help-0

[pseudo notch]

.close

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[ashen badge]

Ok weird question.

Lets say i roll 10 dice and i want to get at least 1 10. The probabilty is 65%.

If I roll 20 dice the probability is 87%

Now if I roll 30 dice the probability is 95%

Now lets say I roll 20 dice until i make a roll without any 10s.

If I then roll another 10 dice, but this is the only roll that counts, is the probability that i will have rolled a 10 higher than if I just roll 10 dice

[ashen badge]

I would guess it doesnt, and this probably is a dumb questiob

[prime badge]

it's not higher no

[ashen badge]

Ok that makes sense i guess. Thanks

.close

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[sage pecan]

i need help

[sage pecan]

Suppose the wedding planner forgot the total number of people attending the reception. If they remembered that 45 people were likely to choose the fish option, about how many people will they have in total?

How many of that total will likely choose the vegetarian option?

[last ether]

There is missing information

A lot of missing information

[sage pecan]

ik

thats the whole problem

[last ether]

If there were 100 people, and there were two choices, fish and veggie, then would 45% choose the fish?

I highly doubt that's the whole problem

Send a screenshot or photo

Of the entire page

It's probably some entailment

[sage pecan]

im on bluestacks

and its super hard to do that

[last ether]

Take your phone and take a photo of your computer screen

[sage pecan]

my mom took away my phone until i do all my homework

[last ether]

No one is going to help you if you ask a problem with missing information

[sage pecan]

ok

fine

here

also that is notme in the bottom left

[last ether]

There is no way that's the actual problem. That's impossible to solve

[gray isle]

based on the wording of the question, there is definitely related stuff immediately before this

[last ether]

Go to the question prior to this one

[sage pecan]

ok

A wedding planner asks guests to RSVP with their dinner preferences before the big day.
35% will likely choose the steak option
27% will likely choose the chicken option
20% will likely choose the vegetarian option
18% will likely choose the fish option
If 300 guests responded, about how many steak dinners will they need to prepare? 105

About how many chicken options will they need to prepare? 81

ok froget that problem

i just wrote unsolvible

[gray isle]

it's solvable

[sage pecan]

whish one

[sage pecan]

i alredy did this one

[gray isle]

the one you originally posted

[sage pecan]

this was the question prior

[gray isle]

I know

[sage pecan]

rly

[gray isle]

the question you posted is a follow up to this question

use those % stats

[sage pecan]

ok

dont close yet

ok

got it right

i need help with this one

350 middle school kids signed up for stuff

if 84 is signed up for soccor

i need the redused frsaction

ok?

@gray isle

[gray isle]

set up your fraction, cancel common factors

[sage pecan]

ok

.close

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[primal galleon]

6 graffiti artists paint 4 walls in 2 hours. How long does it take 4 graffiti artists to paint 8 walls?

[primal galleon]

$$\frac{6}{4} \times x=2$$
$$x=\frac{2}{\frac{6}{4} } =\frac{8}{6} =\frac{4}{3}$$

[ocean seal]

dgh

[primal galleon]

Is that the hourly rate for each individual grafitti painter?

How long does it take 4 graffiti artists to paint 8 walls?

$\frac{4}{8} x=1,x=\frac{4}{3} \Rightarrow \frac{4}{8} \left( \frac{4}{3} \right) \times t=1\Rightarrow \frac{16}{24} t=1\Rightarrow 16t=24\Rightarrow t=\frac{24}{16} =\frac{3}{2}$

[ocean seal]

dgh

[primal galleon]

3/2 hours?

[waxen flame]

Think of it as Work times Time equals Walls. You have six workers painting for two hours and finish six walls.

6W x 2 = 4

[primal galleon]

From what formula is this?

[waxen flame]

If I can make 1/2 of a widget in one hour, how many hours does it take me to make one widget?

If six workers can each take one hour to make 1/2 of a widget, how many hours would it take them to make 12 widgets?

[primal galleon]

2

[primal galleon]

24

[waxen flame]

In two hours, six workers would make six widgets. That means it would take four hours.

[primal galleon]

6 graffiti artists paint 4 walls in 2 hours.
This means that they'd paint 2 walls in 1 hour, right?

@waxen flame

So the hourly rate for 6 graffiti artists are 2 walls.

If we assume their work rate is constant.

This means that it takes them 1/2 hours to finish painting 1 wall.

And subsequently, if we assume that each painter work at the same rate as the others, then that'd mean each are doing their part in 5 minutes in that half hour.

[primal galleon]

What is W here? Is that unknown?

[waxen flame]

Work

[primal galleon]

6W = 2
W = 2/6
What does this mean?

[waxen flame]

Think of it as production/time.

That means each work is completing 1/3 of a wall per hour.

[primal galleon]

What do you mean by 'each work'

[waxen flame]

Work = Productivity per Unit of Time

[primal galleon]

Okay I think I got it now.

[waxen flame]

👍

[primal galleon]

Give me a moment.

$\frac{1}{t} =\frac{\frac{6}{4} }{2} +\frac{\frac{4}{8} }{t}$

[ocean seal]

dgh

[primal galleon]

Is this correct?

