#help-26
226100 messages · Page 236 of 227
We know that the minimal value of the function is -4, right?
And when x = 0 that the value of the function is -1
So the amplitude would be the value between these two
Is it (-4+(-1))/2?
So -5/2 🤔
When we write the absolute value of y_min, what does it mean?
Good point
No I mean like graphically
nothing
it’s the distance from that number to the x-axis
the amplitude of a sinusoid is how far away the maximum/minimum values are from the axis of symmetry
So 4?
yes
yes
Or is that not important
y=c, where $f(x)=A\cos(\omega x+\varphi)+c$
Mosh
here c=0, so y=0 is the axis of symmetry
Interesting
think, what is the maximum and minimum values of cos(x-v)?
So we've found A, now v?
yes
yes.
v = ±104,477 + 360n…
approximate, yes
,w solve cos(x)=-1/4
4*cos(180-v) = -1
cos(180-v) = -0.25
180-v = 104,477 + 360n
-v = −75,522… + 360n
Ah yes, same answer 😄
Yeah
Could you send me a link so I can read more about this, bc my textbook doesn't have everything in it
Like this ”axis of symmetry trigonometry”?
I only get stuff about trigonometric identities, you know anything @knotty osprey ?
function transformations as a whole as well probably
The axis of symmetry usually refers to graphs of polynomials, i think what your talking about is the sinusoidal axis (or the midline)
it’s the line that is perfectly in the middle of the maximum and minimum values of the sinusoid wave
so for your example, the maximum value is $4$ when $\cos(x-v)=1$ and $-4$ when $\cos(x-v)=-1$
lgargaro
so the midline would be the x-axis, the line y=0
the only time it would be different is if there was a constant being added/subtracted like here
@keen kindle Has your question been resolved?
Okay so I used this graph https://www.integral-domain.org/lwilliams/Applets/precalculus/trigTransformations.php
If the vertical shift is 1, does that mean the axis of symmetry is at y = 1?
👆
A should be -4
But it's essentially the same I think
For example, y = sin(x) + 2 has a midline at y = 2
I think that's the answer, the vertical shift is what determines the center line.
Thanks!
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so this is really puzzling me at the moment; of all the questions so far that I've gotten through so far, none of them have asked me do find/write the equation out myself, given only a single point. Also no where in the lesson portion (writing the notes, showing how to use X formula for a given problem, etc.) has given me an example of one of these and now I'm at a lose as to how to go about doing this question.
I'm probably wrong here, but it has a slope going through the x-axis and it has to pass through the given point
it does have to go through given point
and it does have to go through x-axis
but its more specific than that
here
parallel to y = perpendicular to x
so from here you should see that we need a vertical line that goes through that point
oh okay, yeah I had no clue what it was asking of me because like I said it never gave an example of one for me to later figure on my own.
So because it's asking for a perpendicular line, why is the quote, unquote answer the opposite of what it's asking for, exactly?
@idle oracle Has your question been resolved?
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Help?
find the slope
alr
then use either point to write an equation in point slope form
M.E.G. Yottachad
how do i find the a,b
(a, b) is a point on the line (which you already have 2 of)
I see
he already got slope
diffrent name depending on where and when you were taught in the world
.
.open
If 2x + y = 5, then 4x + 2y is equal to _______.
pls help me
im a highschool math student
@broken steeple Has your question been resolved?
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Ay yo
ah oki oki
but is my peeps from before here tho?
21.364212231655
how do I find the ref and the theata?
Dude
xD
xd
ndam your still here :DDDD
yes please
You already found the x and y of the r vector
yee
You need the angle
360-21.364212231655?
where did 21 come from
Vr
uhm seems weird
Just sketch a triangle that has the x and y of the r vector
then use trigonometric
aight bet
Tan^-1(8/19)
What
other math course
thats electrical class
u don’t even need to draw you can see the triangle in the picture
Yes
Tan= 8/19
tan-1 8/19
Yuh
22.83365418
Idk if its right but it should
aight
Thats all ?
