let me check what symbolabs think about that
#help-26
tawny surge
symbolabs cooperates with us
meaning?
topaz sinewBOT
@maiden wave Has your question been resolved?
maiden wave
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
tired orbit
topaz sinewBOT
tired orbit
can someone tell me whether my answers are correct for the question....tq
golden mesa
great name
thorny flameBOT
topaz sinewBOT
@tired orbit Has your question been resolved?
magic raft
@tired orbit That name isn't going to work here
magic raft
I have things I gotta do but it has been 15 minutes so you may ping helpers now
topaz sinewBOT
topaz sinewBOT
Available help channel!
floral nacelle
topaz sinewBOT
golden mesa
you know your difference of two squares?
floral nacelle
I know that 10/2= 5 and /2=2
So we got that out of the way
Its asking for the value of x^2- y^2 btw
2 x5 = 10
And 2x2=4 so do i need to simplify it?
golden mesa
simplify what
floral nacelle
Sorry i meant like add them up (10+4=14)
restive gate
you only need to find two values, x and y which satisfy both of the equations above
once you find those two values, take both of them ^2 and subtract
golden mesa
literally multiply them together
golden mesa
yeah
topaz sinewBOT
topaz sinewBOT
Available help channel!
sterile vector
I've tried to solve this problem at least 6-7 times and cant get anything out of itt aaaah
topaz sinewBOT
I've tried to solve this problem at least 6-7 times and cant get anything out of...
topaz sinewBOT
I've tried to solve this problem at least 6-7 times and cant get anything out of...
Show your work, and if possible, explain where you are stuck.
neon iron
I've tried to solve this problem at least 6-7 times and cant get anything out of...
how familiar are you with free variables
sterile vector
neon iron
one sec let me tex the matrix
sterile vector
mhmm, I would say that I am okay with it, we laerned it about a week and a half agoo
Alrighty thank youu
neon iron
I'm assuming you did the row operations correctly, i'll re verify them should we run into problems
$$\begin{pmatrix}
1 & -3 & 0 & 0 & 5 & 5 & -8\
0 & 0 & 1 & 0 & 4 & 4 &-2\
0 & 0 & 0& 1 & 4 & 2 &5\
\end{pmatrix} $$
thorny flameBOT
sen
neon iron
mhmm, I would say that I am okay with it, we laerned it about a week and a half ...
what do you know about them
neon iron
i learned that free variable can be any real numbers
so here the free variables would be the non pivot ones
sterile vector
column 2, 5 and 6
neon iron
x^2=s
x^5=t
x^6=u
x_6 btw not x^6
neon iron
x_2=s
x_5=t
x_6=u, s,t,u in R
now from this can you give me values of x1,...x6 in terms of this
sterile vector
yes
neon iron
you can write the matrix in equation form if you're more comfortable with that
x1 - 3s + blah blah = -8
neon iron
now lets get the exact values of
x1 to x6 like
x1= ?
x2=? etc
neon iron
perfect
ok now we're gonna write that like
$$\begin{pmatrix}
x_1\
x_2\
x_3\
x_4\
x_5\
x_6\
\end{pmatrix} = s () + t() + u()$$
thorny flameBOT
sen
sterile vector
I think we are missing another column, for the -8, -2 and 5
neon iron
I think we are missing another column, for the -8, -2 and 5
good
we'll add that on the side since it doesnt have any variables dw
what do you get for s
sterile vector
Oooh okay thanks,
x_1= 3
x_2= 1
and the rest are zero I believe
for the S Column
neon iron
$$\begin{pmatrix}
x_1\
x_2\
x_3\
x_4\
x_5\
x_6\
\end{pmatrix} = s \begin{pmatrix}
3\
1\
0\
0\
0\
0\
\end{pmatrix} + t() + u()$$
sterile vector
yess
thorny flameBOT
sen
$$\begin{pmatrix}
x_1\\
x_2\\
x_3\\
x_4\\
x_5\\
x_6\\
\end{pmatrix} = s \begin{pmatrix}
3\\
1\\
0\\
0\\
0\\
0\\
\end{pmatrix} + t() + u()$$
sterile vector
No worries! take your time, the system look complicated haha
sterile vector
$$\begin{pmatrix}
x_1\
x_2\
x_3\
x_4\
x_5\
x_6\
\end{pmatrix} = s \begin{pmatrix}
3\
1\
0\
0\
0\
0\
\end{pmatrix} = t \begin{pmatrix}
-5\
0\
-4\
-4\
1\
0\
\end{pmatrix} + u()$$
thorny flameBOT
Dreamy
sterile vector
okk
sterile vector
$$\begin{pmatrix}
x_1\
x_2\
x_3\
x_4\
x_5\
x_6\
\end{pmatrix} = s \begin{pmatrix}
3\
1\
0\
0\
0\
0\
\end{pmatrix} = t \begin{pmatrix}
-5\
0\
-4\
-4\
1\
0\
\end{pmatrix} = u \begin{pmatrix}
-5\
0\
-4\
-2\
0\
1\
\end{pmatrix}
sterile vector
$$\begin{pmatrix}
x_1\
x_2\
x_3\
x_4\
x_5\
x_6\
\end{pmatrix} + s \begin{pmatrix}
3\
1\
0\
0\
0\
0\
\end{pmatrix} + t \begin{pmatrix}
-5\
0\
-4\
-4\
1\
0\
