Or how
#help-38
crystal summit
alpine saffron
The equation
crystal summit
How tho
alpine saffron
So you have $u^2-u-2=0$ where $u=\lg x$
solid kilnBOT
otheol
alpine saffron
Right?
crystal summit
Yea
alpine saffron
You can factor the left hand side by trying to rephrase it into something that looks like $(u+a)(u+b)$
solid kilnBOT
otheol
crystal summit
Yea right
alpine saffron
Do you know how you could solve for a and b here?
crystal summit
Yea I think so
alpine saffron
Give it a shot
crystal summit
Dang
wraith hinge
No
Wait
The rootsmare wrong
Roots are
It is -1 and 2
And find the roots of a equation by completing square method or factoring
Substitute them in thr original quadratic to check weather your roots are correct or wrong
crystal summit
K
wraith hinge
Also learn the formula -b+-sqrt.....
crystal summit
Is it the discriminant u mean?
wraith hinge
Google it :))
wraith hinge
Is it the discriminant u mean?
Discriminant is a part of it
crystal summit
The pq formel
wraith hinge
?
wraith hinge
Yes
crystal summit
So I just flipped the 1 and -2
alpine saffron
This is correct
wraith hinge
So I just flipped the 1 and -2
Yess
alpine saffron
Since you have (u + 1)(u - 2) = 0, either u + 1 = 0 or u - 2 = 0
crystal summit
Oh yea
I thought the other way around cause I figured a was positive
But yea thanks for the help
Rlly appreciate it
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proven chasm
No clue how to start
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No clue how to start
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nova pumice
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nova pumice
Am I doing this right?
I need to use difference quotient
To find the slope thing in y-y2=m(x-x2)
Thingy
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subtle fulcrum
what are you trying to get? the intersection?
nova pumice
what are you trying to get? the intersection?
no just quotient difference thing
Tangent line
I am doing it wrong somehow
<@&286206848099549185>
subtle fulcrum
no just quotient difference thing
ohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
kk wait let me look at it
the only thing is that the 3 should be negative and take the radical out of the denominator
nova pumice
the only thing is that the 3 should be negative and take the radical out of the ...
Yea
subtle fulcrum
is ur teacher making u guys do it the long way or are u allowed to use the power rule
bc it would be much more efficient
nova pumice
is ur teacher making u guys do it the long way or are u allowed to use the power...
long way
subtle fulcrum
aw darn
subtle fulcrum
there must be a hole somewhere since that 6 is negative which would just give you an imaginary number
maybe instead of dealing with the roots just raise it all to the 1/2 power
nova pumice
i had to have done something wrong
subtle fulcrum
just check over it u prob missed a negative thats it
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vale radish
can somebody tell me where they got 2a=8 please?
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can somebody tell me where they got 2a=8 please?
wraith hinge
Use method of undetermined coefficient
vale radish
what does that mean
wraith hinge
ohh they just subbed it all back into the original
Wait how
wraith hinge
Right right
wraith hinge
in the original they replaced it all with 0 and a
Are u learning non homogeneous
vale radish
i have no idea but i learnt this in high school and im relearning
for a test
so im going through some solutions
okay gtg thank u again]
wraith hinge
in the original they replaced it all with 0 and a
they put y=a right
vale radish
ya
wraith hinge
ya
It works when there's a constant in right hand side ig
But when there's another function
Nvm
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formal meteor
is this right
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is this right
formal meteor
-4
frail yarrow
Yeppers
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cursive arrow
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cursive arrow
if this was a power series
would i have to rerwrite the x^2n
or do i justu se the ratio tst
torn pasture
I am reading about complexity theory and I came across the claim that we don't know if $BPP \subseteq NP$. However, shouldn't this be the case since a probabilistic turing machine is simply a type of nondeterministic turing machine? I feel like I am missing something obvious in my reading
solid kilnBOT
Nash
torn pasture
Here is an example of what I'm talking about
spiral kettle
a probabilistic turing matchine doesn’t have to be right every time
for something (a problem or set A) to be in NP there has to be a ND TM M deciding A and M has to be 100% accurate
shrewd ridge
but that also sounds like bpp is worse
torn pasture
a probabilistic turing matchine doesn’t have to be right every time
Ah good point. Thanks
torn pasture
but that also sounds like bpp is worse
wdym?
spiral kettle
but that also sounds like bpp is worse
you have to specify what you mean by worse here
spiral kettle
okay so
shrewd ridge
a non deterministic machine chooses all paths at the same time
a probabilisitic machine chooses one
so it's not a type of non deterministic machine at all
is that right?
