#help-10
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You can get constants out of derivative actions
ah ok
Do you know how derivatives work
Or do you just want an answer
they're separate
none of the variables are related to each other by anything other than that equation
Then just plug in y hat
ok
The rest will act like a normal derivative
so the +c part will just disappear?
Yes
ok give me a minute let me work it out
so im getting -2Uxy(sech^2(Wx+b)) for the first part
like -2y y hat part
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yo
can someone explain this to me
x is 20 because log 6 is same
but how did they get that equation
nvm its just one of the rules
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this is as far as i can get
in ax+bx+c=0 idk what a is and what b is, or how to get them
<@&286206848099549185>
can anyone perchance tell me what a, b and c represent so i can try to solve?
I can help you with that
y = mx + q is your typical formula
move everything to lhs
y - mx - q = 0
whats lhs?
yeah but what about ax+bx+c=0
rearrange as follows
-mx + y - q = 0
compare with ax+by+c = 0
a = -m , b = 1 , c = -q
so if you can solve using mx+q you can move to the ax+by+c form
oh ok
it's the term with no x or y
ok lemme try rq
aight
take ur time
find the derivative of the function
y = 2x^2
y' = 4x
gradient = y'(2) = 8
gradient for normal = -1/y' = -1/8
formula for line:
y - py = -1/8 (x - px)
px = 1
py = 2
y - 2 = -1/8 (x - 1)
y = -1/8x +(-1/8+2)
using previous identity:
a = -m , b = 1 , c = -q
a = 1/8 b = 1 c = -(1/8+2) which is 9/8). so the solution should be 1/8x+y+9/8=0
can you verify it's correct? I'm a bit rusty
what does y' mean
y' is the derivative of the the function
hold on let me double check
oh
I'm silly
I think I found it
find the derivative of the function
y = 2x^2
y' = 4x
gradient = y'(1 (not 2) ) = 4
gradient for normal = -1/y' = -1/4
formula for line:
y - py = -1/4 (x - px)
px = 1
py = 2
y - 2 = -1/4 (x - 1)
y = -1/4x +1/4+2 = y = -1/4x + 9/4
using previous identity:
a = -m , b = 1 , c = -q
a = 1/4 b = 1 c = -9/4 -> 1/4x+y-9/4 = 0 multiply everything by 4 to make it look cleaner = x+4y-9 = 0
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you welcome haha
probably there's a faster way but I only remember these formulas
so like solving without using the y = mx +c form
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could someone please explain this q to me, Im stuck on what to do
if I had to guess it would be (0.8+0.06)/2 but Idk how to explain it in the proper way
@wanton oar Has your question been resolved?
@wanton oar Has your question been resolved?
there are 2 ways this can happen
- they have it and the test is right
- they dont have it and the test is wrong
you find probabilities and add
please do the guessing again, with this new knowledge
I think you meant test is right
i meant test is wrong
so like I have, I should just add? like 0.8*0.1 + 0.06*0.9
that's perfect
okay cool
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Unsure of where to start for this particular problem?
drawing it is usually a safe start
this is pretty improper
Yeah I got a little lazy, let me try and fix it
(I might've drawn it wrong again, I'm terrible at visualizing these things and for some reason it's throwing me off rn)
why have you written "v=4"?
Oh, I forgot to write it as specifically magnitude of v = 4
Fixed it
you should probably write that properly
now what does "magnitude of v = 4" mean graphically?
The size of the vector itself?
on your graph specifically
that's the physical interpretation of magnitude in general
I don't believe I understand the question, sorry. On my graph specifically I would assume it means the size of the vector that I drew, which is 4.
what does "size of the vector" mean?
please indicate on your graph exactly how you're illustrating the magnitude of the vector
ok now we're getting somewhere
what you've illustrated is the magnitude (which means size or length, so you can stop repeating those) of the x-component of the vector, not the vector itself
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Hello!
Can anyone give me a run down of how to solve special right triangles?
Im in geometry and doing a trig unit right now. But I dont really understand how to solve them
pls ping me when you respond btw
it would be more helpful if you described the problem first
btw, can you also explain a 45 90 45 when your done?
alright
thank you
say the shorter leg of a 30-60-90 triangle is x
yeah
the longer leg is $x \sqrt{3}$ and the hypotenuse is $2x$
Gamer Sans The Gamer Skeleton
in a 45-90-45
the leg (both legs are same size) is $x$, and the hypotenuse is (by pythag) $x \sqrt{2}$
Gamer Sans The Gamer Skeleton
wait so how would you solve them after that?
what do you mean
for this one, how did they get 11 for x and 11 square toot of 3 for y?
