And what about x^2 for numbers less than 0 ?
#help-17
iron flame
im not sure what you mean
vast shale
im not sure what you mean
Suppose that x=-2 and a change occur in time so x became x=-1 y’-y=4-1=3 but the derivative is 2x= so 2*-2=-4 therefore how is that possible ?
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foggy thunder
A Carnot engine operating between temperatures T1 and T2 has efficiency 1/6. When T2 is lowered by 62 K, its efficiency increases to ⅓. Then T1 and T2 are, respectively
vocal sleetBOT
A Carnot engine operating between temperatures T1 and T2 has efficiency 1/6. Whe...
foggy thunder
Uh frst found the efficiency now m confused
fathom torrent
how do you do this: Show that 25x^2+4y^2-200x+16y+316=0 is the equation of an ellipse and from its center find the length of each axis.
im upto here: 25((x-4)^2-16) + 4((y+2)^2-4) = 316.
vocal sleetBOT
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young blaze
how do you do this: Show that 25x^2+4y^2-200x+16y+316=0 is the equation of an el...
Leave the perfect square expressions divisible alone, then you get the form $25(x-h)^2+(y-k)^2=\lambda$ for some $\lambda$. Can you get this into the desired form $(x-h)^2/a^2 + (y-k)^2/b^2 = 1$?
twin meteorBOT
adzetto
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opal topaz
Can someone help me with the second question please
vocal sleetBOT
Can someone help me with the second question please
opal topaz
With question b please
dapper bone
Can someone help me with the second question please
2,5 means 2.5?
dapper bone
I'm so lost with question b I don't know where to start 💀💔
put value of A and B
you get
9a+q=2.5
and 4a+q=0
solve
@opal topaz done?
opal topaz
So I am solving for a and not q?
dapper bone
So I am solving for a and not q?
it is 2 variables in a eqn
simplify it to one
solve
and use the 2 variable eqn to find the 2nd one
we found a
a=1/2
q=-4a
this means q=-4(0.5)
=-2
cobalt skiff
cobalt skiff
ig so
but i want to know the method and stuff
like for i, a=5+4n and x can equal 1
but is there like more that im missing
boreal star
There's a lemma that $ax\equiv 1 \pmod{b}$ has a solution if and only if $(a,b)=1$
twin meteorBOT
Tardis
cobalt skiff
oh damn
so any number that isn't even for i?
boreal star
Yes
cobalt skiff
and for ii is just not any multiple for 5
boreal star
Yes
cobalt skiff
if m was equal to 6, would it just be 6n+-1
since 6n+2, 6n+3 and 6n+4 has a gcd>1
okok
tytyyyy
boreal star
Even for any general c, $ax\equiv b \pmod{c}$ has a solution if and only if $(a,c)|b$.
twin meteorBOT
Tardis
cobalt skiff
okok tytyyyyy
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keen bramble
Ignore the incorrect working on line 2, can I ask if there is any significance to theta not being pi, pi/2 etc in this question?
vocal sleetBOT
Ignore the incorrect working on line 2, can I ask if there is any significance t...
keen bramble
Because the question could work entirely fine without those right
next sleet
Because the question could work entirely fine without those right
presumably one of the trig functions would be 0 at those points, although it wouldn't be undefined or anything, some cartesian equations with division wouldn't work?
something like that i think
keen bramble
Ohhhh
I see
By eliminating all the special angles where cos x or sin x = 0
U remove the possibility of having some expression that doesnt make sense at x = 0
next sleet
yes
vocal sleetBOT
vast shale
,w x^2+10x+11=0
twin meteorBOT
vast shale
well it factors, but not nicely
use the quadratic formula
you've dropped your brackets
the quadratic formula
,tex .quadratic formula
twin meteorBOT
toby____
vast shale
you've dropped your brackets
you should fix this issue first
only one of the x values would make sense
(you need to check which one is the minimum)
use the one of the derivative tests https://en.wikipedia.org/wiki/Derivative_test
hazy jacinth
Hi
vast shale
first derivative test might be slightly easier here
(alternatively look at the geometry of the curve - ie where are the asympototes)
hazy jacinth
Anyone taking calculus
vast shale
Anyone taking calculus
hazy jacinth
Cause I need help
vocal sleetBOT
Cause I need help
Please read #❓how-to-get-help
vast shale
yes, you can find the second derivative of your function and use the second derivative test
dont worry about them then
stick with the second derivative test
huh?