,w \frac{1}{t} =\frac{\frac{6}{4} }{2} +\frac{\frac{4}{8} }{t}

[ocean seal]

Results provided by WolframAlpha

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Requested by dgh#0553

[primal galleon]

No… can't be 2/3

Wait I made a mistake

,w \frac{1}{t} =\frac{\frac{4}{8} }{t}

[ocean seal]

Results provided by WolframAlpha

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

Requested by dgh#0553

[waxen flame]

Determine how much work each worker is doing per hour.

6W * 2 = 4
W = 1/3

Each workers completes 1/3 of a wall per hour.

Now you are asked to find how long it would take 4 artists to complete 8 walls while completing 1/3 of a wall per hour.

4(1/3) * T = 8

[primal galleon]

So we're saying 6 * productivity per unit of time * 2 hours = 4 walls?

[waxen flame]

Yes.

[primal galleon]

And to get productivity per unit of time, we divide 4 walls by 2 hours.

Whereby we get 6 * productivity per unit of time = 2 walls / hour

Productivity per unit of time = 2 walls/hour / 6 artists

I.e. productivity per unit of time = walls/(hour*artists)

[waxen flame]

Yes.

[primal galleon]

$\text{productivity per unit of time} =\frac{\text{walls}}{\text{hours × artists}}$

[ocean seal]

dgh

[primal galleon]

Hmm

What is this in terms of the v = s/t formula?

Walls = s?

t = hours*artists

v = productivity per unit of time

So artists count as time?

[waxen flame]

Velocity = Distance/Time which is equivalent to the amount of work being done.

[primal galleon]

Yeah but artists*hours is in the denominator

I'm wondering why we've artists down there

[waxen flame]

$Artists \times \frac{ Walls}{Artists \times Time} \times Time= Walls$

[ocean seal]

Kookiemon

[primal galleon]

Ok

[waxen flame]

Always go back to calculating units to make sure you are doing the math correctly. 😉

[primal galleon]

But here we still are having artists in the denominator

You don't say 100km/2humans*1hour

[waxen flame]

$\cancel{Artists} \times \frac{Walls}{\cancel{Artists} \times \cancel{Time}} \times \cancel{Time} = Walls$

[ocean seal]

Kookiemon

[waxen flame]

$6 \text{ \cancel{Artists}} \times \left(\frac{1}{3}\right) \frac{ \text{Walls}}{\text{\cancel{Artists}} \times \text{\cancel{Hours}}} \times 2\text{ \cancel{Hours}} = 4 \text{ Walls}$

[ocean seal]

Kookiemon

[waxen flame]

Now apply that to the time you are trying to calculate.

$4 \text{ \cancel{Artists}} \times \left(\frac{1}{3}\right) \frac{ \text{Walls}}{\text{\cancel{Artists}} \times \text{\cancel{Hours}}} \times x \text{ \cancel{Hours}} = 8 \text{ Walls}$

[ocean seal]

Kookiemon

[waxen flame]

Or

$4\cdot \frac{1}{3} \cdot x = 8$

[ocean seal]

Kookiemon

[lone heart]

@primal galleon Has your question been resolved?

[primal galleon]

Why 1/(3 artists * hours)?

[waxen flame]

You calculated that productivity from the initial equation given.

And we assume the same productivity holds when building 8 walls.

[primal galleon]

Okay so 4 artists multiplied by the hourly rate (walls per unit of time and artists) multiplied by time gives us the amount of walls.

[waxen flame]

Yes.

[primal galleon]

Edited it

Still correct?

[waxen flame]

Yes.

[primal galleon]

It’s a bit different from the typical “combined labor” problems

Do you know which ones I’m referring to

[waxen flame]

One worker does 1/8 of a wall, another works does 1/2 of a wall?

Type of question.

[primal galleon]

Something like that, then you want to find the amount of time it takes

For them to finish the wall

So we have 1/t = (1/8 + 1/2)

I think

Or no

Now it’s correct

1 = (1/8 + 1/2)t

1 = t/8 + t/2

1 = 5t/8

t = 8/5 hours

Right?

[waxen flame]

Looks right.

[primal galleon]

What’s different with the problem I gave?

We needed to find the hourly rate

Right

And we were already given the time

And the amount of walls they had to paint

But we only needed the hourly rate

[waxen flame]

The first problem you asked assumes equal productivity.

[primal galleon]

Yeah

What else

[waxen flame]

That's it.

The second one takes into account unequal productivity.

The second one does not require the worker unit because that is taken into account as the productivity of each worker.

[lone heart]

@primal galleon Has your question been resolved?

[lone heart]

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[frozen matrix]

can someone help

[lone heart]

Please don't occupy multiple help channels.

[manic wind]

integrate using separation of variables

[manic wind]

Also ^

[frozen matrix]

other one is a different question

[frozen matrix]

but how

[manic wind]

Still, use the same help channel

Or close the previous one and use the help forum

[manic wind]

p’ can be rewritten as dp/dt

[frozen matrix]

so p is kp^2/2+c?

[manic wind]

There should be no p in the equation for p

[frozen matrix]

oh

so 2=kp

[manic wind]

No

[frozen matrix]

isnt the integral of dp/dt equal to p

[manic wind]

Show your steps, how did you get that

[frozen matrix]

?

