thank you
#help-28
hazy onyx
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torn jolt
how do i solve this ?
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how do i solve this ?
kindred grove
have you tried a) or something ?
if you know what cofactor expansion is, it's not like there 3million ways to do that
hazy onyx
Factorials:
8 sits,
4 boys,
4 girls,
must seat therefor 2 kids of the same sex can't seat next to each other
how many possible combinations
kindred grove
this channel is already taken
you can go in #help-46 for example, it is free at the moment
@hazy onyx
@torn jolt still here?
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gilded tapir
arethmatic sequences third member is positive and it is 5/3 part of the fifth member. how many members of the sequence are positive
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arethmatic sequences third member is positive and it is 5/3 part of the fifth m...
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gilded tapir
<@&286206848099549185>
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void nova
You have $a_1 + 2d > 0$ and also $a_1 + 2d = \frac{5}{3} (a_1 + 4d)$
glossy valveBOT
Alberto Z.
void nova
This because the $n^{th}$ general term of an arithmetic sequence is $a_n = a_1 + (n - 1)d$
glossy valveBOT
Alberto Z.
void nova
From the 2nd equation you get $a_1 = -7d$
glossy valveBOT
Alberto Z.
void nova
Which gives the first to be $d < 0$
glossy valveBOT
Alberto Z.
void nova
Hence, $$(n - 8)d > 0 \Rightarrow n-8 < 0 \Rightarrow n < 8$$
void nova
Thus, only the first 7 numbers are positive
(because n < 8 is equivalent to n ≤ 7, since we're working with whole numbers)
slender pond
what does differentiating give me the max value of r?
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what does differentiating give me the max value of r?
short niche
when the derivative is zero, we get a local minimum, local maximum or inflexion point
all local maximas must lie on some point where the derivative is zero
slender pond
so did the person in the video assume that its the local maximum?
since it could have been the minimum or inflextion point
short niche
i guess
but from the diagram u can tell its on the circle
the only one not on the circumference is 0
to show it is a bit of work
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wicked cliff
why is 0 , pi and 2pi?
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why is 0 , pi and 2pi?
lone venture
wicked cliff
if are cosine then is 3pi/2 and pi/2
wicked cliff
hey
lone venture
if cos(theta) = 0, then yes
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mighty grove
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mighty grove
I need help with iv)
this is the solution
why is it 7/12 and not 5/12?
when it intersects the 1500 line at 5/2 and 15/2
does that not mean the first lot is 2.5 months, second lot is 5 months, ans third lot is 4.5 month ?
so its 5/12 ?
but i find if you account for first 10 months then you get 7/12
i need help 😭😭😭
<@&286206848099549185>
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mighty grove
Please only use the <@&286206848099549185> ping **once** if your question has no...
?
split swift
it's because it's starting from march
I'm assuming the graph is plotted with 0 being jan 1st
but if you shift it along by 3, you begin with the population being <=1500
so you get 5/10 for the first 10 months
mighty grove
are we able to make that assumption?
mighty grove
it was given to me by someone who was showing me their solution
since i got 5/12, and the answer was apparently 7/12
and this is the solution they gave me for it
but i just couldn’t understand it still
split swift
if the graph begins with 0 being march 1st then 5/12 looks more reasonable
mighty grove
do you reckon it’s a mistake and the answer is 5/12? or you have to make the assumption it wants from when march starts and onward?
it would make more sense in that idea to mention a restriction in domain though
split swift
rereading the question, it looks like it does want the graph to start with 0=march, so it's probably a mistake
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torn jolt
If I evaluate a limit and get 0^- from the left side and 0^+ from the right side, is the answer just 0 for both and so the limit exists or are the answers different and so therefore the limit does not exist?
alpine vigil
limits of both sides converge to 0 so safe to say it exists
umbral dome
that just says which direction they approach 0 from, approaching 0 from above or below is still approaching 0 so it does exist
alpine vigil
If I evaluate a limit and get 0^- from the left side and 0^+ from the right side...
if it helps you can think of it graphically - even if one side is approaching from 0- and the other 0+, they still "meet" at 0 and the function is continuous over that very tiny interval
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torn jolt
is this implying leibnez notation?
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is this implying leibnez notation?
nimble dust
i dont think so
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signal bolt
I am stuck. I was thinking of using the geometric dot product to help solve it but i don’t know if it did anything
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signal bolt
<@738808901834637382> Has your question been resolved?
