#help-26
226100 messages · Page 251 of 227
to isolate dy/dx we need to take them to opposite sides of each other?
No
Both terms with dy/dx in it are already on the same side
Factor it out of both terms
so itd be 3x^2+4y=2x
Ok, let's assume I'm too distracted to recognize your genius
I'm trying to get there hang on
4x(dy/dx)+3y^2(dy/dx)=2x-3x^2-4y
3x^2 + (dy/dx)(4x + 3y^2) + 4y = 2x
dy/dx = (2x - 3x^2 - 4y)/(4x + 3y^2)
Yes, you were on it in your last post
is it possible to isolate dy/dx from 4x(dy/dx)+3y^2(dy/dx)=2x-3x^2-4y?
is it possible to get dy/dx = (2x - 3x^2 - 4y)/(4x + 3y^2) from 4x(dy/dx)+3y^2(dy/dx)=2x-3x^2-4y?
why is (2x-3x^2-4y) on top and not the other one
The terms without dy/dx as a factor will be on top, you can try this experiment
...on this problem, I mean
Or I guess
2x - 1 = 6, solve for x
Term without x in it on top
would you multiply dx/dy on both sides
also we dont end up using the points for anything is that alright?
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how to prove they are equal without using calculator
factor both equations
didnt work
are you trying to find the solution or prove they're equal?
prove they are equal
hm
wtf they aren't equal though
they are equal for certain solutions
u have to find these solutions?
no you're not proving they're equal you're proving they intersect/the equaiton has a solution
it isn't equal for all v
multiple the four by each term
then subtract the common terms from each side
make it a quadratic
i tried everything m8
they intersect in 2 points
kaynsu
so u telling i can only prove they are the same only when x is equal to 2 solutions
not quite that
are you looking for real or complex solutions?
yes y ouare
you are trying to find the place where the equality holds
they aren't equal that doesn't make any sense
they are equal in 2 points only
yes
but not in other points
yes
thkx m8
those are the solutions
Do you have the exact question?
Like post a screenshot of it
Because whatever you are asking makes no sense
ok
let me get some paper
multiply the four on the LHS
then combine like terms
set it equal to 0 and use the quadratic equation
that's the game plan
let me see
25v^2+21v+2=0
have you learned about complex numbers
yes a year ago
ok so you may have two complex or one complex or no complex solutions
just use the quadratic equation
this is true only if x is in solutions of the combined = 0 thingy
which part?
all gucci
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i need help plz
anyone able to do 5th grade math?
whats the probleM?
Just plug in your point's coordinates into the transformation formula
can u show me the formula?
The formula is written there
First, read #❓how-to-get-help
Don't ask in an occupied channel
oh sorry im new
Second, don't give out answers
sorry
Which is why I linked #❓how-to-get-help
can u explain step-by-step on how?
Plug in the P values into T(x, y) equation given
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Are you stupid?
No need for that. Everyone is at a different level.
@neon iron Has your question been resolved?
I can see that
One, don't ping helpers for other people, it's not necessary because people are capable of doing that on their own
Two, don't be rude
And three, literally a rule
.close
Ok
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Nah
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Butler
can u not
am i allowed to ping a mod
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Fyi, don't ping specific mods
k
That's why the mod ping exists
Yeah listen to the police
stop picking fights
hop off
<@&268886789983436800> Can you deal with this user? Being rude to others and seems very trollish
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Can someone please explain this limit law, I don't understand what it means
simply put x equal to a
this law literally means to limit the observation of a function to the point 'a'
could you give an example?
let's say, we take the limit of a function: f(x)=sin(x)/x
at 'x' = 0
that basically implies that we are observing what the function returns when the value of x becomes 0
All continuous functions do this.
Like, the limit of 2x
as x approaches 3
is 2(3)
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Hi I have a question about discrete mathematics
what have you tried?
