help-10

[viral quail]

oh lol

[south viper]

Make sense?

[viral quail]

I got a question on that

[south viper]

Go ahead

[viral quail]

do I always make x the subject for the first equation?

[south viper]

Nope you don’t have to

x or y

[royal basin]

@viral quail @south viper do not encourage channel intrusion

[supple granite]

tan(theta)=PB/PC=1/PC
you can find PC using the similar ratio from triangle PAB and PBC

let PC=x

so PA=4-x

whats the corresponding side to PA?

PA:PB=PB:PC

[obtuse pebble]

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[timid silo]

pls help

[timid silo]

yes?

are u a teacher

can u teach me algebra

thats the example im learning rn

[timid silo]

hello?

no help from here it

.close

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[timid silo]

i would like some help and tips on solving math competition geometry problems such as this one:

[median lava]

2

[timid silo]

i have no idea on how to approach this

[timid silo]

are you trolling or something

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

<@&286206848099549185>

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

<@&286206848099549185>

[wintry swift]

do you agree that the triangle ABC is not clearly defined with the existing data?

[wintry swift]

C is somewhere on a circle with midpoint A and radius 18.

[timid silo]

i dont get your point as it is not asking for the ABC triangle

the result is apparently 3/2

[wintry swift]

the solution is obviously not dependend on the position from C. Do you agree?

[timid silo]

yes, i think i can see why. is it because we cant know the angles that MN forms in respect of CB?

[wintry swift]

if it does not depend on C, why not choose an appropriate C? for example C in the way that the angle BAC is 90 degrees?

[timid silo]

you lost me there and i actually have to go now

anyways ill keep looking into it, thank you for giving me some hints

[obtuse pebble]

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[obtuse pebble]

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[bold cedar]

Hello. I am obviously doing something very wrong here

[bold cedar]

I tried plugging in 2.1, 2.05, and 2.01 and that apparently doesn't work

[gilded needle]

plugging those values into what

[bold cedar]

The given equation y

[gilded needle]

why would that give you the average velocity?

[bold cedar]

Because I have no clue what else to do

[abstract apex]

idk much either but for finding instantaneous velocity, you gotta differentiate the given equation with respect to t

[bold cedar]

Ah, so find y' then plug into that?

[abstract apex]

you'll get -32t by doing so, substitute the given value for t which in this case is 2, so -32x2 gives -64

[gilded needle]

how do you get the average velocity over a time interval [t1,t2] if you know the position at t1 and t2?

[bold cedar]

Add them together and divide by 2, but I think sahan's solution here is going to be more beneficial

[gilded needle]

that's for instantaneous velocity, it won't help for the first set of questions

[abstract apex]

that's only for instantaneous thingy pls, not average one

yeah

[bold cedar]

Nvm

[gilded needle]

does a formula like (change in position) / (change in time) sound familiar?

[bold cedar]

Somewhat?

[abstract apex]

basically average velocity

[gilded needle]

yep

that's how you find it given a formula for position

[bold cedar]

So find the position after 2.1 seconds, find the position after 2 seconds, and put the difference of those over 0.1

[gilded needle]

yep exactly

[abstract apex]

yepp

[bold cedar]

I am still incorrect

Hang on launching discord on my iPad to post my work

[gilded needle]

maybe it wants -65.6 instead of 65.6

since the velocity is downward

[bold cedar]

Ah

That would make sense

[abstract apex]

oh it's case sensitive

nice

[bold cedar]

Yup changing the signs of them all got me the correct answer

Thanks y'all

[gilded needle]

nice

[abstract apex]

ayyy nice nice

[bold cedar]

.close

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[formal prairie]

Can someone help me confirm this is the correct result?

The key had a more complex answer, which was not too easy to simplify

[knotty crow]

problem is

du isn't 4cos^3(x) dx

(so your answer is incorrect)

[formal prairie]

Oh cause it would be 4sin^3 (x) cos x?

[knotty crow]

yep

[formal prairie]

Oh damn I forgot about chain rule

Thank you

.close

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[alpine heron]

im confused guys please help me

[gusty dagger]

all you do

is substitutio 2 for wherever x is

[alpine heron]

i did and i got 32

but somehow the answer is 48

ive been trying to figure out how they got 48 but its confusing the fudge outta me

[gusty dagger]

its 48

2 squared is 4

times 8 is 32

• 12 + 4 is 48

[alpine heron]

my bad ive been wondering what number to square bro

my mind turned into mush

thanks for the help

[gusty dagger]

ok

yw

gl on the rest

[alpine heron]

thank you i got the next answer correct

thanks for the help

[gusty dagger]

gj

[obtuse pebble]

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[glacial gust]

Can anyone explain the working out here? I got to 21km < 15km/h * t
But I don't understand how this next part came up.

• how come h is now over 15km,
• why is 15km now in 3 places
• how did 15km get to the left side without being negated

[neon eagle]

We have literally zero context

[glacial gust]

Okay my bad, I thought it was straight forward enough. I will give more context

So I'm doing 'comparing linear rates'

This is the original question, I got 3. But was wrong, I will show how I got there

First I made them equal each other, like this:
149km - 95km/h = 170km - 110km/h

Then I simplified it, and included t variable on each side also, down to this: 54ht = 60ht
And simplified more:
2t = 6h
So I got 3 hours

I also worked it out like this another time around:
When I simplified it I got to
2t * 15km/h = 21km
So I got rid of the km as they canceled each other out
So left with
2t*15h = 21

<@&286206848099549185>

[timid silo]

hello what seems to be the problem

[glacial gust]

Hello sir

[timid silo]

conversion of rates?

