f(c) = 1-2c^2
#help-36
ebon walrus
ebon walrus
so, I defined a function g(x) and If I am able to prove that at some point between x belongs to (0,1) it passes through 0 that this statement is true
which I prove further using Intermediate Value Theorem
finite spire
Yup
ebon walrus
If you see any gaps in my thoughts please tell
finite spire
f(c) - 1 +2c^2 = 0
This is just a special case of a function g(x) = f(x) + 2x^2 - 1
ebon walrus
otherwise I would close it now
final saddleBOT
Available help channel!
tranquil pine
Can anyone help
final saddleBOT
Can anyone help
final saddleBOT
@tranquil pine Has your question been resolved?
valid hemlock
final saddleBOT
valid hemlock
I dont understand the ratio part
I know like direction vector is in the same direction as the velocity vector
and like for example if the magnitude of the velocity vector is like 7 and the mag of direction vector is 10 we would need 7/10 of the direction vector but I dont understand why -4/3
.close
final saddleBOT
final saddleBOT
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final saddleBOT
raw mural
final saddleBOT
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zealous hatch
hellu... what does the standard deviation sign look like?
final saddleBOT
hellu... what does the standard deviation sign look like?
zealous hatch
im getting ox or sx i dont know the difference
trail lance
im getting ox or sx i dont know the difference
ox and sx are almost similar
except ox is N while sx is N - 1 in the formula
trail lance
do you know the standard deviation formula
trail lance
Okay do you know variance
Do you know what’s that
it’s basically the square of standard deviation
zealous hatch
i do not
oh
well because when i input the information im getting 2 different things for the ox and sx so i dont know which one to put in context
trail lance
well because when i input the information im getting 2 different things for the ...
okay look
I was taught to use ox
but depending on your syllabus
it’s different
zealous hatch
wdym by syllabus
trail lance
Do you see the n - 1 as the denominator?
zealous hatch
yes i do
trail lance
wdym by syllabus
as in how you were taught
in your bath
math*
I was taught differently
zealous hatch
im mostly familiar with ox so should i just go with that one?
trail lance
im mostly familiar with ox so should i just go with that one?
Which method does your teacher teaches you?
Did he/she tells you to use sx or ox?
zealous hatch
im sure it was ox
trail lance
Type .close when you’re done @zealous hatch
zealous hatch
okay thanks
when the problem asks you to make a conclusion about 2 variables, how can i describe it? i'm not sure how to do it
ill send the problem for context
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zinc nimbus
hi guys, i need a help to understand this alogorithm running time, here we have constant 1 and constant 2, and in the concrete example of sorting an array of 10M items, the constant 1 have a value of 2 and the constant 2 have a value of 50, why 2 and 50 ?
final saddleBOT
hi guys, i need a help to understand this alogorithm running time, here we have ...
lost heath
It's just an example
It says that the skilled programmer coded it such that the constant is small (2) and the beginner coded it such that the constant is large (50)
final saddleBOT
@zinc nimbus Has your question been resolved?
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@zinc nimbus Has your question been resolved?
clever vault
Q7. The following results give the heights of sunflowers in centimetres.
180 184 195 177 175 173 169 167 197 173 166 183 161 195 177 192 161 165
Represent the data by a stem and leaf diagram.
final saddleBOT
Q7. The following results give the heights of sunflowers in centimetres.
180 184...
clever vault
bro no one is helping me <@&286206848099549185>
runic kiln
then you be patient
final saddleBOT
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.
minor storm
occupy one channel at a time please
grim badger
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slim jolt
hey guys
slim jolt
how do i cancel an addition and have always the same number
supple jolt
Can you give an example?
supple jolt
Yes
slim jolt
but i need to do that for a sequece
real problem is how do i reference
how do each cell returns to 6 when it increases +1 every new row
vital crag
this is an excel / sheets question
slim jolt
i just need the math logic behind it =
=/
so i can write it
but i can't figure the logic
vital crag
google "excel formulas"
slim jolt
not what i'm looking for though that was just a real life example
i'm just wondering if there's an math equation that always return to the same number
vital crag
$y=x$
soft zealotBOT
riemann
vital crag
,w plot y=x
soft zealotBOT
worldly vale
$x \mapsto x + (6-x) = 6$
soft zealotBOT
ΣAC
slim jolt
noice thanks
worldly vale
Or just take each cell and set it to 6?
