precalculus

[quartz garnet]

FIrst one is x < 1

[clever inlet]

oh whoops

yeah

[quartz garnet]

Second one is x < 2

[viscid thistle]

how do I know if it's < >

[clever inlet]

it's not much difference from solving an equation

[viscid thistle]

yeah I know what x is

[clever inlet]

5x - 1 < 5 - x

move numbers to one side

variables to the other

[quartz garnet]

6x < 6

[viscid thistle]

I know

but I don't know

if it is

<

and that is my question

[clever inlet]

if you did the moving

[quartz garnet]

just keep it as it is

[clever inlet]

and had no negative variables

[viscid thistle]

I did

[clever inlet]

the sign stays the same way

[viscid thistle]

and it is wrong??

[quartz garnet]

5x - 1 < 5 - x
5x + x < 5 + 1
6x < 6
x < 1

[clever inlet]

^

[viscid thistle]

well I guess I'm scrapping the whole idea of doing it graphically in general then

serves no purpose

[clever inlet]

you should know both

[quartz garnet]

7 - 4x > 2x - 5
7 + 5 > 2x + 4x
12 > 6x
2 > x
x < 2

[viscid thistle]

yeah but there is no way I can calculate if it is < or > without doing it the algebraic way

[quartz garnet]

You'll sometimes need to solve it graphically when it comes to more complex ones

There is, of course, a way to calculate if it's > or <

[viscid thistle]

then how

[viscid thistle]

I understand

nada

[quartz garnet]

For what range of x is f(x) above g(x)?

"above" means >, and "below" means <

[viscid thistle]

when x is above a?

[quartz garnet]

yea

x>a is the solution to f(x)>g(x)

[viscid thistle]

I'll just solve it with algebra when my test comes up

[quartz garnet]

Yeah algebra is much faster

But you'll need to know how to solve graphically

for future uses

[clever inlet]

there probably will be times

where they straight out give you the graphs to compare

[viscid thistle]

I'll just ask my teacher on monday

[quartz garnet]

Ye learn it in your own language

that'd be way easier for you to comprehend

[viscid thistle]

so 6263

Study the graph to the function y = f(x) below

For which value(s) on x are correct a) f(x) = 30 b) f(x) > 0 c) f(x) < 20 d) 20 < f(x) < 30 e) e - 10 <_ f(x) <_ 10

[clever inlet]

actually

this one of the cases where the graphical approach is nice

[viscid thistle]

well

I have no idea how to solve this

[clever inlet]

so for the first question

basically

for what x is y equal to 30

[viscid thistle]

none

or what

no

wait

x=3

[clever inlet]

let's assume the line is to scale

should be x = 20 shouldn't it?

[viscid thistle]

yeah

I didn't look at the picture so I just assumed it was x3 lol

but same thing

[clever inlet]

and for the next question

what values of x makes y less than 0

basically, what values of x is the graph under the x axis

[viscid thistle]

you mean more

[clever inlet]

x

ah yeah

whoops

above the x axis

[viscid thistle]

that would be x > 0

wait

no

x > -10

[clever inlet]

exactly

[viscid thistle]

keep looking at the wrong axis lol

[clever inlet]

you understand it now?

[viscid thistle]

and c is

x < 10

[clever inlet]

yep

[viscid thistle]

so for d

it's the same thing?

so it would be like

x < 15?

[clever inlet]

it should be a compound inequality

[viscid thistle]

one of those <_

[clever inlet]

it should be

something < x < something

[viscid thistle]

ogh

x < 15 < y?

wild guess tbh

[clever inlet]

for what values of x

is y between 20 and 30

[viscid thistle]

15

[viscid thistle]

yeah isn't that 15?

[clever inlet]

the y values are between 20 and 30

when the x values are between 10 and 20

10 < x < 20

[viscid thistle]

oh

so like

the lowest x < x < lowest y

[clever inlet]

you should only have x values

[viscid thistle]

oh

so just

10 < x < 20

[clever inlet]

yes

[viscid thistle]

so let's say it was 30 < f(x) < 40

it would be 20 < x < 30

[clever inlet]

yep

exactly

[viscid thistle]

so then for e?

-10 <_ f(x) <_ 10

it would be

-20 <_ x <_ 0

[clever inlet]

-20 < x < 0

yep

[viscid thistle]

not <_?

