help-23

[knotty pier]

factorise numerator

[slate violet]

So it will be (n+8)(n-8) right?

[knotty pier]

yes

cancel n-8 now

ull be left with n+8

[slate violet]

Right

[knotty pier]

tht solves the question

[slate violet]

So the value is 16?

[knotty pier]

yes

[slate violet]

Ohh thank you

[knotty pier]

np

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[rough storm]

!status

[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 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

[harsh sinew]

1

[rough storm]

the integral is the area 'under' the curve you are typically taught, but i assume you're confused about the fact that the area under this curve wouldn't make sense?

think about it more like the area between the curves formula then. f(x)-g(x) where g(x)=0 (y=0). note that this makes this figure make sense

https://tutorial.math.lamar.edu/classes/calci/areabetweencurves.aspx

[harsh sinew]

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[unborn void]

can someone explain this? how did i get 2x-1

[old chasm]

ok, so you understand the $2x^2+3x-2$ part?

[flat frigate]

᲼

[old chasm]

if you understand where that came from, you factorize the $2x^2+3x-2$. One way to do this is to solve the general equation for polynomial $(ax+b)(cx+d) = acx^2 + (bc + ad)x + bd$. Here, you have $ac = 2, bc+ad = 3, bd = -2$.

[flat frigate]

᲼

[old chasm]

You can start from the $ac = 2$. Usually, it will be something like $a = 2$ and $c = 1$.

[flat frigate]

᲼

[old chasm]

Then the last part, generally to get the product that is negative, one should be positive and another will be negative. You can try $b = 1$ and $d = -2$ for example and see whether this works or not. If not, you can try other combination of $b$ and $d$ that will yield the product of -2.

[flat frigate]

᲼

[old chasm]

You should get something like $a = 2$, $b = -1$, $c = 1$, $d = 2$ as your final answer. You can solve the equations formally (but it somewhat requires you to solve another simpler quadratic equation) or guess the right number to get there.

[flat frigate]

᲼

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[grim plover]

What does it mean to say 'x is a rational function of y'

[grim plover]

does it mean x(y) = P(y)/Q(y)?

Original problem: if $(ax^2 + c)y + (a'x^2 + c') = 0$ and $x$ is a rational function of $y$ and $ac < 0$ then which of the following is true?

[flat frigate]

rak³en

[grim plover]

Looking at the solution rn, how the hell is x rational? its a rational function 😐

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[grim plover]

<@&286206848099549185>

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[lean otter]

it means that x = f(y) where f(y) is any function in the form of k/g(y), where k is a constant term and g(y) is a non-rational function

[grim plover]

hmm

still

g(y) could be irrational

[lean otter]

that's what I say

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[crisp gyro]

How would i do this question? ik i have to use the trapezium rule and find y_0, y_1 y_2 etc but the vertical strips is throwing me off like usually its horizontal strips right?

[narrow ridge]

huh

somehow, i feel like actually getting the area is easier

[granite idol]

no, just split the x interval into 4 equal-width sections

[crisp gyro]

so the hieght is 8/4, but how do i get the y values?

[granite idol]

height is 8/4? what do you mean?

the y values are the heights

[crisp gyro]

so 17/4?

[granite idol]

you will have 4 sections. not all of them will have the same height

[crisp gyro]

how?

[granite idol]

because the function is not constant

I recommend you watch and understand this: https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-2/v/trapezoidal-approximation-of-area-under-curve

[crisp gyro]

i thought this is what is meant by strips

[granite idol]

how would that help you calculate the area under the curve?

[crisp gyro]

ye im not too sure how to use the trapezium rule on this graph

[granite idol]

watch the video, it should help

[crisp gyro]

ye ik how to use the trapizium rule, using the formula 1/2 h((y_0+y_1) + 2(y_1+y_2+y_n-1)) but how would i do it vertically?

[granite idol]

he does it vertically in the video. look at the screenshot

[crisp gyro]

so thats what its meant by vertical strips, i thought for some reason it meant that they are on the y axis

[granite idol]

no. vertical means up and down

[crisp gyro]

ok so i got y_0=17 y_1=5 y_2=1 y_3=5 y_4=17, now i just put it into the formula right?

[fathom adder]

there is a " + y_n " between the two last parentheses no ?

