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Free neurons in development
Didn't know that we humans would be so small by then

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[merry crane]

When doing partial fraction do you have to do long division or does it not matter

[merry crane]

I just did an exam where the top heavy of the fraction was greater than the bottom

And I just did it

In terms of it degree

I got nice answers but I’m a bit lost because some people did long division

[dreamy sand]

Partial fractions are for bottom heavy equations

[merry crane]

Damn it

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[last saddle]

how do they get eqn 3v = 3ex - 3ey from v = e(x+y)?

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@last saddle Has your question been resolved?

[willow patio]

They literally multiplied both sides of the equation by 3.

v = e(x+y) becomes v = ex + ey and then we can multiply both sides of the equation by 3 to get 3v=3ex+3ey. Same equation, just manipulated a bit

[last saddle]

ah yeah mb

said -3ey in the mark scheme so was confused lmao

thx

[willow patio]

np, glad to help

[last saddle]

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[sharp obsidian]

just incorporate z-score in this

in any way

[rotund junco]

Yo I was wondering what should I do to practice my 4u exam. I already finished the cambridge and mastering mathematics and I was hitting trial papers but my partial fractions are weak. I was wondering if you had any advice

Sorry wrong chat

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[chrome depot]

Can someone tell me why is this true

[analog falcon]

is it sending?

[chrome depot]

Yes xD

For PI < alpha < 3PI/2

Like 7PI is 3 full circles + 180 degrees

And yes ultimately the angle will be in the first quadrant

But it still is not clear to me

[vale crag]

tan(x + pi) = tan(x), tan is pi-periodic

spam this 7 times

you get tan(x+7pi) = tan(x)

@chrome depot

[chrome depot]

Oh okY

And if it was sin for example

Then it would be sin(x+7pi) = sin(x+pi) with + or - whatsoever

Well most likely with - sign

[vale crag]

nah sin is 2pi-periodic

repeats every 2pi, not every pi

but same idea yes

@chrome depot

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[frail bane]

Hey

[proven leaf]

what's your question?

[alpine sable]

i think they're having problems factorizing

[proven leaf]

I figured but didn't give a lot of context 😅

[frail bane]

I would love to know everything about the technique to factor polinomials like this one, which would consist of factoring a trinomial into two trinomials

First, how would you get to factor this?

I have no idea how to get to this result

[vale wigeon]

some completing the square bullshit

[frail bane]

I've tried it. Still don't get it

[vale wigeon]

x^4 - 2x^2 + 1 - x^2

first three terms group into (x^2 - 1)^2

[frail bane]

But how could I go from (x² - 1)² - x² to (x² - x - 1)(x² + x - 1)?

[vale wigeon]

difference of squares

[proven leaf]

a^2-b^2=(a-b)(a+b)

[frail bane]

Ooooh

👌

Nice

Thank you

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[foggy mica]

Can someone explain how to algebraically manipulate the original inequality to the one in the answer

[alpine sable]

what does x > y tell you about x/y?

[queen cove]

As $x > y$ when you try to find $\frac{y}{x}$ from $\frac{x}{y}$ the inequality flips with the fraction to $x < y$

[ocean seal]

WeAreIngram

[foggy mica]

x/y is greater than 1?

[alpine sable]

keep in mind that x and y are negative

[foggy mica]

ohh so its less than 1

but still les than zero

sorry greater than zero

because the negatives cancel

[queen cove]

yes

[foggy mica]

ok

so what do you mean the inequaliy flips

can you give me like the before and after look of the inequality?

how do you know that y/x is greater than one?

ohhh

ok i get it

can you help me with this one as well then?

I understand how they got 6/5 but how did they get greater than 1

?

@eternal plover pls help

[surreal meadow]

what happens if x = 1?

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[shrewd ruin]

I have a vector question

[echo socket]

What do you think A^5 means?

[shrewd ruin]

doesn't it just mean A^5

or A * A * A * A * A

[surreal meadow]

what have you tried

[shrewd ruin]

not much

I don't know how to start

[surreal meadow]

what is A^5x in terms of y and A

use the fact that Ax = y

[shrewd ruin]

is it

y^5?

[mortal trellis]

no

y is a vector. it makes no sense to multiply that with itself 5 times

can you tell me what A^2 x is?

like you said, A^2=A*A, so A^2x = A*(Ax)

what can you do now

[shrewd ruin]

huh

[surreal meadow]

Ax = y

[shrewd ruin]

right

[surreal meadow]

multiply on the left by A

[shrewd ruin]

A(Ax) like that?

[surreal meadow]

on both sides

[shrewd ruin]

A(Ax) = Ay?

[surreal meadow]

yes

A(Ax) = A^2x

so we have A^2x = Ay

[shrewd ruin]

right

wait so

A^5x = A^4y?

[surreal meadow]

what did they tell you Ay was equal to

yes

[shrewd ruin]

x + 2y?

Ay = x+2y

[mortal trellis]

now multiply on the left by A again

[shrewd ruin]

A(x+2y) = A^2y?

[mortal trellis]

and what is the left side?

[surreal meadow]

yes

[shrewd ruin]

A^2y

is that not it?

