Now, how would you conclude the total number o fpages in Sam's case ?
#help-23
crisp lodge
cedar crystal
Now, how would you conclude the total number o fpages in Sam's case ?
wouldnt you just say that 60x - 135
crisp lodge
not quite
cedar crystal
hm
crisp lodge
sam's pace is FASTER than usual
crisp lodge
wouldnt you just say that 60x - 135
yet here you indicate that after x days of reading 60 pages per day, he still doesnt reach the goal
which coincides with 2 parameters
cedar crystal
true
cedar crystal
that, and an extra one
um
i think you would do
- 135
then on top of that
or minus
im not sure
crisp lodge
just one little thing
cedar crystal
what is that
crisp lodge
65x is reading 65 pages each day
crisp lodge
noooo
cedar crystal
im not quite sure
crisp lodge
60x
cedar crystal
ok
crisp lodge
60x - is the standard case we're comparing to
cedar crystal
ok well i know so
crisp lodge
check what your equation is saying
crisp lodge
check what your equation is saying
I give that as a general advice hehe
cedar crystal
for reading 60 pages per day
crisp lodge
sort of a sanity check
cedar crystal
sort of a sanity check
lol ok
i dont know
to be honest
im thinking of every possibility
crisp lodge
60*x is the total amount of pages
cedar crystal
ok
crisp lodge
sam has read 65(x-4) so far, but he still has 135 pages togo
cedar crystal
yep
crisp lodge
so 135 is the complement to john's reading so far that would get him to 60x
so the equation checks out
cedar crystal
so 135 is the complement to john's reading so far that would get him to 60x
john?
crisp lodge
sam***
cedar crystal
ok
crisp lodge
idk why I had john in my head lol
cedar crystal
lol
crisp lodge
you mean +135?
crisp lodge
then yea
crisp lodge
np :)
cedar crystal
.close
hard venture
could someone help me with number c? Im not sure how to do partial derivative with summation
safe radishBOT
could someone help me with number c? Im not sure how to do partial derivative wi...
@hard venture Has your question been resolved?
hard venture
<@&286206848099549185>
fair dagger
Can you explain what the issue is?
If I am reading correctly they just want you to derivate this.
hard venture
yup
fair dagger
Okay good
I think it may be more obvious if you just write it out
we can also fix K = 3 for a moment
$$\frac{e^{z_k}}{e^{z_1} + e^{z_2} + e^{z_3}}$$
flat frigateBOT
M8732
fair dagger
can you do it in this case?
hard venture
yes, but why did u write it out like that?
fair dagger
To make it more clear that it is literally just plain old summation 🙂
even if there is a fancy sum symbol
hard venture
no i mean, why 3 terms?
fair dagger
I want you to see the pattern
hard venture
oh
wait
so i can do the partial derivative for $e^z_l$ and keep the summation part?
flat frigateBOT
An Actual Anxious Hamester
fair dagger
Not sure what you mean by "keep".
hard venture
can i show you my answer in a bit? @fair dagger
fair dagger
sure
hard venture
Could you help me verify please?
I would send the steps, but I wrote it in paper, and it is a mess
fair dagger
,wolf d/da e^a/(e^a + e^b + e^c)
flat frigateBOT
fair dagger
square in the denominator seems to be placed wrong
also I think the sums somehow did not work out correctly.
@hard venture Should we try work it out step by step?
fair dagger
constants? Which constants
hard venture
$e^{z_k}$
flat frigateBOT
An Actual Anxious Hamester
fair dagger
I don't think this is the place to start.
hard venture
oh
fair dagger
When you derivate you need ot work your way from the outside inwards
hard venture
oh
fair dagger
in this case the first thing to do would be to work with the quotient
flat frigateBOT
An Actual Anxious Hamester
fair dagger
if we want to apply the quotient rule for f(x) / g(x) we need to find the derivative of f(x) and g(x)
$$f(z_k) = e^{z_k}$$ and $$\frac{df(z_k)}{d{z_k}} = e^{z_k}$$
flat frigateBOT
M8732
flat frigateBOT
M8732
hard venture
@fair dagger Sorry, I had to check on my baby. I think I will take a rest for 30 minutes, been working since the morning! Sorry 😄
fair dagger
Ok
safe radishBOT
@hard venture Has your question been resolved?
lone crane
safe radishBOT
lone crane
Anyone can do this i wanna know whats the answer
blissful gate
what have you done so far
lone crane
551/65 x 100
blissful gate
it is correct
lone crane
Okay thank youuu
Is there any way that could be easy when i see "reduction"?
