help-38

[dapper swift]

then we can do a substitution

replace 2^x with u everywhere

[wraith garden]

how

[dapper swift]

$(2^x)^2 + 3 \cdot 2^x + 4 = 0$

[solid kiln]

south

[dapper swift]

becomes $u^2 + 3 \cdot u + 4 = 0$

[solid kiln]

south

[wraith garden]

what is u

[dapper swift]

u = 2^x

[wraith garden]

oh

u substriture?

substiture**

[dapper swift]

yes

[wraith garden]

then what do you do

is it

$u^2+u+7$

[solid kiln]

Inuji

[wraith garden]

is that final answer

or we do

(u+4)(u-3)

[dapper swift]

nah it's $u^2+3u+4 = 0$

[solid kiln]

south

[dapper swift]

shit this one isn't factorisable sorry

[wraith garden]

oh

how do u factor something unfactoriable

???W

[dapper swift]

you have to use the quadratic formula

you'll get imaginary numbers

[wraith garden]

the long sh

no

:((

i hate formulas

[wraith garden]

is there no other way

i really hate formulas

cuz u have to memorize so long

[dapper swift]

nah

don't worry your problems won't be this nasty

[wraith garden]

can u give more

[dapper swift]

do you have any textbooks?

[wraith garden]

can u solve this

.

[wraith garden]

do u need formula\

[wraith garden]

for this

[dapper swift]

no

you just need to use the prime factorisation

you want the powers of 2 and 5 from 30^9

cause 400,000 is only made up of powers of 2 and 5

so that gives 10^9 = 2^9 * 5^9

and 400,000 = 4 * 100,000 = 2^2 * 2^5 * 5^5 = 2^7 * 5^5

[wraith garden]

how

what is the 30^9 for?

im actually a competitor for math olympiad, idk how i qualified

😆

[wraith garden]

and what to do next?

[dapper swift]

oh wait you do need the 3^9

so 30^9 = 10^9 * 3^9

so 2^9* 5^9 * 3^9

yeah so if you have 2^7 * 5^5 that will work

if you have 2^7 * 5^5 * 3 that will work

if you have 2^7 * 5^6 that will also work

as long as you're under 30^9 = 2^9 * 5^9 * 3^9

[dapper swift]

how many ways are there to choose the power of 2

such that it's between 7 and 9?

[wraith garden]

uhh

hAHHSHS

sorry bro

[wraith garden]

ii dont seem to understand

$oh wait you do need the 3^9
so 30^9 = 10^9 * 3^9
so 2^9* 5^9 * 3^9
yeah so if you have 2^7 * 5^5 that will work
if you have 2^7 * 5^5 * 3 that will work
if you have 2^7 * 5^6 that will also work
as long as you're under 30^9 = 2^9 * 5^9 * 3^9$

[solid kiln]

Inuji

[dapper swift]

let's try with smaller numbers

like 300 and 10 for example

[wraith garden]

30?

is it 30

[dapper swift]

nah 300

so 300 = 3 * 100 = 3 * 2^2 * 5^2 right

and 10 = 2 * 5

[wraith garden]

yes

yes

[dapper swift]

so 2^2 * 5 will work

cause (2^2 * 5)/(2 * 5) = 2

[wraith garden]

$cause (2^2 * 5)/(2 * 5) = 2$

[solid kiln]

Inuji

[wraith garden]

yes

[dapper swift]

so we just need to choose a power that is 2^1 or greater

and a power of 5^1 or greater

as it will divide evenly into 10

[wraith garden]

so $300 = 3 * 100 = 3 * 2^2 * 5^2 right$

[solid kiln]

Inuji

[dapper swift]

yeah

[wraith garden]

where did the 5^2 go

[dapper swift]

we're considering the 10

not the 300

[wraith garden]

so it disappear?

[dapper swift]

no

[dapper swift]

like 20/10 = 2 right

and 50/10 = 5 right

[wraith garden]

yes

[dapper swift]

20 and 50 are all multiples of 10

[wraith garden]

yes

they produce

whole no

[dapper swift]

so if our prime factorisation has 2 * 5 or greater

it will also be a multiple of 10

[wraith garden]

what does greater mean

[dapper swift]

more

[wraith garden]

examples

[dapper swift]

if it's a multiple of 2 * 5

like 2 * 2 * 5 = 2 * (2 * 5), it's a multiple of 10

[wraith garden]

ohhhhh

however u do it

its still multiple of 10

[dapper swift]

yeah

but it has to be less than 300 though

[wraith garden]

2 * 5 * 0.5 is 5 tho

[dapper swift]

we're not counting fractions

[wraith garden]

ok

[wraith garden]

then

how do we determine

its less than 300

[dapper swift]

right, so for the powers of 2

we have 2^2 in 300

and 2^1 in 10

that means our power of 2 can either be 1 or 2

[wraith garden]

can u show it in numerical form

[dapper swift]

so like 2^2 * 5 = 20, a multiple of 10

2^1 * 5 = 10, a multiple of 10

2^2 * 3 * 5 = 60, a multiple of 10

but we can't have 2^3 * 5 = 40

that's a multiple of 10

but it doesn't divide evenly into 300

cause 300 = 3 * 2^2 * 5^2

only has a power of 2^2

in other words, the maximum power of 2 that can divide evenly into 300

is 2^2 = 4

so 2^3 = 8 or any higher won't work

[wraith garden]

so that means

3?

or 8..