[mortal trellis]

yes but can you simplify the left side

[shrewd ruin]

how will I do that

[mortal trellis]

can you multiply out the left side

[shrewd ruin]

how do I do that

I can't just to Ax + 2Ay

[echo socket]

Yes, you can

[shrewd ruin]

I can?

So Ax + 2Ay = A^2y?

[echo socket]

Yes

[shrewd ruin]

ok

well how can i use that to solve the porblemn

[echo socket]

Ax = y and Ay = x + 2y

So it turns into y + 2x + 4y

or 2x + 5y

[shrewd ruin]

right

how do we get A^5 then

[echo socket]

A^5x you mean?

Okay I will show the first half of the entire process

A^5x = A^4y = A^3(x + 2y) = A^2(Ax + 2Ay) = A^2(y + 2x + 4y) = A^2(2x + 5y)

Can you continue?

[shrewd ruin]

umm

how will i

wait

so A^5x = A^2(2x_5y)

• i mean

but then what will i do with that

[echo socket]

Yeah, now turn it into A(2Ax + 5Ay)

[shrewd ruin]

A(2Ax + 5Ay)?

we have to get A^5 in

ax + by form right?

[echo socket]

Yeah

[echo socket]

Ax = y and Ay = x + 2y, so that turns into A(2y + 5x + 10y) or A(5x + 12y)

So, now simplify 5Ax + 12Ay

[shrewd ruin]

how do i simplify that

do i just plug in

[echo socket]

Yes

[shrewd ruin]

Ax = y and Ay = x+2y?

[echo socket]

Yes

[shrewd ruin]

ok

thank you so much

.close

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[proper dragon]

Hi, I'm trying to solve this exercise, I have the solution but I don't understand what happens in the yellow box, how that x^2* + y^2 appears?

[tacit arch]

F dot k

[proper dragon]

aaaa

thank you

.close

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[spring condor]

I need help

[spring condor]

Why is this wrong

[gleaming granite]

it’s close but when you substitute a back into a=x^2, you need a plus or minus

[spring condor]

Why is 6i wrong

[gleaming granite]

how did you get 6i?

oh

[gleaming granite]

$\sqrt{-6} = \sqrt{-1 \cdot 6} = \sqrt{-1} \sqrt{6} = i\sqrt{6}$

[ocean seal]

keto11

[spring condor]

What

oh shoot yea I meant root 6i

But it’s still wrong

Why

[gleaming granite]

huh

,w roots x^4 + 4x^2 - 12 = 0

[ocean seal]

Results provided by WolframAlpha

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

Requested by keto11#8349

[spring condor]

Oh

[gleaming granite]

it should be one of the roots

[spring condor]

That’s weird

Photomath and Mathway said it was wrong

[gleaming granite]

are you entering it into an online thing?

[gleaming granite]

what did you type into mathway?

[spring condor]

The same question

It said the only solutions were root 2 and -root2

[spring condor]

Oh

Ok whatever guess I typed something wrong

Thank you!

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[hard aspen]

the "a piece of equipment.." one

[hard aspen]

would it be $600,000 - \frac{15}{100} x 600,000$ in the first year which is 510000

[ocean seal]

SirGareth

[hard aspen]

and $51000 - \frac{13.5}{100}510000$ in the second

[ocean seal]

SirGareth

[hard aspen]

and so on

or would the second year be $510000 - \frac{13.5}{100}600,000$

[ocean seal]

SirGareth

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[hard aspen]

<@&286206848099549185>

.close

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[placid venture]

I was able to do the first one. I am stuck on the second one as I believe I have not done that kind of things before

[tardy stag]

what's about it is unfamiliar or giving you pause? Have you done integrals in general before?

[placid venture]

I have not

or it was too long ago for me to remember

[tardy stag]

ah okay well you'll probably want to review or relearn that on a simpler problem first

[placid venture]

how do you read this part?

[tardy stag]

"the integral from 0 to 2"

[placid venture]

thanks

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[flat sphinx]

calc 2 application to hydrostatic force and centroids

[flat sphinx]

i really don't understand where to start or what to do

pointers would be greatly appreciated

[alpine sable]

hello u all! I am knid of new here, I would like to help and maybe get help, how do I do that?

[flat sphinx]

#❓how-to-get-help

[alpine sable]

thx!

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[flat sphinx]

@mental coyote

(my apologies. pinged wrong person)

<@&286206848099549185>

[flat sphinx]

<@&286206848099549185>

[balmy aurora]

hey

[balmy aurora]

hi

[flat sphinx]

need help with the problem

haven't gotten any advice so far

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@flat sphinx Has your question been resolved?

[lone heart]

@flat sphinx Has your question been resolved?

[flat sphinx]

<@&286206848099549185>

[flat sphinx]

.close

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[sullen vortex]

So I need to find the eigenvalues given that lambda is greater than 0. I end up with the equations in the 2nd picture. I know cos is an even function so I can get the equation 10sqrt(lambda)c1sin(5sqrt(λ)) = 0. Then I set 5sqrt(λ) to any n*pi and solve for lambda

[sullen vortex]

I get lambda = n^2/25 but the actual answer is n^2/100, anyone know why

[torn elk]

Where did you get that answer from? I mean the actual answer.