[clever inlet]

actually yeah

should be that

wait

ah yeah

you're right

didn't read the original question

[viscid thistle]

wow

actually learnt somethinh

[clever inlet]

nice

[viscid thistle]

shitty pic

wow Discord doesn't let me upload pictures

for fuck sake Discord why do you always have problems

[clever inlet]

rip

[viscid thistle]

6264

The figure shows a monthly price y currency, as an fuction of minutes spent talking on the phone, x minutes for three different telecoms

I figured out a and b

c) is just weird to me

[clever inlet]

what's och?

[viscid thistle]

and

h(x) = 2g(x)

I don't get it

[clever inlet]

find where

h(x) is double as tall as g(x)

actually

h(x) is constant

so find where g(x) is half of h(x)

[viscid thistle]

half?

so like

110

[clever inlet]

yeah

[viscid thistle]

answe sheet doesn't say so

[clever inlet]

find the x value

for when g(x) = 110

[viscid thistle]

80

[clever inlet]

somewhere around that

yeah

[viscid thistle]

wait

so how do I solve questions like these

[clever inlet]

h(x) = 2g(x)

with these

so h(x) is the same as the y value for that function

and g(x) is the same as the y value for the other function

[viscid thistle]

oh yeah

so 1 g(x) is 110

[clever inlet]

you need find the x value, where the y value of h(x) is double the y value of g(x)

g(80) is roughly 110

[viscid thistle]

so with these

I should basically think that

h(0,5) = g(x)

and h(0,5) is y 110

and with the y I can find x

[clever inlet]

you're not inputting the half into the function

[viscid thistle]

but half of h is g(x)

so I should basically think like that

[clever inlet]

i think i screwed up

you need to find the x value where h(x) is double g(x)

[viscid thistle]

-_-

what's the question ? @clever inlet

[clever inlet]

https://cdn.discordapp.com/attachments/363224154469826562/381644116196458506/23758048_1603834109660535_1841916948_n.png

[viscid thistle]

but bruh

I don't speak swedish

The figure shows a monthly price y currency, as an fuction of minutes spent talking on the phone, x minutes for three different telecoms

ok

so g(x) is telecoms

all are telecoms

ok

what's the question

Figure out from the graph for which x are actual

direct translation

idk how to say it in another way

h(x) = 2g(x)

gtranslate?

nah

ah I see

my translation but I don't know how to put it in an actual translation where they mean exactly the same

for which x, h(x)=2f(x)?

for which x, h(x)=2g(x)

yeah ok

that's not possible

it's not the correct choice

because no matter x h(x)=220

they want to know for which x

h(x) is double as expensive

as g(x)

[clever inlet]

If you have g(80)

Thats roughly 110

Double

And you get 220

[viscid thistle]

ah

how do I get g(80) though

[clever inlet]

You determined that earlier

[viscid thistle]

I mean how you put it was good

[clever inlet]

You did it yourself

[viscid thistle]

just half the h(x)

and use y to see what x is

with the help of g(x)

well I'm done then

I'm not even gonna bother with the last one

yeah basically divide 220 by 2 and then find what is the value of x at that value of y '

yes

I just didn't get it why there was a multiple choice

and c circled

thought it was like

which one is true

[dusk raft]

who here plays fortnite

Need 1 more person for squads [NA] 2.5+ kd

[viscid thistle]

At sea level the boilinmg point is 100 degrees celsius, on the heigh 4,8km the boiling point is 84 C, the boiling point (y) gets lower exponentially with the height (x).
Calculate the boiling point on Mount Everest's tip, which is 8800m high.

[sour hemlock]

Y = exp (-x) and just plug in the value for x

No wait

[willow bear]

=tex y = 100 \cdot 0.84^{\frac{x}{4800}}

[willow bear]

x in meters, y in degrees celsius

@viscid thistle

[viscid thistle]

lmao I already figured it out

thanks anyways

[fleet kayak]

hello guys im pretty new

im having a hard time anwering a question in my quiz, can somebody help?

[patent beacon]

@fleet kayak
2sin(2x)cos(3x) + cos(3x) = 0
[2sin(2x) + 1][cos(3x)] = 0
sin(2x) = -1/2, cos(3x) = 0

[fleet kayak]

thank you very much @patent beacon i hope to learn this one day

[patent beacon]

From there, how do you normally handle finding the inverse of a trig function? Solve over an interval?