I have tried like finding the pattern with it. Too see if it would be true for every like example but I dont really know how to "prove" it
or is like all the variatons the proof or is there actually a physical format proof that I need to show
Im pretty sure its true for every combination of x y z but idk how to prove it unless I should list out every possibility
I've never done something like this before but I think that should be a good enough proof right?
how many cases are there though
y and z are interchangeable so assume without loss of generality that y < z
reduces cases to check by 1/2
I think there are 8 cases
meaning you only need to check x < y < z, y < x < z, and y < z < x
there are 3 cases
Why only 3
i just said why
oh sorry missed that
´
Oh ok I see what ur saying
so do you think just listing out those variations should suffice
thats what I would assume as well but just double checking
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yo
test?
perimeter is the outer boundary so
maybe the simplest way is to recognize that there's a related rectangle with the same perimeter
then you just need to find two left sides (which are the differences of two sides)
"not drawn to scale"
just extend the right side so that instead of turning left where it does, it turns left at the bottom of the figure
you get a rectangle with sides 5x+4 and 3x
with the same perimeter
the x+1 and 2x are irrelevant
weird problem imo
the x+1 and 2x are irrelevant
this is only part i)
supposedly they'd be useful in later parts when the area is requested
fair enough, then just consider my observation a short cut for part i 😄
amusing and somewhat related:
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so for this question i alreayd got the answer for it but i used trial and error, i was wondering if there is a formula for this type of question or can i only get it out of trial and error.
hmm
How I got it was by 150/10 = 15
the question alone has multiple solutions
To make it easier
are there any other requirements
Is anybody here an expert in statistics?
What do you mean?
like other requirements for the solution or something
Well I’m not really good at math so I don’t know
Do you mean do I have to solve it in a specific way?
no like other attributes that would limit the solution
im working with a language barrier here so sorry if i dont make any sense
I don’t understand
ok its fine
Sry
I’m pretty sure what you’re saying makes sense but I’m just stupid and don’t understand it
so since each piece we cut would be related (each piece would be twice as long as the previous one) it would be helpful to possibly write each pieces length as a term of a variable
so lets assume that the shortest pieces length is x
can we work out how long the next piece would be
Would it be 2x?
Uh
the piece after the one with length 2x
2(2x)?
2•(2 x 2x)
so 2*2*2*x?
No
you mean 2*2x*2x?
Is that it?
no think again
K
if the next pieces length is double of the current one (which is 2(2x)) what would be its length
Yup
so the pieces length would be x, 2x, 2²x, 2³x, ... right
Do I keep going?
no lets see what we have right now
which is x, 2x, 4x, 8x, ...
now the problem here is that the question doesnt tell us how many pieces there are
which we will see why later
yeah
so if we were to assume the wire is cut into 4 pieces what would be x
15
think again
X+2x+4x+8x=
yes
indeed
Wut
and what is 15x
Wdym
right here what youve done is add the lengths of all the 4 pieces right
Yup
the answer we get here is still in terms of x
but does the question give us a constant value of the total length of the wire
How would u know that tho
Is it because we got 15?
15x
because the wire is cut into 4 pieces
I don’t understand
right now were assuming the wire is only cut into 4 pieces
I don’t think they told us the max would be 4 pieces
?
What do you mean by that
see it doesnt and we'll see why thats a problem later; for now were just gonna assume its cut into 4 pieces
what does the question tell you about the length of the wire
that we got in terms of x as 15x
ok lets summarize the information that the question gave us first
K
You want me to do it?
does it tell anything about the length of the wire
or any constant value
Yup
what is it
true
And that the smallest piece/ first piece is over 9m long
so what did we get for the length of the wire in terms of x a while ago
15x
so if the question tells us that the wire is 150 long
and we get that the wire is 15x long
can we form an equation
to solve for x
15x=150?
so now lets check our answers
so the four pieces length would be x, 2x, 4x and 8x
which would be 10, 20, 40 and 80
Yup
which adds up to 150
Yes
now this is the problem
the question doesnt tell us how many pieces the wire is cut into
so lets look at it again
but this time assume that its cut into 2 pieces
only
chill out for a second
what would be the length of the 2 pieces in terms of x
when x is the length of the smallest piece
and then you do the same; add those together to get the length of the wire in terms of x then solve for x
what do you get
X+2x?
yes
3x
3x=150
X=50
correct
Yup
and if we check our answers; 50, 100
50+100=150
Yea
this is why the question has multiple solutions
OHHHHH
because both the solutions we found still satisfy the question
because theres no extra condition that limits it enough
What the heck
so yeah
Wtf
thats about it
So basically the question is still trial and error?
