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#help-26
topaz sinewBOT
topaz sinewBOT
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thorn cairn
Hey guys.
thorn cairn
Where is the general channel?
pseudo sonnet
Where is the general channel?
if you have a question, please ask now 
otherwise, I'm gonna close this channel
hm, well
.close
blazing tartan
can someone help me with this integral? the question asks me to evaluate the integral. What i dont understand is that after I finish integrating and substituting the upper and lower values of the integral, i end up with 'ln | 0 |' and i believe its undefined there. So i dont understand if i did something wrong along the way or if im missing something
topaz sinewBOT
can someone help me with this integral? the question asks me to evaluate the int...
ivory sorrel
,w limit of (3x^2-x+5)/(x^3-x) at x=1
ivory sorrel
well, doesn't look like the integral exists
,w integrate (3x^2-x-5)/(x^3-x) from 1 to 2
thorny flameBOT
blazing tartan
okay. thank you, i was confused if i did something wrong but i guess it doesnt exist.
.close
topaz sinewBOT
thorn cairn
@pseudo sonnet Thank you so much.
topaz sinewBOT
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rain hinge
I am trying to understand this function:
topaz sinewBOT
I am trying to understand this function:
rain hinge
Not sure what the TT symbol is
coarse tusk
it's like the Sigma but for products instead of sums
rain hinge
Oh so everything right of it from 1 to i-1 is multiplied by itself
pseudo horizon
it's a product of i-1 terms
each term looks like (1-alpha_j)
with different values of j
i guess "term" might not be the right word
rain hinge
is it like a nested forloop where as i increases it restarts the capital pi?
pseudo horizon
for i in N:
product = 1
for j in [1...i-1]:
product *= 1-alpha[j]
C_p += c[i] * alpha[i] * product
return C_p```
ripe maple
I have an issue with quadratic equations
topaz sinewBOT
I have an issue with quadratic equations
topaz sinewBOT
@ripe maple Has your question been resolved?
ripe maple
and solve the quadratic to find the roots
Yea. Thx though
fast sluice
how do i implicitly differntation
topaz sinewBOT
how do i implicitly differntation
fast sluice
so would xy be 1 times dy/dx
fast sluice
y + x timed dy/dx?
hoary burrow
Yeps I guess
topaz sinewBOT
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tiny pawn
topaz sinewBOT
tiny pawn
please someone explain it to me
topaz sinewBOT
@tiny pawn Has your question been resolved?
topaz sinewBOT
@tiny pawn Has your question been resolved?
tiny pawn
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topaz sinewBOT
velvet briar
@topaz sinew
topaz sinewBOT
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still bough
how do i begin to solve this?
still bough
<@&286206848099549185>
topaz sinewBOT
@still bough Has your question been resolved?
topaz sinewBOT
@still bough Has your question been resolved?
wispy hedge
hi, i'm stuck in this question (my working is below the question in blue)
wispy hedge
depth is 14cm/s, find out what it is for 3 minutes
2520cm
wispy hedge
area*depth should give volume
so around 8870 cm^3?
deep forum
👍
topaz sinewBOT
deep forum
ur welcome
topaz sinewBOT
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glossy sun
Does anybody know how I can solve this equation with exact values
dusk lava
start by factoring a 2cos^2x out of the first 2 terms then factor by grouping
you also need to factor a -1 from the second 2 terms in order to factor this way
maybe will help with finding values?
glossy sun
Yeah I tried that but then I keep getting stuck
dusk lava
can i see your work
glossy sun
dusk lava
hmm
glossy sun
Square both sides then expand and simplify maybe?
dusk lava
i mean maybe but seems tedious
just looked at the answers and they seem really really messy
topaz sinewBOT
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exotic saddle
how to answer?
topaz sinewBOT
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twin pollen
help plz
twin pollen
this is the answer to the queston and I was wondering why my teacher adds a plus one in the blue box
plz @ me when replying
thx
I have to get going within the next 30 mins also
so hopefully i can get some help before then
acc no my question is why are we minusing 233 from 112
topaz sinewBOT
@twin pollen Has your question been resolved?
mint crescent
acc no my question is why are we minusing 233 from 112
You need it to be between days 112 and 233 since those are the endpoints of the interval
twin pollen
ic alr. i dont get this tho
topaz sinewBOT
@twin pollen Has your question been resolved?
twin pollen
sorry wrong question this is it
desert atlas
f(x) is the notation for a function
you cant change stuff about it
other than the x inside
twin pollen
so u cant say this @desert atlas
desert atlas
nope
desert atlas
the notation f|x| makes no sense
twin pollen
cause for this question my teacher kinda did that
:
like for a why is there all the sudden absolute value lines
@desert atlas
twin pollen
oh ok but like for a cant u also just write y= f(x+4)
since the orginal graph is y=f(x)
and its going to left by 4
@desert atlas
desert atlas
oh ok but like for a cant u also just write y= f(x+4)
this is fine as well
yes it shifts the graph to the left
twin pollen
so then why did my teacheer add those absolute value lines?