No
opal isle
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wispy marsh
Why is r=3 but the circle has a radius of 1.5
wispy marsh
Mb didnt mean to have 2 channels
spiral vigil
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real musk
for part c, how did they find the values of j for both Fs?
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for part c, how did they find the values of j for both Fs?
real musk
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remote terrace
its just trig, remember soh cah toa. For the 95N force, the j component (opposite) it is o/h = sin(73), or o = h*sin(73), where h is the hypotenuse, (aka the magnitude) of the force, in this case 95N
real musk
its just trig, remember soh cah toa. For the 95N force, the j component (opposit...
but like whts the working to find -27.78, 90.85, 53.33 and 96.21
remote terrace
-95cos(73) = -27.78,
95sin(73) = 90.85, etc.
remote terrace
but like whts the working to find -27.78, 90.85, 53.33 and 96.21
this picture might help you understand it a bit better
real musk
this picture might help you understand it a bit better
thank you
remote terrace
thank you
no prob, just be careful to account for the direction of the i and j components. In this case, make sure you note that the i component is in the -i direction, so make sure you calculate it as -95cos(73)
hard gate
Hey
hard gate
The thing that always confuses me on sequences is what the n means
what is the n+1 mean after (-1)
supple sail
what is the n+1 mean after (-1)
it translates to
-1 times (-1)^n
n is basically the number of term
hard gate
dont understand
hard gate
so n+1 is 2
hard gate
So how would I do T2
supple sail
put n = 1
so we have this relation
T2 = -(1)^(1+1) 2T1
which is 1 times 2 times 3
= 6
so ur second term is 6
you just keep on putting n= 1 then 2 , 3 , 4
hard gate
So t3= -1^(2+1) 2T2
supple sail
-1x6
its -1^(1+1)
that is minus 1 squared
= 1
this is called alternating series
so you get first term positive
next you get negative nd so
hard gate
I got -1 from squaring -1
hard gate
so you get first term positive
next you get negative nd so
I dont get it
supple sail
I got -1 from squaring -1
💀
you're prolly doing it wrong
dont do this
-1^2
do this
(-1)^2
supple sail
hard gate
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slender kraken
You're given a word: "JJKKLM"
How many arrangements have “J” and “K” next to each other?
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You're given a word: "JJKKLM"
How many arrangements have “J” and “K” next to ea...
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@slender kraken Has your question been resolved?
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@slender kraken Has your question been resolved?
void nova
Consider it as having the "letters" J, K, L, M, JK or the "letters" J, K, L, M, KJ. From this you subtract the intersection, which consists in those words formed with the "letters" L, M, JK, KJ
Hence the answer will be:
5! + 5! - 4! which gives 216
alpine vigil
looks fine and correct
dire osprey
the diagnols are equal yes
pale cargo
how do you apply trig here btw
nvm yea
dire osprey
I mean you can't really figure out anything about the upper/down length and the height
Not really
you have to use diagnols for something
damn it would be really convenient if anything else was given lmao
I'm not really seeing any formula that revolves around using diagnoals to find a trapezoids area so I assume you sort of split it into other shapes
but I kind of have no idea
yeah
dire osprey
I mean if the diagonals happen to be 90 degrees then obviously all the sides are 90 degrees
"they will not form a right angle unless it is a right trapezoid"
well this appearently is not a right trapezoid.
I mean
duh?
the upper and lower length of a trapezoid must be parralel
so that you can make a trapezoid
in the first place
i'm not sure how that helps lul
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runic spruce
How’d they get the equation of the tangent
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How’d they get the equation of the tangent
split swift
the partial derivatives tell you two vectors that lie inside the plane (the ones with direction -12x and 89y), then the 50, 3 and 2 are from the point on the surface
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weak pelican
how do you derive $e^{-10t}$
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how do you derive $e^{-10t}$
weak pelican
it should be e^-10t
fast peak
put {} around the exponent in latex
weak pelican
is that -10e^-10t ?
glossy valveBOT
wakamole
weak pelican
ty
fast peak
is that -10e^-10t ?
yes
weak pelican
is it $-10e^{-10t}$
glossy valveBOT
wakamole
weak pelican
ok so you move the sign
weak pelican
so in that case ... what if it is $v(t) = t^2e^{-10t}$
glossy valveBOT
wakamole
fast peak
product rule
weak pelican
would it just be $2t(-10e^{-10t})$?
