#help-36
fading berry
final saddleBOT
@fading berry Has your question been resolved?
final saddleBOT
@fading berry Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
wanton pine
how do i solve for the values of x in the equation $e^x(1+x)=1-x^2$
final saddleBOT
how do i solve for the values of x in the equation $e^x(1+x)=1-x^2$
soft zealotBOT
Galaxy
soft zealotBOT
Umbraleviathan
dry light
Factor out 1+x from both terms
final saddleBOT
@wanton pine Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
vale reef
I’m not sure how to use the Pythagoras method
final saddleBOT
I’m not sure how to use the Pythagoras method
vale reef
Do u plot (1,1) on a graph and make a triangle to start?
After that i get confused tho
vale reef
Hmm
trim crown
so first find where x-unit vector goes to
vale reef
To 0?
final saddleBOT
@vale reef Has your question been resolved?
chrome cove
Can you tell what the module of the vector you are trying to find is supposted to be?
vale reef
Wdym
final saddleBOT
@vale reef Has your question been resolved?
vale reef
The length of the vector you’re rotating basically
Oh
Idek
I’m gonna back to this
.close
hallow idol
hi my channel just got closed
hallow idol
.close
empty leaf
hi
empty leaf
.close
final saddleBOT
unreal anvil
please do not troll.
final saddleBOT
Available help channel!
nova wasp
final saddleBOT
nova wasp
I'm stuck on b and c , part a was simialr but didn't have the inequality but rather a equality sign
I solved it using the theorem that says the amount of solutions is ( n + r -1 choose r)
I can't apply it this scenario
fallow wren
I'm stuck on b and c , part a was simialr but didn't have the inequality but rat...
did you get several summation (everyone for each variable) that were nested ?
final saddleBOT
@nova wasp Has your question been resolved?
nova wasp
did you get several summation (everyone for each variable) that were nested ?
I'm not sure how to even approach , I know that you can't apply the n choose r formula since it's an equality so I have to split it up but I though 42 cases was a bit much , is it someway reducible
fallow wren
my previous question was refered to part a)
tender jewel
can anyone help me get started on this one?
final saddleBOT
can anyone help me get started on this one?
vital crag
Uhhh what theorems have you learned
tender jewel
|integral| <= ML
Im thinking maybe i try applying this inequality when f is a polynomial of over degree five and try to get a contradiction
but at the same time that doesnt show f is necesarily a polynomial
final saddleBOT
@tender jewel Has your question been resolved?
tender jewel
<@&286206848099549185>
tardy fox
tender jewel
im doing good
final saddleBOT
@tender jewel Has your question been resolved?
final saddleBOT
@tender jewel Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
brazen quest
final saddleBOT
brazen quest
by taking limits on both side how we are getting the result?
desert mantle
you have to show lim n->infty of U(...)-L(...)=0
you have 0 <= U-L <= 1/n
squeeze theorem
0 <= lim U-L <= 0
brazen quest
its not <=1/n
scarlet sequoia
0<=U-L<0+ right after taking limits
First of, when you take limits, strict inequalities become large inequalities
Second, when unneeded to know if 0 is 0+ or 0-, we just write 0 as the limit
So 0 <= U-L <= 0
brazen quest
yeah i dont have issue with writing 0 but its less than 0
scarlet sequoia
yeah i dont have issue with writing 0 but its less than 0
Less or equal to 0
brazen quest
can you explain bit about this
brazen quest
hm i get this thing after taking limits it become large inequalities so we took <= sign
desert mantle
or an even easier example of course, 0 < 1/n but if you take limits you get 0 = lim 1/n
brazen quest
yeah i got that point
but can you tell why strict inequalities become large inequalities
scarlet sequoia
but can you tell why strict inequalities become large inequalities
Because the theorem for limits of inequalities only works for large inequalities
If an <= bn, the theorem of limits of inequalities states that lim(an) <= lim(bn)
desert mantle
what do you want to hear for "why". I gave you two examples of why it cannot keep <
brazen quest
Because the theorem for limits of inequalities only works for large inequalities
an<bn then lim(an)<=lim(bn) it would work like this also?
brazen quest
what do you want to hear for "why". I gave you two examples of why it cannot kee...
well u cant just prove anything by example
desert mantle
ok are you confused about why it keeps some form of inequality at all?
scarlet sequoia
an<bn then lim(an)<=lim(bn) it would work like this also?
