,rotate
#help-23
severe pond
flat frigateBOT
severe pond
you’re stuck?
boreal epoch
yes
covert yoke
Combine the next logs
Also might help to simplify the 9^(7/3). That's 3^(14/3) = 3^4 * 3^(2/3) = 81 cbrt(9)
safe radishBOT
@boreal epoch Has your question been resolved?
boreal epoch
yes
fallen fulcrum
safe radishBOT
fallen fulcrum
We can rewrite this equation as
10x+y=120
60x+y=220
Is that the right way of thinking about it? or would it be easier a different way?
fallen fulcrum
We can rewrite this equation as
10x+y=120
60x+y=220
after this my thought was just subtracting both equation so you get
50x=100
x=2
If someone could confirm this is correct, and whether or not there is an easier way to think about this i would highly appreciate it
safe radishBOT
@fallen fulcrum Has your question been resolved?
fallen fulcrum
<@&286206848099549185>
austere cypress
That is the right way to solve it, but that's not quite what the question is looking for.
You found that the price of each unit (x) is 2, but you also need to find the fixed price (y) and form the final equation.
To do that just plug it in one of the previous equations, such as 10x + y = 120
substitute x = 2
10×2 + y = 120
20 + y = 120
y = 100
So x = 2 and y = 100
This tell us that the cost is £100 pounds and £2 for each unit, therefore, the equation relating the cost to the number of products produced is:
Cost = (N° of products) × £2 + £100
fallen fulcrum
Ahhhh ok, so y is the fixed cost of the business existing whereas x would be the additional cost of making products
austere cypress
Yes, that's right
safe radishBOT
rough cairn
4/612/9+(-3/8)(-12/9
plucky elk
4/612/9+(-3/8)(-12/9
stop spamming everywhere
bold fable
stop spamming everywhere
But, is it a him problem or a lack of support problem?
plucky elk
But, is it a him problem or a lack of support problem?
!volunteers
safe radishBOT
But, is it a him problem or a lack of support problem?
Helpers are just people volunteering their time to help you. Be polite and patient.
safe radishBOT
Available help channel!
balmy goblet
does anyone know how to factorise this expression easily ?
safe radishBOT
does anyone know how to factorise this expression easily ?
balmy goblet
doing it the hard way
developping the expression
then factorising is annoying as hell
well i dont have the tools for it actually
flat frigateBOT
knief
severe pond
that good?
severe pond
question, is this from a derivative or something?
balmy goblet
question, is this from a derivative or something?
it is lol
the derivate of another function
safe radishBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
severe pond
just show the original function
balmy goblet
you gotta derivate this
severe pond
you gotta derivate this
you’re taking the derivative of this?
balmy goblet
you gotta derivate this
i gotta derivate this function
and i got the thing i first sent
severe pond
ok then let’s restart because you just made it messier
you’re familiar with the quotient rule yes
balmy goblet
well i used the property from (u/v)
balmy goblet
well i used the property from (u/v)
'
balmy goblet
you’re familiar with the quotient rule yes
that is what i used
severe pond
$(\frac{u}{v})’ = \frac{vu’ - uv’}{v^2}$
flat frigateBOT
knief
severe pond
now
balmy goblet
i'm not gonna lie i kinda struggle with derivating composed functions
balmy goblet
have you tried logarithmic differentiation
no lol
what is that 😮
it looks hard tho lol
severe pond
it’s essentially designed for this sort of problem
suppose $y = \frac{x^4+9x^2}{(x^2+3)^2}$
flat frigateBOT
knief
flat frigateBOT
knief
severe pond
you know implicit differentiation right
severe pond
what is ln
natural log
balmy goblet
oh we haven't studied that yet
severe pond
logarithms?
severe pond
you’re doing calculus but don’t know what a log is
it’s the inverse of exponential functions
severe pond
yea that’s true for ph and all that
balmy goblet
yes
severe pond
-log
balmy goblet
but how do you write it ?
severe pond
wdym
severe pond
do you know the function e^x
balmy goblet
like log = ?
log(x)*
balmy goblet
do you know the function e^x
yes
balmy goblet
so it is 1/e^x ?
severe pond
given an input x, ln(x) tells you the exponent e must be raised to to get x
severe pond
and you don’t know implicit differentiation either?
balmy goblet
no...
balmy goblet
alright...
severe pond
for implicit differentiation, logarithms, and logarithmic differentiation
but for now
balmy goblet
but then how do i solve the exercise the hard way
severe pond
we can do it the tedious way
balmy goblet
cause i suppose he doesnt want us to use you method
balmy goblet
we can do it the tedious way
oh well i tried but then i get x^4 + a constant and other stuff and idk how to factorise that
severe pond
$f’’(x) = \frac{(x^2+3)^2(4x^3+18x) - (x^4+9x^2)(4x(x^2+3))}{(x^2+3)^4}$
flat frigateBOT
knief
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
severe pond
you can cancel one factor of x^2+3 immediately
severe pond
which gives us
balmy goblet
i find it kinda hard cause you gotta be careful that nothing can be simplified on each step
severe pond
$f’’(x) = \frac{(x^2+3)(4x^3+18x) - (x^4+9x^2)(4x)}{(x^2+3)^3}$
flat frigateBOT
knief
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
severe pond
then we have
balmy goblet
**knief**
Compile Error! Click the <:errors:504266556054962196> reaction for mor...