[fleet kayak]

im not really sure ive been sick for the past few weeks and got left out of school. so here i am struggling with youtube

[viscid thistle]

In a test with dry conditions the braking distance was measured for a car with new tires to 38,5m in the speed 100km/h

Calculate the braking distance for 50, 70, 90, 110 and 130

[viscid thistle]

yeah, I've already forgotten most of everything that I need to my test

:/

[small hollow]

how fast is the car slowing down

[viscid thistle]

idk

38,5m at 100km/h

is all I know

[small hollow]

feels like a ratio problem to me then

[viscid thistle]

yeah

it is

[small hollow]

38.5/100 is your ratio just apply that to the other speeds

is there a bot that applies LaTeX here?

[viscid thistle]

that's wrong tho

[small hollow]

hmm

[viscid thistle]

it's on the right note

[small hollow]

tex \frac{38.5}{100}={break dist}{speed}

[viscid thistle]

but the ratio is 0.00385^2

I have no idea how to get that

[small hollow]

that

is latex stuff

set the fraction equal to the distance over the new speed

for instance 38.5/100=x/20 for 20km/h

solve for x using this method

[viscid thistle]

so 0.385/20?

[small hollow]

no, that's just an example of how you would solve if your speed was 20km\h

lemme try again with LaTeX

tex \frac{1}{2}

=tex \varepsilon

[small hollow]

awesome

=tex \frac{38.5}{100}=\frac{break dist}{speed}

[small hollow]

substitute in your speed and solve for the break distance

[viscid thistle]

so 0.385/speed?

[small hollow]

0.385*speed

you multiply the equation

=tex \frac{38.5}{1000}speed=breakdistance

[viscid thistle]

well

0,385*speed isn't correct

[small hollow]

ok that's wierd then

is this a webwork?

[viscid thistle]

since0.385*50=19.25

the answer sheet says 9.6

[small hollow]

ooooh ok

[viscid thistle]

someone pls help

[small hollow]

can send picture?

[viscid thistle]

yh

[small hollow]

does it say how long it takes the car to stop

im guessing not

[viscid thistle]

in the answer sheet?

[small hollow]

in the question

[viscid thistle]

no

it doesn't involve time

[small hollow]

fail phys don work

[viscid thistle]

do you know anything about functions

f(x) stuff

[small hollow]

is the answer for 130 65.1

and yes I know all about that

doesn't have to be exact

[viscid thistle]

65

[small hollow]

Ooooooooooookaaaaaaaaaaaaaayyyy

i got it

[viscid thistle]

110 47

[small hollow]

had a hunch

[viscid thistle]

how did you do it

[small hollow]

=tex r=\frac{speed}{100}

[small hollow]

=tex distance=38.5*r^2

[small hollow]

it's just the way acceleration works in physics

[viscid thistle]

r?

[small hollow]

this was a really bad problem to have on your hw it doesn't explain what to do well

I'm just using r as a local variable

inactuality:

=tex distance=38.5(\frac{speed}{100})^2

[viscid thistle]

huh

so how do I solve a problem with this

[small hollow]

It was really problem specific I feel

poorly explained

If I were you i'd ask about it in class tomorrow

[viscid thistle]

I have my test tomorrow lmao

[small hollow]

FAIL

well worst comes to worst remember that

[viscid thistle]

well it's only some parts of this kind of stuff I have problems with

[small hollow]

any other questions?

[viscid thistle]

f(x) = 4x -3

a) f(0)

I've forgotten these

entirely

[small hollow]

ok

all f(0) means is you plug in 0 for x in f(x).

[viscid thistle]

yeah I know

[small hollow]

f(x)=4x-3 then f(0)=4(0)-3

[viscid thistle]

oh

yeahh

with a f that is 0

gives me no x's at all

which ends me with having -3

[small hollow]

exactly

[viscid thistle]

if I have f(4) then

[small hollow]

you are not solving for x here you are just evaluating the function

[viscid thistle]

16x?

my bad

f(3)

[small hollow]

substitute 3 for x and the number you get is your answer

[viscid thistle]

substitute?

oh

12-3

[small hollow]

replace all xes in the equation with a 3

yes exactly

[viscid thistle]

how can I forget this shit

[small hollow]

lol idk

[viscid thistle]

this is literally the first shit in the book

and I forget that

so

if we have f(x) = 7x - 3x^2

and f(4)

28 - 3x^2

x=4

4^2 = 16

16*3

28-48

=-20

and with f(-4)

7*-4=-28

-4^2

-16

-16*-28

wait no

I'm going back

-16*3

= -48

[small hollow]

nonononnono

[viscid thistle]

I keep confusing myself

[small hollow]

f(-4)=7(-4)-3(-4)^2

f(-4)=-28-3*16

[viscid thistle]

yh

-28-48

[small hollow]