@desert atlas
is it because the orginal graph of y= f(x) can also be written as y= f(lxl)
twin pollen
ya idk why i said that im just tryna make it make sense
it makes all y values positive
right @desert atlas
?
desert atlas
stop pinging me
twin pollen
oh sorry
desert atlas
what does it do geometrically to the graph
twin pollen
but what if there is a vertical translation down
then would it still not be negative
twin pollen
oh ok
so then bavk to my question of why is there all the sudden absolute value lines in my teachers answer
desert atlas
because the graph shows it
twin pollen
wait so y=f(x) is like input x into a specific function?
right
im confused on difference between y= lxl and y = f(lxl)
cause my teacher gave us this
desert atlas
y = |x| is the absolute value function
y = f(|x|) could be anything
depending on f(x)
twin pollen
if u have (y-6) squared and u take the root shouldnt it be plus minus
@desert atlas
o wait sorry for pinging
my bad
desert atlas
sqrt (x^2) = |x|
twin pollen
but how
and so does that mean that root of 9 and root of 3 different
i meant root of 3 squared
topaz sinewBOT
@twin pollen Has your question been resolved?
topaz sinewBOT
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quiet phoenix
topaz sinewBOT
quiet phoenix
could this be solved just by plugging in the integral into my calculator and adding 1200?
topaz sinewBOT
@quiet phoenix Has your question been resolved?
topaz sinewBOT
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ivory sorrel
How would I prove that the set of rationals with 10|p| \geq q is dense
ivory sorrel
wdym
gilded plume
By p and q do you mean numerator and denominator?
chilly walrus
although this is the same as (-1)/2, hmm
topaz sinewBOT
How would I prove that the set of rationals with 10|p| \geq q is dense
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.
gilded plume
Isn’t this false
ivory sorrel
It is?
gilded plume
It is notably empty on the subset between 0 and 1/10 right
ivory sorrel
I mean one counter example I thought of is 1/10 and -1/10
ivory sorrel
It is notably empty on the subset between 0 and 1/10 right
oh right, I messed up my defns
sorry
.close
topaz sinewBOT
ivory sorrel
thanks
topaz sinewBOT
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modern berry
How would you calculate the depth of a well from just knowing the speed of sound, the amount of time it takes to hear a rock hit the bottom and how fast the rock is falling?
topaz sinewBOT
How would you calculate the depth of a well from just knowing the speed of sound...
deep forum
if you hear the echo back in 4 seconds, that means the well is 2 sound seconds deep
how fast the rock is falling depends on the g
warm turtle
How would you calculate the depth of a well from just knowing the speed of sound...
if it's stated that it's okay to assume the temperature is 20 degrees C, then speed of sound is 343 m/s
u can use that fact to determine the exact depth of the well, based on how many seconds it took for the sound of the rock hitting the bottom to reach the top of the well
for that second part, a hint is that you can use the kinematic equations for free fall!
which cannot be solved unless you first solve how deep the well is
topaz sinewBOT
@modern berry Has your question been resolved?
modern berry
Speed of sound is 333 m/s and the rock is falling 4.9x^2 meters every x seconds
warm turtle
Speed of sound is 333 m/s and the rock is falling 4.9x^2 meters every x seconds
okay, so use 333 m/s as the velocity value to solve for the well depth
modern berry
what formula could be used for that?
warm turtle
hold on, but the seconds taken to hear the rock fall is not given right?
warm turtle
okay
modern berry
so isolate distance: distance = velocity/time
warm turtle
so isolate distance: distance = velocity/time
distance = velocity * time
modern berry
oh yeah, sorry
warm turtle
it's ok!
modern berry
so d=333*2
warm turtle
yes
modern berry
d=666
warm turtle
yes
for the second part, since now you have a distance
you can use kinematic equations to solve for the velocity of the rock as it is about to hit the floor
it would be the final velocity
that you are looking for
warm turtle
you can use kinematic equations to solve for the velocity of the rock as it is a...
note that you should choose the equation that does not have any variable that is not given in your problem!
there are actually two valid equations you can use
topaz sinewBOT
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static juniper
rho(h) is the density of a liquid in a container upto a depth h from the free surface and is given by rho(h) = k(1 + h/b) where k and b are positive constants with units of density and height respectively. How would you calculate the density of the liquid upto a depth d? Would you just put in h=d? Or how would I integrate it?
topaz sinewBOT
rho(h) is the density of a liquid in a container upto a depth h from the free su...
whole geode
If you want the average density of the material you would need to integrate and then divide by the height. If you want the density at the depth d then you just plug in the equation.
