Hero472
#help-27
woven radishBOT
visual spire
something its wrong cause is divergent
long fog
something its wrong cause is divergent
That's possible
visual spire
well yes
long fog
,w d/dx (x³+y²)/(x+y²)
woven radishBOT
long fog
Yeah right
visual spire
well thanks for the help
long fog
You're welcome
visual spire
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sick thunder
In △ FGH, ∠F = 42° and ∠H = 70°. FH = 60 CM. Draw △ F′G′H′ under the same condition as △ FGH.
Leave all construction marks as evidence of your work, and label all side and angle measurements.
what is the measurement of the side F'G' ?
Group of answer choices
6.2 CM
4.9 CM
8.2 CM
4.3 CM
devout snowBOT
In △ FGH, ∠F = 42° and ∠H = 70°. FH = 60 CM. Draw △ F′G′H′ under the same condit...
whole parrot
quasi dragon
In △ FGH, ∠F = 42° and ∠H = 70°. FH = 60 CM. Draw △ F′G′H′ under the same condit...
what do you have so far
devout snowBOT
@sick thunder Has your question been resolved?
neat spire
devout snowBOT
neat spire
Ok so I plotted 2 points but I dont know where the asymptote should be
neat spire
i put the function in a calculator and went to the table and plotted 2 points
but i dont know the asymptote
bold prism
forget the asymptote fix your graph first 🤦
x=-1 isn't in the domain of log(x-2)
finding the domain first is a good step
what is the domain of f?
neat spire
all i know is i have to see the graph but how do i put log with the subscript 3 in desmos?
bold prism
if you just see the graph what is the point of the exercise?
but if you want to idc, for subscript 3 do log_3
neat spire
ok ty
devout snowBOT
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subtle trout
- On the occasion of his receiving second Nobel prize, Dr. Linus Pauling, the chemist, remarked that, while the chances of any person in the world receiving his first Nobel prize were one in several billion (the population of the world), the chances of receiving the second Nobel prize were one in several hundred (the total number of living people who had received the prize in the past) and that therefore it was less remarkable to receive one's second prize than one's first. What is the flaw in Professor Pauling's joke?
devout snowBOT
1. On the occasion of his receiving second Nobel prize, Dr. Linus Pauling, the c...
devout snowBOT
@subtle trout Has your question been resolved?
subtle trout
O alr
subtle trout
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simple sonnet
number 4 please. I understand that revenue=(sales)(price) so I get 52000= (2.00+0.05x)(6500-5x)
devout snowBOT
number 4 please. I understand that revenue=(sales)(price) so I get 52000= (2.00+...
simple sonnet
I just dont know how to get the number of pucks sold and the price per unit now.
I cant find anything in my notes like it and quadratic things like this are scarce online
devout snowBOT
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simple sonnet
<@&286206848099549185>
man what the
45 helpers and no one knows what to do with this
Can someone at least get to this within 10 hours
Some help is better than none
devout snowBOT
@simple sonnet Has your question been resolved?
devout snowBOT
How is this wrong
supple knot
I've never seen a 10 being a stem
supple knot
Oh yea try that
rough rune
Because
Slowest
Cant i already finished the test lmao
I jyst wanted to know why it was wrong
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devout snowBOT
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astral light
How do I sketch this regions in the complex plane?
devout snowBOT
How do I sketch this regions in the complex plane?
astral light
w1 is given but z is not
Now my question is should I treat it like an equation and put z on one side and the contents of w1 on the other or is there something else?
astral light
z + 1 + 1i < 1
If i substitute the w1 with it's values I get 1 + 1i
But it doesn't make much sense how can the real part of w1 be 1 and imaginary 1 and be less than 1 😅
normal crater
Do you understand the loci for that expression
spice oyster
The inequality has absolute-value bars, meaning magnitude... its $|z+1+i| < 1$. Do you know what the magnitude of a complex number is?
woven radishBOT
daveamayombo
astral light
square root of a^2 + b^2?
spice oyster
Ya. So if $z = a + bi$, what is $z + w_1$, and more importantly what is its magnitude?
woven radishBOT
daveamayombo
astral light
Should that just be sqrt(1^2) which is one?