\end{pmatrix} + u \begin{pmatrix}
-5\
0\
-4\
-2\
0\
1\
\end{pmatrix}
omg
we did it
neon iron
take ur time
sterile vector
actualyl no we didnt
neon iron
x1, x2,x3...,x6 = not +
sterile vector
$$\begin{pmatrix}
x_1\
x_2\
x_3\
x_4\
x_5\
x_6\
\end{pmatrix} = s \begin{pmatrix}
3\
1\
0\
0\
0\
0\
\end{pmatrix} + t \begin{pmatrix}
-5\
0\
-4\
-4\
1\
0\
\end{pmatrix} + u \begin{pmatrix}
-5\
0\
-4\
-2\
0\
1\
\end{pmatrix}
thorny flameBOT
Dreamy
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
sterile vector
x_1=8
x_3=-2
x_4=5
neon iron
$$\begin{pmatrix}
x_1\
x_2\
x_3\
x_4\
x_5\
x_6\
\end{pmatrix} = s \begin{pmatrix}
3\
1\
0\
0\
0\
0\
\end{pmatrix} + t \begin{pmatrix}
-5\
0\
-4\
-4\
1\
0\
\end{pmatrix} + u \begin{pmatrix}
-5\
0\
-4\
-2\
0\
1\
\end{pmatrix} +
\begin{pmatrix}
8\
-2\
0\
5\
0\
0\
\end{pmatrix}$$
sterile vector
$$\begin{pmatrix}
x_1
x_2
x_3
x_4
x_5
x_6
\end{pmatrix} = s \begin{pmatrix}
3
1
0
0
0
0
\end{pmatrix} + t \begin{pmatrix}
-5
0
-4
-4
1
0
\end{pmatrix} + u \begin{pmatrix}
-5
0
-4
-2
0
1
\end{pmatrix} + \begin{pmatrix}
-8\
0\
-2\
5\
0\
0\
\end{pmatrix}
thorny flameBOT
Dreamy
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
sen
sterile vector
yes there you go sorry
neon iron
good job!
neon iron
I'm assuming you did the row operations correctly, i'll re verify them should we...
im assuming you did the row operations
correctly
let me recheck your matrix one sec
empty sail
Wait
sterile vector
Oh really?? I was trying to turn the system to a row echolon form
neon iron
[0, 0, 1, 0, 4, 4, -2]
[0, 0, 0, 1, -4, -2, -5]```
nah nah your ref is correct👍
empty sail
```[1, -3, 0, 0, 5, 5, -8]
[0, 0, 1, 0, 4, 4, -2]
[0, 0, 0, 1, -4, -2, -5]...
No it was wrong initially
That there
They lost the negative
neon iron
They lost the negative
ah
empty sail
@sterile vector
neon iron
yeah correct this and do the exact things we did
neon iron
but you can do this on your own right now
sterile vector
I believe I can, if there's anything, I will let you know!
neon iron
mellow venture
Yay back to school
topaz sinewBOT
Yay back to school
plush bramble
topaz sinewBOT
topaz sinewBOT
@plush bramble Has your question been resolved?
topaz sinewBOT
@plush bramble Has your question been resolved?
plush bramble
.close
lucid junco
how do I find the antiderivative of x^-1 without using natural log
drifting swift
you cannot.
drifting swift
yes it does
drifting swift
$\int x^p \dd{x} = \frac{x^{p+1}}{p+1} + C$
thorny flameBOT
Ann
lucid junco
so reverse power rule works for any number except -1
drifting swift
indeed it does
lucid junco
btw
im finally past that riemann sum stuff
nightmare fuel
so i can now use the shortcut
fundamental theorem of calculus
thing
drifting swift
i mean yeah it is not pretty
lucid junco
is the main purpose of it to build intuition for how definite integration works?
drifting swift
intuition and conceptual understanding
you'll need to grapple with modified forms of it for shit like arc length and SoR volumes
lucid junco
sounds fun 
drifting swift
i mean not necessarily in a computational sense either
but like you gotta be able to visualize
lucid junco
for $\int_{0}^{2}\left|x^{2}-1\right|dx$
thorny flameBOT
water beam
lucid junco
How do I set-up a piecewise thing for this
because i know i cant just integrate it with the absolute value there
golden mesa
check intervals for where x^2-1 is positive/negative
lucid junco
check intervals for where x^2-1 is positive/negative
how do I do that?
golden mesa
find roots first
lucid junco
set x^2 - 1 = 0?
lucid junco
x^2 = 1 and 1 = x^2
wait they are the same thing
x^2 - 1 = 0
Then we have x^2 = 1
and what else?
wait
im dumb
lol
x^2 = 1
then its -1 and 1
right
x = -1,1 @golden mesa
lucid junco
yeah
lucid junco
so only x=1 matters here
so whats the next step?
golden mesa
check intervals for where x^2-1 is positive/negative
now that you know it reaches 0 at x=1
so for x<1, is x^2-1 positive or negative?
lucid junco
wait where does the inequalities come from
fallow heart
wait where does the inequalities come from
Definition of absolute value
,tex .abs def
golden mesa
wait where does the inequalities come from
we're checking what x^2-1 does on both sides of x=1
thorny flameBOT
Alberto Z.
golden mesa
yeah
lucid junco
yeah
wait so i dont really get it
so after finding only +1 works in the bounds of the integral
what next?
do we plug in 1 for x?