[crisp gyro]

ye i wrote it down wrong 1/2 h((y_0+y_n) + 2(y_1+y_2+y_n-1))

so i got an area of 112

[granite idol]

yeah

[crisp gyro]

apparently 112 is wrong

i did 8/4((17+17) + 2(5 + 1 + 5)) which got me 112

[granite idol]

what'd you get for the area of the first trapezoid

[crisp gyro]

i was taught to use this formula which is given in the formula booklet

[granite idol]

where is 8/4 coming from?

[crisp gyro]

bc we're intergrating from 8 to 0 and h = (b-a)/n so 8-0/4

oh i think i forgot to multiply by 1/2

ye im dumb

[granite idol]

h is simply 2, is it not

[crisp gyro]

ye which is also 8/4

thanks bro for the help, i managed to get the answer

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[dense wadi]

how did this become this

[fast badge]

are u asking about the equality or inequality?

[dense wadi]

how did this appear

[fast badge]

its k^2 + 4k^2

which is 5k^2

square root distributes over the 5 and k^2

leading to \sqrt{5} and \sqrt{k^2} = k

[dense wadi]

ahh tyt

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[earnest wharf]

Quick question, ive only been seeing the relative acceleration method in a crank and shaft examples (2 arms, 3 links) Is it also accessible to use it in for 3 arms, links and more?

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[cursive wing]

I need help on how they arrived at 1.25 x 10-3

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[stoic sage]

Can someone check this question for me, I’m getting the values of a and b wrong and the answer given should be x-99

[thin bridge]

you messed up your signs at the very end

**-**198 = 2b

you seemed to have forgot about that -

[stoic sage]

ooh right

[stoic sage]

thanks

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[candid ocean]

@proud galleon hi

[candid ocean]

You helped me before about the exponential growth and decay problems and i wanted to ask

what do i write for this percentage

because ik if it was like 0.08 then id write in the formula y=(0.92)^x

but this is 8.3

[granite idol]

.083?

[candid ocean]

oh

im kinda confused then

[candid ocean]

what would be the formula for this

y = a(b)^x

[proud galleon]

yeah it would just be [original] - decay

1 - 0.083

that what you'd multiply by every year

[candid ocean]

oh wait wait

ohh

[proud galleon]

so instead of writing (1 - 0.083)(1 - 0.083)(1 - 0.083)... however many times

you can just raise it

to the power of the no of years

so 5 in this case

(1 - 0.083)^5

[candid ocean]

ohhh yeah

[proud galleon]

I think they just want you to assume that the dollar was worth $1 originally

[candid ocean]

yeah

[proud galleon]

so it would be 1 x (1-0.083)^5

[candid ocean]

ok now my answer is correct bc i have the answer key

[proud galleon]

which just gives you the same thing anyways

yeah aight nice

[candid ocean]

omg ok tysm

🫶

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[gritty quarry]

I am not able to understand the question

If I had to find cubes with 2 sides painted I can solve that but I am unable to solve for 3 sides painted

[thin bridge]

do you have a Rubik's cube?

[gritty quarry]

Not right now

[thin bridge]

do you know what they look like?

[gritty quarry]

Yes

[thin bridge]

specifically which parts have 3 Stickers/colours

[gritty quarry]

Corners

[thin bridge]

yes

[gritty quarry]

Yea but in the question 3 sides are painted out of the six, but after this I can only find 1 corner with 3 sides painted

[thin bridge]

the wording is pretty poor but the way I interpreted it was that
each side and it's opposite was painted the same colour

[gritty quarry]

Yea in that way we will get 8 which is correct answer

I was thinking that only 3 sides were painted

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[dense wadi]

im not too sure why it is wrong

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@dense wadi Has your question been resolved?

[cloud citrus]

1/(2n) is not 1/(2 4 6 … 2n)

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[jovial linden]

I'm being told the answer is D when I have C which one is wrong? I just need to clear the air a bit

[solid perch]

who is telling you the answer is D???

It says they are offered a 10% discount if the bill is over 20$

not for how MUCH over 20$

so C should be correct

[jovial linden]

A friend lol

[jovial linden]

Ohhh alright thxx for clearance!!