Yes this is how it would work
scarlet sequoia
well u cant just prove anything by example
Yes, you can prove a statement is false by counterexample
brazen quest
but here we are proving right
brazen quest
Yes this is how it would work
ok then its fine
scarlet sequoia
but here we are proving right
Denascite proved that the statement "for all an, bn, if an<bn then lim(an) < lim(bn)" is false by counterexample
brazen quest
but its not false
final saddleBOT
final saddleBOT
Available help channel!
final saddleBOT
can someone help me pls with this quesiton pls?
hidden kiln
can someone share their answers for this question pls
just to check with my answer
my answer: ||Mr Greenwell||
final saddleBOT
@hidden kiln Has your question been resolved?
hidden kiln
<@&286206848099549185>
final saddleBOT
@hidden kiln Has your question been resolved?
thick herald
final saddleBOT
thick herald
Today with my teacher we were studying on finding the smallest and largest function in a given interval
And i struggle to remember how we found this f(4)
urban maple
You just plug $4$ into $f(x)$
soft zealotBOT
OssihLikesBlue
thick herald
so it's like my x is 4
ahhhh i get it now, that's why we use the given interval to find it
thanks a lot!
.close
tranquil pine
wouldn't the x-intercepts of x(x+5)=0 be 0 and -5?
final saddleBOT
wouldn't the x-intercepts of x(x+5)=0 be 0 and -5?
tired walrus
you mean the solutions?
tranquil pine
answer for this is x=-5
tired walrus
or x-ints of y = x(x+5)
tranquil pine
solutions i mean
tired walrus
answer for this is x=-5
yeah, that's correct. do you see why x=0 doesn't make sense?
thorn grotto
Try plugging x = 0 into the original equation
tranquil pine
0 does not equal 0
hmm
weird
then why do people regard x to be (x+0) and take it as a solution
thorn grotto
0 / 0 is not 0
tranquil pine
or is that only if it would work in the original function?
so say the original function didn't have 0 in the denominator
would 0 be a solution?
@thorn grotto
thorn grotto
If the equation was 2x/5 = x^2 - 5x, then 0 would be a solution
final saddleBOT
final saddleBOT
Available help channel!
acoustic finch
I have been taught to solve this problem by using trig substitution and letting x = 5sin(theta); theta element of [-pi/2, pi/2]. Would it theoretically be possible to instead say: x = 5cos(theta); theta element of [0, pi]?
final saddleBOT
I have been taught to solve this problem by using trig substitution and letting ...
acoustic finch
.close
weary canopy
how do i do this limit without using l'hopital?
final saddleBOT
how do i do this limit without using l'hopital?
weary canopy
x-> negative inf of (x^3 + 2x -1)/(1-x^4)
urban maple
Why would you need L'hopital here?
weary canopy
my point is to not use it
urban maple
fair enough but it's not really related
anyway
what do you know about limiting behaviour?
or end behaviour?
acoustic finch
x-> negative inf of (x^3 + 2x -1)/(1-x^4)
You can take out a common factor of x^4
acoustic finch
lmao all good
weary canopy
I've been using l'hopital for so long
i just forgot all limit techniques lmao
.close
echo sinew
Need help with proportion if any ones free
final saddleBOT
Need help with proportion if any ones free
echo sinew
It’s pretty simple iirc
I have 10000 ppl being 45% out of 100%
How do I figure out the 55% like the number
Do I do 10000/45?
warm ether
many ways, most directly 10000/x=45/55 ie (10000/45)=(x/55)
or find 5% and multiply by 11 or something
warm ether
where did 500 come from
echo sinew
nvm I confused myself
Okay lemme re explain it I think I explained it bad
45% is 10000
I’m trying to find the number that would be 55%
warm ether
ik
echo sinew
many ways, most directly 10000/x=45/55 ie (10000/45)=(x/55)
Let me calculate this really quickly
If j do 10000/45 it comes out as 22
Does this mean the 55% is 22000?
warm ether
22?
warm ether
Does this mean the 55% is 22000?
no
echo sinew
Oh I thought I should always take the 2 first numbers
warm ether
its okay
warm ether
many ways, most directly 10000/x=45/55 ie (10000/45)=(x/55)
which of the two ways do you find more appealing
that ^ or finding 5% then multiplying
echo sinew
First one
warm ether
alrighty
as a ratio
the whole number can be written as 10000/0.45 since 0.45(number)=10000 is 45% of said number
say x is 55% then x/0.55 is also the whole number
so we can say 10000/0.45 = x/0.55
i multiplied both sides by 1/100 for the fun of it before since it doesnt matter but this is what we have
from there you just solve for x
echo sinew
I have a question then, so why does the 222…. Show up when 10000/45?? Would that be part of the calculation??
echo sinew
To solve for x what should I do then??
warm ether
what do you think?
warm ether
theres no particular reason to multiply by 100
how would you get x=...
from 10000/0.45=x/0.55
echo sinew
So sorry for this again but I don’t know
warm ether
how could you solve $a=\frac{x}{b}$ where a and b are just some numbers
soft zealotBOT
AℤØ
echo sinew
I’m really confused rn, let me try and explain what I know
I know that na: would be 10000 + 55%
Ne: would be 10000
And p would be 45
So to find na they tell me do 10000/45 but then the same issue comes up where its 222.22222222…
Is that how you do it normally??
