#help-33
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yes
72,755,45.06 ?
approximately that would be the right amount
does the question demand you to find it in integer?
yes
how tf did i say 72
so the rounded 2 decimals would be 04
you got it
it's actually quite related to geometric sequences
yeah still incorrect
this is a finance problem
i do not know about geometric sequences
haha
ahh
try putting in 03
nope
hmm
im not sure if this answer would make sense looking at it normally
how can a payment for a car be over the cars original amount?
or is it 7,000 instead of 75,000
ahhh
yes!
875.26
np i missed it aswell
did i not round correctly
uhuh
hm
now im even more confused
that seemedl ike it shouldve worked
/12 maybe?
for monthly
instead of 72
nah that wasnt right either
nahh
the only clue are the apr and the 72 months annuity
to put it in, $\frac {44,300 * (1+0.0605)^6}{72}$
hm
sho
yeah this is what we did
figured it out
728.59
@storm fern
did it a different way
thanks for your help
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um
im confused
why is ans5 wrong
it's asking for inv of matrix B right?
why do i need a 3x1 matrix?
@ember flame Has your question been resolved?
it's asking you to solve for x in Bx=y, where your answer will include a B^-1
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Could someone please help me with question 9? I'm stuck.
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But the four vertex theroem states that the curvature of an ellipse should be 0 at 4 points
here its only 0 at 3 points
yeah it repeats but i restricted t to be 0<t<2pi cuz thats how the ellipse is drawn
so just kinda curious as to why. and if my understanding of the four vertex theroem is correct
hang on
"two local maxima of curvature, and two local minima of curvature"
so i do have 4 points
nevermind
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HOW TF DO I GRAPH this thingy
im trying to calculate it but its
such a mess
for u(x,1)
its nice they give formula for integral of exp(-x^2)dx but The I(y) is exp(-y^2) and i can't pull it out cuz of the exp from before OR CAN I
nvm i cant
PLZ Hep
plz hep <@&286206848099549185> i just want to know how to start
sure i can set k=1, t=1
but then integral is ??? to compute
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I was sick during this unit and im tryna catch up on the work
I gotta know what the steps are to get those 2 answers
eh... <@&268886789983436800>
huh
I cant set a nickname in here
Can you change it to just Gaylord?
okay
thanks
i think i also misinterpreted it being something more offensive than it was
ive been trying to solve it for quite a while and what I have for the equation is this
is this correct?
if it is how do I get x from this
yeah that's correct, tanx = 13/16, are you allowed a calculator on this?
,tex .sohcahtoa
hayley!
yeah
well okay let me rephrase, arctan(x) != 13/16, but x = arctan(13/16)
can you simplify that a bit
i dont know what arctan means
or what != means
sorry
okay sorry, arctan is the same thing as tan^-1 or inverse tangent, some people call it arctan cause it's better to type out
!= isn't really official symbols (unless you're a programmer) but it's basically not equals
so i was trying to say that based on your triangle, tan(x) = 13/16
look at the soh cah toa diagram above if you don't understand why that's true
so then to isolate for x, you'd apply the inverse operation of tangent to both sides, since arctan(tan(x)) = x
they're inverses so they undo each other
so this is right?
so aplying arctan to both sides of tan(x) = 13/16 gives x = arctan(13/16)
yes
thank you
no problem
so this
and it gives me this?
correct
thank you so much
and whatever your calculator gives you for that should be the right answer
depending on what your teacher says, x could be in degrees or radians so that would affect the answer you'd want from your calculator
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thanks
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Let $W=\left\langle(1,1,1,2)^T,(1,1,0,-1)^T,(3,1,1,1)^T\right\rangle$ be a subspace of $\mathbb{R}^4$ with the standard scalar product. Express the vector $v=(1,1,-2,0)^T$ as the sum $v=w+u$, where $w$ belongs to $W$ and $u$ belongs to its orthogonal complement $W^{\perp}$.
