help-23

[serene quest]

please

[dapper venture]

either use product rule or expand it

[dapper venture]

bro your brackets

[serene quest]

I'm sorry for not using brackets, I was in a hurry.

[dapper venture]

the rest seems correct

[serene quest]

I need you to help me solve it and explain to me step by step what comes after what I did

[dapper venture]

expand the brackets and combine the powers

[analog burrow]

Basically you need to put the brackets

[dapper venture]

what help do you need

[analog burrow]

6x²(√x +8x)

[analog burrow]

You have to do the same for the second part as well

Once that is done you could expand the brackets, and simply the terms

[serene quest]

I know

so

[safe radish]

@serene quest Has your question been resolved?

[safe radish]

@serene quest Has your question been resolved?

[safe radish]

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[lean otter]

might be an odd question, but anyone mind explaining to me how the standard method of conversion from base-r to binary works exactly?

[lean otter]

you got your number x in decimal, divide it by r, then you can check if that division results in a remainder or not

[peak estuary]

imagine what those same steps would do if your number was already written in base r

[lean otter]

I can understand the computation, but why does this work?

[lean otter]

You mean?

[peak estuary]

the last digit in base r is precisely the remainder after division by r

if you have $(a_2 a_1 a_0)_r$ in base $r$, that means $a_2 r^2 + a_1 r + a_0 = r(a_2 r + a_1) + a_0$. so $a_0$ is the remainder

[flat frigate]

Denascite

[lean otter]

OH

Oh wow this makes so much sense, never thought of it this way

thank you!! that's so intuitive

[peak estuary]

youre welcome

[lean otter]

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[cunning shard]

I recently watched a video, which was about repeating decimal in the decimal expansion of reciprocal of primes

[cunning shard]

when divding using the standard long division way, for some p, the remainders we can get are from 0 to p-1, if some point we visit a remainder which we have seen before we get into a loop and the repeated decimal is obtained

The worst case scenario is we use get all of p-1 remainders. In that video they mention this happens if it’s primitive root or something

how is it connected with the notion of primitive root of integers?

[peak estuary]

pick some p

[cunning shard]

say p=7

[peak estuary]

and then on one hand do the long division, and on the other calculate the powers 10^n mod p

[cunning shard]

If 10 is a primitive root, then it visits all of p-1 integers mod p

[peak estuary]

yes but you have to see how it relates to the long division

[safe radish]

@cunning shard Has your question been resolved?

[cunning shard]

sure let me try

[safe radish]

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[frigid locust]

quick question is this correct?
$$u=(logx)^{(sinx)}$$
$$logu=(logx)\cdot(sinx)$$

[flat frigate]

JustToPro

[frigid locust]

<@&286206848099549185>

oh wait there is supposed to be another log there

$$u=(logx)^{(sinx)}$$
$$logu=(sinx)\cdot(log)(logx)$$

[flat frigate]

JustToPro

[tacit idol]

ya

[frigid locust]

ok ty

.close

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[dreamy copper]

need help with this one

[dreamy copper]

i) and ii)

[desert juniper]

draw the polygon

[dreamy copper]

and?

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[vapid epoch]

help with equation check function 2nd degree equation

[stray socket]

Post it

[vapid epoch]

sure

1 minute

find the canonic form of f(x) = 2x^2 -16x + 24

a(x- alpha)^2 + beta

a = 2

b = (-16)

c = 24

[stray socket]

Mmhm

[vapid epoch]

Alpha =-b/2a

[stray socket]

Yup

[vapid epoch]

= 16/2*2

= 4

[stray socket]

Yup

[vapid epoch]

1 min

beta = -delta/4a

=-(b^2-4ac)/4a

= -(-16^2* 4 * 24)/4*2

=-(256-192)/8

=-64/8

=(-8)

@stray socket

[stray socket]

Yes

Although to make your life easier

[vapid epoch]

yes?

[stray socket]

β = f(α)

[vapid epoch]

a(x- alpha)^2 + beta = 2(x-4)^2+ (-8)

[vapid epoch]

whats that????

[stray socket]

Just plug α into f(x) to find β

[vapid epoch]

Is this canonic formula?

or what thing?

[stray socket]

I mean, canonic form is the same as vertex form

[vapid epoch]

yes i think

but this hasnt been mensioned by the teacher

let me check tmr

[stray socket]

Okay well the vertex form of a parabola who has vertex, (h,k), is just f(x) = a(x-h)^2 + k

which is nice because f(h) = k

[vapid epoch]

ohhh yeah

[stray socket]

Just let h = α and k = β and you get whatever your teacher gave you

[vapid epoch]

okkk lemme check

yeahh

truee

its in my note book

[stray socket]

So instead of having to go through that formula for β, just plug α into f(x)

[vapid epoch]

also do you know about variation tables

yeah

f(of alpha)= beta

[vapid epoch]

and thenn

[stray socket]

Haven't heard of them but if you show me them, I might know

[stray socket]

Well that's beta

[vapid epoch]

a(x- alpha)^2 + beta = a(alpha- alpha)^2 + beta

[vapid epoch]

whats the difference?