no
Because there’s no exact formula for it
Wut
the method i presented is one apparent way of doing it
that doesnt involve trial and error
the problem here is the question doesnt have enough conditions to only have 1 answer
Yea
because the question didnt tell us how many pieces its cut into
i was demonstrating why thats a problem
Oh
because normally questions would only have 1 solution
Yea
and it would have to give us conditions that could only lead to 1 solution
but this problem doesnt have that
so yeah thats about it
np
but if im going off what they want here they probably want the solution where its cut into 4 pieces because its "elegant" or something if thats the right word (integer sides, not too simple like the 2 pieces case, also satisifies that the smallest piece is more than 9 m long)
you can close
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Why are two diff approach giving me diff answers?
Yes
What the hell am I doing here?
What you did would be correct if you had $\log_5{x^2}$
What the hell am I doing here?
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hihi! could i please get help with the second question?
i dont really understand how to get the perpendicular height of the triangle
i know that AB is 5 root 2 from the distance formula
can you find the distance AP
uhh root (p^4 -17p^2 -6p +90)
in the solutions, theres a thing like this
but i dont really understand what its saying-
but how do you know that the triangle is right angled tho?
i never made that assumption
how do i find BP if its not right angled?
just the distance formula
but i dont know what P is and i only know BP and AP
now this is going to get a bit messy but it will work
let k be the semiperimeter of this triangle, which is one half the sum of all the sides
$A = \sqrt{k(k-AB)(k-BP)(k-AP)}$
EndTimes
Heron's formula, just to save us from having to mess with all the trig
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how do i solve this
The idea of (1,180) is not correct
Why do you think that when x is 1, y will be 180?
Cause its a single period
yep he has read it
Initially here means when time is 0 because he hasnt begun to read it
SO it shoud be (0,180)
how do u know that its initial?
When he just started to read the pages left is 180
So t must be 0
If the pages left is not 180, then he must have started to read some time earlier
So t cannot be 0
oh the word left
wait i dont understand
the sentence said Conrad read a 180 page book cover to cover in a single session
it didnt said left
But the question mentioned he took 6 hours to read 180 pages
So when he just started to read, at t = 0, the pages left must be 180
that means he already read it
oh ok
now?
,rotate
so theres a y intercept
yes
so after 6 hours he read 180 books
180 pages not books
Yes
so in this question will be (180-0)/(0-6)
= - 30
but since -30 is not stated in the question, so the slope is not given
i got 30 instead of -30
i think -30 and 30 is the same for the slope
right?
this
thats right
oh -6
but -30 and 30 for the slope is same tho
think about it
1/30 1/-30
Slope is -30 only
Yes, it is (0, 180)
Slope is (y2-y1)/(x2-x1)
x2 is 0 y2 is 180
x1 is 6 y1 is 0
(0, 180) and (6, 0)
Slope wud have been 30 if your y was no. of pages read
its the same as 30
How is it same, graph only changes
In the question given its moving -30 y
Draw the graph
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can someone helpp
15000 is the principle , 4.5 or 0.045 = interest rate , number of periods the interest compounded per year = 1
i supposed we need to use this formula right? mv = p ( 1 + r/n ) nt
@cold sigil Has your question been resolved?
do you need help with the formula or have you already tried this question?
no i dont know how to do it and which formulae to use
where it says per annum I assume it's asking for compounding interest
yes
the compounding interest formula is A=P(1+r/n)^nt
P is the principle amount, r is the rate (0.045) n is the number of times it compounds in a year and t being the number of years
so we could solve this by plugging the values in A=15,000(1+0.045/2)^2
wait isnt it 0.045/1
hold on
OH YEAH THATS RIGHT
thats right
it was 0.045/1?
no no
oh ok do you need help with question B as well? :]
sure
all you have to do is use the same formula, but change n to 6 since it compounds every 2 months and 2/12=6
so i calculated (1+0.045/2)
i got 1.0225
do i have to take all the numbers of just two numbers after the decimal point?
