#help-10
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@lone shore Has your question been resolved?
You have to express length in terms of breadth or vice versa.
$your length is 6m less then your breadth,
So if l=length
b=breadth
=>l=b-6
Now form equation with perimeter and solve it by substituting value of l or b$
@lone shore Has your question been resolved?
with ur brain
`So let the width be x
//They said the length of the rectangle is 6 less than 2x the width
//so we can say
2 * width - 6 = 2x - 6 = length
//We know how to calculate the perimeter right?
2(length + breadth) = 2(2x-6 + x) = 2(3x-6) = 6x - 12
//They said the perimenter is equal to 150m
//So now we know
6x - 12 = 150
x = 27
//Now we know -> breadth = x = 27
//So length is -> 2x - 6 = 2(27) - 6 = 48`
@lone shore Has your question been resolved?
@pure iron #❓how-to-get-help, open a new help channel to get help.
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@meager dagger Has your question been resolved?
@meager dagger Has your question been resolved?
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how do i draw this, what are the steps
like random ?
usually you make choices that give you nice numbers
a line works like
you pick an x, then you have no choice in y
theres only one y that makes the equation true, once you pick an x
it works the other way too, you pick a y, theres only one x
a common choice is 0
if y is 0, whats x?
if x is 0, what does y have to be?
then u have 2 points
honestly idk
there's a line
(1, 0) (1, 5)
what do i do next
gradient is 5-0/1-1= 5
wait what do you do if there is no y intercept
okay ill just avoid using a parallel line
(1, 0) (0, 3)
3-0/0-1= -3
y=mx + c
y=-3x + 3
what now
3
nice
id just write 12 somewhere
on the y scale
then connect those
done and done
yea
like that ?
what just connect a couple point?
2 points define a line so yea in general
sometimes one of the variables is never 0
but this is an easy problem
okay
but
doesnt it usually look like y=mx+c
why is it y=12-4x
is it just a different way of writing it to create problems ?
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Please don't occupy multiple help channels.
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I must say i dont know where to start any clue to how i might start would be helpfull thanks
Apply log properties
This is simple
Lets try this
...
Take the base 10 exponent of both sides
whats that?
Like you have a=b rn. Make it 10^a = 10^b
I am aware of that thank you
10^a
a meaning?
The expression on the lhs
Just raise 10 to the power of both sides of the equation
okay and a = log10(x^3) - log10(x)?
Yep
So on the right you have 10^4. And on the left you have 10^(log10(x^3)-log10(x))
Now you can express the lhs as a quotient
Because you have subtraction in the exponent
im unsure of what to do i dont fully understand
10^(5-3) = 10^5/10^3
I googled quotient rule... scawy
Thats something different
hold up where did x^2 come from here
Look at this
Typo
oh alright but it still becomes 10^(5-3) = 10^5/10^3?
Just as an example
ohh
So we have 10^(log(x^3)-log(x))
yep
What can you do with that
Yes
Yeah, problem is i dont truely know what that means
A quotient is something divided by something else
4/5 is a quotient
Fractions are quotients
Look at this
Simplify this
so is basically just x^3/x
?
yeah
so x^2=10^4
10^4 = 10000 meaning x = 100
?
Yes
Oh i thank you dearly wow. That felt harder than it was... hahaha
thank you
I belive you can thank people
how?
thank you
thanks
.thank
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Do you know what irrational means?
Money
@timid silo Has your question been resolved?
@timid silo Do you know what irrational means like dldh06 said?
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Lram means what
Whats a midpoint sum then
Write out the formulas for all three and compare them
You can probably deduce the right Riemann sum from the left and trapezoidal terms +- some endpoint values
My guess is you don't need to
Just leave it as a variable
What formula does your textbook give
Mram
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hello, I'm trying to set up my dfq for this, figured out 2lbs = k(0.75ft), so k=8/3 lb/ft
but idk how to get the mass, since pounds are force.
any help?
it looks like slugs, the imperial units for mass, can be found here as pounds/accel gravity
so 2/32 = 1/16th of a slug
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Have no idea how to solve
what does mean and sd mean?
@final urchin Has your question been resolved?