static juniper
how would you integrate it? i started by writing dm/dV = rho(h)
dm = rho(h) × A dh ( A is the area of the bottom)
idk what to do next
No response, sad
.close
topaz sinewBOT
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sharp chasm
Given the following linear map:
[
f: \mathbb{R}^3 \to \mathbb{R}^3
]
such that ( f(x,y,z) = (3x, x+y, y-z) ). Given the basis ( \mathcal{B} = { v_1, v_2, v_3 } ), where ( v_1 = (1,0,0) ), ( v_2 = (0,1,0) ), and ( v_3 = (0,0,2) ), determine the matrix associated with the linear map ( f ) with respect to the basis ( \mathcal{B} ): ( \mathcal{M}_{\mathcal{B}}^{\mathcal{B}} )
thorny flameBOT
jandro0103
sharp chasm
Advice on what I should start?
jade thunder
well, M_B^B and M_B, B is the same thing
since it's the same basis in and out you needn't worry about it much
sharp chasm
@jade thunder thx
sharp chasm
@jade thunder like that?
halcyon owl
can some one help me problem inner product 105 so that i have ideas to solve 105 to 108 , i think inner product is x1x2+y1y2 so what i should do now and when i have the idea can i apply same idea for 107 c
topaz sinewBOT
can some one help me problem inner product 105 so that i have ideas to solve 105...
alpine mist
can some one help me problem inner product 105 so that i have ideas to solve 105...
That’s the dot product, which is an inner product.
An inner product is a generalization of a dot product.
You need to verify that your <v>u satisfies the 4 inner product properties.
halcyon owl
wow i see 4 propertise, ive used them a lot in high school now i know their name are inner product hh
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steel frost
Hi
topaz sinewBOT
@steel frost Has your question been resolved?
steel frost
Or is it just all of them?
Whole question
topaz sinewBOT
@steel frost Has your question been resolved?
topaz sinewBOT
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sharp flower
is this correct?
topaz sinewBOT
is this correct?
vernal shard
is this correct?
Looks correct
topaz sinewBOT
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topaz sinewBOT
topaz sinewBOT
@brittle summit Has your question been resolved?
eager flicker
Hello, can someone explain what does this mean?
topaz sinewBOT
Hello, can someone explain what does this mean?
thorny flameBOT
Badr
eager flicker
all polynomials except... $0_\mathbb{K}[X]$, i have no idea what that is
thorny flameBOT
Badr
eager flicker
The zero polynomial
so... just 0?
then what will 1_{K[X]} mean? is it the highest degree?
vernal matrix
so... just 0?
then what will 1_{K[X]} mean? is it the highest degree?
Yep, or otherwise, 0 + 0X + 0X^2 + ...
As for the 1_{K[X]}, well, the polynomial 1 + 0X + 0X^2 + ... (with the 0 and 1 from K of course)
eager flicker
sorry i am still confused
is it related to this?
so n = 0 => 0
n = 1 $a_kx^0+a_kx^1$
thorny flameBOT
Badr
eager flicker
something like this?
vernal matrix
You could choose n = 0 for both, and a0 as the 0 or 1 from K for the respective 0 and 1 from K[X]
eager flicker
$0_\mathbb{K[X]} = 0 \
1_\mathbb{K[X]} = a_k \
2_\mathbb{K[X]} = a_0+a_1x \
3_\mathbb{K[X]} = a_0+a_1x+a_2x^2$
thorny flameBOT
Badr
vernal matrix
The 0 and 1 are referring to the fact that those are the 0 and 1 from the ring K[X]
eager flicker
what ring?
vernal matrix
K[X], the ring of polynomials in X over K
eager flicker
so then 0 and 1 are just 0 and 1?
vernal matrix
Pretty much, yep (any other coefficient of X, or any higher power of, is zero)
vernal matrix
Not quite no, and usually these aren't used
eager flicker
this confuses me so much. so then all polynomials with a degree of two or less?
vernal matrix
You only care about 0 and 1 because of e.g. "0 + anything is the same thing, and multiplying 1 by anything doesn't change it"
No, not at all, they are specifically 0 and 1 only
$0_{\mathbb{K}[X]}$ is only $0 (+ 0X + 0X^2 + \ldots)$, and $1_{\mathbb{K}[X]}$ is only $1 (+ 0X + 0X^2 + \ldots)$
thorny flameBOT
@vernal matrix
vernal matrix
Whole point being those are the additive and multiplicative identities of K[X]
eager flicker
Not quite no, and usually these aren't used
so these are not used at all
vernal matrix
There may be cases where they are, but I have rarely seen them (and in the cases I have seen, then e.g. 2 is just taken as 1 + 1, 3 is just 1 + 1 + 1 etc, with the 1 from the respective ring that you're from)
glossy wave
if you have 5 types of balls and 20 of each in a box. You pick 70 of them at random, how many ways can u do this?