[stray socket]

No difference

β = f(α)

That's all it is

[vapid epoch]

alrightaa

[stray socket]

Are you talking about function tables and you need to find a function that dictates that table?

[vapid epoch]

so a is also equal to alpha

[vapid epoch]

let me show you

[stray socket]

Oh no I'm using the literal Greek letter alpha (α)

α

$\alpha$

[flat frigate]

Umbraleviathan

[stray socket]

That's not an "a"

[vapid epoch]

yes so this

β = f(alpha)

[stray socket]

Yeah

[vapid epoch]

great i was saying that

[stray socket]

Mmhm

[vapid epoch]

1 min

do you speak french by any chance?

[stray socket]

No

I can get someone that speaks French for you

If she's online

[vapid epoch]

sure but you can also help 😄

so do you know about this?

[stray socket]

Looks like a function behavior chart

I mean I understand it

[vapid epoch]

this is the one sorry

now does this make sense?

[stray socket]

Those are just possibilities for parabolas

I get what they're trying to show

[vapid epoch]

Si a>0, la parabole est tournée vers le haut.
• Si a<0, la parabole est tournée vers le bas.

If a>0, the parabola faces upwards.
• If a<0, the parabola is turned downwards.

[stray socket]

Yeah so if a > 0, the parabola is concave up (opens up)

If a < 0, the parabola is concave down (opens down)

[vapid epoch]

so now

the question says

show for all reels x, f(x)= or > than -8

using the variation table

how would you do it?

[stray socket]

Okay so you know that (α,β) = (4, -8) is the vertex of the parabola

And you know a = 2 > 0

So is f(x) opening up, or opening down?

[vapid epoch]

can u show me using the variation table thing?

[stray socket]

I'll give you an example

[vapid epoch]

its opening up

since its greater than 0

[stray socket]

Ye

And so you'd plot (4, -8) on the variation table

And then you would have an arrow pointing down to that point, and an arrow pointing up away from that point

So

[vapid epoch]

let me try to make one right now

and then

howdo i do the graphic

[stray socket]

a > 0 since a = 2

not a < 0

also wrong way

[stray socket]

I drew it up here

[stray socket]

Kinda like follow the arrows

But make it like bowed out

[vapid epoch]

?

[stray socket]

I did it up here

[vapid epoch]

how

[stray socket]

Look up here for example. Note how I kinda followed the lines, but bowed it out

That's an example though, not for this f(x)

[vapid epoch]

?

[vapid epoch]

explain pls

[stray socket]

I mean idk how else to explain it, I already did and showed you an example

Just trace the arrows, but bow them out a bit

Like a cup

Or the letter U

[vapid epoch]

yeahh

now it says

what can we say about the function f

[vapid epoch]

where do i put

[stray socket]

Lemme graph f(x) for you

,w graph 2x^2 - 16x + 24

[flat frigate]

Results provided by WolframAlpha

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Requested by umbraleviathan

[stray socket]

What does it look like

What's the minimum point?

Is there a maximum?

Opening up or down?

That's what they want

[vapid epoch]

-8?

[stray socket]

Like describe it

-8 is the minimum, yes

[vapid epoch]

14 is the maxium?

[stray socket]

No

There's no maximum

The graph is just cut off

But if you think of x for all reals, there's no maximum

It'll just keep growing

[vapid epoch]

how can i explain this?

and how can i explain both the variation table with this

[stray socket]

You just state it

[vapid epoch]

how can i say it for example?

@thin bridge seee this is what i was talking about

@stray socket

hmmm okkk

<@&286206848099549185>

.close

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[vapid epoch]

.close

.reopen

[safe radish]

✅

[vapid epoch]

.close

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[severe moon]

can someone help with this one pls

[severe moon]

pls

<@&286206848099549185>

[lunar rampart]

label the angles using a variable

like

label BAC as alpha

ABC as 3/2 alpha

label DAC as phi

DAB as 2 phi

ok for ease of typing, alpha = å, phi = ø

2ø + ø = å = 3ø

sub in ABC so you have ABC and CAB in terms of å

we know ABC + CAB + ACB = 180 so you get ACB in terms of å

similarly by knowing sum of angles is 180, you can find the angle CDA and ADB in terms of å by considering the two triangles seperately

now you have all the angles

hmm

i need a pen and paper bro my head is sm where else

[severe moon]

k

can u name them with english variables pls, to make things a bit more easier.

english letters

[lunar rampart]

i used alpha and phi

ran out of letters

i alr started before u said that

[lunar rampart]

basically doing this and finding every angle in terms of alpha and phi reveals that triangle CAD and triangle ACB are similar (have the same angles)
@severe moon

[severe moon]

it's alright

did u use trig

can u explain what u did pls

i'm in 3rd year in secondary school(9th grade)

[safe radish]

@severe moon Has your question been resolved?