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Question 9)I don’t even understand the wording of this question, what are they asking?
how many hours are there during the weekend that this sign does not address
Saturday and Sunday combined?
yeah they say the weekend ends at 12 midnight on sunday
For Sunday the parking ends at 12 midnight and there are 24hrs in a day so I did 24-12 to get 12hrs
Ok I got it thanks
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hi guys for ii, do i use integration by parts
oh
i meant the x^2 infront of the tanx^3 sorry
Still same thing, u sub
ohh
so i need to solve this question using integration by parts?
Yes
ok
ok
is it like this
im confuse why does this question deosnt need by parts
cuz theres algebra and trigo
Not everything needs integration by parts
@radiant cobalt Has your question been resolved?
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can someone please explain how to solve this using partial decomposition
How well do you know PFD?
Partial fraction decomposition
i dont think i know it that well
pershmaps learn it
This precalculus video tutorial provides a basic introduction into partial fraction decomposition. The full version of this video contains plenty of examples and practice problems with repeated linear factors and repeated quadratic factors. Partial fraction decomposition is the process of taking a complex fraction and breaking it into multiple...
@wintry stream feel free to ask questions about the video. I'm sure @short spruce has watched and understood it 10 times by now
@wintry stream Has your question been resolved?
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How would it be possible to simplify/solve this
Ive tried using geometric but the "a" changes
wat
So in a/(1-r) formula is almost relivent because of the 1/2^n but the numerator changes with n
welp
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Is it possible to compute the upper limit $b$ in an expression $$\int_{a}^{b}f(x)dx=t$$ where $b>a$and t is given?
wrong \ on your \int
3rk
If you can compute an antiderivative of f, or at the very least compute its value at 0 and b it should be pretty easy. just solve F(b)-F(0)=t for b
if you know the antiderivative of f yes
One sec, ill get on my computer to type this out faster
Okay, so I know that $\int_{-3}^{b}2^{-x}dx=24$ and that the indefinite antiderivative is $-\frac{2^{-x}}{\log2}+c$
3rk
I would just compute the antiderivative at $x=0$, then?
3rk
Or would it be $x=-3$ in this case?
3rk
yes
Right, and that would return the value of b. Makes sense, thanks and sorry for the sloppy tex
Uh there's more to do after computing -2^(-x)/log(2) when x=-3 if that's what you mean
just solve F(b)-F(-3)=24 for b
where F is that antiderivative of 2^(-x)
i gtg now sorry if you have anymore questions
np, ty
When I compute this, I keep getting $b$ such that $a>b$. Any thoughts on why this would happen?
3rk
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do u know hwat a discriminant is
Have you tried anything so far?
I know what a discriminant is but how would I use that here?
When does a quadratic equation have at least 1 solution?
do u know the quadratic formula
Ye
from the quadratic formula what does the discriminant tell u
When the discriminant is equal to zero
I said at least 1
not quite
Not just 1
When the discriminant is greater than zero, it has 2 solutions
Yeah, so it has at least 1 (1 or 2) solutions when the discriminant is great than 0 or equal to it
Ok
Yes in this case b, the coefficient of x, is k + 1
Well first of all here you'd need k to be positive, because if it was negative then the parabola would go downwards
Meaning it'll be negative somewhere
And secondly, if a quadratic is always positive, it means that it has no real roots
Do you'd need its discriminant to be negative
What'd the discriminant of the quadratic be in this case?
Yeah, now you need 9k^2 - 36k < 0
Ok
So k^2 - 4k < 0
Yep
Oh yeah btw you'd also need to consider the case when k = 0, because the discriminant and quadratic formulas don't work in that case
As you can see k = 0 works
Because 9 > 0
In this inequality you can divide both sides by k
The signs won't flip because k is positive
As I said earlier
But this is the answer
In the photo you sent you made the discriminant positive
Meaning the quadratic does have roots
Which is opposite of what we needed
So you mean to say the signs are “less than?”
So I got this
Thanks for your help
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Any videos about this topic
Thank you so much
👌 
@feral swallow Has your question been resolved?