[manic wind]

Again, show your steps

[frozen matrix]

I just took the integral for both sides integral of dp/dt and integral of kp

[manic wind]

You don’t know how to find the integral of kp wrt t

Do you know what separation of variables is?

[frozen matrix]

o

I kinda remember it

dp/p=k dt?

[manic wind]

Yes

[frozen matrix]

so ln|p|=kt

p=e^kt

?

[manic wind]

yes

[frozen matrix]

it says wrong

[manic wind]

you need to solve for C as well

you're given the initial condition p(0) = A

(you forgot your C)

[frozen matrix]

ahh

[manic wind]

this should be ln|p| = kt + C

[frozen matrix]

ah got it thanks

.close

[lone heart]

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[autumn plank]

hi

[autumn plank]

anyone help

[alpine sable]

Find $\int x(t) \dd{t}$.

[ocean seal]

Maxim

[autumn plank]

isnt htat 1/4t^4 + t + c

[alpine sable]

yes

[autumn plank]

fill in 2

c = -2?

nvm c = 2

[alpine sable]

yes

[autumn plank]

.close

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[short veldt]

A farmer has 20 meters of fencing to build a chicken run for his chickens. He can use the side of his barn as one side of the chicken run. What's the largest area his chicken run can be if it must be rectangular?

[short veldt]

a square is a rectangle so it can be a square right

and do I set 2x+y<=20

how do I maximize the value of xy

[fallen verge]

to maximize, it is expected to ude all of the fencing so 2x+y=20

then you isolate one of the variables, lets say x
2x=20-y
x=10-y/2

or actually y is easier

y=20-2x

plug this value into xy
so you get xy=x(20-2x)

use the first derivative of the polynomial above to fine the maximum

[dense sleet]

Or axis of symmethry

[fallen verge]

or axis of symmetry yeah

if you dont know calc

[short veldt]

alr

how does using first derivative work

[manic wind]

A(x) = x(20-2x)

[dense sleet]

Use axis of symmethry if you dont know calculus. The formula is $$\frac{-b}{2a}$$

[ocean seal]

Pluton

[manic wind]

^ is also just the x coordinate of the vertex

[short veldt]

axis of symmetry?

[manic wind]

the goal is to find the vertex

that's where the area is the largest

[short veldt]

oh

got it

could you explain to me how first derivative works tho 😅

[manic wind]

are you in calculus?

[dense sleet]

$$0 = \frac{d}{dx} (x(20 - 2x))$$

Solve for x

[ocean seal]

Pluton

[fallen verge]

do you know what a first derivative is?

[dense sleet]

The notation may be very wrong

[fallen verge]

looks right

[short veldt]

I don't but I think I'll understand

[manic wind]

if you aren't in a calculus class it'll be beyond your scope for now

find the vertex using algebraic methods instead, it'll be useful to know them anyways

[short veldt]

so I got -20/-4=5

what does that mean tho

y=5?

[manic wind]

x

[wary stream]

X coord of the vertex

[short veldt]

oh right you use that to find x and plug in x value to find the y value

[manic wind]

note x(20-2x) is A(x), there's no y in there

xy = A(x)

[dense sleet]

Your y is 20 - 2x

[manic wind]

y = A(x) / x

[short veldt]

oh

so it's 10*5?

[manic wind]

no

[dense sleet]

That is the maximum yes

[manic wind]

well yeah thats the maximum, not the value of y though

[short veldt]

y=10

[manic wind]

yes

[short veldt]

wait but if x is 20/3 and y is 20/3, wouldn't that have a bigger area bc it's a square

[dense sleet]

You dont have that much area

Oh you actually do

[short veldt]

wait nvm

[dense sleet]

But no its not

This is the max if 20/3 was max it would give you 20/3 as your x

[short veldt]

yea I figured

[fallen verge]

400/9<50

you can tell by mulitplying by 9

[short veldt]

yep

how does first derivative method work

[dense sleet]

Take the first derivative

$$f(x) = -2x^2 + 20x$$
$$f'(x) = -4x + 20$$
$$0 = -4x + 20$$
$$4x = 20$$
$$x = 5$$

[ocean seal]

Pluton

[short veldt]

ah ok

[manic wind]

💀

[short veldt]

what if it's higher than powers of 2

[dense sleet]

Then it has no max probably

[short veldt]

rly?

[dense sleet]

I never seen a cubic have a max

Maybe it exists but idk about it

[short veldt]

to the power of 4?

[dense sleet]

That would have a max

[short veldt]

oh wait 4d doesn't exist-

[dense sleet]

Every even power would have

[short veldt]

do you take multiple derivatives

[dense sleet]

This isnt about dimensions

This is about powers

[dense sleet]

No you only take first

Really?

[short veldt]

and then solve the eqn?

[dense sleet]

I wanna see that. What would be the function

[dense sleet]

Yes

[short veldt]

why?

[dense sleet]

Why what?

[manic wind]

sorry lack of sleep

[short veldt]

why do you not take more than 1 derivatives

[manic wind]

I read it as cubic at first, then read it as quartic for some reason

[dense sleet]

Because 1st one is the only one you need

[manic wind]

@short veldt really stop worrying about calculus right now

if you want to learn it, you need to start from the basics ie limits

[short veldt]

...