[lethal wedge]

i got 149 - 95t = 170 -110t

[glacial gust]

I am stuck on comparing linear rates in Algebra 1

[timid silo]

ah ok let me see

[glacial gust]

Okay so instead of km && km/h you use t?

[lethal wedge]

yea t is expresed as hour

[timid silo]

so we have to make a formula?

[lethal wedge]

and the term by itself isss km

[glacial gust]

This is what I'm really confused about, how did it go from this to that (See text attached)

[timid silo]

idk

[glacial gust]

Hmm, it seems random?

That's relieving in a way

[lethal wedge]

this becomes 21/15t

to find the value of t

[glacial gust]

Omg

You helped

A lot

Damn

Yeah

[lethal wedge]

to find which one does it first you find the value of each

[glacial gust]

I remember now how this relates to other stuff I've learnt in algebra 1

[lethal wedge]

so 149=95t chimaka

and 170=110t valente

[glacial gust]

Okay so the hour is t, but km cancels each other out?

[lethal wedge]

yea it cancels out when you dimensional analysis which is why I ignore it

[glacial gust]

Okayy

I will quickly solve next question now it will take 6 minutes, and I will complete this help chat once done, as I don't want to come back

I know I have it though

Thanks man

Yea I think I got this

Appreciate it

Thanks yall!

✌️ ☮️

.done

.close

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[lost tree]

hello, quick question, if i wanted to approximate the distribution of X with a normal distribution, it shud have a mean of 49/2, standard dev of 7/2. if i wanted to find F_x(14), wud i integrate the normal distribution from 13.5 to 14.5

[wise talon]

may I know what F_x is

[lost tree]

im thinking its the distribution function of X

[wise talon]

X is a binomial I'm assuming

[lost tree]

F_x(14) = P(X=14) ig

[lost tree]

yeah

[wise talon]

,w binom(49, 0.5)

[warm shale]

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[wise talon]

Ok I believe there is an explicit formula to obtain this

Doesn't require integration

[lost tree]

there is, but i want to know how i might approximate a binomially distributed variable with a normal distribution when sometimes the formula gets too complicated

[wise talon]

P(x) = nCx p^x q^(n-x)

where C is just the combination function whatever blah blah

[lost tree]

yeah

[wise talon]

hmm

,w binomial distribution 49, 0.5

[warm shale]

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[wise talon]

for the discrete outcome I am genuinely not too sure

because integrating that specific point gives 0

[lost tree]

i have got this

[lost tree]

yes but we are supposed to do a "continuity correction" when u change from a discrete one to a continuous one

a +/- 0.5

[wise talon]

ok integrating a normal distribution is integrating a gaussian function

if you mean do it by a calculator

im sure thats doable

[lost tree]

yeah

and do u know how to use these standard normal distribution tables

[wise talon]

ah shoot sorry I forgot all my HS stats

I usually plugged it into my calculator

and let it handle it for me

[lost tree]

oh lol

how do i use wolfram alpha to find where the area to the left of a standard normal distribution is 0.03

[brisk matrix]

,w inverse normalcdf(.03)

[warm shale]

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[lost tree]

can i find a value?

[brisk matrix]

i don’t even know if we want inverse cdf, i forgot all my stats lol

[lost tree]

idt this is what im looking for

im looking for z such that 1/2erf(z) = 0.03

ig

[brisk matrix]

,w erf^-1(.03/2)

[warm shale]

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[lost tree]

,w erf^-1(0.06)

[warm shale]

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[brisk matrix]

wow 1/1/2 = 1/2

forgive me 😂

[lost tree]

this is what im trying to do btw

,w erf^-1(0.5 - 0.03)

[warm shale]

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[lost tree]

,w erf^-1(0.03 - 0.5)

[brisk matrix]

i believe the problem is your mean and standard deviation don’t necessarily correlate to the error function (unless you’re using z scores)

[lost tree]

yeah, im trying to find the z score such that the area behind that is 0.03

idk how erf works really, is erf(z) = area to the left of z in a standard normal distribution ?

[lost tree]

or is 0.5 + erf(z) = area to the left of z ?

[lost tree]

well what i really want to know is how i might do this using tables

this is my table

the solution they have given is this, and idk why K = -1.8807

[lost tree]

at -1.8807 this table shows 0.03053

why wud we pick that and not 0.02999 or 0.03005

[obtuse pebble]

@lost tree Has your question been resolved?

[lost tree]

🙁

[lost tree]

<@&286206848099549185>

[lost tree]

.close

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[vernal schooner]

Need some help with 3b please

unsure of what to do

[lost tree]

set the vector equation of L1 equal to the vector equation for L2

[obtuse pebble]

@vernal schooner Has your question been resolved?

[vernal schooner]

Hey sorry

So for L1 equation I have (-7j,4k) +t(3i,-j,-2k)

bit confused rn

[obtuse pebble]

@vernal schooner Has your question been resolved?

[frosty spoke]

you have two points on line L_2

can you find the equation of line l2 given that?

well actually you have a point and the slope

but whatever

[vernal schooner]

is L2 not already the vector equation?

[frosty spoke]

yeah but you don't have the starting point

[obtuse pebble]

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[smoky zenith]

Sorry for the weird question, but whats the name of this notation?

