why have you posted a chemistry question in a math server and that also in a channel that says calculus lmao
#precalculus
lunar viper
is the map of a vector b which underwent a transformation by an nxn matrix equal to the vector v given by the vector b multiplied by the matrix?
also i understand what these means in terms of functions but what does it mean with matrices
lunar viper
why have you posted a chemistry question in a math server and that also in a cha...
😂
some people man
lunar viper
is the map of a vector b which underwent a transformation by an nxn matrix equal...
<@&286206848099549185>
paper oriole
Someone explain to me what the hell the prime notation (') symbolises please
I am braindead
oblique sapphire
Depends on the context
Usually when u see f'(x) it means the derivative of f(x)
Usually y' is also a derivative of y
rotund crystal
Why does f(x) have negative zeroes? Isn't its leading coefficient x^4, an even number meaning it should have only positive zeroes?
summer ruin
Isn't its leading coefficient x^4, an even number meaning it should have only positive zeroes
not sure why you would think that would ever be true
rotund crystal
> Isn't its leading coefficient x^4, an even number meaning it should have only ...
I mean x^4 goes like this
summer ruin
x^4 - 1 has negative zero
hushed sphinx
You may be interested in (or misremembering) https://en.wikipedia.org/wiki/Descartes'_rule_of_signs
drifting root
hushed sphinx
That doesn't seem to belong in precalculus.
olive whale
j'
remote mesa
explain slope intercept
pine geyser
explain slope intercept
do you know the way of graphing a slope?
remote mesa
do you know the way of graphing a slope?
Y = mx+b? Can't remember, our teacher isn't using books
pine geyser
Y = mx+b? Can't remember, our teacher isn't using books
yes mx + b
but that khan academy video would help you alot
<@&268886789983436800>
pine geyser
Y = mx+b? Can't remember, our teacher isn't using books
if you want i can explain it to you, there is no problem
remote mesa
if you want i can explain it to you, there is no problem
Sure I don't have a problem on hand atm but I don't mind
After I find the y intercept the rest is like thin air to me, also our instructor switches the numbers around without showing their work so it's irritating
pine geyser
alright
pine geyser
After I find the y intercept the rest is like thin air to me, also our instructo...
when two slopes intercept, their x and y is equal
for example, im asking you to find the intercepts of x+2=y and -x+4=y
remote mesa
when two slopes intercept, their x and y is equal
x+2=y (2,0) (0,2) and -x+4=y (4,0) (0,4)
arctic dragon
Guys I need help with one question
I have it partially completed
it's very likely that the last part of the question is wrong
arctic dragon
I need help with this.
what are you supposed to do
end behavior? forgot what that was
but ur doing logarithms right?
turbid creek
but ur doing logarithms right?
Idk what that is.
hushed sphinx
will pay
If you ask an actual question, there's a chance that someone will answer it for free!
turbid creek
I need help with this.
Does noone here know how to do this?
arctic dragon
quadratic formula
turbid creek
That from a test?
arctic dragon
turbid creek
y= b^2+-squrt -b+4ac over 2a.
vestal lake
That from a test?
no
turbid creek
100^2 +- squrt -100+4(4.9)(318) over 2(4.9) =y
vestal lake
ok i think i know it
thank u my king
arctic dragon
A is 23 seconds. B:828.204 peak
turbid creek
don't know if thats what you are looking for.
arctic dragon
that's what I got
use the -b/2a equation, whatever you get from that plug it in the equation and that gives you the answer for num 3
q.3
arctic dragon
no one answered my question 
arctic dragon
is it exponential stuff?
turbid creek
no one answered my question <:sad:532803514892812288>
I don't know that.
arctic dragon
looks like it
turbid creek
is it exponential stuff?
adding functions and determining the end Behavior's.
arctic dragon
do you have any previous work
that is the same as that question
so we can kinda guide ourselves
lol
turbid creek
not really.
arctic dragon
so is this the first time you are seeing this?
damn like I need some material else I won't be able to help u
turbid creek
Yeah.
turbid creek
Like I have tryed to look stuff up so I could figure it out on my own and can't find anything.
arctic dragon
have you asked chatgpt
vestal lake
u know how to do this one
arctic dragon
yes
arctic dragon
help me with this one my king
i think it's x^{2}-5x+2
check on desmos
oh you changed pics
lol
vestal lake
my bad
arctic dragon
my bad
lowkey forgot but I just know that y is 1 and that it opens down
vertex is -3,1
I can't remember correctly, sorry
arctic dragon
👍
somber onyx
arctic dragon
long division
synthethic there might work but use long division
lmk what you get
arctic dragon
I still don't get this:
arctic dragon
ok I think i get it now
alpine flicker
I would like to hook you guys up with some free courses, Check 1T 0u7!!:
https://alison.com/course/clep-pre-calculus-trigonometry?utm_source=alison_user&utm_medium=affiliates&utm_campaign=33806002
worthy bridge
anybody know the inverse function formula?
im trying to solve $x=y^2+y$ and get y alone
obsidian monolithBOT
x927373
summer ruin
this is quadratic equation in y
solar olive
there will be two inverrses though
storm gust
Can I have a rectangle where the domain of the length of one side is [0, p/2] where P is the perimeter?
In this case the rect will have two sides and both of them will collapse to be on the line
Is this valid? This is mentioned in the solution to one of the questions in the book I am reading
pine geyser
x+2=y (2,0) (0,2) and -x+4=y (4,0) (0,4)
What is the intercept point? I mean (x, y) [they intercept at one point]
Just tell me what are the answers for x and y. Let's not talk about intercepts for now
x+2=y
-x+4=y
arctic dragon
anybody know the inverse function formula?
Don’t you just have to switch Y with X?
I think that’s how it goes and then just solve for x
grim oyster
I tried by taking (dz/dy)^2 common from rha, but idk
arctic dragon
is that derivates
fleet crater
how to draw the graph of x^6(1-x)^7
pine geyser
im trying to solve $x=y^2+y$ and get y alone
if you remember, we could find "x" in a quadratic equation and we say x=(-b +or- sqrt(b^2 -4ac))/2
basically you only have to do the equation for y and find out y= your answer
but im not quite sure if that function can be inversed, because there are two "y"s for one x.
but if you want to get the y alone, you just have to put it in the quadratic equation and solve it
prisma oriole
red knot
People here seem to type whatever random things to these channels
Partial derivatives? Seems pre-calculus to me!
haughty tapir
Yo
this is the prompt for my assignment "Sketch the graph of each function by transforming the graph of an appropriate function of the form
y = xn
from the graphs below."
Just wanted to know if there was a quick vid that explained how it all worked
ashen bolt
i think it might be -1, 1, 2
im not sure if 4 would be one of the actual zeros since you dont see it hit the x axis on the graph
normal coral
im not sure if 4 would be one of the actual zeros since you dont see it hit the ...