Not sure why you need to be doing it by subtraction
slim jolt
i need to bypass a absolute referece! when copying multiple stuff
much appreciated sir. this works
hot oracle
final saddleBOT
tranquil pine
yes you are on the right path
I'd suggest dividing both sides by 11^(2x) to get a quadratic
hot oracle
I'd suggest dividing both sides by 11^(2x) to get a quadratic
Okay I’ll try that
hot oracle
I'd suggest dividing both sides by 11^(2x) to get a quadratic
well I got y^2+y-1=0 for the quadratic and thought it was wrong because it wouldn’t give me a simple answer and I’d have to use logs
but turns out the answer was in logs so all good
.close
dull hull
help
dull hull
how did they get it
if it's 3-6x + 6x - 2
-6 + 6 = 0
3 - 2 = 1
so how did the 12 appear
fathom walrus
They meant to write a -6x instead of a +
Take a look at the second distribution
It’s -2(3x+1)
Which becomes -6x -2
dull hull
that's right
fathom walrus
U understand now?
dull hull
Yes, thank you 🙏🏻
fathom walrus
Np
round pine
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dull hull
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noble mist
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tranquil pine
The rate water is Being Pumped in at: w(t) = 95sqrt(t) * sin^2 * (t/6)
I'm curious what the derivate of w(t) would represent in this situation?
in otherwords, w'(t)
final saddleBOT
The rate water is Being Pumped in at: w(t) = 95sqrt(t) * sin^2 * (t/6)
I'm curio...
glossy lion
basically the rate at which the rate changes
so like if the rate is 5 gallons per minute for example
then w' would be like how that rate is changing
tranquil pine
the problem says to evaluate w'(3)
so would that mean the rate at which the rate of water is being pumped at time 3?
glossy lion
it is the rate at which the rate of water pumped changes, so if your answer is 3 for example, then the rate of water increases by 3 units per time
like acceleration for example
tranquil pine
so how would i solve for w'(3)
using calculator, so i dont have to find the derivative by hadn
glossy lion
it depends on the calculator
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dusty harbor
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dusty harbor
in this definition we allow infinity as the limit of the simple functions
but
here we determine that f must be finite almost everywhere if it is integrable
is it because of the almost everywher?
or is it because the functions in 5.7 are just measurable hence not necessarily integrable
final saddleBOT
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dusty harbor
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dusty harbor
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✅
dusty harbor
how can the integral be infinity if we require finiteness for integrability?
dusty harbor
.close
tranquil pine
final saddleBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
recall that acceleration is the second derivative of distance
do I need to use antiderivatives
at all
yeah, you can
im having trouble building the position function
but im thinking that I may have to use antiderivatives in order to do it
do you have any tips
!show
final saddleBOT
Show your work, and if possible, explain where you are stuck.
tranquil pine
I don't have work
im clueless
integrate acceleration to get a function for velocity
$$\int \frac{32}{t^2}dx$$
soft zealotBOT
Inversality
soft zealotBOT
Inversality
tranquil pine
**Inversality**
why /t^2?
acceleration is constant
acceleration due to gravity
acceleration does not depend on time
32x+C
yeah
now use the initial value for velocity to find c
?
tranquil pine
32x+C
this was fine
why did you make the 32 into 48
how do I find c
the velocity at time x=0 is 48
so c is 48 right
yeah
now integrate 32x+48 again to get distance
16x^2+48x+c
yeah
what's the initial condition for distance?