Slowaq
what went wrong? the only thing that might be the issue is the scaling coefficients you put in front of the vectors
@fallow furnace Has your question been resolved?
those two vectors w and u are not perpendiculat as they should
<@&286206848099549185>
oh it seems like w1 and w3 aren't orthogonal so the formula doesn't work yet, you need to gram-schmidt or something to the subspace vectors first to make it orthonormal
yes it works now thx
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how did they do a and c?
What's the expansion for ln(1+x)?
i know its supossed to be in that form
but idk how to derive it algebraic
ly
@upbeat sable
What does that mean?
this is the answer
Oh you don't know how to derive the expansion for ln(1+x)?
but idk how they get x = 1/3
no idk how they got to the part in orange
Right
Are you in a test rn?
smidgin
there isnt a x
did they multiply the equation with 1/3^n?
No
smidgin
im lost man
I got it in this form
smidgin
smidgin
Yes
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β
@upbeat sable
so how did they do c
i get the (-1)^n in the denumartor
@upbeat sable pls
Write down the series for ln(1-x) and ln(1+x)
is (-1)^n * s (-1)^n equal just 1?
they maybe i got it
then *
i want to cancel out the (-1)^n it seems in the denumarotr
i got 2^n in the form of sqrt2)^2n
then doing the antiderivatve
just the (-1)^n in the denum throws me off
smidgin
Oh yes use that
You will get your value for x
smidgin
Now compare the sums
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0.03407811
@tall sun Has your question been resolved?
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Why is sin2theta = positive and negative 1/2, instead of just positive 1/2?
Im supposed to be finding the points of intersection
to be honest idk
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Anyone can find the idea how to solve this? Been stuck
@lapis knoll Has your question been resolved?
<@&286206848099549185>
Use the formula $$1+2+3+\cdots+n=\frac{n(n+1)}{2}$$
Civil Service Pigeon
then telescope w/ partial fractions
$\frac{1}{n(n+1)}=\frac{1}{n}-\frac{1}{n+1}$
Civil Service Pigeon
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Can anyone tell me what am I supposed to do here?
O
I'm guessing I have to use the Gaussian-Jordan matrix to solve this but yeah I really don't have an idea how to start (Subject is Linear Algebra)
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I was tasked with proving that for three non-negative real numbers x, y and z, the following is true:
xy/z + xz/y + yz/x >= x+y+z.
I want to know if my proof, which follows, is correct. And if there's something I should improve.
xy/z + xz/y + yz/x >= x+y+z
<-> (xy)^2 + (xz)^2 + (yz)^2 >= xyz(x+y+z)
<-> (xy)^2 + (xz)^2 + (yz)^2 >= (x^2)yz + (y^2)xz + (z^2)xy
Let a=xy, b=xz and c=yz.
a^2 + b^2 + c^2 >= ab + ac + bc
(should I make it more clear why the above is true, specifically for the right side??)
<-> a^2 - ab + b^2 - bc + c^2 - ac >= 0
<-> ((a-b)^2 + (b-c)^2 + (a-c)^2)/2 >= 0
(should I make it more clear why the above is true??)
<-> (a-b)^2 + (b-c)^2 + (a-c)^2 >= 0
yeh i think you should mention when you multiplied both sides by 2
but its true π
((a-b)^2 + (b-c)^2 + (a-c)^2)/2 >= 0
<-> (a-b)^2 + (b-c)^2 + (a-c)^2 >= 0
is imo very easy to understand
but
a^2 - ab + b^2 - bc + c^2 - ac >= 0
<-> ((a-b)^2 + (b-c)^2 + (a-c)^2)/2 >= 0
is a lot less obvious
should I explain more for the latter?
mhm not really
if its a teacher who is reading this
it doesnt really matter
she/he should understand
the presentation is being graded
like how well it's written
So it should be easy to understand
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angle sum of triangle is 180 degrees, does that help?