i think you forgot one element
the (x^2 + 3) should dissapear right
oh yeah no ok sorry
severe pond
$f’’(x) = \frac{(x^2+3)(2x)(2x^2+9) - 4x^3(x^2+9)}{(x^2+3)^3}$
flat frigateBOT
knief
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
severe pond
hmm from here it’s probably best to just distribute through
i don’t see anything else to do
balmy goblet
so what do you get when distributing
severe pond
$f’’(x) = \frac{(4x^5+30x^3+54x) - (4x^5+36x^3)}{(x^2+3)^3}$
flat frigateBOT
knief
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
severe pond
then the 4x^5 cancels
and 30x^3 - 36x^3 is -6x^3
so
$f’’(x) = \frac{-6x^3+54x}{(x^2+3)^3}$
flat frigateBOT
knief
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
severe pond
you can factor the numerator if you’d like
balmy goblet
you can factor the numerator if you’d like
wow it seems so simple
balmy goblet
well i think the simplifying part isn't easy to see
severe pond
don’t expand things immediately
notice how i waited until nothing could’ve been factored further
to expand
safe radishBOT
safe radishBOT
Available help channel!
dire harness
I have a probability of getting a VIP when opening one crate, which is 0.5%. I want to calculate the probability of getting 4 or more VIPs when opening multiple crates.
So say I got 1000 crates and I open them all in a row, how do I calculate the chance I get 4 or more VIPs?
I found the formula for the binomial probability: P(X = k) = comb(N, k) * p^k * (1 − p)^(N − k)
I used this formula to calculate the probability for 750 crates and got approximately 19%. However, when I increased the probability to 1%, the result dropped to about 7%, which seems counterintuitive.
I suppose that is due to the formula being X = k, so it doesn't account for me getting more than 4 VIPs
safe radishBOT
I have a probability of getting a VIP when opening one crate, which is 0.5%. I w...
@dire harness Has your question been resolved?
dire harness
What did u do to find the probability?
I think I just realised how to solve this
knotty pier
Mhmm
dire harness
I use the formula I provided earlier for X = 1, X = 2, X = 3
knotty pier
Mhm
knotty pier
Yes
dire harness
so that's P(X>=4)
knotty pier
But X=0?
dire harness
Yes that's the method
thanks, it was for a small python program, so this works out perfectly because I can just do a for loop
.close
novel iron
Anyone that could point out my mistake? Trying to prove that $E(g(X)) \approx g(u)$ by approximating the probability function $p_x(x) \approx p_x(u) - (x-u)p(x)$. Using the law of the unconcious statistician, I tried to evaluate the expected value $E(g(X))= \sum_k g(k)p_x(k) \approx \sum_k g(k)(p_x(u) +(k-u)p'_x(k)) = \sum_k g(k)p_x(u) + g(k)p_x'(u)k -g(k)up'_x(k) = \sum_k g(k)p_x(u) + g(k)p_x'(k) k-g(k)\sum_k(kp_x(k))p'_x(k) = \sum_k g(k)p_x(u) + g(k)p_x(u) -g(k)p_x(u)kp'_x(k) = \sum_k g(k)p_x(u) $
safe radishBOT
Anyone that could point out my mistake? Trying to prove that $E(g(X)) \approx g(...
flat frigateBOT
Pen
novel iron
I used the fact that $\sum_k g(k)up'(k) = \sum_k g(k)\sum_k kp(k) p'(k) = \sum_k g(k)kp'(x)$
flat frigateBOT
Pen
novel iron
Since the sum of the probability function is just 1
safe radishBOT
@novel iron Has your question been resolved?
novel iron
Anyone that could point out my mistake? Trying to prove that $E(g(X)) \approx g(...
Unsure why it's not updating, there's an extra u there by mistake
Corrected: $E(g(X))= \sum_k g(k)p_x(k) \approx \sum_k g(k)(p_x(u) +(k-u)p'_x(k)) = \sum_k g(k)p_x(u) + g(k)p_x'(u)k -g(k)up'_x(k) = \sum_k g(k)p_x(u) + g(k)p_x'(k) k-g(k)\sum_k(kp_x(k))p'_x(k) = \sum_k g(k)p_x(u) + g(k)p_x(u)k-g(k)p_x(u)kp'_x(k) = \sum_k g(k)p_x(u)$
flat frigateBOT
Pen
novel iron
<@&286206848099549185>
safe radishBOT
@novel iron Has your question been resolved?
novel iron
.close
woven quartz
how do you find the derivative of Sin^-1?
safe radishBOT
how do you find the derivative of Sin^-1?
hard crest
y = arcsin x and solve for the derivative implicitly
safe radishBOT
Available help channel!
halcyon light
safe radishBOT
plucky elk
a^3 (a + b) = a^4 + a^3 b
safe radishBOT
@halcyon light Has your question been resolved?
scenic bough
safe radishBOT
scenic bough
,rotate
flat frigateBOT
scenic bough
how do i solve this
austere cypress
You need to draw the lines and find the one with the smallest slope
f'(A), f'(B) and f'(F) represent the slope of the lines tangent to the points at A, B and F respectively.