[wraith garden]

answer is 8??

[dapper swift]

no

so there are only two choices for our power of 2

2^1 or 2^2

[wraith garden]

hm

i still odnt understand bro

HUHUHU

i hope u get my situatuion

[dapper swift]

nah I would recommend you work on your fundamentals first

[wraith garden]

which

[dapper swift]

specifically prime factorisation

and combinatorics

cause this is the example with 300 and 10

the original question has much larger numbers

[wraith garden]

i actually know the prime factors

but

idk how to use it

[dapper swift]

you don't know combinatorics right

[dapper swift]

and that ok

[wraith garden]

no

[wraith garden]

like if u tell me

what is the prime factor of 100

i know

[dapper swift]

yeah but there's no point then

[wraith garden]

but idk how to use

[dapper swift]

so you couldn't find a prime factorisation yourself?

like say 72

[wraith garden]

72

36(2)

then

[dapper swift]

yep

[wraith garden]

12(3)(2)

[dapper swift]

yeah

[wraith garden]

(3)(2)(2)(3)(2)

[dapper swift]

yep!

so what's that using exponents?

[wraith garden]

(2^2)(3^2)(2)

$(2^2)(3^2)(2)$

[solid kiln]

Inuji

[dapper swift]

yeah nearly there

[wraith garden]

how

i know how to prime factor but idk when to use

[dapper swift]

$2^3 \cdot 3^2$

[solid kiln]

south

[dapper swift]

yeah so you can do it

[dapper swift]

cause the olympiad problem is testing skills way ahead of where you are now

[wraith garden]

yeah but idk how tf i got qualified to join

[dapper swift]

idk

[wraith garden]

right??

[dapper swift]

yeah that's really strange

[wraith garden]

i only joined cuz the teacher told us there were extra grade for joining

i didnt expect to get in

[dapper swift]

lol

[wraith garden]

so whats the answer?

[dapper swift]

you won't understand the answer to the original problem

[wraith garden]

300 and 19

10

[dapper swift]

oh for 300 and 10

that's easier thank god

I was trying to do the original one

[wraith garden]

i wont understand it anyway

[dapper swift]

yeah so 300 = 3 * 2^2 * 5^2

[wraith garden]

so go for the smaller

[dapper swift]

and 10 = 2 * 5

so (2 - 1 + 1) = 2 choices for the 2
(2 - 1 + 1) = 2 choices for the 5

and (1 - 0 + 1) = 2 choices for the 3

so 2 * 2 * 2 = 8

https://www.wolframalpha.com/input?i=divisors+of+300+

if you count there are 8

[wraith garden]

but it shows 18

[dapper swift]

nah but only 8 are divisible by 10

10, 20, 30, 50, 60, 100, 150, 300

[wraith garden]

where did u get -1 from

[dapper swift]

there are 10 numbers between 1 and 10

that's the same as 10 - 1 + 1 = 10

so we're finding how many numbers there are between 1 and 2

[wraith garden]

2?

[dapper swift]

yeah

you can think of it as 2 - 1 + 1 = 2

adding 1

[wraith garden]

so its completely useless?

since answer is 0

[dapper swift]

nah

2 - 1 = 1

1 + 1 = 2

[wraith garden]

eh

2 5 3 are the main prime factors right

[dapper swift]

yes

btw you can get 18 divisors in total

you can choose 3^0 or 3^1

2^0, 2^1, 2^2

and 5^0, 5^1, 5^2

so 2 * 3 * 3 = 18 choices in total

18 divisors

[wraith garden]

;-;

[dapper swift]

yeah that's the principle behind it

[wraith garden]

should i quit math

lol

[dapper swift]

nah

you just need more time

[unreal eagle]

so u say tht you are struggling with variables(e.g: x, y)?

@wraith garden

[wraith garden]

yes but only those with more complex

[unreal eagle]

like rational function?

[wraith garden]

depends

[unreal eagle]

can you give me an example, maybe that can help

[wraith garden]

alr

like

quadratic equations

and the letter e

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[jaunty topaz]

https://gyazo.com/0615e041b5aa174c3486a0d665d153ed?token=2977a434977dc6971284b2c51a5f7df0 hello could anyone help with a)? i have no clue how to approach it

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[jaunty topaz]

<@&286206848099549185>

do i just multiple each y value by its corresponding joint probability?

and add them togethe

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[magic cosmos]

I don’t remember what gets that summation be negative and then positive

[magic cosmos]

I see that it goes to 10, being squared, though I don’t see how to get the minus and addition in it

[delicate belfry]

What is (-1)^2 and (-1)^3 ?

[magic cosmos]

1 and -1

[delicate belfry]

Exactly, -1 changes depending whether the power is odd or even.