If I understand correctly you have to substitute w1 and its values and then get z so you can get its magnitude
spice oyster
Nope, not quite. Here's a start -- in this problem, $w_1$ is like a constant. It's just defined to be $w_1 = 1 + i$. So if $z = a + bi$ is any other, completely arbitrary complex number, we would write $z + w_1 = (a + bi) + (1 + i) = (a + 1) + (b + 1)i$.
woven radishBOT
daveamayombo
normal crater
It means the distance from the point -1 -i is less than 1
What does that mean if you represent it on an argand diagram
What do you see
astral light
I am sadly lost here. I know that the argand diagram is the picture I sent. But if I understand you correctly it means that - iy and +iy are mirrored?
normal crater
No
Right so z is just a complex number
a +bi
w1 tells you how z is ofset
From the origin
Then the modulus less than 1 means that that is all of the complex numbers that are less than 1 away from -1-i
So what shape is that
devout snowBOT
@astral light Has your question been resolved?
fathom pewter
Does someone know how would one find the dimension of W ?
devout snowBOT
Does someone know how would one find the dimension of W ?
restive river
(that's dim of the matrix space, not dim of a subspace)
wouldn't it be 1 as there's only 1 degree of freedom?
fathom pewter
In this case the degree of freedom is a ?
wooden veldt
yep, a good thing to do when trying to determine the dimension of a space is finding a basis
fathom pewter
Right, so if we had something like a + b = 0
we would be able to have a higher dimension
wooden veldt
more like if your matrix was [[a,a,-b],[b,0,0]] then W would be 2 dimensional
fathom pewter
more like if your matrix was [[a,a,-b],[b,0,0]] then W would be 2 dimensional
Right, that make senses x) Usually that's what they end up looking like so that's why I got confused this time x)
Thank you !
.close
restive river
x
restive river
If x-y=5 and xy=10 then what's (x^2+y^2)?
restive river
10
restive river
yes
restive river
x=y+5
restive river
how
restive river
yes
normal crater
so replace the x with what you found earlier
restive river
what does that mean
normal crater
if you don't understand this maybe you need to do a little research on algebra first
I suggest you look at khan academy
they have great resources on fundamentals of algebra
and algebraic manipulation
restive river
what's the answer though
or wait
when i solve something on it
i will dm you
can you send me their best video for this equation
devout snowBOT
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wintry vine
While dividing we can split the dividend and then solve according to distributive property like for ex- 72/2 is same as (70+2)/2. Why does this thing don't apply for divisor why we cannot split divisor?
devout snowBOT
While dividing we can split the dividend and then solve according to distributiv...
@wintry vine Has your question been resolved?
restive river
While dividing we can split the dividend and then solve according to distributiv...
Imagine you had 72 apples, dividing it by 2 could mean that you get rid of 36 apples, or it could mean that you cut each apple in half. Now, think about it, what's the difference between cutting each of the 72 apples in half and cutting each of the first 70 apples in half then cutting each of the remaining 2 apples in half? It's the same thing. As for the divisor... the same logic just can't be applied
Like, if you had 40 apples and wanted to divide them by 22
Would you think to just divide each apple up so that you only keep one half plus one 20th, since 2+20=22? No, that just isn't the same as divide an apple in 22 slices and only keeping one, you'll end up with a lot more apple
This is honestly the best explanation I can give, but feel free to ask questions
wintry vine
Would you think to just divide each apple up so that you only keep one half plus...
I understood thx
restive river
Please help me to solve this:
devout snowBOT
Please help me to solve this:
devout snowBOT
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restive river
My question is how can we differentiate $$\sin^{-1}\left[\frac{5x + 12\sqrt{1-x^2}}{13}\right]$$?
devout snowBOT
My question is how can we differentiate $$\sin^{-1}\left[\frac{5x + 12\sqrt{1-x^...
woven radishBOT
Contour
restive river
I tried substituting $x = \sin(\alpha)$ and $\frac5{13}$ as $\cos(\beta)$.
woven radishBOT
Contour
restive river
Then I got $\sin^{-1}\left[\sin(\alpha + \beta)\right]$.
woven radishBOT
Contour
restive river
How to go further about differentiating this? I mean how to even simplify it?
copper flower
My question is how can we differentiate $$\sin^{-1}\left[\frac{5x + 12\sqrt{1-x^...
chain rule
restive river
How can we make sure that $(\alpha + \beta)$ lies in principal branch of sin(x).
woven radishBOT
Contour
copper flower
you're making this more complicated than it needs to be
restive river
chain rule
I know that, but I want my answer in the form of case wise function.
turbid locust
My question is how can we differentiate $$\sin^{-1}\left[\frac{5x + 12\sqrt{1-x^...
the easiest way would probably be implicitly
sin(y) = (5x + 12sqrt(1-x^2))/13
so cos(y) dy/dx = d/dx (5x + 12sqrt(1-x^2))/13
turbid locust
ye?
restive river
ye?
