the successful execution. This reward corresponds to 10% of the profit generated by the order. The reward is distributed equally among the team members.

The employee can influence the order's profit by making an effort to find cost-effective solutions for its realization. The relationship between his effort 𝑒 (𝑒 = 𝑠), the efforts of his colleagues 𝑘𝑖, and the costs of order implementation 𝐶𝑈 is given by: (see pic1)
The personal costs of effort 𝐶(𝑠) for the employee and his colleagues are given by: (see second pic)
a) What level of effort will the employee choose? Assume that he wants to maximize his own benefit.

b) How much will the reward for the employee be if his team members choose the same effort level as him?

I do have the results but I dont understand how to get there.
So for a I get this equation (see pic3) but how do I get this? (see pic 4)

[tawny prairie]

oh and then for task b all I have to do is put the 100 in s so that I have this: (see pic) their answer to that is 5262 but I dont know how if I type it into my calculator something eles comes up (plus i dont know what to do with the weird E symble)

[topaz sinew]

@tawny prairie Has your question been resolved?

[tawny prairie]

<@&286206848099549185>

[flat kindle]

yo

differentiate with respect to s

[tawny prairie]

does that mean that I am using the chain rule? (i'm sorry english isnt my first language)

[tawny prairie]

so it means that everything that hasn't an s just gets deleted but the 40000*1/10000 becomes that way cuz thats what you have to do when you deriviate from ln ? but shouldnt the 10000ki be deleted too?

[tawny prairie]

or is this correct so far?

A friend sent me this over but its also confusing me too cuz idk what the d/dx is

[tawny prairie]

and here for task b I cannot come to the result. if I type it into the website I get this

in the whatapp group all they told me to is to put it into my calculator, I didnt get more help from them

[topaz sinew]

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[marble igloo]

idk how to do part g

[marble igloo]

could someone help me?

I think it has to be rotated by 45 degrees, but idk what to do after that

<@&286206848099549185>

[topaz sinew]

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[shut belfry]

konsi grade me ho?

[fickle briar]

9th

[shut belfry]

board?

[fickle briar]

No like, for iit foundation

[shut belfry]

oh

[fickle briar]

Ntse or olympaid exams

[fickle briar]

From india ?

[shut belfry]

yea

[fickle briar]

10th ahh

[shut belfry]

isnt that obv lol

[fickle briar]

What r u doing here ?

[shut belfry]

Clearing doubts

[fickle briar]

U have exams bro ?

[shut belfry]

lets get back to q

[shut belfry]

Yea ezz

[fickle briar]

Ok

[shut belfry]

!status

[topaz sinew]

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

[fickle briar]

1

[shut belfry]

uk formula for SI?

[fickle briar]

PIT/100

Principal
Time period
Rate of interest

Divided by 100

I solved it that way but it is not the way

[topaz sinew]

@fickle briar Has your question been resolved?

[topaz sinew]

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[uneven verge]

The total length of a lemur, including the tail, follows a normal distribution with a mean of 40 inches and a standard deviation of 1 inch.
Find the probability that a random lemur is greater than 39 inches long

[topaz sinew]

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[stray finch]

Need help proving this sentence. This is translated to English so sorry if it's not very clear

[topaz sinew]

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[agile badger]

My task is to calculate the area of ice needed and the total length of the safety fences.

[neon iron]

Oh

[topaz sinew]

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[bold nexus]

hi!, how do i get to know what numbers are part of this set?

[tough nest]

Solve for alpha no?

[topaz sinew]

@bold nexus Has your question been resolved?

[bold nexus]

so i clear the left side and multiple alpha to the power of 2 by the divisor?

[tough nest]

clear the left side?