yea
I would try to calculate it all together because you need all the digits and then you round after
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Anyone tell me (h) and ( i)
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I have a 3x3 covariance matrix that describes how xyz values correlate. How can i reconstruct xyz values from the covariance matrix
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let u =1-x
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how to solve
use exponential definitions of sinh and cosh
What went wrong here?
all good
.close
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$\int e^{e^x} dx$
Gilgamesh
u forgot
+C
and you can pull of the n=0 term from the sum before you take the integral , the n=0 term is just 1, so the integral becomes x + the sum from n=1
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how does this make any sense?
i cant understand why the initial velocity cant be expressed as itself
,w 29 yards to feet
This is when living with imperial system is like living on hard mode
Supposedly they expect you to use acceleration due to gravity in terms of ft/s^2
(Which I have literally never seen)
But in order to use this measurement, you need units to agree
So velocity needs to be in ft/s
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Help with 29th question please
You realize it gives you the answer and explanations, right?
Wouldn't that be cheating
If I take a look
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reviewing riemann sums and im not understanding why they're multiply by 2.5 and 4 and stuff
like what i would do for the right riemann sum is f(1)(1-0) + f(2)(2-1) + f(2.5)(2.5-2) + f(4)(4-2.5)
finding the areas of these rectangles, right?
which is just base*height, with height being f(x) and base being the (b-a) stuff
so where does that other term they're multiplying by come from?
here's the actual question if you want it
@grizzled badge Has your question been resolved?
@grizzled badge Has your question been resolved?
note that it is the integral of rf(r), not just f(r)
the extra term comes from the value of r
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@grizzled badge ur good, just make sure to read everything carefully
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How to write this out and solve it
@distant rapids Has your question been resolved?
Length X width?
Ayo?
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so basically my question is this
and i figured out this
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so an equation for the tangent line towards the end of the problem would be y-y1 = m(x1-x)
just really not sure how to set this up
or why im given f(x)
I know that f(x)^x is also xln(x) I believe
this may or may not be some form of logarithmic differentiation idk
<@&286206848099549185>
Why do you believe this to be true
wait i forgot f(x) is just y
but there has to be natural log somewhere right?
so y^x
should be xln(y) no?
well you know what the point is right? just plug in 5 into G(x)
so y = y^x then
G(5) = e^15 thats why you are given f(5) = e^3
have you trying getting a derivative of G now to find the slope?
not yet no i am not sure where to start
would it be something like derivative of e^-12^x
why does G(5) = e^15?
f(5) = e^3 right?
yes
and 5 comes from the x=5
ya
okay thats established i understand that
okay let me check my notes for tangent line
im trying to figure out how to differentiate that now, its tricky since x is both in the base and exponent, so you can't use either power rule or exponent rule by themselves
since those only work if the exponent or base respectively are constant
hmmmm maybe its asking for dy/dx?
yeah we need to get G'(5) thats the slope of the tangent line
okay let me attempt that
remind me how can we rewrite f(x)^x so that its base e instead? multiply by some sort of logs but apparently ive forgotten how logs work : )
ln(a)a^x ???
a^x = ln(a)a^x
e^x = e^x
if we used the power rule instead itd be 15e^14
but i dont think thats allowed given "e"
is there a typo here? you have a^x on both sides, e^x on the right?
hold on
i think we need to multiply both sides by ln
because y=g(x)
so 5y*ln=xln(e^15)?
ok i think heres how you need to think of it
because im assuming this is logarithmic differentiation
using $G(x)=f(x)^x$ take ln of both sides
Sooshon
ahhhh thats probably right
then $\ln G(x) = x \ln(f(x))$
Sooshon
now you should be able to do some implicit differentiation
that has to be it
and get G'(x) in terms of f'(x) and some other stuff you can find
okay i will attempt it
product rule on the right etc
5y?
because g(5)
say what is 5y?
or just dont think of constants for now
g(5) = 5y? or just 5
can we agree on the left side of the equation
im confused about what youre asking, sorry
yep
okay great let me attempt the right side
given f*g' + f'*g
okay right side should be x * 1/f(x) + (ln(f(x))*1
i think you forgot to chain rule the first term
its not just x?
i get $x \frac{f'(x)}{f(x)} + \ln(f(x))$
Sooshon
so ln(f(x)) is not 1/f(x)?