[lone heart]

@sullen vortex Has your question been resolved?

[sullen vortex]

it's online hw so it just checks it

[torn elk]

if there is a different scaling factor in the differential equation or the boundary conditions, it could lead to a different result for λ

but the boundary conditions also made me get the same

n^2/25

sry but I have no more time for now so I can't check deeply

wait for other to help

[sullen vortex]

no worries

<@&286206848099549185> ?

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[amber plover]

can i get help with this please

[amber plover]

i did x(79+6(1-x))-0.0001x^2-0.35x-40 for my revenue

after simplifying i got to -5.999x^2+5.65+39

i took derivative and got -11.998 + 5.65 = 0 x = 0.47

0.63/ 0.03 = 21 21x6 = 126 126 + 79 = 205

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[amber plover]

<@&286206848099549185>

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@amber plover Has your question been resolved?

[queen river]

first why the coefficient of x^2 is -0.001?

it supposed to be -(-0.001)

=0.001

second how did you get x(79+6(1-x))?

i assume x is the number of bread

[amber plover]

i'm pretty sure i did that in my calculations

it was just a typo unless i'm mistaken

[queen river]

ok

[amber plover]

this is the formula for the bread being lost isn't it

79 is the initial sold amount 6(x) is the amount increasing and -1 is the amount of money lost

[queen river]

then where is the 0,03 they provided

i dont think its a useless info

[amber plover]

hmm yeah i think you're right

i need to double check this one sec

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[queen river]

.reopen

[lone heart]

✅

[queen river]

not yet

[amber plover]

so far i've done (1-0.03x)(79+6x)

going to subtract the cost then take the deriviative

[queen river]

lets separate the formula into 2

number x price = profit

and number of bread is x

so we only need to find the price

profit - cost is net profit

[queen river]

i dont hink this is the profit

[amber plover]

why not?

[amber plover]

do you think it should be x(1-0.03x)?

[queen river]

What is (1-0.03x)?

[amber plover]

revenue

[queen river]

but why you multiply 0.03 by x

[marble coral]

To get revenue you have to remove the cost

[queen river]

x is the number of loaves of bread

[amber plover]

x(1-0.03)(x+6) maybe?

[queen river]

lets say 85

[amber plover]

ok

[queen river]

LET the number of bread be 85

then what will be the price?

[amber plover]

the price will still be $1

sold 85 though

do you mean the profit formula?

[queen river]

i mean

when the price decreased from 1 to 1-0.003

what will be the number ofbread sold out

[amber plover]

85

[queen river]

exactly

[amber plover]

because 79+6

[queen river]

but as the number of bread is 85, then isnt this weird?

you wont multiply 0.03 by 85

instead you multiply it by one

[queen river]

i mean this

[amber plover]

ok

[queen river]

But it only appears in the case of x=85

Which actually is $$ \frac{85-79}{6} $$

[ocean seal]

MochaOhwelp

[queen river]

so that the price will be $$1-0.003 \cdot \frac{x-79}{6} $$

[ocean seal]

MochaOhwelp

[queen river]

do you agree

[amber plover]

yea yea but hold on i gotta do something rq

brb

[queen river]

k

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[lost flax]

Hi, I’d appreciate if someone can guide me through this

[thorny patio]

Ok so first of all do you understand how to plot a polar coordinate point

They come in the form

(r , theta)

Cause that's most of the battle in this problem I'd say

[lone heart]

@lost flax Has your question been resolved?

[lost flax]

Not really, I do know that the r is tha radius

The

[thorny patio]

Ok so lets start there

Consider the point

(2 , 3pi/4)

There are two pieces of information here

Length and direction

The length is the radius 2

The direction is indicated by the angle theta

You point in the 3pi/4 direction (135 degrees)

And then you extend out 2 units in that direction to reach the point

So 2 units in the 135 degree direction

If you had (3, pi)

That would be 3 units in the pi/180 degree direction

That point would correspond to (-3,0) in our regular coordinates

Do those examples make sense?

Unfortunately this topic is very hard to explain solely through text

[lost flax]

mhm

sorry im back! ill read everything rn

[lost flax]

yes! i understand

[thorny patio]

Ok great real quick we should address negative radius

[lost flax]

okay

[thorny patio]

If you had

(-2 , pi/3)

[lost flax]

mhm

[thorny patio]

Youd first point in the pi/3 direction

[lost flax]

would it be the opposite side?

[thorny patio]

Then youd go backwards in the opposite

Yea exactly

[lost flax]

across the origin?

okayy

[thorny patio]

And it would be expressed by another point as well

With a positive radius

(2, 4pi/3)

[lost flax]

ohh and the angle being changed

i see

[thorny patio]

180 degree away from each other

[lost flax]

so is taht what the problem is asking?

[thorny patio]

And since you can keep spinning around and around

[lost flax]

mhm

[thorny patio]

You can make infinitely many points

[lost flax]

ahh

[thorny patio]

That go to the same location

So (1, pi/2)

[lost flax]

yes

[thorny patio]

Theres another angle that points to that same direction

In the 2pi to 4pi range

[lost flax]

5pi/2?