[f(C) - f(B)]/(C - B) and [f(F) - f(A)]/(F - A) are rise over run and represent the slope of the lines that pass through the points at C and B and the points at F and A, respectivelly
you need to draw the lines and see which is pointing downwards the most
austere cypress
f prime of f?
what do you mean?
scenic bough
what do you mean?
is the answer f prime of f
safe radishBOT
safe radishBOT
Available help channel!
rancid sand
Interesting question: If f(x) is a polynomial function, will the result of integrating it infinitely many times converge to zero?
safe radishBOT
Interesting question: If f(x) is a polynomial function, will the result of integ...
rancid sand
Don't know where to start
arctic raven
you mean converge to the zero function?
safe radishBOT
@rancid sand Has your question been resolved?
drifting ridge
Can i get help with this task?
safe radishBOT
Can i get help with this task?
drifting ridge
find the asymptotes
i know that when the denominator is = 0 theres a vertical asymptote
drifting ridge
Do they also want horizontal?
or the oblique asymptote
drifting ridge
Yeah so that gives you the vertical asymptote
But how do you write it?
my friend wrote it like this:
but idk how to prove that
32/0 ?
how is that infinity
@shy lynx
hidden gyro
I don’t think it has a horizontal asymptote
drifting ridge
I don’t think it has a horizontal asymptote
why
shy lynx
my friend wrote it like this:
your friend is wrong, the limit does not exist (even if you allow +-inf)
since it depends which side you approach it from
drifting ridge
because it's a grade difference?
drifting ridge
your friend is wrong, the limit does not exist (even if you allow +-inf)
since i...
then what is right?
shy lynx
a rational function p(x)/q(x) has a vertical asymptote at a if p(a) =/= 0 and q(a) = 0
that's how I'd justify it
hidden gyro
why
if I recall for rational any function
a(x)/b(x)
where a(x) and b(x) are polynomials
if a(x) degree is greater then the degree of b(x) then it does not have a horizontal asymptote
drifting ridge
hmm i see
shy lynx
but it can still have oblique asymptotes
hidden gyro
but it can still have oblique asymptotes
yep (if oblique asymps are what I think they are)
shy lynx
through polynomial division?
to find an oblique asymptote first calculate lim_{x to inf} g(x)/x
if that exists call it a
then calculate lim_{x to inf} g(x) - ax
call that b
then your oblique asymptote is ax+b
If either limit fails to exist then there is no oblique asymptote
(then do the same process for x -> -inf)
drifting ridge
to find an oblique asymptote first calculate lim\_{x to inf} g(x)/x
if that exis...
how do i do that?
shy lynx
Write down g(x)/x
calculate its limit at inf the same way you would when calculating a horizontal asymptote
drifting ridge
calculate its limit at inf the same way you would when calculating a horizontal ...
i dont seem to quite understand
gilded pine
the horizontal asymptotes are where the function stretches out to the left or right and seems to settle on a specific y-value
for example, this part of y=1/x has a horizontal asymptote at y=0 and a vertical one at x=0
drifting ridge
the horizontal asymptotes are where the function stretches out to the left or ri...
i know what they are
drifting ridge
to find an oblique asymptote first calculate lim\_{x to inf} g(x)/x
if that exis...
but this looks like a different language to me
gilded pine
see what value your function approaches as x gets higher and higher
oh oblique asymptotes
idk how to do those nvm
shy lynx
Polynomial division should also work
In this case you get $g(x) = -x - 7 - \frac{32}{x-5}$. (I cheated and asked WolframAlpha to do that for me.)
flat frigateBOT
Morrow
shy lynx
So the slant asymptote is -x-7
shy lynx
The point is that that doesn't matter, since that part goes to 0 as x -> inf
drifting ridge
where is the infinity in the equation
also is this correct to check if it has a vertical asymptote?
shy lynx
where is the infinity in the equation
drifting ridge
so you check by placing x to infinity if it's a oblique asymptote?
shy lynx
Yeah so $g(x) - (-x-7) = \frac{32}{5-x}$ which goes to $0$ as $x \to \infty$.
flat frigateBOT
Morrow
shy lynx
So it satisfies the definition
drifting ridge
**Morrow**
how is that equal
shy lynx
Because you did the polynomial division and got $-x-7$ with a remainder of $32$. What that means is that $g(x) = -x - 7 - \frac{32}{x-5}$. Then you just subtract $-x-7$ from both sides.
flat frigateBOT
Morrow
drifting ridge
is a considered (-x - 7) ?
shy lynx
a is -1, b is -7
(wikipedia uses the letters m,n instead of a,b but it's the same thing)
drifting ridge
but when you do polynomial division
wont you get the answer
@shy lynx
im stuck here
im trying to understand but im stuck here
shy lynx
yes you do get that
drifting ridge
and when you do lim x -> infinity or lim x-> -infinity you get 0? in 32/5-x
shy lynx
yeah
shy lynx
that's your asymptote
at infinity
for -infinity the exact same logic works
so it's also an oblique asymptote at -infinity
drifting ridge
and when you do lim x -> infinity or lim x-> -infinity you get 0? in 32/5-x
if i were to write this on paper how would i do it?
@shy lynx
shy lynx
$$\lim_{x \to \infty} \frac{32}{5-x} = 0$$
flat frigateBOT
Morrow
drifting ridge
$$\lim_{x \to \infty} \frac{32}{5-x} = 0$$
do i not include (-x - 7) ?
shy lynx
$$\lim_{x \to \infty} [g(x) - (-x-7)] = \lim_{x \to \infty} \frac{32}{5-x} = 0$$
flat frigateBOT
Morrow
drifting ridge
**Morrow**
wait im confused again how is it = not +
shy lynx
why would it be +
drifting ridge
why
shy lynx
what do you get
drifting ridge
but why do you subtract
shy lynx
Because we want one side to look like g(x) - (ax + b)
shy lynx
.
drifting ridge
but wont the whole equation change if you remove it?