glossy valveBOT
wakamole
weak pelican
product rule
this? ^
fast peak
no
fast peak
do you not know what the product rule is?
weak pelican
i dont know when to apply it
weak pelican
i think it is f(x(g) = f(x')(g) + f(x)(g')
fast peak
i think it is f(x(g) = f(x')(g) + f(x)(g')
(f(x)g(x))' = f'(x)g(x)+f(x)g'(x)
weak pelican
ok i might as well show you the entire equation then.. it is $i(t) = C \frac{dv(t)}{dt}$ and C = 2
weak pelican
(f(x)g(x))' = f'(x)g(x)+f(x)g'(x)
so would it be like $Ct^2e^{-10t}$?
glossy valveBOT
wakamole
weak pelican
then it would be $2t^2e^{-10t}$?
fast peak
sry I have to go
weak pelican
@fast peak so would i just put the 2 in front of the equation? or do that after?
weak pelican
sry I have to go
ok that is my last question
do you mind just answering that?
@fast peak plz
<@&286206848099549185>
i have $v(t) = t^2e^{-10t}$, and $ i(t) = C\frac{dv(t)}{dt}$ so is the derivative of v(t) = $i(t) = C(2t)e^{-10t}+t^2(-10e^{-10t}$?
glossy valveBOT
wakamole
weak pelican
which equals $2(2te^{-10t}+t^2 *-10e^{-10t})$
glossy valveBOT
wakamole
weak pelican
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patent hamlet
I'm struggling with part (ii) of this
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I'm struggling with part (ii) of this
patent hamlet
this is what i've done but that won't actually give me a matrix
which is why I'm confused
leaden ermine
how did you get 1/x?
glossy valveBOT
𝔸dωn𝓲²s
leaden ermine
Other then that, L(1) and L(x²) look good
torn jolt
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torn jolt
im struggling
how do i graph this
from -3 to 4 its negative
but how am i suppose to draw that if the only way it comes in from left to right is by increasing
not decreasing
question is asking for local max/min btw
sharp void
to the left of -3, which is your local min, the function is actually decreasing
it goes: decreasing on the left, going right it hits x = -3 and starts increasing, then when it hits x = 4 it starts decreasing again
so you'd start graphing with something like this
torn jolt
Let T : R^3 -> R^3 be a Linear transformation with eigen values l1,l2,l3 and respective eigen vectors as (1,1,2) , (0,3,-1), (4,0,1l
Let x = (3,7,.5)
Find Tx
Could anyone please help me?
To find Tx
Should I write x as a Linear combination of the vectors given
After finding c1 (v1) + c2(v2)+ c3(v3)
T(x) = l1(c1 v1) + l2(c2 v2) + l3 (c3v3)
torn jolt
I'm not sure how this gives the transformation though.
Do you by any chance know why we did this?
civic surge
the transformation is linear right
torn jolt
yes
civic surge
so you can decompose your vector into many other vectors whose transformations are known
and then add them up
thats what your idea is
torn jolt
so you can decompose your vector into many other vectors whose transformations a...
Ah I see
Okay thank you so much both of you!
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cold sail
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cold sail
this notation is confusin me a bit
dont rly understand how they went from line 2 to line 3
torn gust
like from D to the sums?
it's like (ud1+ud2+ud3)(ud1+ud2+ud3)f(a)
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smoky temple
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smoky temple
How am i supposed to solve this..
zealous wasp
Have you tried plugging in some values?
Cant read your righting, is that raised ot the power of 2 or e? and is the denominator e ?
zealous wasp
Sure
smoky temple
zealous wasp
You still have to break them down into their prime factorization in terms of n I think
smoky temple
Yess but i couldn't calculate the gcd of n^2 and (n+2)^2
zealous wasp
Sorry, i m not sure how to manipulate the equation., i can see the answer because I wrote them down.
smoky temple
Ohh that's fine
torn jolt
This is it the question says calculate Dn
شو عندك اختبار شي حاليا؟
smoky temple
شو عندك اختبار شي حاليا؟
لو قصدك السؤال من اختبار ف لا بس مراجعة
torn jolt
ok
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smoky temple
No
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hoary belfry
Hey! May I ask for assistence for a Pre-Calculus problem that I'm stuck on? Below is the question and what I've done so far to solve the problem:
Question
Use trigonometric identities to find the solution of 2cos² (x) = 2sin² (x) + √2 in terms of integer k and the solutions in a single period [-π, π]. Give your answer in radians.
