help-0

[peak niche]

and i dont want answers

and i just wanna factorise something

[mellow hearth]

say this is the eqn you are dealing with

[peak niche]

ok

[mellow hearth]

multiply by - 1 first (cuz you want less negative factors)

ok

[peak niche]

ok

so 4x^2+7x-12 right

[mellow hearth]

ya

then you look at the equation and see a*c= 48

[peak niche]

yep got u

[mellow hearth]

now you try to split b (7x) such that the two factor +gx-fx have fg=ac

ya

[peak niche]

what

[mellow hearth]

go it?

you want to solve by middle term splitting method right?

[peak niche]

oh right

so like fg = 48

[mellow hearth]

ya

[peak niche]

so what youre saying is what adds to make 7

from f and g

wait

youve lost me

[mellow hearth]

I wish I had pen and paper rn

ugh

[peak niche]

sorry its -48 isnt it

thats why i was lost

[rustic badger]

Can someone help?

[peak niche]

channel bein used rn

@mellow hearth so im trying to multiply to make -48 and add to make 7?

i cant find anything

[mellow hearth]

this equation might not be solvable with this method but you get the point right?

[peak niche]

absolutely not

[mellow hearth]

quadratic formula isalmost always faster tho

[peak niche]

can you get a solvable one

[mellow hearth]

ok wiat

[peak niche]

just expand some random brackets or something

[mellow hearth]

gettit now?

[peak niche]

why -5x + 2x

oh they equal -10

[mellow hearth]

https://youtu.be/MtHEk6Yy6N4

[peak niche]

so we have -5 and 2

but whats that in brackets

because

one is gonna have 2x

and one is gonna have x

so how do i know what to put in what

[mellow hearth]

take x common

x(2x-5)+1(2x-5)

you get (x+1)(2x-5)

[peak niche]

Gott go for dinner but ill watch that vid

[mellow hearth]

And I gotta sleep

ttyl

[wet fulcrum]

someone please

im gonna die

[charred flint]

any ideas?

[sonic osprey]

X=rcos(T), y= rsin(T)

Then solve

@wet fulcrum factorise the denominator

[rustic finch]

bump

[peak niche]

WHY DID MY TEACHER NOT TELL US THIS

It's so much easier

[brazen harness]

prolly cause she/he wants you to have stress

[peak niche]

my teacher is quite good for everything else

but that damn process of elimination method

is horrible

[brazen harness]

LOL

but I can’t disagree

my teacher is so boring that I’m stuck playing slope throughout class

[peak niche]

like if a quadratic had -12x^2 or something i'd have to do 12 and -1, -12 and 1, 6 and -2, -6 and 2, 4 and -3, -4 and 3 to see which one is right

it was so much effort

[glass lichen]

RZT is just the generalization...

[brazen harness]

I feel really bad for Oscar

[queen reef]

https://cdn.discordapp.com/attachments/793676391413186610/847191551398117386/Screen_Shot_2021-05-26_at_12.16.42_PM.png

hi

[glass lichen]

I mean learning RZT earlier is a fine thing

[brazen harness]

hi

[queen reef]

can you help me

idk

[ocean seal]

Mosh

[queen reef]

is it 21

[glass lichen]

yes

[queen reef]

j

k

[dull storm]

hi guys i have a trouble with this thing

i can't find a mistake where i am making

[glass lichen]

i mean that's what wolfram said, not what you said

[dull storm]

i must find X so that result of 1.1 will be satisfied

or less than 1.1 but i simplified it with =

so. i tried this, using iterations of assumptions

i used 2.1 (realistic x)

so how come i got a good answer by this way and not a good answer by equation above

equation above should have had given me an answer of x=2.1156 for example in order for equation to be = -1.1 right? since when i put x=2.10 i get = -1.0157

oh for f0cks sakes...

i forgot to put - in front of 1.1 😦 xD

how come i can make mistakes like this and can't find them emediately

but right after i lose my mind @glass lichen

is there a cure for this curse?

[knotty sleet]

Lol

I do that as well sometimes

Find my mistake immediately after I ask

But then just can't figure it out without asking..

[dull storm]

hahaha 😄

i think the thing with that is

that you are asking urself on one way, and others on another way

and two ways provide different approaches

therefore by using 2 "methods" you enwiden your abilities somewhat

hm

[grand drift]

how would i work this out?

[small flare]

What's the shortcut to (ii)?

[alpine sable]

Multiply by a conjugate

[alpine sable]

They literally gave u the formyla

[grand drift]

what does conjugate mean?

[small flare]

yeah but ii

[alpine sable]

Narutooo

[small flare]

it says sum, there must be some kind of shortcut to get ot the answer

[alpine sable]

That formula is the sum

[small flare]

oh wait

[alpine sable]

Go read your notes or something

[small flare]

so you just substitute n with 25?

[alpine sable]

Yes

[small flare]

and for (i), with 20?

oh wait no

20^2

ig

[grand drift]

okay thanks for help...

