precalculus

[viscid thistle]

I think

[astral mountain]

can anyone explain why its 4.?

I dont understand it

[viscid thistle]

Why what is 4

[astral mountain]

anwser 4. f(-2) = f(6)

[viscid thistle]

What is this exercice in German

I hate German

[astral mountain]

its dutch lol

[harsh condor]

f(x^2 + 4) = f(x^2 - 4)

I might be wrong, but would it be right to assume:
if, x^2 + 4, then x^2 - 4

So (-2)^2 + 4 = 8
And 6^2 - 4 = 32

Whoops nvm im wrong lol

[viscid thistle]

I don't understand the exercice 😂

[astral mountain]

neither do i lol

i cant wrap my head around it

[harsh condor]

een functie waarvoor geldt dat voor alle. Wat kan je besluiten over de functiewaarde

a function that applies to all. What can you decide on the job value

[past meadow]

oh of course

the job value

[astral mountain]

lol

[harsh condor]

a function f(x^2 + 4) = f(x^2 - 4) that applies to all x element of R. What can you decide on the job value f(-2)

Idk googie translate told me

[astral mountain]

a function for which all x are elements of R, what can u conclude about f(-2)

[harsh condor]

Ya see

[viscid thistle]

x^2 - 4 = - 2
x^2 = 2
x=sqrt(2) or -sqrt(2)

x^2 + 4 = 6
x^2 = 2
x = sqrt(2) or -sqrt(2)

[harsh condor]

I assumed this was like:
a^2 + 4 = b^2 - 4
What is the value of b, when a = -2

[viscid thistle]

Look at my post

[harsh condor]

Oh

Big lul

true dat

thats very true

[astral mountain]

but how is the anwser f(-2) = f(6) than lol

[harsh condor]

big brain time

So what the question meant in a wierd way was:
x^2 - 4 = -2
then what is
x^2 + 4 = ?

[viscid thistle]

Yes I think

[astral mountain]

oh i get it now

lol

[viscid thistle]

[astral mountain]

big brain

[harsh condor]

big brain

praise ye mighty big brain

[vagrant stirrup]

anyone know?

[willow bear]

this is calculus

not precalc

you're in the wrong channel

[vagrant stirrup]

oh

i thought it was the same

[willow bear]

and in any case you're given literally everything you need to do to apply the product rule

and nothing else

[vagrant stirrup]

ok

[willow bear]

did it not occur to you that if you have a function defined as a product then it may be a good idea to apply the product rule to it

[vagrant stirrup]

ok

[turbid crow]

How can i prove this rule, my book just throws it at me and i cant seem to understands the steps taken inbetween:

[willow bear]

it's an instance of the chain rule

[turbid crow]

Ah nice, the function sign made me blind ty

[viscid thistle]

Is anyone around?

[amber rain]

yes im anyone

[viscid thistle]

How do I get the maximum height? I feel like plugging in random numbers for t till I get the maximum height but that's not the right way to solve the problem.

[amber rain]

physics

noice

[viscid thistle]

Lol

[amber rain]

take the derivative of the equation with respect to t

wait

one moment haha

yeah that one was for part b

If you plugged in s(0) then you will get the height of the cannonball above the ground

cus the cannon is on top of the hill right

and then for part b, take the derivative of the equation with respect to t

set it equal to zero, and solve for t

then proceed to plug it back in s(t)

would you like for me to write it down instead

@viscid thistle

[viscid thistle]

I think I get it but yeah plugging in 0 will get me the height of the ball above the ground

I'll solve that

[viscid thistle]

Forgot to reply

I got 2 seconds for my answer

On B

[amber rain]

2 seconds yeah but u still gotta plug it in the function

What does s(2) equal

@viscid thistle

[viscid thistle]

Oh yeah

224 ft

S(2)= 224 ft.

[amber rain]

coolio

[viscid thistle]

I had my answer down as 2 seconds lol

[amber rain]

:c

[fleet yew]

Same

[tawny pilot]

Could someone please help me with limits

how am i supposed to do this

[patent beacon]

What's the limit of h, as x approaches 0?

[tawny pilot]

There isn't one?

because the point is empty

i think

[viscid thistle]

U guys know how to do this 🙃

[tawny pilot]

wait no the limit would still be -1 but the function would not exist

right?

[patent beacon]

Yeah you got it. Also important, the function goes to -1 from above on both sides.

So you can think of the limit as "-1, plus a little more"

[tawny pilot]

okay

[patent beacon]

Now, what's the limit of f, as x approaches "-1, plus a little more"?

[tawny pilot]

infinite?

wait

wai

-1

wait I dont understand the "plus a little more" analogy

[patent beacon]

I suppose I'm saying "from the right"

Specifically we're looking for the one-sided limit

You had it right, the limit is positive infinity

[tawny pilot]

ohh okay

ty ty

So if the two sides of the graph approach a different limit/value, then the value doesn't exist right?

like this

they dont approach the same y value

[viscid thistle]

Two sided limit

[tawny pilot]

okay so then would would be the limit for h(x)

okay i got it

[patent beacon]

@tawny pilot
In this case, each of f and h don't exist, but the function f - h actually does

Take them from the left and right, and you can reason it out

[tawny pilot]

yeah that makes sense

[amber robin]

someone help with #8 please?

so confused

and with this quarantine thing going on my teacher aint helping

[lone lynx]

I assume you are familiar with the unit circle?

