Exactly
#help-19
fervent peak
mystic wigeon
So what about this one
2x^2-11x+15
fervent peak
That’s a bit harder
mystic wigeon
Where a≠1
fervent peak
Here I’d use a different method called the quadratic formula. It basically says that every root of that polynomial is described by x= (-b plus or minus sqrt(b^2-4ac))/2a
mystic wigeon
I've used that before I think
fervent peak
So x = (11+-sqrt(121-430))/(22)). Thus x = 3 or x = 2.5
With this formula you can also verify if it can be solved, since anything under the square root has to be positive, since a root of a negative number does not exist without using complex numbers
mystic wigeon
This is what my answer key stated for this question
So does solving for x from that point get you 2.5?
fervent peak
for example with your question 12, we get that sqrt(81-41827) is a square root of an obviously negative number. So it can’t be factorized without using complex numbers
fervent peak
is that why it is 2x-5 not x-2.5 ?
Yes, sorry I forgot to follow up on it
mystic wigeon
I should have mentioned, the directions are to factor completely, not solve for x
How do I use the quadratic equation and what I got for x to get to the factored statement/expression?
fervent peak
So x = (11+-sqrt(121-4*30))/(2*2)). Thus x = 3 or x = 2.5
If we say x1 is the first root (in this case 2.5) and x2 is the second root (in this case 3).
Then to factorize the polynomial we get that the factorization is a(x-x1)(x-x2). Where a is from the generic formula for a polynomial. In the answer key they simplified a(x-x1) to a single factor to eliminate the 2.5 and make it an integer.
mystic wigeon
So by multiplying x(1 or 2) by the x in a(x-x(1 or 2))
So in this instance multiply x1 which is 2.5
By 2 to get 5
But to keep the equation true you say 2x
For 2x-5?
I'm not making sense
And it doesnt seem to work in this other problem
Wait nvm i was looking at the wrong problem yes it does
fervent peak
By 2 to get 5
We multiply (x-2.5) by 2, so we get 2(x-2.5)=(2x-5)
mystic wigeon
Ok, I think I got it!
I'm not doing this by finding the root of polynomials anymore thats so much harder. I like just being able to plug into the equation and know for every problem
Your a lifesaver man
.close
smoky marten
Could someone
odd edgeBOT
Could someone
smoky marten
explain
Does it follow by the prob that since any x in V can be formed through set S, set S spans V?
so thats one property of it being a basis
now we just have to prove it is a basis
i mean it is Linearly independent
smoky marten
Right
lyric marlin
the important bit is that the scalars are unique
smoky marten
so since there are unique scalars such that x can be formed by S
that implies S spans V
lyric marlin
oh I meant for the linear independence
smoky marten
ok ok
i was clarifyinh
bet
so for LI we need to show b1v1 + ... + bnvn = 0 For some scalars b1, ..., bn in F where 0 = b1 = ... = bn
lyric marlin
that's not quite the definition of linear independent (or anything that shows it)
smoky marten
there
lyric marlin
no
what you've written is always true
Linear independence is that if b1v1 + ... + bnvn = 0 for scalars b1,...,bn, then they are necessarily 0
so the logic is going the other way kind of
smoky marten
sure
so then
we start with the assumption that b1v1 + ... + bnvn = 0 for scalars b1,...,bn
We also know that a1v1 + ... + anvn = x for such scalars and vector x in V
would we subtract eq 2 by x to get zero on RHS?
lyric marlin
you would have to subtract x from both sides
smoky marten
right
so we have a1v1 + ... + anvn - x = 0?
a1v1 + ... + anvn + (-1) x = 0?
and b1v1 + ... + bnvn = 0
then
lyric marlin
reminder: you're supposed to somehow use that the scalars are unique
smoky marten
a1v1 + ... + anvn + (-1) x = b1v1 + ... + bnvn
right i am trying to see where that would come into play
dam
lyric marlin
you've overcomplicated slightly btw
lyric marlin
We also know that a1v1 + ... + anvn = x for such scalars and vector x in V
no need to introduce an arbitrary x
smoky marten
if the scalars are unique then we know a1 =/ a2 .. =/ an right
so did we just need to say since V is a vector space it contains zero?