(Give your answer in the form of a comma-separated list if needed. Express numbers in exact form. Use symbolic notation and fractions where needed. Use k to represent any integer.)
What I've done so far
I have already gone ahead and solved the equation in two ways based on the Pythagorean identities for sin² (x) and cos² (x), but the reason I'm coming out today and asking this question is because of the result I got when solving for x:
# if using the identity `cos² (x)` => `1-sin² (x)`
x = arcsin(√((2-√2)/4))
OR
# if using the identity `sin² (x)` => `1-cos² (x)`
x = arccos(√((2+√2)/4))
What Im confused about is neither clearly look like a value that's on the unit circle, so I don't know what sort of angles these two values give back that are solutions to the equation above. I predict that they look similar to π/4 / 3π/4, but I have tried several answers on the period [-π, π] but I'm getting nowhere. I'm not sure on where to go from here, so I'm hoping someone can point out what I'm doing wrong/missing. Thanks!
hoary belfry
Here's the steps I took:
empty sapphire
you're very close!
but rather how about factoring out a 2 on both sides, then moving the sin^2(x) to the LHS and using a known trig identity
hint: I think you're knowledge with double when you use this identity
hoary belfry
but rather how about factoring out a 2 on both sides, then moving the sin^2(x) t...
Divide both sides by 2?
empty sapphire
yep, like this:
ignore the warning lol
then subtract sin^2(x)
then you have a known identity
hard sigil
then subtract sin^2(x)
i was just about to say lol
empty sapphire
yep exactly
empty sapphire
_hint_: I think you're knowledge with **double** when you use this identity
hint hint hint
hard sigil
But it would be cos^2(x) - sin^2(x)?
well -sin^2(x)+cos^2(x) = cos^2(x) - sin^2(x) too lol
-a + b = b - a
hard sigil
_hint_: I think you're knowledge with **double** when you use this identity
key word: double
hoary belfry
dang, gotta think about this. this seems like something I'd let slip by very easily
hard sigil
dang, gotta think about this. this seems like something I'd let slip by very eas...
keywords: double and identity
hoary belfry
Is this something related to even/odd ...?
hard sigil
not quite
hard sigil
siiii
hoary belfry
So it'd be cos(2(theta)) = sqrt(2)/2, then use another formula for cos(2(theta)) to solve for x?
I think Im getting it
hard sigil
So it'd be cos(2(theta)) = sqrt(2)/2, then use another formula for cos(2(theta))...
yeah youre right
hard sigil
Would this be the answer?
You could check by plugging x into the original equation and test both sides.
hoary belfry
okay got it
If it's not then I'll keep working it out. Thanks for the help!
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torn jolt
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Remlis
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Remlis
glossy valveBOT
Remlis
torn jolt
holon lemme try something
okay
so based on the roots being
(x+3)(x-1)
$c(x^2+2x-3)$
glossy valveBOT
Remlis
torn jolt
"c" is a constanta
$c(x^2+2x-3)=3x^2+2ax+b$
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Remlis
torn jolt
my question is
is it safe to assume here that c=3
that seems to have worked
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fair warren
not really sure how to solve this question
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not really sure how to solve this question
@fair warren Has your question been resolved?
fair warren
<@&286206848099549185>
fossil stump
Triple integral, try using a diagram to help you visualize the solid
fair warren
my question is how to get the bounds for r
like i assume z is from sqrt(98-r) to sqrt(r^2) and
slate violet
my question is how to get the bounds for r
You just substitute in to get $z^2 + z^2 = 98$ so $z = r = 7$ (taking the case where $r > 0$)
glossy valveBOT
south
slate violet
You just substitute in to get $z^2 + z^2 = 98$ so $z = r = 7$ (taking the case w...