@limpid bison Has your question been resolved?
Ok i mean idk any angles in the ABC triangle
all i know is that it is icosseles
But i rly need the angle ABD
you found ACB right
then you can get DCB, and since the triangle DCB is isosceles you can get ABD
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wait is AD a straight line?
idk how im meant to get ACB
also can you ping me if u dont mind xd
if u respond
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oh yikes canβt believe I just made that assumption
what is the bot doing
idk bro
I think youβre supposed to make that assumption because nothing else works
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Is it possible to solve this without multivariate optimization?
f is increasing radially, so the maximum value must be at the boundary somewhere
hmm maybe the intersection point?
Because that's farthest from centre
the parabolic curve is what makes it uncertain
But with straight lines, yeah you can do just the intersection points
Alright
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ure correct
The website tells me im wrong
wait which website
ive just realised i had to put the 0 before it
sparx
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Hello! How are you? Could someone help me with this fraction multiplication? The answer should be 37/5 = 7.4, but instead, I get 74.
where this 10 came from?
you hade 43/30 before and now you wrote 43/10/30 from nowhere
ok i see
its 4,3/30
i dont see the problem
maybe your initial formula is wrong?
for h
in calculator its also 74
its 74 then
Okay, thank you for the help! I suppose the note might be wrong.
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guys can you help me what is this
fractions?
yea
yea thatβs what it is
yea but i dont understand where the answer got like the big numbers
as in the 8/3?
might be
wym might be itβs a yes or no
like the 2 and 1 what is that for
theyβre whole numbers
You add them to the fraction by multiplying the denominator (bottom number) by the whole number then adding it to the numerator (top number)
Eg if you have 1 and 2/5 youβd do 5x1+2 to get 7/5
alr thanks
yup
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For some reason that answer is wrong? is my input syntax invalid?
s(0)
why?
they gove you a value for s(0)
so sub and find C ?
yes
ah ok
thatβs so weird why anti derivative why not integral
mhm
weirdddd
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Itβs like instead of saying plus saying anti minus lol
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can anyone help me in my stats homework? kinda confused with the question
Express the probability distribution of the random variable of the sum of the outcomes on rolling two dices.The sample space of the discrete random variable for the sum of the outcomes on rolling two dice is 6. (just incase my handwriting canβt be read)
i am not gonna make the table but i can tell you what to do
basically you just have to calculate the probability of each sum possible
like firstly, the sum is 2
this only happens when the first dice rolls 1 and the second dice rolls so individually its 1/6 and 1/6
and together it is 1/36
wait, I made a table. can you check if its right?
sure
yes
this is not what the problem is asking you to do at all
the table will look something like this :
$\text{Let X represent the sum while P represents probability} \newline X = 2 \newline P = \frac{1}{36}$
Barbie
and the table will move in this order
so theres 36 outcomes right? since theres 2 dices
ohh
what grade are you in?
11th
i see
try understanding this and then construct the table
do i make two tables?
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Book says solution is 1/3, am i not seeing something or did they accidentally use the limit of x approaches 0 instead of infinity?
Because sinx/x; x->inf goes to zero, but it just seems highly likel they used the wrong limit
Idk tho
nope, they used the right limit
you can solve this limit by either using l'hospitals rule or by using taylor series
No, theres a method without these
ah sorry then I can only think of those 2
Oh wait im stupid
1/3x as x-> inf goes to 0
So its just lim x->0 sinx/x
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you still have that 1/3 there
you can again use subtitution or the other limit
sin(ax)/x
whatever you want
β
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I need help with proof by induction (screenshots following)
This is the homework i have to do with some hints
As of right now i have proven the base case for both formulas and started with the inductive step but tbh i dont really know how to continue here
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@mystic basin Has your question been resolved?
ive started over again and got this for the inductive step right now but i dont know how to continue
(ive proven the base case already)
can any <@&286206848099549185> help? :)
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Does anyone mind explaining how the two equations after (2x)(2y) are equivalent to each other?
y was probably equal to sqrt(1-x^2/4)
Yes. That is correct.