I just got that straight from the problem yk
lyric marlin
I think I'm confused by what you were initially asking
smoky marten
or should i just say suppose b1v1 + ... + bnvn = 0 and a1v1 + ... + anvn = 0 for scalars ... in F
like can we assume a1v1 + ... + anvn = 0
since V is a vector space it contains zero
so x can be the zero vector
lyric marlin
0 is in the vector space, so there is a unique set of scalars a1,...,an such that a1v1 + ... + anvn = 0, yes
smoky marten
ok
nice nice
so then we set the two equations equal to eachj other
a1v1 + ... + anvn = b1v1 + ... + bnvn
=
(a1 - b1)v1 + ... + (an - bn)vn = 0
0 is in the vector space, so there is a unique set of scalars a1,...,an such that a1v1 + ... + anvn = 0, yes
OHH and since the scalaers are unique, it follows that a1= .. an = 0 as desired
right?
smoky marten
so since the scalaers are unique it allows u to say all a1, ... , an = 0
lyric marlin
yep
lyric marlin
at most you could also say 'but also 0v1 + ... + 0vn = 0' to justify why exactly uniqueness gives 0
odd edgeBOT
@smoky marten Has your question been resolved?
mystic saffron
Make the graph of the following functions. Then, find its range and its offset.
odd edgeBOT
@mystic saffron Has your question been resolved?
mystic saffron
<@&286206848099549185>
mystic saffron
I think it's offset is -1309/2500?
The offset is how horizontally the function is displaced from its usual position.
odd edgeBOT
@mystic saffron Has your question been resolved?
mystic saffron
Make the graph of the following functions. Then, find its range and its offset.
I think it's offset is -1309/2500?
and R = (-3; 3)
odd edgeBOT
Available help channel!
mystic saffron
Make the graph of the following functions. Then, find its range and its offset.
I think it's offset is -1309/2500?
and R = (-3; 3)
odd edgeBOT
@mystic saffron Has your question been resolved?
mystic saffron
<@&286206848099549185>
odd edgeBOT
@mystic saffron Has your question been resolved?
odd edgeBOT
@mystic saffron Has your question been resolved?
marsh basin
odd edgeBOT
marsh basin
i initially thought this had something related with trigonometric functions and quadrants but after looking at the answer of sqrt1-p^2, i don't really get it
wooden python
you mean sqrt(1 - p^2).
you cannot omit those parentheses.
anyway, $\sin^2(x) + \cos^2(x) = 1$.
clever fjordBOT
AnnGhost
wooden python
this is the pythagorean identity
how did you not learn this?? its like the first thing you learn going into trig
marsh basin
well my syllabus is different 🤷♂️
wooden python
follows directly from the pythagorean theorem
marsh basin
i have heard of trigo identities but i do not take the specific modules that cover them
is there an alternative method to this that doesn't require identities? or is this like the only one
wooden python
no this is impossible without
mystic saffron
what concept is this 😅 or is this just well known haha
okay then try sketching a triangle with angle 20 degrees and fill in the sides given that sin(20 degrees) = p
marsh basin
essentially find a ratio that fits sin 20?
mystic saffron
yeah and since sin = opp/hyp what will be your opp and hyp
viscid flint
**AnnGhost**
this is the second most important identity in trig
the first being tan = sin/cos
mystic saffron
yeah and since sin = opp/hyp what will be your opp and hyp
@marsh basin fill in for me
marsh basin
currently doing
mystic saffron
okay
marsh basin
marsh basin
it's sqrt(1-p^2)
wooden python
sqrt(a-b) ≠ sqrt(a)-sqrt(b)
mystic saffron
show your work
please always do this to avoid mistakes
marsh basin
since sin 20 = p/1
cos 20 = adj/hyp
adj^2= 1^2-p^2
adj = sqrt(1-p^2)
cos 20 = sqrt(1-p^2)/1
= sqrt(1-p^2)
mystic saffron
yay
odd edgeBOT
odd edgeBOT
Available help channel!
copper bone
could someone help me with ii) of this? The answer doesnt make sense to me, where do you get h from and how do you remove it in the second step
upbeat drum
h is the height of the smaller triangle BOC
using area = 1/2 base x height, you get the first line
second line comes from expanding the brackets
copper bone
can you help me with expanding the brackets?
so i get 3 *sqrt18 + 3h
i clearly did something wrong but what was it
oh i see
you dont fully expand sqrt 18 but you do with h, so blah blah 3h - 3h
to get 1/2 * 6 * sqrt 18
ty
.close
whole jolt
i think i messed up somewhere but idk wherehttps://media.discordapp.net/attachments/936100524531523594/1166644930115026964/IMG_20231025_034932497.jpg?ex=654b3dc2&is=6538c8c2&hm=a4799c6eb61596ebe5d34125c31e850d4cf809a35003f735e23de73da32629ef&=&width=856&height=1141
shrewd adder
You didn't
whole jolt
wait
shrewd adder
Just make the 7x^2 box yellow
whole jolt
then where do i go 😭 im getting lost
shrewd adder
Top right of the circle?
