help-17

[wicked shard]

Jk yeah

[ruby kernel]

ok good job dream team

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[fading cove]

i'm sorry it wouda been easier if you just sent a pic of the instructions

visually yk

[ruby kernel]

👌

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[prime breach]

I'm trying to solve this rational equation division problem, I think the solution I got is wrong. Wolfram alpha is giving me another result and I think it might be because I got one of the roots wrong somewhere while doing factorization

[prime breach]

I seek help with pointing out mistakes and if you need a clearer picture or transcribing into another format for clearer reading, I don't mind doing it

Noticed a typo while dividing x^3 -4x^2 - 28x - 32.
i wrote -12 instead of 12 as the result from -2 . -6

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[hoary mortar]

can h be infinity? we were in class on friday and mr. peters said that h is in [0,infinity]

[hoary mortar]

i don't get why h can be infinity

these are mr. peters' notes

i thought infinity wasn't a number

[loud walrus]

It is not infinity, it is in that interval

It means h>=0

Also, the ] is not used for infinity, but ) instead

@hoary mortar

[sly sierra]

[0,infinity] means any positive real number or positive infinity

if indeed mr. peters wrote $h \in [0,\infty]$,then $h$ can be $\infty$

[twin meteor]

Bungo

[hoary mortar]

but infinity isnt a number

?

sorry my aunt called me

back

[sly sierra]

https://en.wikipedia.org/wiki/Extended_real_number_line

[hoary mortar]

so are you saying mr. peters made a mistake

[hoary mortar]

but mr. peters said that we can't plug in infinity

[sly sierra]

do you have a screenshot or something so we can see the context?

[hoary mortar]

this was the gist of what mr peters was saying

he was trying to tell us that not every function is differentiable

it is just this one thing i dont understand

[sly sierra]

yea i'm pretty sure in this context it should have been [0,infty) and (-infty, 0]

[hoary mortar]

okay thank you! I will tell mr. peters

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[median vigil]

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[hoary mortar]

nothing is impossible if you try hard enough

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[timber prairie]

why is this not -2?

[timber prairie]

My process was

wait i figured it out

oops

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[jaunty haven]

can somebody help me step by step on this

[shrewd moth]

get all x's to one side

[jaunty haven]

so 2 = sqrr x-3

[steep crater]

i think let x = a^2 then square the equation

[shrewd moth]

not how square roots work

[steep crater]

so the equation becomes a+2=sqrt(2a^2-3)

[jaunty haven]

ive been stuck on this problem I am so cofnused

[shrewd moth]

it will just stay as:

2 = rad(2x-3) - rad(x)

[steep crater]

and then square it

like square both sides

[jaunty haven]

so what do I do from here

[short bobcat]

Yeah

[shrewd moth]

lol dont use subsitution man

[steep crater]

why

[shrewd moth]

he obviously doenst understand whats going on

subsitution is just gonna confuse him even more

[steep crater]

okay i guess

[shrewd moth]

square both sides

this means squaring both sides

so what happens to the rads?

[steep crater]

but that would make it harder

[jaunty haven]

so x+ 4 = 2x-3

[steep crater]

you would get a very ugly term 2sqrt(x(2x+3))

but it might still work

[shrewd moth]

heh?

[jaunty haven]

im so confused abot how to do this

[shrewd moth]

how are you still getting a sqrt in theere xd

sorry im just trying to deal away with mr death man lol

[steep crater]

oh oh

...

i think substitution would be more intuitive but okay

yeah both methods work

[shrewd moth]

well no not really

you would be squaring the entire side

aka (radx + 2)^2 = 2x - 3

do you know how to foil?

[jaunty haven]

I know how to foil

so what do I do

ah so I do that

[shrewd moth]

ye, foil out the (radx + 2)^2 term

[jaunty haven]

so i foil this -- aka (radx + 2)^2 = 2x - 3

[shrewd moth]

well yeah you just foil it out then simplify, then sqaure again, then simplify, then solve

[rotund arrow]

FOILING you will get:

Then simplify:

Combine the x and the constants:

[winged stream]

Where did u multiply 2ab ?.

It should be 4rootx? Right?

[rotund arrow]

yeah it should i messed up

one sec

[winged stream]

Yup

[rotund arrow]

then square both sides of equation to finish

[ebon sable]

Chicken

[winged stream]

U get quadratic at the end find x by that and take a positive value

[winged stream]

Sup?

@rotund arrow

[rotund arrow]

yeah?

[ebon sable]

Hi

[winged stream]

Hey I have one question to solve can you help

[rotund arrow]

sure

[ebon sable]

Oh my I just said it radomly

[winged stream]

2nd question? I don't understand what method to follow

[rotund arrow]

are you familiar with power of point?

^In this diagram we have BA^2=BC*BD

For your problem it's the same idea. Since BDC is a right triangle, you can circumscribe a circle about it.

[winged stream]

No what the ?

[rotund arrow]

Then since AB is tangent to the circle it's AB^2=AD*DC

[rotund arrow]

ok one sec

[rotund arrow]

did you get this as your diagram

[winged stream]

Yes

[rotund arrow]

are you familiar with finding lengths in a circle?