shy lynx
you subtract from both sides, you still have a valid equation
drifting ridge
from both sides how does that work
shy lynx
it's algebra
just like if I have 3x+5=8 then I can subtract 5 from both sides to get 3x = 3
shy lynx
no
drifting ridge
but im moving it over the = ?
shy lynx
g(x) = (-x - 7) + 32/(5-x)
===>
g(x) - (-x - 7) = (-x - 7) + 32/(5-x) - (-x - 7)
===>
g(x) - (-x - 7) = 32/(5-x)
drifting ridge
g(x) = (-x - 7) + 32/(5-x)
===>
g(x) - (-x - 7) = (-x - 7) + 32/(5-x) - (-x - ...
oh yeah i meant the second
forgot to add the last part
is it right now?
drifting ridge
g(x) - (-x - 7) = 32/5-x ?
shy lynx
yes
drifting ridge
do you do lim -inf and lim inf now?
shy lynx
yep
shy lynx
$$\lim_{x \to \infty}$$
$$\lim_{x \to -\infty}$$
flat frigateBOT
Morrow
shy lynx
on both sides
shy lynx
you didn't calculate the limit on the left correctly because you ignored g(x)
but the point is you're not supposed to calculate the limit on the left
we want to show that the limit on the left is zero
drifting ridge
how do i do this?
shy lynx
and we do that by showing that the limit on the right is zero
because we know they're equal
so just calculate lim_{x to infty} 32/(5-x)
you said 32/-inf
which is zero
drifting ridge
can you do it visually?
shy lynx
wdym
drifting ridge
**Morrow**
like show me like this
shy lynx
**Morrow**
literally just that
but if you want you can write
$$\lim_{x \to \infty} \frac{32}{5-x} = \frac{32}{5-\infty} = \frac{32}{-\infty} = 0$$
flat frigateBOT
Morrow
shy lynx
if your class lets you write it that way
drifting ridge
**Morrow**
arent you supposed to shorten the first part of the =
shy lynx
include the $$\lim_{x \to \infty} [g(x) - (-x-7)] =$$ part
flat frigateBOT
Morrow
shy lynx
no
drifting ridge
x is infinity?
shy lynx
you're ignoring the g(x) part
drifting ridge
how is that relevant
shy lynx
because it's part of the expression
you can't just ignore parts of the expression
the whole point of this exercise is that g(x) is very close to -x-7 when x is large
so g(x) - (-x-7) is going to be very small
drifting ridge
so you add x = infinity on the right side of the equation but not the left?
shy lynx
I'm only evaluating the limit on the right
because it's an easy limit to calculate
That's the whole reason I wrote the equality
drifting ridge
my friend did it like this, is this wrong or correct?
shy lynx
it's the same thing, just more disorganized
drifting ridge
drifting ridge
**Morrow**
how does this equal 0
shy lynx
the red circle is g(x)
drifting ridge
because x is 5?
drifting ridge
**Morrow**
so youre not adding x to infinity on the left side but the right side?
shy lynx
I'm only evaluating the limit on the right
.
drifting ridge
**Morrow**
okay im here
shy lynx
The full answer is
$$\lim_{x \to \infty} [g(x) - (-x-7)] = \lim_{x \to \infty} \frac{32}{5-x} = \frac{32}{5-\infty} = \frac{32}{-\infty} = 0$$
flat frigateBOT
Morrow
drifting ridge
**Morrow**
is g(x) = y?
shy lynx
what
drifting ridge
the point was to find the asymptote
shy lynx
g(x) is our function
drifting ridge
**Morrow**
how do i find the asymptote with that
drifting ridge
because it equals to 0?
flat frigateBOT
Morrow
shy lynx
all the stuff in between are the steps
drifting ridge
**Morrow**
should i write that in the end?
drifting ridge
wait
so if it's - infinity
what do we then
the same?
just that its 32/-infinity = 0?
shy lynx
if what's -infinity?
shy lynx
oh you mean x -> -infinity
drifting ridge
yeah
shy lynx
yeah it's pretty much the same thing
$$\lim_{x \to -\infty} [g(x) - (-x-7)] = \lim_{x \to -\infty} \frac{32}{5-x} = \frac{32}{5+\infty} = \frac{32}{\infty} = 0$$
flat frigateBOT
Morrow
drifting ridge
Is this correct? @shy lynx
shy lynx
looks great
drifting ridge
looks great
im curious if the answer is -x - 7
why do we have the extra - there before
why do we decide to ignore it?
shy lynx
because we want to look at the difference between g(x) and -x-7
and show that the difference is small if x is big
by doing that, we show that g(x) gets closer and closer to -x-7
that's why we subtract
shy lynx
it's a bit late, I need to sleep
shy lynx
np
drifting ridge
.close
safe radishBOT
safe radishBOT
Available help channel!
austere turret
hi
austere turret
in rules of inference
for rules of conjuctive simplification
can it be used for both "and" and "or" statements or is it just one of them. and if it's the latter, which one is it?