torn pasture
It is, the nondeterminism comes from the randomness
shrewd ridge
ok but it's not as powerful
torn pasture
Determinism means that we make the same decision from state to state each time, randomness introduces nondeterminism
torn pasture
ok but it's not as powerful
Well, probably not but it is technically possible though very unlikely that $NP \subseteq BPP$ would would make it as powerful
solid kilnBOT
Nash
shrewd ridge
i don;t get it
torn pasture
In this case, if by "powerful" we mean have the most problems included in it, then BPP might be "more powerful" than NP but we also have the probability of failure
shrewd ridge
we have a mchine that chooses a path according to a distribution
and we have a mchine that chooses the best possible path
torn pasture
But there are no problems we can guarantee 100% success with using just randomness that can't also have the same thing happen with general nondeterminism since randomness is just one type of nondeterminism
spiral kettle
it’s also not known whether BPP subset P actually
torn pasture
Right
shrewd ridge
okay, bpp is easier because you;re allowed epsilon mistakes
torn pasture
Not epsilon actually, just any amount not arbitrarily close to 1/2
Because then polynomial iterations reduces it
shrewd ridge
and harder at the same time because the machine is stupider
or the other way around
fair enough
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latent notch
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latent notch
what does this mean
i though you couldnt multiply matricies like this
and null means equaling the matrix to zero
i dont get ti
it
someone please explain
true sierra
Why couldn't you multiply them?
the left one is 3x4
the right one is 4x1
so the columns of the first match the rows of the second
meaning you can multiply them
and the result will be a 3x1 matrix
which is shown
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marsh forum
if the AM of two numbers a and b , a>0; b>0 is five times more than their GM find $\frac{a+b}{a-b}$
solid kilnBOT
ƒ(Why am. I here)=I don't Know
solid kilnBOT
ƒ(Why am. I here)=I don't Know
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amber python
amber python
that sounds overly complicated
marble wharf
find a similar formula for (a-b)^2
shy nacelle
,w (x+1)² = 100x
marsh forum
I mean 96 ab
amber python
**ƒ(Why am. I here)=I don't Know**
you should be able to get the answer with this
marsh forum
sorry
amber python
close enough
marsh forum
yes
amber python
then yes
obsidian hornet
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storm ocean
shouldn't it be -x^2+ x + 12 = 0?
mighty canyon
shouldn't it be -x^2+ x + 12 = 0?
!occupied
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shouldn't it be -x^2+ x + 12 = 0?
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
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whole coral
same time haha
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ebon merlin
im on part C of this question
i dont understand why the markscheme says cost cannot be -1/2
vivid schooner
I think my answer is correct but this exersie is kind messing with me with the way its worded ¿is it correct?
vivid schooner
hot plume
that looks correct to me
worn grail
Anyone have any idea how to solve this?
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Anyone have any idea how to solve this?
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storm smelt
(x^2)+(y^2)=6.x.y according to this, What is the answer of? (x^3)/(y^3)+(y^3)/(x^3)
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(x^2)+(y^2)=6.x.y according to this, What is the answer of? (x^3)/(y^3)+(y^3)/(x...
@storm smelt Has your question been resolved?
storm smelt
<@&286206848099549185> guys please help i dont know what to do really
fathom turret
Idk
signal bobcat
so x/y + y/x = 6
crude phoenix
(x^2)+(y^2)=6.x.y according to this, What is the answer of? (x^3)/(y^3)+(y^3)/(x...
= 6 or = 6xy?
storm smelt
=6xy bro
storm smelt
plus symbol?
signal bobcat
k why dot.
is multiplications sign ???
crude phoenix
is multiplications sign ???
yes but its like not in the line
a lil up from it
⋅ this
signal bobcat
yh but its discord its not like u can write LaTeX in here right ?
crude phoenix
yh but its discord its not like u can write LaTeX in here right ?
yes but @trim jolt
here
storm smelt
so x/y + y/x = 6
i think this is the most progression so far
signal bobcat
i think this is the most progression so far
its more in the form of the answer
but now u can say that x/y = 6-y/x
and substitute ?
storm smelt
it may be related to the expansion (x^3)+(y^3)
[(a+b)^3]-3ab(a+b)
i'll try this
so 216-3ab(6)
how can i find ab?
signal bobcat
is ab a function of 6 ?
storm smelt
ah man how did i forget
ab means (x/y)(y/x)
🫠
so the answer is 198
thx everyone who tried to help
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rapid rivet
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rapid rivet
How like i cant find the middlepoint angle so I dont
Quick please its like ez math
Like v2 + 180(M) sound be like the angle of v1 + v3
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hexed thunder
I am getting frustrated in the coding language R and would love some small assistance.