[winged stream]

Meaning?

[rotund arrow]

like finding the length of chords, secant lines, and tangent lines

[winged stream]

Yeah

[rotund arrow]

so in this problem AB is tangent to the circle, and you also have one secant line. what's the relationship between these segments?

[winged stream]

the square of the length of the tangent equals the product of the length of the secant with the length of its external segment is it

[rotund arrow]

So AB is the tangent. So if we take AB^2, we get that this equal to the product of what two other lengths in the diagram?

[winged stream]

Ac *ad Thanks bud

[rotund arrow]

you're welcome!

have a good night!

[winged stream]

Night?

[rotund arrow]

or day wherever u r

[winged stream]

Its morning in India lol

[rotund arrow]

do u still need help?

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[jaunty haven]

no I think that was it the step by step explanation helped

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[jovial parcel]

sorry to ask simple question i havent use cosine rule since 2 year i forgot... how to use cosine rule here to find AB?

[warm vine]

i dont think cosine rule will work here

[twin meteor]

amitt
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[warm vine]

angle D isnt given

[jovial parcel]

yeah that why im confused because im watching video and this guy used cosine rule and it dont make sense to me

[warm vine]

oh yes that works

2rAB is missing in denominator tho

[jovial parcel]

yes he did that but i dont understand how he used the formula

can u kindly explain : -)

[jovial parcel]

AB^2 = r^2 + r^2 - ???

[warm vine]

try to write for angle X just like the image did for angle A

[jovial parcel]

ohhh thank u i got it :- ) thx

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[silk rampart]

How do I even begin with this

[vast shale]

y = mx + 1

use discriminant to find m

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[silk rampart]

Discriminant?

[silk rampart]

of what equation

[vast shale]

put mx + 1 instead of y

[silk rampart]

got it

next?

i think i have the tangents now

[vast shale]

what did you get for m

[silk rampart]

0 and -4/3

[vast shale]

can you find the angle bisector

[silk rampart]

yeah

@vast shale

[vast shale]

find the slope of blue lines

the red lines are perpendicular to blue

[silk rampart]

2 and -1/2

slopes of red are the same as the blues

[vast shale]

then you have m1 and m2

[silk rampart]

okay can you explain why did you ask me to take out the bisector

oh lol sorry im an idiot

haha

I see now

Yep

@vast shale thank youu

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[tame river]

Do I have to worry about that 3 that is outside the () ?

[bronze osprey]

the 3, or any vertical stretch, only changes the y-intercept

and the horizontal asymptote

so 1), 3), and 4) remain the same without the 3

[tame river]

alright thanks

[bronze osprey]

no worries!

[tame river]

how exactly?

[bronze osprey]

so like a vertical stretch only changes the y-values

by scaling them by some amount

[tame river]

like -8/15 * 3 ?

[bronze osprey]

so out of these questions, only 2) and 5) have to do with the y-values

[bronze osprey]

yep

I mean the concept is right

[tame river]

k. -8/15 * 3/1

[bronze osprey]

,calc 3 * 2 * -4 / (3 * -5)

[twin meteor]

Result:

1.6

[bronze osprey]

basically sub x = 0 into the whole thing and you get this

[tame river]

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[white gulch]

I am trying to visualize the mandel brot set in Desmos but in doing so I am getting an entirely different shape

[white gulch]

This is what is constructing it

Where capital A or B is actually some particular x and y coord on the plot

Is there something wrong which is giving me this geometry instead of the mandelbrot bulb?

(A1,B1) is plotting the visual where the color is decided by rgb(255(4-sqrt(A2^2+B2^2)),0,0) i.e. red when within a radius 4 of the origin and black when outside there, (A2,B2) is another space of points which is being "mandelbrotted," and (A3,B3) which just stores the points temporarily so the complex multiplication works

The red/black points are (A1,B1), the blue are (A2,B2). Why no mandelbrot 😭 ?

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@white gulch Has your question been resolved?

[white gulch]

It seems clear that I am plotting something correctly since iterations of z appear bounded when c is in the red but it isn't the Mandelbrot bulb so my error must be in the my definition of z_n+1

How is the Mandelbrot set defined? Why does my definition not work?

[white gulch]

.close

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[jade rapids]

hi can someone help me with part (ii) of this question:

[jade rapids]

these are the answers but I don't understand how they got the first equation in it:

[dull bear]

The "inserted" cone would take up the volume of 1/8th of the whole original cone

7/8ths of the bottom cone would be the water, and 1/8th would be replaced with that part of the upper cone, if you get me?

[jade rapids]

yep i understand that

[dull bear]

Ah, did you mean this part here then?

[jade rapids]

nooo i get the 1/8 and 7/8ths thing but using that how did they get this equation?😭

using this formula?

[dull bear]

Well, as per above, you'd basically have a "sub-cone" of this volume in the larger cone displacing water, but the water it displaces...

...is 1/8th of the original volume of water (remember the cone was filled completely, so it had pi * h^3/3 cm^3 of water to begin with, but it loses an eigth of that to the inserted cone)

[jade rapids]

OHHHHH

so its basically making the volume of a new cone equal to the volume of the water displaced from the original cone?