[manic wind]

especially since how Pluton is evaluating the derivative using "tricks", it won't help you learn the concept anyways

[short veldt]

power rule?

[dense sleet]

Yes power rule.

[short veldt]

ok got it

is there a good place to learn the concepts

[dense sleet]

You dont need it trust me

[manic wind]

there are full courses on youtube, khan academy, and Paul's lecture notes

[short veldt]

Paul's lecture notes?

[manic wind]

https://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx

[short veldt]

is cemc waterloo courseware a good resource

[short veldt]

o

[manic wind]

again though, I really don't advise you jumping ahead, especially if you don't have mastery of all the prereq material

[short veldt]

like?

[manic wind]

Everything precalculus and below

[short veldt]

precalculus?

[dense sleet]

Number Theory , Combinatorics , Geometry , Algebra

All the beutiful topics you can learn before calculus

[manic wind]

you can get an idea of some (not all) in the review section here

[short veldt]

what's precalculus

[dense sleet]

Basically Algebra

And some other stuff

[short veldt]

ty

[manic wind]

pre calc also goes more in depth with trig, logs and e functions which are all very important for calc

[short veldt]

when do I learn trig?

[dense sleet]

Do you mean which grade or when shoulld you learn trig?

[short veldt]

um ig both?

[dense sleet]

High School maybe even before

[short veldt]

and when should I learn trig?

[dense sleet]

I dont think you really need any pre knowledge

If you know algebra , geometry you should have no problems learning trig

[manic wind]

what math are you in right now?

[short veldt]

wdym?

[dense sleet]

What are you learning in school

[short veldt]

im in gr8 and my teacher is using cemc courseware for gr7-8 so currently it's multiplying/dividing negative and positive integers
I take tutor and I'm pretty sure I know some algebra, counting/combinatorics, geometry, a bit of number theory and very little trig

I'm doing advanced functions using the cemc courseware also

[dense sleet]

Why are you taking a tutor to teach you number theory / combinatorics

The fields that are almost not even touched all the way until college

[short veldt]

well they call it number theory and counting

the info is from introduction to counting and probability book from aops

[dense sleet]

So your tutor is teaching you competitive math

[short veldt]

I'm not sure abt that

but I think so

[manic wind]

yeah only time number theory is really taught precollege is for competition math

[dense sleet]

So are you at least going to math competitions?

[short veldt]

yep

a few

[dense sleet]

Well that makes sense. Then calculus is not goona help you

[manic wind]

(ngl I remember some comp problems could be cheesed by calculus )

but yeah not worth learning though

they can usually be solved just as fast if not faster if you know the tricks

[short veldt]

which ones

[manic wind]

competition math at lower levels is really just pattern recognition

[dense sleet]

I just wanna know which book. The art and craft of problem solving or the art of problem solving

[manic wind]

aops = art of problem solving

pretty well known site

[short veldt]

art of problem solving I think

[dense sleet]

Ye ik. Theres just 2 books with pretty much same names

[short veldt]

the geometry and number theory version too

[dense sleet]

Depends on a level

[manic wind]

really at lower level comps its just practice

practice practice practice and you'll do great

[short veldt]

thanks

what about higher level problems?

[manic wind]

lower level comps meaning for like middle school

[short veldt]

ok

[short veldt]

^

[dense sleet]

Then may only the knowledge that you possess save you

[short veldt]

so more of like creatively thinking and outside the box knowledge?

[dense sleet]

I mean it will be something that you should know. It will just be something you never seen

Like on lower levels you may see questions you solved before

[short veldt]

questions you've solved before?

[dense sleet]

Basically same question just with other numbers

[short veldt]

ok

Thanks for helping me with the question and answering some other questions as well!

.close

[lone heart]

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[vagrant tusk]

calculus in 10th grade is annoying dude, can someone please help me (yes, my teacher got it from the internet)

[lone heart]

@vagrant tusk Has your question been resolved?

[lone heart]

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[west girder]

Triangle ABC has side lengths 9, 10 and 13, with D the midpoint of side BC.
What is the length of segment AD?

[west girder]

How do I know which side length corresponds to which side?

[plain flame]

they didnt give you a picture?

thats evil

[lone heart]

@west girder Has your question been resolved?

[lone heart]

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[mellow crane]

I originally got 288pi but that's not an option so my teacher told me to draw the triangles and rectangles on the diagram but now I'm even more confused. Could anyone help please?

[lone heart]

@mellow crane Has your question been resolved?

[west girder]

no, thats why i was confused. this was from mathcounts so it probably intended for you to find the all of the medians and see which one was an integer, since it didnt say answer as a common fraction or radical

[gray isle]

how did you get 288 pi

[mellow crane]

i added 16 and 9 to get 25 as the radius of A and tried finding each of the areas

[lone heart]

@mellow crane Has your question been resolved?

[lone heart]

@mellow crane Has your question been resolved?

[alpine sable]

So we can already find the areas of Circles B and C right, what did you get for these?

[mellow crane]

81pi and 256pi

[mellow crane]

.close

[lone heart]

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[shell narwhal]

evaluate this with an error inferior to 0.01

[tacit arch]

are you supposed to use taylor series?

[shell narwhal]

yhea something like that but idk how

[tacit arch]

do you know the taylor series for $e^{-x^2}$ ?