[lunar rampart]

no

[lunar rampart]

so youre given two relationships right?

each relationship is between two angles

i represented one of the angles with a vairable and the other in terms of that variable

does this make sense?

now i have all 4 angles in terms of some variable

now in the diagram you can see that DAC + DAB = BAC

so i wrote that using the variables

[lunar rampart]

now i have a relationship between the two variables i can substitute into any of these

so i can get all of these angles in terms of either variable

now i know the angles in a triangle add up to 180

and theres 2 small triangles inside 1 big triangle so i use that theory to find every angle in terms of the variables

[severe moon]

yes

[lunar rampart]

then i notices that angle CAB = CDA, and angle CBA = CAD, meaning triangle CAD and triangle DAB are similar (the same triangle but upscaled/downscaled)

so i know that all the side lenght are multiples of eachother (respecively), but i dont know by what factor so i call the factor k

ignore the (k E N)

so b = ek
a = bk
c = d*k

i find k in terms of a and b and sub in the other two equations

and get e and d in terms of b, c and a

makes sense?

[severe moon]

k

but if u cross check it will u get the correct ans

?

.close

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[mortal sandal]

Let it be at height h and calculate the increase in length

The string should make 2 tangent lines touching the earth

Ye

So just length of the tangent lines - length of the original arcs they would be instead

nah that's how I first pictured it too

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[leaden scaffold]

Could someone help with this problem?

[safe radish]

@leaden scaffold Has your question been resolved?

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[lean otter]

.help

[safe radish]

Commands:
clopen: .close, .reopen, .solved, .unsolved
consensus: .poll
factoids: .tag
help: .help

Type .help <command name> for more info on a command.

[lean otter]

.help solve

[safe radish]

No command called "solve" found.

[lean otter]

.solved

[urban eagle]

For Q3 is I_0 e?

[mortal sandal]

No, show work

And #❓how-to-get-help

For both of you

[urban eagle]

??

[mortal sandal]

Click on the link and read the text

[urban eagle]

What I do wrong

[mortal sandal]

Posted in an active channel

[urban eagle]

It wasn’t active

It was available

[mortal sandal]

Wait wtf

ok that's bizarre but I guess it was

in that case just post the work you did

[urban eagle]

Why would it not just be e
Cause wouldn’t the integral be timesed by 0 so it’s just e

[mortal sandal]

wym the integral is timesed by 0

it shouldn't be

oh

[urban eagle]

I_n = e - nI_(n-1)
If n = 0

then that integral is gone

I_0 = e

[mortal sandal]

Right but the recursive formula doesn't work for n=0

It starts at n=1

[urban eagle]

Oh

Ffs

Ty

[mortal sandal]

,w integral from 0 to 1 of x^-1*e^x

This is why

[flat frigate]

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Requested by a_mog

[mortal sandal]

This is "I_-1"

np

[urban eagle]

.close

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[cerulean tusk]

Does fg(x) mean multiplying the functions?

[lean otter]

think of it as f(g(x))

so g(x) is thought of as something plugged into f(x)

[cerulean tusk]

Ahhh ok let me try that

Is differentiating with respect to x just normal differentiation? @lean otter

Or is it the other way around?

Here

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[vagrant oar]

Can someone help me with this word problem? What I was thinking was, the base of the triangle is 2 feet so the bottom is 2 feet and the height is 3. So, 2x3/2 = 3. So the area of the triangle is 3. Then I multiply that times each height. I am not sure if I am doing that right and the wording makes it confusing:

Mrs. Brown wants the class to make some concrete forms that she can use as plant stands in the yard. The forms have a triangular base that measures 2 feet with a height of 3 feet. She wants three forms: one is 24 inches tall, the second is 36 inches tall, and the third is 48 inches tall. What is the volume of each?

[safe radish]

@vagrant oar Has your question been resolved?

[vagrant oar]

<@&286206848099549185>

[vagrant oar]

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[tight hound]

ok im really not sure how to approach this one: find (2x + 3y) dot (x-4y) exactly if |x| = 3, |y| = 4, and the angle between x and y is 30

[plucky elk]

you use your previous formula

and another equation that relates angle between vectors with their dot product

[plucky elk]

#help-26 message

[tight hound]

when do the magnitudes come in?

[plucky elk]

did you see this formula

it has magnitude in there

[tight hound]

ok ty i will give it a shot

.close

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[urban eagle]

With reduction formulae if you have an integral I_n and it’s equal to
I_n = … + nI_(n-2)

[urban eagle]

Do I start at I_2
?