[dull bear]

Yep, it's like if you went to the beach, dug a hole and let it fill with water instead

[jade rapids]

🤩

[dull bear]

Oh yea, also, did you get the thing we were doing yesterday btw?

[jade rapids]

omg yes i was just about to have a look at that one

im so sorry i had to go to sleep!

[dull bear]

Awwww, don't worry, I know those ones (in fact I really should get some rest at some point myself )

As long as you're alright with it

[jade rapids]

ok im gonna have a look at it now

[dull bear]

If you want a link and haven't found it #help-22 message

[jade rapids]

omG THAnk you so much for picking up on the squared term!!!

it worked out

I literally can't thank you enough for the amount of times you've helped me!! 😭 ❤️

[dull bear]

Awwwww you're a pleasure to work with, it's always great to see you

[jade rapids]

🥺 🥺

[jade rapids]

hey!! sorry quick question about this but how did they get rid of the h in the equation?

[dull bear]

As in getting h = 2l, or?

[jade rapids]

like i see how it is supposed to be the volume of the sub-cone but how exactly did they get this formula

[jade rapids]

using this

[dull bear]

It isn't so much that they used this formula, more that...

[jade rapids]

oh

[dull bear]

...they just argued that the "sub-cone" would have the same volume as the amount of water lost

[jade rapids]

oh but is this like the volume formula of a cone?

oh so they used something like this instead of the formula?

[dull bear]

Basically like that, but for one, because you know the "semi-vertical angle [is] 45 [degrees]", you know that the radius and the heights must be the same

So e.g. for the big cone here, you see that you kinda have a triangle which is effectively a 45-45-90 one, and which has non-hypotenuse sides h and l, but of course that forces it to be isosceles and so h = r (for the "big cone")

It's a similar idea for the "subcone", for the amount of the other cone you've dipped in, it's kinda like you've added a small cone of height l (and, by the other angles having to be 45, you know its radius is l too)

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[open valve]

.reopen

[open valve]

help me to mirror the graph according to the straight line y=x

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[open valve]

.reopen

[vocal sleet]

✅

[open valve]

<@&286206848099549185>

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[open valve]

<@&286206848099549185> \

[vast shale]

oh yeah

i forgot about this

which graph

@open valve

[open valve]

all of them i just dont know what to do with them :/

[vast shale]

there are 6 graphs

Graph 1: Still a straight line, but swap the axes.

Graph 2: Curve flips to grow horizontally instead of
vertically.

Graph 3: Horizontal part becomes vertical, slanted part mirrors.

Graph 4: Starts horizontally, then rises steeply.

Graph 5: Parabola turns sideways.

Graph 6: Curve rises horizontally after the flip.

Just swap (x,y) to (y,x) for each graph!

[open valve]

could you please paint the lines in some program or something because i really dont understand these y and x and graphs and all of that

it would really help me

@vast shale

please

[vast shale]

I honestly don't know how 😭

ill try

[open valve]

or just on paper and send photo please it would help me a lot

[vast shale]

i suck at graphing

[open valve]

please bro it would really help me

[open valve]

is this good ?

[vast shale]

i think so

let me check

i think thats good

[gentle sleet]

only 6 looks correct here

[open valve]

i fixed these two ?

what do you think @gentle sleet

[gentle sleet]

yea looks right
for number 2, maybe put the line closer at the top parts

[open valve]

thanks i will, and can you help me with number four because i really dont know what to do there

[gentle sleet]

pick some points on the curve

[open valve]

like this ?

[gentle sleet]

swap their x and y
then connect those points

[gentle sleet]

lemme check

[gentle sleet]

that's not right

[open valve]

can you show me how to do it ?

[open valve]

like this ?

[gentle sleet]

the general shape is right
but it's not that great

pick some points, like these ones

flip their x and y coordinate

then approximate the rest

[open valve]

oh okay thanks and can you help me determine D(f) and H(f) for the functions.

[gentle sleet]

not sure what that means
is D(f) the derivative of f?

[open valve]

d is x and f is y , f is like f4 = number of the graph

for examble D(f4) (4,-5), H(f4) = (-1,6)

[gentle sleet]

is it domain and range?

[open valve]

yes

[gentle sleet]

ah, for D(f), since it's one unbroken curve,
you can just look at the minimum x and maximum x
that'll be your domain

[vocal sleet]

@open valve Has your question been resolved?

[vocal sleet]

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[prisma linden]

can someone guide me through this

[vocal sleet]

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[prisma linden]

.close

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[dim vessel]

Hello i already know the answer to this and yes its harmonic. Tho idk how did it became harmonic can someone pls help me how did it became harmonic😭

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[finite seal]

I need help calculating all the different possible states of a problem, the problem is there is a maze with 808 open spaces which looks like the image i am sending below. in this maze the black parts are places where a player can move and white are walls no one can step over. with a probability of 0.0085 of a gold coin spawning on an empty space and 2.5 of a slime spawning on an empty space.

[vocal sleet]

@finite seal Has your question been resolved?

