help-39

[midnight haven]

can you type it

[final gate]

k

95=3.6 mil
1=0.03789mil (simplified by 95)

then * 100

[midnight haven]

yea that looks good

[final gate]

100= 3.7

[midnight haven]

just round however they specify in the question

[final gate]

oh alr

ty

[midnight haven]

np

[final gate]

.close

[pearl pond]

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[hollow barn]

can someone explain these

[hollow barn]

its for practice and i am confused

[jolly falcon]

For number 1?

[hollow barn]

well all of them

but lets start with 1

[jolly falcon]

1 is easy

It says that all the sums of diagonal, horizontal, and vertical are all the same

[hollow barn]

yea

[jolly falcon]

So just equate two of them together

What I did is just equate v+18+25 with v+24+ww

we can see that the v will cancel out

and equate for w

[hollow barn]

how does it cancel

[jolly falcon]

v+18+25 = v+24+w

[hollow barn]

oh

nvm

[jolly falcon]

See u will get ur w

then substitute the new value to w

just do the same for all of them

[hollow barn]

then its simple

[jolly falcon]

This is just system of equation

[hollow barn]

from there

kk

and for 2

?

meant 3

[jolly falcon]

Sry bout just, I was busy chatting with someone

wait a minute

[hollow barn]

no rush

[jolly falcon]

@hollow barn

still there?

[hollow barn]

yessir

3 is needed

tho

[jolly falcon]

Ok

My gad, I was trying to say sus but can't remember the spelling because of among us memes

Ok so the question suspiciously states that BC = AB + DC

[hollow barn]

mhm

y is suspiscous

tho

[jolly falcon]

And it says that both the angles at the bottom right and left are right angles

[hollow barn]

yea

[jolly falcon]

So it has something to do with Pythagorean theorem

[hollow barn]

k

[jolly falcon]

My god, i remember the spelling of pythagorean but not suspicious curse u among us

And I think I got it

[hollow barn]

lol oki

[jolly falcon]

What do u think will be the new side of this triangle

[hollow barn]

new side

[jolly falcon]

Yeah but what it would be

Base that AB+CD = BC

U have this side BA and side CD

[hollow barn]

where the new shape from

lmao

or is it just

the same

made smaller

[hollow barn]

yea

that would be

[jolly falcon]

We are trying to find out the length of the red line

[hollow barn]

B and call it Z

so BZ

[jolly falcon]

Yeah it was made smaller

[hollow barn]

kk

[jolly falcon]

Nah no need for substitution here

[jolly falcon]

Base on here

[jolly falcon]

BA is just the length of the other side

[hollow barn]

yes

[jolly falcon]

I just cropped it closer together so u can connect the dots

[hollow barn]

wait im stupiud

BC

lol

[jolly falcon]

YEAH

U got it

Ah Nah u almost got it

So close

[hollow barn]

CB

or what

[jolly falcon]

It's just DC - AB

Since BC is the line slanted

[hollow barn]

k

[jolly falcon]

We already have bc

And that is the slanted line

Cause u can't just name another point B because they have the same height but I see where u are coming from

[hollow barn]

yh

[jolly falcon]

So The red line is CD - BA

[hollow barn]

B prime

tho

yea

[jolly falcon]

If u subtracted the height of BA to CD, u get something like this

A right triangle

One side is 7, the other side is DC - AB, and the hypotenuse is DC + AB

We know that pythagorean theorem a^2 + b^2 = c^2

And I think the square of DC-AB and DC + Ab will cancel out and u will be left with 4ab

[hollow barn]

wait a sec

[jolly falcon]

Kinda similar to the theorem of AM GM

[hollow barn]

hypotenuse

DC+AB how

[jolly falcon]

It says at ur equation

I mean picture

BA and CD are perpendicular to AD

@hollow barn U must always draw a picture of ur problem first

Sry bout that really busy rn

SO lemme show u tha answer @hollow barn

49 + (DC-AB)^2 = (AB+DC)^2

49 + DC^2 - 2AB DC+ AB^2 = AB+2ABDC+DC^2

CANCEL ALL LIKE TERMS

49 = 4ABDC

49/4 = ABDC

[hollow barn]

thanks

i have a little more knowledge now

[pearl pond]

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[pearl pond]

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[rustic cobalt]

anyone know what symbol is in the denominator we're currently discussing scientific notation but that symbol just appeared in our activity

[pearl pond]

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[tiny dagger]

do the diaganols of a trapezoid, kite, or isoceles trapeozid bisect the angles? are the consecutive angles of kites, trapezoids, or isosceles trapezoids supplementary?

[pearl pond]

@tiny dagger Has your question been resolved?

[tiny dagger]

<@&286206848099549185>

sorry for the ping but i have a quiz tmrw and im just a lil unsure abt these two questions

[pearl pond]

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[pearl pond]

@tiny dagger Has your question been resolved?

[pearl pond]

@tiny dagger Has your question been resolved?