384
no
what?
that would be the end point
recall that we used a positive acceleration
so we move from small to big numbers
ok
How do I do that 😭
how far has the ball moved if it hasnt moved?
set it equal to 0?
it hasn't moved
so
it must have
reached its end point
so 384 feet down 😭
wait
it never moved?
or it hasn't moved
?
tranquil pine
set it equal to 0?
yes
so what is c?
c=-16x^2-48x
huh?
c is a constant
do I do the quadratic formula
at time 0, x=0
c=0
yeah
so we have distance=16x^2+48x
soft zealotBOT
tranquil pine
how did you get that?
-48+-sqrt(48^2-4(16)(0))/2(16)
oh
c is -384
that's why
also its -b at the front
yeah I accidentally put ^2
hm
why does that answer look so akward tho
hehe
u sure that's right?
yes
if you know physics, you can check using kinematics
thx
.close
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tired bramble
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tired bramble
i need help pls
final saddleBOT
@tired bramble Has your question been resolved?
noble plinth
final saddleBOT
rancid idol
find the eq of the line
tired bramble
<@844944759217848363> Has your question been resolved?
no
slender oyster
try again in a new help channel
noble plinth
c=6?
rancid idol
then find slope. or plug in a point
rancid idol
no/
look up a tutorial on how to find the equation of a line
he other way is to plug in another point
y = mx + c
y = mx + 6
plug in something other than (x, y) = (0, 6)
For example (6, 0) is something u can plug in
or (5, 1)
and solve.
noble plinth
please can you tell me what it would be i watched videos on yt amd i keep getti ng wrong asers
rancid idol
y = mx + 6
Say we plug in (x, y) = (5, 1)
because that's on the line
Now what does the equation become.
noble plinth
1=m x 5 + 6
noble plinth
-7
rancid idol
1 = 5m + 6
Show all your steps in solving this equation
noble plinth
how would i solve m by dividing 5? an takeayw 6?
<@&286206848099549185>
@rancid idol
rancid idol
I gtg
noble plinth
.close
misty meadow
How do i find the values of c?
final saddleBOT
How do i find the values of c?
misty meadow
wouldnt this go on for infinity?
rustic musk
You're right, there is no real number c such that this equation has no real zeroes.
misty meadow
WHAT?
rustic musk
ikr
So you could say "no such c exists"
or you could write {} signifying the empty set
or you could write the symbol for the empty set which I can't write in text
plush holly
final saddleBOT
plush holly
I don't understand how taking the derivative of that left side gives the right side
If u' is 2x then shouldn't the answer be ln 2x
celest crane
$\frac{d(\ln{u})}{dx} = \frac{1}{u} \cdot \frac{du}{dx}$
soft zealotBOT
Kookiemon
celest crane
No matter what u is, it just winds up 1/u and then you apply the Chain Rule to u.
plush holly
No matter what **u** is, it just winds up **1/u** and then you apply the Chain R...
So if it's ln u^8 the derivative will be 1/u^8?
Wait but he has a 2x on top
soft zealotBOT
celest crane
plush holly
You cancel the things
So at first it's 8u^7 / u^8
And then you get rid of some u's
Oh i get it
It's like ln x = 1/x and since it's inside ln it's chain rule
vital crag
Just use log properties
celest crane
Yes.
plush holly
But when you do just ln x it gives you 1/x * 1 so just 1/x
celest crane
Or what riemann said.
celest crane
$\ln(x^{a}) = a\cdot \ln(x)$
soft zealotBOT
Kookiemon
plush holly
So it'll be 8 ln u
celest crane
But you are just learning about derivatives of the ln() function so it is a good idea to understand how to evaluate the derivative this way and apply the Chain Rule.
eg. ln(cos(x))
Get that step down first and then run. 😉
plush holly
I don't know why i can't think
This feels so hard for me even though i feel like it's so simple
celest crane
This is a new one to wrap your head around for sure. It's not like any math you've probably learned about before.
plush holly
I've always done good with math
But what I've been learning that i think it's the worst it's ever been
So if i wanna take the derivative of ln cos x
celest crane
Calculus definitely exercises your brain. 🙂
plush holly
It'll be 1 / cos x * - sin x?