[kind narwhal]

if series is in hp then the series of reciprocal will be in arithmetic prog. then 7/15 - (-5) = 17/15-7/15=10/15 (common differences of the ap)

[dim vessel]

can i dm u?

[kind narwhal]

yeah sure

[dim vessel]

can u accept my friend request it its fine, it says i cant message u

[kind narwhal]

yeah

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[open ridge]

someone please tell me why?

[raven zephyr]

??

[open ridge]

nvm

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[ruby aspen]

A right circular cone is cut by a plane parallel to its base, resulting in a smaller cone at the top and a frustum (the portion of the solid that remains) below the cut. The height of the original cone is 15 units, and the radius of the base of the original cone is 5 units. A circle with radius 2 units is drawn on the base of the original cone. A line tangent to this circle and passing through the vertex of the original cone intersects the base of the smaller cone at point P. Find the distance between point P and the vertex of the original cone.

[ruby aspen]

<@&286206848099549185>

[vast shale]

!status

[vocal sleet]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[vast shale]

also it might be beneficial to draw this out

[vocal sleet]

@ruby aspen Has your question been resolved?

[ruby aspen]

1

[vast shale]

Did you draw it out

[ruby aspen]

i am not experienced in cones and that's what my mind imagined

[vast shale]

the diagram looks to be correct to me

[ruby aspen]

It's said that a plane parallel to the base of the cone cut the cone to two pieces , the frustum and a smaller cone.
the height of the original cone = 15
the radius of the original cone = 5
a circle is drawn at the base of the originial cone with radius 2, a line tangent to that circle passes through the smaller cone base at point p and all the way to the vertex of the original cone ( which i believe the same as the vertex of the smaller cone )
what's needed is to find the distance between such vertix and point P

@vast shale

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[hushed portal]

Guys how can we find A from this graph?

[vast shale]

what is A ?

[hushed portal]

Idk we have to find it

I only know the vertex cause it’s the first point on the graph

[cold hedge]

it’s the stretch factor in y = a(x - h)^2 + k

i’m assuming

[hushed portal]

Yeah that equation

[cold hedge]

okay plug in h and k

what do you get

[hushed portal]

Y=a(x-1)^2+4

[cold hedge]

alright now choose an (x, y) value on the graph and plug it in

then solve for a

[hushed portal]

I wanna do 4,8 but how do you plug it in

Like when you say plug it in wdym

[cold hedge]

x = 4, y = 8

8 = a(4 - 1)^2 + 4

just plug in to the equation

[hushed portal]

Ohhh

Okay one second

I got 4/9

[cold hedge]

alright

so a = 4/9

[hushed portal]

Dang that was it?

[cold hedge]

then just write in the final equation in the last box and you’re done

[cold hedge]

yep

[hushed portal]

I was tweaking for nothing 😭

[cold hedge]

it happens

[hushed portal]

Thanks bro 🙏

Oh wait hold on can you help me with something else?

How can I tell if this is even odd or neither I forgot what we plug in

I think it’s even cause it’s a parabola but I gotta prove it algebraicly

[minor marten]

do you remember what even and odd mean

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[dim moss]

can someone verify my proof. this is hyperbolic geometry btw

[dim moss]

the question is (1b). the highlight didnt move with the text

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[dim moss]

<@&286206848099549185>

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[viral igloo]

hi, can someone explain me why the lim sup in the explanation below is 1 - x²? thank you https://math.stackexchange.com/questions/3422454/limit-of-sequence-of-functions-f-nx-nx1-x2n

[viral igloo]

ah no i understand

.close

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[wraith imp]

can someone explain how this isnt the answer

average rate of change is (f(1,2)-f(3,1))/√5

[(1 + ln2) - (9 + ln1)]/√5

which is approximately -3.27

[chrome steppe]

Where is sqrt(5) coming from?

Or rather, what is b-a?

[wraith imp]

b-a is |(1,2)-(3,1)|

at least i believe so?

which is sqrt5

[chrome steppe]

Sorry I'm quiet.. assumed that might have been the issue before I punched it into my calculator.. yeah, it's sqrt5..

And.. now I'm confused, because I'm getting the same answer as you

[old badge]

Hi I need help

[oblique kettle]

youre comparing it to how we compute the avg rate of change for the single variable functions

its not the same imo

i tried another method, i got 8.17

but i dunno if its correct

[vocal sleet]

@wraith imp Has your question been resolved?

[wraith imp]

sorry its not correct- but what was the method you used?

[oblique kettle]

the magnitude of the gradient

wait ill give it another shot

4.06?

[wraith imp]

not correct...

[oblique kettle]

this tough lol

[wraith imp]

in the first place, shouldnt the answer be negative?

f(3,1) > f(1,2)

so we should expect it to be negative

[oblique kettle]

yeah yeah, i was trying something related to the gradient

true fr

you got unlimited attempts?

i rlly want to find this lol

[wraith imp]

i have 12 more attempts

[oblique kettle]

-8.17 , -4.06

[wraith imp]

neither are correct :/

[oblique kettle]

omgggg

yknow, i tried googling this

no formula for average rate of change for 2 variable function lol

[wraith imp]

my textbook has an example

this is the answer

but this is just [(arctan(3) + 1) - (arctan(1) + 4)]/sqrt(5)

[oblique kettle]

interesting

[wraith imp]

and thats [f(3,1) - f(1,2)]/sqrt(5)

[oblique kettle]

mhm yes

[wraith imp]

so im legitimately not sure how -3.27 isnt the correct answer

[oblique kettle]

yeah weird :/

maybe its something silly, you tried -3.26

no way though..