golden mesa
**Alberto Z.**
so finding the root x=1 for x^2-1=0 tells us that the integral will look different for x>1 and x<1, because of the absolute value
lucid junco
okay i sorta get that
golden mesa
**Alberto Z.**
so if x^2-1 is negative, we'll have to add a - sign according to this
lucid junco
so if x^2-1 is negative, we'll have to add a - sign according to this
What next I have -x^2 +1 <0
.close
analog moat
https://www.youtube.com/watch?app=desktop&v=3nENiosGnJw
I tried to solve it but got wrong, anyone can help??
analog moat
I tried solving it but got wrong result. Anyone can enlighten me where's the wrong part??
slate temple
this is just plug and chug right?
gray storm
More like solve for a and then plug and chug
slate temple
oh didnt see the video above
analog moat
It should be
But i took different approach for the last step
That's why the last parts are kinda different
But i wonder, is it possible or not
topaz sinewBOT
@analog moat Has your question been resolved?
topaz sinewBOT
@analog moat Has your question been resolved?
undone flicker
undone flicker
How to solve this one?
vital moth
hi arjunn
by triangular inequality |x|+|y|>=|x+y|
so the minimum of |a+bw+cw^2|+|a+bw^2+cw| is |2a+(b+c)w+(b+c)w^2|
you know that w is a cube root of unity different than 1
so it is either (-1-isqrt(3))/2 or (-1+isqrt(3))/2
now notice that if you square one of these 2 complex roots you will get the other root
so ((-1-isqrt(3))/2)^2=(-1+isqrt(3))/2
and ((-1+isqrt(3))/2)^2=(-1-isqrt(3))/2
what will you do next ??
@undone flicker
undone flicker
Wow you are making the problem so easy for me
undone flicker
and ((-1+isqrt(3))/2)^2=(-1-isqrt(3))/2
I just checked it yes true
vital moth
no you are smart thats why you are finding it easy
ok now choose one of these 2 roots and plug it
then plug the other root
i didnt check but ig they will be the same
yes it should be the same answer
vital moth
now notice that if you square one of these 2 complex roots you will get the othe...
bc of this nice thing
undone flicker
so the minimum of |a+bw+cw^2|+|a+bw^2+cw| is |2a+(b+c)w+(b+c)w^2|
How to tackle this?
I meant if we give any value in it
We have a,b,c
Something is cancel out
|2a-b-c|
vital moth
let me think about this for a sec
undone flicker
I cancel out √3i terms
undone flicker
Ohh sry please point out
vital moth
$|2a+(b+c)\omega+(b+c)\omega ^2|=|2a+\frac{(b+c)(-1-i\sqrt{3})}{2}+\frac{(b+c)(-1-i\sqrt{3})^2}{4}|=|2a|$
vital moth
Ohh sry please point out
np dw
check the calculation again
to know where your mistake was
thorny flameBOT
calculus is fun
undone flicker
Only imaginary part is cancel out
vital moth
you are right i was wrong sorry for that trouble
undone flicker
So what next?
vital moth
i have something in mind
i am not sure if this is valid but it is as follows
so you want |2a-b-c| to be a minmum
undone flicker
Yes
vital moth
where a,b,c are non negative integers
undone flicker
Yes
vital moth
ok a has the highest coeff ,namely 2, so we need to get minimize this first
so we can assume that a=0
this leaves us with |-b-c|
now b and c are non negtaive integers
undone flicker
Yes
vital moth
so |-b-c|=b+c
to minimize this we choose the smallest non negtaive integers which are not 0 (bc we chose a to be 0)
these are 1 and 2
it doesnt matter which one is 1 and which is 2
there sum is 3
now this is the minimum why
bc we chose the minimum non negative integers where a was chosen to be 0
bc it has highest coeff
this leads to the answer 3 which is d
but i am not sure if this is valid
lets wait for someone to confirm or deny this
<@&286206848099549185>
mild hemlock
i think we can say it is true for certain values and false for other it is true for values of b and c being greather than or equal to zero
neon iron
so the minimum of |a+bw+cw^2|+|a+bw^2+cw| is |2a+(b+c)w+(b+c)w^2|
All this says is that the minimum value of |a+bw+cw^2|+|a+bw^2+cw| is greater than or equal to the minimum value of |2a+(b+c)w+(b+c)w^2|, not that the minimum of |2a+(b+c)w+(b+c)w^2| is the minimum of |a+bw+cw^2|+|a+bw^2+cw|. Or am I missing something?
vital moth
This says that the minimum value is when they are equal?
vital moth
i think we can say it is true for certain values and false for other it is true ...
a,b,c are non negative integers
topaz sinewBOT
@undone flicker Has your question been resolved?
topaz sinewBOT
@undone flicker Has your question been resolved?