To find na?
echo sinew
They taught me that na is the total number, and ne is the number that are being experimented on basically
15 would be the ne of 30 (na) which 15/30 would be 50%
echo sinew
and why is 10000/45=222.222 an issue?
10000/45=222.2222...=x/55
It’s not an issue then??
warm ether
i never said it was
echo sinew
Ohh
Wait
I think I understand it
So now I multiply it by 100 to make it inline with the other numbers?
And then the total would be
22222 + 10000?
warm ether
idek what you did
stop thinking about 100
theres no way for you to get an addition from this
echo sinew
Alright
echo sinew
how would you get x=...
from 10000/0.45=x/0.55
Let me reread this really quickly
I just tried another way rq
Since 45 is 10000 I multiplied 10000 twice to get 90
And then I just found 10% of 20000 which is 2000
And that would add up to 22000
Would that work?
warm ether
i mean, no, that would be 54%
if youre going to go about it that way, why not just get 5% and multiply by 11
or get 1% and multiply by 55 or something?
echo sinew
Uhhh, can you explain the 5% way then if that’s possible
warm ether
its okay, take your time dw about it
warm ether
how do you get to 5 from 45?
warm ether
Since 45 is 10000 I multiplied 10000 twice to get 90
think of how you got from 45 to 90 and do a similar logical process
echo sinew
45/9?
echo sinew
900?
echo sinew
Alright
warm ether
how would we now get 55%?
echo sinew
Multiplying the result of 10000/9 6 times?
soft zealotBOT
Result:
12222.222222222
,calc 10000/0.45
soft zealotBOT
Result:
22222.222222222
ish
echo sinew
Alright, thanks a lot
warm ether
np
echo sinew
.close
supple nest
final saddleBOT
tender jewel
,tex $\int_1^{e^x} ln(u^5)du = F(e^x) - F(1) $
soft zealotBOT
epiphonically
tender jewel
,tex then ${d \over dx} \int_1^{e^x} ln(u^5)du = {d \over dx} F(e^x) - {d \over dx} F(1) $
soft zealotBOT
epiphonically
supple nest
see i dont know what this means is the issue
tender jewel
,tex ${d \over dx} F(e^x) - {d \over dx} F(1) = f(e^x) {d \over dx} e^x - 0$
soft zealotBOT
epiphonically
supple nest
could you try to put this into simpler terms lol
before, i just had the lower boundary as 1 and the upper boundary as x
so for the answer i could just enter the function given
tender jewel
,tex do u know that $\int_a^b f(x) dx = F(b) - F(a)$
soft zealotBOT
epiphonically
supple nest
yes
tender jewel
,tex do u agree then $\int_1^{e^x} f(x) dx = F(e^x) - F(1)$
soft zealotBOT
epiphonically
supple nest
i guess that would make sense yes
tender jewel
,tex Then ${d \over dx} \int_1^{e^x} f(x) dx = {d \over dx} F(e^x) - {d \over dx} F(1)$
soft zealotBOT
epiphonically
supple nest
let me show you where i get hung up
tender jewel
kk
supple nest
is it because d/dx(F(1)) is 0
tender jewel
yea
supple nest
so its just taking the derivative of ln(e^x)^5)?
tender jewel
not exactly
supple nest
or like
tender jewel
,tex its $ln(e^{5x}) \cdot {d \over dx} e^x$
supple nest
oh wait
soft zealotBOT
epiphonically
tender jewel
yes
supple nest
would the answer just be 5ln(e^x)
tender jewel
no
supple nest
but f(x) would be ln(e^x)^5)
tender jewel
,tex u wanna find ${d \over dx} F(e^x) $
soft zealotBOT
epiphonically
tender jewel
no
tender jewel
,tex ${d \over dx} F(e^x) = f(e^x) e^x$
soft zealotBOT
epiphonically
tender jewel
using chain rule
supple nest
e^x * 5e^5x?