differentiate the first derivative
dont substitute until after finding the second derivative
you've differentiated the wrong function
this is the first derivative
vast shale
first derivative test might be slightly easier here
(its a mess to differentiate, thats why I suggested this ^)
yes for vertical asymptotes of rational functions
yeah looks fine
hm thats weird
lemme check your working
you've evaluated the squareroot incorrectly
yeah
use the quadratic formula
twin meteorBOT
toby____
vast shale
then leave "b^2-4ac" as a number without evaluating the squareroot
yeah, if you dont put the squareroot into a calculator, you will get that exact form
eek you didnt need to erase your second derivative
you can still use it
yeah
(for the second derivative test, dont bother doing exact arithmetic, just stick everything into a calculator)
yw :)
vast shale
help
vast shale
guys
PLEASE
HOW DO I INTEGRATE sin^2x/cos^3x
<@&286206848099549185>
@grand frigate
vast shale
help
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grand frigate
i'd personally just simplify the expression first
grand frigate
yeah
vast shale
and then ?
grand frigate
what is tan^2 in terms of sec x?
vast shale
but that would lead me to integrating sec^3x which is what i am doing
grand frigate
you cannot do it by parts?
grand frigate
:/
grand frigate
yeah he went there already
marble vine
oh sorry
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grand frigate
.reduction formula is a viable option tbh
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tulip pilot
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tulip pilot
Did I do my derivative wrong or something?
Limit on the left, derivative on the right
dull maple
You have done the derivation correctly. But
You have put it wrongly in the limit expression.
tulip pilot
oh
tulip pilot
i thought i had to take the derivative of the 3x in the front as well
tulip pilot
ah ok so it's 3 - 3 - 3tan^2x
tulip pilot
unfortunately i still get 0 in both num/denom so i have to take yet another derivative?
tulip pilot
dang then im lost
dull maple
Try considering another approach.
from the start.
firstly how about we get rid of those 3x ?
Maybe substitute it with u.
@tulip pilot
tulip pilot
writing it
dull maple
Okay.
tulip pilot
dull maple
Okay. Well, i can't really think of another way to move on. Let me think for a moment.
dull maple
do you mean the double angle stuff
No. No. Expansion form of sinx as an infinite degree polynomial.
tulip pilot
oh then nope
dull maple
I still can't think of another way to solve this.
tulip pilot
oh that's alright
dull maple
I can tell you using the expansion if you would like.
tulip pilot
alright
dull maple
Okay. Cool
So, sinx has an expansion form which goes like this.
sinx = x - (x^3)/3! + (x^5)/5! + (x^7)/7! + ....
This is taylor series expansion for sinx. Interesting thing is that for values really really small that is very close to zero, it gives fairly accurate values.
So, since our limit says that u goes to zero, i.e. u is very very small, we can replace sin by this series.
tulip pilot
this is with the u substitution?
dull maple
Another important thing is that we need not take many terms. As terms with higher power will be even smaller so we can ignore those.
dull maple
sinx = x - (x^3)/3! + (x^5)/5! + (x^7)/7! + ....
You can imagine x to be u here. everywhere in the expression.
tulip pilot
alright
dull maple
Variable name doesn't matter.
Now, in the denominator, we put value of sin(u) using this series.
u - sin(u)
= u - (u + (u^3)/3!)
tulip pilot
in the denominator?
dull maple
We'll not take rest of the terms because this enough to remove the indeterminacy.
dull maple
in the denominator?
Coming to that.
tulip pilot
uh (u + u^3 / 6)?
dull maple
Umm... No. See properly. There was a u at first. We are subtracting (u + (u^3)/3!) from that.
We'll have
u - (u + (u^3)/3!)
= u - u - (u^3)/6
= -(u^3)/6
Is that okay?
tulip pilot
yeah i see how you got that
dull maple
Cool. Similarly, we'll use tan x expansion in denominator.
tan(x)= x + (x^3)/3 + (2x^5)/15 + (17x^7)/315 + ...
tulip pilot
Do you just remember the expansions for these trig functions?
dull maple
Here also, we'll take only 2 terms.
dull maple
Do you just remember the expansions for these trig functions?
Nope. I look them up. They are often provided in exams if their usage is expected.
dull maple
so the terms are
1) u
2) u^3 / 3
?
for tan x ?
tulip pilot
yeah
dull maple
yes
tulip pilot
is there a reason why we only take 2 terms?
dull maple
is there a reason why we only take 2 terms?
yes. First term is so that u cancels out. Right ?