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[oblique jacinth]

can someone help me i have no clue how to solve this

[oblique jacinth]

so i just add the corresponding numbers in each collum?

like 0+ -1 and 2+ 3 and so forth

wow im so confused 😭

it asks for D+E

i think im gonna try to find a youtube video

@lean otter is this correct?

i think it is im gonna submit 😅

nope 😭

wait its cus i did -5 +5 = 10

i sold

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[junior sapphire]

Problem #76, triple integral (cylindrical/spherical coordinate)

Should I use the cylindrical coordinate

How can I set up my triple integral

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[brazen parrot]

how do i draw this

[vale oriole]

anyways like I was saying, we should create 2 vectors say 'u' and 'v' for the speeds of the current and the boat respectively

vector u, the current, should have a vector of 4.5(cos340i+sin340j)

and vector v, the boat, should have a vector of 12(cosθi+sinθj) as we know the speed but not the angle

[vale oriole]

the angle 340 comes from converting the bearing of 110 into an angle used in unit circle.

we know that the resultant vector should have an angle of 235 (same as bearing of 215) since it needs to be travelling straight towards T

hence u+v=λ(cos235i+sin235j)

unrelated, but im going to eat a burger, lemme know if u still want help

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[vale oriole]

yo im back

[brazen parrot]

Yo im eating now ahhaha

[vale oriole]

oh

has everything upto this point atleast made sense?

[brazen parrot]

um naur..

can u draw pls

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[vale oriole]

what about that sentence dont u get?

[brazen parrot]

this is hwo i would draw the 110 degrees bearing

.closed

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[dreamy kestrel]

Hey

[dreamy kestrel]

I need help

How can I solve binomial expansion in calculator

There is obviously a way

[thin bridge]

wdym

like you want your calc to directly give you the full expansion of something like (2 + x)^7?

[dreamy kestrel]

Binomial theorem, I can only get the answers somehow

[dreamy kestrel]

Yes

[thin bridge]

well most calculators aren't capable of doing that

[dreamy kestrel]

Is there a way to only get the answers

[dreamy kestrel]

My one is the latest one

[thin bridge]

what model

[rough storm]

what do you mean by 'the answers'

[dreamy kestrel]

Casio Fx 991ex

[dreamy kestrel]

(2-x)^6 . I have to expand this so theres got to be a way where I can get the binomial answers like 64x + 192x^2 + 279x^3

[old chasm]

you can calculate each individual coefficient manually as factorial is probably implemented in your calculator

and your calculator definitely can calculate this

[rough storm]

some calcs even just have a choose/combination function

[dreamy kestrel]

Manually, but theres a table option in my calc. WIll it work

[thin bridge]

you'll have to check the manual

[dreamy kestrel]

How

[old chasm]

well, you said to use binomial expansion. Your calculator should have a function to calculate binomial coefficient (also known as nCp button)

or nCr or something C something

[dreamy kestrel]

Yes

There is

[old chasm]

yes. That should give you the coefficient you want. Look at the manual on how to use that function and you can easily calculate each coefficient

The rest is your carefulness on the exponent term. You need to iterate all possible combinations (which, again, using Binomial expansion, you should be able to iterate to all possible one)

[dreamy kestrel]

Thanks

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[median tangle]

is there smth wrong with this? especially part c

[median tangle]

this is the question

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[ebon elbow]

How to solve
2sinx + secx = 4cosx

[ebon elbow]

For -Pi<x<Pi

.close

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[hard crest]

no, you may not constantly close and reopen help channels.

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[thin abyss]

.help

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[thin abyss]

hi i have some doubts

[thin abyss]

how do i ask for help

the question is, let a polynomial px when divided by x -1, x -2, x-3 leave remainder 4, 5, 6, respectively. if px is divided by (x-1)(x-2)(x-3) the remainder is Rx. find R(100)

please help i have a test tomorrow

[indigo birch]

let p(x) = (x-1)(x-2)(x-3)g(x) + r(x)

since r(x) should be a lesser degree than (x-1)(x-2)(x-3)

r(x) = Ax^2 + Bx + C

Now let x= 1, 2, 3 and solve for a,b,c

then let x = 100

[safe radish]

@thin abyss Has your question been resolved?

[thin abyss]

can tpu soove

you solve

[indigo birch]

ay

cmon

[indigo birch]

you can do it ureslf

its not hard really

[thin abyss]

im not able to bruh

i wouldve

[indigo birch]

you can solve equations like x+y = 2 x-y=9?

[thin abyss]

yes

[indigo birch]

ok its the same thing

but with three variables

and three equations

@thin abyss got it?

[thin abyss]

trying

yeah okay ill do it now

thanks

.close

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[kindred sentinel]

can somebody help me with c, e and f?

i don't know where to get started

[indigo birch]

there is an alternating sign so you should use (-1)^n

[kindred sentinel]

the numerator is always one yeah

but what about the denominator?