I don't want to get some cumbersome results. My book shows that answer is 1/sqrt(1-x^2). But I'm not quite satisfied with this answer.
turbid locust
I don't want to get some cumbersome results. My book shows that answer is 1/sqrt...
are you sure?
turbid locust
d/dx (sin(x)) = 1/sqrt(1-x^2)
restive river
Here's the solution of book
https://www.desmos.com/calculator/qynvdhwgsb
and see here
Book's answer is correct only for the interval (-1 , 5/13).
Derivative of given function = 1/sqrt(1-x^2) for (-1, 5/13).
and = -1/sqrt(1-x^2) for (5/13, 1).
Derivative is undefined at 5/13.
Or in the form of case wise function,
$$\frac{d}{dx} f(x) = \begin{cases}\frac{1}{\sqrt{1-x^2}} , x \in (-1, \frac{5}{13})\ -\frac{1}{\sqrt{1-x^2}}, x \in (5/13, 1) \\text{Else \ undefined.} \end{cases}$$
woven radishBOT
Contour
turbid locust
not sure then
restive river
**Contour**
I'm sure about this answer but having some trouble in solving the inverse trig. function.
Anyways <@&286206848099549185> , may I have some help?
devout snowBOT
@restive river Has your question been resolved?
devout snowBOT
@restive river Has your question been resolved?
signal flame
I tried doing something but I don't know what to do
||(i know the last 2 lines are obviously wrong)||
||new to 11th grade trigonometry so uh help||
devout snowBOT
I tried doing something but I don't know what to do
||(i know the last 2 lines a...
restive river
You could use $\sin^2x=1-\sin x$ and keep substituting into the largest power of $\sin$
woven radishBOT
Toby
restive river
yeah, just keep doing what you were doing, But do it methodically starting from the largest power
signal flame
restive river
the largest power is $\sin^6x=\sin^4x-\sin^5x$. substitute this in and simplify, then you will find that the new largest power is $\sin^5$
woven radishBOT
Toby
restive river
We have $\sin^6x+3\sin^5x+3\sin^4x+\cdots$ (lower order terms). Substituting, we get $$(\sin^4x-sin^5x)+3\sin^5x+3\sin^4x+\cdots= 2\sin^5x+4\sin^4x+\cdots$$. Now we have gotten rid of the 6th power term, so let's do the fifth: $\sin^5x=\sin^3x-\sin^4x$. Substituting, $$2\sin^5x+4\sin^4x+\cdots=2(\sin^3x-\sin^4x)+4\sin^4x+\cdots\=2\sin^4x+2\sin^3x+\cdots$$ etc
woven radishBOT
Toby
signal flame
How sin4-sin5? 
restive river
multiply $\sin x+\sin^2x=1$ by $\sin^4 x $ on both sides, then rearrange
woven radishBOT
Toby
signal flame
thanks
restive river
yw!
signal flame
I'm gonna try this now and if I get stuck I hope I can count on you again 
restive river
sure thing :)
signal flame
I think I messed up somewhere...
restive river
,rotate
woven radishBOT
restive river
I think you are cancelling out too many things
restive river
no worries, gl
devout snowBOT
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feral dawn
devout snowBOT
feral dawn
how do we solve this?
woven radishBOT
Toby
feral dawn
I'm still stuck
wait nvm
I do get it
but one question
how do we get 7,6,5,-4
I understand we get 3,4,5,-4 and 4,4,1,-3 by adding
ohhh
icic
I get it now
kinda weird though
simple than it looks
restive river
(0,2,1,-3)+(3,2,4,-1)+(4,2,0,0)
restive river
yw!
feral dawn
.close
restive river
Can anyone tell me how do you divide 40/0.58
devout snowBOT
Can anyone tell me how do you divide 40/0.58
restive river
Is it possible to divide it with decimal
maiden bridge
Is it possible to divide it with decimal
divide 4000/58
restive river
do you know how to represent 0.58 as a fraction
Its 58/100?
maiden bridge
yeah
restive river
How did you get 4000
winter patrol
multiply numerator and denominator by 100
to work towards simplifying the fraction
green nymph
Its 58/100?