whole jolt
wut
shrewd adder
$5x^2+11x-12$
clever fjordBOT
RomeNunt
shrewd adder
There
shrewd adder
Bruh
whole jolt
😭
shrewd adder
It's the one with 5 in the denominator btw since the coefficient of x^2 is 5
odd edgeBOT
odd edgeBOT
Available help channel!
hollow ice
hello
hollow ice
question 6
i know how to solve geometric series and arithmetic, but when there’s both series and arithmetic, would i just add/subtract them?
wooden python
also $\sum_{k=1}^n k^2$ is \textbf{not} the sum of a geometric progression
clever fjordBOT
AnnGhost
hollow ice
it’s not?
wooden python
it's not
you might be confusing k^2 with 2^k
1 + 4 + 9 + 16 + 25 is not a GP sum
just as an example
hollow ice
ohhhh i see
wooden python
like ok for calculation you would break these like ee.g. $\sum (i^2 + 3) = \sum i^2 + \sum 3$
clever fjordBOT
AnnGhost
wooden python
(stuff above and below the sigma omitted)
and then you'd need to know the formula for the sum of the first n squares, one way or another
hollow ice
i see, so i would just break it up?
wooden python
you would yes
smoky marten
odd edgeBOT
smoky marten
Does anyone mind explaining this proof, if we could walk through it, it would be great
lofty spade
Does anyone mind explaining this proof, if we could walk through it, it would be...
What’s the proof? This is a question
smoky marten
sorry I meant to say the thought process of proving this
We can start with the => direction
and if you could ask questions and ill respond, this we we can just walk through the question to form a proof
lofty spade
and if you could ask questions and ill respond, this we we can just walk through...
First, can you expand the question’s statement using the definition of linear dependence?
smoky marten
sure sure sure
ok so we know something is linearly dependent if for some linear combo a1u1 + ... + anun = 0, there are some non zero scalers a1,...,an
So if u1 is the zero vector (u1 = 0), then the set S is linearly dependent because it can be expressed as a non-trivial linear combination of vectors that equals the zero vector
not sure if that is what you were asking
lofty spade
not sure if that is what you were asking
You went a bit ahead, but what you’re doing is correct so far
and please include reply ping
lofty spade
So if u1 is the zero vector (u1 = 0), then the set S is linearly dependent becau...
you’ve proved a part of the required statement
smoky marten
Ok but yes the case the if u1 is zero you can have a a1(0) = 0 so a1 can be non zero and thus lin dep
anyways
For the second part
lofty spade
Ok but yes the case the if u1 is zero you can have a a1(0) = 0 so a1 can be non ...
No
Can you send a picture of the definition of linear dependence?
smoky marten
Can you send a picture of the definition of linear dependence?
we need to show that this vector uk+1 can be expressed as a linear combo of vectors {u1,...,uk}
lofty spade
Ok but yes the case the if u1 is zero you can have a a1(0) = 0 so a1 can be non ...
because 5u_1 = 0, for example
lofty spade
we need to show that this vector uk+1 can be expressed as a linear combo of vect...
I thought the definition was that you could have a nontrivial linear combination of all of the vectors that is 0, which is different from this
smoky marten
smoky marten
I thought the definition was that you could have a nontrivial linear combination...
the last sentence?
lofty spade
Oh, it says right there that if it contains 0, then it’s linearly dependent
lofty spade
the last sentence?
No, the definition is the paragraph that follows just after the word “definition”
but the last sentence is useful
smoky marten
ok bet
smoky marten
because 5u_1 = 0, for example
so is this incorrect?
lofty spade
so is this incorrect?
Oh, I was a bit confused by your wording
lofty spade
Ok but yes the case the if u1 is zero you can have a a1(0) = 0 so a1 can be non ...
Could you rephrase that
smoky marten
Could you rephrase that
sure sure, so suppose S is linearly dependent. Then we can express this linear combination in a non trival manner where u1 = 0
lofty spade
I think so
Anyway you get that S is linearly dependent because 0 = 1 u_1
Can you do the second case?
smoky marten
Can you do the second case?