$\frac{d}{dx} (\ln f(x)) = \frac{1}{f(x)} f'(x)$
Sooshon
hmmm
just basic chain rule
you multiply by the derivative of the inside
the inside is f(x), its derivative is f'
ahhh very true
so ill type equation we have now
1/g(x) * dg(x)/dx = x * f'(x)/f(x)+(ln(f(x))) * 1
would you say x * f'(x)/f(x) is just (xf'(x))/f(x)
and now that we have this format
its safe to multiply by G(x) on both sides
yes
to isolate dG(x)/dx
im going to write this out in latex in outside program since its kind of a confusing one without math notation
ill put it here after and see if you agree with my steps
yes okay sounds great
multiply by G(x) on both sides at what step?
oh you mean by the e^15 yes i did it at the end there
yes, i multip-ied through by g(5) = e^15 we got earlier right at the last step
so it'd look like = G(x) * ((xf'(x)/f(x))+(ln(f(x))))
yeah, whenever you want to do that, i started plugging in values already before that
so point slope form would be i guess: $y - e^{15} = (5+3e^{15})(x - 5)$
Sooshon
yes, if i didnt make a mistake
no you're correct
which isnt entirely unlikely, this problem doesnt want to simplify too nicely : )
yeah my teacher will except exact answers and not too simplified
you multiplied e^15 on both sides
oh wait
how'd you get the right side of the equation
just plugging in x = 5, f(5), f'(5) etc
oh i guess after that then
at here how'd you get here
e^-12 / e^3 = e^-15
then when both sides get multiplied by e^15 that just becomes 1
it would be e^15 * G'(5) then on the left ?
we had a e^15 in the denominator on the left right? so the step involves multiplying both sides by e^15 to cancel that out
yes
so left just becomes G'(5)
and each of the terms on the right get multiplied by e^15
lets just go back a quick sec
our equation is now G'(5) = 5e^-12/e^3 + 3
g(x)=e^15 yes
now its just algebra, you know the point (5, e^15) and you know the slope and have to write the line equation
I've got to go eat so good luck : )
okay thanks
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divide numerator and denominator by x
x = sqrt(x^2) also
so 5x -> 5
while sqrt(x^2 + 3x) -> sqrt(1 + 3/x)
and sqrt(x^2 - 2x) -> sqrt(1 - 2/x)
makes sense
you can do this because dividing by x/x is the same as dividing by 1
so equality is maintained because x/1 = x
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<@&286206848099549185> pls 👉 👈
@dawn cloud Has your question been resolved?
<@&286206848099549185> hope this is allowed
<@&286206848099549185> tell me if / what part of the question is hard to comprehend
@dawn cloud Has your question been resolved?
no youre right
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I dont understand hint b and onwards with this series
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@bold cloud Has your question been resolved?
<@&286206848099549185>
you might wanna take this to #advanced-analysis
sure
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Hi, I don't understand what happens with the log(x+1) :c
why can I write log(x+1) like log(1+1/x) + log(x)?
prod to sum law for logs
Please, can you explain me that? 
log(ab) = log(a)+log(b)
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not sure if its b or c
this doesnt sound like a math question
however
what is your defn of an 'unbiased question'?
its from a stats class so 
ig unbiased question meaning it doesnt lead to biased answers
biased data* is probably better
eh i'll just sitck with that
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I got a good idea for this one
I would first multiply both sides by cos to get cos^2 on the left and just 1-sin on the right
@lofty elm
Idk how to use the bot but I’ll try
kk thank u
$\frac{cos(\Theta)^{2}}{1 + sin(\Theta)} = 1 - sin(\Theta)$
VictorLee
It would look like this
Thank you so much
Then the trick i had in mind is to multiply the 1+sin on both sides
And then the magic happens
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Pls help
With what?
Math
pls
it’s physic
im french
it’s like
i need to calculate the light of speed
Instead of it being in kilometer
It need to be in meter
in a scientific notation
i think it’s
300 000 x 1000
=
300 000 000
but in scientific notation
ru here
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@shut obsidian Has your question been resolved?
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I've been given this
I would like to do this