[heavy gulch]

@amber robin

[amber robin]

not familiar sorry

well

I am but im not used to it

[lone lynx]

Do you know the basics of it? If not I suggest reviewing it and the answer may become more clear.

[amber robin]

yea I know a general idea

[lone lynx]

Okay so you know that one half of the circle is equal to Pi and full circle is equal to 2pi.

[amber robin]

yea

[lone lynx]

So let’s say you have 8pi/17 that means you have 8/17 of half the circle. You get that right?

[amber robin]

yea I get that

[lone lynx]

Okay so if you subtract 8pi/17 how much of the total circle remains

[amber robin]

2pi?

[lone lynx]

you want to subtract 8pi/17 from that

That will give you your answer

[fierce ridge]

have a math test, dont know if this is the right place to ask

but how do i derivate (2x+1)*e^x

[uncut mulch]

wdym by

have a math test,

[fierce ridge]

oh shit i figured it out

im having a math test

[unique hill]

right now?

[fierce ridge]

yes

[unique hill]

it's a bannable offense to ask for help during an exam, read #rules

[amber rain]

damn, got'em

[unkempt burrow]

Please

[unique hill]

eliminate one variable to get the other

have u tried it?

[unkempt burrow]

No. The square confused me

[unique hill]

well, try it :P

you can use the elimination method or substitution

ur choice

you should get a quadratic for y

[amber rain]

@unkempt burrow always pick the easiest first to eliminate

[unkempt burrow]

? I’m not sure

[amber rain]

nah fam lol

one moment

[unkempt burrow]

Thank you

[amber rain]

Since we're all quarantined now I'm getting into a habit of scanning all of my homework

My friends take pics but I rather show it in better quality

aight sorry for the wait

@unkempt burrow

proceed to factor

[unkempt burrow]

So that’s not the final answer right?

[unique hill]

you're solving two of the variables, so no

[unkempt burrow]

Can I change y^2 inyo 1y

[unique hill]

?

y^2 into 1y?

no

[unkempt burrow]

Ok nvm

[unique hill]

it's squared

[tardy ridge]

uSe QuAdArAtIc FoRmUlA

[unique hill]

you can factorise it normally :|

[unkempt burrow]

OH HAHA

[harsh cipher]

good afternoon

[unique hill]

hi mirrion

[harsh cipher]

covid checking in!

hello nighty

question

solve exact value for x

3(5^x) = 7^(3x+4)

log both sides and expand and simplify

[amber rain]

whats with the covid role btw lol

[tardy ridge]

Mirrion

[harsh cipher]

I get....log(3) - 4log(7) = 3xlog(7)-log(5x)

yea?

how do we cancel the x

[tardy ridge]

separate 5x

into log 5 + log x

don't forget the negative sign

[harsh cipher]

what about the 3

[tardy ridge]

factor the x's after

put all the x on one side

and all the non x on the other

$x(log5-3log7)=4log7-log3$

[obsidian monolith]

Fishraider:

[tardy ridge]

The values I have might be wrong but the idea is you do that

[harsh cipher]

oh so we have to factor the x out

[tardy ridge]

I rushed through this question

but that's how you would do it

[harsh cipher]

okay let me ask one qustion

[tardy ridge]

no you divide by log 5 - 3log7\

to isolate x

[daring yarrow]

fishraider math wizard

[harsh cipher]

how can you write 3(5^x) into log5 and logx

is that even allowed?

haha

[tardy ridge]

You did it wrong

that is log 3 + log 5^x

xlog5

[harsh cipher]

that's what i originally wrote up there

[tardy ridge]

I get....log(3) - 4log(7) = 3xlog(7)-log(5x)
@harsh cipher

log 5x ?

[harsh cipher]

and what you're saying I need to seperate log5x

[tardy ridge]

I didn't realize you messed up there, if it were that then yes, but it's xlog5

[harsh cipher]

okay let me try

[tardy ridge]

since $log (3(5^x)) = log 3 + log 5^x = log 3 + x log 5 $

[obsidian monolith]

Fishraider:

[unique hill]

mirrion which steps rn

[harsh cipher]

I didnt move likely terms and separate LHS properly. give me a moment please!

[unique hill]

take ur time

[harsh cipher]

okay I got

I figured it out. I forgot to factor the x from

3x(log7)- log(x5)

[unique hill]

so u got the answer right?

[harsh cipher]

yes I did

@tardy ridge thank you

thank you nighty too 😛

[unique hill]

i did nothing...

[tardy ridge]

no pr'l,r.bem

[fierce ridge]

does anybody know how i can find the "turningpoint" of this graph

when f''(x)=0

[unique hill]

which graph

the top one

?

[fierce ridge]

yea

everything is based on that graph

its just derivated

the bottom x values is the ones i get out of f''(x)=0

but it doesnt feel right

[unique hill]

i dont get what's going on in the pic below the question

but did u derive it twice correctly?