So here, we have to show that if S is LD, we can express uk+1 as a linear combination of vectors {u1,...,uk}
lofty spade
Let’s get the implications straight first
lofty spade
So if u1 is the zero vector (u1 = 0), then the set S is linearly dependent becau...
we proved that (0 is in S) => (S is linearly dependent)
smoky marten
so thats the <= direction
lofty spade
So here, we have to show that if S is LD, we can express uk+1 as a linear combin...
this statement says (S is linearly dependent) => (u_(k + 1) can be expressed as a linear combination of vectors {u_1, …, u_k})
smoky marten
and thats the => direction
for the second part
ah shit i see
makes complete sense
lofty spade
not quite, because if you read the original statement, what you have to prove is this: (S is linearly dependent) <=> (u_1 = 0 or u_(k+1) is in span{u_1, …, u_k})
that “or” is important
smoky marten
right so if S is LD => prove that u1 = 0, u_(k+1) is in span{u_1, …, u_k}) (2 seperate cases) AND
IF u_1 = 0 OR u_(k+1) is in span{u_1, …, u_k}) then S is LD
smoky marten
not quite, because if you read the original statement, what you have to prove is...
im not really confused here
lofty spade
right so if S is LD => prove that u1 = 0, u_(k+1) is in span{u_1, …, u_k}) (2 se...
for the first sentence, it is not necessarily true that if S is linearly dependent, then u_1 must be 0. You have to prove that one or the other is true
Not both
lofty spade
Yes, the second statement of the proof is what I said
You prove that either u_1 = 0, or some vector is in the span of the others
So either u_1 = 0, or u_1 is not 0
Then you can prove that if S is linearly dependent, and u_1 is not 0, then the second part is true
Because if u_1 = 0, that’s the first part of the statement, so you’re done
smoky marten
is this also valid?
lofty spade
is this also valid?
Yes
smoky marten
Could you explain the syntax where they let k = max{i : a1 is not equal to zero}
lofty spade
Could you explain the syntax where they let k = max{i : a1 is not equal to zero}
Ok
Some of the a_i are 0
But there are some that aren’t 0
So they choose one of them
Any of them will do, so they chose the maximum i
The syntax just says that
smoky marten
So in other words, k is the biggest index of the nonzero scalar in our linear combination right
lofty spade
So in other words, k is the biggest index of the nonzero scalar in our linear co...
The biggest number out of all the indices of the scalars
smoky marten
The biggest number out of all the indices of the scalars
and the rest have to be zero, which is why we omit the rest of the vectors and just conside a1u1 right
lofty spade
and the rest have to be zero, which is why we omit the rest of the vectors and j...
no, it’s not that the rest have to be zero
it’s that the maximum of the indices could be anything from 1 to n
and if it is 1, then that means none of the other indices are nonzero
so all of the others are zero
and we can ignore them
smoky marten
no, it’s not that the rest have to be zero
isnt that what i said tho
lofty spade
it’s not that the first scalar is chosen to be nonzero
smoky marten
is this also valid?
is this question equivalent since or does the differnt notation change anything
smoky marten
compared to this
lofty spade
is this question equivalent since or does the differnt notation change anything
the question is equivalent
can you see this for yourself?
Try using different numbers for k and n
lofty spade
What are you confused about?
smoky marten
if k >1 that implies all our scalars > index 1 but less than index n are non zero
right
right
lofty spade
if k >1 that implies all our scalars > index 1 but less than index n are non zer...
No
smoky marten
sick
lofty spade
Consider 0u_1 + 2u_2 + 0u_3 + 7u_4 + 0u_5
In this case, the maximum index would be 4
smoky marten
I said less than n tho G
here n would be 5
and I said index less than n would be non zero
and index n would be zero
right?
oh nvm
i get it now
can you explain why uk being in span {u1, ,,, uk-1} finishes the proof, since I thought we needed to show for => direction that uk + 1 in span{u1, uk}
lofty spade
can you explain why uk being in span {u1, ,,, uk-1} finishes the proof, since I ...
It is the same thing
You can just rename k - 1 to K, and rename k to K + 1
smoky marten
can you walk me though the k > 1 until the => part is proven
i understand the rest just this part
im having trouble
smoky marten
You can just rename k - 1 to K, and rename k to K + 1
pls
lofty spade
can you walk me though the k > 1 until the => part is proven
Let K = k - 1
Then can you see that u_(K + 1) is in the span of {u_1, …, u_K}?
smoky marten
would the biggest nonzero vector then just be n?
since k = K + 1
and since k < n
n < K + 1
n - 1 < K
im lost lmao
smoky marten
nvm we dont know yet that k (1 ≤ k < n)
lofty spade
nvm we dont know yet that k (1 ≤ k < n)
you do
odd edgeBOT
@smoky marten Has your question been resolved?