[indigo birch]

not rly

it alternates from 1 and -1

[indigo birch]

thats just n

[kindred sentinel]

ooh

[indigo birch]

like for c

the answer is (-1)^n/n from 1 to 100

you see why now right?

you have to look for patterns

[kindred sentinel]

wait

cuz this is the answer

[indigo birch]

ya what i wrote is the same lol

2 * 1/n = 2/n right?

[safe radish]

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[eternal creek]

I don't know how to show the additive identity, or in otherwords the zero

The f + g = 0+0

Combine lambda and the last two steps are straight forward

[obtuse jackal]

the zero is just the constant function equal to 0 ?

[eternal creek]

Exactly, but why does b have to be zero for itnto be a subspace

[obtuse jackal]

look at the stability requirements

[eternal creek]

Im unsure what that is

[obtuse jackal]

characterisation of a subspaces: what properties must they verify

[eternal creek]

Yes it has to contain the zero element

The only way would be if b is zero???

[obtuse jackal]

that's one argument yes

[eternal creek]

But if b is zero then f is zero?

Because the integral can't be non zero anywhere?

[obtuse jackal]

looks poorly worded

[eternal creek]

I mean if f is nonzero anywhere on 0,1 then b would be nonzero

[eternal creek]

I'm just trying to understand the argument behind it that's all.

Thanks!

.close

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[obtuse badger]

hi

[fair fossil]

what is your question

my i

ask

[obtuse badger]

hold up

how to finde the funkson f(x)

[oak ibex]

find the slope/gradient

[obtuse badger]

?

[fair fossil]

what is funkson

[oak ibex]

function

[obtuse badger]

yes

[oak ibex]

y = mx + b

find m

[obtuse badger]

?

[oak ibex]

looks like i'll be needing google translate for this

[obtuse badger]

how to solv

[oak ibex]

f(x) is a linear function

or atleast it appears to be

[safe radish]

@obtuse badger Has your question been resolved?

[lean otter]

y = mx + b

First, what's b?

[obtuse badger]

?

[lean otter]

y = mx + b
m = Slope
b = y intercept (when x = 0)

Does that help?

[obtuse badger]

no

[lean otter]

Hmm okay teaching time ✨
The formula I am using is called slope intercept form, as the name suggests you need a slope and a intercept (the y intercept). By using slope intercept form we can make a linear function identical to that one

First we can find the y intercept, which because you have a graph doesn't even require math to do

What is y when x = 0, or what is y when the graph touches the x axis

[obtuse badger]

.close

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[tidal yarrow]

Hi I cannot figure this one out

could someone help me out plz

<@&286206848099549185>

[lean otter]

!15mins

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[trail otter]

How can i split $\bar{Z}=\frac{Rj\omega L}{-\omega^2 RCL+j\omega L+R}$ into real and imaginery part?

[flat frigate]

Slowaq

[safe radish]

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[rustic token]

its so basic and yet

i stillc ant get it right

ive learned it before but i cant remember

ive resorted to joining this server

[faint seal]

one method you can use for this is just to solve both linear equations simultaneously

but there's a shortcut here

[rustic token]

i amanged to get uh

660/47

or smthin

[faint seal]

no

[rustic token]

oh wait cant i just

no that doesnt

[faint seal]

just?

verbalise

[rustic token]

brain is

working but not working

doesnt make sense

i dont know why i c ant solve it anymore

ive done it before

so like how d o isolve it then

for future cases

[faint seal]

in this particular question you can simply add the two equations given to you

[rustic token]

Oh my god

im

[faint seal]

that gives you the exact expression you're looking for

[rustic token]

so stupid

IM DONE

alright thanks

hold on wait

my sister has a similar question here

-4x + 6y = 9
-2x - 7y = -8
-2x + 13y = ?

[faint seal]

here you can subtract

[rustic token]

I KNEW IT

okay

so

to solve those, either add or subtract?

[faint seal]

it depends, but I guess that might be a pattern

[rustic token]

huh

so in general whats the method

aside from those cases

[faint seal]

well you have two linear equations

that's enough for you to just solve for x and y explicitly

[rustic token]

when i tried, i just

couldnt get it

even though its so basic

i forgot it all idk how

nvm

figured it out finally

thanks

[safe radish]

@rustic token Has your question been resolved?