[fierce ridge]

i used a math program

so it should be right

but i dont know why it started using ln

[unique hill]

what can u learn from it?

some math programs stick to one way of solving it

have u tried doing it urself?

[fierce ridge]

mmmhm

well

i derivated it once

but then i get 3 factors

like

if u get it

[unique hill]

why is this in pre-calc channel lol

[fierce ridge]

english isnt my best side

wait im on the wrong channel?

[unique hill]

this is precalculus

it's about trig, logs and stuff

[fierce ridge]

ohjhhhhh

sry

wait what channel should i ask about this in

[unique hill]

i pinged u

[harsh cipher]

question

log_5((x-5) + log_5(x) = log_5(6)

is there an easier way to solve this problem without using quadratic formula?

[tardy ridge]

(x-5)x=6?

You don't need quadratic formula for this @harsh cipher

[gaunt bay]

if there isnt a session being held. can someone help me with this. a bit confused. also have 2 more question i need help with after this. @ me please

[lilac pier]

what's troubling you?

[gaunt bay]

how to make the left side equal to 2/sinx

[lilac pier]

you don't have to do it yourself, just cancel out the wrong options

[harsh cipher]

oh

[lilac pier]

you can then see how it was done in the right option

[unique hill]

@harsh cipher you can do log_5 (x^2-5x) cuz log laws :p

then get RHS cuz same base

[lilac pier]

@gaunt bay Just so you know, cotx = cosx/sinx. Options B and C are wrong because 2cosx/sinx just magically becomes 2/sinx

[harsh cipher]

yea

but the answer says 6

x=6

i got x(x-5)= 6

[unique hill]

yea it's 6

looks correct

[past meadow]

Its 6

[harsh cipher]

did I type it incorrectly

[unique hill]

did u get 6?

[harsh cipher]

no

[unique hill]

i think u did ur quadratic wrong

x(x-5)=6

[harsh cipher]

i thought quadratic was not necessary

[unique hill]

because it's factorisable

you can factorise it normally

[harsh cipher]

x^2-5x-6

[unique hill]

i meant factorising quadratic, not using quadratic formula

that=0

[harsh cipher]

x=3 and x= 2

[unique hill]

ok mirrion

[harsh cipher]

lolll

[unique hill]

ur answer comes from (x-3)(x-2)=0

try simplifying it

[gaunt bay]

can someone @ me when you guys are done so i can ask a few more question

[unique hill]

its meant to be (x-6)(x+1)=0

[harsh cipher]

x=6

[unique hill]

yea that's correct

[harsh cipher]

I'm so stupid

thank you

[unique hill]

np

[maiden furnace]

quick question using unit circle the tan90 and tan-90 is undifned correct?

[past meadow]

yup. dividing by zero

[willow bear]

yes

undefined*

and assuming you're doing this in degrees

[past meadow]

90 radians

[willow bear]

,w tan(90 rad)

[maiden furnace]

nope 90 degress

[obsidian monolith]

Display results online and refine query

Requested by Ann#0413

[willow bear]

ok yeah tan(90°) is undefined you're right about that

[maiden furnace]

but 90 radian comes with the answer

i see thanks

and just to be sure the cos of pi (unit cirlce once again) is -1 corect

[past meadow]

yes

[versed basalt]

Are monotonic function always differentiable?

<@&286206848099549185>

[steel venture]

monotonic?

[versed basalt]

yeah

[steel venture]

no

i don't believe so

ah wait nvm

im not so sure

[tiny verge]

well say the function looks like this

it's monotonic but not differentiable at that point where it turns

[fleet yew]

At that sharp point

[steel venture]

no they're not always, peacewise functions can be used to prove it

[fleet yew]

Slope of the tangent isnt the same from both sides

Which is kind of annoying sometimes

Ever tried to d|x|/dx

[versed basalt]

it's monotonic but not differentiable at that point where it turns
thanks good example

[tiny verge]

np

[versed basalt]

i googled and found Lebesgue theorem and it said it is almost differentiable and I didn't understand what "almost" means.

[tiny verge]

ah, fair

[viscid thistle]

what is a piecewise function?

is it like a limit?

[willow bear]

no

[viscid thistle]

ah i see

ez

[harsh cipher]

good morning Ann

I have a question, a word problem

An original investment of $4000 lost 5% per year compounded monthly. How much is the investment worth after 7 years?

is this a 2 step answer

?

[willow bear]

what's a "2 step answer"

[harsh cipher]

lol

ok it's not

what I meant was do I need one answer to get to the final answer

[willow bear]

what does that mean

[harsh cipher]

sorry it was dumb

never mind

[zinc spoke]

A pair of boots price sank with 50%, then it sank another 40% of those 50%. Lisa then bought the pair of boots and saved 49euro, how much did the boots cost before the discount?

Can someone please help me? Me and my friends keep arguing about the answer , I just want to know the correct one. 🙂

[uncut mulch]

did you attempt this problem yourself?

[zinc spoke]

Yes

I came up with 0.6x0,5=0,3 . 490/0,3=1633

Is that correct

I meant 49/0,3=163

[uncut mulch]

49 isn't how much she paid

its how much she saved

the boots were effectively discounted 70%

and you should've used:
0.7x = 49
x = 49/0.7

[unique basin]

How to solve this: You have a function y=tan x and you have to find equation of a tangent which abscissa is 45 deg?