wooden whale
odd edgeBOT
copper quarry
You should use y-y1 = m(x - x1)
copper quarry
I know. So?
wooden whale
You should use y-y1 = m(x - x1)
whats that for
copper quarry
y-y1 = m(x-x1) is the equation of the tangent line
silent temple
but this chapter is differentiation tho
find m using differentiation, then use point slope form to make the equation
copper quarry
You have to find those components
To find m you have to evaluate the derivative at x = ln5
and you know what x1 is
Do you know how to find y1?
copper quarry
you dont find x, you find x1
you are using y-y1 = m(x-x1) to get it in the form of y = mx+b
which is the equation of the tangent line
copper quarry
how do you find the equation of a tangent without finding its derivative??
wooden whale
one of the y is sqrt26
wooden whale
how do you find the equation of a tangent without finding its derivative??
i did?
wooden whale
how do you find the equation of a tangent without finding its derivative??
wait so d²y/dx²???
💀
copper quarry
do you know differentiation
wooden whale
yes
copper quarry
$y=\sqrt{e^{2x}+1}$
clever fjordBOT
water beam
copper quarry
do you know differentiation rules?
wooden whale
wait lemme show u how i did the other ones
copper quarry
is there a specific method ur teacher asked you to use?
wooden whale
btw did u see the other image?
copper quarry
well you did use derivatives
copper quarry
**water beam**
what rule do you think you use here?
wooden whale
what rule do you think you use here?
idk thats what my teacher taught💀
u multiply the power in front first, no?
heres how i did 3a
copper quarry
have you heard of chain rule
wooden whale
have you heard of chain rule
yes but i dont use that here
only for rate of change / approx change
copper quarry
**water beam**
well you cant differentiate this without chain rule
copper quarry
only for rate of change / approx change
okay but the rate of change is given by the tangent to a curve aka the derivative
wooden whale
do u mind if i come back in 10 mins?i have smth to do. sry
copper quarry
sure ig
wooden whale
will be back asap
sry im back
@copper quarry i still dont get how u get the other x and y
copper quarry
<@722683408190406667> i still dont get how u get the other x and y
want me to go from the beginning
wooden whale
ok
copper quarry
what is your understanding of a derivative
wooden whale
equation of gradient
copper quarry
well not equation
but the slope of a tangent to a curve
or gradient of a tangent to a curve if you wanna call it
wooden whale
alr
clever fjordBOT
water beam
wooden whale
yea
copper quarry
so we will use the equation of a tangent line $y-y_{1}=m\left(x-x_{1}\right)$
clever fjordBOT
water beam
copper quarry
we dont have to worry about this right now
but we will use it
it is important to note that m is the derivative at x = ln5 here
x1 is our given point, ln5
y1 is something we can find
but lets focus on m here
you get that?
wooden whale
yes
wooden whale
y1 is something we can find
yea but idrk how to apply it here
copper quarry
okay
instead of the square root
you can think of it as
$y=\sqrt{e^{2x}+1}=\left(e^{2x}+1\right)^{\frac{1}{2}}$
clever fjordBOT
water beam
copper quarry
because a square root is the same thing as 1/2 power
wooden whale
i did write it that way
copper quarry
okay
now you have to differentiate the outer function
which is
the power of 1/2
if it helps
$Let\ u\ =\ e^{2x}+1,\ u^{\frac{1}{2}}$
clever fjordBOT
water beam
wooden whale
oh
wooden whale
i subbed it into dy/dx
copper quarry
so do that tell me what you get
copper quarry
something is wrong
copper quarry
you should be getting $\frac{5\sqrt{26}}{26}$
clever fjordBOT
water beam
copper quarry
yes but you mustve done something wrong
copper quarry
**water beam**
because this is the correct answer
wooden whale
but the out come i got is the same tho
copper quarry
wait
im gonna try something
ok ur correct lol
i misinputed
lol
25/sqrt(26)
wooden whale
so what do i do after?
copper quarry
so thats ur m right
wooden whale
25/sqrt(26)
btw ur calc would show this?cz i had to change it mentally since my calc shows in decimals
is there a way to change it?
copper quarry
depends what calc u got. some newer calculators rationalize and put things nicely for you older models dont
copper quarry
idk i only know about the casio fx models because those are the only ones i have
copper quarry
lets just focus on the problem first
wooden whale
ok
copper quarry
so what did we say x1 was again?
wooden whale
so thats ur m right
since ive gotten my m id usually sub it into y=mx+c to get my c
is that wrong?
wooden whale
so what did we say x1 was again?