Or so like
I just use the reduced percentage
blissful gate
hm? what do you mean?
twilit wadi
551/65 x 100
wouldn't that be finding it if the phone was 65% the original price?
lone crane
Like for example what i did was i made 2 bars and first bar i put 65% and the second bar 35, we need the original price which has the percentage 65 and not the 35 since 35 is for the reduction price i assume?
lone crane
Yeah thats where iam confused
twilit wadi
it's reduced by 65%
blissful gate
and not 65 percent off?
youre right, I read it is 65% of the original price
good catch!
twilit wadi
yes
twilit wadi
yeah
lone crane
Since its the original thenn it has the 100% and the reduced price is.. 551
So 100-65 is 35
551 =35%
And so on
Correct?
twilit wadi
yea
lone crane
I dont know..
twilit wadi
if a store applys a discount to an item and it gets more expensive, it's not much of a discount innit?
let's try solving it
0.35x=551
lone crane
551/0.35
lone crane
Okayy umm last thing iss
twilit wadi
ye?
twilit wadi
0.80x=500
twilit wadi
dw dw
lone crane
100-20=80%
twilit wadi
mhm
flat frigateBOT
Result:
625
YYYYYESSSS
Tyyyyssmmmm@twilit wadi @blissful gate i reallly appreicate it
Take care and stay safe
blissful gate
that was all bremperor!
twilit wadi
could you clarify it a little?
lone crane
Okayy sooo
Finding the price the has been reduced
Since we got the original price which is 625
625 - 500
Is 125
twilit wadi
sure
lone crane
That is the redudced price ye?
twilit wadi
u as well
languid brook
how do i calculate the area of a triangle with 3 points on the coord plane given
steel stag
shoelace formula*
thin token
red glen
are there no absolute values?
What
languid brook
i got a negative area
languid brook
oh ok
red glen
Take absolute value
rugged hound
How
plucky elk
Jesus this problem
lime robin
Can I get some help please
rugged hound
um sorry this channel is occupied lol
plucky elk
Can I get some help please
This channel is occupied. See #❓how-to-get-help
plucky elk
Is one side 5-2x^2?
plucky elk
are the cross sections parallel to the xz plane?
i guess so since that's the definition of perpendicular to the y-axis
,w plot y=x^2, y=5-x^2, y= 5/2
flat frigateBOT
desert hinge
i can do part a for q 9 and 10 but not part b
safe radishBOT
i can do part a for q 9 and 10 but not part b
worthy hemlock
i can do part a for q 9 and 10 but not part b
If you were able to simplify part a in 9 and 10, all you do is plug in the given values into the simplified expression
safe radishBOT
@desert hinge Has your question been resolved?
desert hinge
Part a
Part b (attempt)
when I do 48828125x1677216 I get 8.18953124 x 10^13 in my calc
@weak dirge @worthy hemlock
worthy hemlock
You can use your answer from part a to do part b
worthy hemlock
Same thing for 10
And the others, I suggest that you simplify then plug in the values
safe radishBOT
@desert hinge Has your question been resolved?
prime prawn
,rotate
flat frigateBOT
red glen
Why you doing so much calculation
safe radishBOT
@desert hinge Has your question been resolved?
lean otter
,calc (2/3)^1/6
flat frigateBOT
Result:
0.11111111111111
Result:
3.5407061614721e-12
,calc simplify ((2/3)^1/6)^12
flat frigateBOT
The following error occured while calculating:
Error: Unexpected type of argument in function pow (expected: number or Complex or BigNumber or Fraction or Unit or Array or Matrix or string or boolean, actual: Node, index: 0)
opaque wedge
safe radishBOT
opaque wedge
Hi
Pls help I’m stuck with this
20 overs = 20x6=120
50overs= 50x6=300
<@&286206848099549185>
quasi bison
why are you multiplying 20 and 50 by 6?
