YEAH
#help-0
stiff tree
OH
stiff tree
So when I cut both -72, the negative still remains?
abstract fractal
Don't be mean
proud basin
he was moyaing me
stiff tree
~~how did you pass elementary school~~ YES
But I learnt this recently at high school
lone heartBOT
@stiff tree Has your question been resolved?
karmic rapids
,rccw
ocean sealBOT
high rapids
What is √x?
solar moat
struggling to find a succession bn to satisfy this equation
lone heartBOT
struggling to find a succession bn to satisfy this equation
solar moat
found some possible solution, but it's wrong
since obviously can't subtract any number to infinity
this is where i got to with the meaning of the right part of the equation
lone heartBOT
@solar moat Has your question been resolved?
solar moat
.close
lone heartBOT
lone heartBOT
Available help channel!
viscid pagoda
How is this simplification done?
lone heartBOT
How is this simplification done?
viscid pagoda
From this?
viscid pagoda
12x = 3x + 9x
Yes sorry i know that i meant the other photo
viscid pagoda
Yes i get that but the fact that they do (3x + 1 + 9x)
shrewd canyon
yeah yeah I answered too quickly
you can take out (3x+1)^2 from both expressions
so (3x+1)^2 ( (3x+1) + 9 )
viscid pagoda
Why van you take out the (3x+1)^2
shrewd canyon
they both appear in the expressions
shrewd canyon
so (3x+1)^2 ( (3x+1) + 9 )
what happens when you simplify this?
viscid pagoda
Yes you get (3x+1)^2 (12x + 1)
willow tinsel
Can someone help me figure out recursive procedures/sequences
willow tinsel
alpine sable
satirical (but mathematically sound) answer
Theorem: n points define a degree n-1 polynomial.
Hence, these sorts of problems require fitting points to a polynomial. Since I'm lazy, we can use a polynomial regression tool (eg https://stats.blue/Stats_Suite/polynomial_regression_calculator.html), ie the x coordinate represents the x-th term
a) $f\left(x\right)=\frac{1}{3}x^{3}-2x^{2}+\frac{17}{3}x-5$
ocean sealBOT
Toby
willow tinsel
uhhh I got no clue what this is. My current topic is recursive procedures. This makes no sense to me?
alpine sable
plug in x=6 and x=7 into the polynomial
willow tinsel
why? This isnt a polynomial equation. How did you get it as a polynomial.
why is it a polynomial
@alpine sable
tepid hearth
yo toby i am erens friend
and im trying to help him
i dont understand how you figured out it is a polynomial function
alpine sable
uhhh I basically plotted all the points (n,a_n) where a_n is the n-th term in the sequence, then drew a curve through them
tepid hearth
huh
alpine sable
it technically works, but isn't the spirit of answering these sorts of questions
alpine sable
(basically, i hate teachers who give these questions and expect a reasonable answer)
tepid hearth
of the sequence
tepid hearth
(basically, i hate teachers who give these questions and expect a reasonable ans...
faxs
these teachers are fucktards
alpine sable
what did u graph exactly?
for part a I graphed (1,-1), (2,1), (3,3), (4,7), (5,15) and found f(x) goes through all these points
willow tinsel
im gonna tag helpers
<@&286206848099549185> Can you help us with recursion sequences?
willow tinsel
This
alpine sable
ok here are serious answers:
a) double then add 1 then take absolute values
b) signed difference of previous two terms
c) multiply by 3/2
@willow tinsel @tepid hearth ^
alpine sable
you werent asked for a formula right? only to find the next terms
shrewd canyon
ok here are serious answers:
a) double then add 1 then take absolute values
b) s...
a) doesn't work out for a1 and a2
alpine sable
make an exception for the first term
tepid hearth
i dont think that is possible lmao
alpine sable
or maybe it's double, then add 1, then take absolute values
or double, then add 1, and if it's -1 make it +1
alpine sable
if it's negative, make it +1
these sorts of questions are way too open ended to make good maths questions out of
shrewd canyon
the jumps are 2,2,4,8
shrewd canyon
if it's negative, make it +1
still no
alpine sable
take absolute values, it works
lone heartBOT
@willow tinsel Has your question been resolved?
real gazelle
https://cdn.discordapp.com/attachments/490557019623915520/991438963665551430/unk...