ln5
copper quarry
$y-y_{1}=m\left(x-x_{1}\right)$
clever fjordBOT
water beam
wooden whale
y - sqrt26 = 25/sqrt26 ( x - ln5)
clever fjordBOT
water beam
wooden whale
oop
copper quarry
can you simplify this into the form y = mx+b now?
wooden whale
hold on
y = 25x/sqrt26 - (25ln5+26)/sqrt26
its kinda messy
is that right
@copper quarry
clever fjordBOT
water beam
copper quarry
this should be ur final answer
copper quarry
ew
wooden whale
LMAO
copper quarry
the hell
copper quarry
wait
okay nvm
our answer is defo correct
that answer is wrong
because look
thats not even a tangent
thats a secant
wooden whale
that answer is wrong
bruh deadass i spent so much time on that
copper quarry
lol
sue the book
what a weird answer
yea theres no way that can be the correct answer
copper quarry
who is she
wooden whale
sue the book
HELP I CANT
OMG
I THOUGHT U WERE REFERING TO THE PERSON
her name is sue pemberton
💀💀💀
wooden whale
alr thank you:))
copper quarry
np
wooden whale
.close
odd edgeBOT
odd edgeBOT
Available help channel!
dusk wind
odd edgeBOT
fervent hawk
sorry, no clue, but usually we use v for velocity
odd edgeBOT
@dusk wind Has your question been resolved?
odd edgeBOT
@dusk wind Has your question been resolved?
woeful schooner
odd edgeBOT
woeful schooner
im confused as to how that equals (12 x 11)/ (100 x 99)
where does the 11 and 99 come from
fair prism
They skipped multiple steps but all they did was apply the formula for nCk then cancel out parts of the factorial
static totem
the numerator is ....................... × 12 × 11 and the denominator is 100 × 99 × ............................
and the dots are the same thing
odd edgeBOT
@woeful schooner Has your question been resolved?
woeful schooner
ah okay tyy
wheat apex
Can someone show me how to do notation for a tangent line for implicit differnetiation
cold sage
you could do (x,y)=(a,b) at the bottom
wheat apex
Then for this how am I supposed to show this
I know what I wrote is wrong but I also know there is a way ur supposed to show that
wheat apex
you could do (x,y)=(a,b) at the bottom
Ty
odd edgeBOT
@wheat apex Has your question been resolved?
cold sage
hey, im not too sure what you mean by this
wheat apex
I’m supposed to write like m given m= something
And you use that to find the equation of the tangent
I’m not 100% sure tho
Worst case I’ll use full sentences but
cold sage
do you happen to have the original question i could look at?
wheat apex
It’s a general thing
Imagine you find the slope of the tangent
Now find equation of tangent
cold sage
okay
wheat apex
How am I supposed to show what I’m doing?
cold sage
I assume you have a point on the line - where the tangent intersects the function is probably the one you have
you can then just use point slope form y-y1=m(x-x1)
not sure what much else you can show really
m is dy/dx evaluated at (x,y)=(x1,y1)
wheat apex
I guess how do I show why I’m using the coordinates and the slope I’m using to do the equation
Yes I know
cold sage
youd be using the values you calculated or found earlier, so theyd already be in your working, you dont really need to show anything beyond just actually using them
wheat apex
Alright
cold sage
oh you said why, right, its what the question tells you to do, thats the why
its not as though youre doing it for no reason
so no need to really explain that when writing it out
odd edgeBOT
@wheat apex Has your question been resolved?
hushed island
How do I do part b?
odd edgeBOT
How do I do part b?
dull fossil
Treat it as 2 different series
At one end u have summation of (-1)'s
And other is a geometric progression of common ratio 2/3
hushed island
And other is a geometric progression of common ratio 2/3
Now what?
warped glacier
Now what?
you're almost there
the -1 in the summation means that you need to add -1 15 times
warped glacier
no worries!
dull fossil
odd edgeBOT
@hushed island Has your question been resolved?
tight dove
Find CFD and CAB
odd edgeBOT
Find CFD and CAB
quaint pewter
CO and OD is the same lenght because both are the radius of the circle
tight dove
Yea
quaint pewter
you know what angle C is
tight dove
No
quaint pewter
CDA is 90 degrees
^
tight dove
16 = CFD
quaint pewter
how did you get that
tight dove
Alternate angles so 180-120-44
tight dove
6?
quaint pewter
show me your working out
tight dove
I did it in my mind
Like we found ACD is 44
So ECF will also be 44
Alternate angles
So 180-120-44
= 16
quaint pewter
So ECF will also be 44
this is also wrong
odd edgeBOT
@tight dove Has your question been resolved?