[marble ingot]

i know it as scientific notation

[smoky zenith]

k, ty

.close

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[hot monolith]

How do I explain?

[hot monolith]

And how to find the domain and range for k-¹(x)
k-¹(x) is (x-5)²+1

[floral canopy]

You mean on b)?

[hot monolith]

Yeah b)

[hot monolith]

And this for c)

[floral canopy]

ok. For b, you’re gonna need to find the domain of 1/g(x).

[hot monolith]

How do I find the domain again? I forgot 😶

[floral canopy]

I think they have a mistake

Can someone back me up on this?

[floral canopy]

1/g(x) is defined when g(x) is not zero.

[daring rock]

g^-1(x) is the inverse function of g. It is not 1/g(x)

[floral canopy]

Oh I thought the -1 was on all of g

Thanks

[hot monolith]

So uh, how do I explain it

[daring rock]

Informally, the function g: R -> R (defined with a domain of all real numbers) is not a one-to-one function, so its inverse does not exist.

However, the function g: [1,inf) -> R (defined with a domain of [1,inf)) IS one-to-one, so its inverse does exist.

[hot monolith]

I don't understand anything I'm only 11th grade 😭

[daring rock]

Do you know what the inverse of a function is?

[hot monolith]

Yeah it's like the opposition right

[floral canopy]

What

[hot monolith]

I haven not yet to learn the theory part

[floral canopy]

Fine the inverse and there will be a root then the domain is when the thing inside The root is greater than zero

Greater of equal

[daring rock]

The inverse of a function swaps all the inputs and outputs. In other words, if f(a) = b, then f^-1(b) = a

[hot monolith]

Ah

Ohh I see

[daring rock]

This function, g, is not one-to-one, meaning that there are two inputs for any given output.

For example, g(-1) = -2, but also g(2) = -2

Which means its inverse function does not exist

because what would be g^-1(-2) ?

Is it -1 or 2?

It cannot be defined so we say the inverse doesn't exist

[floral canopy]

It’s just a +-

[daring rock]

That's not a function

[floral canopy]

Because of the quadriceps formula

[floral canopy]

You’re right

It’s two

[daring rock]

So yes, you could also say "the inverse is not a function" rather than "the inverse does not exist"

But I'm using the language from the original question

[floral canopy]

But for x greater than 1

Both aren’t defined

[daring rock]

Only one is, exactly

[floral canopy]

Both are not defined

[hot monolith]

It's alright Its just 1 marks

[daring rock]

The first graph is g defined on all real numbers.
The second is g defined only on x>= 1

[hot monolith]

How do I find the d and r tho

[hot monolith]

Now I'm considering if I want to study further mathematics

[daring rock]

The question just says explain why x>=1 is a suitable domain for g if you want g^-1 to be defined

[hot monolith]

[hot monolith]

I mean

Sec

cii)

[daring rock]

okay, so k is a sqrt function

In your head can you see what the graph is basically shaped like?

like what a sqrt function in general looks like

[hot monolith]

Something like this?

I don't remember

[daring rock]

Yeah

Importantly, it only ever increases

which means it is one-to-one (there's only one possible input for each output)

k^-1 is the inverse, so the inputs and outputs switch

The domain of k is 1 < x < 101
so this will be the range of k^-1

[hot monolith]

Yeah I understand this

[daring rock]

Similarly the range of k becomes the domain of k^-1

Since k is one-to-one, you can find its range by just plugging in the endpoints

Find k(1) and k(101)

[hot monolith]

I just don't remember how to find the range

For k(X)

[daring rock]

The range is the set of all possible output values

Since k only increases, its minimum value is k(1) and its maximum value is k(101)

[hot monolith]

Isn't range <x<? Why is it domain?

[daring rock]

I'm sorry, I don't understand your question

[hot monolith]

For example

-1>x>2 means 0,1 right? Isn't this a range?

How come 1<x<101 is a domain?

[daring rock]

I think you have a couple of misconceptions here

[daring rock]

First, there are lots of numbers between -1 and 2, not just 0 and 1

We're not concerned only with whole numbers, but with all real numbers

[hot monolith]

Well

Just an example

You get my point right? Isn't that a range

[daring rock]

That's the other misconception. It think you're saying "range" when you mean "interval"

-1 < x < 2 is an interval on the number line

"range" specifically refers to the set of numbers which can be an output for a function

[hot monolith]

Oh

[daring rock]

This can be an interval, like "all numbers between -1 and 2" which is what you're talking about

But it can also be "all real numbers" or even just a single real number

like h(x) = 1 has a range of only the number 1

since that's the only output

The domain and range can both be intervals on the number line

Often, they are

[hot monolith]

Yup

Isn't "all numbers detween -1 and 2 a range?

[daring rock]

I would not use the word range

[hot monolith]

My brain is fried

[daring rock]

"Range" specifically means the set of all output values of a function

So a function can have a range of -1 < y < 2
But it can also have a domain of -1 < x < 2

[daring rock]

Don't worry about this too much right now

You're using the word range when you should be saying interval

Let's just answer this question and I think it'll help

[hot monolith]

Alright

[hot monolith]

So it means the graph starts at -1 and end at 2?