How did you figure they are equal to each other?
because thats the only substitution that would give you the equation, or are you asking about something else?
No. I am asking about the same equation; I just can't figure out how 4x(β1 - x^2/4) equals 2x(β4 - x^2)
@elder glacier
take 1/4 as a common factor
which is gonna be half outside the root
1/4? Doesn't 1/4 Γ 4x = x? (The problem simplifies to 2x. . .etc.)
inside the root
hold on]
ill show you what i mean
is that what you were havin trouble with?
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I have a trigonometry question. I have the answer of 14.36, although my exam is asking to write the sum of how I got that answer. They have given the formula of 1.08/14x3240/2 but nothing else..
is this an exam?
i have finished the exam
but this question is a bonus one for us to try
and i canβt figure it out
I don't understand what the question is
,rotate
Question number 1.35
sorry i forgot how to calculate sounds, like all of it
i just wanted to help everyone by using the bot to turn the picture
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Hi there
bro use one channel
@ruby axle Has your question been resolved?
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surely y can be anything no???
not just 0
this is the question we r doing f(z)
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- isn't 5! 125
oh wait
so you can actually effectively simplify it to G1, G2, G3, G4, G5 and B1, B2, B3, B4, B5, right?
however G1 can't sit in B1...
so G1 must sit in B2, B3, B4, or B5, so that's 4, then, if she sits in B2, G2 has 4 choices, but if she sits anywhere else, G2 has 3 choices
so your current number of choices is 4+3*3 = 13 for the first 2 girls
now repeat this for the next 3
yeah
but we're simplifying the problem and renaming the girls and chairs
G3 -> G1, G4 -> G2... and B1 -> B1, B4 -> B2...
@still temple Has your question been resolved?
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B1,B4,B5,B6,B7 are left for G3,G4,G5,G6,G7 so if G3 sits in B1 there is a perfect case for derangement so 9 possibilities , next for any other girl sitting on B1 , we get a number telling different combos which is same for all those 4 girls..... so lets take G4 occupying B1 then if G3 takes B4 then by derangement we get 2 combos but if not then assuming G3 taking one of B5,B6,B7 then by counting we get 3 for each selection so final answer is: A=9+4(2+3(3))=53
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can I get help for part c?
Please don't occupy multiple help channels.
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thx
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A group of 6 boys and 3 girls wants to take a photograph. Find the number of
ways that the group members can be arranged in a row if the three girls sit next
to each other?
A. 3P3 x 7P7 C. 3P3 x 6P6
B. 3P3 x 7P7 x 2P2 D. 3P3 x 6P6 x 2P2
Not really sure but D?
@velvet elk Has your question been resolved?
it's c
no okay
d
no
a
d would work if the boys had to stay together too
then you have 2 ways to arrange the groups, boys first or girls first
but there's 7 ways: 0 boys before girls, 1 boy, 2... 6 boys
so 3p3 Γ 7 Γ 6p6 = 3p3 Γ 7p7
I already changed my mind with a earlier but thanks for confirming it
Cuz I was doubting too xd
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How to proceed?
Hold on one moment. Let me contact my sir. @stark trail help us please.
what is the trig function in the denominator? Sine?
I suggest you cancel the common factor of x^3 from the numerator and denominator
then recall that trig functions such as sine and cosine are bounded between -1 and 1
yep
Hint: $\lim_{x\to 0} \frac{x}{\sin(x)} = 1$
Ultimate Chad
x do be limiting to infinity doe
Yeah it was harder then I thought
You get 3/infinity * 0
there's a substitution that trivializes it
I will let my sir @knotty frost figure it out though
My thought was to cancel the x^3 then multiply by something to get 1/x/sin(1/x) and use that limit
But there's nothing much to do with this because X goes to infinity, isn't it?
can we do lim (1/x) tends to 0 if lim x tends to infinity? (just curious, i dont know it myself)
But 1/x goes to 0
Yes exactly
This is what Iβm using
0*infinity is undefined
not sure πΎ i will let more experienced ppl handle this
A hint?