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Can anyone explain how to solve this combination problem:
How many ways can you select 4 letters in the word "connection"
10C4/12
nope
it would have been the answer if there were no repeated letters
i think it's 10C4 divided by the ways you can choose each repeat, so divided by 2! * 3!
no
unless there are any letters repeating that aren't 'n' and 'c'
there is also o
no based on what i watched you cant just devide them i know what you mean but i think its just applicable to permutations
i think its just applicable for permutations if you are to arrange the whole word
yea
my final answer there is 71 i added a couple of possibilities that are not in my solution
but idk if what i did is right
i think it's... 48?
how?
yeah
thats the right answer but how do i put it in equation
HOLY CRAP I GET IT NOW
so the correct answer is 53
so this solution is correct i just missed only one possibility
the possibiity of getting
2n, 2o or 2c
which is 3
so 50 + 3 = 53
thankyouu
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could someone help me with this
Turn it into a system of linear equations
@maiden veldt Has your question been resolved?
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Hello, how i can find Y ?
oh ok thx
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what if all the a's = 0 and all the b's = 1, then the equality holds but the equation has no solution for x? is this a mistake?
Seems to be a mistake. The correct statement is supposed to be:
... if the sequence a and the sequence b is linearly dependent.
Whoops, a typo that completely changes the meaning.
what do you mean by sequence a and sequence b is linearly dependent? you mean if the set of vectors formed like <ak, bk> is linearly dependent?
no, he means that the two vectors $(a_1, \dots, a_n)$ and $(b_1, \dots, b_n)$ are linearly dependent
Alexander42
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Can anyone explain this to me in the dumbest way possible
Is this a transformation based on the basis
Is this just explaining matrix multiplication in regards to a transformation with the basis?????
Ping me if you can help!
@timid silo Has your question been resolved?
you write a vector as a linear combination of basis vectors
the scalars that make up the linear combination becomes the coordinate vector
Yep the xs form the scalers of the basis right?
like if I have $f=1+2t-t^2$ and write this wrt the canonical basis, then $[f]_B=[1,2,-1]^T$
Mosh
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I have 2 values for a interquartile range
Q1=81 Q2=151
How do I solve?
Sorry. How do I find the outliers
The full question being asked is
For a set of observations, Q1 = 81 and Q3 = 151. Values greater than X and less than Y are possible outliers
What would the formula for solving this be?
to find outliers take Q3-Q1 = IQR *1.5 to find outliers
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Wait. But how would I find two values?
So 151-81=70
70*1.5= 105
But thats 1 value? I need to find 2 outliers
@tropic lava Has your question been resolved?
<@&286206848099549185>
All you need to do now is add 105 to your Q3 and subtract 105 from your Q1
Any values higher than that ceiling or lower than the floor are outliers
Thanks.
No problem
So it be greater than 186 and less than 46?
Juzt making dure
Cause 105+81=186
And
105-151=46
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How to do this?
We're learnt sine n cosine rule
We've learnt radiant:
Length of arc: S = r (theta)
Area of sector: 1/2 (r^2) (theta)
Area of segment: 1/2 (r^2) [(theta) - sin(theta)]
@vocal verge Has your question been resolved?
<@&286206848099549185>
@vocal verge Has your question been resolved?
@vocal verge Has your question been resolved?
@vocal verge Has your question been resolved?
Well use trigonometry to calculate OAP
$SinA =OP/OA$ correct?
There you have it then.
Sakata Yaksha
same For ODQ
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blue area must be calculated. I know I have to do primitive functions subtracted from eachother, but im a bit stuck.
show what you've got so far
I made both functions primitve:
However I quickly realised that doing ln0 gives math error.
The area under the y1 line from 0 to 2 is 8/3.
And the area under the y2 line from 0 to 2 is, well, undefined?
might be better to separate your problem into two steps
- integral setup
- solving the integral
what'd you get for 1?
8/3
which seems reasonable.
Dividing the problem might be the best solution
Just making sure that I have all functions ready
Oh my
I just found out how to solve it
I'll try a method
Taking the area from y2(0 to 2) and subtracting it from y1, will give me that large empty space to the left.
Then I just subtract that area from y2's total area.
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Use double angle formula twice
Don't we need triple angle formula?
If they've learned it sure
Heres my log tables
That's angle sum formula
😄
Top left sin(A+B)
Do this
Can you go into more detail
A = 2x, B = x, apply "compound angle" formula for sin from your sheet .
Where are you getting 't' from?
Riemann named it t in his text, it's called x for you.
Wait what happens to the cos's tho?
Man can someone do it on a page I think i'm just dumb
We are starting with the sin.