one would think that ||a sensible first step would be to find how many runs they have already, hence find how many runs they have left to score, and how many overs they have left to do it||
quasi bison
let OP respond
mortal meteor
ups, i didn't pay attention to the name
lean otter
@opaque wedge
thin token
please can someone tell me how to solve recurrence relation
safe radishBOT
please can someone tell me how to solve recurrence relation
thin token
and if possible please also provide some resources
frigid geyser
safe radishBOT
safe radishBOT
Available help channel!
lean otter
safe radishBOT
lean otter
Then I need the same if B is just a prebase.
Thanks in advance! Don't solve it for me, just point me in the right direction, please. I want to understand it.
ruby rapids
Thanks in advance! Don't solve it for me, just point me in the right direction, ...
recall the definition of f being continuous is that preimages of all open sets under f are again open
lean otter
recall the definition of f being continuous is that preimages of all open sets u...
Yep!
And a base is only open sets, right?
If so, then I have the forward direction.
ruby rapids
well yes a basis consists of open sets
but more than that
every open set is a union of basis elements
by definition of a basis
likewise, every open set is a union of finite intersections of subbasis elements, by definition of a subbasis
lean otter
And since all open sets in the topology for X can be constructed from sets S in the basis B, all open sets U have open preimages if all sets S do?
So that's the other direction?
lean otter
likewise, every open set is a union of finite intersections of subbasis elements...
By subbasis do you mean pre-basis?
ruby rapids
And since all open sets in the topology for X can be constructed from sets S in ...
well thats what you have to show
lean otter
My book actually doesn't use the terms, apparently.
ruby rapids
By subbasis do you mean pre-basis?
probably, i havent heard the term prebasis, but i'd guess its the same as what i mean by subbasis
lean otter
well thats what you have to show
Right. Well, if the preimage of S is open, then the preimage of S1 U S2 U ... = U will be open? Since it's the union of those sets.
lean otter
probably, i havent heard the term prebasis, but i'd guess its the same as what i...
Hmm... interesting... I'll take a look at my book and see if anything is in there about it.
ruby rapids
Right. Well, if the preimage of S is open, then the preimage of S1 U S2 U ... = ...
well what do you know about preimages of unions and intersections in general?
lean otter
well what do you know about preimages of unions and intersections in general?
They're the same as the union of the preimages, yeah?
For a bijection.
ruby rapids
preimages generally behave well with respecto to most set-operations
ruby rapids
For a bijection.
not only for a bijection
for any function between sets, you have $f^{-1}(\bigcup_{i \in I} X_i) = \bigcup_{i \in I} f^{-1}(X_i)$
flat frigateBOT
Phil
ruby rapids
where $X_i, i \in I$ is any family of sets
flat frigateBOT
Phil
ruby rapids
for direct images you have to be careful though
ruby rapids
Set theory?
well elementary set theory maybe
set theory for me is more like cardinals, logic, forcing etc
lean otter
Right, right.
ruby rapids
for direct images you have to be careful though
there it still works with unions, but not with intersections
lean otter
there it still works with unions, but not with intersections
Then I have the first part.
Now I have to figure out what a prebase is.
ruby rapids
Then I have the first part.
that shouldnt help you with the exercise though?
lean otter
Also, what is the difference between a base/basis and a cover?
ruby rapids
where do you take the direct image of sets?
lean otter
where do you take the direct image of sets?
Nah, the preimage.
ruby rapids
there it still works with unions, but not with intersections
well here i was talking about the direct image
lean otter
I needed f-1(S) for S in B is open in X implies f is continuous.
ruby rapids
as i said, preimage behaves well for everything basically
lean otter
well here i was talking about the direct image
Yeah.
ruby rapids
union, intersection, complement
lean otter
as i said, preimage behaves well for everything basically
Yeah, exactly.