And hence r ranges from 0 to 7
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slate violet
Npnp
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cerulean compass
what you finding man
ocean mist
x
cerulean compass
you heard of trig or nah
ocean mist
ya
cerulean compass
what ratio do you think this is
ocean mist
i’ve got a test tomorrow and i’ve been overthinking this so much
cerulean compass
you know double angles or no
ocean mist
what ratio do you think this is
is it sin?
cerulean compass
is it sin?
yea
ocean mist
how would i answer it do i do 8 over sin29
ocean mist
ok this my problem pls help
cerulean compass
sin is opposite over hypotenuse
cerulean compass
okay you good?
cerulean compass
lemme get my calculator
ocean mist
thanks so much
cerulean compass
remember to round corectly
ocean mist
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white roost
Can someone tell me what are the other scenarios i got like nothing in mind
white roost
i also need help with this
this is my work
the thing here is i dont understand what the question is asking me
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limpid trail
consider the function ( f(x) = \frac{x^3 - 4x^2 + 5x - 2}{\sqrt{x+1}} )
determine all the x-values for which ( f(x) ) has a local maximum or minimum
getting stuck at handling the critical points
glossy valveBOT
SupaJay3
limpid trail
<@&286206848099549185>
reef pilot
Helping...
limpid trail
Tysm
I’m sleeping soon so if i dont reply when you post the solution dw i appreciate it yk?
Ty in advance though
reef pilot
I’m sleeping soon so if i dont reply when you post the solution dw i appreciate ...
I am solving it baby girl
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limpid trail
Sleeping now bye
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solemn fable
Given a prime number p > 3:
Prove that the above expression is divisible by p^3
solemn fable
I think im on the right path? but im stuck completely after this
pseudo cape
Maybe something with Fermat's little theorem
solemn fable
((p-1)!/k)^p + ((p-1)!/(p-k))^p = ((p-1)!/k(p-k))^p * (k^p + (k - p)^p)
solemn fable
Maybe something with Fermat's little theorem
maybe
kinda unlikely that the comp would give a question related to such
solemn fable
((p-1)!/k)^p + ((p-1)!/(p-k))^p = ((p-1)!/k(p-k))^p * (k^p + (k - p)^p)
(\frac{(p-1)!}{k})^p + (\frac{(p-1)!}{p - k})^p = (\frac{(p-1)!}{k(p-k)})^p * (k^p + (k - p)^p)
,, (\frac{(p-1)!}{k})^p + (\frac{(p-1)!}{p - k})^p = (\frac{(p-1)!}{k(p-k)})^p * (k^p + (k - p)^p)
glossy valveBOT
autism incarnated
solemn fable
Im thinking of using the choose function
cuz the k^p + (k-p)^p looking real good
<@&286206848099549185>
im so dead
ive been stuck on this for like an hour and a half
Ok yeah no i solved it
💀
solution surprisingly easy tbh
anyways
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sacred parcel
hello, i need help in topology.
if S1 x S1 = Tours = T
then what T x T = ?
vocal coyote
This space does not have an embedding in R^3
Do you need to know certain properties about this space?
What do you need to know about this space
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uneven ingot
I got kicked out fam
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I got kicked out fam
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sacred rivet
why did the (5+cos 7x)^4 just suddenly jump to the numerator
also idk what youre doing with the f and g there
the whole blue RHS looks wrong
uneven ingot
Ohhhhh that’s why
Okay
So my logic was this
I forgot what this rule was called
I was doing this
sacred rivet
so it looks like youre trying to apply integration by parts
but it looks like you are applying basic integration rules wrong
the integral of (5+cos 7x)^4 is not 1/5 (5+cos 7x)^5
the power rule doesnt work like that
you should have learned chain rule by now
sacred rivet
i mean
separation of variables is just basic algebraic manipulation
that part is correct
you can start at the step after youve separated variables
uneven ingot
Wait let me check if it’s even a thing 😢
Thisss
Oh wait
I forgot to times 2 the inside
sacred rivet
yeah
uneven ingot
Idk how sin^2 really works
I wanna clear up
Is it
(Sin(x))^2 = sin^2(x) =sin(x^2)
sacred rivet
the first two parts are correct
the last = sin(x^2) is not
this is one of those weird notation things in math where
sin is a function
and usually, when we superscript next to a function
like f^2(x)
it should mean f(f(x))
thats why f^-1(x) is the inverse, its like applying f negative 1 times
but trig functions are weird
sacred rivet
for some reason we have decided that positive superscript is exponentiation of the entire term
uneven ingot
Oh
sacred rivet
so yeah once you understand that sin^2 x = (sin x)^2
the trig identities should make more sense
but these are honestly some really basic things to make mistakes on
it sounds like you got through a lot of math by muscle memory
uneven ingot
Ye
sacred rivet
and not really understanding the concepts behind what is happening
uneven ingot
I mean I know the sine waves and cosine waves
Signals in engineering but idk like basic basic
sacred rivet
so youll find yourself constantly making silly mistakes because you dont have an intuition for the rigorous rules
uneven ingot
so youll find yourself constantly making silly mistakes because you dont have an...