Well not start because it isn't ≤

[daring rock]

If the domain is between -1 and 2, then horizontally, the graph exists between x=-1 and x=2

if the range is between -1 and 2, then vertically, the graph exists between y=-1 and y=2

[hot monolith]

OH

I get it

[daring rock]

For example, this function has a domain of 1 <= x <= 4
and a range of 0 <= y <= 9

[hot monolith]

Like this? For example

[daring rock]

yes exactly

[hot monolith]

Finally I understand

[daring rock]

Hell yeah

lol alright

[hot monolith]

I can do every topic except functions

[daring rock]

You'll get used to it, just takes some practice

[hot monolith]

What are you studying?

Is A levels for math worth it? I'm considering

[daring rock]

I'm not in school, I just study math in my free time

And I'm in the US lol, there's nothing called A level here, I'm not exactly sure what that is

[hot monolith]

It's like further studies

For math

And I might take further maths but I'm still not sure

[daring rock]

That's totally a personal decision, I can't give you much advice

except

Take a few more math classes, and see if you enjoy it 🤷

[hot monolith]

I'm kinda enjoying additional mathematics currently

It's kinda fun

[daring rock]

If you continue studying math, it'll be a lot more rigorous logical proofs, and a lot less calculating things with numbers

[daring rock]

I agree 🙂

[hot monolith]

I was thinking statistics since I'm going for actural science

[daring rock]

You'll definitely have some math classes then, but they might be more focused on computation rather than proving things

[hot monolith]

Oh yeah and what does this mean

I'm pretty sure it's X is not a real number

But I don't understand

[daring rock]

no, the opposite

[hot monolith]

Oh

[daring rock]

"x is in the set of real numbers"

[hot monolith]

I see this in some function questions but I don't know what it does or

[daring rock]

This symbol: $\in$

[warm shale]

tatpoj

[daring rock]

means "an element of"

So

[hot monolith]

Isn't that venn digram

[daring rock]

$x \in \R$ means "x is an element of the set of real numbers"

[warm shale]

tatpoj

[daring rock]

I mean, you can use venn diagrams to represent set relationships, but that's just a visual aid

[hot monolith]

I see

What does no real root mean?

Or discriminant

[hot monolith]

Yeah Ik it's b²-4ac<0

[daring rock]

Hm, you're going off in quite a few different directions here

[hot monolith]

I just don't know what it means

[hot monolith]

Idk 😭

[daring rock]

It sounds like you're talking about quadratic functions now?

[hot monolith]

I think so

Isnt it associated with quadratic

[daring rock]

this certainly is. This is how you find the discriminant of a quadratic

[hot monolith]

What is a discriminant

[daring rock]

That b^2 - 4ac, that's just a piece of the quadratic formula

Do you know the whole quadratic formula?

[hot monolith]

Yeah

[-b±sqrtb²-4ac]/2a

[daring rock]

so

look at that part in the sqrt

b^2 - 4ac

[hot monolith]

Yeah it's the same

[daring rock]

If that's negative, then the quadratic formula is not going to give you a real number

because it'll be the square root of something negative

so if b^2-4ac < 0, then the quadratic has no real roots

[hot monolith]

Which is a imaginary number

[daring rock]

right, you'll get complex roots instead

[hot monolith]

Cuz it has the i thing

[daring rock]

yes

[hot monolith]

I see

Alr then, thanks for the troubles

.close

[obtuse pebble]

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[daring rock]

👍 no problem

Feel free to dm if you want, I'll answer when I can

[obtuse pebble]

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[novel crystal]

help pls

[marble ingot]

think of the argument of a complex number geometrically

[novel crystal]

sorry i dont get what you mean

[marble ingot]

The argument of a complex number is the angle between that number on the complex plane and the real axis

[loud tangle]

draw out the complex number line

plane

[novel crystal]

oh yes I know this

[novel crystal]

do i draw a line with the angle 3pi/4 ?

[marble ingot]

you need to draw all complex numbers whose angle is less than 3/4 pi

just a line won't do

*angle from the real axis

[novel crystal]

i'm confused by what you mean by this

[marble ingot]

for instance a line through the origin with angle 1/2pi would also be part of the set

since 1/2pi < 3/4 pi

[novel crystal]

so i draw all the complex angles from 3/4 pi to -pi?

since -pi is the domain of an arg

<@&286206848099549185> am i correct

[obtuse pebble]

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[spare oracle]

I have no idea how to do this

pls help

[knotty crow]

hint: 9^n = (3^n)^2

[spare oracle]

by no idea I mean I haven't learnt it all

I mean that'd be too hard to do for me

so can someone tell me the name of this type of question

so I can search up a guide

[knotty crow]

wait

don't you understand how 9^n = (3^n)^2 ?

or further process

[spare oracle]

nope

well I do but like idk what the n =/= 0 means

it throws me off

[high lily]

where n isn't equal to 0

as if n=0, you'd have division by 0

[spare oracle]

ohhh

[high lily]

in the simplest form of that notation
x/x = 1 when x isn't 0

[spare oracle]

yeah

ok thx I will try to solve it now

close.

wait what was the command

[high lily]

dot before the close

[spare oracle]

.close

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[spare oracle]

ohhh ok I get that now

[spare oracle]

so after that factorisation, just simplify?

and answer

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[daring canyon]

Hi

[lost tree]

hi what is ur qusetion

[obtuse pebble]

@daring canyon Has your question been resolved?

[daring canyon]

Yes

[obtuse pebble]

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[languid shuttle]

Can you integrate both sides of an equation ? So like if we had , 2x = 3y, could we just get x^2 = 3y^2/2

[sacred root]

Ig ye but you've to do it with only respect to one variable

[languid shuttle]

so you cant do it to different vareiables

[sacred root]

Nah

[languid shuttle]

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[gentle shard]

How do I evaluate the indefinite integral?