soft zealotBOT
epiphonically
supple nest
e^x (5x^4/x^5)
tender jewel
no
soft zealotBOT
epiphonically
supple nest
so that would be the answer
tender jewel
yes
supple nest
ok
oh yeah
i forgot i wouldn't need to take the derivative of ln(x) because thats already the derivative
ok i dont know why that took me so long tysm
i think the introduction of another function totally threw me off
.close
quiet holly
Let A ⊂ R be non-empty. If A has a supremum but no
maximum, then for every ε > 0 there are infinitely many a ∈ A with
sup (A) - ε < a < sup (A).
final saddleBOT
Let A ⊂ R be non-empty. If A has a supremum but no
maximum, then for every ε > 0...
tired walrus
how prove this question <@&286206848099549185>
!15m
final saddleBOT
how prove this question <@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
quiet holly
sorry homie
tired walrus
!status
final saddleBOT
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
didn't know
tired walrus
well now you do
quiet holly
tired walrus
ok
If A has a supremum but no maximum, then for every ε > 0 there is at least one a ∈ A with sup (A) - ε < a < sup (A).
i've replaced the "infinitely many" with "at least one" in this statement
do you know how to prove this one?
quiet holly
lemme think
tired walrus
(yes, it's weaker. but trust me, it's a stepping stone towards the real thing)
tired walrus
not really, no.
quiet holly
not really, no.
ok lemme try to sketch on a number line to better understand it. one sec
quiet holly
not really, no.
ok it makes sense. Sup(A) - ε is itself in set A as it is a value that is smaller than the supremum yet it exists in the set A. Right?
tired walrus
Sup(A) - ε is itself in set A
incorrect
quiet holly
> Sup(A) - ε is itself in set A
incorrect
so a number that is just a tiny bit smaller than the supremum is not garantied to be in the set? or what am I not understanding?
tender jewel
ok it makes sense. Sup(A) - ε is itself in set A as it is a value that is smalle...
u know sup(A) - ε < sup(A) for sure
tired walrus
so a number that is just a tiny bit smaller than the supremum is not garantied t...
indeed, nobody said sup(A) - ε had to belong to A.
sure it belongs to A for some epsilons, but not for all of them.
quiet holly
ahh
quiet holly
sure it belongs to A for _some_ epsilons, but not for all of them.
I get that. but then how would we prove that there's at least one element between sup(A) - ε and sup(A)
would we use the fact that the set is non empty?
tired walrus
well
i wouldnt say so directly
the way i know how to prove that (∀ε>0)(∃a ∈ A)(sup(A) - ε < a < sup(A))
is by contradiction
if this werent the case, then sup(A) would be separated from the rest of A by a gap of some size (corresponding to the epsilon for which there does not exist any a)
and we can't have that, bc then the supremum would not be the supremum.
tired walrus
so then you can say
each interval of the form (sup(A) - 1/n, sup(A)) contains at least one point of A
and these fuckers are nested
so within each one theres actually infinitely many points of A bc of that.
quiet holly
and we can't have that, bc then the supremum would not be the supremum.
could we like say that: lets assume we have ε which is an infinitely small number. and lets assume that sup(a)-ε is not ∈ A. then we would conclude that Sup(A) would actually not be the supremum of set A which would be a contradiction. and prove this way that sup(A)- ε must be part of set A
would that be a valid proof to show that at least one element exists in the set A between sup(A) - ε and sup(A) ?
tired walrus
and lets assume that sup(a)-ε is not ∈ A. then we would conclude that then, Sup(A) would actually not be the supremum of set A
no
sup(A) - ε ∉ A by itself doesnt place a gap between sup(A) and A.
or.
ok fuck your wording of it is clunky sorry
quiet holly
lemme try to reword it
tired walrus
im going off to sleep
ive said everything i wanted to say and i dont have the energy to pick through and unclunk wording
quiet holly
ok
well
thanks for the help eitherway
<@&286206848099549185> Can someone help with this question? The previous helper went to bed. 
final saddleBOT
@quiet holly Has your question been resolved?
tender jewel
<@&286206848099549185> Can someone help with this question? The previous helper ...
u agree because sup(A) - ε < sup(A) it is not an upper bound?
soft zealotBOT
epiphonically
tender jewel
since sup(A) - ε is not an upper bound
tender jewel
and this repeats to infinity
final saddleBOT
@quiet holly Has your question been resolved?