[bold nexus]

i mean

solve the equation in a way i get alpha = a Real number

[tough nest]

you should get a fourth order polynomial = 0

which using a trick will allow you to find the valid values for alpha

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[bold nexus]

.reopen

[topaz sinew]

✅

[agile badger]

.reopen

[bold nexus]

you are saying i should add a 0?

im sorry my fisrt language is not english

they dont teach english math at school lol

[tough nest]

$-\frac{8}{\alpha^2 - 6} = \alpha^2$ => $-8 = \alpha^2(\alpha^2 - 6)$

[thorny flame]

Katharine

[tough nest]

and then move the 8

to get 0 =

[bold nexus]

oh yeah thats what i meant when i said clear the left side

i just didnt know how to express it

so i solve the equation now and get the roots

[tough nest]

yes

[bold nexus]

aight thanks i now i just have to remember fourth degree equations

[tough nest]

you don't need to

it's symmetrical around the y axis

what i mean is

you can say $\alpha^2 = \beta$ and solve for beta

[charred rampart]

sub in u=a^2

[thorny flame]

Katharine

[charred rampart]

and it’s actually just a quadratic

[charred rampart]

lol

[bold nexus]

wait what does that mean

i end up with something like this right?

[topaz sinew]

@bold nexus Has your question been resolved?

[charred rampart]

right, notice that a^4 is just (a^2)^2, so we can set a variable u so that u=a^2 and end up with 0=u^2-6u+8

[topaz sinew]

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[neon iron]

Hello I’m having a problem with a math question on Pearson

[neon iron]

So 6x is the circumference according to this and with the circumference I can get the radius

Because circumference = 2(pi)(r)

If I plug in 6x the radius should be 6x/2pi

And from there I should be able to plug it in the area

A = pi r^2

So pi (6x/2pi)^2 should be (36x2/4pi^2) x pi

[cinder hawk]

yes

[neon iron]

But Pearson insists that the answer that the answer is 9x^2/pi

[cinder hawk]

same thing

[neon iron]

What about the pi that was outside the parentheses

[cinder hawk]

it cancels with one (!!!) of the pis in the denominator

[neon iron]

Oh

How come

[cinder hawk]

$\frac{\pi}{{\pi}^2}=\frac{1}{\pi}$

[thorny flame]

baro | awake

[neon iron]

Ok this makes sense but there is no pi in the numerator

[cinder hawk]

yes there is lol

[cinder hawk]

the pi you multiply is in the numerator

[neon iron]

But wouldn’t it be pi^3 then

Since I already squared the whole thing and it became pi^2

[cinder hawk]

$\pi \cdot \frac{9x^2}{\pi^2} = \frac{9\pi x^2}{\pi^2}$

[neon iron]

And then the pi from the numerator would cancel out and pi^2 should be left in the denominator no?

[thorny flame]

baro | awake

[cinder hawk]

those pis are in the denominator

$\pi = \frac{\pi}{1}$

[thorny flame]

baro | awake

[cinder hawk]

if you think of every term seperate that might help

$\pi \cdot \frac{9x^2}{\pi^2} = \pi \cdot \frac{1}{\pi} \cdot \frac{1}{\pi} \cdot 9 \cdot x \cdot x$

[thorny flame]

baro | awake

[cinder hawk]

do you see how the pi cancels now?

[neon iron]

Hmmm

Oh

Ok

Ok yeah that makes sense

I don’t know why I thought that I multiplied both the numerators and the denominators by pi

[gilded totem]

I'll just comment now so I can take credit in the server even tho I was late

[cinder hawk]

remember, anything over itself (with the notable exception of zero) is one

[neon iron]

Yeah so I only multiply the numerator by pi and the denominator would be multiplied by 1

So the denominator is the same and only the numerator changes

And then they cancel out and only one pi is left in the denominator

[cinder hawk]

oui

[neon iron]

Thank you so much

I feel so stupid

[cinder hawk]

don't feel stupid!

correcting mistakes => learning!!

and now you probably have a deeper understanding of fraction multiplication. so yay!

[neon iron]

Yay indeed

[topaz sinew]

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[shell bough]

Square numbers are whole numbers that could be the area of a square. THe series begins: 1, 4, 9, 16, 25, .... Write an equation to find the n^th square number

[outer carbon]

Its a formula

wait wait

isnt it just n^2

[shell bough]

yes it is lol I just don't understand how to get n^2

[outer carbon]

oh u gotta prove it

that its n^2

[shell bough]

ya

[keen venture]

"Square numbers are whole numbers that could be the area of a square"
This seems wrong

[grim sable]

How?