What is the other angle ?
it says determine theata=
what does that mean ?
oh
What does theta mean
it says Determine the Theta ref angle from standart position
the circle with the uhh
thats what we did no ?
thing that cuts it
Theta ref=
theta=
that's the question
from standard posotion
Uhm
lemme reword for you
Do you know what is the magnitude?
hey ndam if you need to go then it's aight man
I can wait for another person yk
you need sleep
i dont know for the angles but the magnitude is the length of the arrow
so use pythagorean’s theorem
im sure you can solve these questions by your own just think well and apply basic math rules and you will 100% find the answers
I believe in u
U got this
thx have fun solving math stuff
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question: let a,b,c be positive integers such that bc/(b+c), ca/(c+a), ab/(a+b) are all integers, prove that gcd(a,b,c)>1
i've assumed the gcd to be 1 and tried multiplying/adding the 3 terms given and i don't think i've found anything useful
Do you want a hint?
given (a + b) divides ab, try pressing conditions on a, b for which $\frac{ab}{a+b}$ can be an integer.
Ansh
a+b is obviously bigger than either so it has to pull at least one prime factor from either number
is there anything else i should've gotten from that condition?
so gcd(a, a + b) or gcd(b, a + b) > 1?
i see
I'm only rephrasing what you said :o
and this is equivalent to concluding gcd(a, b) > 1
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It's C, correct?
100% = 1
50% = 0.5
1/0.5=2
2=200%
Just need to ask if i did any mistakes
Or am overlooking something
i think that's correct @paper umbra
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Im currently looking over a problem sheet I have been given, and I made the mistake of using an estimate for the coin toss, rather than the probability equation given in the second image (from solution sheet). Could somebody explain why the probability is:
@analog grove Has your question been resolved?
I've formed a probability mass function, but I dont understand how to form equation 14
you have the likelihood function i assume?
Yeah, that part is ok, just struggling with understanding how to form this equation from the pmf
f(x) = { p, x=1
1-p, x=0
and X_i is...?
A random variable
Im assuming at a coin toss i, Xi is the observation
right okay
in this case, X_i will be either 1 or 0
say for 1 it's heads and for 0 it's tails, yeah?
ye
so $Pr(X_i = 1; p) = p$
Camilleone
and $Pr(X_i = 0; p) = 1-p$
Camilleone
this is precisely your pmf but written in one line because $X_i$ only takes 0 and 1 values
Camilleone
I follow
yay great
The thing thats not clicking is why they are multiplied
well, you could really do anything as long as "it is p when X_i = 1 and 1-p when X_i = 0"
the simplest way is to use the fact that p^0 = 1 and (1-p)^0 = 1
al0-
yep
🙂
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I am trying to derive the second equation from the first equation. But I do not know how to proceed, could you please help me?
@carmine prism Has your question been resolved?
hint: it's an addition by zero trick. To the numerator of the first term, add $rB_0 - rB_0$. To the numerator of the second term, add $rB_1 - rB_1$. So on and so forth
Camilleone
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u can divide the similar radicals and get 18 alone right
$\frac{18\sqrt{2}}{\sqrt{2}} = 18$
Saccharine
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Show that if f is an odd function such that 0 is in the domain of f, then f(0) = 0.
I know how it came to be 0 but how do I write it down formally?
you can start right with the definition of odd functions
so I should just say that they are symmetric wrt origin?
no you dont have too go too deep in the symmetry of the graph or how it looks
the property f(-x)=-f(x) is always true for all x in the domain
ah I see
but we don't have a concrete function though
we dont need to
here, if we plug 0 into the equation, we get f(-0)=-f(0) dont we?
and what is -0? it is still 0
so basically your equation now becomes f(0)=-f(0)
you now essentially have an equation in terms of f(0) which you can solve for
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How do I do this
using index law
You have a common factor that can be cancelled
Do you know $\frac{a^m}{a^n}=a^{m-n}$
Sakata Yaksha
But what do I do with the ab
wdym
the one on the bottom is ab to the power of 2
that's a bit vague and may be misinterpreted
Wdym
the one on the bottom is ab to the power of 2
will most likely be interpreted as (ab)^2 which isn't what you have in the denomintor
if you wanted to express it in words, the denominator would be a times b squared
anyway consider properties of multiplication you could express your fraction as
$$\frac{a^3}{a} \cdot \frac{b^2}{b^2}$$
ℝamonov
idk
It's 2 am in the morning and I need to get this done idc as long as at least 50% of it is right
@sturdy holly Has your question been resolved?
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I've been dealing with partial differentiation but I'm stuck on this question and don't even really know where to begin to solve it
jeez terrible quality image though
Rewrite that as $ee^xe^y$
Beans
You differentiate partial by treating the other variable as constant...
Surely you can differentiate wrt $f(x) = e^{x+c}$ normally?
Shuri2060
wait so aren't they the same? ∂x and ∂y would both be e^x+y+1?