Other term is for giving us answer.
See here.
Now, in denominator we'll have
u - (u + (u^3)/3)
= u - u - (u^3)/3
= -(u^3)/3
Does that make sense ?
tulip pilot
Yeah I have this
tulip pilot
i got positive 1/2
dull maple
Yes
dull maple
You are done. Now, perhaps there's some other way as well but i can't think of it.
Although, you can learn this method.
Oh. Wait. Yes
we did.
tulip pilot
oh
dull maple
u - sin(u)
= u - (u + (u^3)/3!)
Here term is actually u - (u - (u^3)/3!)
So we get (u^3)/6
tulip pilot
o
dull maple
Not the negative sign.
tulip pilot
so the expansion was actually (x - x^3 / 3!) instead of (x + x^3 / 3!)
dull maple
sinx = x - (x^3)/3! + (x^5)/5! + (x^7)/7! + ....
See here. the second term is negative.
tulip pilot
i see! thank you
dull maple
No problem. Using expansions sometimes helps. Perhaps you can employ this cool method at times now.
tulip pilot
yeah im not sure if we can use it since we haven't covered it yet, but i'll do it anyways
again thanks for the help!
.close
prime umbra
vocal sleetBOT
prime umbra
wiat nvm i sent the wrong screen shot
I am just confused as to why the top does not multiply out just like the bottom
because I thought the only difference was the negative
karmic imp
Because the denominator is difference of squares and the numerator is not
prime umbra
ok thanks thats all
karmic imp
vocal sleetBOT
karmic imp
Even says here
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solid mist
So I have actually asked this question in the probability, math topic, but I don’t think I’m understanding completely how to finish it off. Figured I’d go ahead and posted in the homework help to get more detailed answers. The person that was helping me is awesome, but I did not want to blow up that feed with a single question.
vocal sleetBOT
So I have actually asked this question in the probability, math topic, but I don...
floral pike
So I have actually asked this question in the probability, math topic, but I don...
what is "c" vs "C"?
solid mist
C is the same throughout. I think that just represents the constant.
sly sierra
AM-GM inequality should help with the last inequality
solid mist
I think I am unsure as to how to get the c^2/4. I can somewhat follow how to come up with the m(c-m), but the last part I do not understand.
solid mist
AM-GM inequality should help with the last inequality
AM-GM?
shrewd dagger
i dont think AM GM is necessary
twin meteorBOT
shrewd dagger
or just use the parabola vertex formula
since you know this is a downward facing parabola
solid mist
so differentiate d/dc?
solid mist
So deriving with respect to mu, I come to c-2m. If I were to do that again, I just get -2
solid mist
I am going to brainstorm and come back in a second...
Alright, so honestly I am not too sure what that means being -2. BUT taking the antiderivative of cm (which would be E(X^2)) gives me c (m^2/2) for E(X) which is also the mean?
I think I went down the wrong rabbit hole, but I am drawing a blank...
cyan talon
we have dV/d(mu) = c - 2*mu
what's the condition on dV/d(mu) so that mu could potentially minimize V ?
@solid mist
solid mist
It cannot be above 0?
cyan talon
it has to be 0
your typical calc 1 stuff
@solid mist
and since the 2nd derivative is negative everywhere, you know it will be a maximizer
solid mist
I haven't had to do calculus in a while. Thank you for the help!
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lament arch
Math, WHYY
vocal sleetBOT
Math, WHYY
lament arch
I’m confused with square roots..
19:45
Can someone please explain what he said
Another question
With the second pic
If do f(0) = | 0 - 2 | - 3
Doesn’t that give you -1
But if you plot x = 0 thats not y = -1
karmic imp
Can someone please explain what he said
He's saying the domain and range has the same inequality.
karmic imp
But if you plot x = 0 thats not y = -1
Yes it is
lament arch
He's saying the domain and range has the same inequality.
You mean that the domain and range must both be equal or greater than zero?
karmic imp
It's not "perfect" but it passes through y = -1
lament arch
Thats not the part I mean. The part that follows
lament arch
Ok I get it better now
Yes
Now I’m confused on
How do you factor out the two
Because your horizontal transformation only works when its factored out
2x - 5
How do you think about factoring out the 2?
karmic imp
How would you factor out a 2 from 2x - 6?
lament arch
Can u give simple bit about factoring
Ok so the common factor between 2 and 5
@karmic imp
1
2x/1 -5/1
??