-28-48

-76

[viscid thistle]

yeah

[small hollow]

yes you have the right idea

[viscid thistle]

I was trying to say that but I confused myself

[small hollow]

just be careful when using negatives inside squares

[viscid thistle]

think I took the same numbers twice

[small hollow]

here lemme give you a hard one

f(x)=3x^3-2x^2-8x+5

find f(-2)

=tex f(x)=3x^3-2x^2-8x+5

[viscid thistle]

jeez that's a lot of numbers

[viscid thistle]

so

-2^3

= -8

-8*3

=-24

-2^2=-4

[clever inlet]

careful

that one you need to be careful

[viscid thistle]

-24 - -4

-24 - -8 -16 + 5

[clever inlet]

-2x^2

you need to be careful with that one

[viscid thistle]

that's 8

[clever inlet]

positive or negative?

[viscid thistle]

anthing - * +

is -

[clever inlet]

yeah

[viscid thistle]

-24 - -8 -16 + 5

[small hollow]

take it term by term and add the numbers you get at the end

one thing I do ALL OF THE TIME

is think of this:

=tex f(x)=3x^3-2x^2-8x+5

[small hollow]

like this:

=tex f(x)=3x^3+-2x^2+-8x+5

[small hollow]

makes things easier to understand

[viscid thistle]

I could probably just do this all

in one big calculation on my calculator

since I will probably use one for these

[clever inlet]

i tend to write down the working out with substitution

then calculator

[small hollow]

the more you do it out by hand the less confused you will be later

[viscid thistle]

Well the result is -43

[clever inlet]

you sure?

[viscid thistle]

yes

[small hollow]

no

[clever inlet]

3(-2)^3 -2(-2)^2 - 8(-2) + 5

actually that's terrible

ignore that

basically unreadable anyway

[viscid thistle]

3*-2^2 - 2*-2^2 - 8*-2 + 5

[small hollow]

yes just be mega careful you know which negatives are inside exponents

[clever inlet]

it's probably useful to use parenthesis

cause

-2^2 =/= (-2)^2

[viscid thistle]

yeah I am

[small hollow]

=tex 3(-2)^3 -2(-2)^2 - 8(-2) + 5

[viscid thistle]

for every thing I use them

[small hollow]

god i love this thing

any other questions Jonathan?

I want you to ace your test

[viscid thistle]

I barely pass them

[clever inlet]

what'd you get for the above one?

[viscid thistle]

well

I got one calculator crash

[clever inlet]

the one vlazer4 posted

[viscid thistle]

uh

"Error

[clever inlet]

rip

[small hollow]

check syntax

[clever inlet]

well, this is one of the nicer cases:

• 24 - 8 + 16 + 5

if you want

i'd probably enter the original anyway

[viscid thistle]

3(-2)^2-2*(2)^2-8(-2)+5

[clever inlet]

to prevent arithmetic errors though

[small hollow]

be careful because the symbol for subtraction "longer -" is different from the negative symbol "little -"

it treats two seemingly identical keys totally different

it's stupid and I hate it but we all have to live with it

[viscid thistle]

yeah I know

I don't use that one

unless 2^-1

[small hollow]

try entering in the thing but with the right negative sign for each

that's probably the cause of your crash

[viscid thistle]

it wasn't

[small hollow]

hm

anyway it should spit out -11

[viscid thistle]

wait

plus 16?

[clever inlet]

yeah

[viscid thistle]

I'm dumb

[clever inlet]

somewhere in the working

[viscid thistle]

I didn't see the -

[clever inlet]

there should be a plus 16

[small hollow]

=tex 3(-2)^3 -2(-2)^2 - 8(-2) + 5

[viscid thistle]

I keep forgetting

so let me try to calculate it again then

[small hollow]

-28 -8 +16 + 5

-11

[viscid thistle]

-8^2*3 - -4*-2^2 - 8*-2+5

I keep getting fucking syntax

I'll just do them manually

[small hollow]

gooooood GOOOOOOD

[viscid thistle]

fuck you ti84

Okay so far this is the last one I have had problems with

Rewrite the formula and figure out if y is proportional against x
If so, write the propotional constant

[small hollow]

type =.tex without the period and then type it like normal and it will come out nice and pretty

[viscid thistle]

should maybe write the variables should I

I'm dumb

[small hollow]

typing it normally is probably easier tho

[viscid thistle]

=tex 2y = 3x

[granite stirrup]