[plucky elk]

!original

[safe radish]

Please show the original problem, exactly as it was stated to you. A picture or screenshot is best.

If the original problem is not in English, then post it anyway! The additional context might still help helpers help you. Do your best to translate.

[plucky elk]

and

!show

[safe radish]

Show your work, and if possible, explain where you are stuck.

[urban eagle]

Q9

[plucky elk]

yea n >= 2.

annoying they don't tell you that

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[plain hedge]

I really wish I understood what I did wrong

[plain hedge]

I gotten to the point where I checked with chat gpt 4 and nd came to the same answer as I did

wait on sec let me update it

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[plain hedge]

I did the operations right just got the solution wrong

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[urban eagle]

For Q12b

[urban eagle]

Is this correct? Cause I end up with tanx but then tan pi/2

Ignore

Maybe

I think ik what I did wrong

[little mesa]

$2I_2=1I_0$

[flat frigate]

chlamydia

[urban eagle]

Should I just integrate (cosx)^2

[little mesa]

you can

[urban eagle]

Oh

[urban eagle]

I see

What I did wrong

@little mesa what would I do for part c

[little mesa]

$I_{2n}=\frac{\pi(2n)!}{2^{n+1}(n!)^2}$

[flat frigate]

chlamydia

[little mesa]

how much have you done

[urban eagle]

None 💀

[little mesa]

you know how to prove by induction right?

just go through how you would normally

[urban eagle]

Like prove true for n = 2
Assume true for n
Then whatever?

[little mesa]

do n=0

[urban eagle]

I only learnt how to do proof by induction for certain things like matrices, series, inequalities, and divisibility
Idk how it’d work for this

[little mesa]

it's a bit similar to series

[urban eagle]

Ok so I proved true for n = 0
I then assumed true for n = k
How do I now prove true for n = k+1

[little mesa]

$nI_n=(n-1)I_{n-2}\implies(2k+2)I_{2k+2}=(2k+1)I_{2k}$ innit

[flat frigate]

chlamydia

[urban eagle]

Ohhh

Ok ty

[safe radish]

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[signal cove]

hello

[safe radish]

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@signal cove Has your question been resolved?

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[toxic bone]

i cannot figure out how to make that solution point of f(1)=64

[worthy hemlock]

But you did it in the blue writing

You just need to plug in A now

[toxic bone]

that answer wasnt accepted... is it right then?

[icy lance]

might want (x+i)(x-i)

rather than (x^2+1)

[worthy hemlock]

For part A, it does say fully factored, and (x^2 + 1) factors to (x + i)(x - i)

[toxic bone]

i have tried both of those as answers... maybe i'll forwward it to my teacher and se whats up

right i hear ya, i figured i'd try as many options since it wasn't accepted as a correct answer

[icy lance]

2(2)(-4)=-16

not-8

so A=-4

[worthy hemlock]

[toxic bone]

you're absoultely right

right on thank you

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[severe marten]

Ten percent of Americans are allergic to ragweed. If a random sample of 200 people is selected, find the probability that 10 or more will be allergic to ragweed. Use Normal Approximation.

[severe marten]

I got the mean (20) and the standard deviation (18) but I am having trouble with the continuity correction and the rest of the problem.

<@&286206848099549185>

[safe radish]

@severe marten Has your question been resolved?

[cunning shard]

What’s your z score?

[severe marten]

the z score i got was .72 but when i input it into my Answer box it says it is wrong

[cunning shard]

you have found mean and S.D through binomial approximation?

[severe marten]

Yes

[cunning shard]

I suppose you are looking for P(x>=10)

[severe marten]

yes

[cunning shard]

ie P(z>(10-20)/18)

P(z>-0.555) right?

[severe marten]

yes

[cunning shard]

ie 1-P(z<-0.555)

using symmetry of normal curve

[cunning shard]

This can be found from normal tables

[safe radish]

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[bold hornet]

looking at the second line

for the last *x at the end

when i bring it forward does it make the sign positive since it’s a -x

[granite idol]

yes

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[safe radish]

@velvet kettle Has your question been resolved?

[plucky elk]

Use the fact that sin(a) is positive in that quadrant and what you know about the domain of inverse cosine

[velvet kettle]

domain of inverse cosine is 0 to pi

so the range of sinalpha has to be o to pi

umm yea

idk lol

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[young elk]

I need help understanding what I got wrong on one of my math assignments so I can be prepared for the test

[cunning shard]

[young elk]

I understand generally what I got wrong here

Not that much here

Here I did the problems multiple times is it just how I put my answers

<@&286206848099549185>

[jaunty terrace]

ill try to help..?