[magic cosmos]

Yes

But those summations are being squared

Like n^-2

[delicate belfry]

Still, it doesn't matter how the sequence change, put a - sign infront, it still changes.

[magic cosmos]

Hmhm

[delicate belfry]

See how the sequence appear with $-\frac{1}{n^2}$

[buoyant trench]

Bot is down

[magic cosmos]

Oh

It be continuous negative fractions

Ooo

-1^n/n^2

Nah

-1^n/-n^2

Yh it is that

Thank u

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[wraith hinge]

Basically solving this term (sequences and series)

[surreal bough]

rearrange the terms

[surreal bough]

oh nice

let me see

[wraith hinge]

Check the answer

[wraith hinge]

Thank you

[surreal bough]

hm

I got something different

[wraith hinge]

How

[surreal bough]

your answer is negative

[wraith hinge]

Yes

[surreal bough]

but by inspection I think the answer should be positive

logically

[wraith hinge]

True

But the thing is

Where does the -8 term go?

[surreal bough]

what do you mean?

[wraith hinge]

The 8,64,512

[surreal bough]

yes

[wraith hinge]

Has a negative sign before it

[surreal bough]

yes

[wraith hinge]

So the sum of GP also has a negative sign before it

[surreal bough]

yes

[wraith hinge]

So where am I wrong

[surreal bough]

try it this way

[wraith hinge]

Sum of 30 powers of 2

-twice the sum of 2^3+2^6...?

[surreal bough]

((2+4)+(16+32)+(128+256). . .) - (8+64+512))

or

[wraith hinge]

Shouldn't the last bracket be positive?

-(8+64+512)

[surreal bough]

yes

sorry

[wraith hinge]

Man this is confusing 😭

[surreal bough]

(6+48+384...) - (8+64+512...)

[wraith hinge]

I will try using this

[surreal bough]

two geometric series

[wraith hinge]

Hmm

But why is my answer wrong

[surreal bough]

let me see

[wraith hinge]

This is the given answer

[surreal bough]

your brackets are different

from the given

let me try it that way hold on

I don't get the given answer either

$\frac{2(8^{36} -1)}{7} + \frac{4(8^{36}-1)}{7} - \frac{8(8^{18}-1)}{7}$

[solid kiln]

WOWWA

[surreal bough]

aren't these the correct exponents?

there aren't 30 negative terms in the sequence.

[surreal bough]

how did you get 8(8^30-1)/7

there's 36,36,18 not 30,30,30

[wraith hinge]

There are 90 terms so 30 terms for each series

Since -8 is the 3rd term the 90th term will be from the -8 series

Hence the remaining will also be 30 and 30

[wraith hinge]

How?

[surreal bough]

I mean

look at the sequence

for every 4 positive terms

there's 1 negative term

[wraith hinge]

Uhm

For every 2 positive term

There's a negative term

2,4,-8

16,32,-64

[surreal bough]

oh what ur right hold on I'm tripping

[wraith hinge]

128,256,-512

[wraith hinge]

lol it's okay

[surreal bough]

wow that was big mind blunder

[wraith hinge]

We will get there together

[wraith hinge]

Happens

[surreal bough]

ok wait with this newfound knowledge

[wraith hinge]

I just don't understand how he just adds these up and brings it to 14/7 [~]

[surreal bough]

no I see that

wait it's 142/7

right

[wraith hinge]

No..?

[surreal bough]

wait

I can't read his writing

what does it say

[wraith hinge]

He took 8^30 -1

Common

[surreal bough]

yes

[wraith hinge]

14/7 = 2

He divided it

[surreal bough]

oh

u know some people write the 7s

with the cross

so I thought that was that

[wraith hinge]

So,( 2 + 4 - 8)

[wraith hinge]

Nah it's 14/7

[surreal bough]

yes I see now

[wraith hinge]

Let me complete the lec and check in again

[surreal bough]

he wrote it incorrectly here?

why is it 2(8)^30-1 and not 2(8^30-1)

[wraith hinge]

Bro...

He corrected it

I should have watched the entire thing 😭

[surreal bough]

ohh lmao

I was tripping hard

[wraith hinge]

Same thing

[surreal bough]

not same thing doe

[wraith hinge]

He probably forgot to add the bracket

[surreal bough]

ye probs

[wraith hinge]

Does that sometimes

[surreal bough]

lmao what

ok

[surreal bough]

ah great

it worked out

[wraith hinge]

Corrected it lmao

Yeah

Thanks

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[cedar flower]

!status

[trim jolt]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[daring meteor]

idk how to solve

ig 7

[cedar flower]

okay, can you do g(5)?

[daring meteor]

uhh no?

[cedar flower]

why not?

[daring meteor]

cause idk how to

solve

complicated for me

[proven hound]

Just substitute x=5 in g(x)

[daring meteor]

i know but what does the small 3 do

[cedar flower]

cube root

if x^3 = y then cube root of y is x

[daring meteor]

g(x) = 3 i think

[cedar flower]

well not quite, g(5) = 3

it's only true when x=5, not when x is anything

okay, so now we have g(5)=3 - what's f(3)

[daring meteor]

so x is 5?

