help-27

[compact hawk]

Oh 👍

Tysm

Tysm

[merry patio]

we generally use radians but its not always needed

[compact hawk]

●<● (idk what radian is so I had to go online to search it)

[merry patio]

and uhhh for the last one i have the idea but im not good at probability

[compact hawk]

I think I know it maybe?

[merry patio]

but basically how do you get a multiple of 3?

[compact hawk]

Cus there's 30 cards so it's 30 x 29

And since we draw 2 it's 30 x 29 divide by 2

[compact hawk]

Anything besides 3 ig

[merry patio]

you can either draw two cards that are multiples of 3 already

so 3 6 9 12 15 18 21 24 27 30

[compact hawk]

Or draw 2 number which arents 3

[merry patio]

pick two at random

which you can calculate using combinatorics

but there are also other ways to get multiples of 3

[compact hawk]

Oh wait just 1 , 2 , 4 , 5 and etc

[compact hawk]

Meh im not allowed to use calculators so not planning on doing that anyways

[merry patio]

oh maybe there is just an easier way

instead of calculating all possibilities

[compact hawk]

I have no idea 😭 what cus I asked chat gpt a long time ago

And it couldn't give the awnser

[merry patio]

30 * 29 / 2 to find all the combinations is correct!

[compact hawk]

But then what ●~●

[merry patio]

mmm dont want to say stupid things but picking two cards at random always add up to some value right

and only 1/3 of these values are a multiple of 3

[compact hawk]

No idea I just thought that it has to be either picking up 2 cards which are divisible by 3

Or 2 cards which is 1 , 2 , 4 , 5 , 7 , 8 , 10 oh

Wait

[slender mirage]

Umm, there are 30 cards.

10 of which are 0, 10 are 1 and 10 are 2

When I mean cards are 0, 1 or 2, it means they leave remainder of 0, 1 or 2 when divided by 3

[compact hawk]

There's no 0 in the deck it's just 1-3

1-30

[merry patio]

no they are each marked with 1 2 3 4 5 6... 30

but nvm yes you can simplify it

using only 0 1 2

yes

[slender mirage]

Ik. But for instance, 7 = 1, 8 = 2, 9 = 0, 10 = 1, and so on, so there's 10 0s, 10 1s and 10 2s

[compact hawk]

Yea

[slender mirage]

Probability that you get two 0s, or a pair of (1,2)s is

[merry patio]

ye thats easier

[compact hawk]

? What's C

[slender mirage]

Nothing.

[slender mirage]

U focus on this

[compact hawk]

Basically so there's 10 0

10, 1

[slender mirage]

Yes

[compact hawk]

And 10, 2

[slender mirage]

Yes

[compact hawk]

Hm

No idea

●_●

[slender mirage]

So 10 ways of picking a 0 card?

[compact hawk]

Yea

[slender mirage]

N you're left with 9 more 0s?

[compact hawk]

Yea

[slender mirage]

So 10 • 9 ways for picking 2 0s?

[compact hawk]

After drawing a 0 then there's 9

[slender mirage]

Hence, 90 ways of getting 2 0s ✓

[compact hawk]

90 / 435 right now then we move on to the 1 and 2

[slender mirage]

No

[compact hawk]

?

[slender mirage]

Hold up.. we'll move to the denominator later

It's just 90 ways for 2 0s for now

[compact hawk]

Isn't it? 90 ways out of the 435 combination

90 combination are ablento be divided by 3

[compact hawk]

Yea

[slender mirage]

No

Because (1,2) pairs would also be divisible by 3

[compact hawk]

Yea I meant like 90 combinations for 2 0s only

[slender mirage]

So we'll make the whole numerator the discuss denominator

Now, for the (1,2) pairs - it's 10 ways for 1 and 10 for 2? Right?

[compact hawk]

Then 1 , 2 there's 10 • 10

So 100 + 90 / 435

?

[slender mirage]

Yep, and same for (2,1)

So it's basically (90 + 100 + 100)/(30•29)

[compact hawk]

That's basically the same as 1,2 besides the fact it's flipped

That makes it a 1 in 3 chance

[slender mirage]

Yes. But if the order doesn't matter, then the 0s count would be 45 and not 90

Because picking 6 and 9 for our cards is same as picking 9 and 6

So it's 90/2 for 0s
And then 100 for (1,2) pair

So (45+100)/435

[compact hawk]

Oh wait aren't we forgetting to divide by 2 on everything

So it should be 95/435?

[compact hawk]

Since you have to draw 2 times

[slender mirage]

In this, yes

[compact hawk]

So it's 100 for the (1,2) and 90 for the 2 0s

[slender mirage]

In this, no

Because (100) only counts the 1s being picked first draw and 2s being picked second draw

[compact hawk]

But the extra 100 doesn't makes sense to me since (1,2) and (2,1) are the same

[slender mirage]

Yes. So you don't need to divide by 2

[compact hawk]

8 and 1 have the same chance of being pick as 1 and 8

[slender mirage]

It's not (100+90)/(2*435), it's (100 +90/2)/435

Should be 145/435

[compact hawk]

When the first one is being pick there's 20/30 chance you pick (1,2) second one is 19/30

Oh wait no 19/29

[slender mirage]

...