[wraith imp]

i did try it :/

am i missing something?? i dont get it

[oblique kettle]

me neither

+3.27?

lol

[wraith imp]

not correct-

[oblique kettle]

at this point im thinking theres some typo in the problem

[wraith imp]

same...

[vocal sleet]

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[vivid hinge]

where do I go after I plugged in the x's

Im lost

[wraith python]

What have you done so far?

[wraith python]

.

[vivid hinge]

Nvm I got it right

well

actually i have a question

Ok so after i did synthetic division all the way

I ended up with (8x^2+2x-3)

how do i factor this into (_ _ _ )(_ _ _ )

[wraith python]

Several ways to do that which you should hopefully know. The simplest to me would be to use the Quadratic Formula.

[vivid hinge]

Ok thanks 👍

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[late jetty]

How can I show
arg(x) = Im(ln(x))
where
arg (complex number argument)
Im (imaginary part)
ln (natural logarithm)
Or the condition of this being true if it isn't always so.

[late jetty]

I figured this should be equal for at least some values and it helped me derive something but I completely forgot to check when this equals more formally

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@late jetty Has your question been resolved?

[late jetty]

<@&286206848099549185> has it been 15mins?

[spiral turtle]

@late jetty so Arg(z) is the single valued argument of a complex value. This is defined to be in the range (-pi, pi].

arg(z) = Arg(z) + 2πK for some integer K, and is multivalued.

Similarly, ln(z) is also multivalued in exactly the same way.

If we express z in polar form as z = r e^(it) then ln(z) = ln(r) + it

Then we get Im(ln(z)) = t

Which is exactly the argument of z, and you can get any possible value by choosing a different branch

[late jetty]

Oooo ty !!!!

Nice explanation

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[modern sail]

How do you do this

[modern sail]

at least one of them

please

[alpine flame]

series using sin(x) as variable, then series sin(x)

$1+sin(x)+\frac{sin^2(x)}{2}$

[twin meteor]

溯灵

[alpine flame]

then series sin(x) at 0 to get

[modern sail]

wait so i can just plug the sinx function into the e^x maclaurin series?

[alpine flame]

for most series thats ok

[modern sail]

ok thank you

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[ruby aspen]

In a triangle $ABC$, the angle bisector of $\angle A$ intersects $BC$ at $D$. Let $\mathbf{a}$, $\mathbf{b}$, $\mathbf{c}$, and $\mathbf{d}$ be the position vectors of points $A$, $B$, $C$, and $D$, respectively. Given that $\frac{BD}{DC} = \frac{AB}{AC}$, and $\mathbf{b} \times \mathbf{c} = \mathbf{a} \times (\mathbf{b} + \mathbf{c})$, find the measure of angle $BAC$.

[twin meteor]

ZiXO

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[ruby aspen]

<@&286206848099549185>

[ruby aspen]

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[wanton shard]

Hello

[wanton shard]

I need help with this problem

[misty trail]

ah this is a good one

you still need help?

[wanton shard]

Yes

[misty trail]

alright one sec lemme cook something up

[wanton shard]

Ok

[misty trail]

it is just one rectangle correct? no seperation?

[wanton shard]

Yes

Only one

[misty trail]

okay so do you know the first step?

[wanton shard]

No

[misty trail]

You need to look at the coefficients

you see 35, 21, 28, and 7

[wanton shard]

Yes

[misty trail]

not 7 oops

ignore that

[wanton shard]

Ok

[misty trail]

now becasue you want the GCF, you look at the smallest power term for both a and b

so for a the smallest would be a^2

for b the smallest would be b^2

now the 7 I mentioned earlier comes into play here

this is the gcf of the three coefficients

now when you combine this gcf of 7, with the smallest terms you get:

7a^2b^2

and now you have the magic term which lets you factor out to find the other side length

so factoring 7a^2b^2 out of the long equation

you get 5a^2b^2 + 3b + 4a

so the two missing dimensions are as follows:
Dsub1 = 7a^2b^2
Dsub2 = 5a^2b^2+3b+4a

[wanton shard]

Thabks

[misty trail]

yes sir

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[vast shale]

Image
i started proving this by:
x in (g o f)^-1 (H)
(g o f)(x) in H
on left ^
and right:
x in f^-1(g^-1(H))
f(x) in g^-1 (H)
(g o f)(x) in H
both came to same
and conversely it will be same too so yeah hence proved?

[river minnow]

Yeah, once you show the set on the left is a subset of the set on the right, you will be done

[edgy zodiac]

How old are you guys please?

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[vast shale]

me?

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[lone tangle]

I found the period which is 2pi and found the phase shift which is -7pi/6<x<5pi/6 but I am having trouble finding the other 3 points inbetween. Do I count by pi/6? Im not sure what to do.