[cedar flower]

we have set x=5 in g(x) and gotten 3.

and now we want to calculate f(x) where x=g(5), which means when x=3.

[daring meteor]

f(3) is 5?

[cedar flower]

looks like it, yeah

[daring meteor]

so what's f(g(5))

[cedar flower]

well g(5) = 3, so we can replace g(5) with 3

and so f(g(5)) = f(3)

and f(3) = 5

[daring meteor]

so its 5?

[cedar flower]

yes

[daring meteor]

tysm

ima close rn

.close

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[stone garnet]

For differentiation, does dx^2 equal to 2xdx? If yes, what is the logic and the meaning of d?

[stone garnet]

Okay so afaik, d/dx means derivative

So if dx^2/dx = 2x

Then I can say that dx^2 =2xdx

Seems correct but what is the logic here? What do d and dx indicate and why am I allowed to multiply and divide with them as if they are some numbers

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@stone garnet Has your question been resolved?

[golden vale]

they "are" numbers

but they are very small so we represent them by "d" or delta

[tardy hemlock]

d/dx should be looked at more as an operation, that behaves like a fraction, not an actual fraction

(this allows for the chain rule, for example)

There is a very popular question about this on MSE

https://math.stackexchange.com/questions/21199/is-frac-textrmdy-textrmdx-not-a-ratio

See the first answer there

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[still stirrup]

Determine a point and a direction vector of each of the lines that have the following equations:

[still stirrup]

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[celest beacon]

How can you tell which function is represented in a graph?!!

[stark bison]

Mostly it's just guessing from experience

[celest beacon]

wdym?!!

[stark bison]

If you were given a graph and asked what function is presented on the graph, you would need to guess

[celest beacon]

oh ok!

How do you find a domain if it does not touch the x- intercept in the graph?!

[stark bison]

I suppose you mean the x-axis

[celest beacon]

Yeah I do, sorry about that!! xd

[stark bison]

Not touching the x-axis is irrelevant to the domain though, you might want to rephrase the question

[celest beacon]

I guess my brain got comjumbled with information!

How do I find the domain of a parabola?

[stark bison]

Usually parabolas are defined on the entire set of real numbers

So, if you are given a graph with no points missing, you should be safe to assume that the domain is R

But if any points are missing, exclude their x-coordinates from R

[celest beacon]

ok!!

What is an end behavior for lines in a graph?!

[stark bison]

Depends on the context I guess, how does the graph look?

[celest beacon]

The line is l-shaped, meaning it is an Exponential graph!!

The function is g(x)=2(0.5) to the power of x.

[stark bison]

I guess what they are expecting you to say is that the graph approaches the x-axis (or, simply, that the x-axis is its asymptote)

[celest beacon]

It is asking which has the same end behavior for large, positive values of x!!

[stark bison]

Yeah, this should be it then

[celest beacon]

ok thank you!

How do you find the initial value on a graph?

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[pallid cedar]

Need help on question 12. Don’t know how to start

[pallid cedar]

!status

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What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[pallid cedar]

1

[wraith hinge]

Hi, can you crop number 12 and send it here?

[pallid cedar]

ok

[wraith hinge]

Appreciate it. 🙂

[wraith hinge]

Let me solve it for you?

[pallid cedar]

if i can just find out how to start i think i'll be able to do the rest

[wraith hinge]

Ok

Equate 2x + 20 and 5x - 37

to find the value of x and plug in the value to find the measurement

[pallid cedar]

but how do we know they are equivalent?

[wraith hinge]

Wait

this is FGH?

[pallid cedar]

?

[wraith hinge]

Ok hold on, wrong. I apologize

[pallid cedar]

the paper in general is about the perpendicular bisector theorem (and its converse), and the angle bisector theorem (and its converse)

[rough grotto]

try to establish a relationship between traingles FIG and HIG

[pallid cedar]

i found that side IG is shared between both triangles

so i put the 2 lines

[rough grotto]

also do notice both are right-angled triangles

[pallid cedar]

yeah

[wraith hinge]

Oh i checked it again

They are really equal

[pallid cedar]

wait even though the paper is about this you can prove their congruence using HL (hypotenuse-leg) right?

[wraith hinge]

Solve for x

[rough grotto]

well not exactly

so basically SSA does not mean congruent

[pallid cedar]

ik

it's SAS, SAS, AAS, ASA, HL

right?

[rough grotto]

but since the angle is 90 degree the other side has to be same

I did not learn HL at school..but yes this is a case of HL that you have mentioned

[pallid cedar]

so i can say congruent because HL?