[young elk]

ty

[jaunty terrace]

im sorry but i can never read anything in photos

[young elk]

oh uh

I can retake them

on what I got wrong

[jaunty terrace]

ok

[young elk]

Number 3 and the one I got wrong on 6

[velvet kettle]

Oh smart

[young elk]

I hope that’s clearer

[velvet kettle]

But sinx=cos(pi/2 -x) as well though and they both fit in domain

[young elk]

I retook them

[lean otter]

no pi/2 is not in domain check the que

the domain is greater than pi/2 and less than pi

[lean otter]

u are substracting from pi/2 which is below the domain

[young elk]

yo <@&286206848099549185>

pls

[vapid epoch]

Yes what?

What is your question

[young elk]

I just need help understanding what I got wrong

[young elk]

on this I kinda know

[vapid epoch]

What thing?

[young elk]

this not really

[young elk]

and this

[young elk]

some pre-calc questions

[vapid epoch]

What grade is this?

[young elk]

10th

[vapid epoch]

What system?

[young elk]

like what class

[vapid epoch]

No what country

[young elk]

oh us

[vapid epoch]

We are learning this soon in 11th grade

[young elk]

O ok

[vapid epoch]

Please find someone elseeee

<@&286206848099549185>

I don't know the formula

Does this ring a bell?

@young elk

[young elk]

Ya, but it doesn't rlly involve this lol

[vapid epoch]

Which one?

[young elk]

Trig in general

[vapid epoch]

Cos 0= 24/hypotenuse

It's the cross product

[young elk]

oh this is 7

mb mb

ya but sin < 0

so cos and sin gotta be negative

same thing with csc and sec

and it's in Quadrant III

I understand that

[young elk]

idk wtf my teacher wanted me to do for this

<@&286206848099549185>

[safe radish]

@young elk Has your question been resolved?

[young elk]

<@&286206848099549185>

[young elk]

<@&286206848099549185>

I only need help with one thing

[young elk]

.

.close

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[cold mirage]

h = 1 + 15t - 5t^2 how do I find the maximum and minimum points of the equation?

[urban eagle]

Minimum and maximum points occur when $\frac{dy}{dx} = 0$ as the gradient is 0

[flat frigate]

ЖѲTЇЇC

[urban eagle]

Or complete the square

$$h = 1 + 15t - 5t^2$$ \ $$h = -5(t^2+3t) + 1$$ \ $$h = -5[(t+\frac{3}{2})^2 - \frac{9}{4}] + 1$$

[flat frigate]

ЖѲTЇЇC

[safe radish]

@cold mirage Has your question been resolved?

[cold mirage]

-5*3t = -15t, no?

[cold mirage]

how would you do it this way? is it differentiation?

[safe radish]

@cold mirage Has your question been resolved?

[safe radish]

@cold mirage Has your question been resolved?

[crisp kiln]

@urban eagle is t only an integer

[urban eagle]

Yea

$$\frac{dh}{dx} = 15-10t$$ \ $$\frac{dh}{dx} = 0$$ \ $$15-10t = 0$$

[flat frigate]

ЖѲTЇЇC

[crisp kiln]

Hold on

Are there multiple solutions?

I have one

[urban eagle]

No it’s a quadratic

So there’s one turning point

[crisp kiln]

t=0, h=1

[urban eagle]

When t = 0 the gradient is 15 so that’s not a turning point

[crisp kiln]

That’s what I got

[crisp kiln]

Oh ok

[cold mirage]

integers can be negative

[cold mirage]

im confused..

[safe radish]

@cold mirage Has your question been resolved?

[safe radish]

@cold mirage Has your question been resolved?

[safe radish]

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[mystic marsh]

so im a bit confused with this answer key

so the problem says 'that has -2, 2, and sqrt(5) as zeros such that f(3)=-60. right?

but this part of the answer key also has -sqrt(5) as a zero

which is according to the problem not true..

im confused why the answer key would do this

[fading mirage]

looks like it was just missed and was supposed to be included as part of the question?

[mystic marsh]

ah i see

opps i guess i missed this shoot

lol

thank you for your help:)

[fading mirage]

typos will be the end of us all

np!

[mystic marsh]

.close

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[honest bear]

hi

[honest bear]

uh

write the equation of the line that is parallel to the y-axis and passes through the point (-7,2)

how do i do that question

i have exam on this tmr

oh god its midngiht

how am i staying up this late on one question

;-;

YES

COTTON

MY SAVIOR

wait

is that how i spell it

[tulip pivot]

We know that to define a unique line all we need is a point and a direction. Both are given here.

[honest bear]

they are?

[tulip pivot]

So equation of line will be
x- (-7) = 0 or x=-7.

[honest bear]

um

[safe radish]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[honest bear]

could you explain how this happens

[tulip pivot]

Yes.