[stray jolt]

best help ever

[alpine sable]

How does She not know what a conjugate is

Before doing the homework

[stray jolt]

because hes forgotten or something, why else lol

[alpine sable]

Yeah exactly. So simply go review the book

[stray jolt]

maybe hes already done that, so hes come here

[alpine sable]

Then feel free to explain it to her

It will be much less clear then if she just reads a book

[slender turret]

hey

i have these data and the equation x + 3y - 6 = 0 is a line (d)

so i wanna know how do i find the equation of the line perpendicular to (d) passing through point C

<@&286206848099549185>

[midnight geyser]

to find a line perpendicular to another line, you take the -1/slope and that is the new slope

[native temple]

Hey with the geometric sum formula

R^n is actually N +1???

I thought it was this

Explain

[slender turret]

n what about the b of y = ax+b ?

[native temple]

Like when the sum is 2(3)^N

I have to use N+1????

If that's the case

why do the formulas say

S = a(1-r^n)/(1-r)???????

<@&286206848099549185>

[gray isle]

R^n is actually N +1???
wdym

[native temple]

like

R is acturraly raised to N +1

not N

[gray isle]

where?

[timid wind]

hi is this channel occpuied

[native temple]

when the sum

doesn't have r^n-1

but R^N

[gray isle]

do you have a specific example

[native temple]

R in the formula is raised to N+!???

yes

[native temple]

hmm?

oh I have loght mode on

[gray isle]

I still just see a strand of hair

[native temple]

sigh why notes

Sigma N= 0

6

(3)^n

exvalukate

[gray isle]

$\sum_{n=0}^{6}3^n$

[ocean seal]

ℝamonov

[gray isle]

that?

yes/no?

[native temple]

yea

[gray isle]

the n in the geometric sum formula represents the number of terms being summed

here the index starts at 0

which results in the summation of 7 terms

[native temple]

oh

so

[gray isle]

since you the use of variable n in both places may be confusing, gonna change the variable

[native temple]

1. the formula is assuming index starts at one

2. Was my question and problem clear when I typed it out earlier?

3. Thanks

[gray isle]

$\sum_{i=0}^{6}3^n$

[ocean seal]

ℝamonov

[native temple]

ahhh

[gray isle]

no your question wasn't clear

[native temple]

I didn’t know N was a separate variable

also how to type clear questions

[gray isle]

omitting important information
issues with capitalisation

[native temple]

Asking for help seems to be a skill......

[gray isle]

usually best to post the question with full context

don't paraphrase,

[last sinew]

Hello, is this channel taken, or is it open now (or almost open)?

[gray isle]

don't omit information especially if you don't understand it, you may be omitting something very important which occurs here quite often

[native temple]

okay

[last sinew]

Oop i'll assume it's still in use then

[native temple]

almost open

if Ramonkv respeonds inrussian lol

[last sinew]

Thank you!

Ok i'll just post my question here for anybody who's willing to help (tysm!)

The answer to 5 is supposedly d, but i'm not quite sure why

The answer stated that it's P(X<=2)=1-P(X>2)

Which i would reckoned to be 1-[0.75²•0.25 + 0.75³•0.25] but apparently no?

[dull storm]

so seriously

how do u simplify this

[last sinew]

.

[dull storm]

is there a way to simplify this

and not do it "manually"?

[last sinew]

<@&286206848099549185> apologies for the ping and thank you for your time

[gray isle]

P(x>2) is the probability of failing to strike out the first two batters

and the probability of failing to strike one out is 1-0.25 = 0.75

hence failing twice in a row is 0.75^2

[last sinew]

Oh

[noble sinew]

it is possible to find a closed formula (depending on how the series looks it can be pretty annoying tho)

[last sinew]

Omg

Thank you 😭

[noble sinew]

so if you work through it one term at a time you can find a closed formula for that sum from n=1 to x (in what you posted x=25 then). For example sum from n=1 to x of n is
1/2 * x(x+1)

[junior peak]

How do u find instantaneous rate of change when given a position function and then a number

[alpine sable]

derive

[junior peak]

I do the derivative and then just substitute?

[alpine sable]

yes

[junior peak]

Alright ty

[hoary sable]

what would i do with the exponent here to simplify further?

solve*

[golden falcon]

take log_2 of both sides

no need to ask across multiple channels, btw

[hoary sable]

sorry

so if i take the log of two that eliminates the base and turns the current exponent into a base?

ive never done logs but im happy to learn them

[golden falcon]

Yeah, basically $\log_a(a^b)=b$

[ocean seal]

Dmytr

[hoary sable]

that helps a bunch

is this like a function on a caculator?

[golden falcon]

Most calculators have logarithms, but here, I'm pretty sure it'll be enough to simplify it by hand without calculating numeric values

Another useful identity: $\log_a(c^b)=b\log_a(c)$

[ocean seal]

Dmytr

[hoary sable]

what is that subscript of a?

is that a naming system?

[golden falcon]

A base of the log, can be practically(or if we are in a complex plane - any) number

[neon sonnet]

Can someone help me

[golden falcon]

So, in our case a = 2.

By the way, logarithm in base a is defined by this identity: $a^{\log_a(b)} = b$

[ocean seal]

Dmytr

[hoary sable]

could you input my function into the log function

im having trouble understanding

[golden falcon]

Of course. For example, using $\log_a(a^b)=b$ we derive that $\log_2(2^{\frac{x}{10}}) = \frac{x}{10}$

[ocean seal]

Dmytr

[golden falcon]

And for the left side, use $\log_a(c^b)=b\log_a(c)$ and the fact that $100000=10^5$

[ocean seal]

Dmytr

[neon sonnet]

Dmytr can you help me out after him please

[golden falcon]

hopefully

[hoary sable]

do i need to do inverse log

im still confused

what happens to my log after i move it across the equation?