That’s true yk
sacred rivet
i dont mind helping but there are a ton of knowledge gaps for me to fill
i dont want to like, alarm you or anything
after all, you got as far as you did kinda just blowing through
but my recommendation is to go back and review exactly how everything works
uneven ingot
Yep
sacred rivet
it will be massive help to you long term
sacred rivet
i dont mean it that way
iron plover
But yea hunni help me rq
sacred rivet
im sorry
sacred rivet
but anyways @uneven ingot if you have any simple questions i can help but i really really recommend a review at some point
uneven ingot
I actually mostly memorise things and like practice but don’t know the meaning
sacred rivet
id love to help but like i said i am only one person
uneven ingot
but anyways <@719408073885614110> if you have any simple questions i can help bu...
I’ll ping u in a bit to review my question I’m almost done and tysm though
iron plover
Wait I have assignment
Dam can anyone help 😭
sacred rivet
Dam can anyone help 😭
open a new unoccupied channel
uneven ingot
open a new unoccupied channel
Hi there
Bottom right
Am I stuck in an infinite loop
Or am I unaware of some hidden tricks
Tbh I think I could expand the bracket and do sm about it
Can I?
sacred rivet
your g(x) is wrong
if you take the derivative, youll notice you do not get g'(x)
you should check your work more often
checking integrals is really easy because you can just take the derivative
uneven ingot
your g(x) is wrong
Am I cooked, is there something idk about
sacred rivet
yeah this is not looking good
now that youve tried the dead end
and you understand why its a dead end
ill steer you in the right direction
the integral from the beginning doesnt need integration by parts
it just directly uses chain rule, thats it
i had you try the dead end for practice and understanding
uneven ingot
😭 it’s 4am
okay
Wdym the integral from beginning
Like the start of the whole question?
Should I swap fx gx?
Seems like cool idea imma do that
Oh shit
sacred rivet
not the beginning
just the part where you did integration by parts
when you split f and g
uneven ingot
Doneeee
sacred rivet
double check it
uneven ingot
not the beginning
Is this it
uneven ingot
Oh
sacred rivet
there are some bad habits in your work but we can leave that to some other time
uneven ingot
I was about to wolfram alpha
sacred rivet
dont until you have your own work
uneven ingot
Summarise it
sacred rivet
check using wolframalpha at the end
sacred rivet
because right now you need to get into good habits
and know what youre doing
overreliance on calculators at this point
is going to lead to more bad habits
uneven ingot
That’s true
I’m exploiting my calc so hard
It’s carrying my gpa literally
But I shouldn’t be doing that u are right
How did u know
That no need to do f and g
Can use u
Okay I admit I also skip a lotta steps
uneven ingot
How did u know
Imma sleep now ping and lmk when to use f and g and when to use u
Thank u so much
sacred rivet
Imma sleep now ping and lmk when to use f and g and when to use u
its really difficult to give a good answer, basically, because there is no easy way to solve any integral. its almost entirely pattern recognition, and so thats why students who struggle with algebraic manipulation and arent comfortable doing them will struggle even harder, and why experience and practice is so important
chain rule states: d/dx f(g(x)) = d/dx f'(g(x)) g'(x)
(note that the above is written in a way that is slightly inaccurate technically, but i dont think youll notice and this might help you visualize the rule better)
in other words, as long as something looks like the form f'(g(x)) g'(x) then use chain rule
integration by parts is easier in one way but harder in another
product rule: (fg)' = f'g + fg'
integrate: fg = integral f'g + integral fg'
rearrange: integral f'g = fg - integral fg'
if the right side integral there is easier to solve, then apply integration by parts. in this way, its harder to see whether or not integration by parts would be useful to use, but nothing stops you from trying. when all of the easy methods (like chain rule) fail, sometimes i just turn a part of my brain off and just try integration by parts. if it doesnt work, try something else
so yeah, no good answer, but hopefully that helps
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lilac glacier
HELp
glacial pasture
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vapid pawn
Can smb tell me how is angle "42.3 or 127/3" coterminal with 120?
vapid pawn
they're converting that to degrees
Okay, but why was there a need to convert it back to degrees?