[bronze osprey]

you could just note that there is a maximum of sin(x) at x = pi/2

which gets shifted to x = pi/2 - 7pi/6

[bronze osprey]

similarly the min gets shifted to x = 3pi/2 - 7pi/6

with the positions of the max and the min that should be enough info to sketch

[bronze osprey]

!help

[vocal sleet]

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[vast shale]

someone please help me with this

[bronze osprey]

#help-20 and ask

[vast shale]

ty

[bronze osprey]

oh you have to find the x-intercepts as well, so note that sin(0) = 0
so if sin(x + 7pi/6) = 0, x = -7pi/6

then that's all the points the question wants

[lone tangle]

Thank you!

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[vocal sleet]

@untold arrow Has your question been resolved?

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@untold arrow Has your question been resolved?

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@untold arrow Has your question been resolved?

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[vast shale]

because e^(-t²) is always positive so, integral will be positive from x to 0 for a negative x and hence it's opposite will be negative

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[vocal sleet]

Please don't occupy multiple help channels.

[tawdry canopy]

(d)

$fg(x) = 4(x+3)^2-7$

[twin meteor]

e_waste

[tawdry canopy]

my work: since f(x)'s range is $x \leq -4$

[twin meteor]

e_waste

[tawdry canopy]

then $g(x) \leq -4$

[twin meteor]

e_waste

[tawdry canopy]

$2x-3 \leq -4,x \leq -\frac{1}{2}$

[twin meteor]

e_waste

[tawdry canopy]

since the symmetry of fg(x) is -3

so k = -3

<@&286206848099549185> still I'm a bit unsure about the answer

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[bright lake]

hello

[bright lake]

I have an exam on surds

I cant understand how to solve them

[lyric relic]

what are surds ?

[cyan shadow]

square roots it appears

uhh whats the latex command that brings up the radical rules

here we go anyways

@bright lake check out these rules, try out the problems, then post/comment when stuck

[lyric relic]

https://tenor.com/view/loveu-te-amo-teamopreta-gif-20099361

[bright lake]

basically irrational square roots

[lyric relic]

do you know if $e\pi$ is irrational ?

[twin meteor]

everg

[bright lake]

ya its irrational

[bright lake]

<@&286206848099549185>

[lyric relic]

so can you answer to that famous question https://math.stackexchange.com/questions/28243/is-there-a-proof-that-pi-times-e-is-irrational I would be very glad

[lyric relic]

are you still there ?

[hybrid flicker]

I know it's a technically valid argument but why are you bringing this up xdd

[lyric relic]

because I feel like it was so prepared about the theory of irrational numbers, because its previous comment "basically irrational square roots", so I was wondering if he was able to deal with another problem about that

[frozen bobcat]

have you tried using the table of radicals bunny sent?

[vocal sleet]

@bright lake Has your question been resolved?

[bright lake]

ya what about rationalizing surds

[bright lake]

<@&286206848099549185>

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@bright lake Has your question been resolved?

[bright lake]

<@&286206848099549185>

@open sundial

@open sundial

[meager herald]

are you looking for answer to all a-h?

[vocal sleet]

@bright lake Has your question been resolved?

[steep lintel]

4/612/9+(-3/8)(-12/9

[vocal sleet]

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[hardy crater]

Have I done anything wrong or is there a way I should continue to try and simply?

[spare blaze]

What you have done is not particularly wrong, but there is a much better way to do it

You can proceed, but completing the proof will be hard

[hardy crater]

Uh oh, should I have done something first

[spare blaze]

Yeah

[hardy crater]

I have the identities in front of me and I must have missed it

[spare blaze]

Hint: try converting everything to sin and cos

[hardy crater]

And that would simplify to one fraction

[spare blaze]

Yeah

After simplyfing to one fraction apply trig identities

You will get your answer

[hardy crater]

If it’s a fraction do I just square top and bottom

Is it that simple

Yea I do

[spare blaze]

You dont need to square top and bottom

[hardy crater]

I think I got it thanks for the help

[spare blaze]

Nice 👍

I thought you would have squared

My bad.

Anyways good job solving it :)

[hardy crater]

I did initially 😭

.close

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[ocean shale]

I'm really having a difficult time with this question. I'm a little slow with reading, so word problems are a little difficult.

[ocean shale]

I know it starts off with 0.25A+0.3B = 2.15

and A + B = 8

[lime gorge]

the wording on this problem kinda sussy

is it 8 (apples and bananas)

or (8 apples) and (bananas)

[timber wagon]

It's why I deleted my comment

[lime gorge]

I know

can you show the problems above and below this @ocean shale

its probably the first option, but maybe some context will help

[vocal sleet]

@ocean shale Has your question been resolved?

[brisk cloak]

im bill i bought 8 (bananas and apples)

i know because if i bought 8 apples and some amount of bananas, then i would have spent 2 dollars on apples and i cant buy any bananas with the 15 cents

its also in my grocery bag

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[regal spear]

how do I find the primitive of sin^2(x) + 2sin(x)?