[golden falcon]

how exactly did you get this?

[hoary sable]

wait is it like this?

[golden falcon]

Not really

After taking logarithms of both sides you should've got $5\log_2(10)=\frac{x}{10}$

[ocean seal]

Dmytr

[golden falcon]

Because $\log_2(100000)=\log_2(10^5) = 5\log_2(10)$

[ocean seal]

Dmytr

[golden falcon]

Technically you can simplify even further because $\log_2(10)=\log_2(2\cdot5)=\log_2(2)+\log_2(5)=1+\log_2(5)$

[ocean seal]

Dmytr

[golden falcon]

Logarithms can be quite overwhelming when you first learn about them, don't worry. Just steadily read the textbook and try solving some other examples.

[hoary sable]

they are not rying to tech me logs

they are telling me to guess check

[golden falcon]

huh?

[golden falcon]

Nice! Btw, it's a good idea to note the base of the log as a lower index or something. And $\log_2(2)=1$, so you can simplify it to just $5\log_2(10)=\frac{x}{10}$

[ocean seal]

Dmytr

[hoary sable]

what button normally allows to to note the base

i tried looking for it

[golden falcon]

I really don't know what you use to write formulas, so I have no idea, sorry.

[hoary sable]

desmos scientific calculator

[golden falcon]

Try _ maybe, usually works in most software

[hoary sable]

works like a charm

[ashen wave]

I'm a 8th grader, and i'm going to high school next year. This might sound weird but can anyone share with me their notes for like exams from freshman year? Any subject is fine

I feel like its a lot to ask tho

[golden falcon]

great!

[alpine sable]

is any one here good at physics? i have a question

[coral pagoda]

The way it's written suggests they have the common log (which is base 10). So although it will simplify to that, that is not why.

[coral pagoda]

Now if it is in base 2, then it's all fine and dandy

[golden falcon]

That's exactly why I suggested using indexes to explicitly show the base

[hoary sable]

is this the right direction?

[golden falcon]

Almost

[coral pagoda]

You didn't fully distribute the 5

[hoary sable]

how do i solve the log?

[golden falcon]

$\frac{x}{10}\log_2(2) = \frac{x}{10}\cdot1 = \frac{x}{10}$

[ocean seal]

Dmytr

[hoary sable]

ahh

[ocean seal]

dackid (jump king +)

[coral pagoda]

So the left hand side should be 5log_2(5)+5, not 5log_2(5)+1

[golden falcon]

You don't really solve it if the argument is an arbitrary value, if you really want, you can get an approximate value for it.

[hoary sable]

?

so can this be solved further?

[golden falcon]

For example, $\log_2(5) \approx 2.3219280948873623478703194294893901758648313930245806120547563958$

[ocean seal]

Dmytr

[coral pagoda]

Gross

[hoary sable]

seems accurate enough for me 😅

[golden falcon]

Not really, and also, you shoudl've multiplied by 10, not divided

[golden falcon]

😦

[coral pagoda]

I'll save the approximations for the engineers :p

[coral pagoda]

Xela, do not approximate

Your answer is wrong now

[hoary sable]

is it close?

[coral pagoda]

Close is not exact

[hoary sable]

my other option is to guess lol

[coral pagoda]

And the 4th line is still wrong

No, your other option is to keep log_2(5) as it is

[hoary sable]

what do i do instead of aproximate

how do i solve then

[coral pagoda]

First, you still need to account for this

[hoary sable]

the calculator doesn't want to solve the log

[coral pagoda]

You're not solving the log

[coral pagoda]

And you STILL need to account for this

[hoary sable]

better?

[coral pagoda]

There ya go. 50(log_2(5)+1)=x is your solution

[hoary sable]

???

[coral pagoda]

You're done

[hoary sable]

i cant fully solve for x?

[coral pagoda]

Don't approximate: the problem is solved

[hoary sable]

i need a number

[coral pagoda]

This is a number

[hoary sable]

so i can say, there will be one million bacteria at 50\cdot\left(\log_{2}\left(5\right)+1\right)?

[coral pagoda]

Is this a time thing?

Then if it asks for a certain number of years, then you can approximate and round up

But only do your approximation at the very very end

[hoary sable]

so this is ok?

[coral pagoda]

Sure. So rounding up will give 167 years

[hoary sable]

Alrighty! thank you both a bunch!

[ocean seal]

dackid (jump king +)

[coral pagoda]

This is the change of base formula. Given $\log_a(b)$, you can reexpress it with a new base $c$, like so: [ \log_a(b)=\frac{\log_c(b)}{\log_c(a)}.]
The common log (the one used on a calculator) is base 10.

[ocean seal]

dackid (jump king +)

[hoary sable]

😅

one day i will understand what you mean

thanks tho

[spark ibex]

anybody good at functions of several variables?

[alpine sable]

Isn’t that just a circle

[spark ibex]

do you know how to do the x,y,z traces?

basically like this but this is a different equation

[silk terrace]

Is this a power series?

the form is strange to me

[muted raft]

that is power series representation of arctan(x)

[strong furnace]

cannot be

its the power series of ln(1+x)-ln(1-x)

[muted raft]

ah yeah what I said is only true for [-1, 1] I think

[alpine sable]

??