I see the pattern for (b) at least
willow tinsel
please explain
real gazelle
what's the relationship such that 3 <blank> 1 = 2
1 <blank> 2 = -1
2 <blank> -1 = 3
willow tinsel
im not following please explain
real gazelle
like
let's say you were given an equation 3 _ 1 = 2
and you have to fill in the blank
what would you fill in the blank with?
alpine sable
ok here are serious answers:
a) double then add 1 then take absolute values
b) s...
.
real gazelle
(a) is the most bizarre lol, starting from -1 seems so unnatural
willow tinsel
what would you fill in the blank with?
real gazelle
yeah
so then you can check that it works for the rest of the terms
1 - 2 = -1
2 - -1 = 3
-1 - 3 = -4
so what's the general formula here
real gazelle
don't say that :(
willow tinsel
ok i get it
real gazelle
awesome!
willow tinsel
how would i writ eout the formula?
well
i have an idea of how
but i cant write it here
wouldnt make sense with text
real gazelle
convert it to text as best as you can it's okay
willow tinsel
tn-2 - tn-1?
real gazelle
I can probably make sense of it
willow tinsel
something like that
real gazelle
yep!
willow tinsel
tn-2 - tn-1 = tn?
real gazelle
yep!
real gazelle
by t2 do you mean the second number, 1
willow tinsel
yes
real gazelle
in this case you can't get t2 from the formula so you have to specify two base cases
and the reason is because the formula involves the previous two numbers
so you have to say
t1 = 3
t2 = 1
tn = tn-2 - tn-1
real gazelle
no problem!
willow tinsel
https://cdn.discordapp.com/attachments/490557019623915520/991438963665551430/unk...
@real gazelle can you solve c?
real gazelle
ok here are serious answers:
a) double then add 1 then take absolute values
b) s...
Toby already gave the answers ^
willow tinsel
ooohh
lone heartBOT
@willow tinsel Has your question been resolved?
lone heartBOT
@willow tinsel Has your question been resolved?
willow tinsel
.close
molten lotus
The first three terms in a geometric sequence are x, x - 5, and x - 9 . Determine the value of the
common ratio,
molten lotus
Im insure how to do this
near hollow
Common ratio is constant
prime badge
make 2 equal fractions
near hollow
If I do term 2 divided by term 1 what is the value?
molten lotus
-5
near hollow
Nope
molten lotus
But dont the x's cancel
near hollow
(x-5) /x = 1-(5/x)
But ignore these values if I do the second term divided by the first what will the value always be in a geometric sequence?
molten lotus
x?
molten lotus
Constant?
near hollow
Say I wanted to get from term 1 to term 2 what do I multiply by?
molten lotus
common ratio
near hollow
So if I divide term 2 by term 1 what do I get?
molten lotus
common ratio
near hollow
Use this fact and the fact the common ratio is constant (ie it stays the same)
And u should be able to find a solution 👍
near hollow
See how far you can get
near hollow
What's ur working?
near hollow
So term 2 / term 1 = r
molten lotus
Yeah
near hollow
$\frac{x-5}{x}=\frac{x-9}{x-5}$
ocean sealBOT
Max..
molten lotus
Yeah tahts what I have
molten lotus
Wait I dont get how its now squared?
near hollow
I've multiplied both sides by the denominator
We hate fractions in equations so just get rid of them by multiplying by the denominator
near hollow
My bad
ocean sealBOT
Max..
near hollow
🤷♂️ would make sense
molten lotus
Ohh I see nvm I think I got it now
near hollow
Remember we have used the fact it is a geometric series means the common ratio must be constant. Now this equation determines what values of x mean our sequence has a constant common ratio
molten lotus
You have to isolate for x the replace the x into the equation
near hollow
Yeah basically
molten lotus
Alright thank you!
near hollow
x=25? And then r = 20/25=4/5?
molten lotus
I got x = 1.3157
Nvm I isolated it wrong
Yeah I got 25
Okay yeah I got that answer thanks!
.close
molten lotus
A ball is dropped from a height of 15 metres above ground. After the ball touches the ground it bounces to 60% of its previous height. Determine how far the ball has traveled vertically when it hits the ground for the 4th time. Round your answer to the nearest tenth of a metre.
molten lotus
What ive done so far is 100-60 =40
Then 40/100 = 0.4
But do I subtract it from the previous height of 0.4 or do I multiply it?