^^
viscid thistle
its still wrong 😢
there can not be an odd number of rational zeros
leading thing is four
so there has to be four zeros
and imaginary zeros come in pairs
maybe they wnat you to put -1 twice
ashen bolt
ohh yeah, theres a double root at -1 which is why it turns (triple would be inflection , and 1 root would just pass, like at 1 and 2) lol sorry i forgot
fleet crater
how to draw the graph of x^6(1-x)^7
Help
ashen bolt
idk why i dont understand it but that was the answer
it's because there's a double root at -1, which visually just means theres a turning point there
haughty tapir
oooo nice thank you
fast kiln
I’m stuck on part b here, I got the right answer for a by finding each volume individually and finding the difference but im not getting the right answer for b
viscid thistle
is anyone there ?
delicate bolt
Who study math here
no one
warm oyster
any help with this please🙏
digital mirage
how is this possible
log can nver be equal to 0 as per its range and here they have equlity with 0
warm oyster
@digital mirage output of log function can be 0
digital mirage
ohhhh
right
tahts is exponential lmaooo
@warm oyster but still cos(sinx) must not hold equlity with 1
summer ruin
there's no such point where cos(sin(x)) > 1
digital mirage
yes but im saying here as it is written as >= 1 is not possible by log properties
digital mirage
cos(sin(x)) > a^y is what property say
digital mirage
ya but what about this property ?
summer ruin
what property
digital mirage
how these 2 can be true at same time ?
digital mirage
but my Q is stasfying those suitable values
summer ruin
one is true for a > 1, the other is for a between 0 and 1
summer ruin
but my Q is stasfying those suitable values
it only satisfies one of them
3 > 1, but not 0 < 3 < 1
paper cedar
can logarithmic spirals pass theta=2pi? my calculator stops there
flint thicket
can someone help explain what this means 🥲
summer ruin
solve the equation sin(x) = -sqrt(3)/2
primal hill
solve the equation sin(x) = -sqrt(3)/2
are you good with functions and stuff
like I need help like 12 hours from now if your active because I left my HW at school and only have like 30 mins to finish it
summer ruin
I won't be here by that time
primal hill
hm ok
flint thicket
solve the equation sin(x) = -sqrt(3)/2
its asking for specific x values tho
summer ruin
its asking for specific x values tho
can you solve the equation sin(x) = -sqrt(3)/2 though
primal hill
there can not be an odd number of rational zeros
hbu?
flint thicket
can you solve the equation sin(x) = -sqrt(3)/2 though
i got like half the answer right but its asking for 4 values idk
thats where im confused-
summer ruin
well I need to know what you're doing
flint thicket
well I need to know what you're doing
nvm nvmmm i got ittttttttttt
i apprecate the help anyways :)
viscid thistle
nvm nvmmm i got ittttttttttt
For future reference just graph that stuff
Or memorize the key points and know how to apply that into a given equation (in this case it would be pretty simple)
It’s generally easy when dealing with sin/cos
shell nova
ln(a) + ln(b) = ln(ab)
digital mirage
here sin(1/x) can give values from -1 to 1 . now if it gave the value 0 then it will lead to 0/infinty and further leading to 0/0 .... then how to solve it ?
obsidian monolithBOT
saddayyy_
solar olive
here sin(1/x) can give values from -1 to 1 . now if it gave the value 0 then it ...
u = 1/x
x->inf, u->0
lim_{u->0} u sin u
= 0?
lilac sand
do u guys think i could like self study over thanksgiving break
to be ahead / used to precalc or will it be like 2 hard to do
fluid jewel
Anyone know any good videos on logarithmics, its something I just cannot fully wrap my head around no matter how hard I try
hexed charm
tribal jolt
summer ruin
<@&268886789983436800>
fast slate
steady cloud
how do u turn a negative exponent fraction positive again.. 
molten flare
formal forge
Hey guys, been stuck on this for 10 minutes, how do you solve this?
pine geyser
Hey guys, been stuck on this for 10 minutes, how do you solve this?
You have concluded that, log(x^2/7x-1)=0.
10^0=1
Any number to the power of zero equal one
pine geyser
No problem
formal forge
So, it's gonna be 1 = (x²/7x-1) right?
Why do I feel like I'm goin to use the quadratic equation
pine geyser
Ah alright, good night!
thorn grotto
i think for a im supposed to plug in x=1 through x= 12 in to graph the equation but lmk if im not doing this right
but i need assistance with this problem
viscid thistle
i think for a im supposed to plug in x=1 through x= 12 in to graph the equation...
If you are allowed to then just use a graphing calculator for this
Then looking at that would give you the answers to b and c
Just plugging a few numbers in won’t account for any irregularities
Which could affect answers to b and c
viscid thistle
The qst asks us to find the function for this graph
I know this function is 1/x. But it is flipped so that makes it -1/x.
And there is a VA at x= -1 so that means the function is -1/(x+1)
The part i am confused about is how in the world is the x intercept 2 and the y intercept -2? I plugged the -1/(x+1) into desmos but it gave me this
Am i missing something? Does it have to do with the hole?
vocal mantle
Does anyone have anki cards for mathematics
lilac sand
Anyone help me with this?
Did u get the answer
lilac sand
Does anyone have anki cards for mathematics
Oo i remember seeing these but never knew the name ty, pls let me know if you find any
strong roost
Ummm so how can I understand trigonometric identities
turbid creek
Did u get the answer
Yes.
viscid thistle
Ummm so how can I understand trigonometric identities
Derive them
near rampart
hi i was wondering if someone can help me with a question
i need to find the coordinates for a point (x,y,f(x,y)) but all i got is the function f(x,y)=y^2+2xy and the tangentplane z=6x+4y-11 in the point (x,y,f(x,y))
near rampart
alpine bramble
grave gyro
I have an exam tomorrow in calculus
errant pilot
hello my guys
sweet tree
I'm trying to get help in the channel, but maybe I can ask here
I want to know if a table of values is correct or not. A teacher presented me with a table of (x,y) values that looks like this: (0,1) (1,4) (2,10)(3,20)(4,35). This to me appears immediately to be a tetrahedral function/sum of triangular numbers. y=1/6x(x+1)(x+2). Simple. However, of course, a true tetrahedral would have a slightly transposed table of values: (0,0)(1,1)(2,4)(3,10)(5,20)(6,35) etc. So what's up? Did the teacher just mistype the list of values or do I need to figure out a different function?
uncut mulch
divide both sides by the value such that the right side will be 1
what's currently the right side of the equation?
thus what should you divide by?
sinful moth
what's currently the right side of the equation?
thus what should you divide by?