This is what I currently was helped with, but I wanted to add a section of the code that allows the user to input some value of "n"
hexed thunder
Something along the lines of this, but inputs the integer into the function that is made.
sweet hare
instead of having the function take an argument, you can just write the first line as
myfun <- function() {
n <- readline(prompt='Enter a number: ')
n <- as.integer(n)
#etc.
}
You are a blessing.
sweet hare
and by the way, when indexing a variable, you need to use square brackets, not parentheses. so it would be x[i], not x(i)
true sierra
R 
hexed thunder
That is the error that now comes up
sweet hare
I just tested it and it works... what are the first couple lines of the function?
oh, and you don't call it like print(myfun); you should just type myfun() to run it
if you want to view the contents of the function, you can just type the function name alone: myfun
hexed thunder
sweet hare
out[i], with square brackets. in both places in the function
and you can remove the input argument from the function definition. so just myfun = function() {
hexed thunder
I remember a "true" part that was discussed in class. But I did not think that was needed since it is an "if-else" statement
sweet hare
the error is in the loop definition there. it should be for (i in 1:n) {
since n is the length of the variable you are looping over
hexed thunder
HOLY COW!!! IT WORKS!!!
I basically need to just cite you for this question... Thank you deeply.
sweet hare
yw
hexed thunder
Well now I have a technical issue...
It runs in my general code, but when I try to Render it, it halts the download.
sweet hare
it probably has to do with readline
hexed thunder
Am I not allowed to put for it to be rendered properly?
sweet hare
so readline is intended to be used in an interactive session, but rendered documents are non-interactive.
do you call the function later in the document?
hexed thunder
This is the only question where it asks for this, I do not use it again.
sweet hare
if you don't call it later in the document, I think you can add eval=FALSE as a chunk option
hexed thunder
I will make a separate note though that I tired to add this since it mentioned feeding the function an integer.
It ran once I added the "#". Goly there are many rules to code.
sweet hare
yeah, it takes some getting used to
hexed thunder
I really do appreciate the help and I am constantly learning from this class and you!
sweet hare
yw
hexed thunder
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paper geyser
Can somebody help with this? I am stuck after putting everything in the augmented matrix
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sweet hare
you can try asking in #linear-algebra
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paper geyser
ye Ill put in there
urban copper
let $g : (0, +\infty) \to \mathbb{R}$ be defined by $g(x) = 3 + \ln(x) -x$ find im(g)
solid kilnBOT
938c2cc0dcc05f2b68c4287040cfcf71
true sierra
define im
urban copper
image
true sierra
Is that just the range of the function then?
urban copper
yes I think they are asking range
true sierra
Aight, how would you approach this?
urban copper
lowkey unsure, any ideas?
true sierra
Well we know this function is differentiable and continuous since it's made up of elementary functions which are the same right?
I hope that's correct lol
urban copper
yes
true sierra
Then we can derive it and solve g'(x) = 0
then check the maximums and minimums and based on that find the range
true sierra
yeah
urban copper
and by maximums and minimums you mean absolute maxima and absolute minima not just local minima
true sierra
yeah
urban copper
okay
true sierra
So what's the first derivative of this?
solid kilnBOT
urban copper
,w solve 1/x - 1 = 0
solid kilnBOT
true sierra
note x isn't 0 since it's not in the function domain
so it being in the bottom of a fraction is no problem
right so this function has one critical point at x=1
what's the value of the function at that point?
urban copper
its minimum
urban copper
I thought positive sign in the critial point was the way to analyze that
positive sign meaning minimum
negative meaning maximum
true sierra
Not quite
true sierra
you have to take the second derivative
true sierra
and check it's sign at that point
no just take the second derivative
plug in x = 1
and see if it's positive or negative
then apply that rule you said
urban copper
-x^(-2) is g''(x)
true sierra
alternatively plug in x = 0.9 and x = 1.1 in the orignal function and sketch the results
urban copper
g''(1) = -1^(-2)
true sierra
but this is like cheating
So that result is negative right?