[regal spear]

I understand that the primitive of 2sin(x) = -2cos(x) but I dont understand how the other one works

[spiral turtle]

what does primitive mean here?

[flat whale]

old school word for antiderivative

[regal spear]

yeah

english isnt my main language but thats what we call it here

[flat whale]

you can try using pythagorean theorem then double angle formula

[regal spear]

Ive tried this but it doesnt seem to work

this is basically what the answer book says

but I really dont understand how they got the answer here

[vocal sleet]

@regal spear Has your question been resolved?

[regal spear]

<@&286206848099549185>

[civic otter]

There's a double angle formula for cosine: cos(2x) = 1 - 2sin²x
Hence, you can write sin²x as (1 - cos(2x))/2

Therefore you now have to integrate 1/2 - 1/2 cos(2x)

[regal spear]

whats weird is ive looked up a few tutorials and none of them use that double angle formula

the right part starts first and after that they integrate it

and wouldnt - 1/2 cos(2x) turn into − 1/4 sin(2x)

I dont understand how they got -1/2sin(x)cos(x)

[civic otter]

They are using it here 😅

[regal spear]

oh right

but I still dont understand how they got -1/2sin(x)cos(x)

right here

@civic otter

sorry for pinging if you dont want me to

[civic otter]

Where?

[civic otter]

Yea, this is correct

[regal spear]

look at the picture

[regal spear]

or this one

this is the official answer sheet

[civic otter]

Uh ups sorry my internet is very slow tonight

[civic otter]

They've expanded this

Using sin(2x) = 2sinxcosx

[vocal sleet]

@regal spear Has your question been resolved?

[regal spear]

but how is that true

ive never heard of that

[vocal sleet]

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[quartz oriole]

how long is CD

[simple mason]

Is CD a height for the triangle ABC

Or it is not mentioned

[quartz oriole]

because based on 60 30 90 triangle it s 5√ 3

[quartz oriole]

yeah

you see the right angle

[simple mason]

Trigs

[quartz oriole]

I just started trig

is there way to do it without it?

[simple mason]

Well, if he didn't strictly mention the right angle then I can't assume that it is a right angle

[quartz oriole]

wdym

if there s a dot in the angle it s right angle

or is it only in my country

lol

[simple mason]

We use squares to indicate right angle but it is okey

[short bone]

are u aware of cosine and sine ratios?

[simple mason]

I think that is the point of the question
To make you use trig and get used to it

[quartz oriole]

just started it so nah

[quartz oriole]

it s not in trig tasks

it s in triangle heights, before trig

[simple mason]

Okey I understand
You only learned about the 30 60 90 triangles

[quartz oriole]

I mean it s the solution I came up with

and either am slow or it doesnt work on that triangle

[simple mason]

One property of these triangles is that the side that is opposite to the 30 degree is equal to half the hypotenuse

I think that would make you solve it

[uneven pollen]

BDC and BAC angles are equal, aren't they?

[simple mason]

I don't think you can assume that by looking

[quartz oriole]

I dont think so

[uneven pollen]

i thought because of dot symbol

[quartz oriole]

hollup

[uneven pollen]

on triangle

[quartz oriole]

based on that the thingy beetwen 30 and right angle is half of the a

[uneven pollen]

it is generally angle bisector symbol

that's why

[quartz oriole]

and the cd is beetwen 60 and right angle

[simple mason]

That triangle is a bit wrong here

[quartz oriole]

so it should be a√3/2

[quartz oriole]

wdym

[simple mason]

This is a 30 60 90 triangle

[quartz oriole]

oh

lmao

why is the pic one I showed you of the first ones after I serached up 30 60 90 triangle

anyways, appreciate your help🫡

now how do I close the chat (I use this server rarely)

[simple mason]

I don't know but what I know is that you would understand why is that the reason when you get deeper in trigs

[uneven pollen]

with .close

[quartz oriole]

yeah but rn am learning for just geometry test

anyways

thanks for help guys

.close

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[civic otter]

The same way as cos(2x) = 1 - 2sin²(x) is true, they're called double angle formulas

[regal spear]

do you know anywhere where I can find more info about this?

[civic otter]

Any trig course, you can ask in #book-recommendations (I guess you can ask for youtube videos, as well)

[uneven pollen]

it actually comes from sum identity

if you wonder

[civic otter]

sin(A+B)=sinAcosB+sinBcosA. Now put A=B and you get your desired result @quartz oriole

[vocal sleet]

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[orchid kindle]

srry if this is taking up channel space but can someone double check my work if its right or not? thanks!

[vocal sleet]

@orchid kindle Has your question been resolved?

[orchid kindle]

mostly want to know if i set my equations up correctly bc both parts are kinda dependent on that :p

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@orchid kindle Has your question been resolved?

[orchid kindle]

<@&286206848099549185>

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@orchid kindle Has your question been resolved?

[wraith mist]

Thing is, the width of the corss-section at y=4x^2 is 2x, not x

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[fallen locust]

What does this A() mean in linear algebra matrices? I'm asked to find the determinant.