but how about the left side
uncut mulch
you divide both sides by that same value
then do some additional manipulation if needed
the first goal is the get 1 on the right side
do what i mentioned and tell me what you get
sinful moth
do what i mentioned and tell me what you get
uncut mulch
how are you getting 9 in the denominator
sinful moth
36/4
uncut mulch
isn't 1/9
sinful moth
oh yeahh
uncut mulch
also missing the () and ^2 for the y-8
sinful moth
i divided it by 1/4
uncut mulch
you shouldn't be doing that
always remember, same operations to both sides of the equation
divide both sides by 4
or multiply both sides by 1/4
or equivalent
sinful moth
well i divided it by 1/4 as fraction rules so i got 4x2 and (x-8)^2 x1
thats how i got it
uncut mulch
that's not division by 1/4
that's multiplication by 1/4
and regardless that won't give you 9 in the denominator
division by 4 is multiplication by 1/4
sinful moth
no its for the left one'
uncut mulch
?
sinful moth
since its also a fraction
uncut mulch
you might be doing some valid math for some parts but aren't properlly describing what you're doing
sinful moth
you might be doing some valid math for some parts but aren't properlly describin...
yeahh EHAEHAEHAE
wait ill show my work and please judge it
here
dont mind my handwriting 😛
obsidian monolithBOT
ℝαμΩℕωⅤ
sinful moth
ohh
uncut mulch
don't overthink what its supposed to be
sinful moth
its 4/36
uncut mulch
no
sinful moth
wat
sinful moth
aint it just 4/36
uncut mulch
no
sinful moth
and simplified 1/9
uncut mulch
$\frac{36}{4} \redneq \frac{4}{36}$
obsidian monolithBOT
ℝαμΩℕωⅤ
sinful moth
36 divided by 4 is NOT the same as 4 divided by 36
yeah thats why i said 4/36
uncut mulch
and that's why its wrong
sinful moth
4 as nominator
uncut mulch
which is wrong
forget about the elipse equation / the final desired form
this is a simple question about division
sinful moth
alright im joking i know its 36/4
uncut mulch
what is 36 divided by 4
how many times does 4 go into 36
sinful moth
gosh lel
uncut mulch
i can't tell if you're joking
sinful moth
what is 36 divided by 4
how many times does 4 go into 36
1/9 and 9 😛
uncut mulch
those two questions were asking the exact same thing
sinful moth
😛
uncut mulch
yes, 4/36 is 1/9,
but you don't have that here
uncut mulch
36/4 is simply 9
dividing both sides by 4, you should have
$$\frac{(y-8)^2}{8} + \blue{9(x+1)^2} = 1$$
and to explicitly express the $\blue{9(x+1)^2}$ in the form $\frac{(x+1)^2}{\red{k}}$ you can apply the reciprocal relation between multiplication and division. \
$$\frac pq = \frac{1}{q/p}$$
$$9 = \frac{1}{1/9}$$
thus
$$9(x+1)^2 = \frac{(x+1)^2}{\red{1/9}}$$
obsidian monolithBOT
ℝαμΩℕωⅤ
sinful moth
im sorry for all this trouble and its just because i forgot basic math 
thank you for helping mee
Tymsss
viscid thistle
here sin(1/x) can give values from -1 to 1 . now if it gave the value 0 then it ...
everything divided by infinity is 0
for me 3ln(ab)
viscid thistle
I still don't get this:
i got z=7, y=8 and x=-6
arctic dragon
i got z=7, y=8 and x=-6
Yeah I got it
digital mirage
everything divided by infinity is 0
but its 0/0
uncut mulch
here sin(1/x) can give values from -1 to 1 . now if it gave the value 0 then it ...
how does 0/inf lead to 0/0
solar olive
i mean just u =1/x ?
viscid thistle
what is the difference between pre calc and algebra 2?
Pre calc is everything you need before Calculus, Algebra 2 if I remember has functions more in debt alongside polynomials complex numbers and a few fun stuff. But you won't see any geometry (please update if I'm wrong) in Alg2.
opal vault
here sin(1/x) can give values from -1 to 1 . now if it gave the value 0 then it ...
what
the value of sin 1/x approaches 0 and denominator goes to infinity so it should be 0
0/inf = 0
lapis bramble
what do I start now?
novel creek
do a few lessons and see what you feel comfortable with doing :)
lapis bramble
well I want to go to calculus cuz my old math teacher said you don't really need precalculus but I don't want to skip anything to important
novel creek
i would say precalc is very important to calculus
but that just depends on how much precalc you already know
i.e. trig, logs, exponentials, etc
lapis bramble
I did alj 2 so yea I know all those things
sacred junco
if x+1=4, then what is 2x+2? Im really struggling with this question.
soft warren
if x+1=4, then what is 2x+2? Im really struggling with this question.
well theres two ways to go about this
- u can solve for x
- u can multiply both sides by 2 for the first equation and get ur answer directly
dreamy void
hi guys, can anyone check my solution for this problem pls. tysm!
https://discord.com/channels/268882317391429632/1170661519655178301
warm oyster
like trick to memorise them?
hallow lodge
like trick to memorise them?
like what identity should I iuse for this problem
for example
Tan theta can both equal to
sin0/cos0 or tan0 = 1/cot0
hushed sphinx
Most of those I'd derive as necessary by writing everything in terms of sin and cos.
warm oyster
pretty strange sometimes i just dont get notified about the pings
hallow lodge
Most of those I'd derive as necessary by writing everything in terms of sin and ...
but for instance, sin is = 1/csc. when do I use these types of identities
or do i js literally disregard everything there and just write everything to sin and cos
hushed sphinx
As far as I'm concerned, csc(x) is defined as a shorter (and less enlightening) way to write 1/sin(x), so the identity is trivial.
hallow lodge
As far as I'm concerned, csc(x) is _defined_ as a shorter (and less enlightening...
so if i had to prove a problem with 1/csc in it, I js rewritr to 1/sin?
hushed sphinx
No, if it says 1/csc(x), that means 1/(1/sin(x)) which is the same as sin(x).
(Unless the lhs is not defined due to division by zero).
hallow lodge
No, if it says 1/csc(x), that means 1/(1/sin(x)) which is the same as sin(x).
oh yeah mb. wdym by division by 0 btw?
hushed sphinx
1/csc(0) is not defined, whereas sin(0) is.
desert timber
what's with these ridiculous exercises like "express log6(16) using log12(27)"? i don't see any kind of pattern for solving them, you just have to guess the right order of steps that might lead you to the answer?
hushed sphinx
Hmm, you could start by expressing the two values as $\frac{4\log2}{\log2+\log3}$ and $\frac{3\log 3}{2\log2 + \log3}$ ... but that doesn't really seem to point to any nice relation between them in this case.
obsidian monolithBOT
Troposphere
hushed sphinx
But you can reduce the number of "unknowns" by declaring that the logarithms in those fractions happen to have base 3, and then you're looking at expressing $\frac{4x}{x+1}$ in terms of $\frac{3}{2x+1}$ which is a matter of (slightly messy but) straightforward algebra.
obsidian monolithBOT
Troposphere
desert timber
hmm our teacher hasn't used unknowns in any of these exercises so far
this is the solution in my textbook, under 3)
looking at these solutions, I have no idea how I was supposed to think of that... each exercise has its own incredibly specific trick
hushed sphinx
That looks like it's basically the same computation I suggested, but more confusingly written by writing log3(2) all the way through, where I decided to name it x to make it more unobtrusive.
hushed sphinx
The solution in your screenshot is just the final proof, with no easily visible trace of how it was found.