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[stuck widget]

I got up to 2/5x^5/3 - 2/3x^3/2 + C

which is the curve

[patent yew]

didn't i alr do this w/ u?

or was it someone else

[pearl pond]

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[ember cloak]

Why is it x^5/3 though?

[pearl pond]

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[lime remnant]

anyone know how to do this

ive found the values of 6-x and 8-y and x and y

but i dont remember the similar triangles rule

.close

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[stone rose]

How do I find the integral of 1/(x^2+4)^2

[stone rose]

am i supposed to use trig sub?

[pearl pond]

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[grand fog]

Am I correct in saying that the borel sets in R^n is the set of sigma algebra generated by open sets in R^n?

[timid spindle]

indeed

[grand fog]

Awesome just confirming before I continue studying with wrong assumptions lol

Thanks!

.close

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[thorny axle]

After using the quotient rule and subbing in, I end up with 2 = p'(1) - p(1) and I dont know where to go from there

[pearl pond]

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[calm flax]

How do I make a table for the limits when the left side of the number is the same as the limit?

[patent yew]

wdym?

that's just a limit u can solve by plugging in directly

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[empty aspen]

[late moon]

Hmm

Could you show the original question with the parts?

Because it's hard to know what's going on

[empty aspen]

okay let me give a bit of an explanation

from this graph

i have to find an intersection between two lines and plot a third that also goes through the same intersection

and then it says can you use substitution to solve with three equations

[late moon]

So this graph is given to you

And you're trying to find a 3rd line that connects 2 intersection points?

[empty aspen]

no i had to make it

[late moon]

Hmm

[empty aspen]

but that is irrelevant tbh

So i plotted another line at (6,7)

[late moon]

The blue line?

[late moon]

Okay

Well you can make 2 lines equal each other and then use substitution

And the resulting x and y coordinates will surely be the same for the third line

And here's a small hint:

3 equations for 2 unknowns is not fruitful.

[empty aspen]

okay

[pearl pond]

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[weak surge]

why is the range of tan(x)^2 equal to 0?

[plush bramble]

What

[tall flint]

it isn't 0

[vital estuary]

Very weird

[weak surge]

according to Symbolab

[merry carbon]

What did you put in?

[plush bramble]

Show the whole page

[merry carbon]

Range is zero huh

[weak surge]

ya, I don't understand it either

[merry carbon]

What does it give you if you say, like, range(x^2)?

[merry carbon]

Odd asf

[weak surge]

so what is the range of tan(x)^2 supposed to be?

[merry carbon]

Any nonnegative number (note that tan can output any real number)

[weak surge]

now I'm beginning to question Symbolab

if I can trust the answers

[merry carbon]

Suggested by this graph here

[weak surge]

ya

[merry carbon]

[weak surge]

and the graph is from Desmos

not even Symbolab code

whoever made this needs to fix it

I will contact them

paying for Pro and getting this garbage

[supple spindle]

sue them

[weak surge]

wish I went with WA

Is it worth it?

[near echo]

no

you just got what you needed without paying anything

[weak surge]

but it shows steps

helpful for understanding

[near echo]

you can just ask here

it's free

[weak surge]

OK

[near echo]

and you can ask follow up questions

[plush bramble]

Proof that symbolab is hot garbage

[weak surge]

ya

[plush bramble]

That's as bad as ChatGPT

[weak surge]

I sent them an email

with screenshot

Desmos is the best thing about Symbolab

our professor goes to Symbolab to use the graphing calculator. The graphing calculator on Symbolab is just an embedded Desmos

https://tenor.com/view/unimpressed-not-impressed-amused-gif-13997644

[pearl pond]

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[dim rover]

does this look correct

[dim rover]

the problem was to find the inverse of the function at the top

the awnser is at the bottom

[pearl pond]

@dim rover Has your question been resolved?

[tough token]

is this what the first equation is?$$p(m)=4+\sqrt[5]{2m-5}$$

[jolly parrot]

Duh Hello

[tough token]

@dim rover

[dim rover]

yes\

[tough token]

then you have 1 mistake

[dim rover]

oh right

+4

not wait no

[tough token]

actually im a bit unsure how you are changing variables

but ignoring the changing the variables, when you remove the square root you are supposed to raise everything to the 5th power

not the 5th root

[dim rover]

its inverse functions i changed the position of the variable and then solve for it

also yes you're correct

[tough token]

personally would not recommend you do this

[dim rover]

howcome?

[tough token]

or actually it might be alright. depends on what you learn i guess. personally if i have a function which is p(m) then i would try to find the inverse which would be m(p)

[dim rover]

Define a formula for the function m=p^-1(h)

[tough token]

like if i have $y(x)=5x$ then $y^{-1}(x)=x(y)=\f y5$

[jolly parrot]

Duh Hello

[tough token]

so in this case the final equation you have should be $$m=p^{-1}(h)=\f{(h-4)^5+5}{2}$$

[jolly parrot]

Duh Hello

[tough token]

notice how its a function of $h$ and not $m$

[jolly parrot]

Duh Hello

[dim rover]

ah

i see now

that was just a rushing mistake

ok so

here is the fixed one

[dim rover]

i just forgot that when you start solving you swap the position of the variables

[tough token]

thats correct now, would maybe make it more obvious that the 5 is the power of the parenthesis but the math is right

[pearl pond]

@dim rover Has your question been resolved?