$x$ is the shorter leg
since (by the ratio) $2x = 22$ (the hypotenuse), $x = 11$
same goes for $y$
Gamer Sans The Gamer Skeleton
ohhh
im kind of getting it
Do you know anywhere where I can get practice problems for this subject?
wait
so for the 45 90 45
actually let me send a screen shot
so both of the legs would be 10 square root of 2 right?
wait so what would that be
like in a whole number form
and no problem lol
or how would i figure that out
wdym by whole number form
dont you have to solve that
no
you only have to solve for x which is $10 \sqrt{2} \cdot \sqrt{2} = 10(2) = 20$
Gamer Sans The Gamer Skeleton
ohhh
by the formula ofc
so for 45 90 45
what if the current x was a number and one of the other sides was x?
like this kinda
btw thx for the help :)
have a math test tomorrow and needed last minute help lol
if the hypotenuse was a set value, then the leg would (taking the ratio opposite way) $\frac{x}{\sqrt{2}}$
Gamer Sans The Gamer Skeleton
the leg would be $\frac{16}{\sqrt{2}} = 8 \sqrt{2}$
pretty much
Gamer Sans The Gamer Skeleton
wait so without a calculator how would I solve that? Just divide 16 by 2?
here's something better:
$\frac{x}{\sqrt{2}} = \frac{x \sqrt{2}}{2}$ is better
Gamer Sans The Gamer Skeleton
wait so how would I solve that? Srry lol. Would I just do 16 square root 2 divided by 2?
yeah
more like $\frac{16}{2} \sqrt{2}$ (by taking the root 2 out of the numerator)
Gamer Sans The Gamer Skeleton
so I would divide 16 by two and find the square root of 8?
divide 16 by 2
multiply that by square root of 2
thats it
and the square root of 2 is just 2 right?
how is $\sqrt{2} = 2$?
by definition that means $2 \cdot 2 = 2$ XD
Gamer Sans The Gamer Skeleton
ok lol
let me practice for one more and see if i get it right
so for this one
hmmm
its a little more complicated here
wait so what would I do?
so
$x$ is the number we depend on
by the ratio (1 : sqrt(3) : 2), $15 = x \sqrt{3}$
$x = 5\sqrt{3}$
Gamer Sans The Gamer Skeleton
texit formatting 
alright
the ratio between shorter leg : longer leg : hypotenuse is
1 : sqrt(3) : 2
15 would be the longer leg
so x would be 15/sqrt(3)
which (by some quick calculations) is 5sqrt(3)
we know x is 5sqrt(3)
by the ratio, y is double that
so y is 10sqrt(3)
ya getting it?
ohhh mostly lol
let me get one more problem to practice with lol
so this one
the hypotenuse is 16
so I would do 16 (sqrt) 2?
16 divided by sqrt(2)
dont forget
which is 8sqrt(2)
wait why is it divided again?
- the hypotenuse is the longest side of a right triangle
- the ratio from leg to hypotenuse is 1 : sqrt(2)
yep
oh ok
thank you for the help!
have a great rest of your day / night!
i think the command is .close
.close
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um
why does it look like a challenge
problem of the week?
how does it take a week
the circle is 9 times larger
it means the circumference is 3 times larger
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i think i know the formula but im not sure how to use it
i thought it was just (1/35)(integral from 0 to 5 integral from 0 to 7 of 5e^y sqrt(x+e^y) dx dy)
@me if you reply cuz im doing other problems tysmmm
you may want to switch order of integration
its easier if you do y first
@lethal ice
but is the setup right?
yeah it looks good
oh ok thanks
ill do that, i always have a hard time knowing which to do first
generally if the first order doesnt work, try the other one lol
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youre welcome
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not sure what part 2 is asking
also why is 3 wrong?
D will be a function of x
ohoh
-5x/6 +1/2
and part 2 is the same but with x coming first and H being a function of y?
but x is a straight line
or maybe not wait
im not sure
i believe H will be the function still yes, in terms of y
should i use the y = -5x/6 +1/2 and solve for x?
can do
i tried that but it said it was wrong
perhaps try putting it for G
youre ok no worriesss
i have another question after this one it's a lot easier i just forget how to set it up
might be able to just use this but swap x and y
unless im tripping
ill try it one sec it loads
nah
i also tried just using the exact same equation lol
think im going out on a limb here
but maybe x=-6y/5+3/5
i tried that it was my first guess 
my computer has 6% i have to return to my room ill be back in a moment
we can abandon this question
oh dear oh dear
g1 was wrong, can you help me find out why?