Math suks
karmic imp
The logic with factoring, is pulling out that factoring and dividing all the terms by that factor
For 2x - 5, what's the coefficient in front of x?
karmic imp
Yes, you're supposed to get a fraction
lament arch
Now I’m confused about where the 2 goes, how does it distribute
karmic imp
By factoring out a 2
karmic imp
You just can't divide all the terms by the coefficient in front of x, that 2 needs to go somewhere
So it goes outside
lament arch
Oh..
What happens to one side happens to the other
Is that what you mean
I hate maths
karmic imp
If you understand how to factor 2x - 6
The same logic applies to 2x - 5
The difference is, you're going to have fractions
lament arch
You just can't divide all the terms by the coefficient in front of x, that 2 nee...
Why does the 2 need to go somewhere
twin meteorBOT
dldh06
karmic imp
$2x - 5 = 2\left(x - \frac{5}{2}\right)$
twin meteorBOT
dldh06
lament arch
Alright
Do u have a simple explanation for how f(x) = 2x - 5
the 2 compresses the graph
karmic imp
You should understand transformation of functions
You can google things you don't know
lament arch
factoring out -x+5
-(x -5)
are you dividing -x by -1?
How is 5 a factor of -1?
karmic imp
**dldh06**
How was 5 a factor of 2 here? It doesn't matter if it's a factor or not, you can still divide all the terms by some number
You may end up with a fraction, you may not
lament arch
Right
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brave ruin
I don't think I understand this problem very well and I think it's because the example that was provided wasn't very clear. I do think I understand what a probability distribution is.
vocal sleetBOT
I don't think I understand this problem very well and I think it's because the e...
brave ruin
young blaze
I don't think I understand this problem very well and I think it's because the e...
Assume that the total probability of all the events (having no impurities, having impurity A, having impurity B) sums up to 1, i.e., $P(Y=0) + P(Y=1) + P(Y=2) = 1$. You should use this fact along with the given probabilities to solve for the unknowns, $P(Y=1)$ and $P(Y=2)$, which will provide the complete probability distribution for $Y$.
twin meteorBOT
adzetto
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brave ruin
Assume that the total probability of all the events (having no impurities, havin...
Wait I think I'm following.
So y=0 is representing no impurities right? Is this because we start the observations at 0?
young blaze
So y=0 is representing no impurities right? Is this because we start the observa...
Exactly
twin meteorBOT
adzetto
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kindred mesa
Hi
rose raft
plug the t values in the equation?
twin meteorBOT
garlicbredfries
kindred mesa
Confused
urban edge
When you have the table, you are given a value for t (except for the last one, but we will do that one later)
Replace the t in the box with the number you are given
paper depot
what goes in the blank so that P = 2^t?
rose raft
urban edge
Oh its P
kindred mesa
what goes in the blank so that P = 2^t?
2?
urban edge
Yup
kindred mesa
Then 2^0 is 0
rose raft
ok
urban edge
You sure?
paper depot
corrected yourself just in time there
urban edge
There you go
urban edge
Now for the last one, you are goin in reverse
rose raft
16 = 2^x
kindred mesa
16^2?
urban edge
Find some t so that 2^t=16
kindred mesa
Would it be 4
rose raft
ye
urban edge
Yup
kindred mesa
Got it wrong tho
Idk what one was wrong
Hold up let me go to it again
Like that?
rose raft
seems good
kindred mesa
It’s wrong tho
Nope
Nvm
Idk what I typed last time then
U GUYS
ARE
HONESTLY
THE
BEST
I ACTUALLY GET HOW TO DO IT WITHOUT DOING THE UNIT
Thank youuu
.close
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wary mantle
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wary mantle
Up to day 2k, there will be 2k(n-1) played games, so k(n-1) home and away games.
Up to day 2k - 1, it will have to be k(n-1) - (n-1)/2 = (n-1)(k - 1/2) home and away games.
How can we justify that for n teams, this will make it so that the amount of played home and away games will have a difference of more than 1?
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@wary mantle Has your question been resolved?
wary mantle
<@&286206848099549185>
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sudden compass
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vocal sleetBOT
sudden compass
pls use ur current help channel
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wary mantle
I asked a different question in the other one..
sudden compass
.close
vocal sleetBOT
sudden compass
I asked a different question in the other one..
doesnt matter
wary mantle
<#903430333888884736> use this one
That question is different though
sudden compass
That question is different though
u can ask multiple ones
wary mantle
In one channel?