[pearl pond]

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[tired obsidian]

I need help with parts a and b radical equations alg 2

[pearl pond]

Please don't occupy multiple help channels.

[open mist]

you already have a channel open

don't ping individual people

don't ping people in other people's channels

show your work

specify where you're stuck

either close this channel or close your other one

[tired obsidian]

Ok

[bold sail]

well i actually dunno lmao

i guess it gets a bigger amplitude begause the wave is charging with kinetic energy

but i'm really not sure

[tired obsidian]

Wdym

It’s asking to solve algebraically

[bold sail]

ok i have no clue

oh shitttttt

o was thinking about explaining the caus whatever

ok it's easy

you got that s = sqrt(t) -2t +3

[tired obsidian]

Ok

[bold sail]

express t depending on s

and you know s so you can have your t

[tired obsidian]

What’s my s

.close

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[atomic canyon]

am i correct that this is the same as saying "0,1"

[old geyser]

Yeah

I don't know why they don't say $x \in \setb{0, 1}$

[jolly parrot]

Umbraleviathan

[atomic canyon]

same lol :p

.close

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[fluid arch]

Looking for help on this ridiculous problem

[midnight haven]

you can use trigonometry to get height

or use area of equilateral tiangle formula

[fluid arch]

How would the formula help me get height

[midnight haven]

area = sqrt(3)/4 * b * b where b is the side of triangle

b is 3 feet

the area as you have correctly mentioned above is also 0.5 * b * h
Hence 0.5 * b * h = sqrt(3)/4 * b * b
Solve for h here

[fluid arch]

oh I thought you plugged the sides in to solve for the area

[midnight haven]

h will be sqrt(3) * 3/2

[fluid arch]

is 3 ft the base

because right now i have 2 unknowns

[midnight haven]

yes it is

for the 2nd part the smaller triangle is similar to the bigger equilateral triangle
hence the ratio of b/h in both the triangles will be same..use this and replace b with h along with a factor and then differentiate

[fluid arch]

I'm still on the part where i'm trying to find the height

[fluid arch]

Because I don't understand how you got this answer

[midnight haven]

b is 3 feet

as mentioned in the equation

use this fact

[fluid arch]

Yes I know that b is 3 feet

[midnight haven]

yea then solve for h

[midnight haven]

in here the last equation that you wrote

good

same as mine

[fluid arch]

Why is it that we have the area of an equilateral triangle = area of a triangle

2 different area formulas = to each other

Or maybe what height is this for? Small/big triangle

[midnight haven]

big one

[fluid arch]

And the first question is asking for the height of the big one?

[midnight haven]

yep

because the small one is changing with time

you need to calculate the rate of change of the small one in the 2nd part of question

[fluid arch]

Weird as to how it's saying the height is incorrect

~~ 2.59807621

[midnight haven]

pretty sure it's right

[midnight haven]

pretty sure this is the right answer

ready to argue to anyone on this

[fluid arch]

No idea why it's marking it as incorrect then. Doesn't specify to which decimal point I should round to

[plush bramble]

show the whole page

[plush bramble]

click symbolic formatting help

[fluid arch]

its just a broad FAQ

[plush bramble]

ctrl/cmd f for square root

or just root

[fluid arch]

Does not work

[plush bramble]

what does not work

[fluid arch]

I cannot get a root symbol

[plush bramble]

there should be one. keep looking

[fluid arch]

Alright i got the symbol

This good?

[pearl pond]

@fluid arch Has your question been resolved?

[fluid arch]

.close

[pearl pond]

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[thorny crag]

can someone help me out with this question: what is the angle determined by an arc of length 2pi meters on a circle of radius 8 meters

[pearl pond]

@thorny crag Has your question been resolved?

[karmic fern]

draw

[thorny crag]

<@&286206848099549185>

draw what?

[karmic fern]

draw a diagram of the situation

it's geometry

useful technique

[thorny crag]

is the angle 0?

[karmic fern]

no

also what does "determined by" even mean

the central angle or one of the inscribed angles

[thorny crag]

idk, im assuming given the characteristics of the circle, it wants me to find the angle

its a trigonometry question

[karmic fern]

none of that answered my question

[thorny crag]

well ok, it doesnt specify but i think the central angle

[karmic fern]

have you drawn the circle yet

[thorny crag]

yes, i have a circle with a line going halfway through it

radius is 8

[karmic fern]

where's the arc

[thorny crag]

the arc length is 2pi

[karmic fern]

didn't answer the question

[thorny crag]

what do you mean?

arc of length 2pi meters if its not that then idk

i g2g, i'll try again later

.close

[pearl pond]

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[finite otter]

plss help meee

idk what to add first

[jade kite]

the question's to find x and a?

[finite otter]

these are the things to find

[jade kite]

ok

so to find angle K

do you find something special about the angle K and the angle M?