My reasoning might have been a bit brief, but at least the first step in it was pretty systematic: express everything in terms of logarithms of primes.
The trick of choosing one of those primes to be the base of all the logarithms probably is something you only gain from experience.
But after that the only logarithm left was log3(2), which allowed me to use elementary algebra to relate the fractions.
If you haven't even seen algebra, it feels like asking you to come up with such rewritings on your own sounds like a rather big task.
desert timber
thank you, I'll try to apply this in the future
digital mirage
warped cipher
,rccw
obsidian monolithBOT
digital mirage
warped cipher
the range of the sin(x) functions is [-1,1] not [0,1]
digital mirage
the range of the sin(x) functions is [-1,1] not [0,1]
??
fx under cos must be from -1 to 1 ... that what i did
warped cipher
wdym fx?
warped cipher
fx under cos must be from -1 to 1 ... that what i did
I can clearly see you wrote [0, 1/e] tho
digital mirage
I can clearly see you wrote [0, 1/e] tho
sorry its y , by mistake i wrote x
dry cave
depends on the questions
haughty tapir
Hello
How do I read the graph to get the domain n range?
it wasnt tauight from what i remember in class he just guestimated the lines
summer ruin
recall the definition of domain and range
tropic moat
How do I read the graph to get the domain n range?
domain is x axis range is y axis
ruby sparrow
Hi everyone, does anyone know of a location where I can obtain quality exercise with challenging problems and corrections? *
pine girder
Hi everyone, does anyone know of a location where I can obtain quality exercise ...
What level of math?
warm oyster
,, 1=\cos^2 \theta + \sin^2 \theta
obsidian monolithBOT
🐱!Yajat! 【Catfan1398】🐱
warm oyster
can someone explain how (1-sin)(1+sin) = 1 - sin^2
,, 1^2-sin^2 \theta = (1-\sin \theta)(1 + \sin \theta)
obsidian monolithBOT
🐱!Yajat! 【Catfan1398】🐱
hallow lodge
,, 1^2-sin^2 \theta = (1-\sin \theta)(1 + \sin \theta)
oh is it bc 1^2 is 1? im so stupid sry
warm oyster
yes for 1^2 is 1
novel creek
in other words, if f(-x)=f(x), it's symmetric over y-axis, if -f(x)=f(x), it's symmetric over x-axis. The only one not explicitly identified here is symmetric about origin, which means a function is odd which means f(-x)=-f(x)
so just tests these and you should be good :)
@untold python
untold python
Ohhhhhh!!! Thank you sooo much!!! @novel creek
north dirge
Hey does anyone have some good videos to watch for reverse chain rule and integration by substitution?
upbeat falcon
north dirge
thanks
vast quartz
I did alj 2 so yea I know all those things
you need trig
thats what im slaving away at rn
soft warren
you need trig
some people study trig in alg 2
novel wharf
Idk how many people are in Canada
However you would it be realistic to study all of Precalc in 3 months over the course of the summer as with also advance functions?
Would it be good enough preparation of getting a solid 90 or 85?
With also adage of studying more advance stuff on the side as per calc?
fervent yarrow
How do I solve this?
willow skiff
How do I solve this?
g is the inverse of f, since g(f(x)) = x
or equivalently, f is the inverse of g
fervent yarrow
Is it correct?
willow skiff
Is it correct?
yes
willow skiff
no worries
willow skiff
Number 18 how do I solve this?
recall the definitions of odd and even functions:
odd -> f(-x) = -f(x)
even -> f(-x) = f(x)
try substituting x = 1 etc into those definitions
(you can think of these functions graphically: even functions have left-right symmetry, and odd functions have symmetry across quadrants 1 and 3; 2 and 4)
fervent yarrow
try substituting x = 1 etc into those definitions
Wdym can you please elaborate?
willow skiff
Wdym can you please elaborate?
like for the first one, (1, 2) is the reflection of (-1, 2)
and (4, 7) is the reflection of (-4, 7)
so it works out
that function is even
fervent yarrow
Okay
Then for the second option?
It is odd
Cause -x,-y exists?
@willow skiff
willow skiff
yep C is correct
willow skiff
Neither even not odd
in fact, if you substitute x = 0 into f(-x) = -f(x)
you get f(0) = -f(0)
or that f(0) = 0
in other words, every odd function must pass through the origin
fervent yarrow
in other words, every odd function must pass through the origin
Didn't get it please elaborate
willow skiff
Didn't get it please elaborate
f(-x) = -f(x) is the definition of an odd function
and if f(0) = 0, that means when x = 0, y = 0
that point is precisely the origin
like if x = -x, adding x to both sides gives you 2x = 0
or x = 0
viscid thistle
<@&268886789983436800> uh spam ig?
oblique sapphire
Didn't get it please elaborate
If an odd function is defined at x=0, then that automatically means the output of the function at x=0 must be 0 in order to maintain odd symmetry
In other words, if an odd function is defined at x=0, it must pass through the origin
mental sonnet
hey so i feel like I have a solid basis of algebra and trigonmetry but I really don't know how to tackle calculas. Its something that I have heard about and would love to learn about but I don't know where to begin
soft warren
hey so i feel like I have a solid basis of algebra and trigonmetry but I really ...
u need to be rlly good at algebra and decent at trig to begin
lapis bramble
you need trig
you mean like trig funtions unit circle and solving triangle's cuz I did those in alj 2 and geomatry
viscid thistle
hi can someone help me find this limit
i know the answer might be something easy cuz log base 7 of 0 does not exist, but i also got that x > 0 so it might range in the positives?!
magic wolf
I'm pretty sure that the 140 at the end gets the exponent as well
magic wolf
i know the answer might be something easy cuz log base 7 of 0 does not exist, bu...