[keen venture]

Maybe a square with integer sides

[outer carbon]

how does it seem wrong

[shell bough]

I don't think so

[keen venture]

By that definition, 1.44 is a square number

[grim sable]

Yea i guess your right

The def shoulda been more specific

[keen venture]

But, okay, let's say it means "a square with integer sides".
Call that integer n.
What's the area of the square?

[shell bough]

n^2

[outer carbon]

I dont know if theres a proof

but I noticed their differnces are in ap

just that

[shell bough]

i think it should be fine

[shell bough]

thanks that helped a lot

the wording is just kinda funny

.close

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[twin pollen]

👋

[twin pollen]

How do I find acceleration?

Im doing 2b

Do i need acceleration?

[clever verge]

Show me your attempt at modeling the kinetics

[bitter hemlock]

are you familiar with Hooke's law? (the equation that relates force applied to a spring to how much it stretches)

it's straightforward if you know to use the equation

[twin pollen]

Do i need acceleration

For 2b

[bitter hemlock]

do you know F = -kx ?

[twin pollen]

No

[bitter hemlock]

did you have any kind of reading \ lecture for this material? that must definitely be part of your material if you are doing this problem

[twin pollen]

We learned F= k•x

x is change

Like displacement

Or stretched length

Oops

[bitter hemlock]

yes that's it, - sign is kind of arbitrary i guess, im a bit rusty on this but probably just depends how you decide to set up the axes

[twin pollen]

Ic ok

[bitter hemlock]

so x is what you want for the answer is b and what is the force applied to the spring?

[twin pollen]

So Fg?

[bitter hemlock]

you already solved for F in part a)

its 270N

[twin pollen]

Wdym force applied to string

[bitter hemlock]

spring

[twin pollen]

How do I find that

[bitter hemlock]

...?

[twin pollen]

O wait

I think my fbd is wrong

How would U draw it out

I screwed up

Once i get fbd i shoudl be ok

Hopefully

Free body diagram is fbd btw

?

[bitter hemlock]

so youre lowering a rover from your spaceship, hanging by a spring

😛

[twin pollen]

So spring force up

Right

[bitter hemlock]

yeah youve got gravity pulling down, i guess spring force pulling up and they even out

[twin pollen]

But its lowering

[bitter hemlock]

so the spring force is the same as gravity but in the opposite direction

[twin pollen]

But its lowering

[bitter hemlock]

i think you're supposed to think of this as a snapshot in time, think of the lowering as very slow

we aren't given the rate or anything related to that its being lowered

[twin pollen]

Ooo yea so its hanging

Ig

[bitter hemlock]

yeah pretty much think of it that way

so basically just stick the force and the spring constant in that equation and solve for x, no rocket science

[twin pollen]

Got it

Yes

Thx

[bitter hemlock]

270N = 100.0 N/m x
x = 270/100 m = 2.7m thats literally all there is to it

thats a very stretchy spring, sheesh

3 m

[twin pollen]

Yes

Lol

[topaz sinew]

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[flint quarry]

Hi

[flint quarry]

Just trying to solve some practice question before I sleep

[flat kindle]

!status

[topaz sinew]

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

[flint quarry]

I don’t know where to begin

[flat kindle]

First P = P1 + P2

[flint quarry]

Hm well

[flat kindle]

P1 Is easy to find so try to find P2

[flint quarry]

Wait how do i find p1

P1x=8cos(120)

P1y=8sin(120)

?

[flat kindle]

Yes

[flint quarry]

Okay so that’s p1 right

<p1x,p1y>

[flat kindle]

Ya

[flint quarry]

Ok so p2 i would need to find theta first or no

Would i just do the inverse?

P2x=4cos(theta)

[flat kindle]

P2 is parallel to the y axis

[flint quarry]

What does that mean

[flat kindle]

It means x component = 0

[flint quarry]

Ah so by default x=0

[flat kindle]

You can verify this by using theta = 90 degrees

[flint quarry]

Oh since its parallel its a right triangle

Wouldn’t theta be 45

[flat kindle]

No

[flint quarry]

Hm

Why is it 90

[flat kindle]

It's hard to explain qithout drawing :/

[flint quarry]

😦

I wanna understand why its 90

[topaz sinew]

@flint quarry Has your question been resolved?