[zinc spoke]

Aha I get it now, thanks

[eternal anchor]

Hi - im in precalc and im stuck on a second part of a problem. The problem is "Consider cos(3x)=((√3)/2) Find ALL solutions to this equation." so I did that out and got my two final solutions as x= (π/18) + ((2πn)/3) and x= (11π/18) + ((2πn)/3), I've checked and I am confident these are correct, but now it's asking me "What are the four smallest solutions to this equation? (Be sure to simplify.)" and I'm not really sure how to find the smallest ones or know they are the smallest! Any help or explaining is greatly appreciated

[steel venture]

yeah i'm confused too

are they asking for only positive answers?

[eternal anchor]

I would assume so lol

otherwise...

Yea what the heck

thats a bad question

cuz it can be infinetly low

[steel venture]

exactly

so i'd give the smallest possible solutoins

[eternal anchor]

positive?

is that what u meant im not sure i understand

[steel venture]

yes

my b

[eternal anchor]

so I know two would definetly be pi/18 and 11pi/18 correct

but then the others

n would be zero in that case....but then n can be infinetly small to go anything above that

so weird

[steel venture]

no

n has to be an integer

[eternal anchor]

ah ok

then theres just no way to awnser this i guess?

nvm

Well 0 is an integer is it not?

[steel venture]

yes it is

[eternal anchor]

so then would the four smallest just be plugging in 0 and 1 for n?

in both equations

ohhhhh ok I get ya I thought you were saying no earlier to pi/18 and 11pi/18 being two of the smallest...I now see you meant that towards my infinetly small remark

seems thats the awnser then

[elfin birch]

does anyone know how to find exact values using dum and difference formulas ?

[summer obsidian]

You just find combinations of known angles that add or subtract to result in the angle you want to find

[gaunt bay]

https://gyazo.com/bd92f6eaf59f648377bea5b69bc7bee8 can someone help with this. there are a couple of pages

[bronze juniper]

any1 know how to do this problem?

[willow bear]

perhaps

what is giving you trouble here

[bronze juniper]

the whole thing in general. we didnt learn it yet bc of online class

i know sin cos and tan tho

[willow bear]

$\sin^2(x) + \cos^2(x) = 1$ does this ring any bells

[obsidian monolith]

Ann:

[bronze juniper]

not really

[willow bear]

unit circle??

[stable barn]

hey im in trig but we're doing stuff pretty similar to this

maybe we bounce ideas off each other and see if that helps?

[bronze juniper]

i got the first question

i can show u the second tho

[stable barn]

ight go for it

essentially the same question

brother

[bronze juniper]

yeah

[stable barn]

here let me show you what im workin on

well if you look in #geometry-and-trigonometry and scroll up a little bit thats what im on right now

[bronze juniper]

alright ill check it out in a bit thanks tho

[stable barn]

yeah man, i've got to find the sin of theta

starting with a tan theta value, and sec > 0

[daring yarrow]

@stable barn tan²(A) + 1 = sec²(A)

😉

[stable barn]

😉

i think i figured it out

can i post my work and see if you can read/understand it and if i got the right answer

it says i did

[daring yarrow]

then you did

[daring yarrow]

oh u had to find sin

lemme see

whats that in your last line?

[stable barn]

sorry

[daring yarrow]

-sqrt(77)/11?

if so thats correct

[stable barn]

Yeeeee

Sick

[viscid thistle]

Can someone help me in #calculus

Not exactly sure how to approach part c... I've never seen a question like this. (first image is the graph for the question)

[gaunt bay]

i ben waiting 2 hours for someone to msg me and no one even helped xD rip. when people are done either pm me or @ me. https://gyazo.com/bd92f6eaf59f648377bea5b69bc7bee8

[viscid thistle]

@gaunt bay I had an unanswered question above. Would you mind either waiting or asking it in another related channel? Thanks.

[gaunt bay]

i can wait but i posted this 2 hours ago and got not help xD

[bronze juniper]

anyone know of a calculator for solving sin^2(θ) + cos^2(θ) = 1 ?

[daring yarrow]

?

wdym?

[bronze juniper]

these types of problems that use that formula

[dusk elm]

make a triangle on the unit circle and it will be very apparent what sin of theta will be

[bronze juniper]

@dusk elm can you give an example? where do i know where to draw the circle?

traingle*

[dusk elm]

@bronze juniper Sure, the triangle's hypotenuse will always be 1 and in your case 3/8 is the length of one of the legs of the triangle. You can use the Pythagorean theorem to solve for the last side. Should look something like this

[bronze juniper]

oh so x would be 3 and y would be 8, correct?

oh so 3/8 is x

[dusk elm]

Correct as cosine just measure the length and sine measures the height

[bronze juniper]

ok thank you

[gaunt bay]

@viscid thistle idk why our call ended. says we are not in the same server

[maiden furnace]

using referance angles and getting exact values sin 240 will have a ref angle of 60 so the answer for sin240 is - root3/2 correct?

[stuck lark]

yes

[fleet yew]

Partial sum of even natural numbers formula?