topaz sinewBOT
if you have 5 types of balls and 20 of each in a box. You pick 70 of them at ran...
keen raptor
It's convenient to think about the 30 that aren't being chosen here
let's say the number of balls that wasn't being chosen was smaller, like 15
Would you be able to solve it then?
glossy wave
um
maybe in each subset u could number the balls
so in the questions the balls were coloured
Red Blue Green Purple Orange
So you could do like R1 ... R20, B1,...,B20 etc
now u have 100 individual balls
number of ways of picking 15 of them is 100 x 99 x 98 x ... x 86
but we need to now divide by something
keen raptor
The thing you need to divide by to correct for overcounting varies depending on how many balls of each color you have
So this method doesn't work
Have you heard of stars and bars?
glossy wave
The thing you need to divide by to correct for overcounting varies depending on ...
what do u mean
oh right i see
keen raptor
but we need to now divide by something
There's no "something" that you'll be able to find
glossy wave
Have you heard of stars and bars?
no
glossy wave
okay cool
keen raptor
Do you know inclusion exclusion?
thorny flameBOT
Dreyuk
glossy wave
yeah ive seen that
i think i might have seen stars and bars before
it rings a bell
keen raptor
nvm no inclusion exclusion but stars and bars
glossy wave
but i'll need to brush up on it
keen raptor
number of nonnegative integer solutions to a+b+c+d+e = 15 basically
glossy wave
why is that important
oh right
how many reds how many blues etc
and then they add up to 15
topaz sinewBOT
@glossy wave Has your question been resolved?
ruby wadi
topaz sinewBOT
ruby wadi
I feel like the first question should have a simple solution but the usual method doesn't work for me here
if anyone has an idea that would be helpful
topaz sinewBOT
@ruby wadi Has your question been resolved?
ruby wadi
man I feel like it's very simple
sharp vigil
How about geometric mean?
[v_(n+1)]*[v_(n-1)] = [v_n]^2
Put in values
I think you get a linear outta this
Solve it
Get alpha
@ruby wadi
topaz sinewBOT
ruby wadi
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topaz sinewBOT
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topaz sinewBOT
topaz sinewBOT
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south peak
I'm writing some notes for myself regarding linear algebra. Is this a mathematically correct definition of the transpose operation?
topaz sinewBOT
I'm writing some notes for myself regarding linear algebra. Is this a mathematic...
ivory sorrel
I think it is, but leyt someone else confirm
young geyser
correct
topaz sinewBOT
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frozen sun
how do i find x
topaz sinewBOT
how do i find x
zinc spire
5x + 3x = 180 degrees
frozen sun
well yes but thats because i made a new pararell line is that okay
topaz sinewBOT
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dull scaffold
topaz sinewBOT
dull scaffold
I have an idea but dont know what to do next
sweet shard
What is the idea
dull scaffold
i use (2x-3)/(x-1) as F and i get (2x-3)/(x-1)+(x-3)/(x-2) and I think im supposed to plug (x-3)/(x-2) into the equation but idk
sweet shard
F(F(x)) would be difficult to compute yes. But not impossible. The main concern is how you came up with that guess in the first place
topaz sinewBOT
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kindred hollow
Can someone help me understand supremum and infamum. I seem to keep confusing it with max and min
topaz sinewBOT
Can someone help me understand supremum and infamum. I seem to keep confusing it...
kindred hollow
Say you have a set A = [0,2]
The sup A and max A would be 2
Inf A and min A 0
Now say you have a set B = (0,2)
I understand that the max B and min B dont exist
kindred hollow
But I don't understand why Sup B is 2 and Inf B is 0
ivory sorrel
But I don't understand why Sup B is 2 and Inf B is 0
Can you define supremum for me
kindred hollow
Can you define supremum for me
Least upper bound
mystic jay
do you agree 2 is an upperbound
ivory sorrel
Sure, now expad upon the definition of an upper bound
kindred hollow
do you agree 2 is an upperbound
No, because it is not in the set B
mystic jay
upper bound means any value which is greater than or equal to all members of a set
kindred hollow
My guess is that it would be the number before 2 in the set of Reals
ivory sorrel
My guess is that it would be the number before 2 in the set of Reals
What number is that
kindred hollow
What number is that
Im not sure if its even possible to write it
ivory sorrel
if I have a number in the set say $2 - \varepsilon$ and $2$, can you find me a number between tehm
thorny flameBOT
ƒ(Why am. I here)= I don't know
kindred hollow
upper bound means any value which is greater than or equal to all members of a s...