Thanks for the help with that! I did not know that.
ruby rapids
Also, what is the difference between a base/basis and a cover?
we defined what a basis is above. Now an open cover is just a collection of open sets whose union is the whole space, i.e. they cover the space, thats where the name comes from
lean otter
we defined what a basis is above. Now an open cover is just a collection of open...
Is an open cover a base?
lean otter
Got it.
I was trying to find the connection.
btw
I have an A- in topology now after the last quiz.
So I am improving! 🙂
ruby rapids
nice
ruby rapids
yeah subbasis is the more common term i guess
or your book really means something else
lean otter
or your book really means something else
It was my professor's problem.
It wasn't from the book.
I would assume "pre"-basis is a more general structure that is not yet a basis.
So a base but without one or two properties?
oh
It's in my lecture notes. 👀
Okay, a "prebase" is a collection of subsets in X that covers X.
It is a subbase, according to the notes.
lean otter
yeah subbasis is the more common term i guess
What is the definition of a subbase?
ruby rapids
a collection of open sets $S = {U_i \mid i \in I}$ is a subbasis if $B = {\bigcap_{j=1}^n U_{i_j} \mid i_1,\dots,i_n \in I}$ is a basis. In other words, $S$ is a subbasis if every open set is the union of finite intersections of elements in $S$
flat frigateBOT
Phil
ruby rapids
yes
lean otter
Finite intersections?
ruby rapids
i mean yes, but you probably confused something
lean otter
Oh?
ruby rapids
any open set is a finite intersection of open sets by just taking the "intersection" over a single element, namely that open set itself
lean otter
Ah, right.
But this sub-basis S contains entirely finite intersections of open sets and therefore all of its subsets are open, right?
That's what I was trying to confirm.
ruby rapids
the point is that S generates the topology in the sense that if S is a subbasis for a given topology, then that topology is the smallest topology on the given space that contains the S as open sets
because topologies must be closed under finite intersections and arbitrary unions
which are the operations with which you get every open set out of a subbasis by definition of the subbasis
its like a generating system in algebra
lean otter
That makes sense.
ruby rapids
i mean bases are also generating systems in that sense
but bases only need unions, not intersections
hence subbases tend to be smaller generating systems
lean otter
Hence "sub."
ruby rapids
But this sub-basis S contains entirely finite intersections of open sets and the...
the subbasis is just a subset of the topology
the finite intersections come into play when you want to represent things that are not already in that subbasis
for example, the product topology on X x Y has a subbasis that consits of all sets U x Y and X x V where U open in X and V open in Y
if you just used unions, you generally couldnt represent sets like U x V, which are also open in that topology
but U x V = (X x V) n (U x Y)
lean otter
the subbasis is just a subset of the topology
Okay, so unions of finite intersections of S become the topology itself.
ruby rapids
but U x V = (X x V) n (U x Y)
so if you also use finite intersections you get all open sets
lean otter
yes
Got it.
So if f-1(A) for A in S is open in X, then...
All open sets in Y for f: X --> Y are equal to the unions of finite intersections of sets A in S, which are open.
lean otter
So if f-1(A) for A in S is open in X, then...
So naturally this implies that all open sets map back to the unions of finite intersections of open sets back in X as well.
Does that work?
I wrote it down more rigorously, but does the idea work?
ruby rapids
So naturally this implies that all open sets map back to the unions of finite in...
yes, because taking the preimage commutes with unions and intersections
lean otter
yes, because taking the preimage commutes with unions and intersections
Awesome! Thank you so much!
Could I ask one more question?
I have another problem.
ruby rapids
ok
lean otter
Okay.
So:
Let X have the finite complement topology. Then X is compact and for all subsets of X, S is compact.
That's my last problem to prove.
I can't see how the finite complement topology matters for the rest.
lean otter
It's compact if every open cover has a further subcover, yeah?
ruby rapids
generally note that in this topology (often also called the cofinite topology), open sets are very big
ruby rapids
It's compact if every open cover has a further subcover, yeah?
no, compactness means every open cover has a finite subcover
any open cover is a subcover of itself
ruby rapids
but thats not true
at least not for inifinite spaces X
e.g. take the naturals with the cofinite topology
lean otter
But it has the finite complement topology.
lean otter
Hmm...
ruby rapids
you have to find a finite subcover
in this case, note that N \ {0} and N \ {1} already cover N
lean otter
It has something to do with the finite complement topology.