You're confusing everything you rightly understood so far

[compact hawk]

I know 😭😭

I'm getting more confused

[slender mirage]

listen

How many pair of 0s?

[compact hawk]

10

[slender mirage]

"pair"

*how many ways of picking a pair of 0s

It's 45

[compact hawk]

Oh wait 45? Cus it's 10 • 9 / 2

[slender mirage]

Yes

And then 100 for (1,2) pair

Right?

[merry patio]

theres an easier way to think about it

[compact hawk]

Yea

[slender mirage]

Then probability is (145)/435 ✓

[slender mirage]

= 1/3

[compact hawk]

Oh ok thanks a lot but I'm was js confused af cus like I have the anwser sheet and it says 19/87

😭 and I asked here cus I wanted to know why

[slender mirage]

So you got why it's 1/3?

[compact hawk]

Yea alright thanks

[slender mirage]

No wait

Like Ryse said, there's a much easier way

[merry patio]

idk if you have ever done idk what these are called

also apparently yeah if u just sum 2 values only 1/3 of these would be a multiple of 3 is valid

in the case if there are 30 cards

[compact hawk]

I'm so confused now cus like

I got the awnser sheet and it says 19/87

[merry patio]

hm

[compact hawk]

And normally I would think it's because they are wrong but like

They are literally the biggest competitons holder of math in asia

[merry patio]

answer key is wrong right

[merry patio]

if this diagram is right the answer key is just wrong

[slender mirage]

Hmm, so basically (95/435)

[compact hawk]

No idea cus I was thinking if it's unordered pair

Like we count picking (4,5) the same as (5,4)

So making it 10 • 10 / 2

So 50 + 45 / 435 is 19 / 87 that's what I was thinking about

[violet flower]

hey 1 question in #help-33

[slender mirage]

but that can't be because when picking 10 • 10, the first 10 picks from {1, 4, 7, 10, 13, ..., 28} and the second 10 picks from {2, 5, 8, 11, 14, ..., 29}

So there's no (4,5),(5,4) situation

The numerator has to be 145 ✓in an unordered scenario

[compact hawk]

I'm so confused now I'm just gonna ask the organizers if they made a mistake

[devout snow]

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[lusty stone]

!status

[devout snow]

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

[lusty stone]

2

can anyone help

[violet flower]

hey

i will try

[lusty stone]

b^y could be represented as (ac)^-y

[violet flower]

have you tried log

[lusty stone]

no, log is not even in the syllabus

[violet flower]

oh ok

[lusty stone]

apparently the answer is 2/y based on the ak

but idk how

[violet flower]

yes i got it

take a constant let t be equal to a^x , procced from there to get a , b and c then use b^2 = ac

[lusty stone]

okay

t = a^x

t = a^x, b^y, t = c^z,

nah im still stuck

[violet flower]

now a = t^1/x .. b = .. c = ... , b^2 = ac

[lusty stone]

how is a = t^1/x

@violet flower

<@&286206848099549185> not too hard of a question but help?

[violet flower]

from this

[lusty stone]

how??

[lavish raft]

are you familar with indice rules?

[lusty stone]

ye

[lavish raft]

raising both sides of the equation to a power of 1/x

t^1/x = (a^x)^1/x

you multiply the exponents on RHS to get a power of 1

you can also think of it as

[lusty stone]

oh. yeah shit i thought what he was saying is (t^1)/x

[lavish raft]

you take the xth root

which is represented by the power 1/x

[lusty stone]

i understood allat i just thought of the. wrong thing

[lavish raft]

oh yea lmao

[lusty stone]

ye

now moving on to the question

t^1/x = a, t^1/y = b, t^1/z = c

since b^2 is ac

[lavish raft]

lemme repost it so i can see more clearly

ok

[lusty stone]

if we multiple t^1/x and t^1/z

*multiply

we get ac

sorry nvm

i read the question wrong

that's ac

[lavish raft]

tbh no idea

[lusty stone]

t^1/x+1/z = b^2

and since t^1/y = b

t^ 1/x+1/z = b^2 and t^1/y = b, we multiply t^1/y by itself again

and 1/x+1/z = 2/y

so thanks

lol u cleared it up

ty

[lavish raft]

yep all me

you are welcome xd

[lusty stone]

pacifix gon be mad when he reads this 💀

alr have a good day

[lavish raft]

haha i guess im a natural at teaching

you too

[lusty stone]

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[twin solar]

hypothetically, why is it wrong to just divide both sides by -sin(x) and never get sin(x) = 0?