Meaning our point is an ...
urban copper
yes, its maximum
true sierra
right
true sierra
Well it's the only maximum there is
urban copper
how do you know that
true sierra
Because it's the only solution to the equation g'(x) = 0
urban copper
true
true sierra
And since there's no minimums
and we know the function is differentiable and continuous
we can conclude that the function has no values above 2
and since it has no minimums it should have all value to -inf going down
unless there's like a horizontal asymptote, might wanna check the limit too I guess
like, the limit of g(x) as x approaches inf
urban copper
we can conclude that the function has no values above 2
?
true sierra
Just in case
urban copper
how so?
whole coral
like, the limit of g(x) as x approaches inf
You can also e.g. check what happens as you approach zero too 
true sierra
how so?
As for this, well in order to go above 2 the function would have to wind up at some point again, which would require a minimum, since there are no minimums it can't do that
Rolle's theorem or something
whole coral
You can also e.g. check the behaviour of the derivative to deduce if you're increasing/decreasing either side "forever"
true sierra
Or you can do what I love to do and just use desmos lol
urban copper
I dont know how to graph it without desmos haha
true sierra
Yeah, well you're not supposed to
At least not on exams, but like, let math be freeee
urban copper
if we know there is no minimum, what can that says about the graph
true sierra
long live software tools
true sierra
if we know there is no minimum, what can that says about the graph
It tells us that after the maximum it can never go up again
basically
urban copper
unless there's like a horizontal asymptote, might wanna check the limit too I gu...
do I need to check the limit of x approaching 2?
true sierra
since going up again would require a minimum
not necessary, you know the value of g(2)
whole coral
[wait, what's the relevance of g(2) here?]
urban copper
how do I find vertial and horizontal asymptotes
true sierra
it's the maximum
for vertical ones you check the limit of the function as it approaches a suspicious point
whole coral
it's the maximum
[isn't g(1) = 2 the max?]
true sierra
ah yes I mixed it up
urban copper
for vertical ones you check the limit of the function as it approaches a suspici...
sus like x = 2, or x = 1?
urban copper
oh
true sierra
finite border point*
whole coral
[you'd want to think about where you're doing "illegal stuff" like dividing by zero, log of zero, etc etc]
whole coral
You can also e.g. check what happens as you approach zero too <a:nyasSnuggle2:81...
[hence-]
true sierra
basically ask yourself "where would a function want to conduct a drug deal" and then check that
urban copper
what about about the horizontal asymptotes though!
true sierra
you check those with the limit to inf and -inf
since -inf isn't in the domain for this one
you just check +inf
urban copper
,, \lim_{n \to \infty+} 3 + \ln(x) - x
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938c2cc0dcc05f2b68c4287040cfcf71
urban copper
thats literally -inf
urban copper
Or you can do what I love to do and just use desmos lol
but the graph does not agree
true sierra
it is
and it does
as the function goes to the right it just keeps decreasing all the way down
what you might be confusing it with is a slanted asymptote
urban copper
yeah
urban copper
how do I find range though, I am getting confused
we know 1 is a critical point
and g(1) = 2
true sierra
Right
and we know it's the maximum
we also know the function has no minimums
as such 2 is the absolute biggest value this function will ever have
whole coral
thats literally -inf
[or lower bounds]
true sierra
yeah we also concluded it has no lower bounds
well we didn't do the limit to 0, but it's -inf
urban copper
yeah we also concluded it has no lower bounds
due to horizontal asymptote? or what??
true sierra
So it goes from -inf, to 2, to -inf again
yeah due to that limit
you checked how it behaves at infinity and found out it goes to -inf
if you check how it behaves at 0 you'll find -inf again
rough phoenix
,,
Sorry to ramble, but I wanted to say something:
If you study this limit, you can find a possible m for the oblique asymptote y=mx+n
m=\lim_{n \to +\infty} \frac{f(x)}{x}\
If m gives you a value other than zero, find n:\
n=\lim_{n \to +\infty} f(x)-mx
true sierra
Yeah that's correct
solid kilnBOT
Isa
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true sierra
It doesn't help us with the range finding though, but in general you'd do that too for a deeper analysis
urban copper
but wait a moment if this function has horizontal asymptotes then there is no oblique asymptote, right?
true sierra
no it doesn't have a horizontal one
whole coral
due to horizontal asymptote? or what??
In particular, because you have no horizontal asymptote, and also the y axis forms a vertical asymptote
(a minor point of pedantry, but having no minimums doesn't necessarily imply that you have no lower bounds, thought that may be worth pointing out, just in case)
true sierra
if the result of the limit is inf or -inf then there is no horizontal asymptote
urban copper
how do I find the oblique asymptotes
true sierra
In particular, because you have *no* horizontal asymptote, and also the y axis f...