[muted raft]

whats the formula for equation of circle?

[ionic jewel]

I almost answered this before i realized ^

[wicked steeple]

v = speed of the defendent
r = distance traveled until perpendicular to the spot light
T - time elapsed

oops is this channel open?

@ionic jewel Do you have any free time atm?

[robust blade]

Option C

[alpine sable]

Plss

Can anyone help

Plsplspsl

[robust blade]

a. 3.875
b. 4
c. 4

[alpine sable]

Ohh okay thanks how about the second one

If you can

[robust blade]

Obviously can but there are too many

[alpine sable]

Ohh okay

Thanks still

Oh pkay

I added u

[lost steeple]

https://gyazo.com/26f271bcef9292c638a3559b6fee7cf6

How can I do this?

[wary stream]

Change of base

[lost steeple]

Could you elaborate or show examples?

[robust blade]

6. a. Log 8 (base 5)

Like this

You know how to write base

👌

[wary stream]

Don't tell people the answers

Explain how to figure it out

[robust blade]

Sure, I think my answer explains how to do it

[robust blade]

Figurable

From my Answer

[wary stream]

You literally told the answer and did not explain how to figure it out

[robust blade]

(log 8)/(log 5)=log 8 (base 5)
This resembles the formula you gave, if you don't understand the difference and rely on just formula, maybe it applies for you only

[wary stream]

I'm saying that you just gave the answer instead of explaining how to get the answer

Like you gave zero explanation

[robust blade]

I got that and I said my answer includes explanation, if not detailed, still it does

[wary stream]

You just said an answer

[robust blade]

Trust me, that much is all I need to do tons like them

[wary stream]

Literally a rule that says explain the concept and don't give answers

[robust blade]

Too bad for you that I don't follow rules

👌

Have fun

[wary stream]

Well you could get banned for not following rules

[robust blade]

Good luck finding someone to ban me

👌

Much appreciated

[sly mantle]

@robust blade do your best to uphold the server academic standards, and i wouldn't flaunt the suggestions of others as you did just now

[arctic cloud]

Can someone help me? I've literally never seen this before

[gray isle]

start by introducing a variable to represent one of your numbers

express your other two numbers in terms of that variable

[robust blade]

Hmm, I am, I was about to explain when someone barges in and interrupt

[sly mantle]

don't bullshit me. this server isn't for giving answers and you can stand to be less rude to other helpers

[arctic cloud]

so like
the first number would be: x-5
second is: x
third is: 3(x-5)?

[robust blade]

You're just another one talking bullshit, lmao, why am I wasting time with you guys

[wary stream]

You realize he's a mod, right?

[robust blade]

He should behave well

[sly mantle]

muted

[wary stream]

Thank you for that

[gray isle]

yes

now you are told the numerical value of their sum

[wicked steeple]

geez is there always this much drama in the questions channel

[gray isle]

set up an equation to represent that

[arctic cloud]

okay, thank you so much

[willow galleon]

Does anyone know how to do this ?

[wary stream]

Move everything to one side and factor the quadratic/quadratic equation

[gray isle]

note that 43 is prime and 28 isn't close, you'd probably want to apply the quad formula

[arctic swan]

New to combinatorial proofs and I am stumped at how to approach this

[willow galleon]

ohh i see, thank you

[glass lichen]

if you're involving sets then count the number of subsets of cardinality k in a set of cardinality n

[alpine sable]

how do i solve this

[solid flame]

$\log_b (a) - \log_b (c) = \log_b(a/c)$

[ocean seal]

pi

[solid flame]

You can use that identity to solve for it

[alpine sable]

so

which is a

and c

[solid flame]

let a = 5 and c = 3

[alpine sable]

so

[solid flame]

so u basically get this

[alpine sable]

what about the top values

[solid flame]

you substitute the top values for log5 and log3

[alpine sable]

so ignore them?

[solid flame]

so you get a numerical value in the end

[solid flame]

no you use them

[arctic swan]

$\log_b (5/3) = \log_b (5) - \log_b(3)$

[ocean seal]

Jack K.

[alpine sable]

logb(5) - logb(3) = logb(5/3)

and then

where do the top values come into part

the decimals

[arctic swan]

and it gives you the values of logb3 and logb5

[solid flame]

yes

so logb (5 ) = 2.3 and logb(3) = 1.6

and u just subtract them

[arctic swan]

so it's basically asking for 2.3-1.6

[glass lichen]

mathway being wrong, shock

[solid flame]

dont plug the logs into the calculator
you are given numerical values for each of them

[arctic swan]

symbolabs is best imo

[solid flame]

substitute them in the log expression

[alpine sable]

.

like that?

[solid flame]

no

just the decimal

like 2.3 - 1.6

[alpine sable]

so 0.7?

[solid flame]

because the whole of logb(5) = 2.3 so you can get rid of the the log

[glass lichen]

no

[solid flame]

yes

[alpine sable]

thanksss

[glass lichen]

.7=1.4, makes sense

[solid flame]

😂

[arctic cloud]

this is -2 right?