It just means that the closed sets are finite, right?
How does that help?
lean otter
oh
ruby rapids
in this case, note that N \ {0} and N \ {1} already cover N
do you understand this?
the proof generalizes
lean otter
the proof generalizes
So X \ {something} covers X...
ruby rapids
wat
ruby rapids
a cover is a set of sets
ruby rapids
in the above case i started with the open cover ${\mathbb{N} \setminus {n} \mid n \in \mathbb{N}}$
flat frigateBOT
Phil
ruby rapids
then i found the finite subcover ${\mathbb{N} \setminus {0}, \mathbb{N} \setminus {1}}$
flat frigateBOT
Phil
lean otter
lol what
lean otter
Math is my name. This is not the math help channel, lol.
ruby rapids
m8 open your own help channel
lusty grail
SORRY
lean otter
XD
lusty grail
IM SO SORRY
lean otter
np lol
ruby rapids
well first try to do it for every open cover of N maybe
lean otter
Okay.
What is an open cover of N? xp
It just means each set in the cover is open in N?
ruby rapids
well we use the cofinite topology as in your exercise
lean otter
Right.
ruby rapids
so its a collection of sets with finite complement so that the union of all the sets is N
lean otter
so its a collection of sets with finite complement so that the union of all the ...
{empty set, N, N \ {n}}
lean otter
I don't know...
ruby rapids
kek
ok so
we take an arbitrary open cover $C = {U_i \mid i \in I}$ of $\mathbb{N}$
flat frigateBOT
Phil
ruby rapids
each $U_i$ is open in $\mathbb{N}$
flat frigateBOT
Phil
ruby rapids
so that means $\mathbb{N} \setminus U_i$ is finite
flat frigateBOT
Phil
ruby rapids
now you have to find a finite subcover
ruby rapids
i.e. $I_0 \subseteq I$ finite so that $\bigcup_{i \in I_0} U_i = \mathbb{N}$.
flat frigateBOT
Phil
lean otter
Something like U1 = even integers and U2 = odd integers would technically work.
ruby rapids
so we start with any $i \in I$ and note that $U_i$ is huge, i.e. it already almost covers $\mathbb{N}$, since $\mathbb{N} \setminus U_i$ is finite
lean otter
Where their union is N and the sets are finite in number.
flat frigateBOT
Phil
ruby rapids
Something like U1 = even integers and U2 = odd integers would technically work.
bruh you you even know what a subcover is lol
lean otter
bruh you you even know what a subcover is lol
It is a cover where all of the sets in it are equal to the sets in another cover.
ruby rapids
So first, the even intergers are not cofinite, since their complement is infinite, i.e. they are not open in N
lean otter
So for a cover {1, 2, 3}, a subcover is {1, 2}, for instance.
ruby rapids
So first, the even intergers are not cofinite, since their complement is infinit...
but even if they were, who tells you that this set would be part of the arbitrary open cover we chose
lean otter
I just meant...
ruby rapids
It is a cover where all of the sets in it are equal to the sets in another cover...
yes
lean otter
They are technically finite in number.
I was just thinking, they're not covers / subcovers.
nvm
That wasn't my answer.
ruby rapids
you have to cover the rest with finitely many other sets
lean otter
But it's not a subcover.
lean otter
but each element must be in one of the cover sets
What?
ruby rapids
the U_j form a cover. so for every x in N \ U_i there is some U_(j_x) with x in U_(j_x)
lean otter
the U_j form a cover. so for every x in N \ U_i there is some U_(j_x) with x in ...
The union of all of the open sets?
ruby rapids
what
ruby rapids
i dont really understand what you want to do with that
lean otter
I'm just trying to process it.
ruby rapids
im so confused
lean otter
Me too.
ruby rapids
we want a subcover of the U_j
wo chose any U_i
that already covers N up to finitely many elements
ruby rapids
each of the remaining elements is in some U_j
hence you have your finite subcover U_i,U_j_1, ... U_j_n
ruby rapids
You said it "almost" covers N.
yes because N \ U_i is finite
lean otter
Ah.