Support the bot on Patreon: https://www.patreon.com/dxsmiley

[viscid thistle]

Rewrite the formula and figure out if y is proportional against x
If so, write the propotional constant k

[small hollow]

solve for y

write the coefficient next to x as the proportional constant

[viscid thistle]

huh

I know how you figure out k but

y/x=k

[small hollow]

if y is proportional to x then y=c*x where c is any number

[viscid thistle]

yeah

[small hollow]

ah that's another way to do it

that's an easy solve

[viscid thistle]

I still don't know how to solve it tho

[small hollow]

ok I'll walk you through it

2y=3x

divide by two on both sides to isolate y

y=(3x)/2

[viscid thistle]

y=1,5x

[small hollow]

good

[viscid thistle]

lmao

[small hollow]

y/x=1.5

[viscid thistle]

which is k

[small hollow]

yes

[viscid thistle]

how do I know if it is proportional

[small hollow]

if k is literally any number

i know that sounds weird but let me show you a case where it is not

2y^2=3x

there's no way you can get y/x=k in this equation becuase y is y^2

both y and x have to have a degree of 1 (no small number on top of them because the 1 is omitted/invisible)

[viscid thistle]

I'm confused

[small hollow]

I know its a bit weird

[viscid thistle]

so basically if I can't get k

[small hollow]

if you can't get y/x=k

where y/x is SPECIFICALLY y/x

then they are not proportional

usually you can eyeball it

[viscid thistle]

so

with b) y-3/x=0 then

this one makes me so confused

[small hollow]

can you get exactly y/x= some number?

[viscid thistle]

I don't know what y-3 is

so no

[small hollow]

good

if you can isolate a y/x then it is proportional

there can't be any garbage attached to the y/x

[viscid thistle]

answer sheet says y = 3/x

"It is not proportional"

then 0,4x-y=3

that one is proportional?

since it would mean that y= 3,4

wait no

I don't know what x is right

or do I in 3,4/0,4

[small hollow]

=tex 0.4x-y=3

[small hollow]

you mean this?

[viscid thistle]

yes

[small hollow]

x and y are proportional if and only if ax = by where a and b are some numbers

[viscid thistle]

put ` around your text

to not use markdown for your text

or else it looks like this

[small hollow]

cool

anyway if the equation is not in that form then x and y are not proportional

[viscid thistle]

so is it proportial or not

[small hollow]

no

[viscid thistle]

hm

what about

x/3-y/9=0

I assume not

since shit is linked to both x and y

[small hollow]

actually the answer is yes

x/3-y/9=0

x/3=y/9

[viscid thistle]

oh

[small hollow]

9x=3y

boom

[viscid thistle]

so

basically

if I can figure out how to use both x and y equally

[small hollow]

yeah kinda

just get a single x and single y on each side of the equation

thats it

they can have multipliers on them, but any other terms are not allowed

[viscid thistle]

and division?

[small hollow]

yes

division is multiplication

x/3=x*(1/3)

[viscid thistle]

I see

oh functions are back
f(x) = 12-8

Calculate f(2)

12-16

-4

[small hollow]

wait f(x)=12-8?

no xes inside?

[viscid thistle]

8x*

[small hollow]

oh that changes everything

god confuzzled

[viscid thistle]

And if I want f(x) = 2

I do f(1,25)

to get 12-10

[small hollow]

yes good job

[viscid thistle]

is it true that f(2) < f(-2)

yes it is

-8x*2=-16

-2*-8=16

and f(x) < -2

could just be f(2) again

since it gives me -4

ah they wanted 1,75

[small hollow]

fyi I can do voice if you have a mic so we aren't flooding chat

just an idea

[viscid thistle]

I rather not talk

it's like 5:40 here

[small hollow]

ok

[viscid thistle]

AM*

[small hollow]

i'm in the US

[viscid thistle]

yeah so it's like almost midnight

6210

The figure shows the graph to the function y=f(x)

b) What is f(4)

[small hollow]

ok

the horizontal bold line is the x axis

the vertical bold line is the y axis

you could also call it the f(x) axis it's the same thing

to find f(4), go four lines to the right from the center point

[viscid thistle]

yeah I know that

right under B

[small hollow]

and then the height of the curve at that point is f(4)

[brisk fiber]

@small hollow

help me out once ur done with him please?