Wdym
Yeah forget that that's not necessary
ok sorry i was doing $e e^y \frac{∂}{∂x} (e^x)
aw didnt work
i was doing
which im pretty sure is just
and then i dont think it goes any farther then this?
i think this is the same result for ∂y as well? i dont see why it would be any different then ∂x
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how does one simplify this?
@remote grotto Has your question been resolved?
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i was thinking 20 about straight line = 180º
👀
I don't think I'm solving for angle measures
I think somehow, I gotta use Exterior Angle Inequality Theorem
x, and y are angles
👀
🙈
@mortal thunder sorry for the ping, but do you know a little about this problem?
I'm just tryna read 21 for context 
Ah
Well I could say that in this chapter, it introduces Exterior Angle Inequality Theorem, the Saccheri-Legendre Theorem,
having knowledge only about Euclidean Geometry, the first thing that strikes every time I look at the figure is that
AC = CC' => CAC' = CC'A and by exterior angle property: 2y = x 🤦♂️ but I doubt that's anything nearly close to doing this one
That would make sense
Hmmm
I've been having trouble with this problem and other ones
Took a break and studied abstract stuff for an exam ;(
I might just ask my professor about the problems I'm stuck on
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hi! can you help me finish the system of equations at the end?
or point me in a general direction - the numbers i'm getting don't seem right
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A pole leans away from the sun at an angle of 7° to the vertical, as shown in Figure 27. When the elevation of the sun is 55°, the pole casts a shadow 42 feet long on the level ground. How long is the pole? Round the answer to the nearest tenth. help
Figure 27?
right off the bat you should be able to find angle BCA
and then you can just use law of sines
pretty simple!
@whole sun
would that be sin55/7, sinB/b, sonC,42
and then do all the cross multiplication
not quite
let's let that point at the top of the vertical be point D
DBC = 7
so ABC = 90 - 7 = 83
then you can use law of sines
once you have found angle BCA
wat would the law of sines be
for this because i got it wrong when i tried doing it
or is it just the sin55/a
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An inverted conical container of height 3m and radius 1m is full of water, which is evaporating at a rate proportional to the water surface area exposed to air, i.e. $\frac{dV}{dt}=kS.$
(A) Show that the height of water in the container is h m, the bolume V and the water surface area S are $\frac{\pi h^3}{27}$ and $\frac{\pi h^2}{9}$ respectively (which i got)
(B) If it takes one hour to reduce the height of the water by half, find k and the time taken for the water to fully evaporate.
<@&286206848099549185>
@small rampart Has your question been resolved?
@small rampart Has your question been resolved?
@small rampart Has your question been resolved?
Maybe first try to make sense of the statements the exercise gives you. For example, if you have an inverted conical shape as the volume, you may draw something in order to represent the system you're working with
We are talking about the height that is at half of the conical shape
Proportionality seems to be the reasoning
@small rampart Has your question been resolved?
@small rampartHammmmmmm burgler 👀
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How does one do this proof
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hello
So I have this question
That I do not know how to solve
it would be appreciated if you help me out
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can someone see if i got 6) right
riemann
you have to use the quadratic formula
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i need help
please
what do you need help with
The question is, find the perimeter of an isoscleles right triangle with a 6-cm hypotenuse
and i have to use pythagorean theorum
what does an isosceles right triangel look like?
here i'll show
ok
set up the pythagorean theorem with what you have currently
yes
how do i combine x squareds
you don't have to, you already know that the two sides that you need to find are the same
ok
it would be 2a^2=36
yep
15?
number 16
oh right
i know the hypotenuse of the big one is 10
but i dont know what else i am supposed to do
oh
give me a minute
sorry to bug u
no it's all good
ok
yeah but we gotta find the length of the line AD or DB for that
never heard of it
awww
i think im overthinking it too
i got it
2√6
because there is a similar triangle theoru,m
if you rotate triangle CDB 90 degrees left at point d
i guess u were overthinking it
i overthink things too
i think im good for now
right now i am studying for quiz
and finding problems
i will tell you if i find hard one
7th, but i go to high school for 10th grade honors geometry
damn you must be smart
i'm in 11th
i skipped geometry so i'm not very good in that department
it is ok
i skipped 6th, 7th and 8th
lmaoo yeah
algebra is way easier than geometry for me
ooh i found a difficult
cant be good at everything
If the perimeter of a rhombus is 8√5 and one diagonal has a length of 4√2 find the length of the other diangonal
i'm not even gonna try to help you with that 💀
oh
did you forgor that stuff💀
ok
pre calc is hell
is it scary
it's like geometry algebra and trigonometry all together
yeah definitely
I probably can't help much but of course
thanks lol
Just apply Pythagorean theorem multiple times
but how to apply it on 1
sorry can't help i'm currently walking home
good luck
Do you know Pythagorean theorem?