odd edgeBOT
tight dove
.reopen
odd edgeBOT
✅
queen dagger
if my midterm exams consisted of three exams each weighing 50%, and if I got 50% on both my exams, how much would i need to get on the third exam to have the weighted total of all three be >60%?
wooden python
3 exams each weighing 50%??
does that not add up to more than 100%
hows this work
do the exams actually weigh 33% (rounded) each? @queen dagger
queen dagger
oh oops yeah 33%
queen dagger
do the exams actually weigh 33% (rounded) each? <@963071730623086643>
yes
wooden python
ok right
so then you've contributed a total of 33 points toward your final grade
er, 33 ⅓ to be more precise
you need 26 ⅔ points (post-weighting) from your 3rd exam
,w simplify (26 + 2/3)/(33 + 1/3)
clever fjordBOT
late heath
odd edgeBOT
median sequoia
They want you to find relations between the equalities that they gave u in the beginning
You can try to decompose the segments into 2 segments that are added
for example : BC = AC - AB
and : DB = DE - BE
late heath
the letters confuse me a lot, and when they tell me to subsitute them idk how to do that
median sequoia
Well, you need to know that since they say "Given : AC = DE"
in any equation you have, u can substitute AC by DE
and vice-versa
you can also substitute DE by AC
on the second line they say "AB = BE"
so u can substitute AB by BE and BE by AB in any given equation
do u understand?
late heath
kind of
median sequoia
so ok now try to find solve it knowing that BC = AC - AB and DB = DE - BE
median sequoia
yeah
late heath
and DB= AC- AB?
median sequoia
yeah
late heath
so whats after that to prove BC=BD
median sequoia
well compare the equations u have now
late heath
and i subsitute them again?
median sequoia
ok so, if u find that for example BC = DE - BE that means u can substitute BC by DE - BE and u can substitue DE - BE by BC
median sequoia
good job!
late heath
.close
mystic saffron
Hi so an hour ago, I asked this question, where I had to prove this inequality. Kepe gave me this proof, the channel closed due to timeout.
lost helm
Do you know that for any real x, -x<=|x|<=x?
mystic saffron
Yes I do understand
OHHH
Then how do we proceed to the 4th step?
How did we conclude that?
lost helm
Combine the 2nd and 3rd step
desert marlin
Do you know that for any real x, -x<=|x|<=x?
?? x=-5
then 5<=5<=-5 ???
mystic saffron
Do you know that for any real x, -x<=|x|<=x?
Wait?
desert marlin
That’s only true for x non negative
lost helm
?? x=-5
then 5<=5<=-5 ???
I meant for positive real
mystic saffron
I don’t understand
Umm I really need to go rn
So I’ll close this channel for
Thank you so much guys for your time
.cloee
.close
twin wyvern
odd edgeBOT
twin wyvern
for this did i do it correct?
like each angle is 32 degrees ish 360/11
sin(32) = y/1
since hpoyth is a unit vector
and would be cos(32) = x/1
to find x
odd edgeBOT
@twin wyvern Has your question been resolved?
odd edgeBOT
@twin wyvern Has your question been resolved?
odd edgeBOT
@twin wyvern Has your question been resolved?
violet bronze
guysguysugysuyg
odd edgeBOT
guysguysugysuyg
violet bronze
what is 1+on e
ember oak
stark coyote
echo ginkgo
another worthy candidate
violet bronze
so basiclkeay
zenith tartan
basiclkeay
violet bronze
i waus in maf kalss
zenith tartan
okay then?
violet bronze
an d
violet bronze
the tecker ask wauht won pluzs won iszxc
ember oak
Please speak English
violet bronze
so uhh
zenith tartan
itz 2
zenith tartan
youre right, perhaps the teacher is rong
ember oak
Show the actual problem and speak in full sentences
violet bronze
youre right, perhaps the teacher is rong
yesz!
zenith tartan
dude you sound russian lol
violet bronze
one + 1 is 4 karacers so techker in rong
yexzs
ember oak
Ohh.. 1+one
violet bronze
corkect
ember oak
<@&268886789983436800> spam
stark coyote
the teacher speaks in javascript
violet bronze
the teacher speaks in javascript
💀
what is a javdskjvnnjafgnkajvnjenjnva
sckrpivt
zenith tartan
mod is here
worthy needle
Please don't troll / be silly.