[finite otter]

they both intersect with O

right?

[jade kite]

I mean I guess

but something more obvious

[finite otter]

ohhh they both have angles?

[jade kite]

well yeah they both have angles but what do they have in common?

[finite otter]

its ok

is it like an obvious thing?

cuz i feel like it's the little circle

[jade kite]

that's the degree symbol

it's a way to measure angles

[finite otter]

ohhhh yeah

so

do we have to subtract both degrees

to find angle K?

[jade kite]

I don't think so

look

what do these two angles have in common

[finite otter]

ummm a?

or like the + sign?

[jade kite]

do you see any similarity when I put them one next to another?

[finite otter]

the angles

[jade kite]

note that M was rotated 180 degrees

[finite otter]

ohhh so they're both a 90 degrees angles?

[jade kite]

well no but you're close

they're both equal

[finite otter]

im sorry if im slow

[finite otter]

i see

[jade kite]

knowing they're both equal could you find a way to find K?

[finite otter]

K and M are just the same measure then

so K will turn into the measure of M?

[jade kite]

well sort of yes

but you have k= 7a+4 and M=6a+11 right?

and you know k=m

[finite otter]

ye

[jade kite]

could you find a?

[finite otter]

no?

[jade kite]

are you sure?

[finite otter]

hmmm we gonna transpose right?

[jade kite]

transpose?

[finite otter]

like switch the number 4 to the right side

wait

nvm

maybe im worng

wrong*

[jade kite]

wait i dont understand what you mean

[finite otter]

like doing this

[jade kite]

yeah ok

but can you set the equation before to show me you understand?

[finite otter]

is it right?

the only thing I dont know is how to solve it

[patent plover]

where = sign

[finite otter]

oh hold on

there

[patent plover]

nice

[finite otter]

do i like switch it like this?

[patent plover]

to solve transpose unkowns to one side knowns to another

yep

don't forget change signs

[finite otter]

ohhh i see

[finite otter]

ok I'll be back in a minute

so

a=7

am i right?

[jade kite]

yep

now you can substitute your 7 into the K to find the value of K

[finite otter]

ohhh make sense

thanks

[finite otter]

so it's 53 degrees(plz correct me if im wrong)

[jade kite]

correct

[finite otter]

yesss

wait

[jade kite]

to validate your answer you can try to substitute in the other equation and see if it's still 53

[finite otter]

is degrees the right unit for it?

[jade kite]

yep

[finite otter]

ok wait

ohh ok

[finite otter]

wow it's 53 too!

[jade kite]

ok so it works

so now for b)

it's basically the same logic as the one used in a)

[finite otter]

ohh but like

it's a then the other one is x

so how?

<@&286206848099549185> please help

[patent plover]

hey

x for sides, a for angles

[pearl pond]

@finite otter Has your question been resolved?

[pearl pond]

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[pearl pond]

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[slow kettle]

Write the following statement using logical symbols and quantifiers and then negate it as in the form written by you.
For every two non-zero complex numbers there is another complex number with a smaller modulus than the modulus of each of the given numbers.

(seriously have no clue how to solve this)

[hollow cobalt]

Let's do it bit by bit, how would you write "For every two non-zero complex numbers"?

[slow kettle]

this is the problem, our professor added this but he hasn't elaborated a bit on complex numbers

[hollow cobalt]

Ah, well, you can technically do it without knowing complex numbers in-depth

Only knowing that the set of all complex numbers is denoted with C and that the modulus of a complex number z is denoted with |z|

[slow kettle]

only with that

[hollow cobalt]

Yeah, so, how would you do this?

[slow kettle]

okay so

∀ x₁, x₂ 𝛜 C*

[hollow cobalt]

Right; it is more conventional to use the letter z for complex numbers, but, sure, that perfectly works as well

[slow kettle]

just saw in my notes the professor used x

[hollow cobalt]

I believe you should have no trouble writing "there is another complex number with ..."

[slow kettle]

yeah no problem

∃ x₃ 𝛜 C* / | x₃ | < | x₁ | ∧ | x₃ | < | x₂ |

now i need to negate it

or am i not correct?

[hollow cobalt]

Generally, negating p and q yields (not p) or (not q)

[hollow cobalt]

That is correct

Oh, wait though,

Before negating that

We have to change the $\forall x_1,x_2\in{\mathbb{C}^{}}$ into $\exists x_1,x_2\in{\mathbb{C}^{}}$

[jolly parrot]

A Lonely Bean

[hollow cobalt]

So, the negation of $\forall x_1,x_2 \in \mathbb{C}^* \exists x_3 \in \mathbb{C}: \abs{x_3} < \abs{x_1} \text{ and } \abs{x_3} < \abs{x_2}$ should be $\exists x_1, x_2 \in \mathbb{C}^* \nexists x_3 \in \mathbb{C}: \abs{x_3}<\abs{x_1} \text{ and } \abs{x_3}<\abs{x_2}$

[jolly parrot]

A Lonely Bean

[hollow cobalt]

Which can also be rewritten as $\exists x_1, x_2 \in \mathbb{C}^* \phantom{-} \forall x_3 \in \mathbb{C}: \abs{x_3} \ge \abs{x_1} \text{ or } \abs{x_3} \ge abs{x_2}$

[jolly parrot]

A Lonely Bean

[slow kettle]

understood!

thanks a lot!