.close
safe radishBOT
frosty ether
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Available help channel!
ivory vessel
what is the hundreds digit of 20! - 15!
safe radishBOT
what is the hundreds digit of 20! - 15!
plucky elk
Factor out 15!
ivory vessel
WHAT
severe pond
20! = 20 * 19 * 18 * 17 * 16 * 15 * … = 20 * 19 * 18 * 17 * 16 * 15!
ivory vessel
so 20! - 15! = 20 * 19 * 18 * 17 * 16??
ivory vessel
so is the hundreds digit 0?
exotic snow
n! has floor(n/5) + floor(n/25) + ... etc 0s
modest violet
so is the hundreds digit 0?
yes of course
latent moth
i wanna know , is it true for all questions like this or are there some exceptions?
safe radishBOT
i wanna know , is it true for all questions like this or are there some exceptio...
latent moth
like if we have |x| <= smthing , we need both u=> -smthing and u=< smthing
plucky elk
what is "questions like this"
latent moth
what is "questions like this"
i mean like
|3x/5 - 1| <= 2/5
plucky elk
yes whenever you see absolute value, you should use the definition of absolute value
latent moth
like here , we would need union of both the solutions , cuz we need both
plucky elk
,tex .abs def
latent moth
yeah ik that
but my original question was
why did they take intersection here
the problem was |3-1/x| <= 1/2
unlike |3x/5 - 1| <= 2/5 , where we took union of the solutions of both cases
@plucky elk (srry for ping)
flat frigateBOT
riemann
latent moth
yeah i did use those and split into 2 cases
plucky elk
You have to use the union or intersection depending on the question
latent moth
but i dont understand when to take intersection and union
plucky elk
Union is "or" and intersection is "and"
latent moth
Union is "or" and intersection is "and"
how would i know when to use union / intersection
plucky elk
how would i know when to use union / intersection
Do problems
Learn what the question is asking
safe radishBOT
@latent moth Has your question been resolved?
safe radishBOT
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Available help channel!
dull cliff
find the volume
safe radishBOT
find the volume
dull cliff
answer is 11pi/3
hard crest
a sketch would be very useful
dull cliff
would the outer radius be y=x^2?
fathom jewel
The only mistake that I see is that it should be sqrt(y)² - (y²)²
dull cliff
yeah i think i see that now i thought outer radius would be x=y^2
fathom jewel
Oh I realized we rotate about y=1
So basically outer radius is R = 1-x² and inner radius 1-sqrt(x)
dull cliff
how come it is 1-x^2? because rotate at y=1?
how did you get that R = 1-x² and inner radius 1-sqrt(x)
fathom jewel
would the outer radius be y=x^2?
The green represents the outer radius
Which is 1-x²
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cursive wind
starting from the (n+1)f(n+1) - nf(n) = 0, how did they get f(n) = 1/2n
cedar void
here ignore the =0 part
and notice the pattern
3f(3) in first line and -3f(3) in the second
cursive wind
here ignore the **=0** part
and notice the pattern
then
cursive wind
have you noticed pattern?
i mean how did they get 2(f2) = 1/2 without steps
cursive wind
4f(4)=3f(3)=2f(2)
after that do what
cedar void
here ignore the **=0** part
and notice the pattern
here notice that first term of a line will be cancelled by the 2nd term of the second line
this is the pattern you're suppoesed to observe
cursive wind
here notice that first term of a line will be cancelled by the 2nd term of the s...
so they substitute the 2f(2) in the equation cuz all terms cancel except the 2
f(n+1) = 2f(2)/n+1
but how they get 2f(2) = 1/2
rough storm
i mean how did they get 2(f2) = 1/2 without steps
plug in n=0
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cinder delta
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cinder delta
What i've done for this question is, made the taylor for the log(1+x), and then the log(1-x). They however have taken a different route in the working out which i do not understand why becasue we end up with different taylor series in terms of the negative/positive sign
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@cinder delta Has your question been resolved?
cinder delta
<@&286206848099549185>
obsidian oracle
<@&286206848099549185>
is the picture you sent your work or the solution
if it's the solution, show your work
cinder delta
is the picture you sent your work or the solution
Question and the solution, my work just the taylor for the log(1+x), pretty much same as the solution up until the log(1-x) part which is where my question arises
obsidian oracle
show what you did for log(1-x) then
cinder delta
show what you did for log(1-x) then
alright gimme a moment
cinder delta
cinder delta
show what you did for log(1-x) then
here it is, mb i had to finish up dinner
So, i'm not going to question why they do ln1+x - ln1-x because its probably an algebraic strategy that i've forgotten, but my issue is how they go about their taylor series for ln1-x
obsidian oracle
So, i'm not going to question why they do ln1+x - ln1-x because its probably an ...
if f(x) = ln(1-x) you got f' wrong
chain rule remember
cinder delta
if f(x) = ln(1-x) you got f' wrong
Yep, it seems like it was litearlly just that one error that caused the whole issue. Once I fixed it, everything aligned up with solution. And just as a confirmation, is the ln(1+x) - ln(1-x) thing an algebraic thing ?
slate hollow
i cant seem to figure out how my teacher got this answer? what formula am i suppose to be using?
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i cant seem to figure out how my teacher got this answer? what formula am i supp...
lean otter
can anyone help me understand how to solve 10 + x = 6x? i know the answer is x = 2 (correct me if i'm wrong) but i don't understand how to solve it. the thing with me is that i can't just memorize the steps. i need to understand it, the why's and then the how's. i used to be able to solve this but i haven't done math in a long time so now i have no fuckin' idea how to do it argh. i also don't remember having to subtract for both sides but the steps say so, like huh!
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buoyant shadow
yeah 33114 is larger than anything i can make
lean otter
hi
helloooo i'm here
i think this channel is occupied....
oh okay! sorry, that's my fault. should i move somewhere else? or what should i do? it's my first time asking a question on this server and my question was automatically moved here iirc.
lean otter
alrighty, i think that's where i put my question and then it got moved here
oh it worked, haha sorry guys, thank you!
slate hollow
.close
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storm citrus
hey
steel gulch
Use imgur
storm citrus
oh ty
this dumb ipad won't let me upload
Finally
They’re uploading now
just wondering why this doesn't actually work to get the answer
steel gulch
It assumes constant acceleration
storm citrus
wdym? wouldn't (V-U/t) give a constant deceleration?
how could i use a similar approach/ equation to get the right answer?
storm citrus
It assumes constant acceleration
?
steel gulch
wdym? wouldn't (V-U/t) give a constant deceleration?