[honest bear]

in a more expanded way

i am very stressed rn

[worthy hemlock]

The problem says parallel to the y axis, what is the slope of that?

[honest bear]

uh

0?

my teacher didnt even teach us this

and shes testiung us on it

[worthy hemlock]

I doubt that

[honest bear]

bell rung before she could finish

[tulip pivot]

See, line is given to be parallel to y axis. So any line parallel to y axis is of the form x = k. Here given point (-7,2) should satisfy the line. So k cones out to be -7.

[honest bear]

so uh

[tulip pivot]

Is this understandable?

[honest bear]

k is slope?

right

[worthy hemlock]

No

[honest bear]

waht

[worthy hemlock]

The general equation of a line is y = mx + b

Right?

[honest bear]

yeah

slope intercept form

uh

[worthy hemlock]

What is the slope of the y axis?

[honest bear]

thats what im confused about

[worthy hemlock]

The slope of a vertical line is undefined

[honest bear]

ohhh yeah

[worthy hemlock]

Because vertical lines, are in the form of x = ...

[honest bear]

0

[worthy hemlock]

And it passes through (-7, 2)

[honest bear]

um

uh

so uh

wait

2/-7

ok yknow what

ill ask my teacher tmr

its too late for this

too late for me to retain any info

[tulip pivot]

Good. I think that may be best.

[honest bear]

whatrs the command again

.close

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[honest bear]

o

.close

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[rocky beacon]

when finding the area can i just do $$ \int_{0}^{f(P)} f(x)-g(x) dx $$

[flat frigate]

___

[rocky beacon]

where the linear equation is g(x)

[west hedge]

i think so

[plucky elk]

What does f(P) mean to you

[safe radish]

@rocky beacon Has your question been resolved?

[rocky beacon]

it’s a number and i solved it

it’s 5 or smth

sorry not supposed to be f(P)

just P

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[lean otter]

You just need to use the formula.

[fervent bane]

tell me

[lean otter]

Diagonal = root of l^2 +w^2 + h^2

Substitute the values and you'll get your answer

[fervent bane]

what is it?

[lean otter]

Huh

Calculate yourself? 😓

[fervent bane]

what is the answer?

naw

it will be more helpful

and understanding if I get the answer first

[unreal ingot]

Square root of 89

[lean otter]

What

[unreal ingot]

Jk

[lean otter]

89?.

Isn't it 93

[unreal ingot]

Square root of 93

Ye

[lean otter]

U got me

😭☠

[fervent bane]

ty yall

.close

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[umbral nymph]

Hi i need some help with a 3x-15=5x+15
(is it even possible)

[quasi bison]

yes it is

this is a linear equation

[umbral nymph]

Ah okay

[quasi bison]

do you know how to solve linear equations in general?

[umbral nymph]

Isnt it where i want the X on the left side and the numbers on the right

example: x=5

dont know how to explain it

but i have an idea of how to do it

[quasi bison]

well if you have an idea of how to do it, then why don't you do it and show your work?

[umbral nymph]

I can try

3x-15=5x+15
3x- 15+ 15 = 5x+15 + 15
3x=5x+30
3x-5x=5x-5x+30
-2x=30
x=15

@quasi bison

[quasi bison]

everything is correct up until the last step

double-check that

[umbral nymph]

What do i need to do instead then?

Don't i just divide by 2?

oh wait

i gotta divide by -2

right?

@quasi bison

or do i have to do something else

[quasi bison]

yes you need to divide both sides by -2

no you don't need to do anything else but if you insist again i'll come up with something stupid for you to do

[umbral nymph]

Tanks

.close

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[white swallow]

How do equation [1] got to equation [2]

[frigid locust]

sin^2 theta = 1 - cos^2 theta
using the a^2 - b^2 formula , u can simplify sin^2 theta / (1+cos theta) to 1-cos theta

and from 1 to 2
They just multiplied and divided 1+cos theta

[white swallow]

Oh okay that makes sense to me now

Thanks

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[bronze gate]

Well

[bronze gate]

I don't know what to do

Like idk if I'm just stupid and don't understand but

[safe radish]

@bronze gate Has your question been resolved?

[bronze gate]

<@&286206848099549185>

[quiet juniper]

Could always be both

anyways a compound inequality is of the form $a \leq h \leq b$, where $h$ is something like say the height

[flat frigate]

992qqoloy

[quiet juniper]

As for the last one does the problem tell u the height of the summit?

Like somewhere earlier

Cus u need it for the last part

[safe radish]

@bronze gate Has your question been resolved?

[safe radish]

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[lean otter]

how to find this
Sn = 2+5+12+31+86+.....

[vale horizon]

what are u tryna find?