[twin solar]

the question was to find the peaks of a function

[fair juniper]

same reason why its bad to divide by x in x(x+1)=0

you remove the x=0 case because thats a divide by 0 problem

[twin solar]

in that context it makes sense ig

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[dawn lava]

i need to make sure i’m correct. i need to find the period of the function 7sin(3x)+1

[dawn lava]

and i got 2pi/3

[mystic scarab]

Yep correct

[dawn lava]

ty

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[narrow radish]

Help

[narrow radish]

Ehhehehe

Can someone help me with this

That system

The one in the middle

So 3x+y-2 > 0 is a line

And the one above it is a circle

Eheheh

[devout snow]

@narrow radish Has your question been resolved?

[worthy raft]

What is the question asking for?

[devout snow]

@narrow radish Has your question been resolved?

[devout snow]

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[spark hound]

How can I remember this shit, how was it derived?

[supple knot]

use flashcards or practice problems

proof https://proofwiki.org/wiki/Double_Angle_Formulas/Tangent

[spark hound]

tyty

.solved

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[devout snow]

@storm kiln Has your question been resolved?

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[dense jay]

close

3^3 isnt 9

[median patio]

whoops

.close

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[prime narwhal]

Am I trying to find this angle?

At the tip by the puck

[hushed wraith]

Yea

[slender mirage]

Yes

[prime narwhal]

And for this one is the first thing I should do is find the third angle?

By taking the two given away from 180

[slender mirage]

No, the 42° is from North due east, but 137° is the angle from their original path

[prime narwhal]

I'm not sure I understand

[slender mirage]

Basically if you draw it, you'll have a triangle with sides 8km, 5km and included angle 137° and you're asked for the other acute angle

[prime narwhal]

Like this?

Ik it's a bad drawing but

[slender mirage]

You need angle opposite to 8km side

[devout snow]

@prime narwhal Has your question been resolved?

[slender mirage]

@prime narwhal

This is the diagram

[prime narwhal]

Ohhh so the 42 is saying they are 42 off the original direction

Then the 137 is off the original too

Not just 137 from the previous direction

[prime narwhal]

I just don't understand how I solve this without having an angle inside

[prime narwhal]

<@&286206848099549185>

[devout snow]

@prime narwhal Has your question been resolved?

[slender mirage]

Didn't you calculate the distance between Julia and Base Camp? For part b

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[vestal bay]

Question: where do we get f(1-x) from?

[muted mural]

I'm not sure I can help you cause this looks like a competition question, but what f(1-x) are you taking about?

[ancient sluice]

f(x) + f(1-x) right ?

And what is a ? Some constant?

If it is so, a fast way to get the answer would be setting a=1

[valid silo]

Maybe the answer is in terms of a

Also

[strange nimbus]

I think they want you to solve it in terms of an arbitrary a.

[valid silo]

Looks more like
f(x)+f(1/2-x)

[ancient sluice]

He can vary by substituting a=1 in options

[strange nimbus]

Oh, it looks like f(x) + f(1 - x) simplifies to a constant.

[vestal bay]

Oh thanks for the help

I think I understand abit of it

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[spice apex]

what do i do for q1

and what are the symbols in q2

And 3

[alpine python]

these are number systems

[spice apex]

nvm on q 2

okay

what does that mean

[alpine python]

for example do you know the integers?

what are the integers?

[spice apex]

i do know but dont know

yk

x

idk if u told me i would know

[alpine python]

integers are ...-3, -2, -1, 0, 1, 2, 3,...

[spice apex]

ok

[alpine python]

it's represented with Z

[spice apex]

oka

[alpine python]

do you know the rationals?

[spice apex]

ye

just numbers that are actually here

not 1/3

[alpine python]

1/3 is rational

[spice apex]

bro what

nvm

its like pi?

[alpine python]

rationals are like fractions

[spice apex]

okay

[alpine python]

but the numerator and denominator has to be integers

so 2.4 / pi doesn't count

[spice apex]

aight

[alpine python]

rationals are represented by Q

[spice apex]

oki

thanks for helping

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[worldly gyro]

help :C

[worldly gyro]

i suck at bearings

<@&286206848099549185>

[fickle jasper]

is there really nothing else to the question?

Where is point B located?

And Point P

[worldly gyro]

nothing else

i'm also deeply confused

i can show u the mark scheme

oh wait

nvrm i forgot to share the shape thingy

[devout snow]

@worldly gyro Has your question been resolved?

[worldly gyro]

hii

[potent tusk]

i cant explain this at all

[worldly gyro]

yeah its a past paper for igcse international maths

idk why they r making grade 10 kids do this

[potent tusk]

I understand it now

the shortest distance to B from the line segment AC is perpendicular to AC

the circle shows point P

the hard part is finding the distance between A and P

[worldly gyro]

ooh i see

[potent tusk]

once you find that though you just do distance/speed

then add the time on

[worldly gyro]

okok

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[steady onyx]

I'm unsure as to how I should approach this problem:

[slender mirage]

t, when point B is at x-axis gives y_B(t) = 0

[steady onyx]

yes

[slender mirage]

So all t in 0 ≤ t ≤ 2π when cos(2t) = 0

[steady onyx]

could you also do 2sin(2t) = -2 ?

and +2

[slender mirage]

Can we not work with what our mind hypothetically came up with?