[thorny patio]

Yes

[lost flax]

ahh

so (-1, 5pi/2)

[thorny patio]

So what point would be the same

[lost flax]

wait

or just 1?

[thorny patio]

Yes

[tardy stag]

i attempted to give a visual indicator HTH

[lost flax]

ohh its asking for 2 diff pts as well so

[thorny patio]

So the other one

Maybe you can use negatibe

[lost flax]

(1, 5pi/2) and (-1, 3pi/2)

[thorny patio]

Close

But 3pi/2 not in the desired range

[lost flax]

ohh

[thorny patio]

Have to find another angle

[lost flax]

so like

[thorny patio]

2pi < x < 4pi

[lost flax]

uhh

7pi/2

[thorny patio]

Yesss

[lost flax]

oh yayy

[thorny patio]

So (-1 , 7pi/2)

Exactly right

[lost flax]

yay okay

ill try the second one

oh oops

it looks like i need a negative angle

[thorny patio]

Part ii?

[lost flax]

yes

er, part b

does this look correct?

[thorny patio]

Yes looks good

Part i should be 5pi/4 direction

[lost flax]

mhm

[thorny patio]

Part ii should be pi/4 direction

[lost flax]

ye ye

[thorny patio]

Both look good

[lost flax]

now im confused cuz this doesnt have an angle (?)

[thorny patio]

2 is an angle

In radians

[lost flax]

must i convert it into pi form?

[thorny patio]

Just a very odd number when we try to move it to degrees

It IS already in radians

[lost flax]

oh what

[thorny patio]

But the "normal" angles are all ratios of pi

[lost flax]

ah i see

[thorny patio]

But those ratios of pis are all numbers

[lost flax]

so its like between pi/2 and pi right

[thorny patio]

Yea

[lost flax]

hmm

[thorny patio]

Exactly

To go from 30 degree to the next equivalent angle i add 360 degrees

[lost flax]

so would it just be like 2+2pi for i)? 🤔

[thorny patio]

Yessss

Good stuff

[lost flax]

oh wow slay

kinda confused how to flip the angle tho 🤔

[thorny patio]

Negative radius would always be 180 degrees away

No matter what angle

[lost flax]

ohh true

so 2+pi

[thorny patio]

Yes

Perfect

[lost flax]

much simpler than i thought

!!

[thorny patio]

As most math is for now lol

It gets hard later tho xD

[lost flax]

uh oh could u help me w this haha

[thorny patio]

But someone else will tell me how its simple

[lost flax]

thats true haha

[thorny patio]

Ok so converting coordinates is pretty easy

Formula wise

[lost flax]

there is a formula for it?

OHH i think i learned it

r^2=x^2+y^2

[thorny patio]

Basically we transform according to the idea that points (x , y) are making right triangles

[lost flax]

ohh

[thorny patio]

And the x coordinate and y coordinate are legs of the triangle

The angle you get from trig relationships is the angle theta

[lost flax]

mhm

[thorny patio]

From there you get all those formulas

[lost flax]

interesting

[thorny patio]

r^2 = x^2 + y^2

Thats pythagorean theorem

r is the hypotenuse of the triangle made with legs x and y

[lost flax]

yes

[thorny patio]

Then you get

x = rcostheta

y =rsintheta

And we get y/x = tan theta from that

Or x/y = cot theta

[lost flax]

mhm

[thorny patio]

So you figure out r

[lost flax]

so i would jsut plug in the x and y

[thorny patio]

Figure out the angle using inverse tan

But at the end

You have to make sure your angle agrees with the quadrant youre

Because inverse trig functions have a limited rang3

Example 1

(0, 5)

we get r = 5

[lost flax]

yes

how come its not +-?

[thorny patio]

We can intuitively see its pointing straight up

[lost flax]

pi/2

[thorny patio]

Well you could do either plus or minus 5 to describe the same point

[lost flax]

oh true

[thorny patio]

But youd change your angle

So yea

(5, pi/2)

That's right

[lost flax]

okk

[thorny patio]

Next one is a 30 60 90

Its in quadrant 4

Make sure your answer agrees with that at the end

[lost flax]

sry wdym by 30 60 90?

[thorny patio]

The sides here

[lost flax]

the triangle?

[thorny patio]

1, sqrt3

They would belong to a 30-60-90 right triangle

One of the so called special right triangles

[lost flax]

oh ok

using tan i got pi/3 but i would need to make that be in the fourth wuadrant

[thorny patio]

Perfect

[lost flax]

5pi/3

?

[thorny patio]

Yep

[lost flax]

the r is still 4?

[thorny patio]

No check carefully

r is found through pythagorean theorem

Which requires sqrt

[lost flax]

oh oops

2

[thorny patio]

Yea

[lost flax]

wait would it not be in quadrant 3 since both are negative?

[thorny patio]

Oh shit yea xD

My bad

[lost flax]

np haha

[thorny patio]

4pi/3

[lost flax]

ye

yes

[lost flax]

im stuck on finding the theta of (4,-3), i tried using tan again and got arctan(-3/4) but it is wrong 🤔

[lost flax]

@crisp iron could someone help me w this ^ ty

[tardy stag]

is it wrong by 360 degrees offset?