Because I know the answer has to be 15>
.close
molten lotus
Three sums obtained from a particular infinite geometric sequence are
1 2 3
35 10, 15,
2
S S S
Determine the sum of this entire infinite sequence.
lone heartBOT
@molten lotus Has your question been resolved?
molten lotus
<@&286206848099549185>
molten lotus
Ohh what i thought you use the infinite series formula oops
I dont have tn though
Or is tn s3?
willow canopy
well, you can see that there’s a pattern here
from s1 to s2, you add 5
from s2 to s3, you add 5/2
you can assume you add 5/2 to s3 to get s4
willow canopy
so the sum becomes $S_n = \sum_{k=1}^{n} \frac{5}{2^{k-1}}$
ocean sealBOT
Azzurala
willow canopy
do some re-indexing on that sum
molten lotus
I dont have a formula like that on my formula sheet
molten lotus
Not really
I dont really get it
So Im suppose to convert the Sn into an S infinity
molten lotus
10
willow canopy
S_2
molten lotus
15
molten lotus
Yeah
willow canopy
so when I say to do some reindexing, I meant like
$S_n = \sum_{k=1}^{n} \frac{5}{2^{k-1}} = \sum_{k=0}^{n-1} \frac{5}{2^{k}}= 5 \sum_{k=0}^{n-1} \left(\frac{1}{2}\right)^k$
ocean sealBOT
Azzurala
willow canopy
you can then let n approaches infinity to the thing on the right
and that should be something you’re able to do
molten lotus
Wait so am I suppsoe to solve for n
I really dont get this because ive never seen any of these formulas
willow canopy
no, it’s asking what does this geometric series converges to
wait so
have you never seen this
molten lotus
No
willow canopy
$\sum_{n=0}^{\infty} r^n = \frac{1}{1-r}$ when $\abs{r} < 1$
ocean sealBOT
Azzurala
willow canopy
this is the geometric series sum
molten lotus
This is for infinite series according to my formula sheet
willow canopy
**Azzurala**
if you let n tends to infty for the expression on the right here
that’s just a geometric series
and that’s what the question is asking for
molten lotus
Wait so Im not suppose to solve anything?
willow canopy
molten lotus
Okay so I am
willow canopy
if you wanna understand why they are using such wording
you should look back to how infinite series are defined
so
(I’m typing on phone so this is very long to type out)
molten lotus
Ohh i see
willow canopy
Let $S_n = \sum_{k=0}^{n} a_n$ be a finite sum\
Then, construct the set ${S_n}{n=0}^{\infty}$ \
Let S = $\sum{k=0}^{\infty} a_n$ \
We say that S converges when the infinite set ${S_n}_{n=0}^{\infty}$ converges to a value
molten lotus
I noticed that on my formula sheet theres no all the sums sign
Sorry I dont remember exactly what that equation is called
The one that looks like an E
ocean sealBOT
Azzurala
willow canopy
yea there should be an epsilon-N there as well when I said “converge to a value”
but my point here is that
when they say to “determine the sum of this entire infinite sequence”
the sequence here is the ${S_n}_{n=0}^\infty$
ocean sealBOT
Azzurala
willow canopy
and the infinite sum is S, according to what I wrote up top
molten lotus
Yeah
willow canopy
so yea, what they gave you was just $S_1, S_2, S_3$, which is part of the infinite sequence ${S_n}_{n=0}^\infty$, and now you’re asked to find $S$
ocean sealBOT
Azzurala
willow canopy
is it clearer what the question wants now?
willow canopy
so that infinite sequence should start at 1
I messed up with my notation lol
well it’s convention really, and in this case the sequence starts at 1
anyway, I hope this helps @molten lotus
willow canopy
👍
molten lotus
.close
mortal river
Hey simple probability question here
lone heartBOT
Hey simple probability question here
mortal river
mortal river
3 combinations of places for A to go
4^2 possible combinations of other letters
48 possible combinations
willow canopy
then you permute 2 from 4 out of {A,B,C,D}
it’s not combinations, it’s permutations
…so yea, I got 48 too
uhhhh strange
mortal river
Is the work for combination and permutation problems usually different?
willow canopy
yea
BC and CB are the same thing for combinations
but different things for permutations
actually, let’s approach this problem a different way
clever folio
If you count 48 are you sure you haven't triple counted stuff like AAA?
willow canopy
If you count 48 are you sure you haven't triple counted stuff like AAA?
oh yea this explains it
and also letters like
BAB as well
prime badge
combinations is too hard for this
it should be just 4^3 (all words) minus 3^3 (forbidden words)
clever folio
Yeah for 48 you over counted some stuff like AAA, AAB and so on.
prime badge
hm, that's not 38
mortal river
Wait where are you seeing that words like AAA aren't allowed?