Simplify it
winter patrol
and then you con consider consider common integer factors to simplify it further
and then if you want the decimal representation you can perform long division
green nymph
Divide numerator denominator with 2
winter patrol
note that you "could" perform long division for an unsimplified fraction, it'll just be more painful
restive river
Ok so heres wut i did first i did 58/100 which is 29/50?
green nymph
and then you con consider consider common integer factors to simplify it further...
It was asked to represent 0.52 in fraction form aren't you just doing the same that has already been done, once again?
Yes that's it
29 is prime number
maiden bridge
you can write 0.58 as 58/100
=> 40/0.58 = 40/(58/100)
The 100 will get resiprocaled
green nymph
Now when you divide 29 by 50 you actually get 0.58
maiden bridge
you can write 0.58 as 58/100
=> 40/0.58 = 40/(58/100)
The 100 will get resiproca...
=>4000/58
winter patrol
multiplying numerator and denom by 100 is more efficient
green nymph
you can write 0.58 as 58/100
=> 40/0.58 = 40/(58/100)
The 100 will get resiproca...
Where'd you get that 40 from?
maiden bridge
multiplying numerator and denom by 100 is more efficient
its the same thing
restive river
you can write 0.58 as 58/100
=> 40/0.58 = 40/(58/100)
The 100 will get resiproca...
Okeh i'll try this
green nymph
You just can't take it all of a sudden
winter patrol
less clunky
maiden bridge
Where'd you get that 40 from?
its in the question
green nymph
If you take it in numerator you also have to take it denominator
winter patrol
avoids introduction of more fractions than needed
maiden bridge
the question is 40/0.58
maiden bridge
avoids introduction of more fractions than needed
yeah that method is better but I was just explaining the reason behind multiplying
restive river
4000/58 i got lol
Now i need to do this
58/100*40 i did which ended up on 58/4000
This is correct tho right....
I'll solve the rest
restive river
.
winter patrol
40/0.58 = 4000/58 not 58/4000
winter patrol
but you didn't flip it
restive river
40/0.58 = 4000/58 not 58/4000
Ouh thats what i did wrong
restive river
but you didn't flip it
;----; don't remind me of my idiocy
But yes i got the answer
That is
68.96
:DDDD
winter patrol
if you were to convert 0.58 to a fraction
you'd have 40/(58/100), flipping gets you
40 * 100/58 = 4000/58
restive river
Yes thats wut i thought of doing
winter patrol
did you get that by hand?
restive river
But i did in reverse
restive river
did you get that by hand?
Yep
winter patrol
that's not rounded properly
restive river
If i round 68.96 the final answer would be 69
So ye
I can round it up
I left it on the divison
winter patrol
that wasn't really my point
restive river
Wait i'll show u
restive river
that wasn't really my point
:D
winter patrol
the point that i'm trying to make is that there are more digits after the 6
and if you want to round to two decimal places,
you'd need to consider the digit after the 6 to see whether it stays as 6 or gets rounded up
restive river
I see, but my calculation isnt wrong is it......
I only needed the answer 68.96
Cause thats what in my buk
It had
winter patrol
...
restive river
So i was trying to get that answer
winter patrol
the book is bad
restive river
;------------------;
winter patrol
,calc 4000/58
woven radishBOT
Result:
68.965517241379
Seeee
winter patrol
rounding to 2dp properly
since the digit after the 6 is a s 5, you should round up
the correct value to 2dp should've been 68.97
lime swift
The distance between the centers of two circles of radii 10 and 17 is 9. A triangle with sides 10,17,and 9, passes through which three points?
- The center of the large circle, the center of the small circle, and the point collinear with these two on the large circle.