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how does a second order derivative give us the concavity
how does it work
look at the slopes of the tangent lines
second derivative tells us how fast the rate of change is changing, or how fast the slope is changing
if the slope is increasing, the graph curves upwards, and the second derivative is positive.
if the slope is decreasing, the graph curves downwards, and the second derivative is negative
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I can try
do you have a picture of the problem
Is it like triangles or quadrilaterals
a tip for triangles is that the 3 angles always add up to 180
so if you get a right triangle and it only tells you 2 angles you can use that to get the third
can you send an example problem of something youve done in class recently
youre being too general for anyone to give you anything
yeah
well
well
<@&268886789983436800>
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Hey guys, I am a little confused as to what x is
you mean for the x=...
yes
just rearrange u=1-x, dont overthink it
is that just du?
no
wouldn't du be negative 1? Cuz x is negative?
Yeah right
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i have the answers but not sure how to get to it
its undoing a binomial expansion if youre familiar with those
not entirely, brandnew to the topic
ah, the main thing to look out for are the coefficients
in a
you have 1+3a+3a^2+a^3
the coefficients follow the ncr for n=3
3c0=1 3c1=3 2c2=3 3c3=1
and the r values match the power of a, so one can recognise this as the expansion of (1+a)^3
you know its a + because the sign never changes between terms
np
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100 < 22 + 51 + x
it's pretty easy
Find x
?
Awh shoot you’re right. My b
all good
its alr
@cyan thicket just a question, what grade/level is this
7th grade austrlian
This make it any better?
yep
yes it soes
look, profit is basically the selling price minus the cost
Isolate x and you’re done, Goodluck!
shoot i have 20 mins left
because you have to pay off your debts (your cost) as well.
You probably got it wrong since you were using = instead of > or something similar
thats my question
so as bulbasaur said, the cost is $100
in order to make a profit, the selling price must be larger than the cost--so $22 + $51 +$x must be LARGER than $100
that's what he's answering
ok oh
Just curious could you help me with mine? I’m in help 41
Please do not advertise your help channel or thread in other parts of the server. There are many people who need help, so advertising can quickly turn into spam.
and yes i saw ur question, be there in a sec.
Ah, got it. Won’t do that in the future
so i need to finish this by tomorrow
anyway, as bulbasaur said: that can be expressed as $22 + $51 + $x > $100
that can be simplified into $73 + $x > $100
all g
yes he did
so u got it?
sighs
so u know
this isn't really that hard
okay let's see, i'll explain again.
let's say you have $0: you're broke
yea
now, you make three pots for $100. now, you don't have that money, so you promise to pay the dude who sells u clay and stuff $100 back later out of the money u get from selling the pots
this is cost: the $100 is cost
now you sell two pots for $22 and $51, that makes $73. if you want a profit, that means you want some money LEFT OVER for yourself--so you must sell the third pot so that the total selling price is larger than $100--which is the amount u need to pay
np
U helped me
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Is this the correct channel? When did discord become completely insane? I just have a theory question I dont need help with math homework
Okay I CAN read let me type this out
I was reading about n-body problems and it is stated that the 2 body problem is "solved" and the 3 body problem is "unsolved", which on wikipedia is explained as:
There is no general solution that can be expressed in terms of a finite number of standard mathematical operations.
I remember learning trig and finding out the actual sin cosin and tangent equations your calculator is approximating involve hypothetically infinitely recursive equations.
My question is, what does this really mean? I assume it doesnt mean trig is unsolved, I am just confused about these terms
If this is just a case of wikipedia being wrong that would also figure
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I don't understand the hint, why it says common divisors are less than or equal to n-m, shouldn't it be less than or equal to m? If gcd(m,n) = 1 then less than m
Why should it be that instead?
Common divisors of m,n can't be greater than m if m < n
both of that are true actually
You're right, the gcd can't be greater than m. Although, all it says is that any common divisor is less than or equal to n-m
How's common divisor less than or equal to n-m true though?
np
In fact you can say more:
(if n > m, then) any common divisor of m and n is also a divisor of n-m
In particular gcd(n,m) is less than or equal to n-m
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need some help with 2b.