[marble ingot]

By substitution

[sage geode]

Would consider substituting for the insides of cos

(Horrible name for "input", I know)

[gentle shard]

u = pi/x^43?

[sage geode]

Yes

[gentle shard]

now i have du = -43pi/x^44 dx

[sage geode]

Right

[gentle shard]

du/(-43pi/x^44)

[sage geode]

And, as you can see, you already have 1/x^44 dx there

[sage geode]

Or do it like that, yeah

That simplified to -dux^44/43pi btw

[gentle shard]

what did we do with pi?

[sage geode]

My bad

[gentle shard]

so x^44 cos(u)/43pi x^44 ?

[sage geode]

Yeah and x^44's cancel out

[gentle shard]

-cos(u)/43pi

[gentle shard]

answer is -cos(u)/43pi + C?

oops

[sage geode]

Don't forget to resub

u = pi/x^43

[gentle shard]

-sin(pi/x^43)/43pi + C

its correct, thanks

.close

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[half meadow]

You have to find the value of sin in terms of a?

[sand elm]

Q:30

[half meadow]

Right

What's the basic formula for tan?

In a triangle

[verbal herald]

can some1 help me with my hw

[sand elm]

i mean clearly, my answer does not match the answer

[half meadow]

Go to #help-14

[verbal herald]

k

[half meadow]

What's the basic formula for tan in a triangle?

[sand elm]

sin/cos

[half meadow]

In terms of adjacent and Hypotenuse and opposite i meant

[sand elm]

opp/adj

yes

[half meadow]

Yes

Compare that with the given value for tan

[sand elm]

thats why i wrote sin/cos

[half meadow]

You should get the value of opposite and adjacent

[sand elm]

this

[wet drift]

Treat it like tan theta = a/1 = P/B,. Now solve for Sin theta

[hidden garnet]

Absolutely

[sand elm]

so do this instead tanx=a/1, where opp=a and adj=1

[half meadow]

Yes

And find the hypotenuse

Then you can find sin

[sand elm]

hypotnuce will be an unknown variable, since there a is unknown

yea so, i tried and didn't get anywhere useful

[sand elm]

?

sin=a/x

x=hypotnuce

which is unknown

[sand elm]

?

[wet drift]

h = sqrt (p^2 + b^2)

[sand elm]

i went 5 different paths

[wet drift]

Solve this

P is perpendicular and H is Hypothesis and B is base

[sand elm]

how does one get that? is that an identity?

[wet drift]

You call these things adjacent opposite

We call these H P B

[sand elm]

i know that

wait

you apply pythogrean theorm

[wet drift]

Yup

[sand elm]

fk

i get it

[obtuse pebble]

@sand elm Has your question been resolved?

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[plain plaza]

how do

[daring rock]

Plug in the points for (x,y)

Then you have two equations relating a and b

Then you can solve the system with substitution

[plain plaza]

wdum

[daring rock]

Start by plugging in the points for x and y so you get two equations

[mental wyvern]

a.b=3
a.1/b^3=768

[plain plaza]

how so

[mental wyvern]

points are display of functions on plane

(1,3) is when x equals 1 function output is 3

[daring rock]

The form is y = a(b)^x. Take the point (-3, 768) and plug it in. What do you get?

[mental wyvern]

they meant replace the x and y with numbers given

[plain plaza]

so just likee

768 = a(b)^-3

[mental wyvern]

yeah

[plain plaza]

but what do i do w that

[daring rock]

Yes, then do the same with the other point

[mental wyvern]

also do the other point

[plain plaza]

ok then what

[mental wyvern]

solve the system

do you want me to do it?

or will you try

[plain plaza]

how

i need to know how, not just this particular question

[mental wyvern]

wait

its hard to text it

let me write on paper

[daring rock]

Do you remember solving systems of linear equations with substitution?

These aren't linear equations but the process is the same

[plain plaza]

yeah

[daring rock]

So your two equations now
768 = a(b)^-3
3 = ab

Solve one of them for a, for example

then plug that into a in the other equation

[plain plaza]

howw

i dont know how to do it when theres 2 variables

[mental wyvern]

hold

ab = 3 i wrote wrong there

try to remove one of the variables

then solve

[plain plaza]

im just gonna not get this question i think 😭

[plain plaza]

HOW

lmao

im dumb im sorry

[mental wyvern]

i mean

you should be able to transform the equation

[mental wyvern]

check this

i did use "ab=3 equation" and inserted into second equation

so only b variable remains

then solved

after b found inserted into ab=3 equation

to find a

i messed up with numbers but path is true

ask your teacher to teach it again because you are missing the main issue

[obtuse pebble]

@plain plaza Has your question been resolved?

[obtuse pebble]

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[dapper ferry]

Do integrals differ from derivatives in this way; if there is something more in the place of the "x" does the formula still apply?

[dapper ferry]

or is this using a different formula to turn it into ln[3x+1|

I guess my question is just ^^^^ which formulas were used for that

[pine sail]

it's basic u sub.

Or you can simply notice, after they've multiplied and divided by 3.

Numerator is derivative of denominator.

[warm shale]

What the hell am I doing here?