[dire osprey]

yea

[arctic cloud]

okay ty

[dire osprey]

cuz 4 to the power of -2 is

1/16

[minor willow]

yea

[dire osprey]

damn i nvr felt so smart

i joined this server cuz im struggling lol

[minor willow]

same

[alpine sable]

why is it 2.7 here

in the equation

if the rate is 2%

[solid flame]

they put the 2% in the exponent...i'm not sure why tho

[neat dome]

can i ask a question here?

i dont wanna interrupt anyone's questions

I'd just like to ask if a function can exists when theres a jump discontinuity at x=2, such that lim x->2- is not equal to f(2) and lim x->2+ also doesnt equal f(2)

cuz a jump discontinuity need to have both existing limits but they just don't equal right?

[solid flame]

ya i think that's possible

[tawny lion]

if two limits approaching from positive or negative infinity have different outputs then there is no limit if thats what ur asking

[alpine sable]

how do i solve this?

[tawny lion]

like lim --> 2- and lim --> 2 +

with piecewise functions for example

[neat dome]

so... it would exist?

[solid flame]

the function would exist

[buoyant kayak]

a function can exist if it passes the VLT

[tawny lion]

the limit would not exist

at x = 2

[solid flame]

but the limit would not

[tawny lion]

there would be vertical asymptote

[neat dome]

wait a function can exist without a limit?

[buoyant kayak]

there would be no asymptote

[solid flame]

its a jump discontinuity so there wouldnt be an asymptote right?

[neat dome]

wait what is going on

[tawny lion]

im kinda confused, not sure we r talking abt same thing

[solid flame]

basically the function can exist - but there would be no lim as x -> 2

[neat dome]

i thought that jump discontinuities needed two limits that dont equal?

[chilly laurel]

Answer and explanation?

[solid flame]

so you would have one sided limits as x -> 2- and x -> 2+

[royal shard]

yeah, if you want a concrete example, research the sgn function (sign function), which is the function that for every positive x, sgn(x) = 1, for every negative x, sgn(x) = -1 and sgn(0) = 0

[solid flame]

but the left side will not equal the right side because of the jump discontinuity

[buoyant kayak]

bro who says sgn

[neat dome]

wait hold on the teacher never taught any of this

[buoyant kayak]

yeah most of what they said is wrong so i suggest ignoring it

[neat dome]

alright ill ponder more about it ig

[spark ibex]

anybody good at partial derivatives?

[buoyant kayak]

send the question and we'll find out

[spark ibex]

question 7

[chilly laurel]

could anyone help me please?

[spark ibex]

i have most of it but im stuck on fxy

[jagged imp]

for f_xy you first take the partial derivative wrt x, and then the partial derivative of that wrt y

just like how for f_yy you take the partial wrt y and then the partial wrt y

[alpine sable]

can someone help me with this

[buoyant kayak]

another way to write that composition is f(g(x))

so you're plugging g(x) into f(x), which gives you h(x)

[wary stream]

It's already been answered in #help-3

[buoyant kayak]

mosh is a huge douche though and they still don't understand

so i'm explaining it here as well

[buoyant kayak]

you're looking for an outside function

h(x) = sqrt(x+8) + 9

[alpine sable]

thats it?

[buoyant kayak]

that's h(x)

so if i were to say, g(x) = x+8

rewrite h(x) in terms of g(x)

[spark ibex]

im still confused

[alpine sable]

so i put the h(x) in the place of the x in g(x)

[buoyant kayak]

not quite

h(x) = f(g(x))

you're putting a function inside another function, which gives you a function

confusing, i know

let's use simpler variables

[solid flame]

yessss

[alpine sable]

whyd it show this 😭

[solid flame]

no don't put it in the calculator

[buoyant kayak]

because putting this into a calculator is not smart

[candid storm]

can someone help me with my math hw?

[buoyant kayak]

here ya go, simpler terms

how can you rewrite z?

[alpine sable]

um

x+8?

[buoyant kayak]

no

look at the function for z

[alpine sable]

f?

[buoyant kayak]

look at the function for y

[alpine sable]

√x+8

[buoyant kayak]

see any similarities?

[alpine sable]

they both have x+8

z has a 9

[buoyant kayak]

yep

so if i were to take y and put it into the equation for z

what would z be?

[alpine sable]

√x+8^2 + 9

[candid storm]

can someone help me with probanbility statistics math ?

[buoyant kayak]

no

this is just substitution

[alpine sable]

so

[buoyant kayak]

you're substituting a variable in for a value

[alpine sable]

how do i do that

[alpine sable]

so

[buoyant kayak]

you want a function for z that has y in it

[alpine sable]

√2x+16+9

[buoyant kayak]

you're not multiplying anything here

you're substituting

[wary stream]

No, replace the similarities

[alpine sable]

what would you do

[buoyant kayak]

you're plugging in y for a value

[alpine sable]

so just 9

[buoyant kayak]

no

what is y

tell me what i defined y as

[alpine sable]

√x+8

[buoyant kayak]

yes

now what is z

[alpine sable]

√x+8=√x+8 +9

[buoyant kayak]

you're not setting anything equal to each other

what is z

[alpine sable]

z is √x+8 +9

[buoyant kayak]

and y you said was sqrt(x+8)

so if you wanted to replace something in z

and put y there instead

what would it be

[alpine sable]

is sqrt = √

[buoyant kayak]

yes

[alpine sable]

oh so

[buoyant kayak]

short for square root

[alpine sable]

√(x+8)

[buoyant kayak]

that is what you're substituting, yes

and what is that equal to?