Can't we simply have (x,y) as cos 42.pi/3 and sin 42.pi/3 instead of having them as cos 120 and sin 120?
robust slate
,w 254 mod 6
glossy valveBOT
robust slate
Can't we simply have (x,y) as cos 42.pi/3 and sin 42.pi/3 instead of having them...
yeah you can do it in terms of radians
yeah
vapid pawn
,w 254 mod 6
what?
robust slate
ignore that
robust slate
idk
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vapid pawn
How can 42 1/3 be in radians when 42 1/3 is a mixed number tho?
limber forum
What's wrong with a mixed number having radians as its unit?
Radians are dimensionless, you just have a number of them, could have 2 radians, pi radians, 0.000001 radians, 7/3 radians it's all chill
You can convert it into a single fraction if you prefer it that way lol
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vapid pawn
You can convert it into a single fraction if you prefer it that way lol
I meant that it's hard for me to connect the mixed number "42 1/3" to 120 degrees even if the 120 was in radians
Can u pls tell me a solution?
I tried plugging in 11pi/6 with "43 1/3" and still failed
limber forum
Probably cos it's not 120 degrees (edit: it is, when you contextualise it with the Q above, as elaborated on below lmao)
vapid pawn
lol
yea
Our mister may have made a mistake
I'll try to get everything checked.
And tysm again
.close
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vapid pawn
Ill leave this ticket open though so if any1 else knows where's the problem and can reassure me
limber forum
Right I've read through your problem
Wrong wording, the 42 1/3 is right
But that's telling you how many lots of 2pi go into your fraction
So 42 lots remainder 1/3 lots of 2pi
limber forum
So that means you have 2pi/3 rads on the unit circle = 120 degrees
No it is that's fine
But you just need to use it correctly
Take the remainder, multiply it by 2pi and that's how you get the angle on the unit circle
Then you can convert it to degs if you need to
So 2pi/3 x 180/pi gives you the 120
And hence the short way to do it is to just multiply the remainder by 360
vapid pawn
So 42 lots remainder 1/3 lots *of 2pi*
OHHH
limber forum
But 42 1/3 is not 120 degrees in itself, it just is the route to getting 120 degrees
limber forum
Well your division is finding how many lots of 2pi radians go into the overall angle right
So yeah
limber forum
When you divide it tells you 254pi/3 is equivalent to 42 x 2pi + 1/3 x 2pi (radians)
limber forum
Np lol
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vapid pawn
nvm
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unique garnet
whats a c and d
rustic pasture
Hint:What is the area of △BCD
charred ore
ummm not sure how i can even calculate that without the coordinates of c
rustic pasture
Sure △BCD=△ABO-?
rustic pasture
Yes so you can compute the area of it
rustic pasture
Then you can get the ratio of AC:BC,It is equal to △ACD:△BCD
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thick hedge
Let a variable line pass via the centre of $x^2+y^2-16x-4y=0$, meet the positive coordinate axes at points A and B, then find the minimum value of OA+OB where O is the origin
glossy valveBOT
ƒ(Why am. I here)=I don't know
thick hedge
here I suspect I have to use something like AM>GM>HM
am I right?
$\frac{8b+2a}{ab}=1$
glossy valveBOT
ƒ(Why am. I here)=I don't know
thick hedge
hmm
is this simply a calculus problem
assuming it is
ok, that makes it sort of doable
let the angle the line makes with the axis be $\theta$
glossy valveBOT
ƒ(Why am. I here)=I don't know
thick hedge
$\tan\left(\theta\right)\ =\frac{8}{2-l\cos\left(\theta\right)}$
glossy valveBOT
ƒ(Why am. I here)=I don't know
thick hedge
am I overcomplicating it
elfin stream
Let a variable line pass via the centre of $x^2+y^2-16x-4y=0$, meet the positive...
Find the center and radius, then use the radius as hypotenuse, then find OA+OB in terms of inclination, then calculus
And remember that theta is between 90 deg and 180 deg
thick hedge
why must the hypotenuse be the radius
elfin stream
why must the hypotenuse be the radius
Because right-angle triangle?
Its not an ellipse is it?