This is what i have already
but I am not sure about one thing. Is the bird path only describing the x coordinate of the bird when it hits a building? or the horizontal line it flies across and not neccesarily where the bird hits a building?
@lone fulcrum Has your question been resolved?
@lone fulcrum Has your question been resolved?
<@&286206848099549185>
My understanding from the problem description is that a bird path is the horizontal line traveled by the bird, regardless of whether it hits a building.
@lone fulcrum Has your question been resolved?
mmmhh that would make the algorithm quite complicated wouldnt it?
how would i need to change my code?
it is psuedo code btw
Not sure why it would be that complicated. If bird paths only consisted of paths that hit buildings, then the algorithm would never return NIL
Well consider the following scenario, the root of the RB-tree has a x coordinate less then the x coordinate of the path of the bird and a y coordinate smaller than the y coordinate of the bird path
that would mean you would have to search the left and right subtree
The algorithm would be the following:
- Iterate through the redblack tree in order of x (i.e., start with the smallest x and iterate upwards).
- In every node, check if bird y >= node.y: if so, return the node and delete it from the tree.
- If after iterating through the entire tree, no building is hit, return NIL.
Looking at your pseudocode, this is already what you had in mind
Does this take into consideration that the x coordinate of the birdpath could be less than the x coordinate of the building?
Presumably you would have the bird travel as you do the search. The bird travels from (0,bird.y) to (bird.x, bird.y). So, in every iteration, update the bird.x along with the node
Actually, maybe don't update it if it is possible that the bird doesn't traverse the entire x-line, instead just make sure that bird.x <= T.x
I changed it to this. I think this is correct @brittle vessel.
if you initially call it on the root node
hmm, we never traverse right here though?
Great 👍
Don't have it in me to go through the algorithm step by step, but you seem to have the idea figured out
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no worries, gl!
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Hello. Im struggling with a question calc 1
@scarlet yoke Has your question been resolved?
<@&286206848099549185>
solve this question by f(-x)
thats a start
wait since this is calc 1 then i believe they want the derivative first right? I dunno
yes thats what my teacher tells us to do
okay
use the power rule where $$nx^{n-1}$$
アキラ (>_<)
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Can anyone guide me with this one? Don't know where to start
@warm flame Has your question been resolved?
which problem specifically do you need help with?
First one and second one I think is just 3/10 and 5/10
But the 3rd question
I am particularly struggling
Can you help me?
I see, I will take a look
im confused as to what you mean by the third question (sorry) can you type the question specifically in the chat?
A multiple of 3 and a multiple of 2
okay so basically you're combining (adding) the probability of the spinner landing on a multiple of 3 and the probability of the spinner landing on a multiple of 2
The ones with green mark are already answered
3+5?
anyways I'm not even sure if my solution for H and R is correct
But H is 3/10 and R is 5/10
your answers for the first questions are correct
so you just add them together: 3/10 + 5/10 = 8/10
and then you need to subtract overlaps
Oh
did you subtract overlaps?
How do you that?
like for example, 6 is both a multiple of 2 and 3
Sorry I haven't listened to my math teacher for awhile
so you should do 8/10 - 1/10 = 7/10
i believe that's the general idea, is that on the answers?
and does this process sort of make sense?
OH SHIT I JUST REALIZED I DID THIS WRONG
did it ask for AND in the problem
okay let's back up
okay so i accidentally did the problem after (multiple of 3 OR a multiple of 2)
so for the AND problem
Oh so 7/10 is the or problem?
you would only count the overlap (the 1/10 probability from the 6)
i am very sorry for the confusion, let me know if you need me to explain anything
Oh yeah it is lmao for mutually exclusive
yeah exactly
Nah its fine you are helping me
3rd problem: 7/10, 4th problem: 1/10
I think you did a mistake, I thought 7/10 was the 4th problem though
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hello, my question is on the second part of this question, circled in red. my work is in blue. Ive completed the first part of the question, but struggle to understand this second part, would someone be able to help me with this, or link material such as a page or video that will help with this exact second part?
i actually also need assistance with the line right above whats circled, where it says write the signal turned on at t=a
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<@&286206848099549185> ^
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help please: Prove that the sum of the diameters of the incircle and the circumcircle of a right triangle is equal to the sum of the legs. I made a diagram, but could not solve it
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id do it via the squares surrounding
Like how the semicircles are in the squares
yh so that big one is 10 squares
nvm 8
nvm 10
then use the area of the circle equation
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r and w are vectors
r dot w could be considered as the projection of w on r’s span or the projection of r on w’s span
Right
And the value of the dot product would be the parallelogram that form by r and w
**Dot product could be negative right? **
How do I determine whether a dot product of some certain vectors would be positive or negative
Dot product itself isn't a projection. It's pretty closely related to projections!