Since C is a cover for X...
Anything left in X\Ui must be in the rest of the cover!
Right?
ruby rapids
basically yes, but what exactly do you mean by that
lean otter
Right.
So, then...
Any element x in X\Ui...
Must be in the rest of C = X\Ui is finite.
ruby rapids
X \ U_i is just a set
ruby rapids
C\Ui is finite.
no
lean otter
No?
ruby rapids
C is the cover
lean otter
Dang.
ruby rapids
$C = {U_j | j \in I}$
flat frigateBOT
Phil
ruby rapids
you're confusing the space with the cover i think
ruby rapids
So take X\Ui for some Ui int he cover.
yes
lean otter
Then an element x that is in X\Ui must be in the cover, right?
lean otter
Because it's a cover.
ruby rapids
but x must be covered
lean otter
agh
ruby rapids
by some U_j
lean otter
Why?
oh
Is it because U1 U U2 U ... is open?
X = U1 U U2 U ...
X is the union of open sets.
ruby rapids
it has nothing to do with openness
lean otter
Okay?
ruby rapids
x in N \ U_i is in particular some element of N
C is a cover of N
this means the union of all the U_j is N
so since x in N
there is some U_j with x in U_j
ruby rapids
ok but then thats it
lean otter
What is the finite subcover?
ruby rapids
we pick any old U_i and an enumeration {x_1,...,x_n} of N \ U_i
then for each x_k there is U_j_k with x_k in U_j_k
so the finite subcover is U_i,U_j_1,...U_j_n
lean otter
Ah.
covert forge
ruby rapids
and this generalizes traightforwardly to any subset of any space on which we put the cofinite topolgy
lean otter
- Let x be an element of X\Ui.
no
- Take {x1, x2, ..., xn} = X\Ui.
(Since X\Ui is finite).
Then...
- X\Ui is covered by some set of Uj's, each Uj containing some xi.
C. Then This set of Uj's is obviously a subcover of C and is finite because X\Ui is finite.
ruby rapids
yes
ruby rapids
4. X\Ui is covered by some set of Uj's, each Uj containing some xi.
but maybe you should specify this a bit more
just because you can choose a finite covering, doesnt mean you have to
so when you say its covered by some U_j that doesnt directly mean you pick a finite covering
or in you last step you just say "we can choose the covering of X \ U_i to be finite because X \U_i is fiinite"
instead of "it is finite"
lean otter
so when you say its covered by some U_j that doesnt directly mean you pick a fin...
Ah, okay.
So I guess that makes sense.
Then I just need to prove that every subset of X is compact as well.
ruby rapids
its literally the same proof
lean otter
And I'll have survived another weekend of topology homework. 😵
lean otter
its literally the same proof
Do I just say that that "the same goes for a subset of X?"
Basically?
That it's a similar process?
lean otter
Right.
ruby rapids
and subsets are compact if they are compact as spaces with the subspace topology
so in this way you get the general case from the one you proved above
lean otter
so in this way you get the general case from the one you proved above
Got it.
So just say "the above proof applies to S with the induced topology from X, and if S is compact as a subspace of X it is compact as a subset of X as stated by Theorem 7.6 in the book."
ruby rapids
otherwise, what i meant above is that the same proof works because if X \ U_i is finite, then S \ U_i is finite for any subset S of X
ruby rapids
So just say "the above proof applies to S with the induced topology from X, and ...
yes
depending on how harsh they grade i would correct some formalities
lean otter
Okay.
ruby rapids
first you should state that you pick some arbitrary but specific j and then look at X \ U_j
lean otter
It's usually pretty chill as long as the answer is correct. I got a perfect score on a proof on a quiz just for drawing a picture. XD
And I often just draw pictures to prove something about sets on homework.
ruby rapids
next, you dont know what J looks like, so U_1 is not necessarily defined, you would have to pick indices i_1,..., i_n in I and look at U_i_1, ... U_i_n instead
also you switched from J to I midway
rest looks good
lean otter
rest looks good
I fixed the i/j part.