[safe radish]

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[grave ridge]

.close

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[kindred slate]

how do u do part b

using the possion process, not the random variable

[fast badge]

it's independent

so the fact that no defect occured in first 2000m

is irrelevant

[kindred slate]

yh

wait

[fast badge]

even for a poisson process

[kindred slate]

how do u use this formula

[fast badge]

yeah

that's the point

it doesnt depend on s

where s is supposed to be 2000 here

you only need to take t=500 into account

yeah that works

[kindred slate]

surelu i should still get the same answer

[fast badge]

yes

although

[kindred slate]

the answer is e^-1 tho

[fast badge]

not sure if you did the lambda correctly

yeah because the lambda is 1/500

it says 1 defect every 500m

so lambda is 1/500

[kindred slate]

oh why?

[fast badge]

that's what the defn of lambda is

it's the per timestep rate of seeing the event

if you see 1 event every 500

[kindred slate]

so is each time step here 1 metre?

[fast badge]

yeah

[kindred slate]

ohh

[fast badge]

yeahh

[kindred slate]

thank u

[fast badge]

sure yw

[safe radish]

@kindred slate Has your question been resolved?

[kindred slate]

hey u still there?

did a question but dont have a mark scheme so was wondering if u could check if i did it correct if thats ok

[kindred slate]

.close

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[jolly basalt]

What is the height of the Smallest possible cone that can contain a sphere with the radius of 6 units

[jolly basalt]

smallest as in volume

[jolly basalt]

this was shown in a recent exam in which i failed and no matter how much i research i cant find a way to solve it

the topic is derivative

[glass carbon]

Drawing would be a key

[jolly basalt]

i really tried drawing, i even tried to make it into analytic plane

idk i cant seem to do it

i even tried writing the function for such a circle

[glass carbon]

Just a triangle and a circle inside would be sufficient

[glass carbon]

then similarity

[glass carbon]

yeah good

[jolly basalt]

what kinda similarity

cant see anything here

[glass carbon]

These two triangles

[jolly basalt]

hmm

[glass carbon]

You need a function for the volume which depends on one variable, r or H (let's say H is a height of the cone)

[jolly basalt]

similarity is a nice catch, i'll be back in 1-2 mins

i'll see if i can solve it from here

i tend to not use geometry in such questions idk why

[glass carbon]

Take your time.

[jolly basalt]

ohhhhhhhhhh

wait

i think i almost got it

something like this?

sorry for my awfully bad font

i tried to draw it with mouse

what i can do from here is

[glass carbon]

That's good

[jolly basalt]

leave r alone

[glass carbon]

Focus on r^2.

Since you don't need r

[jolly basalt]

ohhh

right

cuz for the volume i just need r^2

well

do i just take the square of both sides

i might have done something wrong lol

[glass carbon]

it's fine

I rather wouldn't expand (H-6)^2

now

find r^2

[jolly basalt]

i did something like this, am i going in the correct path?

wait i think i managed to isolate r^2

with only H on the other side

[glass carbon]

yeah, all good!

[jolly basalt]

now i just multiply both sides with H/3

and then take derivative?

[glass carbon]

yup

[jolly basalt]

like this im assuming

oh god this is gonna take long

[glass carbon]

We should also make some assumptions for H and r (H - 6 > 0 and r > 0) then H > 6, but that's obvious in fact, if the height was less than 6 then it would be impossible to inscribe a sphere inside

[glass carbon]

36/3 = 12

[jolly basalt]

oh right lol

now to take the derivative..

[glass carbon]

It won't be that long

haha

remember that after this you will be looking for when d/dH = 0

so don't even try expanding the denominator

[jolly basalt]

so lets see

[glass carbon]

now equate the top to zero

[glass carbon]

You could take out H^2, but it's fine

by the way, you're fast

[jolly basalt]

im trying to be fast for u lol

answers dont contain 34

i might have done a math mistake

but i get the entire point so

that might as well be what matters

[glass carbon]

wait

[jolly basalt]

wassup

[glass carbon]

You wrote 24

[jolly basalt]

uh oh

[glass carbon]

Then answer is 24, I'm sure you'll get it

[jolly basalt]

yep

answer is 24

i found it

[glass carbon]

Unless you already did it, yeah

[jolly basalt]

lmao ty

this was pretty epic

also one of my friends just dm'd me

wow

they used a pretty epic way to solve it too

uhh

they used this

with here

thats also an epic solution

but i liked this one more

ty for all the help

is there a way to +rep u or something

[glass carbon]

Yeah, that's clever indeed

[jolly basalt]

yeah damn people like you and him are really smart

[glass carbon]

I don't think so, I'm a volunteer haha

[jolly basalt]

much much love, thank you so much <3 how do i close this ticket/channel?