[ocean seal]

riemann

[shell narwhal]

i can substitute -x^2 inside the e^x serie right ?

[tacit arch]

yea

[shell narwhal]

ok let me write it down

like this ?

[tacit arch]

right. then multiply by x^2, then integrate term by term

keep including more terms until each one has absolute value less than 0.01

[shell narwhal]

ok let me try

like this ?

the answer is approximately 1/24

but 1/24 is 0.0416666 and its not under 0.01

@tacit arch

[tacit arch]

where's your sum?

[shell narwhal]

The sum would be negative is that normal ?

[tacit arch]

oh your algebra's wrong

mistake here

[shell narwhal]

oh ok let me fix it

Wait what is wrong ?

[tacit arch]

,calc (-3)^2

[ocean seal]

Result:

9

[tacit arch]

,calc -3^2

[ocean seal]

Result:

-9

[shell narwhal]

Ok ok

[ornate condor]

hm

n is applied to the -1

[shell narwhal]

Ok but in the sum do i include 0.00625 ?

[ornate condor]

wots dat

[shell narwhal]

since it’s smaller than 0.01

[shell narwhal]

Term for n=1

What do i do ;-;

[tacit arch]

fix your algebra first

[tacit arch]

recall what you're doing: integral of a series

[ornate condor]

so weve to use

[tacit arch]

still wrong

[ornate condor]

weierstrass safety net

[tacit arch]

(-y)^n = (-1 * y)^n and apply exponent rules

[shell narwhal]

Is this right ?

@tacit arch sorry for the ping (can i ping you next time ?)

[tacit arch]

where even is your summation?

you can check with wolfram if it's close

,w integral 0 to 0.5 x^2 e^(-x^2) dx

[ocean seal]

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[ornate condor]

phantom ping

[tacit arch]

ndam deleted it

[ornate condor]

ye i saw just as they del

[shell narwhal]

Sorry

[shell narwhal]

Do i include 0.00625 which is smaller than 0.01 in the sum ?

If not answer is 1/24

[tacit arch]

,calc 1/24

[ocean seal]

Result:

0.041666666666667

[tacit arch]

that's not within 0.01 of the answer

you're doing something wrong

[tacit arch]

reread

[shell narwhal]

The second term has an absolute value smaller than 0.01

but not the first

[tacit arch]

,w taylor series x^2 e^(-x^2)

[ocean seal]

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[ornate condor]

ITZ LANDAU

[tacit arch]

,w integral 0 to 0.5 (x^2 - x^4) dx

[ocean seal]

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[tacit arch]

i think i got that wrong. the error is not the same as the nth term

confused it with remainder term

[shell narwhal]

isnt |Rn|<a_n+1 or something

[tacit arch]

yea follow your book/notes

[shell narwhal]

This help channel is my notes

;-;

[ornate condor]

LOL

[shell narwhal]

How should we solve this problem?

@tacit arch so what do we do ?

[tacit arch]

where'd you get this from?

just follow that

[shell narwhal]

thats litteraly all i have

there is no example

its a definition

.close

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[fathom forum]

Can someone explain how to set up the equation.

[lone heart]

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[fathom forum]

Sally is X

How can I set up the equation? Need an explanation

[gray isle]

you deleted the original, make a new one as this will close any minute

<@&268886789983436800>

[lone heart]

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[wary hound]

need help

[wary hound]

<@&286206848099549185>

[tacit arch]

!15m

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

[wary hound]

I don't get what i was wrong

[lone heart]

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[wary hound]

.close

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[coral mica]

.close

[lone heart]

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[lone heart]

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[deep latch]

What is the remainder in division?

[alpine sable]

euler's theorem

[deep latch]

What?

[alpine sable]

https://en.wikipedia.org/wiki/Euler's_theorem

[deep latch]

numbers have different bases

very confusing

[alpine sable]

huh?

2^2020 and 3 are coprime

[deep latch]

i'm so amateur i don't understand

[deep latch]

can you help me please

??

[alpine sable]

have you seen euler's theorem before?

[deep latch]

Yes

[alpine sable]

what is phi(2^2020)?

[deep latch]

Wooww

should i think like this

[ornate condor]

wait phi?

hm

[alpine sable]

euler's totient function

[deep latch]

i am a turkish and my english is not good

[alpine sable]

https://en.wikipedia.org/wiki/Euler's_totient_function

[ornate condor]

looks fun

[deep latch]

i have to try this method

I will be glad if you take a look at the question.

it looks so scary to me

difficult question

[alpine sable]

my method involves inverting 2^4, so there might be a better method lmao

[deep latch]

I will try, can you try too?

[deep latch]

I failed

[lone heart]

@deep latch Has your question been resolved?

[lone heart]

@deep latch Has your question been resolved?

[deep latch]

Help mee 😕😕

[lone heart]

@deep latch Has your question been resolved?

[alpine sable]

@deep latch

translate

using deepl : https://www.deepl.com/translator

[deep latch]

Thanks

[neon hedge]

MOOOOOOOOOORPH

[lone heart]

@deep latch Has your question been resolved?

[lone heart]

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[chilly dove]

So I did this question but apparentally I got C wrong, so could anyone explain to me on how to do C?