[lean otter]

Sn

the sum

till n terms

[cyan shard]

I figured out the pattern here tho

Its prolly an AGP

[lean otter]

it is

i tried doing it like this

i think im wrong

fdkfodfop help

[lean otter]

uhm

[cyan shard]

Or is it not supposed to b done this way ?

[cyan shard]

Lemme chck the method once
Seems like i forgot
Ik this method

[lean otter]

yea i wanna proceed with this

but idk if im going in the right direction

[cyan shard]

I'll chck
A min

[lean otter]

dk how to proceed from that last step

ighjt

[cyan shard]

Hey
The second step itself seems wrong

I'll send u my notes where i hav the method written

Bt need to find out the pattern first

[lean otter]

ohh

but in my screen shot

I got it to a gp summation

4+12+36

[cyan shard]

But
U need to keep the Sn somewhere

Otherwise
Wht will u even solve for ?

[lean otter]

sigma Tn is Sn right

like that

[cyan shard]

So, for that
Need to multiply the whole series with the common ratio
Nd thn subtract so tat the sn still remains

[cyan shard]

Wht did u get as Tn ?

[lean otter]

tn is getting canceled lol I'm getting Tn-1

[cyan shard]

Tat is wht
It shud not get cancelled tat way

[lean otter]

hm

alright

[cyan shard]

M tryanna find it
I'll let u know

[lean otter]

kk

[cyan shard]

Idk if m makin it complicated

<@&286206848099549185>

@lean otter
Check this out

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@lean otter Has your question been resolved?

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[fervent prism]

Can someone help me decipher what this question is asking of me, I dont want to look at the answer just yet

OC and AB are vectors not lines...

and i can find the common perpendicular of the 2 vectors using the cross product?

Im struggling to understand what equation they want me to make

[safe radish]

@fervent prism Has your question been resolved?

[safe radish]

@fervent prism Has your question been resolved?

[safe radish]

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[lean otter]

,rotate

[lean otter]

Is there a way to simplify the term in the brackets

[hasty wagon]

there's a thing called
https://en.m.wikipedia.org/wiki/Arithmetico-geometric_sequence

dunno if this helps

[lean otter]

Oh yes

I knew of this tbh haha

Thx for reminding

Ill wait a bit, im working a thing out

. close

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[thorny juniper]

<@&286206848099549185>

I need help to solve this limit using L'hopital

[vague flare]

my eyes hurts from seeing this

[thorny juniper]

mine too ngl

[zinc hornet]

Use the fundamental theorem of calculus and chain rule on the top and either the product rule or combine it into x^3/2 for the bottom

[thorny juniper]

okey, will try it. Ty ❤️

.close

[safe radish]

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[true flame]

Adding and subtracting dissimilar algebraic expression

[true flame]

I don't get this shi i need helpppp

[thorny juniper]

Equal the denominators by cross-multiplying the numerators. Then solve algebraically

[true flame]

@thin bridge is that wrong?

[thin bridge]

very poor wording and inappropriate use of the term cross multiply

do you know how to simplify sums/differences of basic fractions?

[true flame]

yes

[lean otter]

not their fault either, its what many teachers use it nowawdays :(

[thin bridge]

e.g
$$\frac17 + \frac23$$

[flat frigate]

ℝam()n()v

[thin bridge]

how would you approach simplify that?

[true flame]

is that 3 over 10 right?

my brain is not working anymore im studying for like 6 hours and i am grade 8

i'll do this shi tomorrow in the morning cause its already 12:47 am here

,close

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[glass radish]

please help me with this

[safe radish]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[glass radish]

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

[glass radish]

1

[safe radish]

@glass radish Has your question been resolved?

[quiet juniper]

Expand and set coefficients equal

[safe radish]

@glass radish Has your question been resolved?

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[supple shore]

I don't know how to calculate $\sum k=1$ to n of $k*x^{k}$ ? with another method that seeing it's the derivative of $\sum k=0$ to n of $x^{k}$

[flat frigate]

phoestaclies

[supple shore]

sorry for my latex don't know how to write the sum

[quasi bison]

$\sum_{k=1}^n k x^k$

[flat frigate]

Ann

[quasi bison]

this?

[supple shore]

yes

ty

[quasi bison]

so you've seen the method with differentiating wrt x and want another?