[rough grotto]

yep

[pallid cedar]

ok one last question about this specific problem

[rough grotto]

yes tell me

[pallid cedar]

how do i know that 2x+20 is equal to 5x-37 and not the other angle in IGH (besides 5x-37 and the right angle)

[rough grotto]

that is based on ordering

[pallid cedar]

?

i don't understand

[rough grotto]

we say triangle FGI is congruent to HGI

[pallid cedar]

oh yeah

[rough grotto]

but we can't say triangle FGI is congruent to GIH or IGH

[pallid cedar]

so f=h, g=g, and i=i

[rough grotto]

this means angle FGI = angle HGI
angle FIG = angle HIG
angle GFI = angle GHI and similarly for the sides

[pallid cedar]

oh i get it now

thanks

thank you for your time

appreciate it

[rough grotto]

no problem

[pallid cedar]

.close

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[safe flower]

im sorry if this isnt the correct server to ask but

[safe flower]

how do u get the volume of a cube here

[cedar flower]

you know the side length

so you know the volume

[safe flower]

which the formula is a^3

its stated here, however that it is mm but the density is cm^3

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[safe flower]

.close

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[daring karma]

what is the dot product of 2 parallel vectors?

[daring karma]

it's the absolute value of 1, right?

[left oriole]

what do you think it should be?

[daring karma]

the absolute value of the dot product hsould be 1, right?

[left oriole]

if they are unit vectors then yes

otherwise not necessarily

[daring karma]

and if they are not?

[left oriole]

are you familiar with
$$a\cdot b = |a| |b|\cos(\theta)$$

[solid kiln]

Bungo

[daring karma]

forgot about that. So if they're parallel, then cos(theta) is 1.

[left oriole]

or -1

[daring karma]

So the dot product of parallel vectors is the product of their magnitudes

[left oriole]

but then take abs value, it's 1

[daring karma]

so am i right in saying that if vectosr are parallel, the dot product is the product of their magnitudes

well you need to look at its abs value tho

[left oriole]

the abs value of the dot product is the product of their magnitudes

[daring karma]

right

[left oriole]

the dot product itself is either + or - the product of their magnitudes

[daring karma]

okay thank you so much

[left oriole]

sure, gl

[daring karma]

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[worthy eagle]

Hey quick question, do RYA(reflection in y-axis) makes points for x-axis and RXA(reflection in y-axis) in y-axis when making a new points?

For example,
\begin{enumerate}
\item (f(x)=\frac{1}{2}(2)^{-x+4} -8)
\begin{itemize}
\item \textcolor{red}{VS by 2}
\item \textcolor{red}{RYA}
\item \textcolor{red}{HT 4 (\to)}
\item \textcolor{red}{VT 6 (\uparrow)}
\end{itemize}
\end{enumerate}

My new key points from the equation above makes new point for x as \
$\boxed{\textcolor{OrangeRed}{-x-4}}$ and for y $\boxed{\textcolor{Melon}{2y-8}}$

but why?

[solid kiln]

Akira (fumo)

[worthy eagle]

I want to understand why RYA goes to x section instead of y

does this mean same thing goes for RXA but for y-axis?

I can show my paper to see what my teacher did im kinda confused

<@&286206848099549185>

[unique minnow]

I'm not sure I understand what you mean by "making points for x-axis". What about "new points"?

Are you describing f(x) in terms of translations and reflections? Or are you starting from f(x) and then saying that the point (x, y) is mapped to (-x-4 , 2y-8) after the transformations?

[worthy eagle]

Sorry if this doesn't really makes sense since my English sucks but I'll try my best from what I want to understand. Let's say we're making a new table for g(x) by using the transformations for the function(key points). I'm asking why the negative goes to x part table when it's RYA in the f(x) instead of y part on the table and same thing for y but RXA

[unique minnow]

OK, so if I got this right, you're wondering why reflecting about the Y-axis changes the sign of x, and why reflecting about the X-axis changes the sign of y?

[worthy eagle]

yes

checking the examples from my practice sheet, it's always like that?

[unique minnow]

A point is mapped to it's mirror image with respect to the x axis. The same distance from it, but the other way.

Functions are just collections of points really, so a reflection about the x-asix applied to a function will change the sign of all y coordinates.

This is the other one, same distance to the y axis, but on the other side.

[worthy eagle]

Oh alright I was thinking that, in page 2 where it says $f(x)=-2\left(\frac{1}{2} \right)^{x+4}+8$. When we write transformation in the equation it has RXA. So, the y-axis will be $-2y+8$. Same thing in page 3 where it says $f(x)=\frac{1}{2}(2)^{-x+4} -8$ it has RYA. So -x-4 right? Does this apply to every example? I know how transformations works in other but just getting confused about reflections

[solid kiln]

Akira (fumo)

[worthy eagle]

But I think I got it now

[worthy eagle]

.close

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[karmic solar]

Could someone describe how this equation works?

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@karmic solar Has your question been resolved?

[karmic solar]

<@&286206848099549185>

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[crisp rivet]

Can someone help me with this question

[crisp rivet]

i got the big radius as 1-y^2

and small radius as 4

and i set up the integration but I'm not getting the right answer

[fossil kraken]

As a first thought, you might want to explain the question a little more. We do not all have your context. I guess you are after a volume of something 3D? Not obvious what the x=4 has to do with the curve, without a lot of guessing.

[crisp rivet]

oh yea

my bad lol

im trying to find the volume of the solid created by revolving the region bounded by the graphs

[versed fractal]

I’m assuming interior area here is between x=4 and x=5-y^2 and you need to find the solid if revolution using the ring method

So here what you want to do is find the intersecting points of both graphs to find the bounds of your integration. Since this is around the y-axis you want to find the area between curves down to the y-axis.