[tacit arch]

Do you know the period of tangent

[lost flax]

oh i believe this is it

cuz it must be in Q4

how do i shift this to the fourth quadrant?

is this not already in Q4

oh

i must convert it to a positive rad

did +2pi and it worked. ty

.close

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[native nebula]

this is my working

but my answer is not matching

<@&286206848099549185>

[lone heart]

@native nebula Has your question been resolved?

[finite flax]

outermost brackets are not brackets, they are "ceiling" designators

you are taking the ceiling of that expression

and I'm skeptical that this can work out to anything with a fractional part of 61/120 if you are subtracting an integer from 5 1/6 nevermind that, just isolate the ceiling'd expression and show that it is not equal to an integer.

there is not a solution to this thing @native nebula .

where did you even get this?

$5\frac{1}{6} - 2\frac{61}{120} \notin \Z$

[ocean seal]

Disorganized

[tardy stag]

I'm guessing the ceiling is a mistake and they meant to use real brackets, otherwise you're right

the bottom of the { is cut off

[native nebula]

just a moment

[native nebula]

but how to solve this thing

[finite flax]

you can't.

[tardy stag]

even if they're brackets none of those solutions seem to be correct

[native nebula]

i never heard of ceiling

[finite flax]

https://en.wikipedia.org/wiki/Floor_and_ceiling_functions

[native nebula]

why so?

[finite flax]

🤔

[native nebula]

@finite flax why can't we solve it?

[finite flax]

if it were the ceiling function (and @tardy stag made an observation that suggests it's not), you could rearrange the terms and get a ceiling expression equal to a fraction, which is false

I got 1079/60 as an answer

if it weren't a ceiling function

and that answer is not in the given choices

[native nebula]

you got 1079/60 when you didn't consider them as ceiling brackets?

[finite flax]

yes

[tardy stag]

oh i mistyped a number in my python code

wait no i didn't

[native nebula]

okk

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@native nebula Has your question been resolved?

[lone heart]

@native nebula Has your question been resolved?

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[copper ginkgo]

I'm trying to find the minimum distance between point (0,4) and parabola y=x^2.
I tried making a general distance equation:
d = ✓[(x)^2+(x^2-4)^2]
I got no real solutions. I tried differentiating the derivative again to find its minimum values but I get +-✓14 / 2 and the answer should be ✓15 / 2.
What am I missing?

[upbeat hornet]

No solutions just means it doesn’t equal 0

[copper ginkgo]

I know. it means the derivative is always positive or negative

[upbeat hornet]

and you can use “sqrt” for square root

[upbeat hornet]

What did you find no solutions to?

[copper ginkgo]

sqrt(x^4-7x^2+16)

[upbeat hornet]

Did you expand out the inside?

Two squares of real numbers cannot add to a negative

In this case, neither of them can equal 0 at the same time so it makes sense that you got no solutions when setting it equal to 0

[upbeat hornet]

And this hasn’t been differentiated yet

[copper ginkgo]

Sorry, I forgot to mention

I tried solving it at first by replacing x^2 with t

then doing 0=t^2-7t+16

didn't work either

[quasi sand]

I think d=√[(x)⁴+(x²-4)²]

[upbeat hornet]

There’s a way to see that sqrt(x^2 + (x^2 - 4)^2) never equals 0

[upbeat hornet]

think again, they used the distance formula from (0,4) and then substituted y = x^2 for a point on the parabola

[upbeat hornet]

And that way is like this: If a and b are real, then a^2 and b^2 must be 0 or greater. Therefore a^2 + b^2 must be 0 or greater. The only way a^2 + b^2 = 0 is possible is if both a and b are 0

That can’t happen here

[quasi sand]

Yeah so d=√[(x²-0)²+(x²-4)²], right? Am i wrong?

[upbeat hornet]

So $$ \sqrt{x^2 + (x^2 - 4)^2} = 0 $$ has no solutions

[ocean seal]

(a + b)^2 = a^2 + b^2

[copper ginkgo]

I tried differentiating x^4-7x^2+16 and I am left with x1=0, x2, 3 = +-sqrt(14)/2

[upbeat hornet]

in that formula, you have calculated the distance between (x^2,x^2) and (0,4), which is not what. we wanted to find

[upbeat hornet]

Can you share your working

[ancient saddle]

Mmm I think this is correct for the original problem

[upbeat hornet]

hmm, sqrt is one-to-one and strictly increasing, so you don’t even need the square root to calculate the minimum distance

[ancient saddle]

Not sure why the answer would be √15/2

[copper ginkgo]

yes let me write it down

[quasi sand]

Yeah now i get it

[copper ginkgo]

d/dx[x^4-7x^2+16] = 4x^3-14x
factorized: x(4x^2-14)

therefore x1=0, x2, 3 = ±sqrt(14)/2

answers sheet says it should've been sqrt(15)/2

[ancient saddle]

This is correct

[copper ginkgo]

I don't know what I'm missing then haha

[ancient saddle]

If all they are asking for is x, then answer sheet is wrong

[copper ginkgo]

They're asking for the distance

ohhhhh wait

[ancient saddle]

XD

[copper ginkgo]

OMG I'm so dumb

thank you guys!!!