His hint was u = 1/x
@stray nest Has your question been resolved?
?
I'm still trying to solve it using u=1/x
Where r u getting stuck?
everywhere right after I cancel x^3
@stark trail my friend here needs help
I tried putting the u^2 in evidence so I could get to the fundamental limit
But I ended up with 3/u/1
Was it after I switched to u or when I factorise u^2?
When you went from the first line to the second
Ah
Got it
Finally got it
thank you so much!
Really helpful! Hope you have a nice day/night/whatever over there!
:)
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πu2
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is this test?
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how can i find the angle of an n sided shape
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What is the definition of a system of generators of a vector subspace?
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<@&286206848099549185>
@surreal glade Has your question been resolved?
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If 10^2x = 25, then 10^-x is equal to?
Please don't occupy multiple help channels.
what have you tried?
Dont use multiple channels
You have another channel with the same question, stick to that one
let q=10^x
@still temple Has your question been resolved?
but
I've shown you the steps before
(...)^1/2
then (...)^-1
and you get 10^-x = 1/sqrt(25)
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I need help
<@&286206848099549185>
AC and CB are equal so Angle ABC and angle CAB will be equal
I need to rush to school in an hour can someone help me with these two questions?
Then?
AOB is twice of ACB
Because subtended by chord AB at centre and circumference, respectively
Which means angle ABC (given that AOB is twice of it) and Angle ACB are equal
So?
So what will be the BDC?
Angle BDC + Angle BAC = 180 becuz cyclic quadri
Itβs 180-60
Yeah
!nosols
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
you wont get solutions here.
I'm getting late for school
Its just one question
He might help me
Okay someone please help me to reach conclusion
youre cheating. that violates the rules of this server.
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Find all possible natural numbers with the following properties: \begin{enumerate} \item One of the digits is a 0 and all the other ones nonzero \item The last digit is 5 \item If we remove the zero-digit, then the number becomess 9 times smaller \end{enumerate}
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Hello
I need someone to explain to me how to solve these problem as I have a slight confusion
I have to find the area of the shaded region ( thatβs the question )
So Iβm assuming itβs the coloured ?
Find the area of whole shape, and subtract the area of the white region from it
Just a question do we always subtract the small from the biggest or it can be the opposite ?
Alright it worked with me just one error in one of the questions
I did 240 minus 19.21 and it says wrong
Would you please tell me where I went wrong ?
How did you get 19.21?
how did you get 240
I found hypotenuse
10 times 24
that is not relevant to the area
That not the area tho
Find area of the big triangle
Or you could find the small triangle individually and add them
A = b x h x 0.5
Area equals to 15 times 12 times 0.5? Since we divide the 24 by 2?
No need to divide it by 2
0.5 x base x height
For the blue triangle at top, base is 24 and height is 15
With same formula find the area of those two small triangle at the side
And then add all three
So it will be 25 plus 25 plus 180 equals to 230
240 minus 230?
No need to minus
But I though we do this ^
230 is the total area of blue region
That can be done, but you can also just find the areas of the individual blue regions
Wait so then what is the next step ?
since we got the 230
Mb itβs just that Iβm slightly confused
This is the final answer
Itβs telling me itβs wrong answer
Maybe there is an error with the survey
This bring one last question
How did you know that you didnβt need to minus?
Oh
Well try finding the area of the whole triangle itself, then subtract the area of rectangle from it
Alright man thank you a lot for you help really appreciate it
Have a good day ahead !