- The points on the external tangent to these two circles, and the big circle's center
- The center of the large circle, the cent of the small circle, and a point common to both circles
- The two intersection points of the two circles, and the center of the big circle
devout snowBOT
The distance between the centers of two circles of radii 10 and 17 is 9. A trian...
lime swift
<@&286206848099549185>
devout snowBOT
@lime swift Has your question been resolved?
gleaming socket
Draw the thing
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lime swift
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devout snowBOT
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restive river
I need help with a exercise of physics
devout snowBOT
I need help with a exercise of physics
cyan fossil
I need help with a exercise of physics
this is not physics server
restive river
okay
wide relic
physics is just applied mathematics tho
sharp viper
I agree!
supple knot
physics is just applied mathematics tho
this is a moot point
supple knot
I need help with a exercise of physics
just ask your question in terms of math and i'm sure someone will be able to help
wide relic
this is a moot point
yeah i know but in common cases maths helps you a lot with physics questions
merry seal
I think as long as the formulas are given physics problems are maths problems
restive river
Okay thanks
Let me explain
we usually $$ FT = sqrt{Fa^2+Fp^2+2 cdot Fa cdot Fp cdot Cos α }# $$
woven radishBOT
𝔸𝕝𝕝 𝟚 𝕥𝕙𝕒𝕥
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
merry seal
$FT = \sqrt{F_a^2 + F_p^2 + 2 \cdot F_a \cdot F_p \cdot \cos \alpha}$
this?
woven radishBOT
Doggo
merry seal
seems like law of cosines with a plus
restive river
$$ FT =\sqrt{Fa^2 +Fp^2 -2 \cdot Fa \cdot Fp \cdot cos \alpha}$$
woven radishBOT
𝔸𝕝𝕝 𝟚 𝕥𝕙𝕒𝕥
restive river
This is my problem, with this you can found the value of a force that is Fa + Fp
My problem is that always the formula is $$FT =\sqrt{Fa^2 +Fp^2 +2 \cdot Fa \cdot Fp \cdot cos \alpha}$$
woven radishBOT
𝔸𝕝𝕝 𝟚 𝕥𝕙𝕒𝕥
restive river
I dont know why here is -2
merry seal
are you confused about the +2 version or -2 version?
restive river
Yes , because is the unique problem that we did in that way
merry seal
yes as in +2 or -2
restive river
In +2
merry seal
what is the formula calculating exactly?
I assume one of the forces have a negative turning the - from law of cosines into a +
restive river
It calculate the line in the middle
lyric marlin
If you assume that ghosts don't exist, the proposition "some ghosts are terrifying."
Its true
Its False
Sometimes its true sometimes its not
Can be False
All the answers above are false
devout snowBOT
If you assume that ghosts don't exist, the proposition "some ghosts are terrifyi...
lyric marlin
Can someone tell me what he think is the right answer and why?
wooden veldt
I would interpet "some ghosts are terrifying" as "ghosts exist AND some ghosts are terrifying"
lyric marlin
But wouldn't it contradict the first statement?
The first statement being "ghosts don't exist"
left robin
from intuition i would say that the seconds statement implies that ghosts exists, thus contradicting with the first statement
but i dont know
lyric marlin
Like personally, i would have chosen "its false" as the answer
but as you can both guess, its wrong
left robin
ahhh
since ghosts dont exist
you dont know anything about ghosts
so when you say that the statement is false, you imply that no ghosts are terrifying
which you cant know
lyric marlin
wow
it would never have occurred to me honestly
so what answer would you have given?
left robin
well since ghosts dont exist, you can not know that some are terrifying, you can also not know that they are not, you can not know if it ever is true or false
i would say that you can not give any information about the second statement i guess
i dont like the answers haha
but i havent done logic in a long time
lyric marlin
Well to be fair, there was another possible answer: All the answers above are false
(obviously since i didnt put it as possible answer, its considered not correct)
topaz axle
honestly it's false
lyric marlin
Sadly, the correct answer was "Sometimes its true sometimes its not"
But i can't understand why that is the case
topaz axle
complete mystery
lyric marlin
Like how can something be true and at the same time be false?