The question gets pinned, asking multiple ones in the same channel doesn't really make sense
.close
sudden compass
its close alr
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warm lodge
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warm lodge
guys i may be reall dumb but is the answer jsut 20?
warm lodge
i dont understand
waxen harness
hmm
mild flower
start with 100 marbles in the bag
urban edge
There you go
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civic delta
Can someone check this short proof I wrote?
vocal sleetBOT
Can someone check this short proof I wrote?
civic delta
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glossy maple
looks fine, I would just change the "there exists" (a, t)
to just
therefore $(a, t) \in C$
twin meteorBOT
redstoneplayz09
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kindred cobalt
the answer is step once since it's the "base case"
vocal sleetBOT
the answer is step once since it's the "base case"
kindred cobalt
is that not what the inductive hypothesis is?
brisk moss
the answer is step once since it's the "base case"
doesn't make sense?
sleek idol
the answer is step once since it's the "base case"
i don’t think step one is the base case
kindred cobalt
what does that have to do with the 4 equalities at the bottom?
wdym?
kindred cobalt
i don’t think step one is the base case
yeah my bad
inductive hypothesis is used for proving k+1?
sleek idol
inductive hypothesis is used for proving k+1?
I think yeah
kindred cobalt
I think yeah
so that would be step 1?
does it mean when we finish proving it or start?
sleek idol
The inductive hypothesis is when you assume that it is true for k
These boxes are making me go crazy
kindred cobalt
The inductive hypothesis is when you assume that it is true for k
ohhhh makes sense ok I see clearly now
that would be step 2 since we go from sumnation of 2^j to 2^(k+1) -1?
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vast shale
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vast shale
I'm looking to solve this question without using a graph
vast shale
what are the roots of f(x)?
a and b
vast shale
correct
vast shale
correct
vast shale
theyre not roots
vast shale
wait ik
give me a sec
a is 0 or negative
b is either 0 or negative
so like a is less than 1
fossil ginkgo
huh?
vast shale
b is less than 1
fossil ginkgo
why
vast shale
because that would be the only values that make it greater than 0
fossil ginkgo
make what greater than 0
vast shale
make what greater than 0
the equation
vast shale
are you trying to say f(1) > 0 only when both a and b are 0 or negative?
yeah or less than 1
for a and b
fossil ginkgo
what if a and b are both 10
f(1) = (1-10)(1-10) = (-9)^2 = 81
which is greater than 0
thats incorrect
vast shale
oh
vast shale
yes
vast shale
correct
fossil ginkgo
then at x = 4 its negative
so at some point, it hits 0
because it is continuous
does that make sense?
vast shale
yes
fossil ginkgo
so that tells you that one of the roots is between 1 and 4
apply the same logic to 4 and 7
you get two ranges for roots
right?
vast shale
OHHH
fossil ginkgo
u got it from here
vast shale
so the roots are between 1 and 7?
fossil ginkgo
its more specific than that
vast shale
yeah
fossil ginkgo
and you can determine the ranges of the roots
fossil ginkgo
so the roots are between 1 and 7?
this is true
but its not just that
theres more u can say
fossil ginkgo
so that tells you that one of the roots is between 1 and 4
look ^
can you do the same process for the other root?
using 4 and 7 instead of 1 and 4
vast shale
oh so one root is between 1 and 4
and the other is between 4 and 7
so for example one is 3
fossil ginkgo
yes
vast shale
and the other is 6?
vast shale
in the beggining of solving this question
i tried solving for the possible values of a and b
would that work too?
fossil ginkgo
you could do that but it might be more trial and error
vast shale
yeah i dont wanna do that
fossil ginkgo
yeah thatd be annoying
fossil ginkgo
ofc
vast shale
.close
hearty delta
Hi, I was wondering how this example got rid of the R at the end and where the 1/2 came from?
vocal sleetBOT
Hi, I was wondering how this example got rid of the R at the end and where the 1...
gray yarrow
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mint crystal
Help!
mint crystal
how would I write an equation for the area of the shape shown in figure 1-right as a function of x
I was helped before in here from toby (super helpful) but I dont think I accounted for everything correctly
Here is what I had
If I break down the shape into 3 rectanges I get 1x on left side
ornate ember
the area? You would have to break it up into rectangles
yep you got th right idea 🙂
mint crystal
and for the far right side its 1x aswell
ornate ember
that or you can subtract out the middle square as well
but 3 rectangles is probably easier
ornate ember
and for the far right side its 1x aswell
yep exactly
mint crystal
and for the middle i got a = x - 2 * x/4
mint crystal
that or you can subtract out the middle square as well
how would you go about that?