I just meant U1 as in some arbitrary U that I ordered.
I don't think they'd take points off for a formality like that.
lean otter
rest looks good
Thank you very much! I understand it now! You are very helpful. 😄
.close
lofty holly
safe radishBOT
lofty holly
how would i do this
jade gust
write everything as a base of 2
lean otter
write in the base of 2
lofty holly
please can you give an example
lean otter
what is another way to right 8 in terms of 2^x
lofty holly
3
lofty holly
1 30
2 15
3 10
5 6
lean otter
60 to the power of 4x
Or 15 * (2^(3x+1))
jade gust
Use a calculator 
lofty holly
non calculator please
pulsar condor
<@&286206848099549185> what should i do next
dont spam ping.
lofty holly
ok
pulsar condor
but anyway, just simplify the RHS.
pulsar condor
simplify the RHS, directed at the person getting help
lofty holly
"
jade gust
lofty holly
"advanced"
lean otter
😭
lean otter
Ag, smart idea.
jade gust
sheesh i'm a genius
okay so what i did was
I forgot what i did
Okay right so I've expressed 8^x and 4^(26) with a base of 2
I multiplied 30 to get rid of that fraction
So we have 30*2^(3x)=2^(56)-2^(52)
what
pulsar condor
equations don't become expressions
jade gust
and yeah i've written 30 as its factors, 2*15
wait
oh yeah
2*15*2^(3x) on the LHS
apply the exponent rule
a^b*a^c=a^(b+c)
pulsar condor
You could wait for them to actually be here and respond....
jade gust
they can read
jade gust
Well usually i type and they can read then they can ask
because people just tend to leave and i'm not waiting for them to respond
jade gust
@lofty holly dude are you here
why do people just leave on me
what have i done to deserve this
safe radishBOT
@lofty holly Has your question been resolved?
jade gust
bru
flat frigateBOT
jade gust
any questions just @ me
safe radishBOT
Available help channel!
eternal herald
What did I do wrong?
safe radishBOT
What did I do wrong?
zinc crown
,w sqrt(3)/(sqrt(5)+1) - sqrt(3)/(sqrt(5) - 1)
flat frigateBOT
zinc crown
,w -sqrt(3)/2
eternal herald
sorry
oh
OH GOD
HAHAHAHA
THE ANSWER WAS RIGHT THERE HOW DID I MISS IT IM LITERALLY BLIND
ITS B
BAHAHHA
IM SORRY
narrow kraken
Hi
narrow kraken
When it says simplify for example for a I got 2^3.9 but do i give the exact value for that
same thing with b I got 15^2, do I leave it like that
safe radishBOT
@narrow kraken Has your question been resolved?
lean otter
safe radishBOT
lyric ingot
a(b+c) = ab + ac
That is the distributive property
So 3(3x+6) becomes 3(3x) + 3(6). Can you simplify that further?
@lean otter
lean otter
hmmm
lyric ingot
Let me know if what I said is confusing you
lean otter
So 3(3x+6) becomes 3(3x) + 3(6). Can you simplify that further?
im stumped
safe radishBOT
@lean otter Has your question been resolved?
safe radishBOT
@lean otter Has your question been resolved?
plucky elk
im stumped
try plugging in small values for x: x=1, x=2, x=3
lyric ingot
Yes what riemann said, this is a good way to understand it. (I used this for exponent stuff before)
lean otter
ok
lyric ingot
For example 3(2+4)
Solve it normally using PEMDAS, which would be 3(6) which is just 18
Then use the distributive property,
3(2) + 3(4)
6 + 12
18
The answers are the exact same
rare vale
What's the difference between variance and standard deviation?
I'm confused where they are used for
safe radishBOT
What's the difference between variance and standard deviation?
I'm confused wher...
solid carbon
safe radishBOT
novel atlas
lol
eternal herald
good luck
novel atlas
Where did i go wrong here
tx
<@&286206848099549185>
damn
any1
<@&286206848099549185>
safe radishBOT
@novel atlas Has your question been resolved?
vital zealot
can someone tell me how to do this one?
safe radishBOT
can someone tell me how to do this one?
plucky elk
can someone tell me how to do this one?