It approaches 0, but is greater than 0 implies that it's 0+, because 0+ > 0. Since it never becomes 0, it will approach a value. When looking at the graph of log7(x), there is an asymptote at x=0. Since x approaches 0+, it would be reasonable to assume that the function approaches infinity
viscid thistle
it approaches +inf or -inf?
viscid thistle
k ty
magic wolf
You're welcome
mental sonnet
u need to be rlly good at algebra and decent at trig to begin
I guess but is there any place online where I can learn it. Currently I am watching 3 brown 1 blue's video but thats about it
hallow lodge
how to turn this into logarithmic?
twin vortex
can anyone explain calcules to me please ?
gaunt carbon
what do you want to know
calculus is a pretty wide field
twin vortex
can you explain the bare basic in bare basic terms
gaunt carbon
yeah
so, in simplest terms, calculus is two main operations
differentiating and integrating, and they're opposites
i can't easily explain what they do but they're both based on the concept of a limit
which is a value a certain function approaches (but this doesnt necessarily mean it'll reach it, it's just what it approaches)
so if you have a function like this and you're trying to take the limit as x approaches zero from the right, you're going to get a value of zero
but if you take the limit as x approaches zero from the left, you're going to get a value of three
and thats the bare minimum i can explain easily
the notation looks smth like this
where right and left are noted by plus or minus signs next to the a
delicate thistle
ornate depot
How?
gaunt carbon
How?
so the first step here is gonna be taking the 4x our front and making it an exponent right
ornate depot
gaunt carbon
so the 4x can become an exponent of the 7 because we're working with logs right
yeah that works too
ornate depot
I just don't get the step where (4x+1)In 7
gaunt carbon
i mean if it doesnt i dont see errors there
gaunt carbon
I just don't get the step where (4x+1)In 7
the step where you move the exponent to the front? or the one where you distribute
ornate depot
the one where you distribute the 4x+1
gaunt carbon
yeah so as far as i know that just works like any other multiplication problem
it looks like you did it right from what I can tell
ornate depot
yeah so as far as i know that just works like any other multiplication problem
i...
This from video I was watching
gaunt carbon
OHHH okay
ornate depot
I don't get how (4+1)in7 = 4x*in7+in7
gaunt carbon
yeah so basically. all we're doing in that step is multiplying 4x by ln 7 and then multiplying ln 7 by 1
its the natural log so we treat it like any other number or variable
when we multiply like that
so like. if you have smth like this
ornate depot
okay
O I get so he didnt multiple the Nartual log of 7 with 4x because the number dont share the same variable so he left as 4*in7
short iron
I have an equation ax^2+bx+c=0. What are the conditions on b and c such that the solutions are
- real and positive
- real and negativ
if a<0
shadow summit
I have an equation ax^2+bx+c=0. What are the conditions on b and c such that the...
you need to use the discriminant
the discriminant is sqrt(b^2 - 4ac)
you may see it in the quadratic equation, if the result of the discriminant is positive and larger than 0, than the roots are positive and real. If the discriminant is positive and less than 0, than the roots are negative and real. And if the discriminant is negative the roots have complex feelings and want to be special.
gloomy walrus
(x^2)+3x+9
(-3(plusminus) root[9-36])/2
(-3(plusminus) root[-27])/2
(-3(plusminus) 3root[-3])/2
(-3(plusminus) 3iroot[3])/2
1.5(plusminus) 1.5iroot[3]
1.5+1.5iroot[3], 1.5-1.5iroot[3]
pulsar vessel
I have an exam coming up and I was wondering if anyone would help me study
shadow summit
I have an exam coming up and I was wondering if anyone would help me study
What are the topics?
pulsar vessel
What are the topics?
Systems of equations, exponential and logarithmic functions, finding domain of functions
shadow summit
Systems of equations, exponential and logarithmic functions, finding domain of f...
What are you having difficulties with? (if you are having difficulties that is)
pulsar vessel
Mostly expanding logarithms and giving the exact solutions to them.
I’ll show what my exam says so you understand what I mean by giving exact solutions.
shadow summit
Are you doing everything in base 10 (log_10(x) or log(x))? or are you doing logs of different bases?
How familiar with your logarithm rules are you?
pulsar vessel
Not very familiar
shadow summit
pulsar vessel
Here’s another example of what I need help understanding
pulsar vessel
I’ll save this
shadow summit
Okay lets start with q6a) ln(x^3 * y)
pulsar vessel
Ok
shadow summit
We can apply the law of products which stats that log(ab) = log(a)+log(b)
so we will have ln(x^3)+ln(y) //then we can apply the law of exponents which is log(a^b) = blog(a)
that means the final solution is 3ln(x)+ln(y)
pulsar vessel
Ok I follow
shadow summit
I will go over the second question as its a bit more complex, then have a go at the final question.
pulsar vessel
Ok
shadow summit
log( (sqrt(x)*k^2)/(m+1) )
Start by applying the law of ratios
log(sqrt(x)*k^2) - log(m+1)
actually, i think thats it
pulsar vessel
Oh I don’t need to do anything further?
shadow summit
I don't think so, I though it said sqrt(xk^2), but because it just says sqrt(x)*k^2 we dont have to go any further
pulsar vessel
Ok makes sense
shadow summit
But if you have to, like in the final question, recall that a square root can be expressed as a fractional exponent
pulsar vessel
I don’t think I have to do that
shadow summit
for the final question you have to change the inside of the logarithm from the fourth root to the power of 1/4, then use the law of exponents to move it to the front of the logarithm.
pulsar vessel
Oh ok how do I do that?
shadow summit
Look at the inside, it is
you can change that to be (ab^3/c^2)^(1/4)
then you can use the law of exponents to move the 1/4th to the front of the log
pulsar vessel
Oh I see. Does that get rid of the square root?
pulsar vessel
So it would be written as 1/4 log ab^3/c^2
shadow summit
yes
pulsar vessel
Do I use the law of ratios after that?
shadow summit
yes
pulsar vessel
Ok I think I’m starting to get it
shadow summit
The last question is a bit complex
pulsar vessel
Yes it is
shadow summit
Tell me once you think you have gotten the answer
pulsar vessel
Ok
shadow summit
okay, what did you get?
pulsar vessel
3 (1/4) log3 ab - 2(1/4) log3 c
shadow summit
okay, this is pretty much the answer, and you would probably get full marks, but you can move 1/4th to the front of some brackets to make it look cleaner
shadow summit
3 (1/4) log3 ab - 2(1/4) log3 c
also you cant take the 3 out
pulsar vessel
Oh I thought I could
shadow summit
because log_3(ab^3) isnt log_3(ab)^3
shadow summit
Oh I thought I could
its tricky, but if you are able to tell the difference between ab^2 and (ab)^2 it shouldnt be much of an issue
i sometimes mess up like that as well, so dont worry
pulsar vessel
Right. I’ll make a note of that
shadow summit
do you know how to do question 12a in the original work sheet you posted?
pulsar vessel
No
pulsar vessel
Yep
shadow summit
so for these types of questions you need to make everything have the same base number
so 2^(4x+5)=8 would become 2^(4x+5)=2^3
Now, using the same base rule of exponents, if x^a=x^b, then a=b
so 4x+5 must be equal to 3
so you'll just have to solve the equation 4x+5=3. which gives you the answer x=-1/2
pulsar vessel
Oh right! That makes sense now
shadow summit
And to verify, plug in -1/2 into the original equation.
pulsar vessel
Right
pulsar vessel
Ok
shadow summit
Because both sides have different bases you cannot use that trick to solve for x.