.close

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[quasi sand]

Did you check for √15/2 and √14/2

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[copper ginkgo]

No, ✓14 / 2 IS correct. It's the point on the parabola that connectes the minimum distance from the curve to 0,4 @quasi sand

[copper ginkgo]

I just forgot to put it back in the distance formula

[quasi sand]

Okie

[copper ginkgo]

.close

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[tribal locust]

Is there a formula so single expression in terms of a,b,n for (a+b)*(a+2b)*(a+3b)......(a+nb)? just like n.(n+1)/2 gauss formula? I analyzed it with the binomial distribution to find a correlation, but I could only find how its coefficients changed. The reason i'm trying to do this is i want to make this expression calculatable in calculator without writing thousands of (a+1000b). Any ideas? maybe it can be formulated for at least calculators with combinators etc. ? Thanks

[tribal locust]

(a + nb)! / a!

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[rugged radish]

$x^x = e^{\frac{1}{x}}$

[ocean seal]

Law

[rugged radish]

I tried to solve this and the result is $x^2 \ln x = 1$

[ocean seal]

Law

[rugged radish]

How to solve this ?

[limpid spade]

Numerically I guess

[frosty beacon]

what makes you think there is a nice analytical solution?

[rugged radish]

I don’t know, maybe because it seems beautiful

[rugged radish]

Newton’s method?

.close

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[charred plank]

Hey all, group theory, any help with $1 \to 2$ ?

[ocean seal]

meitar5674

[lone heart]

@charred plank Has your question been resolved?

[charred plank]

never mind 🙂

[pale zealot]

can someone explain this to me ??

anyone ?? please??

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@charred plank Has your question been resolved?

[deep spire]

when you sub in a=0 and negative values you dont get 1 as an answer so from eliminating those you get A

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[loud bronze]

0 idea how to start

i only know that ( 1 + x ) ^ 1/x = e

[vale wigeon]

no, you know that the limit as x approaches 0 of (1+x)^(1/x) is e

[limpid spade]

https://www.youtube.com/watch?v=2nUJMP_ZnnI

[loud bronze]

yes

so how do i solve it?

[limpid spade]

i sent that video for no reason it seems

[wild trail]

A quick change of variable using t=2x should return it to this form

[loud bronze]

i am really short in time

i have an exam

sorry

[limpid spade]

when

[loud bronze]

in couple hours

and i have like many lessons

[loud bronze]

could u show me please

[wild trail]

Ehh.... Just take 2x = t

Substitute and change the limit appropriately

[loud bronze]

what means 2x = t

there is no t

in the equation

[kindred anchor]

We are introducing a new variable that can get us to the answer

[loud bronze]

and how do i utilize this new variable

[wild trail]

By writing everything in terms of it

Wherever you see 2x you replace it with t

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@loud bronze Has your question been resolved?

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[alpine sable]

4c help please

[alpine sable]

The answer is 2.5 but I don't really know how to find the median in this kind of table

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[shell escarp]

<@&286206848099549185> do any of you guys know how to do this?

[vale wigeon]

!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.

[shell escarp]

my bad , theres a deadline so im kind of in a rush

[vale wigeon]

...

well ok like

do you know your triangle congruence tests

[shell escarp]

no maam

[vale wigeon]

so the abbreviation AAS tells you nothing, then?

[shell escarp]

angle angle side

[vale wigeon]

so you do know what it stands for

[shell escarp]

yeah i do

[vale wigeon]

and you should know, or be able to intuit, that congruence by AAS means this:

if two triangles have an angle, an angle and a side match (with the side not between the angles, otherwise you'd be looking at ASA), they are congruent

[shell escarp]

so because they share the same units for both an angle and a side theyd have congruence by angle angle side

[vale wigeon]

no,
here you have two matching elements, but for AAS (or any other congruence test) you need three.

you're asked to say what's missing to make AAS congruence work.

[shell escarp]

might be a dumb question but if they shared both an angle and a side why does the abbreviation AAS imply theres 2 angles and 1 side

[vale wigeon]

AAS means there's two pairs of matching angles and one pair of matching sides.

[shell escarp]

the two matching elements are there tho , no? an angle matches and so does a side

[shell escarp]

ohhhhh

but in this scenario it looks like theres only one of each so… just AS?

im lost

[vale wigeon]

the problem asks you

"we want to prove these triangles congruent by AAS, what are we missing from that?"

[shell escarp]

another angle

that matches

[vale wigeon]

another pair of matching angles.

[shell escarp]

yep

[vale wigeon]

so look at the answer options and tell me

which pair of matching angles, among the ones listed in the answer options, do we want?

[shell escarp]

either C or D ? but those are 2 angles

[vale wigeon]

... i can't tell if you are referring to answer options under letters C and D or to angles on the diagram named C and D

[pale zealot]

thank u

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[median oar]

what have you tried

[foggy current]

You mean approximately?

[dire gazelle]

Finally a question I can answer

[vale wigeon]

calculators exist.

100/3 is 100/3. you can rewrite that in a variety of different forms.