[hollow cobalt]

As a side note,

[slow kettle]

yes?

[hollow cobalt]

If you want to shorten it, the statement "a < b and a < c" can be rewritten as "a < min{b, c}"

[slow kettle]

alright :))

thank you for your help

.close

[pearl pond]

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[pearl pond]

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[arctic pasture]

A train of mass 200tons it's engine's force is 24500newtons, if it starts to move from rest, find the velocity of the train after 30 seconds

[arctic pasture]

I solved it like this, and the numbers check out

,rotate

[arctic pasture]

But my teacher says i can't use integration because F and m are constants

Integration only works when they are defined as functions with variables like f= 3t² + t

But my answer is correct

Is my method really invalid but it happens to give the correct number?

[turbid moss]

you ended up using impulse formula

[arctic pasture]

Not sure what that is, I assume it's related to collisions?

[turbid moss]

yeah, naturally it's how you would solve this problem without calculus, but you were able to derive the same answer

[arctic pasture]

But I am really confused by this argument

[wet osprey]

well

do you have to use calculus or is that just what you want

becuase you really can just plug the values into F=ma

[arctic pasture]

The topic is Newton's second law, so the latter

This was just the method that I thought I should use, but I was told that it's wrong even though it works

[wet osprey]

im not 100% sure but i feel like it's right

[turbid moss]

so you want to know why you came up with the right answer

[wet osprey]

im not seeing any illegal moves in math in your working but maybe someone more experienced can chip in

[meager trellis]

this method is valid, but it's also kind of overcomplicated

[arctic pasture]

I mean I guess you technically answered me at the start, I want to know if indeed the teacher was correct and I was wrong, or the opposite and you did confirm by telling me about the impulse formula

[meager trellis]

you could just like, a = f/m, v = at, and that would be equivalent but way faster

but this method isn't wrong, there's nothing actually incorrect about integrating a constant

[wet osprey]

but there's no wrong math moves here in the working out?

[arctic pasture]

But the reasoning behind why it's invalid made me really feel off towards how I understood the entirety of maths

[wet osprey]

it looks to me like it's all legal moves

[meager trellis]

yeah this is completely valid

[wet osprey]

so you should get the right answer

[meager trellis]

i have no idea why your teacher thinks it isn't

[wet osprey]

even if it is a lot more complicated than the non-calclulus way

[meager trellis]

and it is the right answer

[turbid moss]

its not really that either of you were wrong, its more so that there were easier ways to solve, usually integration is reserved for when integrating things that are dependent, for example if force was a function of time

[wet osprey]

yeah

[turbid moss]

like if force was F(t)

[meager trellis]

i mean your teacher said it was invalid, and that was wrong

[turbid moss]

force here was constant so integrating worked pretty well

[arctic pasture]

I guess I should try to utilize the laws of motion first before calculus, but this semester focuses on dynamics using calculus (how deriving displacement gives velocity and velocity derived is acceleration and the opposite with integration) so my brain automatically went calculus

[wet osprey]

i mean you could always plug values into f=ma then integrate a=dv/dt

[arctic pasture]

This is what I thought was weird, he said f here isn't a function so we can't use calculus, but technically f here is a function but with a constant value

[wet osprey]

that should also work just fine

i mean it is a function, just not dependent on t

[meager trellis]

yeah F is definitely a function and you can do calculus on it

[arctic pasture]

Thanks for clearing it up for me

[turbid moss]

yeah but down the road you'll come across a changing force where integration is useful

[wet osprey]

like when F is dependent on position

(shm!!)

[arctic pasture]

I came across velocity dependent on position so I should be fine

Hopefully

Maybe...

[turbid moss]

its def a good to think about physics from a calculus pov

even if your teacher said youre wrong

[arctic pasture]

Hell yeah I flex being a junior maths nerd by solving everything with calculus in the most convoluted way

It feels great to solve something in a way none of my classmates can comprehend, including myself

Anyway thanks y'all for the help

[meager trellis]

you can actually derive some of the "laws of motion" from calculus
all you actually need to get all of it is like, a couple of laws

[turbid moss]

good point, this is what i meant when i said you just derived the impulse formula

F(t-t0) = m(v-v0)

or just F=dp/dt

[arctic pasture]

Is it related to these? Otherwise it seems that I will not encounter it

[meager trellis]

you might even notice a few suspicious factors of 2

[arctic pasture]

,rotat3

,rotate

[meager trellis]

i think there's like, distance is 1/2*a*t^2?

which has a rather suspicious factor of 1/2

if you d/dt that, you get a*t, which is obviously just velocity
so that's where that formula came from

[arctic pasture]