Yeah, but just by observing your velocity function, you can see that acceleration clearly isn’t constant.
radiant eagle
but isn't 52 the answer
steel gulch
how could i use a similar approach/ equation to get the right answer?
Integrate it lol
radiant eagle
sorry)
storm citrus
but isn't 52 the answer
its 17.33
storm citrus
Yeah, but just by observing your velocity function, you can see that acceleratio...
is it parabolic cos of the squared term?
radiant eagle
ohh ok i get it
storm citrus
im a bit confused
steel gulch
is it parabolic cos of the squared term?
No, it’s piecewise, look at the velocity time graph
storm citrus
No, it’s piecewise, look at the velocity time graph
ye, its made of a 2 constants, that straight line constant and then the constant deceleration
radiant eagle
yeah but if you use the formula with a, you put s=260
but that's the displacement for the whole 20s
steel gulch
ye, its made of a 2 constants, that straight line constant and then the constant...
Yup, exactly
storm citrus
yeah?
the 10u is the distance convered in the first 10 seconds
but the 0.5at^2 doesn't find the distance covered in the last 10 seconds?
radiant eagle
you should sub s = 260 - 10u
storm citrus
so 260-10u = 0.5at^2
thats not right
i still don't understand why 0.5(v-u/t)t^2 doesn't give you the distance covered during the deceleration moment
oh
wait
i did find out that if i swap (v-u/t) for (u-v/t) i get the right answer?
so if i take the deceleration as acceleration in my equation i get the right answer?
storm citrus
I was just messing around n taking acceleration as a positive value gets me the right answer?
steel gulch
idk but i feel like i was just lucky
I think so, idk maybe it works in general, if I was you, I would test it.but in this case it seems wrong, since you used a +ve acceleration for a decelerating body. Idk.
storm citrus
so just integrating would be the best thing to do with questions like this?
so
260 = 10u + 0.5*10u
storm citrus
260 = 10u + 0.5*10u
if thats what u meant by integrating on a piecewise function.
steel gulch
Yeah that’s what I was referring to
storm citrus
ty
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halcyon badge
fleet condor
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untold oyster
so i have solved this equation:
safe radishBOT
so i have solved this equation:
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untold oyster
.reopen
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untold oyster
so
i have this function
but i have a question about the asymptote in x=1
because it the 3sqrt it says (x-1)² and doesnt that mean it stays + on both sides?
because it doesn't make sense with the graph
like i would've thought it would look more like this
.close
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fervent hatch
$\int\frac{1}{cos(x)+1}dx$
safe radishBOT
$\int\frac{1}{cos(x)+1}dx$
flat frigateBOT
Nathan
fervent hatch
How do I integrate
lean otter
not exactly
obsidian ginkgo
In general, $Cos (2x) = Cos^2 (x) - Sin^2 (x)$
flat frigateBOT
Adarsh
fervent hatch
Hey I was close 😎
lean otter
yup yup
fervent hatch
Alr I’ll try it
obsidian ginkgo
You can rewrite that as, $Cos(2x) = 2Cos^2 (x) - 1$
flat frigateBOT
Adarsh
lean otter
You can rewrite that as, $Cos(2x) = 2Cos^2 (x) - 1$
I would probably prefer using this one for this particular question
lean otter
$\cos(2\theta) = 2\cos^2 (\theta) - 1$
flat frigateBOT
Edmund Cloudsley
lean otter
remember that $2 \theta$ here $ = x$
flat frigateBOT
Edmund Cloudsley
fervent hatch
Alr
lean otter
subsequently just $\theta$ = $\frac{x}{2}$
flat frigateBOT
Edmund Cloudsley
lean otter
keep that little thing in mind
fervent hatch
Yeah
Uh
Okay uh I’m missing something
Did I do this right?
@lean otter
@obsidian ginkgo
obsidian ginkgo
Is this the same question?
fervent hatch
Yes
obsidian ginkgo
I see it 1 sec
fervent hatch
Ok
obsidian ginkgo
Yea it's fine
flat frigateBOT
Nathan
obsidian ginkgo
**Nathan**
Rewrite it in terms of cos and sin
flat frigateBOT
Nathan
fervent hatch
how
obsidian ginkgo
Take the lcm
obsidian ginkgo
$1 - Cos x = 2Sin^2 (x/2)$
flat frigateBOT
Adarsh
obsidian ginkgo
$Sinx = 2Sin(x/2) Cos(x/2)$
flat frigateBOT
Adarsh
obsidian ginkgo
Dividing we get tan
fervent hatch
$\frac{2Sin^2(\frac{x+y}{2})}{2Sin(\frac{x+y}{2})Cos(\frac{x+y}{2})}$
flat frigateBOT
Nathan
fervent hatch
$\frac{Sin(\frac{x+y}{2})}{Cos(\frac{x+y}{2})}$
flat frigateBOT
Nathan
fervent hatch
$tan(\frac{x+y}{2}) = x + C$
flat frigateBOT
Nathan
fervent hatch
why would they write it like that? @obsidian ginkgo
is there some other way to get that?