[flint quarry]

So when x component is 0 theta is 90?

@flat kindle

[flat kindle]

Yeah

I got some paper here
lemme draw

[flint quarry]

Ok i see

Hm ok so

P2x=4cos(90)
P2y=4sin(90)

[flat kindle]

Typo

[flint quarry]

I see

Better?

[flat kindle]

Yes

[flint quarry]

So what would be the next step after getting p1 and p2 cordinates

[flat kindle]

Add them to get P

[flint quarry]

Ok let me solve em

P1x=-4
P1y=4sqrt3

P2x=0
P2y=4

P=<-4,4+sqrt3>

[flat kindle]

-4 for x component

[flint quarry]

Oh correct typo

Since 2nd quadrant

Ok

Now that would conclude part a correct?

P=<-4i,4+sqrt3j>

[flat kindle]

You either write it as a vector like <-4,4+sqrt(3)>

Or use i,j and write -4i+(4+sqrt(3))j

[flint quarry]

Ok ok

[flat kindle]

You can't mix them

[flint quarry]

Thanks for that

I would write it in i,j since it asked for that

Now that’s part a right?

For part b would just be the magnitude of P

[flat kindle]

You can think of magnitude as length

[flint quarry]

Hm ok yes

Length of P leg basically

So

Sqrt(px)^2+(py)^2

[flat kindle]

Correct

[flint quarry]

Ok i got 8

Does it that make sense? Cause length of p1 is 8

Sqrt(4)^2+(4sqrt3)^2

Gives me 8

@flat kindle

[flat kindle]

No

Py is 4sqrt(3)+4

[flint quarry]

Hm

Where did the +4

Come from

Ohhh i see

[flint quarry]

So this is wrong

-4i,+4sqrt(3)+4j

I got 11.637

For P’s magnitude

[flat kindle]

Correct

[flint quarry]

Yey ok

So now for P’s direction

Would i do the arctan of P?

[flat kindle]

Yep

[flint quarry]

So arctan(py/px)

And that’s my direction?

If so i got 80.1

Is that correct

@flat kindle

[flat kindle]

I think so

[flint quarry]

Tan^-1(4/4sqrt(3)+4)

Right?

If that’s right then in polar form it would be

P=11.637 angle 80.1

Thanks btw for your help

@flat kindle i just need to know this last bit and I’m done pls thank you

[flat kindle]

Correct

[flint quarry]

Ok so I’m fully correct thank you!

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[weary iron]

over here 1-t+t^2 is always positive

my question is, suppose they give us a quadratic/argument that goes negative. am i still allowed to this step?

oh nvm i dont think I am

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[scenic nacelle]

How do i set up this??

[charred rampart]

similar triangles

[scenic nacelle]

?

[flat kindle]

The Pythagoras theorem on the three triangles

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[eternal viper]

I don’t know what to do with this term

[mild hearth]

how did you get the first line

what's the expression for 'the standard brownian motion' again

[eternal viper]

I just expanded

[eternal viper]

??

[mild hearth]

can you do b_2 + b_3 = (b_2 - b_1) - (b_3 - b_1)

[granite shard]

hmm, that's not the same, but perhaps you could do B_{t_1}^2 (B_{t_2} - B_{t_1} - (B_{t_1} - B_{t_3}) + 2B_{t_1})?

[mild hearth]

wait wrong way round

[granite shard]

then 2B_{t_1}^3 will have 0 expected value

[mild hearth]

can you do b_2 + b_3 = (b_2 - b_1) + (b_1 - b_3) + 2b_3

yeah

or the other other way round

can you do b_2 + b_3 = (b_2 - b_1) + (b_3 - b_1) + 2b_1

ok ok ok

i am good at algebra

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[tender rune]

hi. this is a question that I completed months ago, regarding the quotient rule, and due to my lack of written workings, I can't work out how I got from 1. to 2. It's highly likely that I'm just a wee bit brain dead as I've had a long day, but help is appreciated!