$\sum_{n=1}^{m} 2n$

[obsidian monolith]

AMD:

[rigid beacon]

well you can factor out a 2 from the sum

and then there's a formula for

$\sum_{n=1}^{m} n$

[obsidian monolith]

Spamakin🎷:

[maiden furnace]

for finding amp period and phase shift of y=-1.5sinx/2 the amp is 1.5 period 4pi and phase shift none is this correct?

[fleet yew]

@rigid beacon thanks

One more question

$\sum_{n=1}^{m} (2n-1)$

[obsidian monolith]

AMD:

[fleet yew]

Is that the same as

$\sum_{n=1}^{m} (2n) - 1$

[obsidian monolith]

AMD:

[rigid beacon]

no

[fleet yew]

This is the sum of odd naturals

1+3+5 etc

[rigid beacon]

write out the first couple terms of each and then you'll see they're different

[fleet yew]

Yeah you right

The sequence is the same but the sum isnt

[rigid beacon]

no the sequence is not the same

if I wrote out 3 terms for each

1st series: 1 + 3 + 5
2nd series: 2 + 4 + 6 and then subtract 1 from the end

the 2nd thing isn't just a series

it's a series and then it's being subtracted by a number

I shouldn't have said write out the first couple terms my bad

I should have said to do a partial sum

[fleet yew]

How do i find that formula then

For the first one

1+3+5

And so on

<@&286206848099549185>

[serene heath]

did u figure it out @fleet yew

[fleet yew]

no

@serene heath

[serene heath]

$\sum 2n - \sum 1$

[obsidian monolith]

the one n only:

[fleet yew]

is that the same as the sum of odd naturals

[serene heath]

yes

u already know the first term

it's just m(m+1)

[fleet yew]

m(m+1) - m?

[serene heath]

yup

simplify it

[fleet yew]

m^2 -2m

[serene heath]

no

[fleet yew]

lol mb

m^2

[serene heath]

ye

[fleet yew]

woah

[serene heath]

crazy right

[fleet yew]

that's actually pretty cool

[serene heath]

u can check it works too

1+3=4=2^2

1+3+5=9=3^2

etc

[fleet yew]

damn lol

i'm gonna try to find a geometric explanation for this

it's probably something really crazy

omg that's beautiful

look at that

[karmic wave]

beauty of maths

[maiden furnace]

https://gyazo.com/6e9fffcd90e6f9d854a2698db8561723 need help solving this

[fleet yew]

Rewrite cot

As cos/sin

[maiden furnace]

wait what

[fleet yew]

@maiden furnace cot = cos/sin

Lmao

[maiden furnace]

so re writing would be -1/7/1-(1-7)^2?

[fleet yew]

?

(-1/7)/(sin(arccos(-1/7))

[maiden furnace]

yup was never shown this

[fleet yew]

Shown what?

[maiden furnace]

that u can rewrite cot as cos/sin

[fleet yew]

Wtf

That is literally the definition

What else could cotangent possibly mean

[maiden furnace]

teacher showed us cot as adj over opp

[fleet yew]

What is adj

[maiden furnace]

adject

[fleet yew]

On the unit circle

Adjacent

[maiden furnace]

ahh i see

[fleet yew]

Adj = cos

Opp = sin

On the unit circle because hyp=1

[maiden furnace]

ahh i see

hwo do i continue after the rewriting part?

[fleet yew]

$\cot(\cos^{-1}(-1/7)) = \frac{\cos(\cos^{-1}(-1/7))}{\sin(\cos^{-1}(-1/7))}$

[obsidian monolith]

AMD:

[tribal girder]

f(x)=x^2+1 determine the value of f(f(3))

[fleet yew]

K

What have u tried

[tribal girder]

sub x=3 then multiplying

i dont really know and understand these type of questions

[fleet yew]

f(3) means the value of the function when x = 3

[tribal girder]

so that would go in the inner bracket right?

[fleet yew]

Yeah

What is f(3)

[tribal girder]

3x^2-3

[fleet yew]

No

[tribal girder]

oh my bad

[fleet yew]

f(3) means the value of the function when x = 3

[tribal girder]

i need to sub x=3 not multiply by 3

=8

[fleet yew]

?

You said the function was x^2+1

[tribal girder]

sorry its x^2-1

[fleet yew]

Ok

So f(3)=8

[tribal girder]

yes

[fleet yew]

so f(f(3)) = f(8)

[tribal girder]

so sub x=8 now

[fleet yew]

Yeah

[tribal girder]

63 thank you

[tribal girder]

If you are given the graphs of two functions, f(x) and g(x), explain how can you determine the location of a
point that would appear as a zero on the graphs of
𝑦 = 𝑓(𝑥) + 𝑔(𝑥)

[daring yarrow]

just add them up?

if f(x) = 2x+1 and g(x) = x+2
then y = 3x+3 and the zero is x=-1

[uncut mulch]

determine when f(x) = -g(x)

[fleet yew]

@daring yarrow don't spoil it

[pale pond]

Please help me with the trig identity: (tanx + 1)^2

ive already tried foiling it and ended up getting tan^2x + 2tanx + 1, but i dont know if this is totally simplified

[lilac pier]

@pale pond What trig identity? Can u post the question

[pale pond]

sorry how do i do that?

screenshot?