I understand that part
mystic jay
it doesnt have to be in the set, right?
mystic jay
no
kindred hollow
Ah ok
So in (0,2) that smallest number you could produce in the upper bound would be 2
mystic jay
yes
kindred hollow
Cause I domt think its possible to write a number before that in the set of Reals
mystic jay
yes
topaz sinewBOT
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frozen sun
help how do i find C
topaz sinewBOT
help how do i find C
frozen sun
oh wait
x = c
cuz x + 3x = 4x
but how do i get x
i got x = 36
with the equation
x = 180 - 4x
and yup
.close
hoary fable
Hi for part b, I used reverse chain rule and got everything right except the bounds. How do I know what numbers the bounds change to? (hopefully that makes sense)
topaz sinewBOT
Hi for part b, I used reverse chain rule and got everything right except the bou...
lethal anchor
Hi for part b, I used reverse chain rule and got everything right except the bou...
when applying the "reverse chain rule", what was your substitution?
cunning kayak
hint: try seeing denominator
hoary fable
when applying the "reverse chain rule", what was your substitution?
I didn't substitute anything i just applied
this concept
lethal anchor
this concept
alright, so what was f(x) in your case?
hoary fable
this is what i did
lethal anchor
yeah so you are actually almost right
hoary fable
yea its just the bounds right?
lethal anchor
but but the last line here, you substituted incorrectly
hoary fable
oh huh?
hoary fable
oh crap the 0
lethal anchor
not only that
hoary fable
wait what
lethal anchor
so what is [
\frac{(5\cdot 1^2 + 1)^{-2}}{-2}
]
thorny flameBOT
Aero
hoary fable
-1/72?
lethal anchor
yeah
hoary fable
isn't that what i wrote
hoary fable
oh i read that as -1/12
oh mb lol
topaz sinewBOT
torpid inlet
<@&286206848099549185> what is a trajectory equation? Explain it in brief with some examples if possible, thanks!!
topaz sinewBOT
<@&286206848099549185> what is a trajectory equation? Explain it in brief with s...
cunning kayak
equation of trajectory
trajectory is the path of an object with mass, such as a kicked ball
like this
torpid inlet
Can we say there's a quadrilateral where at the end, the particles are moving? And then we have to find the equation of the curve?( what I meant through the curve is that diagonals of that quadrilateral(let's take square) are behaving as the two curves and we have to find out their equations
Should i show you that figure @cunning kayak
cunning kayak
show
cunning kayak
yes we can say
torpid inlet
Will you help me out with one more doubt man? I'm trying to figure how does that happened
It's from the nuclear physics
cunning kayak
jee adv 💀
torpid inlet
However there was one solution where that educator did that with another thing( I wanna figure out, how?
cunning kayak
sure i rule out
cunning kayak
i mean yeah dont ask me
torpid inlet
Hahha, my bad
torpid inlet
Bbye then, thanks for the help
torpid inlet
ask anything in maths, sure
Lee me add you
cunning kayak
done
topaz sinewBOT
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mystic siren
why do i need to use induction to prove the h_n=2^n-1? this seems sufficient
acoustic pecan
because youre just assuming the pattern continues
its not a complete proof
by all means its logically sound to make that conclusion, its just not a proof of it for all n
hearty turret
why do i need to use induction to prove the h_n=2^n-1? this seems sufficient
well basically you're saying "...and this pattern continues/repeat this process n times" but induction is exactly that but formalised
ofc if like ur like quite far ahead in ur mathematical career, i doubt u'll need to prove it that formally but basically here u want to say "continue this process n times" and the way to do that is induction
mystic siren
well basically you're saying "...and this pattern continues/repeat this process ...
but it's correct to assume that when i've proved the relation h_n=2h_{n-1}+1 though
like it's in fact correct
mystic siren
because youre just assuming the pattern continues
it's a correct assumption
if i have the recurrence relation proved
mystic siren
its not a complete proof of it
u dont make any sense
i have the recurrence relation and the base cases
celest charm
i have the recurrence relation and the base cases
you can determine the closed form without proving it. This is a derivation but not a proof
rigid ivy
i have the recurrence relation and the base cases
Where is your base case?
dawn tulip
Hay I'm 15. and i had a math test not to long ago, one pat of a problam was 48÷3, and i used a method i had thought of two day's ago, and dont remember if i came up with it or not so heres it breakdown:
Step 1: factorization.
Express the divided number (48) as a product of two numbers: 48 = 8•6.
Step two: first divison.
Divide the second factor (6) by the divisor (3) to get 6÷3=2.
Step three: second multiplication.
Multiply the first factor (8) by the result of the first factor by the result of the first division 8•2=16.
And that's hoe i solved it so what methid is it?
rigid ivy
Hay I'm 15. and i had a math test not to long ago, one pat of a problam was 48÷3...
!help
topaz sinewBOT
Hay I'm 15. and i had a math test not to long ago, one pat of a problam was 48÷3...