[chilly dove]

<@&286206848099549185>

[hard patio]

what was your solution?

[chilly dove]

i just divided 600 by the denominators of all the numbers

[hard patio]

why?

[chilly dove]

idk

lol

oh wait

i think i got it

[chilly dove]

isnt it Julia 200 laps Katie 240 laps Lisa 250

cuz the lcm of 20 25 24 is 600

and 600 divided by 1/3 2/5 and 5/12

[hard patio]

basically you had to find the time at which they meet, then you had to divide that by the time taken for one lap for each of them

was that what you did?

[chilly dove]

no but i just thought of that

[hard patio]

so you now understand how the problem needs to be attempted?

[lone heart]

@chilly dove Has your question been resolved?

[lone heart]

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[storm oak]

When calculating exponential growth, does it have to be the exact answer/number ?

[storm oak]

or it can vary by few numbers ?

[sick yarrow]

the final value? depends on your cricullum ig

[storm oak]

so am i safer typing the exact numbers on calculator instead of rounding off?

Ye final value

[sick yarrow]

for (i)gcse's your final answers can be rounded to 2 decimal places (typically it can be even less and they will still accept it)

unless specifically instructed

[sick yarrow]

oh

do you have a scientific calculator?

[storm oak]

ye on phone

[sick yarrow]

you could either just type the whole equation in one go, use variables or the Ans feature

[sick yarrow]

hmm i doubt it has all of that, it should have some sort of basic Ans feature which stores the answer of the previously solved expression, regardless of calculator you could just type the whole equation at once

[storm oak]

sorry for potential image wall
but heres the diff

wheres the ans

i think imma settle with what i got

thanks btw

.close

[lone heart]

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[polar dirge]

what is the answer

[lone heart]

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[outer lark]

so speed (velocity) is the distance travelled per second , so distance / per unit time

we are only interested in the second part of the motion described because it says it wants the speed at the end of the observed motion

[cyan jungle]

yhh

[outer lark]

it says the acceleration is constant so v will be just d / t ( I think ? someone might have to correct me here ) so it's just 200 / 10 = 20ms^(-1)

or around 45 mph

[cyan jungle]

its suvat btw

[outer lark]

should be similar

wait lemme think

vertical component and horizontal components split

[cyan jungle]

velocity is a vector

not scalar

[outer lark]

horizontal component of velocity is always constant

[cyan jungle]

so it cant be that

[outer lark]

shouldnt change the answer

[cyan jungle]

well its wrong

[outer lark]

rip

[cyan jungle]

apparently its 22.7

[outer lark]

ok lets see

okok

I see now

2 seconds

@cyan jungle ok someone else might be able to help, I thought it was 0 acceleration but its constant acceleration so misread, mbmbmbm

[keen plinth]

,w v^2 = 800a, (0.6v)^2 = 400a

[ocean seal]

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[keen plinth]

[outer lark]

ok got my answer

ill post it in

[keen plinth]

,w v^2 - (0.6v)^2 = 400a, 10a = v - 0.6v

[outer lark]

@cyan jungle this is by far the largest suvat q i've done

answer is top right

its kind of all over the place

might have to tidy then post in again

but basically

the u of the second part is equal to the v of the first part

and since a is constant

you can set v and u equal and work a

and then its a LOT easier

because you then go back and work out u for the second part

then you can use 2s/t - u to get v for the second part

[lone heart]

@cyan jungle Has your question been resolved?

[keen plinth]

,w v^2 - (v - 10a)^2 = (v - 10a)^2 - (v - 25a)^2 = 400a

[ocean seal]

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[keen plinth]

,w 68/3

[outer lark]

[keen plinth]

bruh lol

wait no thats right

,w 68/3

[outer lark]

ye

[ocean seal]

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[outer lark]

fun q

[lone heart]

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[alpine sable]

.open

[sacred carbon]

.open

.open

exclude common factor outside parentheses
3(5x+2)-3(2x+1)(-5x-2)

[vocal tapir]

ok so start off with which of those factors look alike?

in the parentheses

[sacred carbon]

(5x+2) and (-5x-2)

[vocal tapir]

yes, and how can you make (-5x-2) look like (5x+2)

[sacred carbon]

change -5x to 5x

and - give to 3?

and now we have 3(5x+2)+3(2x+1)(5x-2)

[vocal tapir]

slight mistake at (5x-2)

is (5x+2)

because

[sacred carbon]

okay

[vocal tapir]

you can take -1 out of (-5x-2)

making it (5x+2)

now, that they look alike, you have 3(5x+2)+3(2x+1)(5x+2)

[sacred carbon]

okay and what now

[vocal tapir]

you have a common factor from both 3(5x+2) and 3(2x+2)(5x+2)

how would you guess taking them out is done?

hint: say (5x+2)=y

if that makes it easier

[sacred carbon]

(2x+2)(3+3)

[vocal tapir]

hmm, not quite

the idea is to take the factor out, so you have

(5x+2)(3+3(2x+1))

think through this

[sacred carbon]

okey i see

[vocal tapir]

there's more to factoring this polynomial

what can you do inside (3+3(2x+1))

[sacred carbon]

add?

3+3

[vocal tapir]

not quite, they are not the same

you have to expand 3(2x+1)

[leaden jackal]

@sacred carbon what is (1+2) divided by 2.7

[vocal tapir]

then you have?