what variable is sqrt(x+8)

[wary stream]

Please look at this example so you can understand composite functions

[alpine sable]

i understand that

but

idk h(x)

i mean f(x)

when hx and gx are given

[wary stream]

The problem wants you to do the reverse

[buoyant kayak]

don't worry about h(x)

just take f(g(x))

because that IS h(x)

[alpine sable]

f(√x+8)(x))

or

f(√x+8)=√x+8 + 9

[wary stream]

You're given an h(x) and a g(x), produce the f(x)

[buoyant kayak]

nothing is being set equal to anything

nothing is being multiplied

we're simply substituting

[alpine sable]

so what would you write

i dont get it

[wary stream]

If you have g(x), "pull" out that part

And replace it with a single variable

[alpine sable]

what variable

like x

F x X = √x+8 + 9

[wary stream]

Why does the left hand side exist

You don't need that side

[alpine sable]

i dont get it

heres the question

[buoyant kayak]

similar problem

look at it and tell me what you don't understand

[alpine sable]

so basically

i would put √x+8 + 9 = (fog)(√x+8)

and itll give me fx

[wary stream]

https://www.youtube.com/watch?v=Fsic3Qnqq1E&t=3s&ab_channel=AnilKumar
Please watch this, it's the same concept

[solid flame]

√x+8 + 9 = (fog)(x)

[alpine sable]

so

is f = I 9 I

[solid flame]

not quite

[wary stream]

There's no absolute value in your question

[alpine sable]

so f is 9

[solid flame]

we know (fog)(x) = f(g(x)) = f(x+8) right?

[solid flame]

did u understand this part?

[alpine sable]

no

[wary stream]

Out of curiosity, what year are you?

[spark ibex]

can someone help me explain 8

[alpine sable]

10 🤡

[wary stream]

Channel is busy

[spark ibex]

ok

[wary stream]

Grade 10?

[alpine sable]

yes

[solid flame]

(fog)(x) is the same thing as f(g(x))

ok?

[alpine sable]

so

just put (fog)(x) in the calc

[wary stream]

No calculator is needed

[solid flame]

no don't use the calculator for this one

[alpine sable]

ik but im using one

D:

[wary stream]

Don't because it's not needed

[solid flame]

now we also know g(x) = x + 8

right?

[alpine sable]

yes

[solid flame]

so we can say f(g(x)) = f(x+8) ?

[alpine sable]

i guess yes'

[solid flame]

does that make sense?

we are just substituting for the g(x) part in the function

[alpine sable]

so

[solid flame]

no no calculator

[wary stream]

You don't need a calculator

[alpine sable]

ok

[wary stream]

Close that

[alpine sable]

illw rite it down

[wary stream]

Don't even write it down

[solid flame]

yes it helps to write it

[wary stream]

That info from the calculation?

[alpine sable]

so i wrote it down

then what

oh i see

you did (f(gx)

ok

then what

[solid flame]

if you're not clear with the concept yet being visual helps

[solid flame]

now set that equal to h(x)

[alpine sable]

so f(x+8)=√x+8 + 9

[solid flame]

oh sorry i didn't mean from the calculator i meant the part i was explaining

[solid flame]

yes

[alpine sable]

then what

[solid flame]

now do you see something on both sides that u can substitute for?

[alpine sable]

what does that mean

they both have x+8

[solid flame]

yes

i meant that

[alpine sable]

so then f=9

[solid flame]

no

[alpine sable]

or √9

[wary stream]

No

[tranquil tulip]

how did u text that sqrt sign

[alpine sable]

option v

[wary stream]

Copying it from the internet

[alpine sable]

so f(x+8) = √+8 + 9

then what but dont use substitute cause i done understand that word

like anything to remove

multiply or add

[solid flame]

we can't cancell the x+8

or multiply or add

[buoyant kayak]

you literally need to substitute

that is how you solve this problem

[alpine sable]

what does substitute mean

[buoyant kayak]

there is no other option

[solid flame]

substitute is like replacing the x+8 with something else

[alpine sable]

like

anything

[solid flame]

so imagine we say x+8 = y or something

[alpine sable]

i could write like 17

[solid flame]

u can pick anything ive picked "y" here

[solid flame]

no u have to pick a variable because there's a variable in the equation

so y = x+8

[alpine sable]

so x

ok so

substitute x+8 with x+8?

wha

[solid flame]

with y

[alpine sable]

ok so

f(y) = √x+8 + 9

[solid flame]

ya

do that on the other side too

[wary stream]

What about the RHS?

[solid flame]

no

no calculator

[buoyant kayak]

stop using a calculator

[wary stream]

Stop using a calcuator

[alpine sable]

i dont know how to mulitply that

[buoyant kayak]

there is no multiplying

there is no adding

[solid flame]

you don't have to multiply

[buoyant kayak]

there is no subtracting

there is no division

there is only subtitution

is this a troll

[alpine sable]

so its just f(y) = √x+8 + 9

[buoyant kayak]

are we being trolled

[alpine sable]

no-

[solid flame]

everywhere u see a "x+8" just put "y"

[alpine sable]

so √y + 9

[solid flame]

yessssssssssssssssssssssss

[alpine sable]

thats f?