What's so difficult about cos(2t) = 0 than sin(2t) = ±1

[steady onyx]

nothing

[slender mirage]

So, cos(2t) = 0 ✓ What value of t's can you come up with?

[steady onyx]

if t = -pi/2 and t = pi/2

[slender mirage]

No, we have a constraint

[steady onyx]

oh wait -pi/4 and pi/4

[slender mirage]

0 ≤ t ≤ 2π

[steady onyx]

oh so only pi/4

[slender mirage]

No

0 ≤ 2t ≤ 4π

So 2t can be π/2, 3π/2, 5π/2, 7π/2

And thus you have values of t

[steady onyx]

okay

[slender mirage]

Now, what can be said about point A in all these 4 times

[steady onyx]

the x is either 1 or -1

[slender mirage]

What?

[steady onyx]

oh wait i was using pi/2

[slender mirage]

2t = π/2... t is what?

[steady onyx]

pi/4

okay then the x value is something like 0.707

and the y value can be either 0.707 or -0.707

oh well

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[upbeat marten]

Can somebody explain this problem to me?

[upbeat marten]

I got the first and second derivative already and I understand that part but I dont see the correlation with the red increasing on g' and the red up on g'' I also dont understand where the zero comes from in our answer

I understand the increasing part and why its concave up but im still confsued on why we use zero

and how we get our final answer

[dire citrus]

Sorry I’ve gtg soon so may not end up finishing this

But

[undone kelp]

For that part, for example from (-∞,-1), you just have to pick any number from the interval and test it on the first derivative and if the answer is positive, then it is increasing

[dire citrus]

Oh wait I misread

Sorry

[undone kelp]

and then it also required that the graph is concave upward so we need to use the second derivative. Again, just pick any number from the intervals and the constants you got to the second derivative and if it is negative then it is concave down and if it is positive then is it concave up

For the last part, we see that it is only concave up from (-√1/3,√1/3) and it is increasing at (-∞,-1) and at (0,1) but the graph is not concave up anywhere in (-∞,-1) since it is only concave up in (-√1/3,√1/3) and for (0,1), it is only concave up at (0,√1/3) then that's your answer. In simple words, you just have to get the intersection of the intervals.

[dire citrus]

You have the answer in your working. During (0,1), the graph is concave up. During (+-sqrt(1/3)), the graph is increasing. The statement asks you to find where both are true, so it’s where the two intervals overlap. In this case, -sqrt(1/3) is smaller than 0, so the graph only increases then. And 1 is greater than sqrt(1/3), so here the graph only concaves up. The interval where the two are happening at the same time is (0,sqrt(1/3).

[devout snow]

@upbeat marten Has your question been resolved?

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[upbeat marten]

thx guys

sorry for the late response

[devout snow]

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[rustic barn]

how to show that Evaluation Maps Generate B(C[0,1])?

[stone stump]

what do you mean by B(C[0,1]) ? bounded continuous or something?

[rustic barn]

borel sigma

smallest sigma alg making C0,1 mwasurable

@stone stump

[stone stump]

then what do you mean by the evaluation maps. surely those are maps while a borel sigma algebra at least needs to be generated by sets

I will not be able to help you with this, its been too long since I've done measure theory

but for others to help you it would be beneficial if you expanded a bit more on your notation and stuff

[rustic barn]

ev_t: f to f(t)

ev_t is a function fromC[0,1] to R

@dry robin

[devout snow]

@rustic barn Has your question been resolved?

[devout snow]

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[dawn basalt]

i was trying to find function if second derivative is known. i calculated the first integral, then i wanted to calculate last integral, but somehow stuck

[dawn basalt]

,,\int ( \frac{3x^4}{4} + \frac{4x^3}{3} + x^2 ) dx

[woven radish]

TLauncherGD

[pure flower]

Also please don’t use tl lol

[pure flower]

Last integral?

[dawn basalt]

.

[uneven talon]

It's all power rule

Every term in the integrand can be integrated like that

[cinder nova]

also you should include the +C in the second integral

[uneven talon]

^

You'll end up getting a +Cx + D at the end of your second integral

[dawn basalt]

oh my god i get it

thanks for help

.close

[devout snow]

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[devout snow]

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[worldly gyro]

can anyone teach me question 5?

[olive snow]

You have -1 =< x =< 2

To make h(x) in the middle

Notice that ^5 is strict increasing

[worldly gyro]

strict increasing?

[olive snow]

Yeah

Growing strictly

[manic pumice]

u got the domain

as tht

[olive snow]

x > y <=> h(x) > h(y)

[manic pumice]

but where s the function

?

it clearly says

that

[-1,2] between this range, the value of y will be defined for the value of x

so its asking to find the value of x to defined for y

wait

so its not possible

theres so specific function related to find the answer

its jsut guven the domain

[worldly gyro]

sorry i'm confused

[manic pumice]

ok let me clear u out

can u dm?