[dire gazelle]

Use the division algorithm and then put the remainder over 3

[foggy current]

,, 33.\overline{3}

[ocean seal]

Math Is Fun

[queen cove]

the exact value is $\frac{100}{3}$

[ocean seal]

WeAreIngram

[queen cove]

Numbers are just annoying

[vale wigeon]

did you come here with an arithmetic question or did you come here with something bigger

do you want to spam more threes in the chat

yes, if you write 100/3 as a decimal, then its decimal expansion goes on forever.

no, there is no end.

no, not all real numbers can be written as terminating decimals.

did OP delete all of their messages or did they just get banned lmfao

no, they just deleted all of their messages.

oh well!

.close

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[harsh granite]

Three ladies have brought one child each for admission to a school. The principal wants to interview the six persons one by one subject to the condition that no child is interviewed before it's mother. The number of ways in which interviews can be arranged, is

[harsh granite]

The answer is 6C2.4C2.2C2 but I don't understand this intuitively.

[vale wigeon]

when considering the placement of a mother and her child, the two of them occupy two places in the queue with the mother always coming second

so you can count the arrangements by arranging not individual people but mother-child pairs

for the first pair, there are 6C2 ways to pick which places they occupy (and once you do, it is uniquely determined where to put the child and where to put the mother)

then for the second pair there are 4C2 selections by similar logic

[harsh granite]

Shouldn't the mother come first?

[vale wigeon]

ah. yes. sorry

my logic still stands

it's mother then child, not child then mother

[harsh granite]

Oh oh I see now thanx. We select the places instead of the people.

[shell escarp]

the answer options, sorry for the delay i had to help my mom

[shell escarp]

no

[vale wigeon]

@shell escarp gonna need to open a new channel, sorry.
repost your problem there w/ all info

[harsh granite]

.close

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[shell escarp]

oh damn no worries

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[undone saddle]

why is 3^0.5 * 3^-0.5 0?

[undone saddle]

like this

[quiet vector]

its 1

u add the indices get 0 then 3^0 = 1

[undone saddle]

oh right yeah

and 1 x anything just says the same

.close

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[undone saddle]

.close

why is this still occupied

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[charred plank]

Assume G is a finite group. Prove that G acting on X is 2-transitive iff $2=\frac{1}{|G|}\sum_{g\in G}|Fix_X(g)|^2$

$Fix_X(g) := x\in X, g.x=x$
2-transitive for all $x,x',y,y'$ there exists a $g\in G$ such that $g.x=x',~g.y=y'$

[ocean seal]

meitar5674

[vale wigeon]

missing {} in the defn of Fix_X(g) i think

anyway

!status

[lone heart]

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

[charred plank]

Honestly got no clue where to start with this, I believe 2 is the number of orbits of a single x since if $g\in Stab$ we get g.x=x otherwise we can use 2-transitive to get to each other $y \in X$

[ocean seal]

meitar5674

[charred plank]

Also I believe I should somehow apply Burnside lemma but not sure how

[vale wigeon]

I believe 2 is the number of orbits of a single x
that seems to make no sense to me.

your entire sentence makes no sense to me actually

[charred plank]

Probably getting it wrong then 😵‍💫

It felt wrong

besides the feeling that I have go apply Burnside's lemma somehow I really got no clue

[lone heart]

@charred plank Has your question been resolved?

[lone heart]

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[vernal timber]

how do i do this? it says rearrange the following equation to make y the subject

[cyan seal]

False

[vale wigeon]

was this y = -x - 1 written by you or by your teacher

[vernal timber]

teacher

[vale wigeon]

your teacher fucked up

[vernal timber]

ik he dumb

[cyan seal]

It's wrong, that's the value of -y

[vale wigeon]

from x - y + 1 = 0 you can do this one step: add y to both sides

and you will have your isolated y right there

[vernal timber]

i dont understand

my answer was -y = -x-1

[cyan seal]

$$x - y + 1 - 1 = -1$$
$$x - y = -1$$

[cyan seal]

That's correct

[ocean seal]

Rub05

[north canopy]

ur lookin for y not -y

[vernal timber]

is it correct if i do -y= -1-x?

[cyan seal]

It's correct, but not the fully answer

[vernal timber]

it just says make y the subject

[cyan seal]

You have to isolate y

And there you have (-1) • y

[vernal timber]

how do i do that

[cyan seal]

So divide both sides by -1

[north canopy]

ye implying it has to b positive

[vernal timber]

ohhhhhhh

ok ok

[vale wigeon]

implying it has to not have a minus sign in front

"has a minus sign in front" and "is negative" are NOT the same thing

[north canopy]

yeah true, mb

[vernal timber]

i also have another question

[vale wigeon]

x - y + 1 = 0
x - y + 1 + y = 0 + y
x - 1 = y

[vernal timber]

i get it

thanks

"find the nth term" what is the best way to solve this

[vale wigeon]

throw that back in the face of whoever writes such questions

though in this case you're presented with the first 5 terms of what could be an arithmetic sequence

[lone heart]

@vernal timber Has your question been resolved?

[pale zealot]

in a right angled triangle ABC angle ACB=90 degree ADis the median. if angle B=45 degree, AD=5cm and CD=3 cm then what is the value of the orthogonal projection of AB on BC?

can anyone give me some explanation please??