[sacred carbon]

3*2x and 3*1?

[vocal tapir]

yup

that's right

now what do you have?

[sacred carbon]

6x and 3

[vocal tapir]

what is inside the brackets fully?

[sacred carbon]

(3+6x+3)

[vocal tapir]

that's right

what can you do here?

[sacred carbon]

add

[vocal tapir]

yup, what do you have then?

[sacred carbon]

(6+6x)

[vocal tapir]

that's right, but 6x is in front

so 6x+6

[sacred carbon]

okey, thats it?

[vocal tapir]

not yet

what do you have as a result of all of this?

[sacred carbon]

6x+6

[vocal tapir]

not quite

we're at (5x+2)(6x+6)

now at (6x+6) do you see a common factor?

[sacred carbon]

okey

i forgot

[vocal tapir]

you have 6

after you take out 6 from (6x+6)

[sacred carbon]

x

[vocal tapir]

what does (5x+2)(6x+6) look like?

[sacred carbon]

(5x+2)(x)

[vocal tapir]

hmm, not quite

remember, you did it earlier

[sacred carbon]

okey

ik

wait

[vocal tapir]

ok

[sacred carbon]

30x^2 30x 12x 12

@vocal tapir

[vocal tapir]

no

you don't simplify it

[sacred carbon]

so idk

[vocal tapir]

look, what was (6x+6) multiplied to look like (6x+6)

you get

6(x+1)

so now it looks like

(5x+2)6(x+1) => 6(5x+2)(x+1)

that's your polynomial factored

[lone heart]

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[chrome mica]

I do not understand why the fourth option is the answer

[lone heart]

@chrome mica Has your question been resolved?

[lone heart]

@chrome mica Has your question been resolved?

[copper rock]

g(x) is to the right of f(x), not to the left i guess

[lone heart]

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[tame nova]

Find the common divisors of a and b
We hve the highest divisor is 18 and a<b

[lone heart]

Please don't occupy multiple help channels.

[tame nova]

Whatever

Can smn help

[high rapids]

Patience is a virtue

[hard island]

Let's consider a related but simpler example. What are the common divisors of a=16 and b=24?

[tame nova]

2/8

[hard island]

Are 2 and 8 the only common divisors?

It may help to list out all the divisors of each number

[tame nova]

yes

2/3/8

sorry

[hard island]

Is 3 a divisor of 16?

[tame nova]

no...

so just 2 and 8

[hard island]

There's two more divisors you're missing; again, it may help to list out all the divisors of each number

[tame nova]

from 2 to 24 there is only 2 and 8.

[tame nova]

the ggf is 8 that's all i can add

but as i said it's only 2 and 8

and 4

[hard island]

Yep, 4

[tame nova]

4x5 yep

so?

[hard island]

Usually we like to consider 1 to be a common divisor, but if you're being taught otherwise we can continue with that

Consider our common divisors: 2, 4, and 8

We see that 8 is the highest common divisor

What are the divisors of 8?

[tame nova]

2,4,8

[hard island]

Yep

Let's consider one other example. Suppose that a and b share common divisors of 2, 4, and 8, but also 3. Is there any number that can be divided evenly by both 3 and 8, and not 24?

[tame nova]

48

[hard island]

48 = 2 * 24, so it can be divided evenly by 24

[tame nova]

yes

..

[tame nova]

maybe im too stupid that's why i dont see ur point

[hard island]

No worries

Effectively, the answer turns out to be no (I encourage you to explore why; consider prime factorization)

There's no number that is divisible by 8 and 3, and not 24

[tame nova]

because all the numbers that are divisible by 8 and 3 are multiples of 24

but in my question the ggf is 18

ohhhh

i just have to find the divisors that are smaller than 18

if it's the ggf then it's itself

18

1, 2, 3, 6, 9, and 18.

am i right ? @hard island

but they said of a and b....

[hard island]

Yes, exactly that

[tame nova]

now they ask me what can a and b be if ab=1944

[hard island]

That's best done by considering the prime factorization

[hard island]

It ends up being the case that factors of GCD(a,b) = common factors of a and b; you can prove this by manipulating the prime factorization. If you'd like, I can attempt to write up a proof, but it may be a bit

[tame nova]

no no need it's ok

[tame nova]

also..

the last question

like all the possibilities

[hard island]

Do you recall prime factorization?

And, if so, could you attempt to find the prime factorization of 1944?

[tame nova]

2^3 x 3^5

[hard island]

Yep

And another thing we'll want to consider; what is the prime factorization of 18

[tame nova]

2 x 3^2

[hard island]

Okay, and one final mini-example

Could you answer

• the prime factorization of 10
• the prime factorization of 15
• the gcd of 10 and 15
• the prime factorization of 15 * 10 = 150

[tame nova]

hmm

[tame nova]

2x5
3x5
5
2x3x5^2

[hard island]

Do you notice any pattern in that final prime factorization?

[tame nova]

what is a pattern

english is not my first language

[autumn heron]

is this where you get help?

[hard island]

#❓how-to-get-help @autumn heron

[tame nova]

?

it looks similar

[hard island]

something that appears to follow a strict set of rules, or repeats itself

[tame nova]

5

!