Your integral should look something like this

Where R is the exterior curve and r is the interior curve

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[wraith hinge]

I'm getting stuck here

[versed fractal]

are you proving a statement here?

[wraith hinge]

I'm proving one side is equal to the other, yes

[wraith hinge]

any luck?

[versed fractal]

workin on it

[wraith hinge]

alright, because according to desmos

it's matching

wait

no it isn't

not matching

gotta check my algebra

nvm

it is

mistyped

lol

nvm I got it

the trick was

to factor out cos^2y

from the first two things

in ba+ab+c, I factored out b

[versed fractal]

Yeah I was kinda getting those steps

This was one of the trickier ones to do

If you solved it don't forget to close the channel #help-38 message

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[wraith hinge]

I can’t get -2 as the answer no matter how hard I try

I know how to solve it but I just can’t get the answer I’m looking for

[trim jolt]

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

[unique pine]

What did you try

[wraith hinge]

Basically

I subtracted one equation from that side to get

(X+5) - (5-2x)

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[wraith hinge]

.close

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[opaque rampart]

I understand you have to bring out the 10. I just don’t get what to do afterwards.

[thorny trout]

sub x = tan(theta)

[opaque rampart]

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[fading narwhal]

Hello! I’ve got three questions that I’m not sure how to start on. I really just need to be walked through the actual steps of completing them.

Thank you

[fading narwhal]

To whoever helps me, we can start with the antidepressant question.

[pallid lake]

Hi

[fading narwhal]

Hello

[pallid lake]

what is the problem with the first question?

[fading narwhal]

I’m not sure how to find the inverse of the function.

[pallid lake]

What I usually do is write f(x) as y and then switch x and y

and then solve for y

[fading narwhal]

So would my f(x)= -0.088x + 2.99 be written as:

y= 0.088x - 2.99

[pallid lake]

Yes

and then switch x and y

and solve for y

[fading narwhal]

So it would be 0.088y instead?

[pallid lake]

yes, -0,088y that is

[fading narwhal]

Okay thank you

Now this one also deals with inverse

[pallid lake]

don't forget to solve for y

[fading narwhal]

Yep 👍

[pallid lake]

alright 👍

well same thing

switch y and x's place and solve for y

@fading narwhal Has your question been resolved?

[fading narwhal]

Okay cool, and the graph is symmetrical with respect to y = x I believe?

[pallid lake]

Yes

[fading narwhal]

Awesome

Okay last one

[pallid lake]

Great :D

Alright

[fading narwhal]

I have the scatter plot graphed

But I’m not sure how to find the function for it

I tried to use y1 ~ mx1 + b and got the regressions etc. for it, but I’m not sure that’s what I’m even supposed to do

[pallid lake]

well it states in question a that it's an exponential function

so that gives us some information, such as that the function in question must be of the form y = a^x + b

[fading narwhal]

I’m not really sure what A and B are in this problem

[pallid lake]

We can solve for b by looking at the first value.

If we take 1955 as the 0 for this graph

we know that b must be 407,8

since a^0 = 1

we can solve for a by plugging in values

[fading narwhal]

So right now we are at:

y = a^0 + 408.8

[pallid lake]

Close

[fading narwhal]

I’m a little lost I think 😂

[pallid lake]

We have y = a^x + 407,8

if we plug in x = 10 and y = 835,5

we can solve for a

[fading narwhal]

Why is it 407, 8? Is that an ordered pair?

[pallid lake]

the first value is 408,8 yes?

that is at x = 0 since we're saying that 1955 is the x coordinate of 0

if we put in x = 0 at the function we get 1

a^0 = 1

if we did not subtract 1 from the last part we'd have 409,8 which is not equal to the first y coordinate we have

[fading narwhal]

Ohhh

Okay I’m on board now

[pallid lake]

Hahaha great XD

then we can fill in multiple values of x and y to get something that's close to a

[fading narwhal]

I lied, maybe I’m not on board. Everything looks like word soup to me right now, sorry 😭

Okay hold on hold on

[pallid lake]

Does your book define an exponential function?

or is it not shown

[fading narwhal]

This is where I’m at

[fading narwhal]

My class doesn’t have a textbook

[pallid lake]

Alright

you want to know 'a' right?

at least, a close enough value that fits with your table of values

[fading narwhal]

I think I’m just trying to get the actual function equation itself

[pallid lake]

well you have everything, you just need a for the full function

[fading narwhal]

I’m losing it a little bit, I’ve been doing math since ~6am this morning 😭

[pallid lake]

Hahaha no worries

[pallid lake]

just fill in the x and y values in THIS function and solve for a

with every x and y value

so first off fill in x = 10 and y = 835.5 and solve for a

[fading narwhal]

Like that

[pallid lake]

Yes

and for y = 835,5

next x = 20 and 2306,5

Hold on gotta see if im correct first

[fading narwhal]

Your commas are supposed to be decimals, right?