tranquil pine
How do I solve
final saddleBOT
How do I solve
tranquil pine
Do I have to foil it all out
toxic arch
Do I have to foil it all out
Yes then factor
It's easy to factor bc the constant terms cancel
tranquil pine
Yes then factor
Can I just do this
Not really sure how id convert that to interval notation tho
gaunt shadow
I need my work checked
final saddleBOT
I need my work checked
gaunt shadow
I’ve gone through my work twice and I caught two mistakes but it’s still wrong
final saddleBOT
@gaunt shadow Has your question been resolved?
gaunt shadow
<@&286206848099549185>
<@&286206848099549185>
<@&286206848099549185>
<@&286206848099549185> I need help
gaunt shadow
<@&286206848099549185>
final saddleBOT
@gaunt shadow Has your question been resolved?
hybrid sun
Can someone factorize this completely everytime i do it i get diffrent answers: 6p^2+7p-20
final saddleBOT
Can someone factorize this completely everytime i do it i get diffrent answers: ...
wraith crater
What’s ur answer
hybrid sun
What’s ur answer
(3p + 4)(2p-5)
hybrid sun
wym
heavy loom
hybrid sun
is it suppose to be subtract instead of + for (3p+4)
hybrid sun
yh but the teacher said factorize it completely
and in class she did smth abt
a b and c
value
idek how to get that
tawny bluff
the -(+4 * +5) = -20 is correct, so one of 4 OR 5 is negative
+4 and -5 gave -7 instead of 7, so flipping the signs will give -4 and 5 for 7
a b and c? You'll have to be more specific, sadly, as those are very common names for coefficients
unlike, say, m and b, which are more distinctive
hybrid sun
wait can i send you a screenshot of my classmates workout and u tell me if its wrong or right
tawny bluff
sure
tawny bluff
genuinely not sure what they're doing
but a b and c seems to refer to standard quadratic form
ax^2 + bx + c
hybrid sun
yh
thats what we doing
the last line on left side suppose to be final answer
the other side i think
is the
values?
and factors
tawny bluff
as shown on the right, the issue is you get -7 for b
when your initial question had +7
on the second line they wrote it wrong
they expanded 7p into 8p - 15p instead of -8p + 15p
from there the mistake is preserved
make sense?
tawny bluff
well, the process is right
[6p^2+7p-20]
[6p^2-8p+15p-20]
[2p(3p - 4) + 5(3p - 4)]
[(3p - 4)(2p + 5)]
soft zealotBOT
Astral
hybrid sun
respect astral
tawny bluff
np
tawny bluff
.close
final saddleBOT
wide folio
cedar copper
final saddleBOT
cedar copper
Hello
I have this one here
So i know some basics rule
that the exponenet will be in front and stuff like that
And that i will add 3 logs here
to expand it
But for example square root x alone will be x^1/2
how about when they have this exponenents
final saddleBOT
@cedar copper Has your question been resolved?
faint edge
You have a nested situation going on.
Easier to write then to type it. Gimme a sec.
,rotate
soft zealotBOT
faint edge
@cedar copper
From this point onward is just simplifying exponents and applying the rules of logs you mentioned.
The easiest way is to probably just work from the outside inward
cedar copper
Oh
Woah that look confuse
Ok
Ohhhh
those square roots on top of each other so 1/2 for 3 of them
final saddleBOT
@cedar copper Has your question been resolved?
pulsar patio
Ok so Im confused with how to find the interest on the second part.
final saddleBOT
Ok so Im confused with how to find the interest on the second part.
pulsar patio
Im basically just asking for guidance in the right direction cause I got no clue
shadow aspen
How much you got from interest is however much more money you got since depositing
pulsar patio
Yeah I would calculate it by saying 36300 = PV PMT = 37,835.30 I/YR = 9.5 % P/YR = 1 N = 42
And then subtract 36300 from the total
but it would be wrong
shadow aspen
I do not understand these units at all. If I means interest though I can tell you 378535.30 I/yr is not right
pulsar patio
36300 is the present value, 37,835.30 is the payments per period, 9.5% is the interest rate, the periods is one per year, the N which is periods times time is 42
cause 42 times 1 is 42
thats my units
final saddleBOT
@pulsar patio Has your question been resolved?
final saddleBOT
@pulsar patio Has your question been resolved?
sturdy cypress
you withdraw 37835 18 times and there's no money left
that's the total
37835× 18
final saddleBOT
@pulsar patio Has your question been resolved?
magic sparrow
@robust mulch
robust mulch
Oh hi
magic sparrow
is this close enough
robust mulch
Bro stop pinging people
wanton mortar
One student argues that a satellite in orbit is in free fall because the satellite keeps falling toward Earth. Another says a satellite in orbit is not in free fall because the acceleration due to gravity is not . With whom do you agree with and why?