celest crane
Remember this one when you start learning about integrals where you are essentially doing derivatives backwards. 😉
plush holly
Is there interns in this
celest crane
?
celest crane
Have you started learning about integrals yet?
plush holly
Yes I learned how to do them a bit
I don't know if we learned it with ln though
Maybe we did that today I'm not sure
celest crane
You will at some point. They should be relatively simple problems. You won't get to more difficult integrals until Calc 2.
plush holly
I am in calc 2
celest crane
Well, give it a week or two then. 😄
celest crane
So you are learning Late Transcendental Calculus then?
plush holly
I haven't heard of that
celest crane
LPT : A lot of people fail Calc 2 on their first try. It sucks but it happens.
Exponential and natural logarithms are classified as Transcendental functions.
There are two different schools of thought on when they should be taught though.
plush holly
My school of thought is that they shouldn't be taught
celest crane
Early Transcendental Calculus teaches exponents and natural logs before integrals.
While Late Transcendental Calculus teaches exponential and natural logarithms after the introduction of integrals.
plush holly
So it'll be 8 ln u
Wait how would I take the derivative of this one
celest crane
Of what?
celest crane
$\frac{d( k\cdot f(x))}{dx} = k \cdot f'(x)$
soft zealotBOT
Kookiemon
plush holly
Is it 8 * 1/u
celest crane
Yes.
oak arrow
could someone help me prove that (A and B) or ((C or A) and (not B)) is equal to A or (C and (not B)) please?
final saddleBOT
could someone help me prove that (A and B) or ((C or A) and (not B)) is equal to...
fossil geyser
@oak arrow What have you tried?
oak arrow
I have the instructor's answer, and I understand it (like follow the process), but I don't think i can formulate a proof like it
also quick question, so this is from discrete mathematics. In the class, it seems like i have to memorize logical equivalency statements, such as A and (A and B) is A. It seems like statements like these are vital to proofs. Do you think im supposed to memorize them? Or "know" them
fossil geyser
I think one of those ands is supposed to be an or?
I'm not sure if you need to know all the names of the specific "laws" and everything
But, you should be able to see sort of intuitively that
A or (A and B) is equivalent to A
for example
oak arrow
I think one of those ands is supposed to be an or?
oh you're right, i meant A and (A or B)
fossil geyser
that's true too, yeah
oak arrow
but i don't really see it, and i think that's why im having trouble with the proofs
fossil geyser
Those are the absorbtion laws
oak arrow
cuz i know if A is false, then the whole statement is false
rustic musk
Um are you sure that's ture
fossil geyser
Um are you sure that's ture
which one?
rustic musk
If A is false, then you should have ((C or A) and (not B))
rustic musk
And since A is false, C or A implies C
oak arrow
like i dont see intuitively how A or (A and B) is A
oak arrow
like i only see it if i do a truth table and i guess its not ideal to always do a truth table
fossil geyser
like i dont see intuitively how A or (A and B) is A
A or (A and B)
on the surface, this means either A is true, or A and B are both true.
Which means, you know for sure A is true, and you don't know whether B is true or false
So, it's equivalent to just saying A is true, and saying nothing about B
fossil geyser
That's the intuitive explanation. You can prove it with the distributive law
oak arrow
and since A and B are true, then A must be true as well
oak arrow
oh okay thank you.
Yeah sorry about that, I thought id just need to focus on the foundations before the proof
fossil geyser
Yeah no that's good
oak arrow
there's one more that I dont intuitively see (and I think this one is pretty vital for the proof):
im assuming the explanation for one will basically be the same for the other
fossil geyser
I think this is easier seen by applying the distributive law
oak arrow
So (A and Not B) or (B and not B)
fossil geyser
yes
oak arrow
oh that is easier lol
fossil geyser
lol yeah
So try to apply similar strategies to your problem
It's a bit longer, but start small, like inside the brackets
oak arrow
okay thank you. I think im just going to close this for now and completely retry the proof. Thank you so much
final saddleBOT
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solid acorn
when you are doing limit as x -> ∞ (√x^2+4)/(2x) why is the answer negative when it is just the ratio of the two leading coefficients
final saddleBOT
when you are doing limit as x -> ∞ (√x^2+4)/(2x) why is the answer negative when...