ornate ember
let's do the first way first 🙂
so left rectangle and right rectangle are both (1)(x) = x. So far the area is 2x since we'd add those together
mint crystal
yes correct 👍
ornate ember
then we do (x-2)(x/4) = x^2/4 - 2x/4 = (x^2 - 2)/4
then you just add that
and that's the area
mint crystal
Im a little confused give me a second to write this down
ohh okay that makes sense since a = lw
I was just confused about this x right here
ornate ember
so let's consider that real quick as well! Suppose we did it the alternative way
if we didn't have that missing piece
the area would b x * x = x^2, right?
mint crystal
yes correct
ornate ember
okay cool
so what's the area of the gap?
we have a base of (x - 2)
whats the height?
mint crystal
x/4?
lyric fossil
@thin vale
mint crystal
so when I do foil I got $x^2 - x^2/4 - 2x + 2/4x$
twin meteorBOT
austinn
mint crystal
not sure if thats correct
ornate ember
all is good except for the last part. It's 2x/4 not 2/4x
mint crystal
oh okay yea i was wondering where to put the x
ornate ember
okay so then you get:
$x^2 - \frac{x^2}{4} - 2x + \frac{2x}{4}$
twin meteorBOT
mellowdramallama
ornate ember
so then we can subtract that from x^2
so we get: $x^2 - (x^2 - \frac{x^2}{4} - 2x + \frac{2x}{4}) \\= x^2 - x^2 + \frac{x^2}{4} + 2x - \frac{2x}{4} \\ = \frac{x^2}{4} + 2x - \frac{2x}{4}$
twin meteorBOT
mellowdramallama
ornate ember
now just simplify the fraction
mint crystal
then it would be -1x/2 simplified
ornate ember
wait no lol
mint crystal
just the fraction
ornate ember
$\frac{x^2}{4} + \frac{8x}{4} - \frac{2x}{4} = \frac{x^2 + 6x}{4}$
twin meteorBOT
mellowdramallama
mint crystal
oh oh i see i firgot to do +2x
ornate ember
yep!
mint crystal
could you simplify that even more
ornate ember
so you see, same answer. Isn't math magical?!?
not really
you could factor out an x but it's not necessary
mint crystal
so you see, same answer. Isn't math magical?!?
that was the anwser you got for the shape?
ornate ember
yep!
mint crystal
bc previously i got a different anser so i mightve did somethin wrong
mint crystal
i got this
ornate ember
$x + x + (x-2)\left(\frac{x}{4}\right)$
$\\ 2x + \frac{x^2}{4} - \frac{2x}{4}$
$\\ \frac{8x}{4} + \frac{x^2}{4} - \frac{2x}{4}$
$\\ \frac{8x + x^2 - 2x}{4}$
$\\ \frac{x^2 + 6x}{4}$
mint crystal
twin meteorBOT
mellowdramallama
mint crystal
oh i see the difference i didnt simpligy it fully through
compared to what you had
would it be okay to ask you another question if you have time?
wispy lotus
vocal sleetBOT
wispy lotus
i need help with these two
wouldnt 10 be O(1) because it just checks one numebr
for 9 im just confusd
vocal sleetBOT
@wispy lotus Has your question been resolved?
dark field
wouldnt 10 be O(1) because it just checks one numebr
Notice that it is a “linear search”, and think about what such search really is doing may help
Hint for Q9: replace all n^(…) term by n^m, what will you get?
vocal sleetBOT
@wispy lotus Has your question been resolved?
hazy crest
vocal sleetBOT
hazy crest
Help it 2
thin vale
, rotate
twin meteorBOT
hazy crest
I want help with 2
upper iron
Are you sure that's all the given information?
Without knowing the supply frequency you cannot determine the supply voltage
vocal sleetBOT
@hazy crest Has your question been resolved?
cosmic sand
Can someone tell me what the above-line mean? Like A, i = 1, n <-- There's a line above the number, comma and letter, in other word, there's a line above everything to the right of "="
vocal sleetBOT
Can someone tell me what the above-line mean? Like A, i = 1, n <-- There's a lin...
cosmic sand
The context is find all M that satisfy: a₁MA₁^2 + a₂MA₂^2 + a₃MA₃^2 + ... = k (With Aᵢ, i = "1, n" <--line above this; k is a constant;
i ∈ {1; 2; 3; ....})
The line at the bottom of the picture.