It says letters can repeat in the problem
clever folio
Wait where are you seeing that words like AAA aren't allowed?
No
clever folio
I'm saying if you count AXX, XAX, XXA where X can be A,B,C,D using product rule then adding you'll get 48 because you're overcounting.
willow canopy
any words with repetition in its letters
mortal river
Yeah I get what you mean now
mortal river
it should be just 4^3 (all words) minus 3^3 (forbidden words)
So this would be the solution then?
To avoid the repeated counting
willow canopy
honestly I can’t quite see a precise formula for it
willow canopy
So this would be the solution then?
not yet, that doesn’t give the right answer
prime badge
yeah but it doesn't give 38
clever folio
Mmm if you count AXX there are 16 diff ways. Then if you count XAX and exclude A as the first letter there are 12 ways and then you count XXA and exclude A as the first or second letter you get 9 ways which gives a total of 37 ways so trying to count like this has a mistake too.
prime badge
the mistake is in the hint then
clever folio
Well okay also if you count AXX, XAX, XXA where X is not A you get a total of 9+9+9=27 ways to have exactly one A. Then you count AAX, AXA, XAA where X is not A and you get a total of 9 ways to have exactly two A's. Then one leftover AAA gives 37 ways to have one or more A's. 
I guess that's just the same thing I did a second ago though.
mortal river
Hey I actually have to go but thanks for the help so far everyone
I will revisit this problem tomorrow
lone heartBOT
@mortal river Has your question been resolved?
sharp moth
Why is this not a valid way to divide polynomials?
lone heartBOT
Why is this not a valid way to divide polynomials?
sharp moth
Why is khan academy doing it like this
I guess that's identical to what I just did I just did it quicker?
abstract fractal
Khan academy is just distributing 1/x to each term
It's identical to what you did
Oftentimes in math, there are multiple ways to get the same answer
uncut depot
how do they get the 1/2 * ab * ac * sin(BAC)
lone heartBOT
how do they get the `1/2 * ab * ac * sin(BAC)`
uncut depot
i don't see how this works, there's no right angles related to alpha + beta
lone heartBOT
@uncut depot Has your question been resolved?
safe niche
lone heartBOT
safe niche
is there something different I have to do when the axis revolves around a line further from the origin?
lone heartBOT
@safe niche Has your question been resolved?
lone heartBOT
@safe niche Has your question been resolved?
slender marten
When I used to do these problem, I used to find it easiest to translate everything so that it rotates about a line going through the origin. I also used to reflect everything so that it was in the first quadrant too by replacing x with -x afterward.
lone heartBOT
@safe niche Has your question been resolved?
midnight halo
lone heartBOT
midnight halo
wait can i just express both as cos or sin
nvm how would i get e then
unless i use the complex definition of cos actually
its like i know what to do but not really 
vale wigeon
you can write $$\cos^5(\theta) + i \sin^5(\theta) = \frac{1}{32} \paren{[2\cos(\theta)]^5 + [2i \sin(\theta)]^5} = \frac{1}{32} ( (z+z^{-1})^5 + (z-z^{-1})^5)$$
ocean sealBOT
Ann
vale wigeon
and then expand (z+z^-1)^5, cross out every other term starting from the second, and multiply what remains by 2
and you will have your expansion
1/16 (z^5 + 10z + 5z^-3)
where z = e^iθ
midnight halo
Ohh
so i shouldve added the z's before converting back to cosines and sines
is that what you are referring to?
vale wigeon
nyeh... i guess?
midnight halo
nyeh... i guess?
so im ending with$\\ \frac{1}{16} (e^{5\theta i} + 10e^{\theta i} + 5e^{-3\theta i})$ but the question wants it in the form of $a \cdot e^{ki\theta}$
vale wigeon
the question wants to have each TERM be of the form ae^(kiθ)
vale wigeon
and your thing works just fine
native nebula
Help
lone heartBOT
@native nebula Has your question been resolved?
native nebula
Well, pretty sure it isn't
How you understand?
dreamy blaze
How you understand?