[small hollow]

sure

[viscid thistle]

so when the point is B

[small hollow]

the y value of point B is f(4)

[viscid thistle]

I'm unsure

oh

[small hollow]

basically how many lines up point b is

[viscid thistle]

wow they just asked for that?

yeah

3

[small hollow]

lol

[viscid thistle]

so

if I want to figure out what x is to f(x) -4

I'd just say -3 x

x= -3

since A is x = -3

[small hollow]

yes it is essentially doing what you just did backwards

[viscid thistle]

jeez

[small hollow]

if you're all set then im going to go help kozmic

hollar if you have any other questions

[viscid thistle]

yeah I'll do so

I'm gonna continue with trying to solve other stuff

[small hollow]

also rule of thumb to acing tests is sleep

[viscid thistle]

hey I woke up at 3 AM

I have sleep

[small hollow]

just saying lol

[brisk fiber]

@small hollow

my man

[small hollow]

yo

[brisk fiber]

ok so

is it possible to find x without using a graph?

[small hollow]

the answer depends on how complex the cubic equation is

let me show you the cubic formula so you get an idea

[brisk fiber]

k

[small hollow]

have fun with this lol

[brisk fiber]

nope

not possible

[small hollow]

yeah it's pretty nasty

degree 4 is even worse and degree 5 and up just doesn't exist

it's been proven to not exist

anyway what i'm saying is that if you have a nice one like x^3-1 you can get it pretty easy

[brisk fiber]

of course

[small hollow]

but more complicated ones usually need the calculator

[brisk fiber]

but what i was trying to do was get the derivative of the inverse of that fuction

at 2

[small hollow]

ah

yeah i'd start by trying to get the inverse

[brisk fiber]

yeas

[small hollow]

replace all xes with ys and all ys with xes

lemme work it out on my board

nah you run into a dead end

[brisk fiber]

yea

gotta use calc

[small hollow]

ye

[brisk fiber]

if i can find where f(x) = 2

and switch the x and 2

i would know

[small hollow]

if you want to find where f(x) is 2 that's pretty easy

[brisk fiber]

then find the derivative of the original function and input what x is

if i use a graph it's easy

[small hollow]

ok

1. find where f(x)=2

2. find what the slope of the function is at that x value

3. do 1/that slope and it will give the slop of the inverse

[brisk fiber]

ye

[small hollow]

you don't actually need to know the inverse function

I can give you it tho

[brisk fiber]

i do need it dont I?

the derivitave of the inverse of the fuction at 2

[small hollow]

you don't need it

but using the magical power of integrals you technically could

but it wouldn't be pretty

let's translate this discussion over to the calc board shall we?

[viscid thistle]

u here?

[small hollow]

ys

[viscid thistle]

So at the sea level the boiling point is 100 (Sorry I don't know fahrenheit)

[small hollow]

don't worry i hate farenheight too

[viscid thistle]

at the height 4,8km the boiling point is 84

The boiling point y degress gets lower exponentially with the height x km

Figure out the boiling point on mount everest with the height 8800m

so I already figured out C

which is 100

cause f(x) = C * a^0

a^0 = 1

(0, 100) and (4.8, 84)

idk how to continue

[small hollow]

ok you know exponential equations have the form

=tex A(r)^x

[viscid thistle]

no

that's too far into the book

[small hollow]

hold oin

y=ar^x

a is your initial value

[viscid thistle]

yes

[small hollow]

r is your rate

and x is your variable

[viscid thistle]

yes

[small hollow]

you know that anything to the 0 power is 1

[willow bear]

did i not give you the equation that models that earlier?

@viscid thistle

[viscid thistle]

hm

maybe you did

I was going over the whole book before

[willow bear]

=tex y = 100 \cdot 0.84^{\frac{x}{4800}}

[small hollow]

was leading him into that

[viscid thistle]

hm

[willow bear]

== 100 * 0.84^(8800/4800)

[granite stirrup]

72.64047763

[viscid thistle]

wait

please lead me then

so I figured out that C is 100

[small hollow]

you have to do it to know it

[willow bear]

when x = 0, y must be 100, thus that constant multiplier is 100

when x = 4800 (meters), y must be 84

[viscid thistle]

yes

[willow bear]

= 0.84 * 100

= 100 * 0.84^(4800/4800)

[viscid thistle]

4800/4800?

[willow bear]

= 1

[small hollow]

He's orienting the exponent around 4800 by dividing

[willow bear]

she

[small hollow]

sorry

i didn't know what gender you were

[willow bear]

my username is Ann 🙃 but ok

[small hollow]

oh i hadn't looked yet

anyway

[viscid thistle]

Well looking into my old notes

[small hollow]

How much sense does the exponential equation make to you?