[worldly gyro]

ya

[manic pumice]

ok com

e

[olive snow]

That means you can apply the power of 5 to all the part of the inequality without flipping the inequality sign

[devout snow]

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[humble carbon]

pls help

[devout snow]

@humble carbon Has your question been resolved?

[humble carbon]

<@&286206848099549185>

[pure flower]

!status

[devout snow]

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

@humble carbon Has your question been resolved?

[humble carbon]

2

begun but stuck

basically idk how to factor in the friction on the boulder

ik how to calculate the friction, the weight, normal force, etc etc of the block

but i've never done problems like this where the pulley like thingy has friction

[humble carbon]

<@&286206848099549185>

[warm crater]

What's the question asking. Can you quote it directly?

[humble carbon]

With what horizontal force P must the worker pull in order to move the 35-kg log up the 15° incline? The coefficient of friction between the log and the incline is 0.60 and that between the rope and the boulder is 0.40.

[warm crater]

Ah ok. Mb I didn't read it right. Ok, I'll try to solve it now

[warm crater]

Have you done pulleys before?

[humble carbon]

yeah

just not this type

ik i can take tension pointing from the box to boulder and from man to boulder

but how does the friction over the pulley/boulder affect it?

all the examples i did before was smooth pulley

[humble carbon]

<@&286206848099549185>

[warm crater]

I'm on the bus rn so I can't really calculate it using paper. I suggest splitting it into its x and y components. And since the sum of of all friction components add, Just treat the friction components as one.

[devout snow]

@humble carbon Has your question been resolved?

[devout snow]

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[devout snow]

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

[sharp garnet]

actually I just want to check if my answer is correct

I got 71

.solved

[devout snow]

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[devout snow]

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[cosmic pelican]

All I Need Is someone to name me this type of integration, it’s on the y and x axis, just give me what I can search on YouTube to find examples, thank you : )

[devout snow]

@cosmic pelican Has your question been resolved?

[undone kelp]

Honestly, its just getting the area of a plane region

[undone kelp]

If youre referring to having two types of functions just like this, then you can use partitions you can search it up

[devout snow]

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[novel island]

28.5g of iron shot is added to a graduated cylinder containing 45.50 ml of water. The water level rises to 49.10 ml, from this information calculate the density of iron.

[undone kelp]

Density is just mass/volume

[dense jay]

okay

[undone kelp]

Mass = 28.5
Volume = 49.1 - 45.5

[novel island]

Ohhhh

I was guessing what the volume was

[dense jay]

you can convert litres to m^3

1L=0.001m^3

[novel island]

So I had to do 49.1 ml - 45.50 of water

28.5/3.6 =7.917

But I would put 7917m^3?

Right?

For my answer

7.917g/m^3

[undone kelp]

Do you have a required unit of measure?

If not, 7.917g/mL is alr good

[devout snow]

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[quaint apex]

how do i do this?

[iron kindle]

try making a drawing

[quaint apex]

ive done that

but im only given ab is 10

and angle b is 30

how do i find out anythuing else

[iron kindle]

can you show your drawing?

[random helm]

you need the least possible distance from A to the line BC.

and it is a perpendicular

so it equals AB/2

as it is opposite of the angle of 30 degrees

[quaint apex]

i dont really get it

i thought i was supposed to find the length of AC?

cus it said calc the least possible length of AC

[random helm]

yep. The needed AC is minimal when AC is perpendicular to BC

[quaint apex]

oh okay

why does it equal ab/2?

[random helm]

bc sin(30)=1/2

[quaint apex]

ohh

so 5?

[random helm]

you solve

[quaint apex]

10/2=5

how do i do that?

ive foudn the first value

45.6

but i dont know how to find the 2nd possible value

[quaint apex]

i did 7/sin30=10/sinx and got x= 45.6

.close

[devout snow]

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[devout snow]

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[granite bough]

Hello! Hello! Hello!

[granite bough]

I know of dy/dx + p(x)y(x) = q(x)

so q(x) is 1 and p(x) is x/(x+1)

[lusty sapphire]

-x/(x+1)

[granite bough]

right

okay yes i mistyped from my notes, i cant take a photo because my phone does not have internet while im home, i only got ethernet

so the integrating factor is e^(indefinite integral of -x/(x+1) dx)

and i can take -1 outside of the integral

e^-(indefinite integral of x/(x+1) dx)

then that x/(x+1) turns to 1-1/x+1 with some tricks

e^(-x + ln(x))

and i can seperate those

e^-x * e^(ln(x))

now i use some formula i dont know the name of

e^(-x) * e^(ln(x)) * y= integral of e^(-x) * e^lnx dx

double checking notes if i typed that out right

oh and reason i get regular ln(x)

is because of that condition that says x > -1

normally it is absolute, like ln|(x)|

anyway, i get stuck here

how the hell do i integrate that

integral of e^(-x) * e^lnx dx

wait

e^lnx is just 1 right?

so i am really just taking the integral of e^-x

integral of e^-x would be -e^-x + c?