Ok I wrote that
I'm only at sin(x+2x)
x+2x = 3x
Man I'm so confused
You can take your time. 🙂
Ok ok
afterwards we can solve the equation system.
So just sin 3x turns into wht
"When asking for help, do not insist with getting just the answer; we are here to help you learn, not do the work for you. Likewise, if you are providing help to others, try your best to explain and elaborate instead of simply giving away the answer." from the rules 😮
Hurry is bad in mathematics
Ok my bad I'm sorry
sometimes we just take time to unconfuse ourselves
this is true at all levels of matheatics.
I'm just really confused and really stressing thats all
Ok so lets start again
What do we do with the sin3x at first
We apply the compound formulae to it?
3x = 2x + x and "compound angle", yes
I would suggest starting a separate calculation for that
Ok
sin(3x) = sin(2x + x) = ...
Sin2x + sinx?
no
look here
The sin (a+b)?
yeah
yeah
Ok how do we do the next part
and we are not done yet because now there is sin(2x) and cos(2x)
we need to replace those too, we only want sin(x) and cos(x).
We want to reduce the number of unknowns
and sin(x) and sin(2x) are like very different unknown numbers.
So what do we get rid of?
I don't rly know what I'm looking for
something with sin(2x)
What’s the question
In double angle fomulae
He is trying to solve sin(3x)/sin(x) - cos(3x)/cos(x) = 2
Hm I think there is something better
Have u tried using de moirés theorem to expand it
You are right that we can use this
Sin 2a = 2sin A cos A?
In terms of powers and then divide
but tan is something new yet again.
I doubt he has been introduced to complex numbers 😮
But Omar is right in that complex numbers are really good for these kind of tasks.
They also make it superflous to keep such tables in mind but that's not today's lesson. 🙂
ok
Oh thats very complicated
hm looks different, did something go wrong?
Wolfy is making 3 suggestions
it's just 3 sin(x) cos²(x) - sin³(x)
le me see, maybe it's actually the same
Oh ok I just needed to join them together
Its awkward
sin(3x) = sin(x) cos(2x) + cos(x) sin(2x)
Is that it final or....
= sin(x) (cos²(x) - sin²(x)) + cos(x) 2 sin(x) cos(x)
Wait what year are you in
I'm from ireland which is my last year of highschool for america
I am a master student.
I’m form the uk not sure how it works there
I'm impressed
Is there a way without using complex numbers?
Yes
Thats what I'm thinking
We are doing it atm
Also to fully explain complex numbers to you will take us some time.
Do you agree with this here?
Oh I get it
and this is now = 3 sin(x) cos²(x) - sin³(x)
which is what Wolfy told us I think
So sin 3x = that?
ye
Ok lemme register this 2 seconds
Ok that makes it more understandable
,rotate
@severe dune Please slow down a bit. See rules, please no giving away the answer.
Ok lets move onto cos3x
My b
Sin x just stayes by itself?
Same rule for cos 3x
What do u right for your final proof sentence or words like out of curiousity
Do u write lhs proven
You asking me?
Yeh
Therefore that equation = 2?
lhs proven? I think in this case you would give a set of possible answers.
Its not asked in the question i don't think
like x = { pi n + pi/4 | n integer } (This is an example, not the solution lol)
Is the final proof sentence needed?
In exams I’m pretty sure
From school's perspective it's not a proof though but a "calculation".
In Germany we never wrote answer sentences in the final years.
Maybe different syllabus they specify for a question like this that we lose a mark without the sentence
Wow okay that's rude 😄
We I don't think thats needed here
I know that I got into trouble in earlier years because they wanted us to write "Question sentences" and "Answer sentences".
Sorry
Does the last like 2(cos^2x+sin^x) the bracket just cancel itself out?
Line^
Just leaving 2?
Yes
Ah not your fault that the schools grade like that.
Sin^2 x
Oh yes
yeah sin² + cos² = 1
They will never get enough of that identity
yeah it's the most basic rule and very good.
Ahh then its 2(1) = 2
Yup
@sudden finch, did you finish?
,wolf simplify cos(3x)
,w unsimplify cos(3x)

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Yo how do I form a radical extraneous equation
I just can't get my head around it
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Q: use a graph to solve the equation on the given interval.
help i don't understand the question
Draw the graph of 6cos(x+pi/6)
Not exactly sure perhaps it’s stating the domain

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Hello, im just confused on this problem. How can you get the measurement when theres nothing given? And does the pentagon make a difference?