No
no i mean squared
a^2 + b^2 = c^2
Apply that, starting with the smallest triangle
And so c is?
√2
Now do it again with the next triangle
That’s all there is
1 x √2
you have to keep repeating until the last one
yes but how to do 1 times √2
It’s still Pythagorean theorem
you have to use the theorem
There’s no multiplying
wait wait you are walking home? it is 5 o clock
oh
yeah i had to do corrections
1 + √2
ah yes
currently in a car right now actually
you drive the car?
yeah it wasn't really a homework 💀
oh
my friend does
tell your friend i said meow
sure
That sqrt(2) is the hypotenuse of the first triangle but it’s also the leg of the next one
yes
That’s the pattern
is it √3?
And then?
why
You forgot the root
im onto the last triangle tjough
The side was sqrt(3) and 1
That hypotenuse isn't 4
It's sqrt(4)
If you applied pythagorean theorem correctly
Did you get the other question?
find the perimeter of a rectangle whose dagonal is 17 and base is 15
yes i did
it is being √5?
for the last one
Yes
ok
Apply pythagorean theorem
1 and 514
You asked what numbers go into 514 and I gave you some
2 is not a perfect square
If you applied the formula right, sure
yaaaaaaay
Still not the end of the problem though
No
You have the sides
Just add them
Did you use a calculator correctly?
what did i do
8 + 8 is 16?
15 + 15 is 30
30 + 16 is 46
AM I DOING SOMETHING SuPER DUMB AGAIN
So then the question is, why are you second guessing yourself if you did everything properly?

um
i thought that um
yeah
um
yeah
.
ok
next problem
find the peremiter of a rhombus with diagonals 12 and 16
That one, don't know
ah yes
oh no
he arent respond
he must be DEAD
NOOOoooooooo


ok
so i have new problem
find the length of the diagonal of a square with perimeter 12 cm
ok
hm
obvious?
unfortunately no
did he say, what a weird child
no i'm a he
my friend is a she
so
yeah
ah
i highly doubt it
yes
this
draw it out first
hmm, send a picture
d r a w i t
paste it?
oh
oh no the screenshot shows my name 😦
dont look
at the top left corner
top right i mean
ok
ok so
i should have been more careful 😮
equilateral triangles sides' measurements are the same right
yes
here ill sketch it
ok
i appreciate it
i am studying
ah ok
what am i watching
idk
did u watch
isnt it epic
but u gotta turn it on full volume
oh wait
i gotta go
i am finished for to day
niceee
same
no haha
the frog dude
reasonable
i am frog dude
i see
and i wear hat
and as an ultimate reward for helping me...
do you have a chromebook
for school and stuff
because i know how to play fortnite, and rocket league, and basically any console game on it
make a geforce now account
and connect your epic games account
and then you select a game
and thenplay
ok anyway good bye
i'm good lol, good luck with your stuff though
ok bye bye
do .close if you don't have more questions
sure
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can someone help me with 6
@real sierra Has your question been resolved?
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how is this incorrect?
look at the square root
have u made the problem simpler?
actually i think you just forgot that your sub was x = 3sin(theta)
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The one with the blue arrow is right and the one with the red arrow is wrong. Ive tried 45 and its still wrong haha
@uneven talon Has your question been resolved?
Ive tried again -63 and 45 just to be sure and its wrong
@uneven talon Has your question been resolved?
Do the blue one first with rules of integration endpoints
Properties 1-6 here
https://tutorial.math.lamar.edu/classes/calci/defnofdefiniteintegral.aspx
In this section we will formally define the definite integral, give many of its properties and discuss a couple of interpretations of the definite integral. We will also look at the first part of the Fundamental Theorem of Calculus which shows the very close relationship between derivatives and integrals.
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woo alrighty
I just wanna make sure I have the right setup for this
one minute while I actually set it up lol
2 = 4
Devide by 2
1 = 2
Raymeen hypothesis solved
wha
oh sorry
I need to find the volume in the enclosed region rotated about x=1
sorry. forgot to also copy the instructions to the problem lol
No idea, out of my leauge, lol. Good luck though.
lol thanks
hopefully a calc1 person can help
is this the answer (once I actually solve the integral)?
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Can someone help solve c
,rotate
hm?
wait
so how did you do (b)