[lusty sapphire]

close, but not 1

[granite bough]

is that wrong 😦

okay

hmm

ehrrr

it is just x?

[granite bough]

i must admit i googled this

okay

integral of xe^-x

now i integrate by parts

because the derivative of x is 1

i set x to equal u

i will try to work that out on paper now

the integral of xe^(-x) dx = -xe^(-x) + the integral of e^-x dx = -xe^(-x) - e^(-x) + c?

oh yeah and now to find c, assuming that's correct

wait frick

im not finding c yet

yxe^(-x) = -xe^(-x) - e^(-x) + c

y = (-xe^(-x) - e^(-x) + c)/(xe^(-x))

[lusty sapphire]

wait, why are you integrating this?

[granite bough]

i will send a pic hold on

i was told to do this

[lusty sapphire]

Oh. For Q. I see

[granite bough]

so the integral of IF Q(x) dx

ye ye ye

and Q(x) is just 1 thankfully

[granite bough]

I am trying to work through this now

i really wish i was better at algebra

[lusty sapphire]

looks good

[lusty sapphire]

this feels wrong. Something feels wrong here

[granite bough]

hmm

does it feel wrong or is it wrong?

[lusty sapphire]

Mistake is here

ln x?

[granite bough]

ooooh

yeah wait a second

yeah lol

it should be ln(x+1) right?

[lusty sapphire]

That's better

[granite bough]

bluuurgh

ARGHHHH

ok

i will work through it again

okay i will still pick the same u as last time when integrating by parts

its derivative is the same at least

[lusty sapphire]

Is this saying $I.Fxy$ or $I.F\times y$?

[woven radish]

SWR

[granite bough]

times

at least I think it says times

I hope it says times XD

that's what I have been working with at least

the integral of (x+1)e^(-x) dx = -(x+1)e^(-x) + the integral of e^-x dx = -(x+1)e^(-x) - e^(-x) + c?

does this look correct?

[lusty sapphire]

yes but you can simplify it

[granite bough]

ye ye

[lusty sapphire]

And do you need the +c here?

[granite bough]

i will get to that

i thought i needed the + c im really bad at determining when to shove it in

should i just keep ignoring it

[lusty sapphire]

I don't think you need it here

[granite bough]

ok i will try to simplify without it

[lusty sapphire]

I could be wrong tho
Just plug in your final result to be sure I guess

[granite bough]

so i get that y(x+1)e^(-x) = -(x+1)e^(-x) - e^(-x)

and i will simplify

y = 1 - 1/(x+1) after simplifying, and I guess that's when you want me to add + c?

y = 1 - 1/(x+1) + c

now i plug in the coordinates

[lusty sapphire]

I don't think you want the +c at all here

[granite bough]

why not?

i want to find c 😦

i need it!!!

[lusty sapphire]

This is only your particular solution

You are forgetting your homogenous solution

[granite bough]

i dont know what that means

im not actually a math guy i just do math and hope no one notices

[lusty sapphire]

[granite bough]

[lusty sapphire]

what they are calling I.F here is normally n=known as the homogenous solution

[granite bough]

okay

yeah i have no clue what that means :<

the homogenous solution

mmmmm

i thought i needed the +c

so i could determine what the original function was

and that's my solution

[granite bough]

if i kept the c here I would get y = 1 - 1/(x+1) + c(e^x)/(x+1)

but that doesnt make any sense

like the answer makes no sense if i were to keep it there

[lusty sapphire]

Ah I'm seeing the several problems here

[granite bough]

yeah usually there are several problems

when i do math

i was a little bit flabbergasted none had come up in a while

[lusty sapphire]

This is wrong. They meant $e^{-\int P(x)\dd x}$

[woven radish]

SWR

[granite bough]

mmmmmmmm

so they forgot a negative sign?

mmm mmmmmmmmmmmmmmmm

mmmmmmmmmmmmmmmmmmmmmmmmmmm

😦 !!!!!

why do all of them forget it

[lusty sapphire]

Maybe integrating factor is a different idea from the one I do

okay yeah I have misled you

this is a method different from the one I do

[granite bough]

it is no problem i dont mind being mislead

[lusty sapphire]

And they happen to differ here by sign

should not be negative

[granite bough]

ok ok ok ok

[lusty sapphire]

Okay, remind me, what is your IF so far?

[granite bough]

okay let me check i think i ssaid IF is (x+1)e^-x

[lusty sapphire]

Okay, we're good there

[granite bough]

and there may be several problems with my algebra along the way

among my many flaws it is truly one of them

i wish i could send you pics of my notes on paper but again my phone does not have internet connection in my apartment

[lusty sapphire]

and what did you get for $\int IF$?