[viscid thistle]

I had written 84/100 = 100/100 * a^4.8

[small hollow]

are you like totally lost or can you handle it

ill explain it if it doesnt make sense

[viscid thistle]

figured it out

with my own method

[small hollow]

cool

[viscid thistle]

84/100 = 100/100 * a^4.8

0.84 = a^4.8 = 0.954

0.964^8.8

=74.67

oh yeah I got 0.954 with rt

[willow bear]

== 0.84^(1/4.8)

[granite stirrup]

0.96432816

[willow bear]

typo?

[viscid thistle]

yh

[small hollow]

root 2 if you got this im going to head to bed

nice working with you Jonathan

[willow bear]

sure

[small hollow]

good luck on your test

[viscid thistle]

thank you

I'll do my best

but I aquired it with 4.8rt 0.84

[willow bear]

yeah, so 0.84^(1/4.8)

should have obtained 0.964

[viscid thistle]

yeah I did

was just a typo

[willow bear]

== 0.964^8.8

[granite stirrup]

0.72423231

[viscid thistle]

8.8^2

[willow bear]

72°C is the answer, then

[viscid thistle]

==0.964*8.8^2

[granite stirrup]

74.65216

[willow bear]

that's

uh

wat

what are you even doing there?

[viscid thistle]

wait maybe not

well ^8.8 works then

uh

the equation 3^x=4x+3 has two solutions, one positive and one negative

which?

[willow bear]

ooffff

this one is ugly

[viscid thistle]

well it is one of the last questions after all

[willow bear]

there's one between 3 and 4

but you can't get it algebraically

[viscid thistle]

well

idk how to solve it

oh

graphically

actually

whatever

If I haave P = k * U^2

U=220 Volt

P=11W

how do I know k

book says 11/220^2 but they said it was wrong

[clever inlet]

11 = k*220^2?

and then isolate k

[viscid thistle]

yes

[clever inlet]

by dividing both sides by 220^2

k = 11/220^2

[viscid thistle]

but that is wrong apperantly

I have no idea

wait nvm

they said the answe sheet was wrong

so it is 2.27 * -10^4

or something whatever how u said E-4

[clever inlet]

2.27 * 10^-4?

11/220^2 is exact

[viscid thistle]

since calculator gives me E-4

[clever inlet]

2.27 * 10^-4 is an approximated value

[viscid thistle]

because of the limit

yeah

I'll just write that

and if U=110^2 in the next question

then I can just do (11/220^2)*11W

to get P

I need to take a shower though

if someone can explain the one I had problem with before

if the braking distance for a car is 38.5m at 100km/h

then how do I calculate the distance for the speed ex. 50

anyone?

[pearl zodiac]

Can't remember this type of problems very well, but starting off with finding the decceleration should help

[viscid thistle]

idk how I would do that

[pearl zodiac]

Have you used derivatives before?

[viscid thistle]

don't think so

[tired cedar]

can someone help me with simple maths

wait wrong chat

[calm whale]

yes

ops

[fleet kayak]

uhh hey could somebody answer 39 and 42? just to start me up because im having hard time solving those tw

two*

oh man being grade 11 is hard

[clever inlet]

What can you rewrite cot as?

@fleet kayak

That would be a good start

[cold musk]

god I forgot my trig identities already

[clever inlet]

And then once you rewrite cot, you can simplify the left side

And get something that will probably be familiar to you

[willow bear]

the thing kanga is hinting at is actually the most sensible definition of cot in my opinion

[fleet kayak]

is that these

cot=cos/sin?

[willow bear]

yes

now, what does (cos(x)/sin(x)) * sin(x) * cos(x) simplify to?

[fleet kayak]

i have no idea but cos^2/sin^2?

wrong i guess

[willow bear]

...no.

[fleet kayak]

lol

[willow bear]

=tex \frac{\cos(x)}{\sin(x)} \sin(x)\cos(x) = ; ?

[fleet kayak]

am i close?

[willow bear]

...with what

no, $$\frac{\cos(x)}{\sin(x)} \sin(x)\cos(x) \neq \frac{\cos^2(x)}{\sin^2(x)}$$

[fleet kayak]

i have no idea, can you give me hint how to/

?

[willow bear]

how to do what?

[fleet kayak]

to simplify this (cos(x)/sin(x)) * sin(x) * cos(x). im sorry if you are losing patience. i have been absent in school the last few days

[willow bear]

surely you are able to manipulate things algebraically?!