ionic oar
,w expand (a + bw + cw^2)(a + bw^2 + cw)
thorny flameBOT
ionic oar
$a^2 + b^2 + c^2 + (\omega + \omega^2 )(ab + bc + ca)$
thorny flameBOT
NEON
ionic oar
$a^2 + b^2 + c^2 -ab - bc - ca$
thorny flameBOT
NEON
ionic oar
$\frac 12 \left { (a - b)^2 + (b - c)^2 + (c - a)^2 \right }$
thorny flameBOT
NEON
ionic oar
right uh
@undone flicker
If you square $x$ and use $|z|^2 = z\bar{z}$ then you I'm pretty sure you'd end up with $x^2 = 3\left { (a - b)^2 + (b - c)^2 + (c - a)^2 \right }$
thorny flameBOT
NEON
ionic oar
now if we know that none of a, b, or c are equal, and the minimum difference between two integers is 1
So you're left with $x^2 \geq 3 \times 3 \implies x \geq 3 \quad (x \geq 0)$
thorny flameBOT
NEON
vital moth
what if he uses triangular inequality
ionic oar
maybe that would work but I'm not sure how the specifics of that would play out
vital moth
applying it and replacing omega by any of the 2 complex roots will lead to |2a-b-c|
now what i said is that a,b,c are non negative integers and we want to get minimum value of |2a-b-c| then since 2a has the hghest coefficient then we can set a=0
then set b=1 ,c=2 or c=1,b=2
this will give 3
ionic oar
Hmm looks good
vital moth
this was easy approach
vital moth
ah you just mean multiplication
ionic oar
yeah
vital moth
i was wondering bc whenever i see these my mind goes to sets
ionic oar
with good reason
pseudo jetty
So you're left with $x^2 \geq 3 \times 3 \implies x \geq 3 \quad (x \geq 0)$
this doesnt look right, if you draw out the triangular lattice there are no lattice points 3/2 distance from the origin
plus, when a, b, c are distinct integers you can only have 1^2 + 1^2 + 2^2 in that sum
topaz sinewBOT
@undone flicker Has your question been resolved?
undone flicker
,w value of sqrt12
thorny flameBOT
undone flicker
.close
severe parrot
Hey there!
I'm a sophomore and I just had a math test. I think I nailed all the answers, but I realized later that I used "=>" as a newline even though it's more commonly seen as implication.
The math course I took the test in doesn't assume or include knowledge about implication, and I've been taught to use "->" for implication, but I'm still worried.
It's totally fine to use "=>" whenever you have an equation which you change (e.g. 2x+3=7 => 2x=4 => x=2) but I used it as a sort of newline character when I was simplifying expressions. So e.g.
2a+2b-(a+b)
=> 2a+2b-a-b
=> a+b
Should I be worried?
slate temple
Hey there!
I'm a sophomore and I just had a math test. I think I nailed all the...
honestly if your instructor isn't a poophead they shouldn't care, I use that new line notation all the time and have seen many of my professors do so
severe parrot
I read that it's not actually new line but rather implication. Are you sure you're talking about people using it as new line?
For example you can chain implication like this if I understand correctly:
2x+3=7
=> 2x=4
=> x=2
(we can actually use equivalence here too)
But it's no longer implication if you use it for simplifying an expression, like so:
2a+2b-(a+b)
=> 2a+2b-a-b
=> a+b
It's a bit annoying that both -> and => seemingly can mean implication though... Same for <-> and <=> but for equivalence
topaz sinewBOT
@severe parrot Has your question been resolved?
topaz sinewBOT
@severe parrot Has your question been resolved?
severe parrot
pls help 🙏 ❤️
topaz sinewBOT
@severe parrot Has your question been resolved?
jade knot
$\frac{\left(1200000\left(1.025\right)^x\right)}{1420+100x}<600$
thorny flameBOT
Leo
jade knot
how would you solve this? i'm a bit stuck
sterile finch
how would you solve this? i'm a bit stuck
Have you tried an iterative method?
jade knot
What's that?
sterile finch
What class is this for? That will give me a general idea for appropriate solutions.
jade knot
Just math class
I'm in 11th
these are two separate equations
and I have to find at what point they give a result smaller than 600
sterile finch
In a Calculus 1 class, you would have likely learned about Picard's Iterative Method.
jade knot
(x was supposed to be t, as in years)
jade knot
In a Calculus 1 class, you would have likely learned about Picard's Iterative Me...
I haven't even started calculus in 11th soooo yeah...
Any other way of solving it?
sterile finch
One of the variables being in the exponent makes it more difficult.
sterile finch
Well, if you knew Picard's Iterative Method, it would be easy as well.
jade knot
But I don't :(
sterile finch
Have you learned about logarithms?
jade knot
yep
I tried using logs too
but didn't seem to work
I got the following:
log_1.025(71/100+n/200) < n
but that's not really helpful
sterile finch
Well, that's in the form in which you could use Picard's Method, but I don't think you did the math correctly. That should be n/20.
topaz sinewBOT
@jade knot Has your question been resolved?
jade knot
<@&286206848099549185>
topaz sinewBOT
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topaz sinewBOT
topaz sinewBOT
Available help channel!
hollow moon
a coat is priced 180.99 and now its 125.99 whats the discount
acoustic pecan
[(original - discounted)/(original) ]*100
hollow moon
what
brisk geyser
subtract the discounted price from the original price
divide by the original price
then multiply by 100 to get the percent
topaz sinewBOT
@hollow moon Has your question been resolved?
hollow moon
nvm i figured it out
topaz sinewBOT
hollow moon
.close
topaz sinewBOT
Available help channel!
distant bison
Is f(x)=-sqrt 9(x+4). +2 the right equation for the graph
topaz sinewBOT
Is f(x)=-sqrt 9(x+4). +2 the right equation for the graph
torpid gulch
looks correct to me
topaz sinewBOT
topaz sinewBOT
Available help channel!
worn mirage
Q: We shuffle a deck of cards, and we pick them one by one until an Ace is reveal. Knowing that the first Ace is picked at the 20th card, what is the conditional probability that the 21st card is a) the Ace of Spade. b) the 4 of Club
topaz sinewBOT
Q: We shuffle a deck of cards, and we pick them one by one until an Ace is reve...