pulsar vessel
Ok so does that mean we need to make the same base?
shadow summit
Nope! We can use logarithms! (yay)
pulsar vessel
Oh ok
shadow summit
We can take the log of both sides (doesnt matter the base of the log)
but because you are learning natural logarithms, i will be using ln(x), which just means log_e(x)
pulsar vessel
Ok
shadow summit
3^(x-4)=7^(2x+5)
ln(3^(x-4)) = ln(7^(2x+5))
(x-4)ln(3) = (2x+5)ln(7)
from here, it should be pretty easy to figure out, but if you havent already, i will continue
xln(3) - 4ln(3) = 2xln(7) + 5ln(7)
xln(3) - 2xln(7) = 5ln(7) + 4ln(3)
x( ln(3) - ln(49) ) = 5ln(7) + 4ln(3) factorise x
x= (5ln(7) + 4ln(3)) / ((ln(3)-ln(49))
@pulsar vessel and that is the exact value
shadow summit
I would probably write this down on a book or a notepad
okay, good job
if you need clarification i am more than happy to make a line easier to understand
shadow summit
a helpful tip you should try doing is writing down the law you are using next to the line you used one in.
pulsar vessel
Oh good idea
shadow summit
Or if you want to be more precise, write down what process you are using if you arent using a specific law, like when i took the common variable (x) out of the logs in the 6th line
pulsar vessel
Oh ok
shadow summit
Do you think you are starting to understand logarithms and exponents now?
pulsar vessel
Yes I think I’ve got it now
shadow summit
okay, try this question
You will need to use the law of exponents, law of ratios, law of products
btw alog(b^c) = log(b^ac)
pulsar vessel
I got logb(8m^12/3)
shadow summit
good job, you got the correct answer!
pulsar vessel
Awesome!
I think it’s finally starting to click. Now that I’m getting more familiar with all the rules
shadow summit
Now, the best way to keep improving from here (aka getting more consistant) is to just do a bunch of questions. Use the textbook your school gives out, or ask your teacher for more resources, and just start doing problems.
pulsar vessel
Ok I will do that. My textbook has a whole unit on this with practice questions
shadow summit
When I was learning logarithms initailly I think i did over 300 logarithm questions in 10 days (outside of school). But you don't have to do that many, just like 50 and you should understand them.
pulsar vessel
Wow that is a lot of practice 😂
shadow summit
It was only like 30-45 minutes a day
pulsar vessel
Ah fair enough
shadow summit
A lot of the questions when i started were stuff like log_2(256)=x
shadow summit
sometimes i type too fast for the math to math
pulsar vessel
Haha I get it
shadow summit
Anyways, you also said you were doing simultaneous solutions (systems of equations) on your exam?
pulsar vessel
Yes but I’ve got those down pretty good
shadow summit
Ahh, thats good. They will show up everywhere in algebra and calculus.
pulsar vessel
I’m starting to notice that lol
That’s why I decided to actually learn them this time around
shadow summit
yeah, good idea.
pulsar vessel
Anyways, thank you so much for helping me! Really means a lot
shadow summit
np
green badger
Can someone help me with my homework? I would really appreciate it .
shadow summit
Can someone help me with my homework? I would really appreciate it .
What topics?
green badger
Analyzing graphs of functions
shadow summit
How much difficulty are you having with the topic?
green badger
A lot, I’ve had covid and I’ve missed the past two weeks of school and I’m really behind.
shadow summit
Okay, give a few examples of the questions you are having difficulties with.
green badger
shadow summit
Do you know what domain and range is?
green badger
Yes I know how to do that just everything else is confusing
shadow summit
Okay, so you don’t know what continuous and disconnected equations are?
lunar viper
<@&286206848099549185>
!15m
tender questBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
pulsar vessel
When solving a system of equations using matrices, how do you know if you have no solution or infinite solutions?
summer ruin
when you have an equation of the form 0 = 1 or 0 = 0
ornate depot
for the quadratic equation does A always have to be equal to one like for example problem 2x^2+3x-10
pulsar vessel
when you have an equation of the form 0 = 1 or 0 = 0
Oh ok
tawdry viper
warm oyster
!da2a
tender questBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
shadow summit
for the quadratic equation does A always have to be equal to one like for exampl...
a can equal anything, but it can always be cancelled out. eg 2x^2+4x+6 can be x^2+2x+3
viscid thistle
Find the sum of all values of $\theta$ such that $\theta\in[0,2\pi]$ and$$ \cos(\theta)+4\sec(\theta)=8 .$$
obsidian monolithBOT
Mathboy123
shadow summit
Find the sum of all values of $\theta$ such that $\theta\in[0,2\pi]$ and$$ \cos(...
To solve that question you must use trigonometric identities and general solutions.
The first step should be to fnd the angle, this can be done by multiplying both sides by $\cos(\theta)$, from there you can move everything to one side you will get the result: $\cos^2(\theta )-8\cos(\theta)+4=0$
obsidian monolithBOT
TheLord26
shadow summit
From there, how I went about solving for $\theta$ was to let $\cos(\theta) = x$, and solve for x using the quadratic equation.
obsidian monolithBOT
TheLord26
viscid thistle
To solve that question you must use trigonometric identities and general solutio...
yes and i solve quadratic equation but i get weird radical
shadow summit
yes and i solve quadratic equation but i get weird radical
What do you mean?
viscid thistle
(x=2\sqrt{3}+4\ x=-2\sqrt{3}+4)
shadow summit
That is correct.
viscid thistle
so 8?
shadow summit
Then you will have $\cos(\theta)=x$, and from there you will find that $2\sqrt{3}+4$ does not have a possible solution, so when you use $-2\sqrt{3}+4$ you will find the value of $\theta$ to be 1.00522.
obsidian monolithBOT
TheLord26
shadow summit
Finally use the general solution to find all values between 0 and 2pi.
And well, add them all together.
shadow summit
yes
frigid trout
if im given this and its telling me to expand
is it okay to write it like this
or would I have to distribute the 1/5 to each one
ex) 1/5 + 4/5 - 4/5
warped cipher
it's correct
viscid thistle
<@&286206848099549185>
lunar viper
<@&286206848099549185>
!15m
tender questBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
viscid thistle
I mentioned people for her question not mine lol
hushed sphinx
Well, don't.
lunar viper
💀
warm oyster
!15m
tender questBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
lunar viper
!15m
tender questBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
viscid thistle
Oh sorry I didn't see the message
lunar viper
Oh sorry I didn't see the message
💀
viscid thistle
Ok I'm sorry what I'm suppose to say
pulsar vessel
Can the domain of a log be negative?
warm oyster
nah
pulsar vessel
Ok 👍
vital cairn
Can the domain of a log be negative?
Yes
Because exponential can be negatives
If you allow stuff the be complex
thorn creek
quite famously, e^(iπ) = -1
turbid garnet
why is this possible to do and why do you do this?
shadow summit
why is this possible to do and why do you do this?