• initial velocity iirc

[meager trellis]

oh yeah there is that
but if initial velocity is 0 then you get what i said

[turbid moss]

oh yeah that 1/2 shows up everywhere, kinetic energy,

[meager trellis]

now i'm trying to work out how to derive the formula for kinetic energy to work out what that 1/2 is doing there

[turbid moss]

yeah i think you have to look at it from the definition of Work, maybe

F=dW/ds

so that energy in general is how much work you put into a system

but this work is just Fds

integrate and take s from 0, so Fs

assuming F is constant, so mas

and i end up getting potential

but kinetic has to do with the loss of potential

huh, im stuck

ok so energy has to be conserved

let W be the amount of energy we put in

and assume that we've moved some distance from the origin so that kinetic energy is nonzero

then ideall W= ma(s-x) + kinetic

so that kinetic = W-ma(s-x)

[meager trellis]

oh wait i get it i think
W = Fs = mas
as and 1/2 v^2 both have a d/dt of av

[turbid moss]

oh you just took the time derivative, good idea

because kinetic energy is really just the change of potential energy over time

damn

[meager trellis]

...i don't think kinetic energy is change in potential energy over time

in fact i don't think potential energy is relevant here at all

[turbid moss]

yeah, i really mean it intuitively

[meager trellis]

we can just apply a force out of nowhere, figure out how much work that was, and how that's related to the velocity

[turbid moss]

i mean potential as in how much work was put in initially, so i kinda use it interchangeably

[meager trellis]

tbh i'm not 100% certain that taking a time derivative here actually makes sense

[turbid moss]

ofc, kinetic energy has somethign to do with a loss in potential

it feels like it makes sense to me tho

[meager trellis]

...oh actually i suppose it does
since that means as and 1/2 v^2 are only different by a constant that isn't changing over time

oh wait i see it

now if we assume the object was initially not moving

then at t=0, s=0 because it hasn't moved yet, and v=0 because it initially wasn't moving

therefore, since they have the same initial value and the same time derivative, they're the same

and since as = 1/2 v^2

that means we can say that mas = 1/2 mv^2

[turbid moss]

yeah

[meager trellis]

so yeah basically, the 1/2 here shows up once again because d/dx x^2 is 2x

[pearl pond]

@arctic pasture Has your question been resolved?

[pearl pond]

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[safe spade]

hey im actually looking to mark this practice paper i found online, does anyone know where i can mark this?

[regal herald]

since its a mock paper - i assume the questions are selected from several papers by your college, so youd likely have to go through several past papers to see the answers

unless its just one you found - in which case id need more info to try find anything

[safe spade]

uhh its not a school paper

uhmm

exam board is Pearson Edexcel A level Maths

[regal herald]

could i see one of the questions?

[safe spade]

yeah sure

would u like me to link the entire paper?

let me see what i can do

[regal herald]

where did you find the paper?

[safe spade]

got emailed it

from a friend

he got it from his tutor but his tutor doesn’t have the mark scheme

ive seen mark schemes for mock sets 1 and other sets just not for this one

[regal herald]

yeah sorry, i cant find anything for it

[safe spade]

no worries!

i appreciate ur willingness to help, plus it isnt that serious anyway, just wanted to know if my answers were corrext or not

ill just get my teacher to mark it for me

thank you again

[pearl pond]

@safe spade Has your question been resolved?

[pearl pond]

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[pearl pond]

@charred grail Has your question been resolved?

[charred grail]

<@&286206848099549185> help me! im stupid!

[charred grail]

thanks man

[charred grail]

<@&286206848099549185> i cant stop being dumb help me

[pearl pond]

@charred grail Has your question been resolved?

[pearl pond]

@charred grail Has your question been resolved?

[empty cloak]

Say no to vectors!

xd

[pearl pond]

@charred grail Has your question been resolved?

[karmic fern]

sorry I can't read that

are you trying to prove that the given formula that takes in a vector is equivalent to the matrix multiplication by that matrix?

[pearl pond]

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[flint monolith]

How do i do (ii)

[torn shell]

each face has 4

[flint monolith]

yes

[torn shell]

6 faces and i dont think there are any others

[flint monolith]

yes

[toxic lichen]

there are

AEC is a right triangle not belonging to any face

[torn shell]

oh mybad

[flint monolith]

so 30?

24 + 6?

[torn shell]

8 i think

AEC, CGA, EGA, GEC

and then duplitcated by the BO diagonal

[flint monolith]

its not 8

[torn shell]

oh i missed 4 other rectangles

GFAO,

and the 3 others also slanted like that

so 4 * 4 more

[flint monolith]

16?

[torn shell]

ye 24 + 8 + 16

[flint monolith]

what how did you do it?

[torn shell]

6 rectangles for faces, 2 rectangles going across and 4 rectangles that are slanted

[flint monolith]

what do you mean?

[torn shell]

every rectangle you can split into 4 right angle triangles

[flint monolith]

where did ou get 16?

[torn shell]

GFAO, FEOC, DEBC, DGBA

those 4 rectangles

[flint monolith]

I get it now , so smart

Do you know how I would do this ?