@worn mirage Has your question been resolved?
worn mirage
<@&286206848099549185>
topaz sinewBOT
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half field
topaz sinewBOT
half field
Hi I'm in trouble with this
Can somebody teach me part a?
should i consider cases with it ?
topaz sinewBOT
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topaz sinewBOT
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tame oasis
pls help
tame oasis
ive been staring at the problem for 30 minutes
ocean terrace
let the radius be r. you can write OR in terms of r. then use Pythagoras on the triangle ORS to form an equation with r and solve for r.
tame oasis
doesnt pythagoras need to be a right angled triangle
or is that another one of my misconceptions
ocean terrace
ORS is a right angled triangle.
eternal wing
No it isn't
vocal escarp
ORS is a right angled triangle.
OTS can be
ocean terrace
OH. it's T not R. oops.
ocean terrace
qwq. sorry.
ocean terrace
is it just radius - 8
yes.
vocal escarp
is it just radius - 8
No
clear lodge
start by what you know.
The radius of the circle is r
OR, OP and OS are all the radius of the circle, r
tame oasis
yes
clear lodge
you also know that RS = 20cm, and that RT = TS
with that, you can get both RT and TS
you know that OP = r = OT + TP = OT + 8cm
With that, you can get OT as a function of r
Now you can form either right-triangle, OTR or OTS, with only one unknown: r. You can solve that with pythagoras.
is this enough information?
topaz sinewBOT
topaz sinewBOT
Available help channel!
frank pulsar
What is sinx equal
topaz sinewBOT
What is sinx equal
frank pulsar
<@&286206848099549185>
rustic cedar
!15min
topaz sinewBOT
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.
coarse pewter
What is sinx equal
!step
Right.
What's your working?
Where are you stuck specifically?
woeful drift
!status
topaz sinewBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
coarse pewter
Ah. Thanks, both of you.
frank pulsar
1
flat kindle
you can factor
frank pulsar
i did but im stuck
frank pulsar
i will wait a bit
i factored up side
But cant the down side
how can i factor the down side
how can i factor downside @flat kindle
<@&286206848099549185> my helper is offline rn
frank pulsar
What is sinx equal
.
topaz sinewBOT
@frank pulsar Has your question been resolved?
frank pulsar
Pff <@&286206848099549185>
topaz sinewBOT
@frank pulsar Has your question been resolved?
topaz sinewBOT
@frank pulsar Has your question been resolved?
frail sundial
topaz sinewBOT
frail sundial
would anyone be able to compute the spectral norm for An and also do part (b). So i can check if i have it right please
frail sundial
show your work
:(
it’s long and i feel like i went wrong somewhere
@odd pagoda <@&286206848099549185>
<@&286206848099549185>
topaz sinewBOT
@frail sundial Has your question been resolved?
topaz sinewBOT
@frail sundial Has your question been resolved?
odd pagoda
right I forgot how fucking awful spectral norm is
right now your b doesnt show anything
the frobenius norm is basically as if you wrote your matrix as a vector in R^4 and then the normal distance there
if you did that with your vector, where would it converge to
frail sundial
if you did that with your vector, where would it converge to
root of 3 no?
odd pagoda
a vector should converge to a vector. not to a number
and your matrices should converge to a matrix
prime path
Hello all, I have a question in which I need to find the permimeter of a teardrop shape, any help would be greatly appreciated as I keep messing up even though I know the basics of how to solve it.
topaz sinewBOT
Hello all, I have a question in which I need to find the permimeter of a teardro...
neon iron
Hello all, I have a question in which I need to find the permimeter of a teardro...
Split the teardrop into simpler shapes
prime path
I believe I have figured it out, I was looking through my notes and saw that I had rounded numbers throughout the calculation which resulted in a difference.
neon iron
you might be messing up with the height of the triangle
frail sundial
and your matrices should converge to a matrix
so An would converge to a matrix??
i’ve no clue how it can do that
neon iron
I believe I have figured it out, I was looking through my notes and saw that I h...
yeah, don't use numbers
use variables
no rounded required
odd pagoda
so An would converge to a matrix??
each entry converges "separately". open another channel if you have more questions
topaz sinewBOT
topaz sinewBOT
Commands:
clopen: .close, .reopen, .solved, .unsolved
consensus: .poll
factoids: .tag
help: .help
Type .help <command name> for more info on a command.
neon iron
.solve
topaz sinewBOT
Available help channel!
burnt ocean
Does this look correct
topaz sinewBOT
Does this look correct
burnt ocean
Wait okay so context:
The bottom one is supposed to pass though the top point , perpendicular, and through the origin
rose sierra
burnt ocean
Yes
But I’ve been wrong before LOL
Find the slope of the line joining (2,7) (-8,7)
I got -0/10
Is that.. right??
And this
Looks right but I’m not sure
topaz sinewBOT
@burnt ocean Has your question been resolved?
nocturne obsidian
Find the slope of the line joining (2,7) (-8,7)
have you learnt what the gradient and the y-intercept is yet?
Plotting will help but i won't recommend
burnt ocean
have you learnt what the gradient and the y-intercept is yet?