[lilac pier]

Okay and what are you asked to do with this

[pale pond]

simplify

[lilac pier]

yes your answer is correct

[pale pond]

thats it?

[lilac pier]

If you've learned the identity tan^2 (x) + 1 = sec^2 (x), you can use that

[pale pond]

i seee

thank you

i have some more questions

im also supposed to simplify this, but i have no clue how to start

[lilac pier]

you should know cot = cos / sin

and cosec = 1 / sin

now you can do this

[pale pond]

This is what i ended up getting

Is it correct

[lilac pier]

Yes

[pale pond]

thank you

i also have to simplify this as well

i also have no idea where to start

[lilac pier]

secx = 1 / cosx

[pale pond]

Ive ended up here and i dont know where to go

[lilac pier]

you can see that the denominator of the first term is of the form (a-b) and the denominator of the second term is of the form (a+b)

You can multiply/divide the first term by (1-cosx) and the second term by (1+cosx)

this way both denominators become (a+b)(a-b) or a^2 - b^2

which you can handle easily

[pale pond]

sorry i dont understand

so my first denominator is 1+ cos

[lilac pier]

yeah I thought so, I think I made it too hard

anyways, you can think of it as cross multiplying

[alpine narwhal]

he’s saying multiply both fractions by a common denominator

[pale pond]

ohhh

so i multiply both fractions with (1 + cos)(1- cos)?

[alpine narwhal]

close

[pale pond]

hmm

[alpine narwhal]

you dont wanna change the value of the fraction

[pale pond]

so for my first "unit"

do i multiply it with

nvm

still confused

[alpine narwhal]

you got the right denominator

but by multiplying the fraction by (1+cosx)(1-cosx) you’ve changed the value of the expression

[pale pond]

what should i do then

[alpine narwhal]

well multiplying things by 1 keeps the entire expression equal

how do you write 1 using (1+cosx)(1-cosx)?

[pale pond]

hmm

(1+cosx)(1-cosx) over (1+cosx)(1-cosx)?

[alpine narwhal]

correct

[pale pond]

Oh wait im on to something

[alpine narwhal]

yes

[pale pond]

i ended up getting this

i think its correct

[alpine narwhal]

i believe so lemme check

sorry i have to do everything in my head lol

[pale pond]

take ur time

[alpine narwhal]

yeah it’s correct

[pale pond]

can i further simplify it?

[alpine narwhal]

you can

you see the difference of squares identity

[pale pond]

uhh

is that the denominator

ur talking about

[alpine narwhal]

yeah

[fleet yew]

A difference of squares is really cool

[alpine narwhal]

agreed

[pale pond]

If i multiply denominator out, then phythagorean it, it turns to this

Is it correct

[alpine narwhal]

you simplified and got (-2cos^2(x))/sin^2(x), right?

[pale pond]

yes

[alpine narwhal]

i don’t know where you got the extra sin^2(x) from

[pale pond]

well since its the denominator

idk if memory serves me right but i thought u could

like

[fleet yew]

Now you can factor out the -2

[pale pond]

"clone it"

[alpine narwhal]

you dont needa do that lol

[pale pond]

ok

OH

so its just

-2 cotx

[fleet yew]

Yes

[alpine narwhal]

you only do that for dealing with addition and subtraction

yes

[fleet yew]

Cot^2

[pale pond]

thank you

[fleet yew]

Cot^2 not cot

[alpine narwhal]

yeah np

[pale pond]

i have some more questions if ur willing to stay

lol

just 2

[alpine narwhal]

go ahead

[pale pond]

simplify, dont know where to start

[fleet yew]

Sin(x) = sin(x) / 1

[alpine narwhal]

there’s a fraction in your expression

[fleet yew]

Common denominator

[alpine narwhal]

amd gave you a hint

and the next step

[fleet yew]

Do u want the answer

[pale pond]

gimme a min

if im rly stumped then yeah

[fleet yew]

This is ez youll get it

[alpine narwhal]

common denom

[pale pond]

1 over sinx

[alpine narwhal]

what do you do to a fraction to give it a denom without changing its value?

[pale pond]

csc x?

[alpine narwhal]

you dont wanna convert sinx and cosx terms to their reciprocals

[pale pond]

hmm

[fleet yew]

Yeah thats right

[pale pond]

niiiice

[fleet yew]

Nice job dude.

[alpine narwhal]

yeah

[pale pond]

thank you

[alpine narwhal]

gg

[pale pond]

i have one last one for the night

i think

floored.

[fleet yew]

Ok

This is ez

Break it into chunks

Start with the first chunk

csc^2*sec^2

[unique hill]

thought someone called me for a sec

[fleet yew]

No go away

[pale pond]

😢

[fleet yew]

Talking to nighty

Not u caprisun

[pale pond]

ik

: )

[alpine narwhal]

convert everything into terms of sinx and cosx

if problems looks like that it’s better to convert everything to sinx and cosx

[pale pond]

ok ill give that a shot

[alpine narwhal]

chances are terms will simplify

[tribal girder]

can any 1 help me with this?