[dapper ferry]

oh right yea it is using that

riight okay

yea thanks my problem is solved

idk how to close this

[pine sail]

.close

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[exotic creek]

how come it is y minus $2pi^2$

[warm shale]

yomiko

[knotty crow]

y(pi) = 2pi

[warm shale]

Modus

[exotic creek]

i get this but i dont get why is it subtracted

[knotty crow]

$\NormalLine$

[warm shale]

Modus

[knotty crow]

move f(x0) into LHS

you'll get y - f(x0)

[fast wolf]

hey guysss

[knotty crow]

in this case f(x0) = 2pi^2

[exotic creek]

this makes no sense in my head

[knotty crow]

other form is

y - y1 = m(x-x1)

you know this?

[exotic creek]

yes

ah right

yes i get it

thanks

.close

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[timid silo]

Can I get help with this please

[knotty crow]

,rccw

[knotty crow]

u know how to draw quadratic?

[timid silo]

Yes

[knotty crow]

and piecewise function's graph?

[timid silo]

The second one no

Well yes

[knotty crow]

so you want to solve f(x) = g(x)

[timid silo]

Right?

Yes

[knotty crow]

so |x^2 - 4| = 2x + k

[timid silo]

Yes

[knotty crow]

I'd suggest defining a function as follows

h(x) = |x^2 - 4| - 2x

then it's h(x) = k

[timid silo]

Ok

[knotty crow]

now you should graph h(x)

[timid silo]

Ok I will do real quick

I have it

[knotty crow]

good

now it will be easy

imagine a line y = k for some k (line parallel to x-axis)

[timid silo]

Yes

[knotty crow]

e.g. for k = -1 it's y = -1, for k = 5 it's y = 5 etc.

[timid silo]

Yes

[knotty crow]

can you determine for what value of 'k' that line would cross your graph at 4 points?

[timid silo]

I’m going to try real quick

[knotty crow]

you can take a ruller and move it from the bottom to the top and see then

[timid silo]

Use discriminate?

Discrimination

Oops

[knotty crow]

no, you don't need math now

[timid silo]

Ok

[knotty crow]

I'll show you an example

for the red one we have 2 points

for the blue one there are 3

[timid silo]

Yes

[knotty crow]

can you find place where it would be 4?

[timid silo]

No

Actually yes

Right above the blue line

Just a little bit up

[knotty crow]

yeah

so for k = 4 (blue line) it was 3

for the orange one it's 4

now you need to determine range of values of k for which we still have 4 common points

[timid silo]

Ok I’ll be back in one minute sorry

Back

[knotty crow]

if you don't understand this

this should help you

[timid silo]

I’m just confused now how to find the range of k even though I know where the four points happen

Wait

Actually

It’s 4<k<5

About

I think

[knotty crow]

yes

exactly

[timid silo]

I can see from the graph, but how would I do it exactly

[knotty crow]

you mean how you can solve it algebraically?

[timid silo]

Well yes or just the graph is like an approximation

Even though in this case you can tell

[knotty crow]

I wouldn't say it is, if you did the graph accurate it's a "legit" solution

(it refers to important points)

[timid silo]

For example what if it was like 4.0815<k<4.9887, how would I get that exactly instead of just 4<k<5

Would you use calculus to find relative minimum?

And maximum

[knotty crow]

if it was (or I expected solution will be like this) I wouldn't use a graph to solve it

[timid silo]

How would you do it

[knotty crow]

we can do it algebraically doing f(x) = g(x) and using discriminant

(we have to consider two cases)

[timid silo]

Somehow I messed it up though and did -5<k<k

Oops I meant

-5<k<5

Could you explain real fast how to do with discriminate

Discriminant*

[obtuse pebble]

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[placid birch]

hello , I have math homewok if anyone can help ( it's not complicated) the math is in french but I can translate it to you !

[placid birch]

Exercice 1
Simplifier les expressions suivantes :
a. 24×23 b. 58

53 c. !
32"4

d. 34×93 e.
49
25 f. 25 − 24

Exercice 2
Effectuer les opérations suivantes :
a. 3×10−3 + 2,5×10−2 b. 254×1030 + 78×1033
c. 94,1×10−13 − 0,012×10−10
Exercice 3
ABCD est un rectangle qui a pour aire 211 cm2 et tel que :
AB = 25 cm.

1. Calculer AD en cm. On donnera le résultat sous forme d’une puissance de 2.
2. Calculer le périmètre de ABCD en cm. On donnera la réponse sous forme a×26 où a est un entier.
   Exercice 4
   Ecrire les nombres suivants en écritures scientifiques :
   a. 312×105 b. 0,00219×106 c. 3 542×1011
   Exercice 5
   On laisse tomber une balle d’une hauteur de 1 mètre.
   A chaque rebond, elle rebondit des 3

4 de la hauteur d’où elle est tombée.
Quelle hauteur atteint la balle au cinquième rebond? Arrondir au cm près.
Exercice 6

1. Donner la troncature au millième près de A= 25,3467
2. Donner l’arrondi à 10−2 près de :
   B = 75,2445 ; C = 0,3596
3. Donner un encadrement au dixième près de D = 23,74

Exercise 1
Simplify the following expressions:

Exercise 2
Perform the following steps:

Exercise 3
ABCD is a rectangle which has area 211 cm2 and such as:
AB = 25 cm.

1. Calculate AD in cm. The result will be given as a power of 2.
2. Calculate the perimeter of ABCD in cm. The answer will be given as 26 where a is an integer.