No
burnt ocean
- C??
topaz sinewBOT
nocturne obsidian
huh
burnt ocean
.reopen
topaz sinewBOT
✅
burnt ocean
We talking here dawg
nocturne obsidian
@burnt ocean are you finding the intersection between two lines ?
burnt ocean
Just the like that joins the two points together
topaz sinewBOT
@burnt ocean Has your question been resolved?
tulip juniper
topaz sinewBOT
empty sail
,rotate
thorny flameBOT
tulip juniper
im sorry if its a little messy
tulip juniper
Does it need to be simplified?
usually webwork (the homework website) takes the answer as is even if its not simplified
but if you also dont see any issue with my work i can try simplifying
empty sail
but if you also dont see any issue with my work i can try simplifying
How did you do this?
It's $\sqrt{(-6 Cos[t]^2 - 6 Sin[t]^2)^2 + (6 Cos[t]^2 + 6 Sin[t]^2)^2}$, correct?
thorny flameBOT
dldh06
tulip juniper
yeah
empty sail
Then I see the probelm
tulip juniper
ohh what is it?
empty sail
You did $(a + b)^2 = a^2 + b^2$, right?
thorny flameBOT
dldh06
empty sail
Do you see now?
topaz sinewBOT
topaz sinewBOT
Available help channel!
spare marsh
hi, how do i do part a?
topaz sinewBOT
hi, how do i do part a?
spare marsh
my issue is that
wouldn't the set S just be the same as T
since we have to show they arent
obviously it wouldnt
but im not sure how to define S then
would S = {y | y = 4m + 2, m is a member of Z} work?
acoustic pecan
does 7 belong to T?
spare marsh
nope
acoustic pecan
T cannot then be S
acoustic pecan
would S = {y | y = 4m + 2, m is a member of Z} work?
this has no odd numbers
spare marsh
but hjow do i define the set S
spare marsh
this has no odd numbers
acoustic pecan
i dont know what the predicate method is
i would define s to be the set of all integers x st x mod 4 !=0
but im not sure if thats what youre to be doing?
spare marsh
would S = {y | y = 4m + 2, m is a member of Z} work?
predicate is just in this format
Set = {members of set | limitations of members}
thats it
spare marsh
would S = {y | y = 4m + 2, m is a member of Z} work?
so here S is the set, y are the members(where y = 4m + 2 ), and the limitations of m are given so u can calculate each member if u wanted to
spare marsh
i dont know what the predicate method is
i would define s to be the set of all i...
what is st?
acoustic pecan
such that
acoustic pecan
$|x\not\equiv 0$ (mod 4)}
thorny flameBOT
AℤØ
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
acoustic pecan
you could maybe write $4\not\vert x$
thorny flameBOT
AℤØ
acoustic pecan
thats a bit messy in format but it means 4 doesnt divide x
spare marsh
okay
acoustic pecan
you might get away with it
spare marsh
its just an exercise sheet anyways ill ask my prof if its fine
but thanks for helping
.close
hollow cave
topaz sinewBOT
hollow cave
May someone please help me with this question.
It's a 2 mark question, says to use geometry, I don't know what I'm doing and it's getting me annoyed
topaz sinewBOT
@hollow cave Has your question been resolved?
hollow cave
<@&286206848099549185>
hollow cave
.close
fleet dagger
hollow oracle
,rotate
thorny flameBOT
hollow oracle
We’re given two separate functions. Which one do we evaluate for x values less than or equal to 2?
fleet dagger
4?
fleet dagger
We’re given two separate functions. Which one do we evaluate for x values less t...
3?
hollow oracle
The 2 functions are the pair at the top
fleet dagger
Oh uh also idk how to do that tbh
fleet dagger
The 2 functions are the pair at the top
My teacher tired explaining to me and I still don’t get it
hollow oracle
My teacher tired explaining to me and I still don’t get it
does this help you understand the graph of this piecewise function?
fleet dagger
Yes
hollow oracle
(x-1)/(x^2-1) is the green graph on the left
notice it gets cut off on the right side at x=2
understand this ^ ?
fleet dagger
Kinda
topaz sinewBOT
@fleet dagger Has your question been resolved?
topaz sinewBOT
@fleet dagger Has your question been resolved?
topaz sinewBOT
@fleet dagger Has your question been resolved?
burnt pilot
topaz sinewBOT
burnt pilot
thorny flameBOT
aaaaaaaa
topaz sinewBOT
Available help channel!
solid swallow
What am I doing wrong here. With limits don’t you plug what the limit is approaching into the equation?
Given:lim as t approaches 2 of [(3t)i+(2/t^2-1)j+(1/t)k]
Note: [] are parentheses, written like this so it’s easier to read
I got <6, 2/3, 1/2>
Apparently the answer is <1,1,1>
topaz sinewBOT
What am I doing wrong here. With limits don’t you plug what the limit is approac...
thorny flameBOT
gritty trout
What am I doing wrong here. With limits don’t you plug what the limit is approac...
seems like whoever wrote the answer is coping. just the first component, the function 3t, definitely does not approach 1 as t approaches 2
and yes, each component is continuous at 2 so you would just plug 2 in to each component
solid swallow
Wait so I’m doing this right? The answer sheet was wrong?
gritty trout
Wait so I’m doing this right? The answer sheet was wrong?
yeah, assuming you wrote everything down right. there's no way the limit can by (1,1,1)
solid swallow
Good to know, thank you. I was super confused on this entire paper honestly
.close
icy carbon
How do I write this as a single fraction?