zenith tartan
youre ded
violet bronze
😛
worthy needle
.close
odd edgeBOT
violet bronze
.reopernjsnabgjhna
.repoerin
.repkgamojfbnojdabkn
.aldkbnfjabojbvnkjvvnrk jenvkjraevnrjnv ougIPJENGVA;IJE MA G
T
AEMADFKMV LJEB;EA
zenith tartan
potato just mute him?
vestal sapphire
bro said repoerin
ember oak
<@&268886789983436800> spam
violet bronze
.reopen
odd edgeBOT
✅
fresh shard
You still here potyate?
echo ginkgo
1+1=2 weeks
fresh shard
I timed them out
worthy needle
Oh lol
vestal sapphire
his status says it all
worthy needle
I did it simultaneously
regal lark
hi
regal lark
I'm trying to find the probability that p(t) has real roots
I'm not sure how to proceed from there
would I split it up as P({ X <= 0 } or { X-1 <= 0 })
viscid flint
you need one of those things to be true but not both
regal lark
that's why it's or right
echo ginkgo
no like
regal lark
X<= 0 would be a subset of X-1 <= 0 so it would just collapse into P(X <= 1) ?
echo ginkgo
you need 1 negative, 1 positive
regal lark
oh
how would this work, im kinda stuck
if X <= 0, then X-1 would also be <= 0
since you're just subtracting 1
if X-1 <= 0, then
idk
echo ginkgo
you have (X <= 0 and X-1 >=0) or (X >=0 and X-1 <= 0)
first case is impossible
so you're left with the second one
0 <= X <= 1
@regal lark
odd edgeBOT
odd edgeBOT
Available help channel!
civic sphinx
a
warped grove
Are we assuming in the definition of tree that there are finitely many vertices?
If so then it seems good
odd edgeBOT
If you are done with this channel, please mark your problem as solved by typing .close
@civic sphinx Has your question been resolved?
spare coyote
odd edgeBOT
static totem
yes
spare coyote
Meaning this is like
Log(A/B) = log(a) - log (b)
Or something right
Maybe Im remembering it wrong
static totem
yes
static totem
it doesn't matter because all options did that anyway
spare coyote
Wha
static totem
it's not like one option equals your answer but it's wrong because it doesn't use prime numbers; if it equals your answer it's automatically right
spare coyote
Im sorry
Are you telling me
My answer is whatever I get when I differentiate f(x)
Bc I understand that
spare coyote
Isnt it log(55) - log(9)
The issue is simplifying this part of the differentiation process
I cant see what my f'(x), and therein my answer, if I don't understand how to simplify this, or break this down
static totem
i'm saying that has notthing to do with prime numbers
static totem
your issue has nothing to do with prime numbers, it's fluff
they rewrote it in 5 different ways, only one is right
spare coyote
Uh
Right
So how am I supposed to go about finding which is right
By differentiating f(x), and rewriting it, with only prime numbers, as the question is asking?
static totem
log(ab) = log(a) + log(b)
spare coyote
Then simply matching what I get, to the answers
Right
What
Except in this scenario its
log(a/b)
static totem
it's both
static totem
you use like 3 rules
spare coyote
I love calc fr
I mean
Alright
But my first step is gonna end up being log(55)-log(9)
Is it not?
Idk
Maybe Im just confused here
odd edgeBOT
@spare coyote Has your question been resolved?
static totem
yes, that's the first step
odd edgeBOT
@spare coyote Has your question been resolved?
weak fiber
odd edgeBOT
weak fiber
how do u find this, i know u have to do the antiderivative but im not sure how since its multiplication
civic bison
try intergral by part or since its in terms of p treat y as a constant
smoky lance
odd edgeBOT
smoky lance
I am kinda lost am i doing it right?
wicked kestrel
this is improper for a few reasons, though your computations themselves don't look too bad
wicked kestrel
that and the 2nd integral shouldn't be there; you've already done the integration
smoky lance
wait so i dont need it?
wicked kestrel
not only do you not need it, it's improper to have it
smoky lance
ah i was confused
cus someone told me i needed it 😭
which confused me even more
aight ill remove it
wicked kestrel
rather than the integral sign, you should instead have $\vert^0_{-2}$
clever fjordBOT
Steakanator
wicked kestrel
ie $k(\frac{4x^2}{2} + \frac{x^3}{3} + 4x) \vert^0_{-2}$
clever fjordBOT
Steakanator
smoky lance
and the is useless?
wicked kestrel
it's also improper
smoky lance
**Steakanator**
not sure how to write this on google docs
but lemme try figure it out
smoky lance
it's also improper
aight ty