[alpine narwhal]

#❓how-to-get-help

[pale pond]

wack

am confused

[alpine narwhal]

yeah that’s not working

back to square 1

you see the last two terms in the back?

[pale pond]

sin sq over cos sq?

or sec sq + tan sq

[alpine narwhal]

the -sec^2(x)+tan^2(x)

you have your trig identities sheet?

[pale pond]

yes

OH

[alpine narwhal]

yeahh

[pale pond]

wait

[alpine narwhal]

try simplifying that first

[pale pond]

is that equal to -1?

[alpine narwhal]

correct

now leave that to the side

let’s go back to the mess on the left

[pale pond]

i think

ive reached

a point

is that my final answer or can that be further simplified?

[alpine narwhal]

can be simplified

think back to question two

common denominator

[pale pond]

cot sq?

final answer

[alpine narwhal]

yeah

[pale pond]

lets go

[alpine narwhal]

correct

gg

[pale pond]

thank you so much

[fleet yew]

Nice job dude

[alpine narwhal]

no problem man

you’re a natural

[fleet yew]

I think ur ready for some more advanced stuff now

[alpine narwhal]

yeah

[fleet yew]

Do you know what a derivative is

[alpine narwhal]

LOL

[pale pond]

ive heard of it

[alpine narwhal]

I WAS THINKING THE SAME THING

[pale pond]

i have

[fleet yew]

You taken physics yet?

[pale pond]

im taking physics A rn

[fleet yew]

Like even basic physics

[pale pond]

angular motion

[fleet yew]

ok

[alpine narwhal]

you learn more useful math in physics than in math class

[fleet yew]

so you know how velocity is the rate of change of position

[pale pond]

yeah

[fleet yew]

and acceleration is the rate of change of velocity

[alpine narwhal]

that’s derivatives

[pale pond]

yeah

wait what

[fleet yew]

in math speak we say that velocity is the derivative of position with respect to time

[alpine narwhal]

the velocity is the derivative of the change of positions

and acceleration is the derivative of velocity

with respect to time of course

[pale pond]

_>

[fleet yew]

dude ur right physics class actually taught me calculus better than math class did

[alpine narwhal]

lmaooo

[pale pond]

?>_>?

[fleet yew]

because it's so intuitive

[alpine narwhal]

yeah

[fleet yew]

have you ever tried taking the area under a function in physics @pale pond

[pale pond]

uhhh

what

no

area under a function

like

[fleet yew]

like how the area under the velocity graph is the change in distance

[pale pond]

yeah

ive done that

[fleet yew]

that's called an "integral"

[alpine narwhal]

you know what an antiderivative is?

another word for an integral

[fleet yew]

ehh technically antiderivative lacks the C

[pale pond]

??>_>??

[alpine narwhal]

correct

[pale pond]

it is

[alpine narwhal]

i forgot lol

[pale pond]

too late for this kind of math 4 me

its almost tomorrow

monakS

[alpine narwhal]

it’s 6:24PM

[pale pond]

what

[alpine narwhal]

what u talking about

[pale pond]

r u in hawaii

[alpine narwhal]

how do you know

[pale pond]

time zone babey!

[alpine narwhal]

where r u rn

[pale pond]

missouri

[alpine narwhal]

oh

11:24?

[pale pond]

yeah

i have to submit this hw in 36 min

[alpine narwhal]

go submit it

[pale pond]

yessir

[alpine narwhal]

what r u waiting for

lmao

jk jk no rush

but lowkey go submit it

[night spade]

How would I solve

te^(t^2) = 25

without a graphics calculator?

for t

[patent beacon]

No algebraic solution. @night spade

[alpine narwhal]

what tf

sorry kaynex that was a mistake

[patent beacon]

Wat lol

[night spade]

what method would a calculator use to find t?

cos it gave me an answer

would it just sub in a ton of values until it got the answer?

[patent beacon]

There's analytic ways to solve any equation. But not algebraic ways

[willow bear]

probably some numerical root finding algo

[patent beacon]

Newton-Raphson is worth looking at

[willow bear]

yeah maybe that

[night spade]

I'll check it out, thanks

[granite pine]

given a matrix M1, M2 and M3

multiplying them by order M1M2M3

does it always need to be multiplied from right to left

even if there are parentheses such as M1(M2M3) ?

[willow bear]

matrix multiplication is associative

[patent beacon]

M1(M2M3) means to multiply M2 and M3, then multiply M1 on the left

[willow bear]

you can do (M1M2)M3 instead. it'll be the same result

[granite pine]

ah so it doesnt matter how theyre multiplied

only the order?

[willow bear]

what you CAN'T do is switch them around bc matrix multiplication is not commutative

[patent beacon]

In real numbers, xyz = xzy
We say real multiplication is commutative.

In matricies, ABC ≠ ACB
We say that matrix multiplication is not commutative.

[granite pine]

icic

[patent beacon]

But you can do A(BC) = (AB)C
We just write both of these cases as ABC

We say that matrix multiplication is associative

[granite pine]

ah alright

also for determinants in matrices

is it the same as determinants in quadratics?

or do they just happen to share the same name

[willow bear]

uh

determinants in quadratics?

[granite pine]

b^2-4ac ?