I think it's like cot(alpha).sin(alpha) is not a decimal
the cotangent must be a whole number
you need to use a whole number there, and I doubt anyone actually uses mixed fractions anymore
dry echo
How you understand?
Imagine trying to write it as an improper fraction
native nebula
the cotangent must be a whole number
Why so?
dry echo
This would unnecessarily complicate the expression for no reason at all
There’s no reason you would write trig functions as mixed fractions
native nebula
Ohh okay
dry echo
It might simplify working with numbers in certain cases
But I can’t see any advantages to doing that in this case
spring jackal
lone heartBOT
ocean sealBOT
spring jackal
I don’t know where to start
alpine sable
Prawn!
spring jackal
My guy
alpine sable
I lowiey cant help you
spring jackal
All good
lone heartBOT
@spring jackal Has your question been resolved?
spring jackal
Got it
alpine sable
What is the formula to get percentage of number X?
0.0 - 50%; 0.125 - 75%; 0.25 - 100%; X - ?%
lone heartBOT
What is the formula to get percentage of number X?
0.0 - 50%; 0.125 - 75%; 0.25 ...
@alpine sable Has your question been resolved?
alpine sable
it can be converted to simple percentages, so
0% - 50
50% - 75
100% - 100
?% - 55 (for example)
gray ingot
it can be converted to simple percentages, so
0% - 50
50% - 75
100% - 100
?% - ...
for this data set it'd be
X% = 50X/100 + 50
viscid moat
hello
viscid moat
how can i find the Asymptote for this
both vertical and horizontal
is there a trick to it ?
gray isle
for vertical, consider when the denominator is 0
gray isle
and whether the numerator is also 0 at that location to determine whether you have a potential hole
for horizontal, you'd consider limits to -inf and +inf
note that there are other types of asymptotes here such as oblique/slant asymptotes
viscid moat
didnt take those "yet"
viscid moat
for horizontal, you'd consider limits to -inf and +inf
im trying to find it by using this
but i keep getting some weird answers for a
while the answer is y=x+1
so a should be one and nothing else
since its like this y=ax+b
gray isle
that's the oblique/slant asymptotes I'm refering to
y=x+1 is not a horizontal asymptote
viscid moat
oh shid
gray isle
and I'd just use polynomial long division for those
viscid moat
and I'd just use polynomial long division for those
how ?
vale wigeon
im trying to find it by using this
are you specifically instructed to do it this way and not in any other way?
lone heartBOT
@viscid moat Has your question been resolved?
floral solar
Can someone explain the question?
So, if f(x) represents the profit if the selling price was x, what does f'(x) represent?
floral solar
the derivative
lol yeah I know that, but what does it mean here?
floral solar
right?
Yea
so what does the slope mean here in terms of the selling price and profit
is it the ratio of profit and selling price?
floral solar
Then what does it mean?
The profit is positive?
lone heartBOT
@floral solar Has your question been resolved?
floral solar
.close
twilit rivet
lone heartBOT
abstract fractal
Explain your answers
abstract fractal
For example, why do you think choice 4 is correct
abstract fractal
You have to select the statements that are true, no?
twilit rivet
stop wasting my time
abstract fractal
You selected choice 4
If I understand your reasoning, I can clear up misconceptions
Though if you wish to be unhelpful, I can leave. I owe you nill
twilit rivet
why 8 vectors in R^5 spans R^5 but why not 7 vectors in R^3 span in R^3
abstract fractal
You can choose 7 vectors that span R^3
Just choose 3 basis vectors that span R^3, then pick any 4 other vectors
So I'm not sure what you mean by "why not 7 vectors in R^3 span R^3"
abstract fractal
There's no trick. All it takes is an understanding of R^n and vectors that span them
twilit rivet
how do you do it ?
twilit rivet
You can choose 7 vectors that span R^3
i don't get what you mena
abstract fractal
Do what? How do I know I can pick 7 vectors that span R^3?
twilit rivet
Do what? How do I know I can pick 7 vectors that span R^3?
does not span
???