[torn shell]

no clue 💀

open a new channel and ask

[flint monolith]

how would we close?

!close

,close

.close

[pearl pond]

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[flint monolith]

I'm really confused

[pearl pond]

@flint monolith Has your question been resolved?

[flint monolith]

<@&286206848099549185>

This was in the projection chapter

[tough star]

it number 10

[flint monolith]

what?

[pearl pond]

@flint monolith Has your question been resolved?

[pearl pond]

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[unborn sage]

help

[unborn sage]

me to vizualise the shape

Pls I've exam tmrw and I have to sleep

Sneha take two charts to do some craft work. she cuts both the chart in the form of parallelogram with same size. to first parallelogram she gives name MNOP that angle N and M are in ration 1:2 respectively. then she gives the name STIR to another parallelogram. She joins edges NO and TI without overlapping and form a big parallelogram

I don't know how to make these both ||gm join

anyone ?

[plucky scarab]

Wait a min

[unborn sage]

I think the question is wrong bcz NO and TI can't be joined

[plucky scarab]

They can be joined

It makes one big parallogram with vertices srpm

[unborn sage]

How can u show me the figure

pls

[plucky scarab]

1 min

[unborn sage]

ohk

@plucky scarabcan u please be quick cz I've to sleep only few hours are left for exam and I haven't slept

[plucky scarab]

Srry for bad drawing

[unborn sage]

np

[plucky scarab]

I hope this makes sense

[unborn sage]

how angle r is 120?

[plucky scarab]

It was specified in question

N : M = 1: 2

Combine both = 180

So n = 60

M = 120

[unborn sage]

I know but how is angle r 120?

[unborn sage]

yes

[plucky scarab]

Parallelogram have two angles that are same length

So M = R

[unborn sage]

*M

[plucky scarab]

Srry

[unborn sage]

M = R (opposite angles) right ?

[plucky scarab]

Yup

I hoped this helped

[unborn sage]

ohh thanks buddy maybe I do good in exam bcz of this help

can i close ?

[plucky scarab]

Yes

Do .close

[unborn sage]

thanks

.close

[pearl pond]

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[solid wharf]

Hello there!

I'm a bit stuck with the question of a)
I understand that i have to put -1 in to graph instead of x.
However, this f(x) function do not have a defined b. So because it says bx that means ill have to do b x (-1) right? And how can i then solve the a) question if the b still remains?

[ebon mesa]

you know the value of f(2)

find b with that

then find f(-1)

[solid wharf]

Sorry, could you help me understand how i know the value of f(2)

[ebon mesa]

read the first line

y = 3 + bx - 2x²

you know a point which satisfied the equation

[solid wharf]

Ohh so you mean 5 = 3 + b * 2 - 2 * 2^2?

And then i solve that equation by putting b one one side and the rest on the other. Then get teh value of b? Put that in to the function and then i get rid of b?

[ebon mesa]

yes

[solid wharf]

Thank you brudda, you truly helped me 🙂 ❤️

[ebon mesa]

yw

[solid wharf]

.close

[pearl pond]

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[compact token]

Can someone tell me where did this 2 come from, the solution says that the first 2 appears from the elementary matrix but idk how

[tropic saddle]

from the theorem point 4

row operations correspond to multiplying by the relevant elementary matrix from the left

[compact token]

but c=1/2 right?

[tropic saddle]

well the new matrix has 1/2*det of the old matrix

so old matrix has 2* det of new matrix

[compact token]

that is B=(1/2)det(A)

and so det(A)=2?

[tropic saddle]

I personally prefer to think about it as just pulling a factor 2 out of the first row tho

[compact token]

how is that related to finding the determinant tho?

[tropic saddle]

if B is that second matrix, then det(B)=1/2 det(A). so det(A) = 2 det(B), yes

[compact token]

then lemme ask you so B here is $\begin{bmatrix}
1 & 1 & 3\
1 & 3 & 2\
\end{bmatrix}

[jolly parrot]

13wrc
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[tropic saddle]

well missing last row but yes

[compact token]

yea I am trying to write that down lol

[tropic saddle]

https://i.imgur.com/1jj8XeB.png

det B = 1/2 det A

det C = det B

[compact token]

so det(B)=-2

[tropic saddle]

and det C = 1*2*(-1)

so then if you rearrange det (A) = 2*(1*2*(-1))

[compact token]

and we know the c =1/2 then if we just re arrange and find the det(A) it would be -4 right

that is what I do not understand

[tropic saddle]

well what part of that do you not understand

you explained it correctly

[compact token]

now if I do the same for det(c) with the theorem 5

is det(B)=det(C)

?

[tropic saddle]

yes

[compact token]

wait now I am confused how will I connect all the dots?

[compact token]

so (2)*2 = 4 the det(A)

nahh

[tropic saddle]

no

[compact token]

-4?

What I do not understand is how they all connect?

[tropic saddle]

what do you mean with connect. you do one step and check how the det changes. then you do the next step and check again how the det changes. and so on until you can actually calculate the det

[compact token]

we know that the det(A)= 2 det(B) since the old matrix has 2* of new matrix

and the det(B)=-2 and det(C)=-2

is that right?