[woven radish]

SWR

[granite bough]

the integral of IF, right, becasue q(x) was 1 that's all we were doing

I got that it was equal to -(x+1)e^-x - e^-x

+c i guess

and then

i would have gotten y = 1 - 1/(x+1) after simplifying, but i think i need the c

i just dont know when

[lusty sapphire]

yes you need the c

[granite bough]

do i need it now or did i need it earlier

[lusty sapphire]

now

[granite bough]

okay so y = 1 - 1/(x+1) + c

now when insert 0 into y and 0 into x

i get 0 = 1 - 1 + c

oh my bad + c

so according to that, c would be 0

and thus the original equation would be uhhh

just y = 1 - 1/(x+1)

and that would be my "answer"

i have the solutions for this problem

so i can check

[lusty sapphire]

this aint it

[granite bough]

ok before i check

in what places have i goobered this time

i wish i had glasses

[lusty sapphire]

Actually, I think a mistake was here

[granite bough]

ok so the simplification went wrong

y(x+1)e^-x = -(x+1)e^-x - e^-x

is what i was trying to simplify

and i did not add the + c

when simplifying

otherwise there would have been a c there

on the right hand side

[lusty sapphire]

yeah you want the +c here

[granite bough]

okay okay

good then i get this instead

y = 1 - 1/(x+1) + ce^x/(x+1)

but when i tried to put in 0 here

it did not make much sense to me

because the two terms cancel like before

and then i have 0 = ce^0/(0+1)

oops wait it does make sense

i did it wrong here

[lusty sapphire]

where did your 1 go?

[granite bough]

yeah oopsies

wait this mgiht make sense

y=c

0=c

uhm wait

[lusty sapphire]

you forgot another 1

[lusty sapphire]

y=1-...

[granite bough]

but that's just 0 isnt it?

[lusty sapphire]

1 is 0??

[granite bough]

1-1/(0+1) = 0

[lusty sapphire]

$y=1-\frac{1}{x+1}+\frac{ce^x}{x+1}$, right?

[woven radish]

SWR

[granite bough]

yes i think that's right

that's what i have as well

the signs are right too

then when i put in y(0) = 0

[lusty sapphire]

oh hah I thought the middle term was x/(x+1)

man, I am super distracted today

yeah, c=0

[granite bough]

is it a coincidence

thant by waiting to add the c

we also got 0

[lusty sapphire]

yea

[granite bough]

ok

so it was right to add the c when we stopped jumbling around a bunch of integrals

and then start doing algebra on the c

as if it were a variable we were solving for

[lusty sapphire]

yeah

[granite bough]

okay

[lusty sapphire]

my bad for the misdirection

too distracted today

[granite bough]

so the answer should be y = 1 - 1/(x+1)

for the original function?

and if i want to be clear i would say x > -1

i will check the solution thing now see if they got the same thing

they got a different answer

but most of our work looks similar

i will send u a pic

oh yeah

wait i think i forgot a negative sign maybe

i did

[granite bough]

this

it should be -1 for the first 1

but i think theirs is wrong too

shouldnt it be c = 2?

this is wrong right

talking about the terms from the left to right on the right hand side

the first term is just c

second one is -1

last one is -1

and y is 0

so it should be 0 = c - 1 - 1

$y=-1-\frac{1}{x+1}+\frac{ce^x}{x+1} + 2$ should be the original function

[woven radish]

Neo

[granite bough]

and when simplifying the answer should be

$y= 1-\frac{1}{x+1}+\frac{ce^x}{x+1}$

[woven radish]

Neo

[devout snow]

@granite bough Has your question been resolved?

[granite bough]

Hello, sorry for disturbing you, if you are still there, could you have a look below about me thinking the given solution is incorrect?

[lusty sapphire]

Oh

I see the mistake

[granite bough]

is it my mistake or theirs?

[lusty sapphire]

Look here

plug in x=0 and y=0

what do you get?

err

wait

[granite bough]

ce^x

[lusty sapphire]

sign error somewhere

[granite bough]

ye ye no i am with you on that

i saw that too here

[granite bough]

here

or at least i think i saw the error?

when i divided -(x+1)e^x/((x+1)e^x) i got 1 when it should have been -1

but they did that right

however i claim they did the next part wrong

[granite bough]

this part is incorrect, right?

[lusty sapphire]

yeah it should be c=2

[granite bough]

okay nice thank you a lot SWR

[lusty sapphire]

And this is where you made your mistake. You should've gotten y=-1-...

[granite bough]

yeah yeah

exactly

it was a sign error, i divided something negative with something positive

and somehow made it turn positive

okay thanks I am happy, when I was at Uni the help for this last part got too confusing, I think the guy who tried to help me was a little too fast and lost track of what u, du and v and dv was

i will close this now

.close

[devout snow]

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[granite bough]

you were more helpful than a third year civil engineering physics student!!!!!!