It's because the you are multiplying by 1, and in trigonometric proofs you can multiply by 1. The reason you do this is you hope to simplify the right side and turn it into the left side, what you should be looking at now is expanding the top of the fraction and manipulating it to be equal to cot(x)-csc(x)-1.
viscid thistle
Hey guy's, i had a question, is algebra 2 enough to proceed into precalculus?
warm oyster
Hey guy's, i had a question, is algebra 2 enough to proceed into precalculus?
go ahead
digital mirage
why we dodnt write g(lambda+pi/2 ) ? lambda is also varibale here
and why lambda cannot be zero ...
stable vessel
Why quadratic functions graphs are always curved?
sinful halo
Why quadratic functions graphs are always curved?
To solve this you must ask what the difference between linear functions and quadratic functions are
stable vessel
a linear function can be determined by y = x and a quadratic function by y = x²?
sinful halo
The difference between the graphs
It's the slope
The slope of a linear function is always constant whilst for a quadratic it changes
stable vessel
why?
sinful halo
Because x is squared — $2^2=4$ $3^2=9$ $4^2=16$ see how 4 changes to 9 which then changes to 16? It changes from +5 to +7 and so on
obsidian monolithBOT
prime
sinful halo
Linear functions don't have that characteristic and change at a constant rate which is "m" in y=mx+b
stable vessel
I am getting to understand it, can I apply this logic for other type of functions like cubic or fraction ones?
sinful halo
By fraction do you mean $\frac{1}{x}?$
obsidian monolithBOT
prime
sinful halo
I am getting to understand it, can I apply this logic for other type of function...
And yes, yes you can
stable vessel
By fraction do you mean $\frac{1}{x}?$
yes
slim steppe
I believe it's called Khan Academy
pulsar vessel
How do I insert this into a calculator? I can’t do the vertical line
shadow summit
How do I insert this into a calculator? I can’t do the vertical line
if its a gaussien just use a 2x3 matrix.
but, that one isnt possible.
pulsar vessel
if its a gaussien just use a 2x3 matrix.
Yea I’m supposed to use gauss elimination. I wasn’t sure if I would just do a 2x3 matrix or if I needed to do something different to add that line
shadow summit
Yea I’m supposed to use gauss elimination. I wasn’t sure if I would just do a 2x...
Nah, unless you are specifically using a program designed to do Gaussian eliminations you just use matrices.
ruby cloud
Hey everyone. I don't understand the statement "Since MA> 0, the extremum points of the function d(x) and MA are the same". Why exactly we can conclude that?
Sorry for such weird typing, I used a translator to translate Russian into English from the image
hushed sphinx
That typography is truly bizarre.
But it must mean: Since MA(x)² = d(x) and MA(x) is always positive, the x that maximizes d(x) is the same as the x that maximizes MA(x).
(This is because the function that squares a number is strictly increasing on the positive reals).
@ruby cloud ^^
prisma bridge
Tropo quick and random question. Are you a Ph.D student by any chance
prisma bridge
That time is long past for me.
Oh wow so ig ur a prof or some sort of researcher
viscid thistle
That time is long past for me.
Incredible
outer patrol
How do I do dis
warm spoke
How do I do dis
first divide both isdes by 8 so u got cos(4x)=3/8 and then do inverse cos each sied so now u got 4x=arccos(3/8) and then divide by 4 so u got x=arccos(3/8)/4 and then plug into ur calculator
also remmeber to set to radians or degrees but idk what u doing
digital pendant
Why quadratic functions graphs are always curved?
If you look at f(x)=x^2 then look at the increase that f(x+1) gives:
f(x+1) = (x+1)^2 = x^2+2x+1
f(x+1)-f(x) = (x^2+2x+1) - (x^2) = 2x+1
You should notice that the function increases by 2x+1 when going from f(x) to f(x+1). Meaning that the amount the function increases by increases as x gets bigger. Whereas if you compare g(x)=x to g(x+1)
g(x+1)=x+1
g(x+1)-g(x) = (x+1)-(x) = 1
You should see that the function only increases by a constant amount which isn't dependent on x.
viscid thistle
I understand this isn’t a help channel but it won’t let me open a help channel 😭
is anyone available?
warm spoke
is anyone available?
i might be able to help
but next time bro when you got a question just ask it otherwise then someone gotta respond to you first asking for the question and wait for u to respond back
warm spoke
guys can someone help me
first one a polynomial is continuous everywhere so u good
warm spoke
guys can someone help me
second one it should be continuous because the asymptote is at x=6 and theres no holes
third one no because its undefined at x=3
fourth one no because u got another undefined point
which also happens to be a hole
paper pagoda
need help with this
ive had no problem with any problem so far, but this one is tripping me up
vernal pine
I have this equation, x^2 + y^3 = b^x. And i wanna find for what values of b (inequality) will give a graph with 3 roots. I started solving this with y as zero, yet im not exactly sure where to go next from this
,tex $x^2$ + $y^3$ = $b^x$
obsidian monolithBOT
J_
vernal pine
im left with:
obsidian monolithBOT
J_
viscid thistle
pls ping with any help!
You can check of trivial solutions via substitution, but the other solutions are non-elementary
vernal pine
You can check of trivial solutions via substitution, but the other solutions are...
so then is there another approach i could take to solving the problem
viscid thistle
I can't think of any other than your approach
The reason why other solutions are non-elementary, is because when you solve the given equation:
vernal pine
Hm thats a shame
viscid thistle
$x^2 = b^x$
$\implies ln(x^2) = ln(b^x)$
For $x > 0, 2lnx = xln(b)$
$\implies lnx - x\frac{lnb}{2} = 0$
$\implies xe^{-x\frac{lnb}{2}} = 1
=> (-x\frac{lnb}{2})e^{-x\frac{lnb}{2}} = -\frac{lnb}{2}$
obsidian monolithBOT
𝓘 .
vernal pine
Hm
obsidian monolithBOT
𝓘 .
viscid thistle
Whose inverse, called the Lambert W function, is non-elementary
viscid thistle
I mean there could be another approach of solving this
But currently I can't think of any
vernal pine
Thank you for your help
viscid thistle
**𝓘 .**
Also b>0 here (and when you solve it in the end using Lambert W, b has to be greater than or equal to e^(2/e) because to solve for ue^u = w, there is a restriction of w≥-1/e, for Real u and w)
worldly crater
How good or bad is the Baron's E-Z Precalculus book?
obsidian monolithBOT
TheLord26
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
shadow summit
need help with this
Take the log of both sides, $\log(6^{1-8x})=log(7^{x})\(1-8x)(log(6))=xlog(7)$ from there, it’s a simple equation, expand brackets and do the logarithms.
obsidian monolithBOT
TheLord26
shadow summit
wonky ahhh sin wave, also i cant see the equation.
chilly summit
hi i have a problem where i want a formula like:
formula(d, f(x)) = a
where f(a) is the smallest number where the number of digits in f(a) = d
is this possible?
for example:
let f(x) = n * (n+1) / 2
let d = 4
then formula(d, f(x)) = 45
because f(45) = 1035, which 1035 is the smallest number where the number digits of 1035 = d ( 4 )
reef hazel
can someone help me with this
Suppose a car is travelling 40 feet/sec and it loses control on wet asphalt. How long will its skid marks be?
viscid thistle
can someone help me with this
Suppose a car is travelling 40 feet/sec and it l...