solid acorn
everything in the 1st () is in the square root btw
worldly vale
Who is telling you its negative
solid acorn
ap calc prep book
worldly vale
Can you show the question and what it says the answer is
solid acorn
how do I do the .text thing
to make it look readable
I'll put it in demos and take screenie
worldly vale
Just take a picture of the actual question
solid acorn
on computer
worldly vale
Okay that changes it completely
solid acorn
lim x -> - infinity
but isn't it just because of degrees so you don't need to plug in x?
worldly vale
The answer is you shouldn't blindly apply "ratio of leading terms"
For negative x, that expression is negative
So if x tends to -infty, the answer will be negative
A square root is always positive no matter what is inside it
solid acorn
but isn't the square root 4 both 2 and -2
worldly vale
No the square root of 4 is 2
But there are two solutions to x²=4
I can't speak on that without seeing an example
worldly vale
Your teacher is wrong
Unless they specified x being non negative
Eh which they probably did because of the sqrt(x)
Either way I don't see how that's relevant
Yeah thats what I've been saying
solid acorn
how do you know the difference between them they look the same
sometimes we have to write plus or minus and sometimes we don't
worldly vale
But there are two solutions to x²=4
.
When you apply it to both sides of an equation
You pick up a ±
If you just apply it to an expression, it's the principal root
solid acorn
are limits expressions
worldly vale
Do you see an equals sign?
final saddleBOT
worldly vale
:p
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Available help channel!
feral siren
For 26b what do I do next
final saddleBOT
For 26b what do I do next
feral siren
Is this correct
final saddleBOT
@feral siren Has your question been resolved?
late knot
final saddleBOT
late knot
How is (1-sin^2)/sin equal to that?
How is 1-sin^2theta equal to cos^2theta
Oh nvm
It’s also related to
Sin^2+cos^2=1
.close
final saddleBOT
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mild trout
Hey everyone, I’m not sure how to do this question. I’ve done simpler ones but I don’t know how to start this.
final saddleBOT
Hey everyone, I’m not sure how to do this question. I’ve done simpler ones but I...
mild trout
chrome cove
It's a chain rule
In this specific case you have g(h(x)) where
g(x) = || e^x ||
h(x) = || sin²x ||
Remember that sin²x = (sinx)²
chrome cove
What specifically is confusing you?
chrome cove
How do you normally do the chain rule?
chrome cove
Yeah, try with
y = || e^u ||
u = || sin²x ||
and it should work
chrome cove
Oh, click on it ahah
It should show some informations I decided not to show immediately
final saddleBOT
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crude dust
final saddleBOT
crude dust
whats the answer for the second one?
severe dawn
y=(-1) ?
tulip coyote
Surely you should be finding the x values?
severe dawn
well even if, y=(-1)?
tulip coyote
I did
...alright, fair enough - think the idea is that you sketch on top of that graph and get a guess of the solution rather than solving it directly, but whichever works 
Where does that y = -1 come from in the first one though?
crude dust
...alright, fair enough - think the idea is that you sketch on top of that graph...
wym
im sorry my first language aint english and this is my first time takin math in english so
final saddleBOT
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crude dust
.close
dense oracle
final saddleBOT
soft zealotBOT
dense oracle
i dont see where i went wrong
pls help thank
wait
im an idiot\
i did it right i just put t in the desmos
instead of x
🤦♂️
.close
rugged mesa
how did BD = 12? the triangle is equilateral? why?
final saddleBOT
how did BD = 12? the triangle is equilateral? why?
final saddleBOT
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final saddleBOT
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oak kraken
Is there a reason besides “Pythagorean theorem” that cosine gets more identities than sin?
final saddleBOT
Is there a reason besides “Pythagorean theorem” that cosine gets more identities...