[supple shore]

yes if possible, I don't know if we can do this with another method

[quasi bison]

ight

right*

yeah i can think of one, hold on

[supple shore]

I'm a beginner in sum and product

[quasi bison]

$\sum_{k=1}^n kx^k \overset{(1)}= \sum_{k=1}^n \sum_{j=1}^k x^k \ \overset{(2)}= \sum_{1 \leq j \leq k \leq n} x^k \ \overset{(3)}= \sum_{j=1}^n \sum_{k=j}^n x^k \ \overset{(4)}= \sum_{j=1}^n \sum_{k'=0}^{n-j} x^{k'+j} \ \overset{(5)}= \sum_{j=1}^n \paren{x^j \sum_{k'=0}^{n-j} x^{k'}} \ \overset{(6)}= \sum_{j=1}^n \paren{x^j \cdot \frac{x^{n-j+1} - 1}{x-1}} \ \overset{(7)}= \sum_{j=1}^n \frac{x^{n+1} - x^j}{x-1} \ \overset{(8)}= \sum_{j=1}^n \frac{x^{n+1} - x^j}{x-1} \ \overset{(9)}= \sum_{j=1}^n \frac{x^{n+1}}{x-1} + \frac{1}{1-x} \sum_{j=1}^n x^j \ \overset{(10)}= \frac{nx^{n+1}}{x-1} + \frac{1}{1-x} \cdot \frac{x(1 - x^n)}{1-x} \ \overset{(11)}= \frac{(n-1)x^{n+1} + x}{(x-1)^2}$

assuming i didnt fuck up any arithmetic

augh enter too soon

[supple shore]

I don't know what to do when I have a multiplication inside a sum and also a sum in a product

[quasi bison]

there is no panacea for that

[flat frigate]

Ann

[quasi bison]

ok yeah done i think

summation switching black magic

[supple shore]

ye ty I have the method now 🙂 ok I see you

it's just the tricks when you make at the beginning the double sum I didn't think of that ty

👍

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[safe radish]

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[jaunty tiger]

why is the answer B instead of A?

[jaunty tiger]

<@&286206848099549185> thankuu

[toxic shoal]

i think you have to account for the fact that if you met an english woman first, this alters who is remaining in the room

what you calculated is correct if you could meet the same person twice, i think

[jaunty tiger]

ohhhh yeah that makes sense

hmm i originally thought that’s why we use hypergeom in these kinda scenario when it’s not independent

[toxic shoal]

i never learned the hypergeometric distribution

[jaunty tiger]

ohhh did u manage to get B as answer?

[toxic shoal]

i didn't actually compute it the right way. you would have to calculate P(first person is an english woman) * P(second person is an american | first person is an english woman)

maybe if you do that you'll get (B) :0

i was just lazy and figured i could point out what seems to be the flaw in your reasoning

[jaunty tiger]

oooo yuppp lemme try

[jaunty tiger]

actly why isn’t it jus the second probability

[toxic shoal]

you want to find P(first person is an english woman and second person is an american). then you use the fact that
P(A n B) = P(A)P(B | A)

[buoyant shadow]

you just do 30/100*45/99

[toxic shoal]

yeah. and that's 3/22 :o

[jaunty tiger]

ohhh i see thanks! wait do u mind if i ask when do u use hyper geometric distribution is this qn a case of it? cuz i have trouble identifying when to use it — here seems like finite population without replacement?

[toxic shoal]

i wikipedia'd it. if you wanted to find the probability that the first 2 people are american women, without "replacement" then i think you could use it

but in this case, what counts as a success changes between draws

[jaunty tiger]

ohhhh okie that makes sense

[toxic shoal]

the hypergeometric distribution is a discrete probability distribution that describes the probability of k successes (random draws for which the object drawn has a specified feature) in n draws, without replacement, from a finite population of size N that contains exactly K objects with that feature, wherein each draw is either a success or a failure.
So if you had 10 american women in a population of 100 and you wanted to find the probability of 2 successes in 2 draws, you could do it

with K = 10, N = 100, k = 2 and n = 2

[jaunty tiger]

oya i gettit

[toxic shoal]

[jaunty tiger]

thanks ves :D

[safe radish]

@jaunty tiger Has your question been resolved?

[safe radish]

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[silent gulch]

<@&286206848099549185>

1. ACB 2. DA and EB 3.DE 4.EF and DF

Are these correct?

[last heath]

!15m

[safe radish]

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.

[silent gulch]

Ok

I am sorry

<@&286206848099549185>

[stable willow]

Hi

[silent gulch]

Yes

[stable willow]

Yes

[vapid folio]

Well

for 1

DEF is a side

so what side is on the opposite

[silent gulch]

ABC

[silent gulch]

ABC

Is the right way

[vapid folio]

yeah thats 1

[silent gulch]

And 2 is correct right?

[vapid folio]

yeah

[silent gulch]

3 i need help

And 4 too

[vapid folio]

3 is right

df and ef too I think

maybe

not an expert at this

[silent gulch]

For no

4 right?

[vapid folio]

3

[silent gulch]

Oh

[vapid folio]

whats the definition of parallel

actually no

[silent gulch]

Lines that have the same

[vapid folio]

i Think ur right for all of em

[silent gulch]

Ye

It is only

DE

And 4?

[vapid folio]

I think

Im not sure for no 4

Never heard of skewed line segments in my life ;-;

[silent gulch]

—

Shoudl i

@