The question is incomplete. What's the coefficient of kinetic friction and the mass of car?
reef hazel
The question is incomplete. What's the coefficient of kinetic friction and the m...
0.5
viscid thistle
And mass?
reef hazel
not given
reef hazel
solving it
i have to find the "How long will its skid marks be?"
and the answer should be stated with feet
viscid thistle
Please send the complete question because it still seems incomplete. While skidding, is the car still being accelerated? Were brakes applied at that time?
viscid thistle
for example:
let f(x) = n * (n+1) / 2
let d = 4
then formula(d, f(x)) = 45
be...
I don't think there's really a formula but you can formulate an algorithm.
I'll give you a hint for this particular example: what are the roots of f(x) - 1000 in this case? (x in R, then subject the condition of x being a natural number)
vapid plaza
Please send the complete question because it still seems incomplete. While skidd...
I believe the assumption is that friction is the only (horizontal) force applied on the car
viscid thistle
I also thought about that too, but it would be better if OP sends the full question
viscid thistle
and the answer should be stated with feet
If you use the above assumption, then you want the car going with 40ft/s to come to a stop at 0ft/s. What do you think that caused this?
viscid thistle
Well, just substitute the values in the given relation
reef hazel
I did but doesnt give the right answer
viscid thistle
Could you please show your working
viscid thistle
You are substituting the values in the relation incorrectly
The speed of the car while it was drifting is given 40ft/s
reef hazel
Yes
viscid thistle
You have to find the distance d (i.e. the length of the skid mark)
viscid thistle
This is one example j was given
And read this passage once more
shadow summit
for example:
let f(x) = n * (n+1) / 2
let d = 4
then formula(d, f(x)) = 45
be...
log_10(n)+1, then just discard the decimal places.
also f(x)=x*(x+1)/2, dont yse n if you say f(x), use x or f(n).
viscid thistle
wonky ahhh sin wave, also i cant see the equation.
y = 4 sin(16/9(x -3pi/8)) + 2
Plot (3pi/8, 0) and (3pi/2,0)
floral holly
Hello
viscid thistle
What’s the best way to cram for a pre calc test
trim kindle
What’s the best way to cram for a pre calc test
do alot of exercises, like alot. Worked good enough for vectors
warm spoke
we have desmos at home
warm spoke
What’s the best way to cram for a pre calc test
pull out the textbook and do as many problems as u can if u run outta problems to do find more
viscid thistle
can anyone help me answer this rq <@&286206848099549185>
warm spoke
can anyone help me answer this rq <@&286206848099549185>
so first make a triangle with ur vector and 2 components
and with trig functions the x component will be 45m * cos61
the y component will be 45m * sin61
make sure ur calculator is in degrees too and not radians
viscid thistle
preciate it
smoky pendant
warm oyster
preciate it?
smoky pendant
is the first one right or do you distribute the expontents and simplify
smoky pendant
which
smoky pendant
alr thanks
warm oyster
no problem mrverdevelt_43754
lunar viper
can anyone help me answer this rq <@&286206848099549185>
!15m
tender questBOT
can anyone help me answer this rq <@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
viscid thistle
Can someone explain why this is true:
Is it just a coincidence or is there a more general trigonometric relation that explains it
warm spoke
Can someone explain why this is true:
i gotchu
i am writing it on the online whiteboard so gimme a sec
wait i messed up somewhere
bro screw this i keep messign up the algebra
i will find out late
later
viscid thistle
Thank you, but I was looking for the explanation of this relationship in a more general way. It seens odd to have two arbitrary tangents summing to an integer. I was wondering if there is a more general relation from which this equation is just an instance
shadow summit
Thank you, but I was looking for the explanation of this relationship in a more ...
There is no general solution. It’s just whether the output of the trig functions sum to an integer.
vernal pine
Also b>0 here (and when you solve it in the end using Lambert W, b has to be gre...
Hello, sorry for the ping but this is a followup to yestardays question
I think it might still involve Lambert but im not sure
,tex $x^2 + y^3 = b^x$
obsidian monolithBOT
J_
vernal pine
For b = 2, will there be three roots on the graph?
Meaning three zeroes
I know there are, i just need help solving
Because im stuck on the step:
obsidian monolithBOT
J_
vernal pine
And im not sure how to continue
viscid thistle
There are actually multiple values of b for which the graph has 3 roots
vernal pine
Yes, but this hones in on just the value of b = 2 now
For simplicity of the question 😂
viscid thistle
Well you can draw the graphs and count the intersection points
vernal pine
Yeah, but from like an algebraic standpoint
viscid thistle
It may require slight amount of calculus
vernal pine
In my guidelines, i am allowed to look at graphs for inspiration, but need to solve this solely without that
viscid thistle
From algebraic standpoint,
for x > 0
2lnx = xln2
=> lnx - x (ln2)/2 = 0
=> x e^(-x (ln2)/2) = 1
=> (-x (ln2)/2)e^(-x (ln2)/2) = -(ln2)/2
So still you have to use Lambert W
vernal pine
Hm, could you perhaps help me tweak this question to be able to solve without using Lambert W
viscid thistle
So using intersection points from the graph and some basic knowledge calculus, you can solve this more easily
viscid thistle
Hm, could you perhaps help me tweak this question to be able to solve without us...
You can't really separate x here
vernal pine
Hm, would using Lambert W help me solve this question, like get a definitive answer
Also, do i need an indepth understanding of it?
viscid thistle
Yeah
vernal pine
Is that Yeah to both questions
viscid thistle
But it's not needed for you at this level, use graphs
viscid thistle
Is that Yeah to both questions
Yep
vernal pine
But it's not needed for you at this level, use graphs
Okay Hm
Thank you for your help
vernal pine
But it's not needed for you at this level, use graphs
If this question didnt have
,tex $b^x$
and instead just b
Would it work?
obsidian monolithBOT
J_
viscid thistle
Yes
vernal pine
without lambert w*
vernal pine
Yea then i can sqrt easily
viscid thistle
Yes, ±√b
vernal pine
Do you think that question would be too simple
Or is it in the slightest challenging
Thats a stupid question sorry
viscid thistle
I mean it depends on context
In the actual question (not this one), is b just an integer?
Or a real number?
If b is an integer, it may become easier to solve
vernal pine
I assume b would be an integer
unreal frigate