@foggy thunder
<@&286206848099549185>
cosmic sand
Well this is grade 10 math, just vector
foggy thunder
The line at the bottom of the picture.
uhh expand that take M common multiply both side by the thing left in the parenthesis
Then u have M = k/ ....
foggy thunder
this looks like something from like pure math
wtf is pure math
stuck girder
real analysis, complex analysis, higher levels of high school math… blah blah blah
cosmic sand
uhh expand that take M common multiply both side by the thing left in the parent...
Can you elucidate? like what is M common and please continue your second sentence
foggy thunder
Can you elucidate? like what is M common and please continue your second sentenc...
like after u expand the summation u get M(a₁A₁^2 + a₂A₂^2 + a₃A₃^2 + ...) = k
oh right now divide not multiply
so u will get M = k/ (a₁A₁^2 + a₂A₂^2 + a₃A₃^2 + ...)
cosmic sand
like after u expand the summation u get M(a₁A₁^2 + a₂A₂^2 + a₃A₃^2 + ...) = k
I'm afraid you got it wrong here. MAᵢ is a line, not M*Aᵢ
foggy thunder
so MAi is a line
cosmic sand
yes
foggy thunder
then idunno mahn
cosmic sand
Also, my question is more about what is line above "1, n" mean, not how to solve the question because the book already write it.
foggy thunder
Also, my question is more about what is line above "1, n" mean, not how to solve...
not sure but i think that means average?
cosmic sand
not sure but i think that means average?
I don't think so, i ∈ {1; 2; 3; ....}
cosmic sand
The context is find all M that satisfy: a₁MA₁^2 + a₂MA₂^2 + a₃MA₃^2 + ... = k (W...
Here's the context (question in pinned) to spare new Helpers from reading the whole chat.
vocal sleetBOT
@cosmic sand Has your question been resolved?
cosmic sand
@paper depot can you help please?
paper depot
vocal sleetBOT
@cosmic sand Has your question been resolved?
urban obsidian
vocal sleetBOT
urban obsidian
I have to choose one of the follow:
A) Quantity A is bigger
B) Quantity B is bigger
C) Quantities are equal in value
D) Can't be determined from given data
Obviously quantity A is : the length of arc ABC and quantity B is the other one from the pic
dull maple
I think that the answer should be D.
urban obsidian
But why?
Sorry i can't geometry
So i'd like to know the concepts required for other questions like this as well
dull maple
Firstly do you understand that Length of Arc AD = Length of Arc BC ?
urban obsidian
indeed i do
paper depot
chord AD could rock back and forth along the circle
without changing the problem data
urban obsidian
chord AD could rock back and forth along the circle
could you elaborate how if possible? I guess it might be hard to actually illustrate
is that cuz i could draw the same chord towards the sides maybe
or perhaps just move it up or something
dull maple
is that cuz i could draw the same chord towards the sides maybe
Yes.
So, there's no data to actually determine which is longer. With given information any of them can be longer than other.
urban obsidian
So, there's no data to actually determine which is longer. With given informatio...
i was thinking something along this lines, in this case both are the same right
would the counterexample of this mean that the intersection of BD and CA is not the center?
was also curious about the chord rocking back and forth along the circle explanation
dull maple
i was thinking something along this lines, in this case both are the same right
Umm... Which both are same ?
urban obsidian
Umm... Which both are same ?
arc ABC and arc ADC
they're both half the circles in my example
are they not?
dull maple
Unless, it's given - you can't assume that.
dull maple
Learn to never assume stuff in geometry. Sometimes, It might seem like some angle is 90° but unless it's given, never assume that no matter how tempting it seems.
urban obsidian
Learn to never assume stuff in geometry. Sometimes, It might seem like some angl...
hmm but what am i assuming though?
i connect AC through the center of the circle
dull maple
hmm but what am i assuming though?
That arc ABC and arc ADC are equal.
urban obsidian
i connect BD through the center of the circle
dull maple
How do you know they'll pass through the center the circle ?
You can sure connect them through center but there's no guarantee that they'll form a line i.e. Points A, center, C are collinear.
urban obsidian
How do you know they'll pass through the center the circle ?
if AD // BC, i don't see why this wouldn't hold tbh
I think they'd be equal
i guess the catch is then just that AD not // BC
looked straight to me at first glance lol
dull maple
if AD // BC, i don't see why this wouldn't hold tbh
What does this symbol "//" mean ?