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
@mystic siren Has your question been resolved?
frozen sun
im confused
topaz sinewBOT
im confused
frozen sun
so the measure of the other two angles are 0-180 right
there are 3 angles and 100 is in the middle
yall idk
is 100 the starting point or is 0 the starting point
hoary burrow
Alright so an arithmetic progression
Is where each number in the sequence has the same difference from its previous number
Right
frozen sun
yes
hoary burrow
Sorry I was having lunch
And yea I made a typo
x+(x+k)+(x+2k)=3x+3k
x is the first term
x+k is the second
And x+2k is the third
So 3x+3k=180
Or x+k=60
Oh and this quite coincidentally gives us our second term
So we can find all 3 measures now
@frozen sun
frozen sun
oh
so since one angle is 100, and another angle is 60, then the last angle is probably 20
cuz they all have a difference of 40
and add up to 180
tyvm for your time 😭🙏
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strong shore
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strong shore
I'm up to part (d) and i'm not quite sure how I can show that $100 < l < 110$ and $64 < w < 75$
thorny flameBOT
Michele
desert atlas
could you send a screenshot
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iron blaze
Two capillary tubes AB and BC are joined end to end at B, AB is 16cm long and of diameter 4mm whereas BC is 4cm long and of diameter 2mm. The composite tube is held horizontally with A connected to a vessel of water giving a constant head of 3cm and C is open to the air. Calculate the pressure difference between B and C. (In centimeters of a column of water)
I tried to solve this by solving for the pressure difference between A and B, which is rho * g* h which is 1 * 980 * 3 = 2940 Ba
Then I recalled the equation of continuity
a1V1 = a2V2 a1 = pi * 0.2 ^2 a2 = pi * 0.1^2 V1 = pi/8 * 2940 * 0.2^4/(η * 16) V2 = pi/8 * p * 0.1^4/(η4)
We want to find p/(rho g) to find the column of water
However when solving for p ( i got 47040) which corresponds to 48 cm of water, but the answer is 2.4 cm How did I go wrong by a factor of 20?
Here is the solution online (which I didn't understand)
https://youtu.be/K7SCruah6ds?si=cMvtRLFyX8eOxQeC
topaz sinewBOT
Two capillary tubes AB and BC are joined end to end at B, AB is 16cm long and of...
iron blaze
here is an image for reference, note that the numbers are different
also i tried my method for this one too, and again my answer is off by a factor of 20
odd forge
close one channel
iron blaze
close one channel
i asked like 4 times and no one helped so i think ill keep both up
<@&286206848099549185>
gilded plume
you literally posted it twice in the span of one minute
close one
nobody is reading that in one minute
ivory sorrel
I think you may get more help in the physics server for this question
iron blaze
you literally posted it twice in the span of one minute
you can check my previous messages
gilded plume
you can check my previous messages
can you just please close one channel
iron blaze
would you help
topaz sinewBOT
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quartz geyser
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quartz geyser
How to start solving this one?
weary crystal
approach (0,0) along two different paths. if the limit is different for those paths, the limit can't exist
for example, maybe one path is along the line y = x
topaz sinewBOT
@quartz geyser Has your question been resolved?
ivory sorrel
approach it along say x=0 and x=y
topaz sinewBOT
@quartz geyser Has your question been resolved?
quartz geyser
So should I put x=y and compute?
quartz geyser
and then try another paths
What to do now?
wintry hill
approach it along say x=0 and x=y
this
quartz geyser
by approach, U mean the +h stuff?
wintry hill
first just plug x=0, so only y left under the limit. Then usual rules for calculating the limit of one variable.
quartz geyser
0o0
wintry hill
0/35(x²)
>->
btw, what is the final answer for limit here?
quartz geyser
0/35(x²)
>->
I put y=x and it seems to give 0?
wintry hill
yep
quartz geyser
first just plug x=0, so only y left under the limit. Then usual rules for calcul...
So I got -1/2 there
And tried putting y=0 and got 1/3 there
Is this the correct progression?
wintry hill
yes, but at this point -1/2 is enough. So you took two different paths approaching (0,0): one along the line x=0 and the one along the line x=y. They gave different results (-1/2 and 0). What is the conclusion?
quartz geyser
It's not continuous at that point
wintry hill
that is the corollary. The main conclusion is: the limit does not exist
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twin apex
How would I find all the intervals in which
h(t)-6.8cos(pi/30(t))+8.3
h(t)-6.8cos(pi/30(t-12))+8.3
h(t)-6.8cos(pi/30(t-24))+8.3
h(t)-6.8cos(pi/30(t-36))+8.3
h(t)-6.8cos(pi/30(t-48))+8.3
these five graphs are all greater than 1.86 meters within two periods.
topaz sinewBOT
How would I find all the intervals in which
h(t)-6.8cos(pi/30(t))+8.3
h(t)-6.8...