[compact token]

I am having trouble at this process

[compact token]

could you tell me why is this so?

[tropic saddle]

theorem point 2

C is triangular

[compact token]

oh yeah I forgot yes now we know what C is, and are we going backwards

[compact token]

okay so then what about B?

[tropic saddle]

det B = det C

by theorem point 5

and then det A = 2 det B by theorem point 4

[compact token]

oh now it makes sense

so are we solving this problem from C to A

or like A to C

[tropic saddle]

yes

more or less

[compact token]

I am so dumb, I thought that the 2 came from the fact that det(B)=det(C), thought we were adding

now I understood

thank you so much

also I did not really understand the the 6th point

[tropic saddle]

if you have a zero column then you have det 0

[compact token]

what is 0^T

how is it equal to 0^T

[tropic saddle]

the vector (0,...,0)

[compact token]

oh so it is not transpose?

[tropic saddle]

ah wait sorry no that notation is zero row

yes its indeed transpose

if you have a zero row then you have det 0

[compact token]

if I have a zero row and that is the only row or like a zero row in a matirx with other rows

[tropic saddle]

?

any zero row automatically means det 0

[compact token]

a zero row in a matrix means det(A)=0

[tropic saddle]

the other rows dont matter anymore

[compact token]

okay okay

here we have a row,

what theorem is used here?

[tropic saddle]

well we have three columns

u, v and 2u+3v

[compact token]

and also does the seventh point mean that if a row and column in a matrix are equal then the determinant of the matrix is zero?

[tropic saddle]

I dont know how the det was introduced to you

[compact token]

okay

the summation formula

[tropic saddle]

but you can for example do this by transposing and then row reducing

using point 5 and then point 6

[tropic saddle]

no, if two rows are equal then det is 0

[compact token]

I am supposed to do this without computing the determinant

[tropic saddle]

you are literally computing it to be 0

[compact token]

okay got it

[tropic saddle]

I mean row reducing in an abstract sense

[compact token]

ig this is what I should do to find the determinant without actually computing the determinant right?

[tropic saddle]

do you not have a theorem which says anything if the rows are linearly dependent?

or columns?

except those two special cases of equal rows or zero row?

[compact token]

those are the theorems written on the book

[tropic saddle]

do you have a theorem about det of A and det of A^T ?

[compact token]

no no I did not read anything of that sort until now

[tropic saddle]

well then read it

otherwise this question is impossible

I have to go now

[compact token]

okay thank you so much for your time

[compact token]

this question belongs to the section that I am reading

[pearl pond]

@compact token Has your question been resolved?

[pearl pond]

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[ornate escarp]

I am gonna try yo translate my problem

[ornate escarp]

I have f:(0,+00) -> R

Where f(x) < x

And f`(x) = x / x-f(x)

x> 0

How do I prove that f is curved?

[cloud zephyr]

did you mean concave?

[ornate escarp]

Yeah

[cloud zephyr]

then that must be related to f''(x), right?

[ornate escarp]

Yes

I tried to solve using f(x)<x

[cloud zephyr]

that's a good start

you can also find f''(x) in terms of x and f(x)

[cloud zephyr]

and using this

to check if f''(x)>0

[ornate escarp]

Yeah

So

I am going to find the second derivative of f`(x)

[cloud zephyr]

nah, just find f''(x)

which is the second derivative of f(x)

[ornate escarp]

Ok so I found that f``(x)<0

[cloud zephyr]

oh good

does it matches the answer?

[ornate escarp]

Nope

One sec

I am gonna solve for f(x)

[pearl pond]

@ornate escarp Has your question been resolved?

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• Show your work, and if possible, explain where you are stuck.
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[pearl pond]

Please don't occupy multiple help channels.

[weak surge]

so for absolute values, is the trick to test from both sides?

I mean, rewrite the expression..

(10x+10)/(x+1)

(10x+10)/(-x+1)

[ebon mesa]

-x-1

[weak surge]

oh

because you are putting - in front of the absolute?

+(x+1)
-(x+1)

[ebon mesa]

yea

[weak surge]

and that's the only thing to do when you see variables inside of an absolute? for finding limits?

test once for positive
test again for negative

[ebon mesa]

im not familiar with limits so cant really help

¯_(ツ)_/¯

[weak surge]

well, absolutes are piecewise functions to my understanding, so to remove the || brackets I need to make two versions of the same equation, I think..

one with +(absolute)
and another with -(absolute)
I think..

[ebon mesa]

thats what i think too, but there probably is a better method to solve

[weak surge]

if anybody knows of that better method for solving limits for absolutes, please let us know

[wind wigeon]

That's the easy way

[weak surge]

which is testing limit for -1+ and which is testing limit for -1-?

if an instructor wanted you to find the limit for -1- for example, only this limit

[wind wigeon]

Yes

[weak surge]

how would you know which one to use?
one with +(absolute) and another with -(absolute)