7 vectors does not span is the correct answer
can you explain why
abstract fractal
The question asks if you can select 7 vectors that don't span R^3
Consider if all 7 vectors lie on the same line
Would those 7 vectors span R^3?
twilit rivet
The question asks if you can select 7 vectors that don't span R^3
the question ask to select the true statements
??
wdym
abstract fractal
Yes
And you can pick 7 vectors that don't span R^3
Just choose 7 linearly dependent vectors
Consider if all 7 vectors lie on a line. Through combining those vectors, can you ever get a vector that lies outside the line?
abstract fractal
Let's go through each answer choice one at a time and see if we can determine its truth value
twilit rivet
I chose options 2 and 5
twilit rivet
Let's go through each answer choice one at a time and see if we can determine it...
yes tks
abstract fractal
First answer choice: is it true or false and why?
twilit rivet
false ?
abstract fractal
Why?
twilit rivet
i am not too sure
abstract fractal
Consider choosing 9 vectors that all lie on a line
For example, the vectors i, 2i, 3i, 4i, 5i, ..., 9i
twilit rivet
yup
abstract fractal
Where i is the unit vector, not the imaginary unit
Do those 9 vectors span R^5?
twilit rivet
yes
abstract fractal
The point is, they can't
If all the vectors lie on a line, then every combination of those vectors also lie on the line
So they cannot span anything except R^1
We have selected a set of 9 vectors that do not span R^5
twilit rivet
ah so basically 2 vectors form a linear get 1 span
9 vectors missing 1
more
10 span 5
right ?
abstract fractal
What're you asking?
abstract fractal
9 vectors can span R^5
But they don't have to
It depends on the vectors themselves
9 vectors can span any dimension up to R^9
Consider just R^2
Two vectors can span R^2. Just conside the unit vectors i and j
But we can also pick 2 vectors that dont span R^2
twilit rivet
does 9 vectors in R^6 span R^6 ?
abstract fractal
i and 2i don't span R^2, because no combination of i and 2i will give j
abstract fractal
does 9 vectors in R^6 span R^6 ?
They can
twilit rivet
They _can_
no does not span
abstract fractal
There exists 9 vectors that span R^6
twilit rivet
i have the answer
abstract fractal
The don't have to
The question isn't asking "do ALL sets of 9 vectors fail to span R^6"
twilit rivet
abstract fractal
The question is asking "is there AT LEAST one set of 9 vectors that don't span R^6"
There is A set
Not EVERY set
You can pick 9 vectors that don't span R^6
You can also pick 9 vectors that do
twilit rivet
ah i see
lone heartBOT
@twilit rivet Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
torn isle
lone heartBOT
torn isle
Hi, I did this as shown below
The answer of my friend is (2pi-2)/pi
But mine is different. May I know where I did wrongly?
lime bobcat
Hi.
torn isle
Could we see your friend's solution?
No, they just posted in chat ask, is the answer (2pi-2)/pi
Then got person agree with his answer
Which I don’t know what’s wrong with mine 😵
torn isle
All seems correct to me.
Guess I know why already
I sub in the wrong value
I sub 1 instead of original z
lime bobcat
Where do you say the mistake is?
torn isle
Where do you say the mistake is?
Here, I sub the differentiate value 😫
Should be t instead of 1
But I’ll check first
Whether I can get the answer or not
alpine sable
f(x)=x³-4x²-6x+k
g(x):inverse of f(x)
6f'(x-1)+12x-28=(f' o g)(2x)
has a root in [0,2]
k_min+k_max=?
lone heartBOT
f(x)=x³-4x²-6x+k
g(x):inverse of f(x)
6f'(x-1)+12x-28=(f' o g)(2x)
has a root in...
@alpine sable Has your question been resolved?
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@alpine sable Has your question been resolved?
cedar vault
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median leaf
i think it should be "u"
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fervent kelp
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thick yoke
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sharp moth
Why is the answer (x-4)+(17/(x+4)) and not what I have written?
sharp moth
languid bolt
try expanding (x+4)(x+4)
sharp moth
I have the wrong factors?
slender gull
Yes you do.
sharp moth
Okay thank you
sharp moth
I guess the addition threw me off
I think I was pretty sure that a^2+b^2 would make it (a+b)(a+b)
sharp moth
What does it produce
slender gull
**What the hell am I doing here?**
ocean sealBOT
MarveI
slender gull
**MarveI**
= (a+b)(a+b)
sharp moth
I am trying to apply (a^2 - b^2) to an equation that does not satisfies the requirements for that equation?