[glass carbon]

.close

[safe radish]

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[vast warren]

does anyone know how to do this question step by step

[vast warren]

<@&286206848099549185>

[hardy lion]

!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.

[vast warren]

oh sorry, I'm new to the server

[hardy lion]

are you familiar with equations of the form $\newline
|z-z_0|=a$?

[flat frigate]

GarlicBredFries

[vast warren]

yes they represent circles right?

[hardy lion]

yeah but what are z_0 and a?

[vast warren]

half lines?

[hardy lion]

no

lets start with a

[tough briar]

(jfyi you can use $$ 1 + 1 = 2 $$ or \[ 1 + 1 = 2 \] to avoid \newline or \\)

[vast warren]

a is the radiuss?

[hardy lion]

im just gonna set z_0 = 0 for now

oh yeah thanks

yeah a is the radius

what about z_0?

[vast warren]

Z_o is a point on the circle

is it the centre?

sorry for late reply

[hardy lion]

yeah its the center

[vast warren]

so the centre of this circle is 2,5?

[hardy lion]

yes

if arg(z_1)=pi/4, what do we know about the line theta=pi/4?

[vast warren]

it is a half line

y=x

[hardy lion]

what is a half line

[vast warren]

a line that starts from a point

so it starts from z1

in this case

?

[hardy lion]

oh i know that as a ray

[vast warren]

a ray?

[hardy lion]

ray is half line

anyway

[vast warren]

oh ok

so same terminlogy

[hardy lion]

what do we know about the line going through the origin and the point z_1

lets say we extend the line through both points

[hardy lion]

yes

[vast warren]

not entirely sure, but is it that it forms a tangent to the circle

as z1 lies on circle

[hardy lion]

yup!

no other point on the circle can be below the line

so it must be tangent

[vast warren]

oh that makes sense

[hardy lion]

so now we have a center and a tangent line

do you have any ideas where to go from here?

[vast warren]

can we find the radius of the circle

from this

[hardy lion]

yes

[vast warren]

I'm not entirely sure how

but can we use the tangent

to find a perpendicular line

[hardy lion]

we draw the radius from the center to z_1

[vast warren]

or something

so from z1 to the centre

do we find the gradient of this line

[hardy lion]

yes

do you remember how to get the perpendicular gradient?

[vast warren]

you just find the reciprical

then opposite sign

[hardy lion]

yes

[vast warren]

is the gradient of the tangent just 1

oh yeah y=x gradient is one cuz pi/4 is 45 degrees

[hardy lion]

yes

[vast warren]

do you just use the y2=y1/x2-x1 formula

what would the coodinates of z1 be

would you just give it x+yi

[hardy lion]

dont worry about finding z_1 exactly yet

just use the fact its on y=x

so we know the gradient is 1

[vast warren]

oh so x and y are equal

in this case

the gradient of the radius is -1

[hardy lion]

yes

now we know one of the points on the line with the radius

[vast warren]

(2,5)

how do we find z1

from this

to get the value of the radius

[hardy lion]

we find where the two lines intersect

[vast warren]

so we we'll sub in the valu of z1 into this formula^

what do we put z1 as

[hardy lion]

you dont need that formula

you have line 1: y=x
and line 2 you know the gradient and a point on the line

[vast warren]

so equation of line is just y=-x

of radius

?

[safe radish]

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[dense wadi]

can i assume that this is 1/sqrtn

if i wanna know if this converges or div

[subtle python]

What do you mean by assuming it is equal ?

[dense wadi]

acc nvm

idk hwo to continue

ik its divergent but idk how to prove it

ill try

limit comparison

i got the right asnwer but i feel like i did bs 💀

anyway

.close

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[lime dust]

Integral test

[dense wadi]

is limit comparison also possible?

i used that

[safe radish]

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[dense wadi]

n^4 + 6/n^5 > n^4 /n^5

n^4 /n^5 = 1/n p is 1 therefore diverge

so the whole thing diverges

i just wanna know

if my thorught process is good

[empty gyro]

yep

[fast badge]

yes

[safe radish]

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[dense wadi]

ty!