Well, thanks everyone who tried to solve this mistery
.close
devout snowBOT
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brisk karma
how is 95^x=0,3125?
devout snowBOT
how is 95^x=0,3125?
long kettle
Wdym
brisk karma
how do i solve for x
brisk karma
idk ive never solved when its "^x"
restive river
how do i solve for x
Take log on both sides
Use your calculator to obtain the log values
restive river
so ill just go ahead and wait with that one then
It's very easy to understand. So you might wanna check it once.
brisk karma
yeah ill prob will, but my teacher will prob think im cheating or sum if i learn it
devout snowBOT
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shy fossil
can someone explain chebyshev's inequality in simple terms to me?
shy fossil
i am so confused as to what it tells us
i have tried reading multiple books and articles for its definition
devout snowBOT
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shy fossil
<@&286206848099549185>
supple knot
i have tried reading multiple books and articles for its definition
Share the statement and proof that you want explained here
devout snowBOT
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brisk tide
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@brisk tide Has your question been resolved?
devout snowBOT
true geode
Saying y = f(x) is meant to make it clear that y is a function of x
And when graphing it means that the y axis is Plotting whatever that function is
For every input there is only 1 output
You plug in a number and you get the same answer every time
I don't know of any video like that
main gull
Yes
f(x) means the same thing as y
People use f(x) and y interchangeably
You can use either one whenever you want
f(x) is normally used when when you are denoting an input value, like f(3)
Meaning plug in 3 into the function
No
true geode
Y is more compact while writing
But f(x) you write when you want to make it clear that what your talking about is a function of x
main gull
f(x) is the y value
Where is the k from?
This makes no sense
No one said y = y
f(x) is equivalent to y
As I mentioned, f(x) and y are used interchangeably
No function will use both
It means you can switch between the two notations
y = 3x is the same as f(x) = 3x
true geode
Its like a synonym
Both mean the same thing but you only use one in a sentence
main gull
No
f(x) is a function in terms of x
Meaning x should exist somewhere in the equation
If you wanted resources, look up function notation, that's what the f(x) part concept is known as
I just told you what to look up
No
You will either use f(x) or y but not both
I literally told you what to look up
true geode
Y-k ≠ f(x)
X-k= f(x)
main gull
It's just a notation
When you are writing transformations, you normally use f(x) since you are relating to the original function
Using f(x) helps with readability because people understand f(x) is a function in terms of x, and if you just use y, people will assume it's just some variable
Relax
Not everything needs a why. It's just how math was created
The highest grade possible is based on your capabilities. If you push yourself too hard, you will be mentally exhausted. You need to understand the importance of how to balance life and school
10 hours is overkill, in my opinion
Falling behind doesn't mean push yourself harder to the point of exhaustion
Everyone has a limit to what they can achieve
Being successful doesn't mean you have to cram everything
main gull
Everyone will have an obstacle in life. People will fail and that's how life is.
empty flame
You can study it alone if you want but you don't need to study for 10hrs a day
I am self studying calculus rn and I am in grade 10 moving to 11
But I am not studying for that much
main gull
Then it means you need to take breaks
empty flame
Also try focusing what you are saying is right focus is the most important
The work you are doing in these 10 hrs cab be done in less time if you focus
Half of these 10 hrs is just making u tired
You should take it easy and rest
main gull
That sounds like a personal problem where you should seek medical attention
empty flame
Are these thoughts leading to a lack in your self confidence?
Look man to pass this stage you should stop caring about these thoughts
You should be more confident
I am not saying it's simple
But you should be sure that you can do it
If you keep thinking that I can't do this or I can't pass this then you definitely won't do that
Trust yourself
We all face problems
But you mustn't give up
I don't like the way they teach us math in school which is to memorize too
But even if you or me or anyone don't like it this won't change anything
You should ask and know more about what you are learning
But just don't let this be an obstacle that prevents you from achieving your goal
That's not true
You believe what you are saying man that's why you aren't able to focus
I got first 87% is good
meager rose
what's hindering you from doing so??
empty flame
You can do better if you focus more
Ok what's your ambition
That's a purpose for you to live
main gull
Don't compare to others. Because not everything is a competition. People do better because all they do is study and don't have a proper school/life balance
empty flame
Everyone have there own goals and ambitions
meager rose
what don't you like about it?
everyone goes through pain and suffering, it's not just you
it's better when you understand that there are others out there going through the same problems
there is a lot of great things about life, you just have to keep living to experience them
maybe you just haven't found these so-called "great things"
but you will
empty flame
Also what you get in school isnt the way to measure if someone is smarter than someone else
What makes you smart and great is what you achieve in your future
Many scientists didn't continue studying in school
But they still made it to the top where they added something new to sciences or helped in developing the world
The grade you get in school depends on how much you study or memorize
That's why what you do in the test doesn't indicate what you are capable of doing
School is just a tiny part of life
main gull
@true tangle Anyways this conversation has completely deviated from the original question asked so if you're done with the channel, use .close
empty flame
You pinged the wrong person XD
main gull
Just realized
modern smelt
🤔
empty flame
He pinged you by mistake 😂
modern smelt
i see haha
modern smelt
no problem at all
devout snowBOT
@true tangle Has your question been resolved?