oak kraken
All based on a^2 + b^2 = c ^2
gritty solar
Uh wdym cosine gets more identities
oak kraken
Just curious.. x gets more love than y. Or are the identities for both exactly equal?
oak kraken
Uh wdym cosine gets more identities
I will show you
gritty solar
wut
gritty solar
Those other two come from the first cosine identity
They just used sin^2 + cos^2 = 1
amber holly
All the cosine identities here are equivalent to each other
gritty solar
There's also the double angle formula for tangent in terms of sine
Which I conveniently forgot
oak kraken
Oh.. it doesn’t appear obvious.. from the first identity of cos the only way to get the 2nd and third identity is to use Pythagorean theorem
oak kraken
All the cosine identities here are equivalent to each other
It’s not simple algebra to get to the second and third identities
hybrid heath
Now you can have more sin(2theta) identities using the cos ones
gritty solar
Forgot the plus minus cough
oak kraken
Plus minus is determined by quadrant 2theta resides in
So its not plus minus in the traditional sense. Only that it changes based on the angle being +y or -y for sin
But still good practice to add +- in front of radical, just to not forget
oak kraken
Now you can have more sin(2theta) identities using the cos ones
I haven’t learned this one yet
hybrid heath
yes you have
oak kraken
Only these
hybrid heath
oak kraken
It's kind of the most important identity
What’s the identity called?
oak kraken
I don’t think it simplifies due to the - operator
hybrid heath
okay.. what about this?
oak kraken
Wait, does this simplify?!
oak kraken
I’m gonna guess sin for the first one, but just because it’s the closest identity on my list
hybrid heath
oak kraken
Not sure how this helps
hybrid heath
pythag theorem
oak kraken
okay.. what about this?
R^2
hybrid heath
What is the radius of the circle?
oak kraken
1
hybrid heath
mhm
oak kraken
When we say “simplify” in math, that means use less writing to describe it?
hybrid heath
oak kraken
Alright
hybrid heath
okay.. what about this?
So this is just 1
hybrid heath
which means this is sin
hybrid heath
Now you can have more sin(2theta) identities using the cos ones
And I use the same identity here (but with 2theta instead of theta)
oak kraken
which means this is sin
Why though?
hybrid heath
solve for sin in sin²+cos²=1
oak kraken
Ohhh
hybrid heath
As neon mentioned though I forgot the +- in the solution
oak kraken
Yes if I recall, sin can be Q1 (positive) or Q4 (negative)
For y
Yeah
Do you find it helpful to draw the unit circle?
Or memorized it all by heart by now
I still can’t remember x,y / pi / degree translation very quickly so I draw the unit circle with all of them
I know Q1 very well and just go with that to draw the other 3 quadrants
hybrid heath
Or memorized it all by heart by now
I memorized sin²+cos²=1. It's fundamental and used non-stop
I only draw the circle for tutoring
I don't know any of the trig identities like sum, double or half
I look them up every time. 
oak kraken
And there are Polar coordinates too, which I haven’t learned yet
hybrid heath
With time, my friend
oak kraken
I don't know any of the trig identities like sum, double or half
Don’t need to know them for exams?
hybrid heath
In a pinch, I use exponent laws to find trig identities
oak kraken
Well, I’m almost done all of Professor Leonard’s Precalculus videos .. 115 in total
I have watched all prior videos of his before Precalculus. On to his Calculus 1 videos after this
Luckily only about 35 videos for Calc 1
I find the real work is in doing problems tho. No hand holding anymore
So I gotta keep practicing daily
mossy kettle
I've tried doing this but then i got stuck on cos(thetha)(cos(theta)+1)=3/4
mossy kettle
idk how to use latex
amber holly
I think you factored too early there
mossy kettle
but i don't know what else to do once i got to 4cos^2(theta) + 4cos(theta) = 3
final tangle
note that this is a quadratic equation in cos(theta)
mossy kettle
so use the quadratic formula?