Well if we have no minimums or horizontal asymptotes then it does imply that, no?
urban copper
unsure
whole coral
Well if we have no minimums or horizontal asymptotes then it does imply that, no...
It does, but thought that pointing out that you want both of those factors in a more general example 
[e.g. arctan(x) has no max/mins but a bounded range]
true sierra
At the end of the day the process of finding the range is basically to check if it's differentiable and continous everywhere, check extreme points, check limits at bounds of domain, check suspicious points, make conclusions based on all of that
What we have found is :
- function is differentiable and continuous everywhere in it's domain
- function has a maximum at x=1 with value=2, and no other extreme points
- functions limit at 0+ is -inf
- function limit at inf is -inf
- function has no suspicious points
Based on that we can conclude that the range of values of the function goes from -inf, to 2, to -inf again
in a continuous manner
and as such it's range is (-inf, 2]
true sierra
yeah making checklists for analyses like these is the best way really
urban copper
how do I know If I analyzed every aspect for the range though
true sierra
If you went down the list
urban copper
okay I also wanted to ask lowkey what is the second derivative sign criterion we used though?
is that whats rolles theorem says?
true sierra
Oh no, Rolles theorem is about needing a minimum to go up again
more or less
kinda
sorta
We used the second derivative to find out if the extreme point is a min or max
whole coral
[Rolles states that if you're cts on a bounded interval and differentiable inside, and the function values at the endpoints are the same, then you have a point inside the interval where the derivative is zero]
urban copper
lowkey we are assuming continuity and differentiability here?
true sierra
Which basically implies that if you're at our extreme point of (1,2) and you want to go to another point that's at height 2, so (x, 2) you'd need to have a minimum or maximum inbetween somewhere
Well the function is a linear combination of elementary functions which we know to be differentiable and continuous so it must also be that (I think)
whole coral
We used the second derivative to find out if the extreme point is a min or max
[the idea of the second derivative test is that a min is where you go from decreasing to stationary to increasing, implying if you have a second derivative, it's positive there, and a max is increasing to stationary to decreasing, so second derivative (if it exists) is negative]
urban copper
how can I check my answer?
true sierra
This is for the Rolle's bit, see how I can't draw a line to get back to 2 without having an extreme
So if there's no extremes, we're not going back to 2 again
urban copper
This is for the Rolle's bit, see how I can't draw a line to get back to 2 withou...
yeah visually its way more helpful
makes sense
,w image of 3 + \ln(x) -x
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delicate lance
delicate lance
whyd they solve for cosb?
gentle sleet
I understand everything but the very last part
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I understand everything but the very last part
gentle sleet
where they talk about findinf the prob that the protein is identified b exactly one method
they started with
P(A u B) - P(A n B) (ok I understand this)
But then the next part they go to P(A) + P(B) - 2P(A n B)
why?
oh shit nvm I understand im acc slow
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gentle sleet
ok im acc confused about the top part here
shouldnt P(A1 u A2 u A3) = P(A1) + P(A2) + P(A3) - P(A1 n A2) - P(A1 n A3) - P(A2 n A3)
why did they add the very last part "P(A1 n A2 n A3)"
I remember the formula being like P(A u B) = P(A) + P(B) - P(A n B)
edgy willow
the pattern is you keep going through all possible combinations alternating + and -
here's why you need to add the middle at the end
gentle sleet
I dont rlly understand
let me draw on my end and see if I can get it because thats kinda confusing
edgy willow
I imagine it as cutout paper circles and you're adding and removing them to get it flat to 1 layer
gentle sleet
ohhhhhhhhhh
makes sense
wait actually
yk where u said 0
thats the part (A1 n A2 n A3) right isnt that already being accounted for in A1 + A2 + A3
shouldnt we actually be subtracting A1 n A2 n A3 at the end
instead of adding
edgy willow
yea if you add A1+A2+A3 it's all 1's and you're good
the singles added 3 to the middle and teh doubles took 3 away
edgy willow
ok
gentle sleet
ok
ok so lets first cover the
P(A1) + P(A2) + P(A3) part then it will look like this
,rotate
solid kilnBOT
edgy willow
yup
gentle sleet
now if we do
P(A1) + P(A2) + P(A3) - P(A1 n A2) - P(A1 n A3) - P(A2 n A3)
,rotate
solid kilnBOT
gentle sleet
right?