[solid flame]

yep

f(y) = √y + 9

[wary stream]

Well it needs to be in terms of x, not y

[wary stream]

Because it's f(x)

[alpine sable]

so

[solid flame]

i mean once u get it to a variable u can put any letter in there

[alpine sable]

whats the answer to the problem tho

[solid flame]

no leave the calculator

[wary stream]

The problem denotes f(x)

[alpine sable]

so what would i type for

[wary stream]

So it should be in terms of x

[solid flame]

f(y) = √y + 9
and they ask for f(x) so f(x) = √x + 9

u would put the RHS into the blank

make sure to use x here cuz they specifically ask for f(x)

[alpine sable]

so

the answer is sqrtx + 9

[wary stream]

Yes

[alpine sable]

thanks

wait so

does the square root go over

the entire answer

or just the x

[solid flame]

just the x

cuz rem the 9 was outside the square root from the beginning

[tepid edge]

i have to do this without l'hospital or finding derivatives

i am incredibly lost

[solid flame]

lim as x -> 0 of sinx/x = 1

so if u factor out sin3x/3x , the rest is substitution

[hollow pelican]

A ball is thrown horizontally from the roof of a building 7.5 m tall and lands 9.5 m from the base. What was the ball's initial speed?

can someone help me please

[slow fjord]

#help-0

[tidal sable]

@hollow pelican Use the eq. D=ut+1/2gt²

[tidal sable]

Take u = 0 bc along vertical direction intial velocity is 0

You get the value of t=1.24s

Then use distance=velocity x time to get the value of intial speed

[hollow pelican]

ok

[tidal sable]

Your answer should be 7.68m/s

[hollow pelican]

yup i got 7.68

[tidal sable]

👍

[hoary sable]

naveed do you know how to help me in questions 2?

[hollow pelican]

For general projectile motion with no air resistance, the horizontal component of a projectile’s velocity:

@tidal sable is it remains a non-zero constant?

[tidal sable]

Yes

[hollow pelican]

ok

[tidal sable]

Because only the gravitational force is acting on the body and it acts vertically

[hollow pelican]

thankss

[tidal sable]

Np

[hollow pelican]

If you decrease the initial launching velocity of a horizontal “zero-angle” launch, the projectile range will increase

is this correct lol

[tidal sable]

No it can't increase of you decrease the velocity

How is that possible? 🤔

[alpine sable]

how do i start this off

[hollow pelican]

yea i was thinking of that too

[tidal sable]

Horizontal and vertical components are completely independent of each other

[hollow pelican]

yea

The catapult used by the soldiers hurls a stone of mass 32 kg with a velocity of 50 m/s at a 30° angle of elevation. What is the range (* the horizontal distance travelled when the stone returns to its original height)?

[hollow pelican]

@tidal sable do u know how to solve this?

[tidal sable]

Let me try

[hollow pelican]

thanks bro

[kindred zodiac]

pls help

[hollow pelican]

@tidal sable From the same height (and at the same time), one ball is dropped and another ball is fired horizontally. Which ball has the greater velocity at ground level?

is this: (Neither—they both have the same velocity on impact.)

[tidal sable]

Both at the same time

Like I said horizontal and vertical components are independent of each other

[hollow pelican]

ahh i see

[tidal sable]

It's the gravity which is responsible for bringing the balls to the ground and gravity acts vertically

[candid storm]

anyone? help pls

[pastel perch]

um sorry but you need to wait

read rules

about how to get help

[tidal sable]

@hollow pelican I think 108.12 m

But I'm not sure bc I don't have any idea why are we given the mass of the stone

[pastel perch]

oh you were not done

im sorry

i will delete my post

[tidal sable]

No it's fine

[hollow pelican]

ohh

[arctic cloud]

should I change it to that or just leave it as 3 over square root of 55

[hybrid radish]

can anyone help me with this?

please ping if you can !!

[alpine sable]

Ok ,let me try

Well ,first you can use the pythagoras theorem to find the unknown side .

[hybrid radish]

yes, i already have that

[alpine sable]

Ok ,so ehat did you get?

[hybrid radish]

i got square root 46

[alpine sable]

Ok

Ok so ,do you know cosine is the ratio of which sides?

[hybrid radish]

yes, adj / hypotenuse

which would be square root 38 / 2 square root 21, i believe?

[alpine sable]

Ok ,so cosine I
= adj/hypotenuse root 46/ 2√21

No ,the adjacent side means that it's an arm if the angle I excluding the hypotenuse.ok?

[hybrid radish]

ahh okay

wait hold on

that's my mistake

[candid storm]

what rule?

its not a test its a hw ?

[hybrid radish]

hold on wait, i got 0.74 for cos but i need help with the sin & tan

i keep on getting the same answers for the two

[tidal sable]

Sin =0.67

[alpine sable]

Ok

[hollow pelican]

@tidal sable is this correct?

[tidal sable]

So tan should be 0.67/0.74

[alpine sable]

So ,
Tan I= Opposite side/ adj side ok?

[wary stream]

They were referring to this rule

[hybrid radish]

yes

[alpine sable]

So,now calculate it

[candid storm]

oh but no one was askign

[tidal sable]

Yes it is

[wary stream]

But there was a discussion still going on

[hybrid radish]

square root 38/square root 46?

[tidal sable]

Tan is simply sin/cos

[alpine sable]

Yep

[alpine sable]

Yeah that too

[tidal sable]

Its easier when u have the values of both

[alpine sable]

Ok,so
Sin I= hypotenuse/adj ok?