Exercise 4
Write the following numbers in scientific writing:

You drop a ball from a height of 1 meter.
Every time she bounces, she bounces three quarters
am
from the height from which it fell.
How high does the ball reach on the fifth bounce? Round to the nearest cm.

ex 6 Truncate to the thousandth near A= 25.3467

Round to 10-2 near:
B = 75.2445; C = 0.3596

Coach the tenth close to D = 23.74

<@&286206848099549185>

[obtuse pebble]

@placid birch Has your question been resolved?

[placid birch]

[placid birch]

<@&286206848099549185>

[crimson berry]

!status

[obtuse pebble]

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

[crimson berry]

Also pick a question, nobody will probably want to do your whole homework assignment with you

[placid birch]

ok

[plush minnow]

For the first exercise you can use the formulas for power:
a^x×a^y = a^(x+y)
a^x / a^y = a^(x-y)
(a^x)^y = a^(x×y)

For example:
a. 2⁴×2³ = 2^(4+3) = 2⁷
b. 5⁸/5³ = 5^(8-3) = 5⁵
(Try doing the rest yourself to practice and lmk if you need help).

For the second one you have to understand how negative power works. Simply:
a^-x = 1/a^x

a. 3×10^-3 + 2.5×10^-2 = 3×1/10³ + 2.5×1/10² = 3/10³ + 2.5/10² (not sure if you're supposed to calculate them)

In exercise 3 you first need to find what AD is equal to 8.84 and then turn that to a power.
8 = 2³, so 8.84 = 2³ + 0.84
Not sure what the second point means, though.

Exercise 4:
You have to first turn them into scientific numbers and then use the formulas for power again to simplify them.
312×10⁵ = 3.12×10²×10⁵ = 3.12×10⁷

Exercise 5:
Each time you drop the ball it will bounce 1/4 times lower.
1×3/4×3/4×3/4... = 1×3⁵/4⁵ = 243/1024 you can turn that into a number and round it.

Ex.6: 10^-2 is just 1/100 we again have to use the formulas for power:
B = 75,2445 = 752445 / 10 000 = 752445 / 10⁴ = 752445 × 10^-4 if we have to turn it to 10^-2 it would be the same as 752445 × 10^-2 = 752445 / 100 = 7524.45 I suppose that's what you mean by rounding but not sure

Ex. 7: Do you mean you want to round it or?

[placid birch]

oh my god

thanks so much ! ffor your time !

[plush minnow]

Np. These are not all, though. I left some for you to solve for practice, lmk if you need help.

[placid birch]

thanks !

[obtuse pebble]

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[obtuse pebble]

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[thick wind]

Can someone explain how to do this

.close

[obtuse pebble]

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[hard minnow]

I got this problem wrong before, so I just wanted clarification on whether I'm going by the proper process..

When they say use eight approximating rectangles and right endpoints., they mean make eight subintervals, right?

Anyone?

[pliant tide]

can u show me ur calculations

[pliant tide]

ye 8 rectangles

[hard minnow]

These are my calculations for the left endpoints

[pliant tide]

Did you add all of those answers and multipled by your delta x

to find your final answer

[hard minnow]

Yup, not sure whats going on

im double checking my arithmetic rn

[pliant tide]

Maybe the problem is how you rounded your answers

[hard minnow]

It says this "Report answers accurate to 4 places. Remember not to round too early in your calculations."

[pliant tide]

When you add all of those up, how much did it give you

and by what delta x did you multiply

because your approach is correct from what I'm seeing. perhaps just the arithmetic isn't

[hard minnow]

I multiplied by 1/4

It gave me .469765

I think my arithmetic is just wrong

[pliant tide]

@hard minnow

[hard minnow]

This is weird, the aruthmetic is all over the place on my end let me try it.

OH

[hard minnow]

I HAD THE RIGHT AND LEFT MIXED UP

[pliant tide]

oh haha

[hard minnow]

.close

[obtuse pebble]

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[lethal cave]

https://cdn.discordapp.com/attachments/326138772477575180/1068669329404604456/image.png

[lethal cave]

so if you revolve this around x=0

[wooden cipher]

Cool diagram

[lethal cave]

https://cdn.discordapp.com/attachments/557748247691788310/1068667459843924090/image.png

is that the integral?

if so anyone know the difference in answer

https://cdn.discordapp.com/attachments/326138772477575180/1068674608875700294/image.png

https://cdn.discordapp.com/attachments/326138772477575180/1068674187239116921/image.png

[knotty crow]

symbolab interpreted it as revolution around y = 0

[lethal cave]

oh

[lethal cave]

but my setup is right?

[knotty crow]

I hope

[lethal cave]

.close

[obtuse pebble]

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[fervent bluff]

Stuck on this limit

[tardy epoch]

write your fraction as the derivative of some function evaluated at the point a

[fervent bluff]

Would that be using (f(x+h)-f(x))/h

[misty iron]

Mhm, and if you look at the limit at hand very carefully you can actually see it.

[tardy epoch]

yup

[fervent bluff]

Ah I do see that now

but I’m not entirely sure how to write the fraction as the derivative of some function evaluated at a

[spiral knot]

just expand (x+a)³ if the derivation method isn't clear for you

(x+a)³ - a³ = x³ + 3ax² + 3a²x + a³ - a³
= x³ + 3ax² + 3a²x

then divide by 4x and calculate the limit when x tend to 0

[fervent bluff]

So then I'd have (x^2+3ax+3a)/4

and then just plug in the x values, right?

so 3a/4

[spiral knot]

yes

for the derivation method

we know that $f'(0) = \frac{f(x) - f(0)}{x - 0}$

[warm shale]

Mehdi_Moulati

[spiral knot]

so

[spiral knot]

sorry , it's should be 3a²/4 not 3a/4 @fervent bluff

( (x+a)³ - a³ )/4x = (x³ + 3ax² + 3a²x)/4x
= (x² + 3ax + 3a²)/4

[fervent bluff]

Ahh I see!