[restive inlet]

factorisation

[vapid plover]

you just factored out a x^4 * e^7x

[tender rune]

ah! I see. not my brightest hour I must admit. thank you very much!

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[wicked patrol]

i need help, me and my dad are confused

[candid cradle]

can you be more specific about where you're confused

[wicked patrol]

so, first, we inversed the first function

and we got sqrt(x)/5

then pluged in -7 which got us $i(sqrt7)/5$

[thorny flame]

its_henrythelemon

[wicked patrol]

but that was wrong

so then, we tried inversing -7 to get -1/7

so then we pluged that into the second function, which got us 7/146 which was also wrong

these were all my tries

[candid cradle]

Does $5x^2=-7$ for any $x\leq -3$?

[thorny flame]

big boy

[wicked patrol]

no

[candid cradle]

Right. This is a piecewise function, and it has an inverse so you know it's injective. The first step is to determine the value of x in the domain of f such that g(x) is -7

[wicked patrol]

oh, ok

can you explain this to me like your talking to a golden retreiver because i still dont really get it

[candid cradle]

No problem, maybe I wasn't clear.
Basically g(x)=-7 for only 1 value of x. This value of x is $g^{-1}(-7)$. As you said, $5x^2$ is not -7 for any $x\leq -3$. So you know the value you're looking for is not in that branch of the function

You can also check that $21+x$ is not -7 for any x between -3 and 10

[thorny flame]

big boy

[candid cradle]

So by process of elimination, the x you want must be more than 10

So if you solve $2-\sqrt{x}=-7$ for x, that gives you the inverse value

[thorny flame]

big boy

[candid cradle]

Does that make sense?

[thorny flame]

big boy

[wicked patrol]

oh, yes that make more sense

oh my god

ur so smart

thanks so much for helping @candid cradle

[candid cradle]

Lol. Np

[wicked patrol]

thanks for helping

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[hallow swan]

On the left side if I want to reduce it to be Vin/VX than could I 1-Vin/Vx

[hallow swan]

Simple algebra question

<@&286206848099549185>

[ivory sorrel]

!15m

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[swift hinge]

Yeah you can do that

[hallow swan]

Okay as thank you

Is this the correct way to try to solve for vin/vx

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[night vapor]

Someone please help me answer the geometry questions (with working out)

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[neon iron]

“If the line 3x - 4y = 0 is tangent in the first quadrant to the curve y = x^3 + k, then k is _____?”

[neon iron]

Not exactly sure where to start

do i just set the derivative of x^3 + k equal to 3x - 4y?

[restive inlet]

not quite

you set the derivative equal to the slope of the line 3x - 4y = 0

[neon iron]

so 3/4?

[restive inlet]

yes.

[neon iron]

alr so d/dx x^3 + k = 3/4

[neon iron]

I found x to be +/- sqrt(1/4), but how does that let us find k?

[fallow heart]

By using the fact that "tangent" also means that the two curves intersect (at the value of x you found)

[restive inlet]

you are told that the line is tangent to the curve in Q1

[fallow heart]

This means you can write f1(3/4) = f2(3/4)

[neon iron]

So x must be +1/2, and 3/4(1/2) = (1/2)^3 + k, and k = 1/4?

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[finite mortar]

For a square Matrix P is the following true : Px= inverse where x is a vector

[finite mortar]

I don’t think that’s right but I’m doing a question that seems to say that

[odd pagoda]

inverse what

[finite mortar]

Inverse of the matrix P

[vernal matrix]

Do you have a picture of the question?

[finite mortar]

Yo chartbit

[alpine mist]

It's not saying those are equal. It's telling you to compute Px and then use the result to determine what P^-1 should be.

[finite mortar]

Oh nvm

Thanks tho

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[finite mortar]

.reopen

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✅

[finite mortar]

Nah I don’t see how u can deduce

Obviously u can

,rotate

[vernal matrix]

I guess you're supposed to notice it permutes the entries, and argue from there

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[finite mortar]

Hmm

[vernal matrix]

Think about what happens if you multiplied (b, c, a) by P again... and then maybe again?

[vernal matrix]

(also respond to the bot )

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