obsidian ginkgo
**Nathan**
They integrated this using partial fractions I'm guessing
open vessel
How and why
safe radishBOT
How and why
lean otter
!status
safe radishBOT
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
1
digital sparrow
Cause it can be factored in the form
(x-a)² + (y-b)² = r²
Where (a, b) is the center
And r is radius
open vessel
(x-a)² + (y-b)² = r²
How to change it in that form? 112 isn’t a square
digital sparrow
Firstly take 8 common
digital sparrow
(x-a)² + (y-b)² = r²
As coeff of x² and y² is 1
Then form x-a and y-b squares
Don't worry about r
open vessel
Firstly take 8 common
Why and how did u think of that
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orchid sentinel
equations with modulus
guys, pls help, I got these roots, but idk correctly or not and where is the module here?
my solve:
x1 = (-1+√29)/(2) ≈ 2,15
x2 = (-1-√29)/(2) ≈ -3, 15
safe radishBOT
*equations with modulus*
guys, pls help, I got these roots, but idk correctly or...
wispy monolith
*equations with modulus*
guys, pls help, I got these roots, but idk correctly or...
Can you show your work
orchid sentinel
Can you show your work
wispy monolith
Ohhhh it's (√x-2)² , well that makes it simple
wispy monolith
Yeah looks fine
orchid sentinel
close values are written just for convenience
I don't got where the module is here? Or should acceptable values here?
orchid sentinel
Yeah looks fine
can u help me?
wispy monolith
I don't got where the module is here? Or should acceptable values here?
What module? Can you paste the complete question
orchid sentinel
What module? Can you paste the complete question
This is an assignment on the topic "equations with moduli", which means that there must be some kind of check here, because this is not just a quadratic equation. We have such a concept as ODZ, for you it means acceptable values, and at first I did not understand that the acceptable values are x - 2 >= 2 => x >= 2 because we have a root in the equation
obtuse linden
the remainder when the polynomial p(x) is divided by x^2-8x+16 is 9. What is the product of the possible remainders when p(x) is divided by (2x+8)
safe radishBOT
the remainder when the polynomial p(x) is divided by x^2-8x+16 is 9. What is the...
obtuse linden
can i get some help with this question please?
<@&286206848099549185>
I calculated that are trying to work out p(-4) through the remainder theorem but not sure where to go realllly
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@obtuse linden Has your question been resolved?
obtuse linden
no
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@obtuse linden Has your question been resolved?
open vessel
Then form x-a and y-b squares
I did it but i couldn’t get the answer
open vessel
the remainder when the polynomial p(x) is divided by x^2-8x+16 is 9. What is the...
Is this a SAT question?
digital sparrow
I did it but i couldn’t get the answer
Should open a new channel now
Btw the a is wrong
,w 112/8
flat frigateBOT
pseudo flax
how to prove that $(\sum_{n=0}^{k}n)^2 = \sqrt{\sum_{n=0}^{k}n^3}$
flat frigateBOT
General_Jacob
pseudo flax
no
pseudo flax
no
lean otter
is it linked with smthg u are currently learning ?
pseudo flax
no
lean otter
ah u just ask for personal knowledge ?
pseudo flax
yes
lean otter
so i think that it would be easy with the formulas
but u want to do without it right ?
pseudo flax
how to figure out the formula for the sum in the sqrt?
lean otter
rigorusly by induction is a good way
pseudo flax
i tried induction and it didnt go well
lean otter
or u see that u can associate the first term with the last, the 2nd with the one before last etc... and u multiply by half the number of time u add numbers (here k/2) so
lean otter
yea
pseudo flax
There was 48 students from different classes. 6 of them had one friend from their class, 9 of them had two friends from their class, 4 of them had three friends from their class and the rest didnt have any friends from their class. How many classes were there?
lean otter
no idea
pseudo flax
@raven vessel
digital sparrow
!1q
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It is suggested that you limit yourself to one question per help channel, opening a new one once your original question is answered and your original channel has been closed. This is to make your channel easier to follow for potential helpers and can bring attention to the fact that your question has changed.
@pseudo flax Has your question been resolved?
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zealous matrix
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zealous matrix
does anyone know if its over for me
i think i might only be 100iq
cant get into oxford
silver glade
30x+10y=700
20x+5y=425
=> 5y = 125
=> y = 25
so C assuming i did my mental math correctly
zealous matrix
=> 5y = 125
how did you get rid of 10x
silver glade
how did you get rid of 10x
elimination
primal parcel
I think x is 15?
silver glade
multiply first equation by 2 and second equation by 3
primal parcel
Also mental maths
silver glade
I think x is 15?
correct, but they only ask for y
primal parcel
multiply first equation by 2 and second equation by 3
Just multiply eq 2 by 2
It’s simpler and we eliminate variable y
silver glade
Just multiply eq 2 by 2
that gives you x lol
primal parcel
For now and solve for x
silver glade
We want y
primal parcel
Ik
silver glade
it's the same thing just do whichever one is easier for you ig ¯_(ツ)_/¯
primal parcel
Then sub it back in to any equation
zealous matrix
this is an admissions test question
primal parcel
For what?
zealous matrix
oxford
silver glade
As in... current round?