[hard island]

as another example, if we consider the same experiment of 4 and 6, we find

2 * 2
2 * 3
GCD = 2
(GCD)^2 * 2 * 3

[tame nova]

but for my case i dont have a and b to do this operation

[hard island]

Yes, but we do have the prime factorization

In 2^3 * 3^5, we can isolate the GCD twice, and find (2^1 * 3^2) * (2^1 * 3^2) * 2 * 3

[tame nova]

this is a bit hard to process

[hard island]

That's alright

In short, I'm attempting to apply
(xy) * (xz) = (x * y) * (x * z) = (xx) * y * z

[tame nova]

the next step?

wait

[hard island]

Sorry, I've adjusted my letters to make it clearer

[tame nova]

so a= 2 b=3^2 or 3

?

[hard island]

Close, but recall that they also need the GCD; it ends up being a = GCD * 2 and b = GCD * 3

There's actually a second option, where a = GCD and B = GCD * 2 * 3

[tame nova]

a=18
b=18x2x3

[last spade]

all common divisors of a and b divide the highest common divisor I think

so you just need to find all divisors of 18

[tame nova]

thank you!

[tame nova]

the problem is how can i justify that in a sentence

[hard island]

That's a good question

I may need a minute to think, but if anyone else has a clear answer, feel free to hop in

[tame nova]

@last spade :) feel free to answer

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[verbal olive]

Where did the 2 queens on the same diagonal rule come from?
I know the slope needs to be either 1 or -1
but the first rule doesn't line up with my math (i+i' = j+j')

[craggy cloud]

is this where i go to make a help channel?

or am i dense

[verbal olive]

#❓how-to-get-help

[craggy cloud]

ye in the how to get help it says to go to help-0

this is help 0 💀

[verbal olive]

choose one the available math channels above

the ones without a name

[craggy cloud]

bet

appreciate it

[verbal olive]

<@&286206848099549185>

[lone heart]

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[mighty berry]

I'm confused on why the answer is "0.1" here. I get that it's a binomial distribution and the sample space is 5, but shouldn't p be "1/3", given that the MGF format for a binomial distribution is "(pe^t + q)^n"?

[lone heart]

@mighty berry Has your question been resolved?

[mighty berry]

<@&286206848099549185>

[sudden hinge]

i think you're right

[mighty berry]

You mean, p should be 1/3?

Freeing this channel for others

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[pearl trench]

im confused if II is right

i dont understand what it is saying

and in between saying if I is right

the answer i got was A

[zinc dagger]

Number I is asking if there is any point in time after x equals -2 when the function is decreasing. In other words look at the function at x=-1,2, and 4, and ask urself “hey, is this function increasing or decreasing”

You should read the equal sign in Number II as the verb “equals”. So “the value of f(x) equals 5…blabla”

[pearl trench]

so II would be no than right?

?

@zinc dagger

.close

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[pearl trench]

.reopen

[lone heart]

✅

[pearl trench]

?

someone help me plssss

im dyinggg

.close

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[lone heart]

@gloomy sorrel Has your question been resolved?

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@gloomy sorrel Has your question been resolved?

[slender mason]

Anyone here do geometrey>

specifically venn diagrams

dam

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[worldly laurel]

i know i have to use the product rule for a but im not really sure what to fill in for my values

[gloomy wolf]

start by writing what (fg)'(x) would be

before worrying about 5

[worldly laurel]

how am i supposed to know what f(x) or g(x) is

[rough sonnet]

You don't, you just need to remember what the rules are

In this case, [f(x)g(x)]'=f'(x)g(x)+g'(x)f(x)

Just plug in the values given

[worldly laurel]

ohh okay that makes sense thank you

[rough sonnet]

Same with the other ones, just with quotient rule instead

[worldly laurel]

okay got it! ty again

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[alpine sable]

i need help on this question, if someone could explain it that'd be great. I'm trash and know nothing about math so it'd be a huge help.

[alpine sable]

Well what's going on is a statistician is making a graph

He asks 1000 ppl their number of friends every year for 15 years

So each year he has the average number of friends per person

[long axle]

Look at sign of slope

[alpine sable]

Then he puts a point on his graph: (age, average number of friends)

What you have is friends=(-2.94)*age+116.14

im confused on what those numbers mean

And what you need to find is if the number of friends is the highest in highschool

Basically if the age is the lowest possible, do you have the maximum friends?

So you can try to find the number of friends at multiple age and find a trend

with friends=(-2.94)*age+116.14

So if age=0 how many friends do you have? With age=1? etc

ah okay

You can yourself do a graph with number of friends per age

Or you can notice something and answer directly

ah okay

in class we used a calculator to graph

is there one online i could use?

sure there is multiple

You can try geogebra online for instance

With f(x)=-2.94x+116.14

https://www.geogebra.org/m/G8Fs6ybQ

You need to unzoom quite a bit

got it

thanks so much

one last thing

what exactly does the 116.14 mean

well it's just that at age=0 the average friends was 116.14

Basically it's the value when x=0

mmm hmm

and the 2.94?

friends=(-2.94)*age+116.14

When age increase of 1 the average friends decrease of 2.94

Can you see it?

ahhh

yea

i get it