final tangle
doing the substitution x = cos(theta) (although unnecessary)
will give you something more recognisable
mossy kettle
note that this is a quadratic equation in cos(theta)
ah thanks for the tip, I've solved the question now theta = π/3, 5π/3, for 0≤theta≤2π
.close
tranquil pine
I need help with this one
final saddleBOT
I need help with this one
prime oar
where it says "the graph" does it mean f(x) or f''(x)
tranquil pine
I literally just finished typing 2 paragraphs to the teacher on how thats not clear
but i think f(x)
final saddleBOT
@tranquil pine Has your question been resolved?
tranquil pine
<@&286206848099549185>
modest birch
if it's the graph of f(x), then what do you think the second derivative tells you about concavity?
tranquil pine
if its positive/negative?
modest birch
so if f'' is positive, is f concave up or concave down?
tranquil pine
up?
modest birch
so if you wanted to figure out where the graph of f is concave up or concave down, what would you do with f''?
final saddleBOT
Available help channel!
inner wind
final saddleBOT
inner wind
I need a hint for this question
i cant seem to wrap my head around making a formula that can succesfuly give me the y values im looking for
question 2^
not 1
from my understanding each triangle has a base of 2 and increases its height by one each time
robust mulch
Consider finding g(1), g(3), so on
inner wind
meaning that the hieght lies on the odd cordinate and at any even number the height is 0
devout falcon
Hello? I need help
inner wind
Hello? I need help
checkout #help-3
inner wind
Consider finding g(1), g(3), so on
i found them and i see the relation but i cant seem to put my finger on it
i noticed the patern of odd numbers having the peak of the triangle and even numbers having a y value of 0
but im confused on how i can model a equation for it
robust mulch
You dont need to model an equation
robust mulch
Yeah but thats not the only way to do it
inner wind
how do you suggest about approaching it?
robust mulch
Hold on, what do you mean by modeling an equation
inner wind
like making a equation so that when we plug in
x=1 we get y=1 and x=3 --> y=2, x=5 --> y=3
robust mulch
We can do it for specific cases, but otherwise there is no equation that will get you exactly what you want
For example f(x)={0, if x is an even number
x, if 0<x<1...
For odd numbers, what is the equation?
inner wind
For example f(x)={0, if x is an even number
x, if 0<x<1...
i didnt really get this part
inner wind
For odd numbers, what is the equation?
im not sure
but how could we compute g(2023)?
i feel like im missing something and keep thinking of making a equation
robust mulch
Is 2023 an odd number
inner wind
yeah
robust mulch
So if we find an equation that will give you the output for g(2023), you can plug it in
so we know g(1)=1 and g(2)=3
Thats g(3)=2 whoops
inner wind
so we know g(1)=1 and g(2)=3
g(2) =0
inner wind
Thats g(3)=2 whoops
ah ok yup
robust mulch
do you know what g(5) is
inner wind
yeah g(5) would be 3
inner wind
ahhhhh
i see
its a linear one
so wed just need to find the slope?
and multiply that by x
robust mulch
Yes, you can model an equation of the peaks like that
inner wind
ahhhh i see
yeah now that i look at the questions diagram that looks better cause on paper i drew 3 of the same height triangle and just said they have different heights
ok ill do that then thnx man!
.close
green thicket
Daniel gets a job with a starting salary of $70,000 per year with an annual raise of $3,000. What will Daniel’s salary be in the 10th year? Write an explicit formula and then solve
The answer is $34,000 but i keep getting 97,000, i dont know what im doing wrong.
final saddleBOT
Daniel gets a job with a starting salary of $70,000 per year with an annual rais...
green thicket
yeah
silk saddle
please send the answer exactly
green thicket
the answer key says
im really confused
okay
give me a moment
my teacher gives us the answers so we can check when were done, but i have no idea how to get 34,000
rain compass
can you reread the question
are you sure they didn’t ask for the total raise in salary?
rain compass
my teacher gives us the answers so we can check when were done, but i have no id...
they made a mistake here too
it’s meant to say 67000 + 3000n
final saddleBOT
gritty solar
h(t) = 48
Yup
But we're concerned with position
yup
It's not h(t) anymore btw
And just solve it
It's a quadratic?