[hybrid radish]

i understand the rules, but i keep on confusing the adjacent angle

[alpine sable]

Adj side??

[hybrid radish]

yes, i confuse it with the base

[tidal sable]

Just remember "base" instead of adj side

[hybrid radish]

is the base always the adjacent side?

[tidal sable]

Base perpendicular hypotenuse

[alpine sable]

Oh ,so the adjacent side is actually that side of th triangle which is also an arm of your angle but excluding the hypotenuse.

[hybrid radish]

i'll figure out the sin on my own and i'll tell you what i get

[alpine sable]

Ok

[hybrid radish]

would 0.67 be correct?

[tidal sable]

Yep

[hybrid radish]

alrighty, thank you

[alpine sable]

Huh??

[arctic cloud]

sin is opposite/hypotenuse

[tidal sable]

0.67 is the value for sine

[alpine sable]

Yeah ok.

[tidal sable]

I think "adjacent side" is a bit confusing

[alpine sable]

Yep

[tidal sable]

So I just remember perpendicular

[tidal sable]

Basically means its perpendicular to the base

[viscid idol]

can smo please help me ):

#83

[snow cedar]

is the partial sum convergent or divergent?

[viscid idol]

i have no idea it doesn t say

this is all that it gives me

[snow cedar]

you should try and figure that out

[viscid idol]

its convergent i think

[snow cedar]

and what does it converge to?

[viscid idol]

1/3

[snow cedar]

there you go

[viscid idol]

but is it that simple? like am i just supposed to simplify it

[snow cedar]

yes this one is relatively simple

you're already give the equation for the partial sum so that takes a lot of the work out

[viscid idol]

im sorry i just started learning these im lowk screwed for my ap calc exam

so like

[jagged panther]

May I please get help at this?

it is trigonometry but I am not good at it

[viscid idol]

its converging because i checked with the direct comparison test

is that ok to use?

i just set the n going to infinity

but idk how im supposed to know when to use that

[wary stream]

Use SOH CAH TOA trig identities

[candid storm]

hi

[snow cedar]

@viscid idol its important to memorize your series tests like a tool belt

[viscid idol]

mhm yeah tyyy

but do i use direct comp test here

like i got 1/3 bc i j set n to infinity but idefk why

i m sorry im basically self studying bc my tutor is so bad he legit leaves me on delivered for a whole week so i gotta find stuff myself

[jagged panther]

alr ty

[snow cedar]

theres are several methods that would work, solving the limit as n approaches infinity is just a limit test

[viscid idol]

ohh then how did u get the answer 1/3 then

[wet fulcrum]

cos rule

[snow cedar]

infinite series are defined as the limit of the infinite sequence of partial sums

[wary stream]

Why cos rule? You can easily apply the trig ratios

[wet fulcrum]

can you?

[wary stream]

Yes

tan = opp / adj

[wet fulcrum]

oh yes i realized

[snow cedar]

@viscid idol if the limit of the partial some is infiniti the series diverges, if the limit does not exist the series diverges, if the limit converges to a some value L then the series converges with sum L

[wet fulcrum]

lucky i read the part where he can use calculator

[snow cedar]

@viscid idol sum**

[viscid idol]

so do i just set the n to infinity to find exaclty what it converges to?

[jagged panther]

I don’t mean to be rude in any way but I still git it wrong 💀

[snow cedar]

sometimes it may not be that easy, so youll have to use things like the nth term test, or comparison test, limit comparison test etc.

[wary stream]

How did you calculate this?

[viscid idol]

got it thank u so much charles!

[wary stream]

Incorrect ratio

If tan = opp / adj, what is opp and adj in respect to B?

[snow cedar]

https://www.youtube.com/watch?v=0wefqjpQyKM this may be of some help, good luck.

[daring violet]

can someone help me go over my final with me? kinda anxious on how i did

[wary stream]

Is it a completed final?

[daring violet]

yes here's proof

just anxious about the bonus questions

[wary stream]

You can post and ask and someone can help you

[charred night]

does anyone know how to do this

[wary stream]

Create a system of equations

[charred night]

what does that mean

[ocean seal]

dldh06

[charred night]

would the total be the $?

[wary stream]

No

That text was called latex, it uses $

[charred night]

so 16a+6.5c=283?

[wary stream]

Nope

[wary stream]

@charred night Hint: I told you what numbers get plugged in, a and b are just variables

[charred night]

i give up

im so fucking tired

[wary stream]

That's great, I didn't really ask you this

[rancid narwhal]

pls help

@solid lintel can u help me?

[jagged panther]

what about this would it be the same? like the same way to set up?

[hidden horizon]

i got only one possible value

[rancid narwhal]

thanks

[hidden horizon]

np

[strong furnace]

how do you go from r^4=1/16 to r=1/2 ignoring r=-1/2 ?

[hidden horizon]

oh mann

i forgot

[alpine sable]

how do u solve this

is this busy?

[hidden horizon]

@rancid narwhalthere will be -1/2 too bcoz 1/16 can be written in that form as well im sorry i forgot

[rancid narwhal]

how to do this

[strong furnace]

do you know about the power property of lograrithm?

[alpine sable]

no

[rancid narwhal]

its positive so no -1/2

[gentle depot]

IIts this proof proof fair