final saddleBOT
One student argues that a satellite in orbit is in free fall because the satelli...
wanton mortar
It would be in a freefall no?
neon slate
l because the acceleration due to gravity is not . --> typo here? what is that supposed to say?
neon slate
what, the problem just says that?
neon slate
well it's hard to agree with that second student then : )
but yeah, objects in orbit are in general in free fall
wanton mortar
well it's hard to agree with that second student then : )
good point lol but what do you think they were attempting to say?
sturdy cypress
"the first student gives no reason, and the second student makes no coherent point at all"
sturdy cypress
"I agree with the second student, it's not our job to explain physics"
wanton mortar
and thats just because the force of gravity
neon slate
definition of free fall is i think if there is no force acting on the object other than gravity
so is that true for the satellite?
wanton mortar
if it was a planet different story right?
neon slate
🤔
neon slate
velocity doesn't imply a force is acting on an object, acceleration is what implies a force
that's the whole point of Newton's law of "an object at rest remains at rest, an object in motion remains in motion" unless a force is acting on it
wanton mortar
that makes sense
neon slate
i guess you can say technically a body is in free fall around the body it is orbiting, not sure if that is a useful description but whatever
even for something like moon around a planet or a planet around the sun
so yeah i'd agree with the first student
i think the main point to understand is an object in orbit only experiences the force of gravity, how you decide to describe that in words is a bit relative, no pun intended
neon slate
well that depends how the body got into orbit, a rocket used its engines to gain velocity, the moon...we don't fully understand how it formed but either from the original momentum of the solar system forming or from some forceful impact with the earth and a chunk breaking off with enough velocity to put it in orbit
then when an object is in orbit, just gravity is acting on it and redirecting that velocity into a slightly different direction constantly
wanton mortar
"Considering that the only force that is being exerted on the satellite is the force of gravity I would agree with the first student that the satellite is in free fall this is because the satellite possessed enough initial tangential velocity to offset the free fall and produce perpetual orbit. "
coolin?
neon slate
perpetual orbit is a redundant term at best and incorrect / confusing at worst, the word orbit by itself implies revolutions around an object
so just strike out perpetual :p
wanton mortar
okay gotcha! thank you
yeah i thought it was in a freefall
i just couldnt exactly state how it was continue to move.
neon slate
just say, it has enough tangential velocity to keep missing the earth as it is falling
because thats basically what it is
wanton mortar
okay thats true!
neon slate
😄
wanton mortar
i appreciate helping me fully understand it! i knew they were not* spending thousands in gas to keep that thing having tangetial velocity.
neon slate
i appreciate helping me fully understand it! i knew they were not* spending thou...
only need it initially, once it is in orbit there is no more need
wanton mortar
to me it reminds me of a basketball when it goes around the hoop for awhile
kinda different ofc lol 😂
final saddleBOT
@wanton mortar Has your question been resolved?
final saddleBOT
soft zealotBOT
Kalgar
final saddleBOT
@rugged yoke Has your question been resolved?
marble wing
final saddleBOT
marble wing
Hello guys what first derivative is correct in this case
marsh temple
The first
You seem to have forgotten about the +2x term in the second between these two lines
final saddleBOT
final saddleBOT
Available help channel!
marble wing
And how do I make stationary points from 4e^x-x^2e^x
final saddleBOT
And how do I make stationary points from 4e^x-x^2e^x
marble wing
.close
ivory lynx
hello, for letter a, how do i do the double angle identity for this? its not a special angle unfortunately
final saddleBOT
hello, for letter a, how do i do the double angle identity for this? its not a s...
ivory lynx
22.5*2 = 45
neon slate
rich tide
sin(2x)=2sin(x)cos(x)
neon slate
its half angle identities not double angle here, but yeah you could derive one from the other
oh sorry yeah youre right @rich tide you can use the double one more easily for a
ivory lynx
sin(2x)=2sin(x)cos(x)
yea but
how do u get sin 22.5 and cos 22.5
the exact values of it
rich tide
You don't need 'em
neon slate
x = 22.5
rich tide
By using the formula I gave, You can achieve sin of an angle that is pretty much known by everyone
neon slate
so 2sin(22.5)cos(22.5) = 2sin(x)cos(x) = sin(2x) = sin(45)
ivory lynx
hello, for letter a, how do i do the double angle identity for this? its not a s...