[devout snow]

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[unborn comet]

How would you go about finding the particular integral part of this discrete equation where y<k+2> - y<k+1> + y<k> = 1/(k+2)

y<n> represents y with subscript n (idk how to write it on discord)

I expanded 1/(k+2) with binomial theorem to get a polynomial in k and then tried y<k> = infinite sum of a<n>k^n as n ranges from 1 to infinity to see if I could get anywhere but I am still stuck

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[winter torrent]

what have you tried?

[boreal spear]

i know its just the prime factors of 60

but i dont understand why

oh nvm stupid mistake

srry

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[distant kite]

is the answer ||4305||?

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[hollow ice]

I might be wrong, but I am getting 4884 as an answer

If you just consider the sequence 1 to 3 instead of 1 to 24 for chelsea, and so on, there might be a pattern that you notice for chandra's sequence.

[topaz axle]

yeah 4884

2 2 2 5 5 5 8 8 8...
sqaure and sum

[hollow ice]

yep

[topaz axle]

that's the real challenge

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[slender mirage]

@distant kite for Chandra's sequence, notice that sum of all combinations obtained from triplets 3n+1, 3n + 2, 3n + 3 is 2(3n+1 + 3n+2 + 3n+3)² = 2(9n + 6)²

Therefore you're asked to compute the sum of 2(9n+6)² from n = 0 to 7

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[marble quarry]

C: |z-i|=1/2

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[marble quarry]

.solved

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[fervent ore]

how do they get the parts in red?

[iron kindle]

integration by parts

IBP

[fervent ore]

the udv formula? or is that something else?

[iron kindle]

yes? im not entirely sure

[iron kindle]

"uploaded integration by parts formula"

yeah i think thats the one chief 😂

[fervent ore]

cheers

[iron kindle]

https://cdn.discordapp.com/attachments/903486480075354182/1326868545136623616/integration-parts-formula.png

integration-parts-formula.png :p

[fervent ore]

trying to apply it now to the problem, lets see if i get anywhere

[fervent ore]

Ok i solved it, how did you recognize it was integration by parts?

[iron kindle]

whenever i smth like $\int (stuff) = (kinda similar stuff) - \int (also kinda similar stuff)$

[woven radish]

Bonk

[iron kindle]

i think IBP

[fervent ore]

reasonable!

thx

take care!

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[iron kindle]

,rotateccw

[lusty wing]

Isn’t the a) that it’d be better it have 10 between instead of 9?

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[dark willow]

hello i need help with A level complex numbers and vectors what do i do

[iron kindle]

!da2a

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No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

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[pure flower]

study?

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[finite skiff]

hello!! I need a bit of help because I dont really know how to answer any of the quesitons being asked. I have a test tmrw which will take be on computer so I will not be able to do any working out on paper and I have to find my answers on desmos with the quadratic regression.

[iron kindle]

you dont need to use regression here

since the quadratic is given

!status

[devout snow]

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

[finite skiff]

ohh, okay!! how would i be able to answer the questions abcd using the desmos?

sorry im kind of lost

I was absent for a whole week while this was being reviewed

[iron kindle]

think about what is being asking in a)

[finite skiff]

the speed of the car i think

[iron kindle]

you are given a function of the distance after the brakes are applied

a) asks what the speed is of the car at the moment the brakes are applied

[finite skiff]

ohhh

how do i figure that out?

[iron kindle]

do you know how to get the speed if the formula for distance is given?

[finite skiff]

uhh nope

[iron kindle]

do you know how to get the average speed between two points?

$v_{avg}=\frac{\Delta x}{\Delta t}$

[woven radish]

Bonk

[iron kindle]

does this look familiar?

[finite skiff]

isnt it divide distance by time

or multiply

[finite skiff]

uhh nope my teacher hasnt showed us this befre

[iron kindle]

speed is distance over time

think of the units

speed (velocity) v =meters/second

distance = meters
time = seconds
distance/time = meters/seconds = speed

$\frac{\text{distance (meters)}}{\text{time (seconds)}} = \frac{x\text{ (meters)}}{t\text{ (seconds)}} = \text{velocity} \left(\frac{\text{meters}}{\text{seconds}}\right)=v \left(\frac{m}{s}\right)$

fk

[finite skiff]

ohhhhh

[woven radish]

Bonk

[finite skiff]

ive never seen this before but i get it

a little

[iron kindle]

okay so, by definition $\dv{x(t)}{t}=v(t)$

[woven radish]

Bonk

[iron kindle]

can you understand why?

[finite skiff]

Im sorry but I honestly have no clue

😭

my teacher he told me to use desmos to figure all of it out which is why im confused rn

idk how I can use desmos only to figure that out

[empty zenith]

Note that the graph in your original post is wrong...

the function given is $s(t)=-6t^2+12t+60$...

you have plotted $s(t)=-6t^2+12t+60^{-1}=-6t^2+12t+\frac{1}{60}$

[finite skiff]

oh so do i remove -1? ok thxx

[woven radish]

Jay

[empty zenith]

yes