Because there exists no negative between a and b in (x^2 + 16)?
languid bolt
yes?
sharp moth
How are they getting the value 17 in (x-4)+(17/(x+4))
Very confused because I don't see how 16-15 is not the same
gray isle
1 = -16+17
sharp moth
But so is 16-15
gray isle
the difference is that x^2-16 is actually divisible by x+4
whereas in the way you chose to manipulate it: x^2 + 16 is not
like sure you could express 1 as 16-15, but it doesn't help you
lone heartBOT
@sharp moth Has your question been resolved?
alpine sable
I was able to factor the denominator into (x-3)(x+6) but im not sure how to factor the numerator.
alpine sable
I tried to take the 3 out and make it 3(x^3-1) but i still get stuck there
normal ingot
There is no need to factor the numerator to find the domain
sterile hill
I tried to take the 3 out and make it 3(x^3-1) but i still get stuck there
It asks for domain
The numerator doesnt matter
well nvm
You can cross
sterile hill
I tried to take the 3 out and make it 3(x^3-1) but i still get stuck there
You can factor the x^3 - 1
using the a^3 - b^3 formula
alpine sable
right right cause Domain is X
alpine sable
3(x-1)(x^2+x+1)
how does this result in getting this as an answer though?
sterile hill
because the denominator cant equal 0
(x-3)(x+6) =/= 0
the denominator factors into (x-3)(x+6)*
because if the denominator equals zero then it'll be undefined
alpine sable
oh my god
i totally misread your comments i thought you said how i shouldnt worry about the denominator LMAO
sterile hill
which means that the set of solutions will be empty set because the solutions arent real
alpine sable
this makes so much more sense now
sterile hill
lol
alpine sable
thank you sm
sterile hill
np!
alpine sable
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tepid drum
Hi
tepid drum
What u said up is wrong @sterile hill
main kraken
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tepid drum
.reopen
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sterile hill
I’m guessing you meant the crossing portion
** I did not mean that
I don’t know what I was thinking
tepid drum
No there are solutions
sterile hill
The problem says to find the domain?
tepid drum
Yes
sterile hill
?
tepid drum
There is a domain which is (-inf;-3)U(-3;6)U(6;+inf)
tepid drum
Yea
tepid drum
There is a domain which is (-inf;-3)U(-3;6)U(6;+inf)
Then the domain is this
sterile hill
Factors into (x-3)(x+6)?
tepid drum
Yes
sterile hill
So why is it negative 3 and positive 6
tepid drum
Since x is different than the solutions to this equation
sterile hill
The roots are x1= 3 and x2 = -6
sterile hill
👍
tepid drum
But what I mean is that u mentioned thjngs abt complex numbers and so on
sterile hill
Ohh
tepid drum
What did u mean by solution is empty set
tepid drum
But it certainly does
sterile hill
If the denominator equals 0?
tepid drum
If the denominator =0 Then it is undefined
sterile hill
Mhm
tepid drum
But here he wants to state the accepted values of x
tepid drum
And there are accepted values of x for this function when it's set = 0
sterile hill
because the denominator cant equal 0
^
sterile hill
So there is a domain in reals
Excluding when it equals the denom equals 0
tepid drum
Yes
sterile hill
If the denom was something like 4 then the d: R
tepid drum
Ik
sterile hill
I’ve just invested myself in other stuff especially since I’d usually dread math class
I took like 4 math classes last year
It was awful
tepid drum
Anyways let's just close this channel to enable someone who have a question to ask
sterile hill
👍
tepid drum
.close
alpine sable
Yo
ocean sealBOT
alpine sable
Ye so
All I know is that MN is 8 cm
And I need to find height of trapezoid
I also know that AB=CD
And I know that diagonal makes 30°
sterile hill
I’m bad with geometry but***** I’ll try to help 😂
So since AB = CD you know that the trapezoid is an isosceles trapezoid?
Does it tell you if MN is a median?
alpine sable
Ye I didn't know how to say it English so I typed ab=cd
sterile hill
Nse?
Oh so it is?
Okay this makes life a million times easier
So you now know that (a+b)/2 = 8
sterile hill
So a + b = 16
alpine sable
I did it halfway but I got stuck
alpine sable
Ok
sterile hill
So now
alpine sable
I think we have to use trygonometry am I right?
sterile hill
Since you know that if you cut out two triangles
sterile hill
I think we have to use trygonometry am I right?