=tex \frac{a}{b} \cdot b = a

[willow bear]

like, this should not be new to you

[fleet kayak]

yeah but what if it is the trigo functions?

[willow bear]

so what? they're still things you can manipulate algebraically

and sin(x) * cos(x)/sin(x) = cos(x)

[viscid thistle]

also they are evaluated so, not functions but just numbers when you say cos(x)

[lucid siren]

Can someone help me with 98

?

[willow bear]

what have you tried so far?

[lucid siren]

So I distributed and then added both of them together so I was left with 13cosx + 25sinx idk what to do after that. Also I feel like there's a shorter way to so it but I'm not sure.

[willow bear]

can you show your work?

because that's definitely not correct.

[willow bear]

why did (4cos(x))^2 become 4cos^2(x)? 👀

this despite the fact that you squared 4sin(x) correctly to get 16sin^2(x)

[lucid siren]

Did I just distribute incorrectly?

[willow bear]

you made a mistake in rewriting (4cos(x))^2 as 4cos^2(x)

would have been fine otherwise

[lucid siren]

Oh okay cool

Is there another way to do this though?

[willow bear]

not that i see anything in this case

simply expanding everything does the trick

[lucid siren]

Okay thank you

[viscid thistle]

hmm what does expelled includes in the description mean ?

[calm whale]

wat

@viscid thistle ??

[viscid thistle]

"Anything in the US precalc curriculum goes here. Expelled include: trigonometry, logarithmic and exponential functions, function sketching etc."

Why are those expelled include

@calm whale

[calm whale]

what the fuck are you asking

please make sense

english

[viscid thistle]

.....SHOULD there be only include, why is the word expelled there? 😦

[calm whale]

I literally do not give a shit 😄

[viscid thistle]

lol okay

oh and btw, for those of you taking common core pre-cal, do you start the year right on trig?

In texas we have to spend the whole 1st semester to redo things on stuffs like college algebra

[calm whale]

cool

[viscid thistle]

do u take common core precal?

[calm whale]

no I take mathematics

steroids

call them

IQ boosters

[viscid thistle]

lol what

[calm whale]

adderall

your ability to focus

on a task skyrockets

[viscid thistle]

lel what state are you in

[calm whale]

england :^)

what grade are you again?

[viscid thistle]

oh hello my almost semi-fellow friend, I went to a british school before I moved to the US, I'm an american high school freshamn, ie british year 10

[calm whale]

such thing does not exist lol

[viscid thistle]

what doesnt

[calm whale]

high school freshman D:

[viscid thistle]

it does

here in the land of the free

we call people freshman, sophomore, junior then senior

[calm whale]

https://lichess.org/0tEafYnc @viscid thistle

[viscid thistle]

Are you taking the gcse?

[calm whale]

i'm a kindergarten freshman

no I'm doing the ib

2nd year

[viscid thistle]

rdy?

[calm whale]

ye

[viscid thistle]

wait highschool freshmen do calculus?

[calm whale]

precalc

[viscid thistle]

precalculus*

@viscid thistle

[calm whale]

you touch on differentiation/integration/optimization and some other things

[viscid thistle]

???

integration in gr9

Fuck probably why im having a hard time learning integrals rn

yeh im one of the 3 kids in my whole school that does this

@viscid thistle What grade u in

You going into engineering?

yeh

Damn, good luck dude

hopefully a Cambridge one

Probably will have a huge advantage

[calm whale]

as in uk cambridge?

[viscid thistle]

Yeh

i still want to hold my values

and not being americanised

[calm whale]

lol harvard/mit ?

[viscid thistle]

MIT has calc course online on youtube

no like trinity college/king's colege in cambridge england

[calm whale]

interesting

[viscid thistle]

it's great

[calm whale]

you need 5 aps with 5's

lol

[viscid thistle]

im doing the ib mate

[calm whale]

aka you're screwed if youre applying from the us

[viscid thistle]

and some aps

[calm whale]

o

1st year?

how much predicted?

[viscid thistle]

hmm pre-ib

MYP not yet the DP

[calm whale]

o pre ib

thats retarded tbh

[loud wasp]

@calm whale

[calm whale]

its just like gsces

which are also retarded

what did you get on your gsces?

[viscid thistle]

im in america, it is a retarded version, i moved halfway through my igcse (international since not in the uk)

[calm whale]

ye ye its the same

[viscid thistle]

Why dont u join this
http://discord.gg/ibo

[calm whale]

mmm I'm on the /r/ibo

[viscid thistle]

yeh and they have a discord for it