We know one of the interior angles of a pentagon 👀
What is it?
The formula for calculating the sum of interior angles is ( n − 2 ) × 180 ∘ where n is the number of sides
That means one of the interior angles should be
So its gonna be ( 5 - 2 ) x 180°?
Yeah
Ohhhhhh
What's that simplified
Man my teacher didnt give a single solution for this, all she said was to research it on the web
Thanks man
Did you get the interior angle?
Wait imma write it down first
Is it 540°?
That's the sum of the interior angles
Since its a regular polygon, what would be one of the interior angles of the pentagon?
Would it be 108°?
So wait if its 108° each side, so PQ, PT, TS, SR, and QR are all 108°?
Oh my bad
I see i see
Man im still confused even with the given measurements
Is m∠PTR, m∠RTS, and m∠QTS all 162°?
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is the singularity of a function at a point just whether or not it divides by zero?
e.g.
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why cant u divide by 0
why
It breaks math
What do you think you would get?
0??
how
but 10/0 = a
but whats a
yes
Check out our Patreon page: https://www.patreon.com/teded
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In the world of math, many strange results are possible when we change the rules. But there’s one rule that most of us have been warned not to break: don’t divide by zero. How can the simple combination of an ever...
oh
and divide them for 10 persons
ok
ted ed
then 100 / 10 = 10
best channel
because 10 * 10 = 100
It's just the way math is defined.
0 / 5 = 0
You can define x/0 = 0 for all x if you want, but some rules would break
and you would have to write exceptions for a lot of things
so why isnt 5 / 0 = 0
Yeah an advanced note is also that in certain parts of complex analysis one can divide by 0.
just to accommodate this one rule
Also you can make limits with 0.
wut is limit
you look at where things go
2/1 = 2 so why isnt 1/2 = 2 as well???
what logic is this
idk
you cant divide a number by nothing lmao
also why does 0 / 5 = 0
I think @fathom harbor managed to hit some topic that triggered every mathematician checking the channel lol.
Because 5 * 0 = 0
loll
but why is 0 /5 = 0
i mena
0
Because 5 goes into 0 no times
see my example above with the apples
How many times does 5 go into 0?
idk
How many times does 5 go into 1?
idk what does that mean
1/5 = 0 remainder 1
Do you know division?
yes
if we say 77 / 11 = 7 we mean by that, that if someone has 77 and divides them equally among 11, everyone gets 7. Because 11 * 7 = 77. You cannot play this game if 11 would have been 0.
1 = 5x0 + 1
Have you seen remainder division?
6 = 5x1 + 1
so 6/5 is 1 remainder 1
yes
Sorry this was wrong, now it's fixed.
Math breaks even more
Doesnt exist, cannot divide by 0
ok i forgor
0 = 5x0 + 0
ok
0/5 = 0 r 0
ok
Hence 0/5 = 0
ok
Keep in mind also that you can define anything in mathematics, one can say 0/0 = 0 for example. But this makes trouble everywhere we divide something so we generally don't like that.
wait what about
if i cant divide by 0
can i divide by negative numbers
like
-1
-2
You mean like 5/-1?
u can divide by anything except 0
ye
Zero breaks math
-1 has a value, 0 is literally just nothing
-1 goes into 5, -5 times
but 0 is equal to 0
Okay I am out, nobody seems to read my expanations here. 😄
i do
-5 x -1 = 5
i do read them
this is hurting my brain
why is -5 x -1 = 5
That's how math works
...
ok
It seems like you are underage, like under 13
i am 13
To be asking those questions
bro i cant use discord if im under 13
Arguably not the best explanation though. 😄

You should have learned some sort of concept on negative numbers
Technically you can lie
my country dont have good education system ok
ok
Alright negative multiplication right?
ye
Imagine i borrow money from you
yes
ye
man this is not easy to explain
positive * negative = negative
negative * positive = negative
negative * negative = positive
positive * positive = positive
this might help a bit - same applies to division
i can never remember these
no im gonna have to scrap that example for now
ok
two same = positive
two different = negative
ok
you have to memorize that
why
Literally one of the basic concepts of multiplication with negatives
you use it in math until you die
Ok ok how about this
ok