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[visual ravine]

I just saw this monstrosity of a question in my homework,

1. Determine the equation of a rational function where its domain is {x € R} and has an absolute minimum point at (-3, -7/2) and passes through (-1,-2)

how would i even start with determining the equation

[visual ravine]

like would a derivative at -3 and sm like that help cause its the absolute minimum point

idk where to go after tho

[fathom jewel]

Why don't you use the vertex formula for a parabola

[visual ravine]

oh wait

ur a genius

ill try that

[safe radish]

@visual ravine Has your question been resolved?

[visual ravine]

bro im clueless

wait lemme redo the work

[fathom jewel]

Vertex formula: $\boxed{y = a(x-d)^2+e} \quad \text{ where } V(d,e) \text{ is the vertex point.}$

[flat frigate]

𝔸dωn𝓲²s

[fathom jewel]

You are given d and e.

So you only need to figure out a

the stretch factor

so that it passes through (-1,-2) effortlessly

[flat frigate]

𝔸dωn𝓲²s

[visual ravine]

oh shoot I mean im looking for an eq for that in terms of (ax+b)/(cx+d) if thats possible with this 😭

[fathom jewel]

well can't you assume cx + d = 1

but ok now that you mentioned

we would need the derivate yes

[flat frigate]

𝔸dωn𝓲²s

[fathom jewel]

We would have 4 information I think

[flat frigate]

𝔸dωn𝓲²s

[fathom jewel]

So you would basically get a system of equations

Seems really troublesome actually

[visual ravine]

seems too troublesome

[fathom jewel]

I don't know a current better approach

[visual ravine]

I think ill ask my teacher ab it

[fathom jewel]

I thought of a parabola because technically every polynomial is a rational function

[visual ravine]

yeah ic what u mean

[fathom jewel]

If we write it in the form f(x) = p(x)/g(x) where g(x) = 1

[visual ravine]

maybe it is that!

ig ill see if my teacher knows what hes doing w it

[safe radish]

@visual ravine Has your question been resolved?

[visual ravine]

.close

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[neat jay]

v+v = 1v+1v = v(1+1) = 2*v via distributive law be fine for part a?

[safe radish]

@neat jay Has your question been resolved?

[finite wasp]

Yes. Maybe state the properties that let you do those steps.

[granite idol]

you could start from 1 + 1 = 2, as well. then multiply by v on both sides, etc.

[neat jay]

ok ty

.close

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[rustic goblet]

#1240121287712575571 message

[rustic goblet]

.close

[safe radish]

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[safe radish]

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[brazen parrot]

how to do the first one

[granite idol]

just keep doing what you were doing, cancel stuff out

[brazen parrot]

its to many

[tepid walrus]

A lot of 55! / 53! cancels out

[brazen parrot]

wait 55!/53!

55 x 54 x 53!/53!

[tepid walrus]

Bingo

[brazen parrot]

oh

ok thz

[brazen parrot]

wait

do u know the second one?

rhe question after it

[tepid walrus]

I don‘t even know what branch of mathematics that would be, i just know how to work with factorials haha

[granite idol]

it's going to be a similar procedure

[brazen parrot]

how so

[granite idol]

replace n P r+1 with its expression, same with the RHS. solve for k

[brazen parrot]

this is what ive done so far

[granite idol]

denominator is wrong

[brazen parrot]

oh

is it n - (r+1)

[granite idol]

yes

[brazen parrot]

n - r - 1

now what?

[granite idol]

solve for k

[brazen parrot]

um... how ):

[granite idol]

it's just algebra. isolate k

[brazen parrot]

where is da K

[granite idol]

you are given the equation to solve

[brazen parrot]

im up to here

[granite idol]

now cancel what you can

[brazen parrot]

wat is there to cancel

wait

wait idk what else there is to cancel?

[granite idol]

it's similar to the first part when you had 55! / 53!

or whatever it was

[brazen parrot]

(n-r) x (n-r-1)!

C

?

[granite idol]

what is C?

[brazen parrot]

what do u mean what is C

[granite idol]

you said C here

[brazen parrot]

oh

i was trying to do a question mark

but i pressed C on accident

[granite idol]

but yes, k = n -r

[brazen parrot]

cuz im on my phone

[brazen parrot]

WOW

ARE U PROUD IF ME

that was so hardx

[granite idol]

good job

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[mild wigeon]

.reopen

The soccer player kicks a ball with an initial speed of 12 m/s with an angle of elevation of 15 degrees calculates:
the maximum height that the ball reaches
the moment when the increase arrives
the horizontal reach
(I only need the horizontal scope but that's the question)

[split fulcrum]

You know suvat?