,calc 172/16
soft zealotBOT
Result:
10.75
soft zealotBOT
gritty solar
:/
Yeah so h(t) = 220 + 48
Because h(t) gives us the height from the origin
And it's being projected from 220 feet
So the height from the origin when its 48 feet above the point of projection is 220 + 48
h(t) gives us the height of the stone from the origin
Which is always 0 by convention
If the point of projection is 220 feet from the origin, and is 48 feet from the point of projection
Then the total height from the origin is 268 feet
Differentiate h(t)
No
Use the original h(t)
To solve the first part
Well
We equated h(t) to the position to find the time at which its at a certain position
That's something seperate
When you want to find velocity
You just need to differentiate the position
h(t)
h(t) is the position equation
Or displacement equation
final saddleBOT
@valid atlas Has your question been resolved?
final saddleBOT
@valid atlas Has your question been resolved?
autumn arrow
In some reports, the mean and coefficient of variation are given. For instance, one report gives the average number of physician visits by males per year. The average reported is 2.0, and the reported coefficient of variation is 2.9%. Use this information to determine the standard deviation of the annual number of visits to physicians made by males. (Round your answer to three decimal places.)
final saddleBOT
In some reports, the mean and coefficient of variation are given. For instance, ...
final saddleBOT
@autumn arrow Has your question been resolved?
autumn arrow
<@&286206848099549185>
digital steeple
2.9% is 50, and your searching for 100%?
digital steeple
cv = 2.9%, x = 2.0. solve for s.
digital steeple
you cant solve 2.9% = 100 s / 2 for s?
multiply by 2, divide by 100 and you have s = ...
autumn arrow
Like that? 😅
inner spoke
final saddleBOT
inner spoke
i understand that theyre trying to use the equation of the line along the perpendicular
but where is this coming from
ruby bramble
-(power of the point)/(sum of squares of coefficients)
inner spoke
-(power of the point)/(sum of squares of coefficients)
Can you explain more
ruby bramble
I dunno the derivation of the formula sorry
inner spoke
Okay i think ive found a way
The length is 3 sqrt (21)
So this
Then this
But i get two diff points
Is this correct?
final saddleBOT
@inner spoke Has your question been resolved?
inner spoke
Okay i think i see why i have two diff points
The distance im measuring from A can go in two different directions
In order to check which one is the point on the plane ,i need to substitute the point in the equation and check that way
wooden marlin
rule
wooden marlin
is this product rile
hidden bough
is this product rile
yes, product rule and chain rule
final saddleBOT
@wooden marlin Has your question been resolved?
wooden marlin
could some one explain how the factorisation is carreid out? i cant wrap my head round it
final saddleBOT
could some one explain how the factorisation is carreid out? i cant wrap my head...
fossil geyser
From the first line to the second, they multiplied both sides by x^4
From the second line to the third, they factored the left-hand side by factoring out xe^(3x-5)
wooden marlin
i see
thank you
for this question i differentiated it fine
for the second part of the question ive subbed x=e into the orignal y = equation
and got ahuge number
in the mark scheme its completly differnet
fluid sky
can u show ur work
final saddleBOT
@wooden marlin Has your question been resolved?
oblique seal
final saddleBOT
oblique seal
How to do Q7?
stark sun
Start by applying the laws of logarithm to simplify given expression
final saddleBOT
@oblique seal Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
rigid parrot
hi
soft zealotBOT
rio.
final saddleBOT
@rigid parrot Has your question been resolved?
shadow cosmos
it's just all values above x-axis
shadow cosmos
rigid parrot
what did u use to plot this
shadow cosmos
no it won't be area under that area under it
shadow cosmos
what did u use to plot this
just windows calculator
shadow cosmos
you can even use Desmos, it's professional
rigid parrot
what
rigid parrot
ok
shadow cosmos
now in this image the solution of your inequality is just the x part
rigid parrot
oh ok
rigid parrot
idk
shadow cosmos
what grade are you in?