@twin apex Has your question been resolved?
twin apex
<@&286206848099549185>
twin apex
I don’t need the answer I just need to know the way to do it algebraically
twin apex
<@&286206848099549185>
topaz sinewBOT
@twin apex Has your question been resolved?
rigid ivy
How would I find all the intervals in which
h(t)-6.8cos(pi/30(t))+8.3
h(t)-6.8...
what is h(t)?
twin apex
what is h(t)?
have a better way to ask my question
twin apex
what is h(t)?
h(t)=-6.8cos(pi/30(t))+8.3
h(t)=-6.8cos(pi/30(t-12))+8.3
h(t)=-6.8cos(pi/30(t-24))+8.3
h(t)=-6.8cos(pi/30(t-36))+8.3
h(t)=-6.8cos(pi/30(t-48))+8.3.
Each one of these five graphs represents a blade on a windmill. within 120 seconds (two periods) how do I find all the intervals in which all graphs are simultaneously greater than 1.86 meters
the context of the question is you are stuck in a windmill and within two periods which is 120 seconds in this case, you have to find all the intervals somebody who is 1.86 meters tall would be able to walk out
how do i solve this algebraically
rigid ivy
You'd have to find the intervals for each function, and then calculate their intersection
twin apex
You'd have to find the intervals for each function, and then calculate their int...
how would i calculate that, is there some sort of formula or i would just have to manually see where they intersect and dont
rigid ivy
how would i calculate that, is there some sort of formula or i would just have t...
Let's start with just $h_1(t)=-6.8\cos\left(\frac{\pi}{30}t\right)+8.3$ for now. We want to find when $h_1(t)>1.86$. So we must solve
$$1.86>-6.8\cos\left(\frac{\pi}{30}t\right)+8.3$$
thorny flameBOT
SWR
twin apex
I’ve gotten to this point so far
I have where they are all part of the interval individually but idk how to find when they all are simultaneously
rigid ivy
I have where they are all part of the interval individually but idk how to find ...
You need to do interval intersections
topaz sinewBOT
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supple yarrow
Hi, I need help with dividing decimals as i've never done it before and I have a math midterm tmr. I heard you are supposed to multiply the numbers by 10 then place them but it's still quite confusing.
topaz sinewBOT
Hi, I need help with dividing decimals as i've never done it before and I have a...
sterile finch
It helps to multiply by a whole fraction in such a way that it eliminates the decimals.
supple yarrow
It helps to multiply by a whole fraction in such a way that it eliminates the de...
so multiply it by 100 if its 5.76/0.3
im also watching math with mr. j lol
torpid sparrow
sterile finch
No, just 2.
sterile finch
10/10 is a whole fraction that is equal to 1. That is a valid math operation that you can use to simplify a problem.
supple yarrow
ok
sterile finch
Another example.
sterile finch
yw
sterile finch
That's what I do. No point in complicating it by counting decimal positions and adding it on at the end imo.
supple yarrow
ok ty
sterile finch
You could do 123/3 = 41 and add the decimal to get 4.1 but that come across as hacky.
sterile finch
Or 12.3/3 = 4.1 which also more direct.
Up to you.
Now that I think about, just eliminating the decimal in the denominator seems the easiest route.
supple yarrow
Now that I think about, just eliminating the decimal in the denominator seems th...
1 more question
how do you know when you're dividing that the decimal is repeating
sterile finch
As in 0.3333...?
supple yarrow
As in 0.3333...?
yeah smth like that
sterile finch
Well, when you start doing the division, it will start repeating at some point.
supple yarrow
👍
supple yarrow
Well, when you start doing the division, it will start repeating at some point.
im in seventh grade so im just starting but could you give me a random division equation and let me try to solve it and then i tell you my answer and you see if it's wrong or not
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weak vessel
hey
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weak vessel
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hollow bough
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spring tide
So if you know how to derivative
You can just derivative the formula
If you dont, just use x=anypoint
Calculate y
fallow igloo
spring tide
And then y2-y1/x2-x1
hoary burrow
And then y2-y1/x2-x1
Unfortunately not that applicable to this question
You don't have to calculate anything
spring tide
I mean most basic way
frigid wyvern
I mean most basic way
i like basil too
faint thistle
The slope is 4
hoary burrow
The slope is 4
!noans
topaz sinewBOT
The slope is 4
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
hoary burrow
But yea I guess
hoary burrow
It's just a 1 second question if you know your stuff
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half compass
This is going to sound stupid but how would you solve this
topaz sinewBOT
This is going to sound stupid but how would you solve this
half compass
Im really bad with fractions
leaden gorge
Im really bad with fractions
what do you mean solve? it's not an equation
is it equal to something
leaden gorge
so you want to simplify it?
sharp vigil
$\frac{x+4}{1-(x+4)}$
thorny flameBOT
lex.in.a.teacup
leaden gorge
like that ^
sharp vigil
This what you should get after multiplying numerator and denominator by x+4
@half compass
leaden gorge
so its x+4 / -x-4?
no the denominator is -x-3
potent linden
how do i solve 36?
topaz sinewBOT
how do i solve 36?
potent linden
i lowk forgot
pearl brook
𝐴
A is the amount of money accumulated after
𝑡
t years, including interest.