I really appreciate the help with that

my problem was algebraic, when expanding (x+a)^3

[spiral knot]

any time

[warm shale]

Mehdi_Moulati

[spiral knot]

derivation method as Riemann said

[obtuse pebble]

@fervent bluff Has your question been resolved?

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[obtuse pebble]

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[quasi needle]

I figured the conversion by assuming the Euroe is worth more than other currencies... So by this chart, 450 Euros should get 450 * 1.111 = 500 CHF.

[quasi needle]

But 500 isn't there, so the only other answer is to assume Euroe is worth less than the other currencies. But how do we know what to assume, besides using the available options?

[quasi needle]

Yup, that's what it has to be for the answer to be right. But how do we figure that before seeing the options?

[quasi needle]

_ _

[trail cloak]

You read the row from left to right.

[quasi needle]

Haha yeah, but why is it necessarily to and not from? And this conversion doesn't align with how currencies usually are (like USD always being worth more than AUD)

[trail cloak]

Well math questions aren't always based on irl

Plus, tables are read like: "Row title/unit, numbers to the right or left to it corresponding to the column"

[quasi needle]

Sure. IT's silly, but doesn't matter to do the math. Is it convention with these tables that the collumns for a given row are the "to" conversion? I can't see any other indication that it should be like that.

[quasi needle]

I see

What a silly question :)

.close

[obtuse pebble]

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[trail cloak]

No no it's not silly

"No stupid questions"

[quasi needle]

I think it's silly. The conversions align almost perfectly with how currencies are, but it's inverted!

And it just assumes people are aware of the convention you mentioned.

[obtuse pebble]

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[viral lake]

.help

[obtuse pebble]

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

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

[fluid walrus]

the answer is 1/5^2/3 but im unsure on exactly how to get there

i see, that helped thank you

[obtuse pebble]

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[wooden cipher]

we know pi

its a number

3.1415 yada yada

so we solve for?

ok

.close

[obtuse pebble]

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[drowsy carbon]

Hey, can someone please verify this for me? ( in red )

[drowsy carbon]

I'm not sure where the 2 disappears

1/2

[tardy epoch]

chain rule

[drowsy carbon]

Not the u^2

[tardy epoch]

what's $\frac{d}{du} u^2$

[drowsy carbon]

So it was Sqrt(U^2+1) --> once derived it would be (U^(2)+1)^(-1/2)

[warm shale]

riemann

[drowsy carbon]

2u

Ohh

[tardy epoch]

missing 2 there

[drowsy carbon]

Ohhh thank you!

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[obtuse pebble]

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[glacial breach]

9x+5+04494944x=94849449494994-9x+9303

[grizzled shore]

,w 9x+5+04494944x=94849449494994-9x+9303

[warm shale]

Results provided by WolframAlpha

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

Requested by Frosst#1111

[glacial breach]

thanks sir

[grizzled shore]

it's just a linear equation with a bunch of big numbers

ax + b + cx = dx - ax + e

2ax - dx + cx = e - b

x(2a - d + c) = e - b

x = (e - b)/(2a - d + c)

[glacial breach]

.close

[obtuse pebble]

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[glacial breach]

.close

[obtuse pebble]

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[onyx gazelle]

Currently working on partB

[onyx gazelle]

Seems it have both "time shifting" and "scaling", how could I find the FT of this?

[obtuse pebble]

@onyx gazelle Has your question been resolved?

[gilded needle]

perform the corresponding operations on the fourier transform

the only thing you need to work out is the order in which they are applied: first scaling then shifting, or vice versa?

[onyx gazelle]

I think shifting first then scaling?

[gilded needle]

you can check by plugging in points

or also by reasoning like this:

[onyx gazelle]

So actually I don't need to write it as x(2(t+3/2)) for x(2t+3)?

[gilded needle]

if you first shift by 3/2 and then scale by 2, then the shift moves the triangle peak to -3/2, but then scaling moves it again

whereas if you first scale and then shift, then the peak ends up at -3/2

so check:

where does the peak end up

[gilded needle]

no you should, that clarifies that there are two operations

[onyx gazelle]

OK I will try

[obtuse pebble]

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[onyx gazelle]

.reopen

[obtuse pebble]

✅

[onyx gazelle]

@gilded needle Hello sir, so I just tried first apply shift first,then scale, do you think it is correct?

[gilded needle]

i believe it is the other order, first scale then shift

X(2(t+3/2)) has its peak at t=-3/2

that would not happen if you first shift to -3/2 and then scale

the scaling moves anything that is not at t=0

[onyx gazelle]

I find it hard to understand🥺

So we must do scale then shift when we encounter question like this?

[gilded needle]

that's just the way it is

X(a(t+b)) means "first scale by a then shift by b"

[onyx gazelle]

So I scale it first and obtaining this result by definition.

But how do I next apply the shifting, so confused rn...

Do I just multiply it by e^-jw3/2 ? Like from the definition too

but that will be just same as do shift first