[pallid lake]

Yes sorry in my country

they're decimals

[fading narwhal]

Oh I gotcha, no worries 👍

I was seeing them at ordered pairs at first, and that added to my confusion, sorry lol

[pallid lake]

haha no problem

[fading narwhal]

I’m blanking right now. How do I solve for a

I’m embarrassed for asking 😭

I need to

[pallid lake]

It's no problem!!

No worries

Im trying to find it myself too

takes a while XD

[fading narwhal]

Ah I gotcha lol

[pallid lake]

Hold on a sec

[fading narwhal]

I’ve found B) and C)

Okay

[pallid lake]

alright

So the exponential function is N = b g^T

with b as starting number and g the growing factor

and t is time

[fading narwhal]

N = 0 408.8^t ?

[pallid lake]

N = 408,8 g^t

I understand your confusion this is hard :(

but I now know how to solve it

Forget Everything I told you

[fading narwhal]

Okay lol

[pallid lake]

im checking if what i did was right lolol

[fading narwhal]

All good : )

If this helps at all

On the example problem for this one

They say the answer is this

So our answer has to be in that same form

y = 337.906 (1.084^x)

[pallid lake]

yes exactly

y = b g^x

Alright I know it

Pick 2 points and divide the highest by the lowest

[fading narwhal]

So like 10231.2 / 835.5 ?

I got 12.25

[pallid lake]

Yea that's fine

and then do root it the number of years apart

so for your point that's 35 years apart

so the 35th root of 12.25

[fading narwhal]

1.07

[pallid lake]

it's more exact if you instantly put the fraction to the power of 1/35

[fading narwhal]

1.074

[pallid lake]

so (10231/835,5)^1/35

Yesa

Correct

1,074

you can do it with more values to get a more exact a but this is basically it

so it's y = b 1,074^x

[fading narwhal]

Okay so that’s one half

[pallid lake]

and now solve for b

well b means the value for x = 0

and that's 408,8

[fading narwhal]

How do I solve for b

[pallid lake]

b = the value when x = 0

the text says that x = the number of years after 1955

so 1955 = (x = 0)

[fading narwhal]

Okay I’m confused again. This is the example problem here:

Why is their’s not 409.1 ?

[pallid lake]

Most likely because this question says that the starting year is not 1957

but some year after that

[fading narwhal]

Their starting year is 1957

[pallid lake]

I actually have no clue

it doesn't even work

I don't think that that equation is correct...

[fading narwhal]

That’s what my college gave us as the example question…

Well crap

[fading narwhal]

Okay just getting it back down here, this is the one we’re working on currently

[pallid lake]

well the answer to your question I THINK is: y = 408,8 (1,074)^x

yes devide the higher value with the lower value

and root it the difference in years

that's your growth factor

[fading narwhal]

Yeah we’ve got that part

[pallid lake]

and your b SHOULD BE when x = 0

[fading narwhal]

It’s just B that we need

[pallid lake]

but apparently your collage disagrees

so lets take a value for b

[fading narwhal]

Should we get another set of eyes on this in case there’s something we’re missing / not seeing?

[pallid lake]

I agree

Because this doesn't make sense

(to me)

:)

[fading narwhal]

Okay so

I don’t want to ping helpers, but is that what I should do?

[pallid lake]

<@&286206848099549185>

https://cdn.discordapp.com/attachments/908078008609431674/1180228270634049536/IMG_2826.jpg?ex=657ca83b&is=656a333b&hm=64b90fac8682d45b97e54d705f5f130351b1ff214102b69534c4ec305ada91ed&

[fading narwhal]

The rules say we get one if we don’t get help in 15 minutes, but I’m not sure what to do in this situation

Oh nvm

[pallid lake]

I think the example question is wrong because it really just doesn't make any sense at all

x = 0 should be 409,1 but the formula says 444,23

which just isn't correct

so I understand your confusion XD

[fading narwhal]

If it was just purely my college, then I’d think it was 100% wrong, but my professor is the one who helps us through the problems and this is what she got, and then the system itself said the answer was correct

So both my professor and college agree on it

But it sounds like it’s not even a possible answer

[pallid lake]

put in 0 for x in the example question

you won't get 409,1 right

I REALLY WANNA KNOW if im just crazy or if this question is wrong

[fading narwhal]

It just gave me 444.23 back

444.23(1.076^0) = 444.23

Is that what you were asking?

[pallid lake]

Yes

and what is the value for 1957 in the example question?

[fading narwhal]

I don’t think any of the helpers are here to help lol

[pallid lake]

Hahaha don't think so either

[fading narwhal]

409.1

[pallid lake]

Is 409,1 the same as 444,23

No

so the equation is straight up not correct

[fading narwhal]

We’ll try it

[pallid lake]

maybe they want an approximation

[fading narwhal]

If I press help me solve this, it runs through TI-84 instructions

Maybe I’ll try that with ours and see what we get?