𝑃
P is the principal amount (the initial money you invested or borrowed).
𝑟
r is the annual interest rate (decimal form, so 5% would be 0.05).
𝑛
n is the number of times the interest is compounded per year.
𝑡
t is the number of years the money is invested or borrowed for.
$A = P \left(1 + \frac{r}{n}\right)^{nt}$
thorny flameBOT
Slimy
potent linden
oh yes thank you
i just forgot what to do when i plug all the values in
since im looking for t
would you happen to know?
potent linden
i don’t trust ai
potent linden
it won’t solve the problem if you didn’t plug in values
i didn’t accuse you of anything i just said i didn’t trust ai
potent linden
um its fine lol
pearl brook
np
potent linden
got it in my own :))
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fading grove
I need help studying for a math test in pre calc tomorrow, I have the study guide. Mainly in questions 7,8 ,and 9
topaz sinewBOT
I need help studying for a math test in pre calc tomorrow, I have the study guid...
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fading grove
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grim pike
I need help studying for a math test in pre calc tomorrow, I have the study guid...
For 7 and 8, try thinking about what each of those transformations do to the graph of a function. Plug in some values into the transformed function for which you know their image, and go from there. More generally, try thinking, given some function $f : \mathbb{R} \to \mathbb{R}$, what $f(x + a)$ and $f(ax)$ look like for some $a \in \mathbb{R}$.
thorny flameBOT
ucheo
grim pike
For 9, use the properties of logarithms: $\log(ab) = \log(a) + \log(b)$, $\log(a/b) = \log(a) - \log(b)$, etc.
thorny flameBOT
ucheo
topaz sinewBOT
@fading grove Has your question been resolved?
fading grove
are you able to explain over vc?
grim pike
I don't think this server has voice channels.
topaz sinewBOT
@fading grove Has your question been resolved?
neon iron
topaz sinewBOT
neon iron
for question b
topaz sinewBOT
@neon iron Has your question been resolved?
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neon iron
how to solve this question
topaz sinewBOT
how to solve this question
wintry nymph
i'll move somewhere else
neon iron
thanks
wintry nymph
np
neon iron
i am sharing my solution
This is what I solved
What I don't understand is, shouldn't it be 2 times -cosycosx?
can someone help please
@wintry nymph sorry for the tag, but can you delete your question.. so that it doesnt create a confusion.. sorry i dont know how this server works
wintry nymph
oh yeah sure
molten spoke
,rotate ccw
thorny flameBOT
coarse herald
What I don't understand is, shouldn't it be 2 times -cosycosx?
no i think because the terms are the partial derivatives of -cosxcosy with respect to x and y
neon iron
but arent we adding both the terms?
coarse herald
-cosxcosy is a function of both x and y to differentiate it you will take the partial derivatives with respect to both x and y which gives you the terms
pallid harness
can someone help please
i don't know how much this would help but have you looked at this
https://youtu.be/HF_wG2VTf4c
?
topaz sinewBOT
@neon iron Has your question been resolved?
obsidian sparrow
How am I supposed to solve for sin(-45) with only the hypotenuse value? cant use pythagorean theorem because i only have 1 sides values
wispy pier
Whoa you discover the other angle of triangle is 45° too
You realise now it's an Isosceles triangle!!
obsidian sparrow
awesome balls now what
wispy pier
Now you further understand it's an Right Angled Isosceles, and you can figure out the lengths
obsidian sparrow
how do i do that
wispy pier
Bruh
obsidian sparrow
lmao
wispy pier
Let one side be a
Then other side is a too
Then apply pythagoras theorem
a² + a² = 1² !!!!!
Pythagoras was really a chill guy, no ?
wispy pier
🤧
wispy pier
Shall I say you
obsidian sparrow
i just woke up
wispy pier
How am I supposed to solve for sin(-45) with only the hypotenuse value? cant us...
The triangle in the figure
Is a right angled triangle
obsidian sparrow
yes
wispy pier
It's a right angled Isosceles triangle
obsidian sparrow
yes
wispy pier
Cool
So lets consider the length of one unknown side "a"
Since its an Isosceles, another unknown side from the figure can also be said to be of length "a"
obsidian sparrow
okay
obsidian sparrow
because its an isosceles the unknown sides are the same length
wispy pier
Have you ever drawn them on a paper and verified ?
obsidian sparrow
yes
wispy pier
He said, "If it's a right, you just remember me, coz i am the only man who was always right"