Sorry
r•w = |r||w|cosθ
Yes
Or, it's the sum of the components, each multiplied together
This is largely why we pay attention to the dot product. It's very easy to calculate.
Can it be negative
Yes, if cosθ is negative
That is, if there's more than 90 degrees between the vectors
Are there any other ways that is more intuitive
I personally think of the dot product as "how well the vectors line up"
The dot product is large when the vectors are aligned, and large.
The dot product is small when the vectors are perpendicular, or small.
The dot product is negative, if the vectors are pointing in opposite directions
Terrific
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Can someone explain to me how I can show if a set of polynomials is linearly dependent, I know how to do a set of 3 polynomials but I dont understand how to do it with 5 since you can get an augmented matrix with 3.
With the particular question I am working on I have 5 polynomials to the 3rd degree, meaning x^3, I have collected all the like terms but it just seems to be a 4x5 matrix which I don't understand how to solve. am I even doing it correctly with a 4x5?
do basically the same thing, perform row reduction and show one of the polynomials get reduced to 0 -> it's a linear combination of other polynomials
well if you're doing it as 4x5 i guess column reduction, but same thing
so you can do it the same as a common 3x3?
yes
the whole point is the techniques works for any collection of vectors (or in your case polynomials) of any size
so arbitrary nxk matrix
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Im having a hard time proving this, could someone help me out?
I found this page, but I dont understand:
and here is the book's thm proof for a similar problem
@lime magnet Has your question been resolved?
<@&286206848099549185>
whats unclear about this?
I got it actually! was just confused about how it applies to the inductive case later on but I see it now
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can someone help
😂
what u tryna find
x and y
ur supposed to find it
no but where is it on the diagram
on the line
this is a weird question
wouldnt y be 68
and x be
112
is that what its asking
💀
i am not gonna freakin help if i cant figure it out
Is it like QR is 68 on centre and is asking y= Q T R , T being poi ?
okay then how to do this
again thats suppimentry
now it gives you 128
which i think personally might be m angle 2
1
1 i meant
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how do I solve the third question
got the answers for the mew + 2 sigma
and the mew - 2 sigma
how do I caculate
and please quick
its due midnight
from my perspective you have a solid 13 hours then, no need to worry
no in my time
if youve done what you said, then you have everything you need
its in 11 minutes
thanks, i didnt think of that one, silly me
like how do I enter them as "Enter answer as an interval using square-brackets only with whole numbers."
@latent walrus
what values do you actually have

Minimum usual value: mu - 2sigma
Maximum usual value: mu + 2sigma
You already have the values for mu and sigma (assuming they're right)
mew 2 sigma postive: 231.16
Mew 2 sigma negative: 182.04
part of me says round them to nearest whole number
other part says round them to the nearest whole number within the bounds they set
@wispy acorn Has your question been resolved?
so how do I round those numbers to whole numbers?
had to contact my professor late at night
thank god he's chill
and extended it for me
<@&286206848099549185>
can I help you?
how can I solve the third question
I have the answers caculated from mew - 2 sigma and mew + 2 sigma
also @inner jolt
You dont know how to round?
like I'm too dumb rn to round to whole number I forgot what it is
I know rounding to other decimal places
I mean, its an integer
so like the positive is 231 and the negative is 182 as a whole number
Could be 183 since 182 isnt inside the bounds, thats up to your own judgement
Aight so I laid it out
Referring to the rule of thumb
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How do I solve these 2 please provide full working out
!noans
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
i do not know how to solve these questions and need help
What have you tried?
dont know where to strt
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<@&286206848099549185>
Yeh
its my last question i need help
Tell
This one ?
ye
<@&286206848099549185>
i called others
Ur 7th class right ?