meaning that very middle part is being repeated three times no?
so why would they go on adding it again
shouldnt it have been - 2(P(A1 n A2 n A3)) ?
oh im sped A1 n A2 will also delete the middle part
and same with A1 n A3
and A3 n A2
so middle part would be 0
thats why they added
smh my bad 
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bronze trellis
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marsh forum
just wanted to be sure, we diff wrt t when using LH right
wraith hinge
t is the variable as it is the one going towards something, so t is changing
wraith hinge
don't think so, nothing immediately comes to mind
marsh forum
ok, so that gives
$10t^9f\left(x\right)+f'\left(x\right)t^{10}\left(\frac{dx}{dt}\right)-10x^9\left(\frac{dx}{dt}\right)f\left(t\right)+x^{10}f'\left(t\right)=9t^8-9x^8\left(\frac{dx}{dt}\right)$
solid kilnBOT
ƒ(Why am. I here)=I don't Know
marsh forum
right?
now I sub x=t
$10x^9f\left(x\right)+f'\left(x\right)t^{10}\left(\frac{dx}{dt}\right)-10x^9\left(\frac{dx}{dt}\right)f\left(x\right)+t^{10}f'\left(t\right)=9t^8-9t^8\left(\frac{dx}{dt}\right)$
solid kilnBOT
ƒ(Why am. I here)=I don't Know
marsh forum
is this right so far?
wraith hinge
you don't need to do dx/dt, x is a constant so dx/dt is just 0
wraith hinge
because x is a fixed value being approached by the variable t
solid kilnBOT
ƒ(Why am. I here)=I don't Know
marsh forum
which is a simple Linear ODE
wraith hinge
yep
marsh forum
$f'\left(x\right)+\frac{10}{x}f\left(x\right)=\frac{9}{x^2}$
solid kilnBOT
ƒ(Why am. I here)=I don't Know
wraith hinge
so the IF is x^10?
it's e^(integral 10/x)
marsh forum
that's x^10
solid kilnBOT
ƒ(Why am. I here)=I don't Know
marsh forum
just wanted to be sure, we diff wrt t when using LH right
I'm not getting any of the options
what am I doing wrong
oh
got it
stupid me
thanks
.close
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wraith hinge
I can't seem to get this right. I don't understand where my professor got the 1/18 or 1/27 from. I get factoring out the 1/2 but no matter what I do I keep getting 81.66. I have everything the same as he does up until the 1/18. I can't take a picture of my own work because it's on paper and my phone is completely shot- new one coming in this week.
ionic pendant
well they perform a u-substitution to find the integral [ \frac 12 \int_1^5 \sqrt{9y-5}\odif y ]
solid kilnBOT
cloud
hasty yew
well they perform a u-substitution to find the integral \[ \frac 12 \int_1^5 \sq...
not need one
don't*
wraith hinge
I think they just factor out 1/4 to get that part
ionic pendant
??
wraith hinge
Yes I got that for the integral as well
because of the power rule or whatever because with integrals you add so it's 1/2 + 2/2 = 3/2 and then divide or multiply by the reciprocal
hasty yew
We want $(9y-5)^{\frac 23}$, so we are off by a factor if 9
solid kilnBOT
normalAtmosphericPa=101,325
hasty yew
So simply adjust your initial guess $\frac d{dx}1/9[\frac 23 (9y-5)^{\frac 32}]=(9y-5)^{\frac 12}$
wraith hinge
well when you look his does show 2/3 (9y-5)^3/2
hasty yew
well when you look his does show 2/3 (9y-5)^3/2
yes
ionic pendant
the 1/9 was factored off and combined with 1/2 to get 1/18
hasty yew
but you also have 1/9 from chain rule
now combine that with the 1/2 outside of the integral sign, you get 1/18
wraith hinge
Wait how does the chain rule work for integrals
hasty yew
Wait how does the chain rule work for integrals
I'm doing it directly
I'm basically asking, "What diffs to give this integrand?"