Parallel ?
urban obsidian
yeah
dull maple
I think if they are parallel, then they should pass through the center although i can't really prove it.
Let me think a bit more.
Okay yes. I proved that.
Anyway, @urban obsidian So are you done with the problem ?
urban obsidian
I think if they are parallel, then they should pass through the center although ...
yeah that's what i meant
urban obsidian
Anyway, <@1108625754897522709> So are you done with the problem ?
i guess so, thanks
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
dim grove
Can someone help me with this question
vocal sleetBOT
Can someone help me with this question
dim grove
<@&286206848099549185>
vocal sleetBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
split wind
Can someone help me with this question
since it's a mutliple choice questions, you may consider to do it in reverse
dreamy viper
Can someone help me with this question
guess you can apply the exponent to num and denom and try to find a trig simplification
dim grove
i tried doing that bt it didnt work
split wind
i tried doing that bt it didnt work
which?
dim grove
guess you can apply the exponent to num and denom and try to find a trig simplif...
this
dim grove
since it's a mutliple choice questions, you may consider to do it in reverse
yeah i could do it bt i m preparing for a test so it wouldnt really help me doing that
split wind
yeah i could do it bt i m preparing for a test so it wouldnt really help me doin...
to be honest, some multiple choice questions set it this way so that you cannot have enough time to "use the right way" to tackle it
split wind
yeah i could do it bt i m preparing for a test so it wouldnt really help me doin...
we would have to use tricks like differentiate the choices to get the answer
dim grove
actually i have tried every way i could , i have tried multiplying num and denominator with sec^2 didnt work
i also tried converting sin and cos into tan x/2 it also didnt work
pallid forge
have you tried multiplying it by tanx/tanx
dim grove
yuppp
dim grove
didnt work
split wind
in our draft we cant write:
pallid forge
what about (sec^2)/(sec^2)
pallid forge
that may give you something to work with in the denominator
hold on lemme right this down
dim grove
okayyy
split wind
\begin{align*}&\dv{(x\sin x+ \cos x)^{-1}}{x}\=&\frac{\sin x+ x\cos x-\sin x}{(x\sin x+\cos x)^2}\=&\frac{x\cos x}{(x\sin x+\cos x)^2}\end{align*}
dim grove
righttttttt
twin meteorBOT
biscuityxd
split wind
?
split wind
**biscuityxd**
this is the draft
now we can consider
what happened when
$\dv{\frac{x\sec x}{x\sin x + \cos x}}{x}$
twin meteorBOT
biscuityxd
split wind
and all other versions of the choices
easily by using product rule (instead of quotient rule)
in the exams,unless you are really lucky, you can't really find the proper u-sub for the integration
dim grove
ohokayyokaayy i get what u mean i will try doing it this way
dim grove
in the exams,unless you are really lucky, you can't really find the proper u-sub...
true
split wind
so, using differentiation would be the fastest way
vocal sleetBOT
vocal sleetBOT
Available help channel!
thin root
bro what is this saying
vocal sleetBOT
bro what is this saying
cyan talon
let f be a function of x and (or x, y and z)
there's actually two statements in there
either for 2 variables
thin root
resp is like or?
cyan talon
or for 3 variables
yeah
if you replace all the resp's you get the statement for 3 variables
thin root
the maximum rate of change of f at a point is the magnitude of the gradient and this occurs along the gradient? tf
cyan talon
yes
thin root
ok
cyan talon
I hope they're proving that just after
thin root
yeah
cyan talon
should help reading the proof then
thin root
should help reading the proof then
nah I am bad at that
I have a hard time reaidng profos
reading proofs
thin root
i just breeze through it because i am just special
ok i understand the proof alittle
ok actually i udnerstand now
i jsut had to readd it
lol
thin root
"2+2 = 5. *trust me bro*"
bro why is this true
what does it look like
how can oyu be orthognal with a point
vocal sleetBOT
@thin root Has your question been resolved?
vast shale
vocal sleetBOT
paper depot
very last step?
vocal sleetBOT
@vast shale Has your question been resolved?
lyric fossil
what is t_stop
is it q/64000 by chance?
oh i didn’t see the last picture
then yeah all they did was plug in q/64000
@vast shale
lyric fossil
it’s here
vast shale
the distance that the car has to stop in
vast shale
so t_stop is the time required to stop