topaz sinewBOT
How do I write this as a single fraction?
rustic cedar
(arccos(11/14)+arcsin(-1/7))/1
golden mesa
nice
icy carbon
thanks
golden mesa
ok
golden mesa
(arccos(11/14)+arcsin(-1/7))/1
i'll go with this then
you could sin(that) and simplify, then arcsin it back at the end - is what i would've said
icy carbon
ah i see
rustic cedar
you could sin(that) and simplify, then arcsin it back at the end - is what i wou...
you are using trig functions!
icy carbon
then for cos just rewrite
rustic cedar
!!!
golden mesa
i have brought dishonor to the chlamydia name
golden mesa
then for cos just rewrite
what do you mean by this
cinder oxide
topaz sinewBOT
cinder oxide
are both of these lines considered exactly the same?
I was told I that I need to treat integral notation S dx exactly the same way I treat parentheses notation ()
An integral requires the opening S and closing dx to enclose the integrand inside of it
So would the second line be correct, or incorrect in this case?
because somehow the first line is correct and I don't understand that. we just added S to the beginning of the LHS and RHS and didn't add a closing statement at all
cursive thorn
What actually happens is taking the integral with respect to x on both sides, without 'multiplying' by dx first
thorny flameBOT
Jelle
cinder oxide
so if dx is already there, we don't need to add a second dx
in other words, we should never see S (dx)^2 as an integral?
cursive thorn
and the dx's 'cancel' after subbing u = y(x)
well treating dx/dy as a fraction is purely a notational trick, what really happens is different
If you substitute u = y(x), where y is a function of x, then du = y'(x) * dx, but y'(x) is another notation for dy/dx
cinder oxide
well treating dx/dy as a fraction is purely a notational trick, what really happ...
i think this is the most confusing part about this notation. it gets treated as fraction but only sometimes. it's not a fraction the other times
thorny flameBOT
Jelle
cursive thorn
I used u instead of y to try and make it less confusing
cursive thorn
i think this is the most confusing part about this notation. it gets treated as...
If it's gets treated as a fraction there will also be a way without treating it as a fraction
cursive thorn
This was what happened if you integrated both sides with respect to x
which is a perfectly valid operation
thorny flameBOT
Jelle
cinder oxide
oh you did the multiplication of 1/dx to both sides first? and then S dx after? maybe there are a few steps involved here
cursive thorn
Well the equation is y'(x) = x^2, right?
cinder oxide
right
thorny flameBOT
Jelle
odd pagoda
(if you don't want any bounds you can just leave them away in your tex)
odd pagoda
oh desmos gives tex output? til
cursive thorn
Wait, did the original question have dy and dx on different sides?
cinder oxide
the cancellation is a trick, but not to be treated as a fraction
yes, the original question is this
am I allowed to multiply both sides by (1/dx)?
cursive thorn
Yeah, well to write the solution down then just put integral signs on both sides
cursive thorn
am I allowed to multiply both sides by (1/dx)?
It's kinda weird, if the equation already has dy and dx on different sides, then just leave it that way
cinder oxide
**Jelle**
i'm trying to reach the same equation you wrote here
with all of the steps involved
cursive thorn
I thought the equation you started with was dy/dx = x^2
cinder oxide
so this is wrong?
odd pagoda
if you want to do it properly then dont start with something that is already an abuse of notation
cinder oxide
if you want to do it properly then dont start with something that is already an ...
multiplying both sides by 1/dx is abuse of notation, I am assuming?
odd pagoda
yes. aswell as this
odd pagoda
it's a very common and convenient abuse of notation. its fine to do. as long as you know that actually it is abuse of notation
cinder oxide
it's a very common and convenient abuse of notation. its fine to do. as long as ...
I am hearing way too much "abuse of notation", it is rather shocking to me
this is normal in math at this level?
odd pagoda
well generally when doing stuff with dy/dx
doing it properly is more effort and has the same result
so why bother
cinder oxide
lol, because it's confusing af for those new to it wondering what is actually going on here
haha.. this course has been really frustrating with the notation
hopefully with more practice I will finally see what is going on
odd pagoda
well its the lesser of two evils basically. either do the abuse of notation which is easier, or do the harder way which more people might not understand
cinder oxide
and a lot of times the prof will just write it bad notation exepct us to follow
like one day 1, it's already abuse of notation, "just do it this way"
but maybe that's normal when learning integrals for the first time
i can see why they teach derivatives first. integrals are definately a step up due to this abuse of notation
has anybody come up with a better way to use notation for integrals?
or is it too late to change that now
it kinda sounds like there's no way around that. but once you get it, you get it
odd pagoda
I would actually say that the notation is good. precisely because you can do these sort of abuse of notations and get away with them
very convenient
which is a good aspect of notation
cinder oxide
"The student of mathematics has to develop a tolerance for ambiguity. Pedantry can be the enemy of insight." - Gila Hanna
Pedanty: excessive concern with minor details and rules.