You understand that integration and differentation are opposite proceses don't yoi
wraith hinge
yes
hasty yew
So computing the integral is equivalent to looking for some anti-derivative of $(9y-5)^{1/2}$
solid kilnBOT
normalAtmosphericPa=101,325
hasty yew
So, a natural chocie would be to first try simply applying the power rule
i.e., "let's look at $2/3(9y-5)^{1/2+2/2}$"
solid kilnBOT
normalAtmosphericPa=101,325
wraith hinge
Ohhhh
hasty yew
Does this "diff to give" $(9y-5)^{1/2}$?
wraith hinge
I just did it with the u-substitution
solid kilnBOT
normalAtmosphericPa=101,325
hasty yew
Well, try computing this derivative
do you get it?
no, you will be off by a factor of 9
wraith hinge
I totally forgot I was allowed to do that. yes
hasty yew
This tells you, "Ah, I need to adjust my initial guess such that when I diff it, I get 1/9'th what I got before"
so put a factor 1/9 in front of your initial guess
Then as a sanity check, does $1/9(9y-5)^{3/2}$ now "diff to give $(9y-5)^{1/2}$?
solid kilnBOT
normalAtmosphericPa=101,325
hasty yew
Indeed it does, so we are done—we've found an antideriative
wraith hinge
Yes that's what I mean. No guessing needed, I did the u-sub method and I go twhat he did , and ues using u sub factors out 1/9 if done right. thank you
hasty yew
but don't forget this factor of 1/2 in front of the integral
so you have 1/18 as a factor overall
wraith hinge
Yes, and then taking the integral 2/3 can get factored out and that's where 1/27 comes from right?
hasty yew
dunno, probs comes from applying the limits now
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@wraith hinge Has your question been resolved?
ancient flame
A group of rocket enthusiasts gather at 4km distance from the liftoff pad of the
Space X rocket to observe the midnight launch. The enthusiasts notice a long
vertical pole with a height of 20m at their location and decide to measure the rocket
speed after liftoff, using the shadow of the pole on the ground cast from the light of
the rocket. They measure that the top of the pole’s shadow is moving at 0.1m/
s when the shadow length is 10. 7 m. Sketch this situation, and compute the both
the height of the rocket and the velocity of the rocket at that moment.
ancient flame
can I get help for this pelase 🙂 a bit confused about the sketcgh
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ancient flame
.reopen
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@ancient flame Has your question been resolved?
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gleaming ermine
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gleaming ermine
i used logarithmic differentiation but im getting this loooong term
should that be the case
and also if it is
i cant figure out how to simplify it
pulsar dust
is there any relation btw a and b that is given?
gleaming ermine
nope
pulsar dust
what did u get at ur expansion?
pulsar dust
yeah
gleaming ermine
cool cool but now what 😭
pulsar dust
what u can do is simplify cosaxcosbx as 1/2(cos((a+b)x)+cos((a-b)x)
similarly do for sinaxsinbx
gleaming ermine
thats the next step that i did but crossed it out
pulsar dust
just trust me bro
pulsar dust
yeah
pulsar dust
just put the 1/2 on the dr
gleaming ermine
ah okay
pulsar dust
it will look more elegant
pulsar dust
this is it
gleaming ermine
oh
pulsar dust
the expansion will just take u back to square 1
gleaming ermine
yeah
i mean my teacher does say that all of these should have like good looking solutions
thats why i was confused
anyway tho
thank you
pulsar dust
welcome i hope i helped u:)
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lilac ridge
Hi again 🤧 i don't know how to continue. The question is SIMPLIFY THE EQUATION
kindred pier
Hi again 🤧 i don't know how to continue. The question is SIMPLIFY THE EQUATION
$a^2+b^2\ne(a+b)^2$
solid kilnBOT
SWR
lilac ridge
Yes i know that
kindred pier
Yes i know that
It's just cuz you wrote it here
kindred pier
But how do i continue
I would consider what $(\sin^2 x+\cos^2 x)^2$ and how it relates to $\sin^4 x+\cos^4 x$. Same with $(\sin^2 x+\cos^2 x)^3$
solid kilnBOT
SWR
lilac ridge
I would consider what $(\sin^2 x+\cos^2 x)^2$ and how it relates to $\sin^4 x+\c...