[willow bear]

b^2 - 4ac is the DISCRIMINANT

[granite pine]

OH LMAO

sorry my head is fucky atm

[thorny bluff]

Anyone can spot the error here?

[uncut mulch]

,rotate

[thorny bluff]

Nvm I found the ans

[analog relic]

Yo

I typed it at the geometry trigo channel

[harsh cipher]

hi~

I have a question I asked yesterday

it's intro to exponential functions

[willow bear]

care to repost it then

[harsh cipher]

An original investment of $4000 lost 5% year compounded monthly. How much is the investment worth after 7 years?

Hello Ann

the formula for compound interest other than annual is A= P(1+(r/n))^nt

A= final amount P= initial amount r= rate n= number of period the rate is compounded in a year t = time

[analog relic]

$4000(1-\frac{5}{1200})^{7×12}=?$

Is it like this?

[harsh cipher]

yes...kind of

but incorrect

[analog relic]

Hmm

[harsh cipher]

rate is 5%

[analog relic]

Oh compounded monthly

[harsh cipher]

period is monthly

[obsidian monolith]

Lσνιηg✧Sσνєяєιgη:

[harsh cipher]

uhhh no!

[analog relic]

Ok

Oh ok ok

[harsh cipher]

what I had was 4000(1-(0.05/12))^12x7

[analog relic]

Sorry continue

[harsh cipher]

answer did not match the answer key

😦

[analog relic]

I see

[harsh cipher]

so I'm doing something incorrectly

[analog relic]

"lost 5% year compounded monthly"

What does 5% year mean?

5% per year?

[harsh cipher]

yes

did I not write the word per?

[analog relic]

Ya

[harsh cipher]

ok yes

lost 5% per year

[analog relic]

Ohh i see ok

$(1-\frac{r}{1200})^{12}=\frac{5}{100}$ right?

[obsidian monolith]

Lσνιηg✧Sσνєяєιgη:

[harsh cipher]

the answer?

[analog relic]

No no, we have to find the rate first

Then find the answer when year 7 comes

[harsh cipher]

I don't get why you're writing the 1200 in the denominator and then 5/100 on the RHS

[analog relic]

Because it's $\frac{r}{100}×\frac{1}{12}$

[obsidian monolith]

Lσνιηg✧Sσνєяєιgη:

[analog relic]

Im putting in fractions not percentages

[harsh cipher]

okay

[fleet yew]

Sorry for spoilinh

[analog relic]

Spoiling what?

[fleet yew]

I said the answer

[analog relic]

Ahh i see

[harsh cipher]

I didn't understand it

[analog relic]

It's ok man

[harsh cipher]

okay

how do we find the rate first

[fleet yew]

It is given

5%

[analog relic]

But that's per year

But it's compounded monthly though

[fleet yew]

Yeah the formula takes that into account

[analog relic]

Ohhhh i see

Ahh

[harsh cipher]

so like I said its

4000(1-(0.05/12))^12x7@harsh cipher

[fleet yew]

A=P(1+r/n)^nt

A = 4000(1-0.05/12)^(12*7)

[harsh cipher]

answer does not match when I sub in the values given

[fleet yew]

There you go

What is the answer

[harsh cipher]

$53.81

did you get that?

[fleet yew]

,w 4000(1-0.05/12)^(12*7)

Huh

[harsh cipher]

answer key is incorrect?

[analog relic]

I got confused too

[harsh cipher]

or we're crazy

[obsidian monolith]

Display results online and refine query

Requested by AMD#4434

[harsh cipher]

answer key must be incorrect

[fleet yew]

Yeah lol

[harsh cipher]

there's no freaken way the answer is 53.81

[fleet yew]

No way itd be that low

[analog relic]

$200=4000(1-\frac{r}{1200})^{12}$ right?

[obsidian monolith]

Lσνιηg✧Sσνєяєιgη:

[analog relic]

I also dk

[fleet yew]

?

Not the right formula

[harsh cipher]

i will msg the teacher right now

[analog relic]

Im so confused

Wait i try on my own

And get back to you

[harsh cipher]

k

[fleet yew]

Answer key is wrong

[harsh cipher]

yea I think so too

it mega frustrates me when I see stuff like this

[fleet yew]

@harsh cipher get a better teacher

[harsh cipher]

hahahaha

[fleet yew]

One who doesn't drink while writing the answer key

[harsh cipher]

true I heard this type of mistakes will be with almost every course

LMAO

[rich light]

Hi, could someone point me to where I went wrong?

https://media.discordapp.net/attachments/442001284011393039/696037318187810886/image0.png?width=1151&height=677

[willow bear]

0 = x^2 - x-1 - x-1 - 1

what the fuck is this

[rich light]

Tbh idk

Just figured you should bring it to one side?

[willow bear]

no i mean how did $x^2 - 1 - (x-1)^2$ turn into whatever the fuck you got that from

[rich light]

🤷‍♀️

[obsidian monolith]

Ann:

[rich light]

My friend said I was supposed to multiply the x-1s together right?

[willow bear]

well it's (x-1)^2 what else did you think that was if not (x-1)(x-1)

[rich light]

Look dude, math is obviously not my forte

If you don't have anything constructive to offer then don't comment at all pls kk thanks