Should be 185
Try that
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if you did that area would come lesser than zero, like a negative number which is not possible
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How do i prove this sss similarity theorem with statements and reasons?
a two-column proof i guess right?
well if u want a hint, XY and ST are parallel to each other
what can u say about the relation between angles RXY and RST?
They're parallel segments???
Ohh
Sorry my math teacher literally rushed our lesson
Grasping them was pretty pressuring so i didn't really get to understand the lesson much
thats ok
What can i do to prove them
well there are some steps and im trying to guide u towards that
i need u to answer this at least
I kind of proven to draw a line xy then replace the seg st
i dont understand what u mean by that soz
We're gonna try using corollary 60.1 to prove them
i dont know what corollary 60.1 is
Yes i know you are expected to do two column proofs
Rhhh
for the third time, can you please try and answer this
the construction of your triangle tells you that XY and ST are parallel, so knowing that, what can you say about the relationship between angles RSY and RST?
Are they equal for example?
Rxy is smaller than Rst, made a mistake in my writing sorry
I see
Apologies for the trouble there
its like 2 and 6 here
i think you call them transversals
well anyways
do you know AA theorem? @inner nexus
Sadly no
aight
sorry i dont know how to help you then. I would suggest studying some of those similarity theorems
SAS, SSS, AA, so on
you can use AA here at least
I see, thank you about that
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1 sec
if for example
AC and AB are tangents from point A to the circle
and AD is angle bisector.
can u say ED is a diameter?
as if two tangents from the same point are connected with a line from the center of the circle, the line is bisector to the angle between the two tangents.
and a diameter is a chord that passes through the center
yea it should be
can u say that " if a line connected to the point where two tangents to the circle meet, which bisects the angle between the tangents, the line comes from the center"?
yeah i thought so too
one easy argument you can make: you draw the 2 tangents, then connect the tangent points to the center of the circle (the tangent lines and radii of the circle make 90 degree anglex). now connect center of circle with the original point to the left. so you have 2 right triangles with two equal sides (1 is shared and the 2nd is both radii) so the triangles are congruent. so the angles at the left are congruent, so the line you drew from the center to the point bisects the angle
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how do i get started with this
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Hey, im making an investigation and need help modeling the parabolas of the macdonald's logo to get the area of the "m" in the red square, could somebody help me make the equations that form the "m", I have tried to model it with a system of equations and desmos but the parabola doesn't match. Please help!!!!
@wispy robin Has your question been resolved?
<@&286206848099549185>
i am inclined to say that those aren't parabolas
for real life archways the equation is cosh(x)
you can approximate the shape with parabolas, but if you found a parabola that passes through 3 the other curve's points and it doesn't match, then the other curve is not a parabola
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@main bough Has your question been resolved?
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for 1b, what am i doing wrong?
the answer's
-11
4
12
The second row is -3 1 0
Wait sorry I'm trying to find the mistake still
Right here actually, why did you flip all the signs on the right when you did R1 = -R1?
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Someone pls help me with this
,rotate
,rotate
,rotate
you're on the right track yeah
My examβs in like an hour and im in a bus could u help me
With working
@potent fog
sure
you figured out we want to use 2theta to find the area of the unshaded region in the quadrilateral
so what are the areas of those two unshaded regions of the circles
Ye 2pi-thera
Then thetar^2/2
X2
Then add it with the shaded area in the middle
But how to find the middel one
On either side
Area pf rhombus-the sectors?
yup
I forgot area of rhombus form
well
we dont need to find the area of the rhombus necessarily
we can see some triangles in the diagram you drew right?
right
I remember that thing i did
(Basexheight/2 - area of sector) x 4
Then add everything up
1:shaded
mhm
well not 1:shaded
This is gonna be the ratio?
shaded:area of the large circle
right
But since the shaded part is inside the circle wouldnt we take it as 1
I mean prwcious time i did take it as pir^2
But u feel like it should be 1
oh sorry 2x squared
right
Oh