primal parcel
Can’t be
silver glade
ok good
primal parcel
If it was
zealous matrix
you need to do it in like 40 secs
primal parcel
I’ll be in Cambridge by now
silver glade
you need to do it in like 40 secs
took me like 10 or so, so reasonable
zealous matrix
the questions are rlly easy but the time limit is bad
primal parcel
Ngl
zealous matrix
50 in 1hr
primal parcel
Oxbridge exams are annoying
zealous matrix
idk if im smart enough tbh
silver glade
Do your grades not matter for oxford lol
primal parcel
I could prob answe le a couple but that’s all
zealous matrix
what do u guys think, does it have to do with talent or no
primal parcel
Do your grades not matter for oxford lol
It does
silver glade
oh ok
primal parcel
You need a min grade req of double A* and A
zealous matrix
so i applied
silver glade
what do u guys think, does it have to do with talent or no
nothing has to do with talent
just practice
zealous matrix
You need a min grade req of double A* and A
thats for med and shit
silver glade
that's all you can do anyway
primal parcel
A level or equivalent
zealous matrix
nothing has to do with talent
some people are smarter than others naturally
primal parcel
thats for med and shit
#oh?
zealous matrix
im applying ppe
primal parcel
I don’t bother doing the medical aptitude use test
I was too lazy and now I regret it
…
silver glade
some people are smarter than others naturally
i mean obviously, but you can still grow your intelligence through practice
zealous matrix
i mean obviously, but you can still grow your intelligence through practice
idk
silver glade
I think i did ¯_(ツ)_/¯
primal parcel
i mean obviously, but you can still grow your intelligence through practice
You also need to develop your mental strength
zealous matrix
youd have to do specific brain training i think
not much can be generalised to intelligence
silver glade
for reference, i ranked below average in grade 9 on junior national CS contest, and ranked among the top 8% in grade 11 on the senior level
all it took was 4-5 hours of practice every day
so you can do this
zealous matrix
i q is best measure
silver glade
I Q is irrelevant here
Ofc if you have a higher one you'll need to do less practice
zealous matrix
ok ill try then, yh its true theres no way hard work wouldnt be effective
with this sort of thing
silver glade
when is it?
zealous matrix
im scoring at 45 rn haven;t practiced at all
a score of 65 is good enough for my curse
its in 9 days
70 is preferrable
i got 21/50 for reference, ran out of time
silver glade
this question is based on 9th grade curriculum math isn't it?
at least here i remember learning it
zealous matrix
this question is based on 9th grade curriculum math isn't it?
yh theres nothing complex only time pressured critical thinking
silver glade
okay fair enough
zealous matrix
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zealous matrix
why is the answer 41
glossy dock
maybe because one of the matinee performances will fall on a Sunday?
covert yoke
So if we write down a weekly calendar of performances, for MTWRFSS that is 1122120 right?
a month of 31 days consists of 4 weeks + 3 days, which must be chosen to be a consecutive block.
if the above doesn't make sense, grab a calendar, and look at each possible starting date of a month of 31 days.
Anyway there are a total of (how many) performances in a week, and then we can choose (which three days) to get another (how many) performances out of the remaining 3 days?
fathom jewel
I would think of it that you have at least (6+3) x 4 = 36 activities at least in 28 days, and the the best case for the remaining 3 days would be thursday (+2), friday (+1) and saturday (+2) = 5 total, so 36+5 = 41
covert yoke
or WRF or TWR, you have a total of 3 different possiblilities
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@zealous matrix Has your question been resolved?
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zealous matrix
.reopen
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zealous matrix
silver glade
For the first question, 40*40=1600, and each brick has area 200
1600/200=8
similarly 550*400/200 = 1100
so it should be B
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haughty ruin
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haughty ruin
I’m so confused on what this is asking
austere cypress
Make a rotation on the plane in a way that the point (5, -1) end up where (1, 5) was, applying the same rotation, where does the point (-4, 6) end up?
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haughty ruin
Make a rotation on the plane in a way that the point (5, -1) end up where (1, 5)...
Thx
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analog sable
having some trouble here, ABCD is a trapezoid, AB II DC
BC = 13cm
DC = 20cm
AD = 15cm
AE = 12cm
AE ⊥ DC
I need to find what AB's length is
cold relic
having some trouble here, ABCD is a trapezoid, AB II DC
BC = 13cm
DC = 20cm
AD...
Introducing a point F in the right spot should be enough to calculate AB
analog sable
i dont understand?
cold relic
You won’t calculate AB with the given lines alone
cold relic
i dont understand?
You need to draw one more line to calculate AB
One that isn’t there yet
Going from one of the points already there to a new point F
analog sable
this one's a real noggin scratcher for me
going down from B, drawing a parallel line to AE where it would meet with DC at point F?
cold relic
Yes
analog sable
and that is surely the only way to solve it? i havent done something like this in other exercises, but i figure i never had to either..
all right well it seems right, i sadly dont have the answers for the exercises, but i'll check if its all right tommorow.
.close
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cold relic
and that is surely the only way to solve it? i havent done something like this i...
Hmm well I’m not geometry expert. But it seems here to be the only sensible solution. Could be wrong though, it’s just the only one I was able to find
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lean otter
Evaluate x:
x-9=5x+51
safe radishBOT
Evaluate x:
x-9=5x+51
lean otter
I dont know the steps
sly plank
$ x - 9 = 5x + 51 \text{ becomes } x = 5x + 60 $ \
This is because we need to add $9$ since it is subtracted from $x$ on the left side. This will give us the first function we will need.
flat frigateBOT
luxzi
lean otter
$ x - 9 = 5x + 51 \text{ becomes } x = 5x + 60 $ \\
This is because we need to a...
So you add the 9 to 51 and have x=5x+60
sly plank
Yes, exactly
lean otter
You dont add 9 to 5x
lean otter
What if it was x+9 instead of x-9
lean otter
Now that you have x=5x+60 what do you do