[cyan shadow]

it seems likely that its defined elsewhere in the book, I don't believe I've seen the notation

[hexed needle]

I think they just mean A = the matrix on the right

if A isn't explicitly defined anywhere, that's most likely it

[fallen locust]

I see. Thank you. I'll ask my prof then

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[vast shale]

How did we get the last 2 terms

[grim lotus]

the same as any other term presumably?

just differentiate

mainly using product rule

[vast shale]

Are we not multiplying the two brackets

I was assuming that was what is happening

[grim lotus]

no we're not

the left bracket is a differential operator

it eats a function f(r,theta) and returns another function in r and theta

the right bracket is a function of r and theta which is input to the operator

[vast shale]

Ahhh we never learnt this in class so I was confused

How exactly does it differentiate the right bracket

[vocal sleet]

@vast shale Has your question been resolved?

[vast shale]

@grim lotus sorry for the ping just need some clarification

or material on where i can see a solved example maybe

[grim lotus]

idk

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@vast shale Has your question been resolved?

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@vast shale Has your question been resolved?

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[night charm]

hello, was wondering how to simplify this further

this is what it becomes later

I think I'm supposed to factor the numerator to cancel out one of the denominator but not sure how to go about it

[vast shale]

i dont think we can simplify it to -1/ (1+t^2)

[night charm]

Yeah I think so too, i tried a couple of ways just couldn't get it to make sense xD

the derivative calulator gives me this

but it doesnt use the quotient rule

[sage solstice]

What are you supposed to calculate? The extrema?

[vast shale]

boy!

[night charm]

just the first derivative

[vast shale]

see how there are two different variables ?

there's t and there's x

[vast shale]

this would be wrong

if this were the question

[night charm]

oh

😭

xDDDD

[vast shale]

if this was the question then you are right

[night charm]

xDDDD anyways

Thanks for the help 🤣

Okay everything is clear now 😌

https://tenor.com/view/bye-im-out-goku-gif-13578748

.close

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[karmic adder]

This is what I have so far. What do I do next?

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@karmic adder Has your question been resolved?

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[edgy estuary]

hm

[edgy estuary]

I don't understand part b and part c, can anyone help

[fading cove]

have you solved a

[edgy estuary]

yes

I did 0.5 = 4 - x^2/8

and solved for x, and multiplied by 2

[fading cove]

well you have the coordinates of the two top points of the barge

see if they are under or above the curvz

using the function associated to it

[edgy estuary]

how?

[vocal sleet]

@edgy estuary Has your question been resolved?

[vocal sleet]

@edgy estuary Has your question been resolved?

[edgy estuary]

bruh

[edgy estuary]

<@&286206848099549185>

[vocal sleet]

@edgy estuary Has your question been resolved?

[edgy estuary]

mad

[humble glen]

Did you try this

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@edgy estuary Has your question been resolved?

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[little flint]

this is my work, please tell me what to fix!

[summer warren]

What does TOA mean

[steep crater]

time of arrival

[vast shale]

the tan ratio gives us opposite/adjacent

[little flint]

okay i figured out part a, i need part b

part a is 113262 ft

[vast shale]

good

[vast shale]

.

[little flint]

i put 107718 for part b and it wasn't working ..

[vast shale]

tan 18 = rd/35000

[vast shale]

it wont

r.d. = tan18 * 35000

[little flint]

i got 11372 is that correct

[vast shale]

im not sure

[little flint]

how did you get that? my calculator is giving me

[vast shale]

did you take 18 in degrees or radians

[little flint]

deg

[vast shale]

good

wait im wrong

[vast shale]

Yes

[little flint]

okay thankyou!

[vast shale]

my pleasure

[vast shale]

i did not use a calc so i made a mistake

[vast shale]

the mistake you did there was

taking cot ration instead of tan

tan 18 = x/35000
cot 18 = 35000/x

practice more trigonometric ratios and you'll be good at it..

[vast shale]

also, close this session

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[fresh tendon]

hello

[fresh tendon]

i need help with this

[blazing wigeon]

Do you know what a scale factor is

[fresh tendon]

isn't it where you resize an object

[blazing wigeon]

That is what’s happening but what is the scale factor

Obviously a number but a number measuring what

[fresh tendon]

like how much the object increased?

so like

1 is enlarged

<1 is reduced

and =1 it stays the same?

[blazing wigeon]

Sure, we can go with that. You should be looking at what you are scaling each coordinate by to get the greater/new coordinates

So (2,2) to (6,6)

[fresh tendon]

okay

[fresh tendon]

so i measure what/how many times the smaller object needs to be enlarged to match the size of the bigger shape

so kinda like this?

[blazing wigeon]

Thats definitely not all needed

Notice a pattern in comparing each coordinate with its newer larger one

[fresh tendon]

ok

ok

let me write this out real quick

i cant do this in my head

[fresh tendon]

okay so

i do it a little more difficult or maybe this the same way

but

the point w on the bigger one

is 0,9 and x 6,6

so with the smaller one being 0,3 and 2,2

you find the distance between the origin

to point w if i remember

so you do the distances between each one and the origin or its origin

and i got 2.22 over 6.66

which is .333

but it wants a fraction answer so i put it as 1 over 3

[fresh tendon]

am i right?