remote hornet
isn't 1^inf indeterminant? how is it 1 then
devout snowBOT
isn't 1^inf indeterminant? how is it 1 then
lone ravine
1^x is always 1
Here we have a “real“ 1. It's not a function, whose limit converges to one, if x goes to infinit, but never exaktly reaches it. If it was the case we couldn't say anything right away about the limit
Like there is huge a difference between the Limits x goes to infinity of 1^x and (1+1/x)^x
stark shuttle
Multiplying 1 by n times would always equal to one, innit?
pseudo basin
Here we have a “real“ 1. It's not a function, whose limit converges to one, if x...
it is a function, it's just constant
lone ravine
You're completely right :/. But the difference should be clear?
pseudo basin
well yes
when we say 1^infty is an indeterminate form this really is shorthand for (function that approaches 1)^(function that approaches infinity)
remote hornet
when we say 1^infty is an indeterminate form this really is shorthand for (funct...
makes sense thanks
so its like (function that approaches 1)^(function that approaches infinity) could have any real value?
,w lim x-> inf (1+1/x)^x
woven radishBOT
remote hornet
really weird 
pseudo basin
it could have any positive real value and in fact it could even diverge to infinity or fail to exist
hidden dragon
I am given a equation
devout snowBOT
I am given a equation
balmy quest
it's not a constant.
when x=1, y=20.5/7, y/x = 20.5;
when x=2, y=18.5/7, y/x = 18.5/14
devout snowBOT
Available help channel!
dusky mesa
find vector d perpendicular to vector c = 4i-3j with a magnitude of 10
proud sonnet
vector d perpendicular to vector c is equivalent to the inner product is zero
opaque garnet
there are infinite solutions to it tho
proud sonnet
try to suppose the vector d = ai+bj , thus 4a-3b=0
and the magnitude of 10 means a²+b²=10²
dusky mesa
there are infinite solutions to it tho
how?
zenith glacier
there are infinite solutions to it tho
they might be looking for a vector in 2d space only
opaque garnet
right
dusky mesa
oh yeah, this is vectors in 2d only
sorry, shouldve specified
so then how do you find the components of vector d
given magnitude
zenith glacier
two vectors $a, b$ are perpendicular iff $a \cdot b = 0$
woven radishBOT
Peppermint Demon
zenith glacier
zamn
woven radishBOT
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opaque garnet
this is for 3d
zenith glacier
💀
opaque garnet
its not very relevant now
zenith glacier
thank you for your contribution
opaque garnet
you can just sub in z=0 and it will still work though
dusky mesa
yerrrr so what about 2d
i havent learnt anything to do with a third component
only y and x
zenith glacier
doing what wifix told should work out
dusky mesa
x^2+y^2=100
proud sonnet
2d vector only has two components
dusky mesa
and dot product = 0
proud sonnet
yeah
dusky mesa
so then
zenith glacier
2 equations, 2 variables, it should be solvable
proud sonnet
you can solve a and b from these two equations
yeah,simultaneous
one is 4a-3b=0 ,another is a^2+b^2=100
and then you get vector d= a i +b j
dusky mesa
ok yeah that makes sense
do you reckon u could help me out with the simlutaneous part too
a bit rusty with this
4a-3b=0
a^2 + b^2=100
i multiply the top by a, and bottom by 4
but then i just get stuck again with 2 variables somehow
4a^2 -3ba = 0
4a^2 +4b^2 = 400
is there smt im doing wrong
proud sonnet
you can get a=3b/4 from the first equation
woven radishBOT
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dusky mesa
what happened in the 9/16y^2 + y^2 line
after that
how did it just become
25/16
?
oh wait right
you factored out y
y^2(9/16 + 16/16) = 100
25/16 * y^2=100
1600/25 = 64
y= +-8
and then you just sub in to x^2+y^2=100 to get x
which is also +-6
opaque garnet
yeh
opaque garnet
your b looks nice
opaque garnet
np
dusky mesa
.close
devout snowBOT