Wait wait
I can like
That's same?
kindred pier
,rccw
solid kilnBOT
kindred pier
No. Same problem
lilac ridge
No. Same problem
Then what do i do
kindred pier
Try expanding $(\sin^2 x+\cos^2 x)^2$
solid kilnBOT
SWR
lilac ridge
Try expanding $(\sin^2 x+\cos^2 x)^2$
Alright please wait
lilac ridge
Try expanding $(\sin^2 x+\cos^2 x)^2$
lilac ridge
These are still not equal
Then what is equal
kindred pier
$(\sin^2 x+\cos^2 x)^2=\sin^4 x+2\sin^2 x \cos^2 x+\cos^4 x$
solid kilnBOT
SWR
lilac ridge
I already wrote that
lilac ridge
$(\sin^2 x+\cos^2 x)^2=\sin^4 x+2\sin^2 x \cos^2 x+\cos^4 x$
Where i am making mistakes
kindred pier
You made a mistake saying this was equal
lilac ridge
Okay how do i correct it
kindred pier
Also this whole thing was incorrect
solid kilnBOT
SWR
lilac ridge
Use this. Solve for $\sin^4 x+\cos^4 x$
kindred pier
,rccw
solid kilnBOT
kindred pier
hey that looks pretty good
lilac ridge
hey that looks pretty good
Okay, should i get rid of ()?
Okay please wait
I think this is correct
lilac ridge
hey that looks pretty good
kindred pier
,rccw
solid kilnBOT
kindred pier
looks good
lilac ridge
thanks God
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winter ingot
tom has 17 coins all of which are either nickels or dimes. if he has $1.10 in all, how many does he have of each?
mighty canyon
ok, you know how to solve equation, right?
winter ingot
ok, you know how to solve equation, right?
yes
mighty canyon
First, you can set up the system of equations. You know that the total number of coins is 17 and you know that the total values of your coins is $1.10
Right?
winter ingot
yes
winter ingot
yeh
mighty canyon
so, let's that be our unknown then
let $x$ be the number of nickels and $y$ be the number of dimes
solid kilnBOT
print("NAME")
winter ingot
yeah
solid kilnBOT
print("NAME")
winter ingot
wait
is this simulatenous equations
?
is that what it's called
im so confused
mighty canyon
I think so... I usually call this a system of linear equation
winter ingot
o ok
mighty canyon
do you know how to solve this?
solid kilnBOT
print("NAME")
winter ingot
yeah
mighty canyon
that means $x = 17 - y$, right?
solid kilnBOT
print("NAME")
winter ingot
yh
mighty canyon
the second equation we have is quite ugly so let's multiply everything to make it a full number and get
$5x + 10y = 110$
solid kilnBOT
print("NAME")
mighty canyon
do you agree?
winter ingot
yh
mighty canyon
and since I know that $x = 17-y$, I can substitute that in to get $5(17-y) + 10y = 110$
solid kilnBOT
print("NAME")
mighty canyon
and solve for $y$
solid kilnBOT
print("NAME")
mighty canyon
this is one of the way you can use to solve the simultaneous equation: substitution method
mighty canyon
There is. In fact, in college there is a class dedicate for this kind of stuff lol
winter ingot
o
mighty canyon
But at your level, I think this is one of the straightforward way to solve this problem
winter ingot
kk
mighty canyon
After you solve for $y$, you can substitute that back to any of the equation you have to solve for $x$
solid kilnBOT
print("NAME")
mighty canyon
and that is your solution
mighty canyon
well, you can check your answer by substitute your value into the equation
I have the solution. It is just that it is inappropriate to give out the solution.
mighty canyon
I think you should get the whole number
mighty canyon
ok, I will simplify things for you a bit so you can see what went wrong: $5(17-y)+10y = 110 \implies y+17=22$
solid kilnBOT
print("NAME")
mighty canyon
no...
mighty canyon
$-5y + 10y = 10y - 5y = 5y$
solid kilnBOT
print("NAME")
mighty canyon
don't forget about the sign
winter ingot
what about the 85?
mighty canyon
85 is there. I just want to highlight what you did wrong there
it will be $85+5y = 110$
solid kilnBOT
print("NAME")
mighty canyon
yes
mighty canyon
then since you know that there is 5 dimes out of 17 coins...
mighty canyon
no worries. this kind of problem is confusing if you don't know how to deal with it
you did great trying to understand it
winter ingot
tyty
winter ingot
no worries. this kind of problem is confusing if you don't know how to deal with...
janice has 2.30 made of dimes, pennies, and quarters. she has just as many dimes as pennies and has 17 coins in all. how many quarters does she have?
would i find the dimes and pennies
oro quarters in this one
using substitatuino
so it would 2x+q=17
right
mighty canyon
yes
mighty canyon
well, x is the number of the dimes here, do you agree?
winter ingot
yes
winter ingot
well, x is the number of the dimes here, do you agree?
yeah
but x is also number of pennies
too
mighty canyon
if you know x, you also know 2x, no?
winter ingot
if you know x, you also know 2x, no?
oh ok