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elfin stream
@thick hedge nvm won't work
Cus the circle isn't centred at origin
I got a better approach
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elder storm
Help me Im struggling to find the missing parts of the triangle
This abt geometric mean theorem
dusky locust
You can find y via pythagorean theorem
w,z you can find because the triangles are similar
and x you add 16+w
elder storm
You can find y via pythagorean theorem
Oh ok gotta search that one coz it hasnt been taught to us thas y Im struggling🥹
But tnx okokok
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sour torrent
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tame lark
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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
1
tame lark
i dont know which law to use
i know it law of cosines
SSS
but i dont know how to apply it
neon geyser
i know it law of cosines
did you draw the triangle?
tame lark
no
let me draw it rq
alr done
idk how to find angle B
when i only have the formula to find angle A
@neon geyser
neon geyser
<@596893067261509633>
can u show me the thing u drew?
tame lark
can u show me the thing u drew?
is it okay or
neon geyser
i prob drew it wrong but okay
yes i think it's okay
neon geyser
what next
can you apply the law of cosines?
instead of using the formula (which you'll confuse yourself with)
think about the formula more abstractly
tame lark
a^2 + b^2 = c^2?
neon geyser
(the side opposite to b)^2 = (side1 adjacent to b)^2 + (side2 adjacent to b)^2 - 2 (side1 adjacent to b) (side2 adjacent to b) cos (angle B)
neon geyser
a^2 + b^2 = c^2?
nah
you can only use that when this triangle is right
can u show that this triangle is not right?
should be trivial ig
tame lark
uh i cant cause i have no angles
neon geyser
uh i cant cause i have no angles
no
neon geyser
a^2 + b^2 = c^2?
if it's right then it'd satisfy this
tame lark
wdym
neon geyser
,w 15^2 + (15*sqrt(3))^2
glossy valveBOT
tame lark
dont you use law of cosines when you have all sides
neon geyser
well that's okay
you're supposed to know by checking
not by drawing
u said law of cosines and i saw 5 marks so i assumed it was law of cosines
do you know what law of cosines is anyway?
tame lark
yeah
neon geyser
Anyway yeah for your question it's fairly easy to see it's right
tame lark
hmm alright
neon geyser
cps A = b^2 + c^2 - a^2/ 2bc
well it doesn't matter
tame lark
how do you know those are the angles?
neon geyser
do you know 30-60-90 triangles?
or 45-45-90 triangles?
they're special triangles
the reason i know their angles is because of their side ratios
x = 15
neon geyser
why don’t you redraw your triangle first
tame lark
i already did
neon geyser
well you know immediately the answer is 60 degrees lol but yeah u can assume u don’t
okay now use sohcahtoa on angle b
tame lark
what is that
tame lark
oh ok
neon geyser
tan = opposite/ adjacent
tame lark
with the sides?
neon geyser
you abbreviate that to sohcahtoa
neon geyser
with the sides?
yes
you can do anything really
sin(b), cos(b) or tan(b)
oh wait your question wants you to use tan
so use that
tame lark
how do i do that
neon geyser
draw the triangle inside the unit circle
scale everything down by 30
btw you wouldn’t have to do any of this
idk what your question means “use the unit circle”
tame lark
me neither
neon geyser
normally you’d just do tan(B) = opposite side/ adjacent side
tame lark
but what is the B
tame lark
oh im dumb
neon geyser
i mean we do know but let’s assume we don’t lol
just send a pic of your new triangle
tame lark
so for part A
neon geyser
wait part A says determine m<B
u can just argue that this is a 30-60-90 triangle
and then show that angle B is then 60 by definition
tame lark
neon geyser
sin(B)
not just sin
sin is a function
you need to feed it some input
same for cos and tan
tame lark
yeah
neon geyser
okay then u can say that
tame lark
ill just explain why the triangle is a right angle
neon geyser
u first verified thag this triangle is right
tame lark
what did you tell me before
neon geyser
and then identified that it’s a 30-60-90 by looking at its side ratio
angle B is the angle opposite to the side 15sqrt(3)
and in a 30-60-90 triangle, the angle opposite to xsqrt (3) has measure 60
neon geyser
what did you tell me before
wot
neon geyser
draw this
tame lark
i cant send pictures in the question answer box thingy
neon geyser
and scale the sides of your triangle side down by 30
neon geyser
i cant send pictures in the question answer box thingy
then what can u do? in that case they want you to use sentences?
tame lark
i have no idea
neon geyser
i have no idea
??
i’m asking how u can submit your answer
do you write sentences or do you write answers or what’s going on?
tame lark
i have to like explain how i did it