[pallid lake]

Sure

I think they'll put in values for x and y to solve for the b value

For better approximation you can try more values but it's more work

[fading narwhal]

Okay interesting development

The second example problem is also different from the 0 value

[pallid lake]

I think I understand how they find that value now

[fading narwhal]

337.906 instead of 400.5

[pallid lake]

alright im gonna check my theory

[fading narwhal]

Okay 👍

[pallid lake]

I think your collage wants you to do this using the TI-84 calculator

instead of calculating it by hand

and sadly I don't know how to do it with calculator :(

the different b value is caused by the calculator being able to do more calculations for the value

a more exact value that is

And I sadly have to go ;/

Good luck though

[fading narwhal]

I got 442.89

Okay thanks

Shit man. If anyone is still here now that he left, I’m still just a bit confused on some things.

Anyone?

.close

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[elder field]

Help quick

[storm grove]

Do you know what 12.3x10^8 is

[elder field]

No

[storm grove]

As a number?

so whats 12.3x100000000

[elder field]

Wait lemme put it in a calculator

[storm grove]

Too many zeros

Sry

[elder field]

23

23000000

@storm grove

[west nest]

A number is usually written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

In your case, 12.3 * 10^8 can be written as 1.23 * 10^9

But that isn't important

You are pretty much multiplying two numbers written in scientific notation

So (a number times a power of 10) times (a number times a power of 10)

What 12.3 * 10^8 means is just that you are multiplying 12.3 with 100.000.000 (notice the 8 zeroes)

If you had for example 5 * 10^4, this would mean 5 * 10.000 (5 zeroes), or 50.000

Anyway

You see that there's just a bunch of multiplication involved.

If you need to solve this without a calculator, you need to know a few properties that multiplication and exponents have and this is a piece of cake

Otherwise you can just plug it in a calculator ... 🙃

mention me when you get back if you need me please

[trim jolt]

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[fading narwhal]

Hello! I’ve been stuck on this for awhile. I think I’ve got the function and the other answers, but they rely on my function being correct, so I just want someone to help me fact check my answers.

(a) Function: y = 442.89(1.074^x)
(b) 15722.077
(c) 2008

[fading narwhal]

I’m just gonna assume that nobody is active. I’ve made three different channels trying to get this one problem, and the only helper I’ve gotten was also confused so we mutually decided to get a different set of eyes on this problem. I’ve been waiting 2 hours. I’ll try later today.

[cinder swallow]

It might be easy to set up a LinearRegression model for this in Python.

[low gazelle]

Your equation is not right

Assuming ur suppose to use a regression line

[fading narwhal]

I tried a regression line in desmos and it didn’t appear to be accurate

[low gazelle]

What did u do to get the equation u got

[fading narwhal]

This was the example problem

[fading narwhal]

I used a TI84 calculator and used ExpReg

[low gazelle]

ok. I did not use a calculator and idk how it works. I can help u do it calculatorless if u want though

[fading narwhal]

Let’s do that so that I can make sure my answers are correct

[low gazelle]

Ok so linear regression line is of the form y=a+bx

We are given the data is exponential though so we need to transform it a bit

First step is to take the log of all the income. This will make the relation ship between year and log(personal income) linear

so log(y)=a+bx is what we are finding a and b for now

b=cov(x,log(y)), a = mean(log(y)) - b * mean(x)

find that out then sub back into the equation and solve for y

[fading narwhal]

OKay so

Im not sure what my a b and x are

[low gazelle]

in general, x is independent var, y is dependent var. b is usually given by cov(x,y)/var(x,y), but we needed to modify it cuz we transformed y values to log. a is usually given by mean(y)-b(mean(x)) but we needed to modify it again cuz we transformed y values to log

[low gazelle]

you find a and b using these equations

[fading narwhal]

Im sorry, everything is looking like word soup to me right now, i'm confused

[low gazelle]

Did you learn about how to manually find linear regression lines or were u told to just use calculator

[fading narwhal]

my professors taught me on the calculator and on desmos

im not sure what var and cov are

[low gazelle]

I see

I will try and figure that out then rq give me a moment

[fading narwhal]

okay thank you, sorry that i dont know these things

[low gazelle]

nvm im dumb. Im getting the same thing.

[fading narwhal]

So I was correct?

[low gazelle]

Yeah

[fading narwhal]

Awesome, sweet

okay so for part b

I just replace x with 50 and solve, correct?

[low gazelle]

yeah

[fading narwhal]

15722.0778 rounded 3 decimal places to 15722.078

[low gazelle]

ye

what did u do for c. Im getting 2009

[fading narwhal]

I dont think I rounded my year up, I rounded down

[low gazelle]

same

if I rounded up I would have got 2010

[fading narwhal]

shit am i messing up

54.7 on the graph is when I reach 22000

so 1955

plus 54.7 is 2009.7

[low gazelle]

Yah

[fading narwhal]

am I doing this wrong, it would round up right? cause its closer to 2010

it says to round up, so the answer is actually 2010?

[low gazelle]

Maybe u could round up. I would say round down since its during the year 2009 that it is reached

like 8 months into 2009 they reach 22tril

[fading narwhal]

The problem specifically says round up to the nearest year in the directions, so would I do 2009 or 2010

[low gazelle]

lol I cant read

do 2010

[fading narwhal]

okay so in totality

y=442.89(1.074^x)

15722.078

2010

i think that all checks out

[low gazelle]

yeah