[lone heart]

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[narrow parrot]

Please tell me how to find real numbers in the degree of complex and imaginary

[fallen verge]

Do you have an example problem?

[vale wigeon]

find real numbers in the degree of complex and imaginary
this does not make sense as stated

[gray jewel]

x^i = a?

[lone heart]

@narrow parrot Has your question been resolved?

[narrow parrot]

yes

[lone heart]

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[junior warren]

could someone help me out with these answers?

not sure which are wrong

[lone heart]

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

[median oar]

Which ones do you think are wrong

[junior warren]

im not sure about CB

but i think the rest should be right

im not sure exactly how this works but i believe BC would exist so id assume its commutative?

[indigo lotus]

if you multiply a MxN matrix with NxP matrix, you'll get a matrix MxP

[junior warren]

right so it is defined

[median oar]

Matrix multiplication is not commutative

[junior warren]

oh ok

[median oar]

If you multiply a matrix axb by another matrix cxd, you get axd if b = c

If b ≠ c, it doesn’t exist

Can’t multiply them

[lone heart]

@junior warren Has your question been resolved?

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[trim ivy]

I'm solving this improper integral

$\int_{3}^{6} \frac{x}{\sqrt{x-3}} dx$

[ocean seal]

Daniel H.

[trim ivy]

I made a change of variable t = x - 3
And solved it by sustitution.

Then I checked my answer in PhotoMath but it's not the same, and I checked and found the place where something changed

I don't get why I have to put that absolute value there.

[tacit arch]

Show your work

[trim ivy]

My bad, I already found the issue.
Thanks!

.close

[lone heart]

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[outer garden]

how to get this @here

[tardy stag]

what other angles can you write down equations for?

[outer garden]

just the 2

[tardy stag]

actually no, better question, what do you know about angles 1 and 5, apart from their formulas given

[outer garden]

their equal?

[tardy stag]

yeah

[outer garden]

so I need to know angle 1

[tardy stag]

you know that angle 1 is 7x + 6 degrees

you know that angle 5 is 11x - 18 degrees

you also know that angle 1 = angle 5

[outer garden]

sooo

I use shift solve?

I think I got it

[tardy stag]

Do you know what x is?

[outer garden]

11x - 18=7x + 6

shift solve

=6

x=6

[tardy stag]

great, now do you need help going forward?

[outer garden]

I use my scical

Is there another way to do it without scical?

[tardy stag]

you can calculate the value of angle 1 and angle 5, that seems like a useful thing to do

[outer garden]

okay

[outer garden]

thank you so much for the help

.close

[lone heart]

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[drifting quail]

Find DB

https://imgur.com/5f6sBwn

[drifting quail]

I've tried to use law of cos, but I'm not really sure how to find DB

do i need to make a set of equations?

[open urchin]

I think law of sines works

find acd then los to get dc

then los again to get db

[drifting quail]

ok ill try, thank you

so to find dc it would be 3/sin 45 = DC / sin 30?

[undone mango]

Wait wait

[drifting quail]

why did you do sin 30 = dc/ad, I though los was Sin A/a = Sin B/ b = Sin C / c?

wait i realised i did it the wrong way

[undone mango]

Tan 30 will be dc/ad

Perpendicular / base

UK the base is 2

Find dc from this

[tardy stag]

that only works for right triangles, ADC is not necessarily a right angle

[drifting quail]

https://images-ext-1.discordapp.net/external/Bpe2WWBx6NXr61C6lQnzYmtPhp3T4xJBz6xWtwm0xFo/https/i.imgur.com/5f6sBwn.png

[undone mango]

OoOoo I see

[drifting quail]

this is the image

[drifting quail]

i got (3sqrt(3))/2

is that correct?

[queen cove]

I got just $\sqrt{3}$

[ocean seal]

WeAreIngram

[drifting quail]

I double checked and now i got sqrt 3

ok i accidently put in 3 instead of 2

[tardy stag]

I get root3 as well yeah

[queen cove]

Seems good then

[tardy stag]

law of sines takes you the whole way

[drifting quail]

Thanks guys, it was correct

.close

[lone heart]

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[ember needle]

Hey, can anyone help me with this question? I really couldn't understand the solution, especially the second part. I would love a simple to follow explanation, as I might not understand anything difficult. Thanks!

[tardy stag]

what does it mean for something to be divisible by 5?

[ember needle]

I think what it means is that, (a - b) is divisible by 5, and so is (x - y). With this information, it wants me to prove that (a + x) - (b + y) and (ax) - (by) are also divisible by 5. But I might be wrong. I would be glad if someone corrected me.

I had a hard time with the proving part

[tardy stag]

it does mean that, yes; what does "(a-b) is divisible by 5" mean, though?

[ember needle]

I think it means that the result of (a - b) should be divisible by 5, so you should do the proof with that information?

I'm really not sure

[heady parcel]

you're defining it in terms of itself there

he's just asking what you know about a-b if you know it's divisible by 5

like write out what that means, mathematically

you're going to have to do some arithmetic to prove the result, so what does "divisible by 5" mean, arithmetically

[ember needle]

I mean, I think I have absolutely no idea

but I can't be sure

[heady parcel]

okay, can you name some numbers that are divisible by 5