[mild wigeon]

what is this?

xdd

sorry my math is terrible

[split fulcrum]

Your kinematic equations

[mild wigeon]

No, the truth is, I don't know that I speak Spanish and a little bit of English.

[split fulcrum]

Ok well do you have equations you use to solve these types of problems?

[mild wigeon]

mmm I don't really know xd but thank you very much for trying to help me, the truth is I'm very disoriented lately

[vapid lantern]

https://phys.libretexts.org/Bookshelves/University_Physics/Physics_(Boundless)/3%3A_Two-Dimensional_Kinematics/3.3%3A_Projectile_Motion

[mild wigeon]

thanks

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[swift torrent]

After proving cot theta = cosec 2 theta + cot 2 theta find the values of cot 15 cosec 15 and cot 7 1/2 as the question said . But how do i prove the last one cot 37 1/2 by using above results? Cot 37 1/2 = cot 5(7 1/2)... now what?

[willow reef]

double check the question to make sure its not cot^3(7.5)

oh wait no you do the compount angle forumla, cot(30 +7.5)

its an identity

[swift torrent]

If i do that i get a value that cannot be simplified to the requested answer

[safe radish]

@swift torrent Has your question been resolved?

[swift torrent]

No

Les hope a question likenwont appear

.close

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[plain herald]

I have no clue what this means

[silent token]

If John got the merit award and Joanne got the distinction award, that's one way
If Joanne got the merit and John got the distinction, that's another way, if Joanne got both awards that's another way
It's asking how many such ways there are with 25 unique students

[plain herald]

ohhh

that makes sense

what's the method for this

[old chasm]

each person can: get nothing, get certificate of merit, get certificate of distinction, and both

there are 25 persons, so...

[silent token]

Clarification: is the certificate of merit something that can be given to multiple ppl?

[topaz tree]

Can you post the full question with part a included?

[plain herald]

i don't think so

[plain herald]

part a is not relevant to this

[topaz tree]

So can certificate of merit and distinction both be awarded to the same person?

[plain herald]

im not sure

this the solution

this is*

i understand the last three but not the first one

[silent token]

Wait so a single person can't get both certificates

And exactly one of each will be given out

[plain herald]

its weirdly phrased

[topaz tree]

@plain herald So To give merit we've 25 choices

[plain herald]

Yes

[topaz tree]

and to give distinction we've 24 choices

[plain herald]

ohhhhh

[topaz tree]

because one already has merit

[plain herald]

im so dumb

[dull sequoia]

No you aren’t!!

Counting is hard (unironically)

[plain herald]

and then you multiply it to find the total?

[plain herald]

lol

[dull sequoia]

I’m not joking

[plain herald]

sometimes i dont notice things

and then it happens in exmas

which is not good

but anyways

thanks for the help everyone

[topaz tree]

Yep

De nada, Adios

[plain herald]

thanks

.close

[safe radish]

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[floral sable]

I cant prove it…. @versed bronze

[floral sable]

<@&286206848099549185>

[topaz tree]

hello

!status

[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 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

[floral sable]

1

I was confused

i dont know where to start

I try to let angle ABC to be X, and then angle BAC will become 90-X and then I stuck

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[balmy mountain]

Can someone please help me plot x in terms of y

[balmy mountain]

I want to get an equation like x = y smth

But it won't work

What am I doing wrong

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@balmy mountain Has your question been resolved?

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@balmy mountain Has your question been resolved?

[solid perch]

you can really do that with ti 84s lol

you kind of have to manipulate it

you have to either rewrite the function in terms of x

or you have to type it in pretending that the y is just written as x

[solid perch]

doing this would require more interpretation

but it would be simpler than rewriting the entire function

[safe radish]

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[dense wadi]

i might be missing smt but how do i converge test this

[lean otter]

alternating series test or uh

what was it called

[dense wadi]

oh i have to use either comparison or limit comp

[lean otter]

absolute convergence test

oh

uh

[dense wadi]

oh turns out

the answer is that i cant use limit comp or comparison

lmao

ty

.close

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[lean otter]

[dense wadi]

[hard crest]

good luck with that

[lean otter]

yea that doesnt work

alternating series test it is

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[obtuse badger]

2x + x(4x-2)-6

[obtuse badger]

i got x = 1,5

<@&286206848099549185>

[woven nova]

!15min

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[summer jackal]

the equation is equal to what ?

we need two side to resolve that

[woven nova]

thats not an equation mate