this is why my profs never really seem to care when their answers are off, or notation messy/unclear on the board. students will try to correct and they will shrug it off saying "minor details, the method is still there"
it's almost like they are tooo comfortable with ambiguity
at their level they have probably seen it a million times, but to fresh eyes, we are struggling to follow most of the time
I really appreciate Professor Leonard for minimizing ambiguity as much as possible. Well laid out lesson plan, prepared, ready to go
Very clear what's going on, step by step
99% of my university math profs are just too lazy to teach effectively imo. i look around sometimes and everyone looks so damn confused
/ end rant
odd pagoda
well teaching isn't exactly the reason someone becomes a professor
cinder oxide
well teaching isn't exactly the reason someone becomes a professor
and they always give "Rate my work" big piece of paper to fill out during an exam, I just want to throw it away and stop wasting my time during an exam
odd pagoda
lol during the exam
cinder oxide
it's rediculous
odd pagoda
we just have it in one of our last classes
cinder oxide
How it should be
topaz sinewBOT
@cinder oxide Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
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supple sun
What can I do to find the maximum value of $\sqrt[n]{n}$ for $n\in\mathbb{N^*}$ ?
topaz sinewBOT
What can I do to find the maximum value of $\sqrt[n]{n}$ for $n\in\mathbb{N^*}$ ...
thorny flameBOT
deus ex machina
torpid matrix
set derivative equal to 0
supple sun
But what would be the derivative ?
thorny flameBOT
torpid matrix
you should be able to differentiate that (if you have taken calc)
topaz sinewBOT
topaz sinewBOT
Available help channel!
heady mulch
hey
coral torrent
hi can anyone verify if this is correct?? it's polynomial functions. thank you !!
topaz sinewBOT
hi can anyone verify if this is correct?? it's polynomial functions. thank you !...
@coral torrent Has your question been resolved?
ornate solar
This complex numbers question has me stumped
Find all the numbers z, real or complex, for which z^2=2z*
(z squared = 2 z conjugate, not sure if there are different notations I should be using)
topaz sinewBOT
This complex numbers question has me stumped
Find all the numbers z, real or com...
odd pagoda
write z as a+bi
ornate solar
write z as a+bi
I attempted this, expanded all the brackets and was left with a^2 - b^2 + 2abi or something. I’ll send my working in a minute
ornate solar
This is my working and where I kinda got stuck
Can someone give me a slight nudge in the right direction
topaz sinewBOT
@ornate solar Has your question been resolved?
topaz sinewBOT
@ornate solar Has your question been resolved?
topaz sinewBOT
@ornate solar Has your question been resolved?
edgy cosmos
How do I do this type of question? Is a table of z values 100% required?
tough cargo
It's a normal distribution so if the question is no calculator then yes
if yes calculator then possiblt yes also tbh calculaters are kinda weaksauce
But some calculators have functions for this sort of thing
Rly depends
If it's yes computer even
edgy cosmos
if yes calculator then possiblt yes also tbh calculaters are kinda weaksauce
So if I’m given this table how would I solve?
tough cargo
u calculate the z value
Well there is slightly more to it than tbat
So the table gives u for the random variable $Z = \frac{X - \mu}{\sigma}$ the probability that, $P(Z <= z)$. It also only lists such for positive $z$
thorny flameBOT
992qqoloy
tough cargo
To get the probability that $Z<= z$ when $z$ is negative, you need to take advantage of the fact that the normal distribution is symmetric and some basic probability rules
thorny flameBOT
992qqoloy
tough cargo
$P(Z \leq z) = P(-Z \geq -z)$ 😒 just cus that's how inequalities work, then $P(-Z \geq -z) = 1 - P(-Z \leq -z)$ cus the event that Z is a number at all number can be divided up into those almost mutually exclusive events (then cus Z is continuous <= is the same as ), and so their probabilities add up to 1
thorny flameBOT
992qqoloy
tough cargo
So basically what that means for u is
In this problem the z value is gonna be negarove
Negative
So when u find the $z$ value, take its absolute value, consult the table, and then subtract that from $1$
thorny flameBOT
992qqoloy
tough cargo
But if the $z$ value is positive then u can just directly consult the table if the question is "probability is less than x (seconds/meters/unit/etc.)
thorny flameBOT
992qqoloy
topaz sinewBOT
@edgy cosmos Has your question been resolved?
unreal oracle
topaz sinewBOT
neon iron
seconds
neon iron
its 56 degrees 19 minutes
neon iron
what?
unreal oracle
dw
neon iron
?
unreal oracle
oh nvm i had it all wrong
i thought u had to convert the whole angle into minute / seconds
its just used as exxtras
when u have an angle that is some decimals
thats whe nu us e it
there a button on the calc that does it for me anyways
ashen iris
How did i get 11 wrong
topaz sinewBOT
How did i get 11 wrong
ashen iris
<@&286206848099549185>
topaz sinewBOT
<@&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.
topaz sinewBOT
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Available help channel!
upper crow
how can I find the domain and range of y= 2x - 4
topaz sinewBOT
how can I find the domain and range of y= 2x - 4
long dawn
What does the graph of that function look like?
upper crow
Question d)
still urchin
The domain is all the x coordinates of the points on the graph and the range is the y ones
topaz sinewBOT
@upper crow Has your question been resolved?
analog quest
Could I get some pointers on how to prove the lemmas. IM SO LOST
thorny flameBOT
Statufi
analog quest
I know they are 1 <= cd <= a and b but I know know how I would go about to prove that . Is the proof calculation based or sentences?
topaz sinewBOT
@analog quest Has your question been resolved?
analog quest
Why am I so stupid
topaz sinewBOT
@analog quest Has your question been resolved?
topaz sinewBOT
@analog quest Has your question been resolved?
cinder oxide