Yes
alpine sable
Ok cool
sterile hill
Then opposite sides of a parallelogram are congruent
So then that means we’re left with 2 triangle bases that equals 8 cumulatively
Each triangle base equals 4
But I’m not quite sure if we are to assume
alpine sable
With tan
alpine sable
Kd is 8 so I connected BD
sterile hill
God I’m so tired 😂
alpine sable
I didn't find side
I found height
Like with diagonal and height I got triangle
So I did tan30°
There's formula where
sterile hill
Wait how is kd = 8
alpine sable
It's formula
sterile hill
?
alpine sable
Idk how to say in English sorry
sterile hill
Ah okay it’s fine!
sterile hill
👍
alpine sable
Like rules
sterile hill
Because I thought there was extra pieces so it doesn’t equal eight
alpine sable
Idk what u mean but ur wrong
Nah u don't have to make 2 heights
Just connect b to d
Then u got triangle
sterile hill
But it’s an isosceles trapezoid so both sides have to be equal
So there’s two triangles
Oh well idk anymore
Geometry is a mess
alpine sable
D will be 30° as said
sterile hill
sterile hill
Yeah but there’s still excesses on the right side
lone heartBOT
@alpine sable Has your question been resolved?
delicate geyser
i had a problem from graphs and im stuck on: how many diagonals does n-sided figure have that dont create a triangle (no 3 sides are connected with each other).
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i had a problem from graphs and im stuck on: how many diagonals does n-sided fig...
@delicate geyser Has your question been resolved?
delicate geyser
<@&286206848099549185>
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@delicate geyser Has your question been resolved?
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@delicate geyser Has your question been resolved?
alpine sable
hi
livid raven
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livid raven
Could someone simplify step 4 to 5
lone heartBOT
@livid raven Has your question been resolved?
livid raven
<@&286206848099549185>
real gazelle
what website is this? this seems like a horribly convoluted way of doing things
can I ask what the original question was
livid raven
Anti derivative of $$sin^2(x)*cos^2(x) dx$$
ocean sealBOT
Cheese Grater
livid raven
Yeah, thanks for the help : )
real gazelle
let me just check that it works real fast
real gazelle
I think the main thing is that you have to simplify this down using trig identities
here is one example:
we know that $\sin 2x = 2\sin x \cos x$
ocean sealBOT
Eric Tao
real gazelle
Therefore, $$\sin^2 x \cos^2 x = \frac14 \sin^2 2x$$
ocean sealBOT
Eric Tao
livid raven
Could you explain the isolated trig rules?
real gazelle
So since $$\sin 2x = 2\sin x \cos x,$$ we can divide both sides by two to get $$\frac12\sin 2x = \sin x \cos x.$$ Then, we simply square both sides to get $$\frac14\sin^2 2x = \sin^2 x \cos^2 x$$
ocean sealBOT
Eric Tao
real gazelle
Does that make sense
livid raven
Oh that makes sense
real gazelle
awesome
livid raven
That was very detailed, thank you : )
real gazelle
no problem!
so next we can simplify sin^2
by using the cosine double angle identity
So the cosine double angle identity says that $$\cos 2x = 1 - 2\sin^2 x,$$ which means that $$2\sin^2 x = 1 - \cos 2x,$$ or $$\sin^2 x = \frac{1 - \cos 2x}2$$
ocean sealBOT
Eric Tao
real gazelle
Awesome
So now the whole thing simplifies as follows:
$$\frac14\sin^2 2x = \frac14\left(\frac{1 - \cos 4x}2\right) = \frac18 - \frac18\cos 4x$$
ocean sealBOT
Eric Tao
real gazelle
Does that make sense
livid raven
Well first we need to u substitute I think
real gazelle
yep!
livid raven
So the 1/8 ends up being u/8 and that’s it’s anti derivative minus 1/8cos4u and the anti derivative ends up being sin(4u)/32
Actually no
That’s not right
real gazelle
you're getting there don't worry
Wait I have to go now, but hopefully you can figure the rest out; if not, someone else should be able to help
real gazelle
No problem!!
livid raven
This is what I have so far
Im not sure where I messed up though : /
Oh it’s all wrong, give me a sec
.close
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