same thing with 2 tan 15 right? its just tan(30)
ivory lynx
thank you
rich tide
hol up
you don't have a square in the denominator tan
You need to manipulate it a bit
rich tide
unfortunately no
ivory lynx
fuck
ivory lynx
hello, for letter a, how do i do the double angle identity for this? its not a s...
so how do i manipulate this
how to get the value of 15 degrees
rich tide
well seems like you'll have to calculate the value of tan(15) for this
using tan(2x)=2tan(x)(1-tan^2(x))
ivory lynx
using tan(2x)=2tan(x)(1-tan^2(x))
so online calculator we go?
rich tide
$\tan\left(30\right)=\frac{1}{\sqrt{3}}=\frac{2\tan\left(15\right)}{1-\tan^{2}\left(15\right)}$
soft zealotBOT
B-eard
rich tide
15 is not a special angle unlike 30 45 and 60
well, it is actually one but is generally not taught at the early stages of learnign abt trig
ivory lynx
why
rich tide
I do wonder the same
rich tide
(extra: even 37,53 are standard angles. tan(37)=3/4, tan(53)=4/3)
rich tide
are multiples of 15 special ang
well, not actually. But you can say that it covers most of them
ivory lynx
ye
rich tide
**B\-eard**
let tan(15) to be another variable let's say y.
So, you have a quadratic in y which can be solved fr two values of y.
One of them will be rejected due to its sign (15 is in first quadrant and so tan of it must be positive)
ivory lynx
let tan(15) to be another variable let's say y.
So, you have a quadratic in y wh...
tan 30 is 2y
rich tide
yes
ivory lynx
let tan(15) to be another variable let's say y.
So, you have a quadratic in y wh...
the latter fraction is a quadratic
ivory lynx
let tan(15) to be another variable let's say y.
So, you have a quadratic in y wh...
the rejected is - tan^2(15)
because, as u said 15 is in first quadrant
ASTC
rich tide
well, no
ivory lynx
ah'
rich tide
$\frac{1}{\sqrt{3}}=\frac{2y}{1-y^{2}}\ ⟺\ y^{2}+2\sqrt{3}y-1=0$
soft zealotBOT
B-eard
rich tide
cross multiplication
ivory lynx
**B\-eard**
ye
rich tide
now, do you know the quadratic formula?
ivory lynx
**B\-eard**
a = 1
b = 2sqrt3
c = -1
rich tide
yes
ivory lynx
ooooo perfect square
rich tide
are you sure?
ivory lynx
sqrt3^2 = 3
2^2 = 4
4*3 is 12
-4(-1) = positive 4
12 + 4 is 16
sqrt 16 is 4
and since 2 is ur denominator; therefore it will be
rich tide
Okay there was abit of misinterpretation
So you mean the discriminant is perfect square
rich tide
well you are near the solution
recheck the last step (coefficient of sqrt(3) is not halved)
ivory lynx
can u cancel +- 4 and denominator 2
rich tide
you should end up with tan(15)=-sqrt(3)+-2
ivory lynx
or no
rich tide
Okay, so you would have tan(15)=2-sqrt(3) or tan(15)=-2-sqrt(3)
But as I said, one value would be rejected
just consider the other value and plug in
ivory lynx
**B\-eard**
so should i replace 15 here with either sign?
rich tide
no
ivory lynx
ay wait
rich tide
But as I said, one value would be rejected
tan(15) should be positive
well I gtg now
ivory lynx
recheck the last step (coefficient of sqrt(3) is not halved)
huh
rich tide
so if you have any questions, ask it real quick
ivory lynx
just consider the other value and plug in
so what should i sub with using these
soft zealotBOT
B-eard
rich tide
so what should i sub with using these
you are asked to find the value of that expression, so plug it there
tan(15)=2-sqrt(3)
as per our calculations
ivory lynx
**B\-eard**
OHH this
rich tide
hello, for letter a, how do i do the double angle identity for this? its not a s...
you solved for tan(15) so, plug that value here instead of tan(15)
final saddleBOT
@ivory lynx Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
spice rapids
Hi, i have a table of weight of sugarcubes. i have to calculate the chance that i only need two sugarcubes to get 9 grams of sugar. how do i do this?
final saddleBOT
Hi, i have a table of weight of sugarcubes. i have to calculate the chance that ...
spice rapids
.close
rapid folio
final saddleBOT
rapid folio
how do i do this
rapid folio
final tangle
and did you do part a)?
rapid folio
6n-1
final tangle
what do you get when you square that and add 5?
rapid folio
wait so do u just do (6n-1)^2 +5?