Draw a triangle
vital zealot
Draw a triangle
traingle??
vital zealot
ohhh
plucky elk
Label the sides and then calculate the various trig functions for A
You know two already
vital zealot
various trig functions?
plucky elk
sec and tan are trig functions
eternal herald
Can anyone explain why the answer is the eighth root of 128?
eternal herald
but i have a different question...
worthy hemlock
but i have a different question...
Still, you just use one channel
eternal herald
oh
worthy hemlock
So you should go ahead and either close this channel or the other one you have
eternal herald
.close
lean otter
help i keep getting 140 but the answer is 153 question : (22)/(5)+(13)/(4)
arctic osprey
wdym 140
lean otter
ya im re learning them for a test
ok
hold on
i re did it
but im going on my phone
arctic osprey
can i see what you tried
arctic osprey
just put it here
lean otter
i cant im on pc i can open this message up but
phone i cant
there
do you see it ?
arctic osprey
you multiplied 13 and 5 incorrectly
lean otter
fr?
lean otter
💀
arctic osprey
everything else looks right
lean otter
ohhhh my god bro
ya u right
i type on the calculator
13x4
bruh this why i dont do math practice at night
im too sleepy
thanks big dawg'
plucky elk
.close if you're done
lean otter
.close
karmic monolith
Hi, I'm trying to do this problem but I really have no idea where to start, any guidance?
safe radishBOT
Hi, I'm trying to do this problem but I really have no idea where to start, any ...
fair dagger
This means that we are given the tanget of something and we call it x
and we are looking for the sine instead.
So I would try writting down the useful equations defining this
and trying to rearrange.
tan(y) = sin(y)/cos(y)
and
(sin(y))² + (cos(y))² = 1
We can use these to accomplish the goal.
@karmic monolith Does this help?
karmic monolith
Sorry, was afk, let me read.
fair dagger
x = tan(y)
karmic monolith
Since it's inverse tangent, how would that work?
fair dagger
If we find some expression of the style
sin(y) = f(tan(y)) using the above formulae
then we can conclude that sin(tan^-1(x)) = f(x)
karmic monolith
sin(y) = f(tan(y)) using the above formulae
What would f be representing here?
karmic monolith
We want to express sin in terms of tan.
Right, so sin(y) = cos(y) * tan(y)?
karmic monolith
(sin(y))² + (cos(y))² = 1
Would we use this ^ to get rid of it?
fair dagger
maybe 🙂
karmic monolith
Ok, so then we'd have sin(y) = (-sin(y)² + 1) * tan(y) if I did that right
fair dagger
I think you lost a square root somewhere
karmic monolith
Oops you're right
fair dagger
because cos was squared before
karmic monolith
sin(y) = -sqrt(sin(y)² + 1) * tan(y)
fair dagger
there is also an annouance with the sign but let's ignore that for now
it could be -sqrt
Now we "just" need to solve this for sin and we are done
karmic monolith
Do you mean for tan? Isn't it already solved for sin?
karmic monolith
Oh right.
fair dagger
if you are given the tan
karmic monolith
Ok I've gotten it to this, not quite sure how to proceed though.
fair dagger
We somehow need to recombine the sin eventually
to this end one large hurdle is the square root
so I would suggest to square the original equation at both sides
eliminating the square root
fair dagger
no, you would need to divide the 1
making it no better
I think we should instead eliminate the fraction
so that it becomes a quadratic equation
karmic monolith
Also I do have the answer for this problem, I've just been lost on how to solve it
Wait... how would I make it a quadratic equation?
fair dagger
yep
sin(y) is the unknown in this case
it's a quadratic equation in sin(y)
you can bring it in cannonical form
karmic monolith
What's that?
fair dagger
a sin(y)² + b sin(y) + c = 0
with a b and c known constants only involving the tan(y)
karmic monolith
I'm not really understanding, how do we turn the equation into that form?
fair dagger
Hint: Distributive law
karmic monolith
Ok, I'm here with distributive
fair dagger
Now you can identify a, b and c and use the standard quadratic formula