Damn me too
!15m
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I have finished my exam so I don't know noe
Check on yt all solutions are there
ok
Explain the process
thats wrong
sooooo i dont know
what?
so the example says
calculating a 10 perecnt dicount
means following thing:
2590000*0.9=2331000
sorry but thats wrong
so... what is answer?
what? my answer is true
Wait. It says "Enter your next step here"
BUT ITS worng 😭
Is it asking for you put in an equation and not the value?
asking foir the ANSWER
Try typing 2590000 - 259000
yeah
no like 1 plus 1 + 2 like 2
this is australia
so wording is different
enter ur next step meaning whats the answer
Question, have you put in what I've said though
Also, is there an online link to this
Login to our award-winning online math program.
A curriculum-aligned digital math tutor with help on demand in the classroom or at home.
this it the link
I don't have a class 💀
That sounds like a terrible move. No
😭 im dead
@inner jolt Your answer should be right. I don't see why it's wrong
Try 2590000 * 9/10
It's literally the same thing
thats what im thinking
Plug in the values man
I think you're just not reading the question
just plz give the answer
i need to go to the bathroom and i cant leave without finishing this
I can't do that.
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!noans
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
i dont give a shit
lmao
Make sure you learn percentages on your way out
bud go upset
shut up for the last time @civic socket
i will
welcome to my block list
thanks for the helping though
fuck off
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Blud rly called mods
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hii can someone please explain how this question works?
we cant use calculators for it thoo so idkk
then i have no idea sorry😭
Have you looked at your study materials/books/references?
yeahh but our teacher hasnt taught us anything like this
so
im not sure why its in our worksheet
Let me see if I can find a relevant Khan Academy video
okayy trhank youu
I cannot seem to find anything on KA, so I'll have to look up for some other reference
This will take some time and practice, I don't think this is something you're supposed to get instantly
hmm okkayy
ill just have to ask my teacher about it tomorrow i guesss
thank you guyss though
🫶
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Hello, does anyone know how to solve this trigonometric equation?
According to the book this is the solution
should there be y on the right side?
yes
if you notice, the solution is a point (x, y)
@muted ember Has your question been resolved?
?
@muted ember Has your question been resolved?
@muted ember Has your question been resolved?
It occurred to me to find the range of the left side of the equation and the right side and then intersect them and see what comes out. Can you help me find the range of f(x)? I don't really know how to get it.
sen is sin
<@&286206848099549185>
i dont think it works. i have only seen it work in very rare situations.
lemme think a little bit more
or maybe it works ?
yeh maybe it does
lemme test it
its like very hard to find the range of f
yeh i died
i couldnt
lemme think
nope it doesnt have a finite range

I don't know, I asked in several servers and nobody knows how to do it xD
I didn't imagine it would be so difficult
yesterday I was graphing and saw that both functions intersect with 17/2
equating both functions to 17/2 gives the values of x and y
but I don't know why
xd
like to solve equation using inequality we need sth like this in their range :
a <= 1
b >= 1
yes
WAIT THEY ACTUALLY HAVE
then?
f(x) range is literally
25/2 <= f(x)
and g(x) range is <= 25/2
but the problem is
finding f(x) range 💀
intersection at 25/2?
no contiguous
so basically if a = b
and we want to solve it if a >= x and b <= x then answer will occour at a = b = x
why?
graphed it 💀
yeh
yeh you subtracted 4
your f(x) and mine are different
i didnt change the original equation
i was talking according to that
brb
1h
ok
yeh solved it
show me pls
why?
its a trivial thing :
(a-b)^2 >= 0
subtracted both equations and squared both members?
there are some inequalities that can help us find ranges easier
yeh
for example if a > 0 then a + 1/a >= 2
hmm?
you shouldnt do this
that was the whole point of defining a and b
you should avoid extra calculations
and follow along that trivial
sorry imma go
:c
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How do I do the square root of 2 to the power of 4?
think about it like this $(\sqrt{2}) \times (\sqrt{2}) \times (\sqrt{2}) \times (\sqrt{2})$
アキラ (>_<)
Oh ok thanks I get it now
np
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Prove that if a number q can be expressed as the sum of two integer squares, then so can 2q and 5q.
Assuming that q = n^2 + k^2, where n and k are integers
We have that 2q = 2n^2 + 2k^2
Or, we have that q = (n-k)^2 + 2nk
and 2q = 2(n-k)^2 + 4nk
But I don't know how to show that 2(n-k)^2 is a perfect square
(if it even is one)
It's never one, as you're taking a perfect square, then adding 2 as a factor
hmm, you are right