final tangle
that'll be the general term of the new sequence
final tangle
yes
verbal steppe
$f^-1(f(x))$
final saddleBOT
$f^-1(f(x))$
soft zealotBOT
Merineth
soft zealotBOT
Merineth
muted ore
final saddleBOT
muted ore
How should I draw M?
desert mantle
can you find some points in M?
muted ore
I wrote it as a square with:
0,1 - 1,1
I I
0,0 - 1,0
desert mantle
yes
muted ore
yes
But I only know this because of something previously that looked similar
I don't actually know how it should be explained?
desert mantle
well if you have any point in the square, then its x coordinate is between 0,1 and same for y coordinate
so M includes the square
muted ore
ah, okay
desert mantle
and if you have a point outside the square then either x or y coordinate is not between 0,1
so it is not in M
muted ore
v1, v2
desert mantle
v1 and v2 are numbers
desert mantle
¯_(ツ)_/¯
pretty normal to write something like v=(v1,v2)
v is a vector with the entries v1 and v2
muted ore
"Let gamma1, gamma2 in R and define.."
Draw L_a(M), which means the amount {...} in the following scenarios:
muted ore
ah, lambda
soft zealotBOT
Denascite
muted ore
I don't know how to understand exercise B
desert mantle
so, you have to check where the square gets mapped to
first do it for the corners
so L_A(v) for v=corners
then for example middle of the edges
then some random point in the middle of M
and at some point you should see whats going on
muted ore
im not sure how to understand
desert mantle
what is L_A(v) is v is one of the corners
muted ore
lambda_1 = 1 and lambda_2 = 2
does that mean that I have to find the vector to times with A to get them in the corner 1,1?
desert mantle
thats for A times (0,0)
muted ore
but why is (0,0) the answer
I don't understand
- lambda_1 = 1, lambda_2 = 1
why is the answer (0,0) here?
desert mantle
matrix vector multiplication
A is (1,0; 0,1)
v is (0,0)
if you multiply that you get (0,0)
muted ore
oh
desert mantle
then took a corner of the square
muted ore
we have the diagnola
desert mantle
and checked where A maps it to
desert mantle
A is (1,0; 0,1)
yes
desert mantle
0 and 0
desert mantle
the lower left corner of the square
we are taking some points in M and just check where they get sent to
next we will take another v
for example (v1,v2)=(1,0)
or (0,1)
or (1,1)
or some other point which isnt a corner
(0.5,1)
or (0.8, 0.3)
and so on
until we see whats going on
muted ore
lambda_1 = 1 and lambda_2 = 1
we get a matrix:
10
01
right?
and because we have the opposite diagonal (0,0), we get 0,0 ?
desert mantle
no no no
muted ore
could you draw it in like paint ?
desert mantle
I am on mobile
muted ore
oh
desert mantle
we have the matrix
10
01
that is fixed
we dont change it for now
and then we check what matrix* v is
where v is some vector in the square M
desert mantle
and because we dont yet know whats going on we just try out some values for v
wr dont "find" it
theoretically we would have to do it for every v in M
but we just do it for a few and then we understand whats going on so we will skip the rest
desert mantle
no
muted ore
im just gonna draw the matrices now then
we have:
(0,0), (1,0), (0,1), (1,1)
in case 1 it means we have corners in (0,0), (1,0), (0,1), (1,1)
Or what ?
like can you show me calcuation/method for:
lambda_1 = 1, lambda_2 = 2
lambda_1 = 2, lambda_2 = 3
lambda_1 = -1, lambda_2 = 2
desert mantle
its the same method as for lambda_1=1, lambda_2=1
muted ore
But why does the teacher write "Corner point in (0,0)" as the answer to lambda_1=1, lambda_2=1
that answer does not make sense to me
desert mantle
the set that you are trying to figure out will again be a square
one of its corners will be in (0,0)
desert mantle
what do you mean with "all of this"
muted ore
The answer says:
" It holds that... in several cases L_a(M) is a rectangle with corner points (0,0) (lambda_1,0), (0, lambda_2), (lambda_1, lambda_2)
I just don't understand what they wanted from me
desert mantle
finding out that the set will end up being a rectangle with those corners
muted ore
but how will the rectangle look with lambda_1 = 2 and lambda_2 = 3
won't it always be a 2x2 matrix ?
muted ore
right, I think I got it
desert mantle
and different matrices change space differently
muted ore
I basically multiply the original A with a set of vectors
and so we get for example a 2x3 square
with corners:
(0,0), (2,3), (2,0), (0,3)
And the idea is just to show that for all cases, it holds that:
(0,0) (lambda_1,0)... is the corner
right? x)
desert mantle
yes
