#help-23
1 messages · Page 197 of 1
For example, 27 = (17 + 5 + 3) - (terms - 1)
It's weird how it's (p + q) - 1 = Prime. Telescopes outwards
There has to be a some sort of bounds on the number of prime terms used, because the (term - 1) will swallow the tail end of the prime terms
Maybe that could be useful to figuring this out?
@steep yacht Has your question been resolved?
Mm You could keep breaking down the primes terms I wonder If some pattern emerges
If you take it to its extreme, all primes would 3*n - (n - 1) = 2n + 1. Because you can keep breaking the primes down in to 3s
Would this be sufficient to prove all primes are (p + q) - 1
<@&286206848099549185>
Does this make any sense?
wait no it doesn't it would imply that (p + q) - 1 = 2n + 1, which would imply that p + q = 2n which is goldbach.
so all primes and (p + q) - 1. then p + q = 2n. because of the recursive nature of the problem
<@&286206848099549185>
@steep yacht Has your question been resolved?
Man if it's not out of a text book it's really hard to find people to help on this server
its always like that
you might have a better chance asking this question on the mathematical olympiads discord, they might know more immediate math
@steep yacht Has your question been resolved?
@left gyro do you have a link to the discord server?
you wont believe the URL: https://discord.gg/mods
its not filled with discord mods
these people (as far as Ive heard) go outside
hahah ok fair, yeah i'm scared to ask question there as my math "education" is barely at a high school level
they have problems at all levels but I think most of the people there arent as high up as you think they are
theyve seen big problems and failed them, thats why theyre presumably here and not souring high on their own
the average textbook problem is much easier than a difficulty 1 problem on there
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This is engineering math integration but this is the basic integration practice and im stuck :<
This is my working so far, i tried to re-write the equation after expanding the brackets but got stuck
this is the answer
Look for a way to make that 16 disappear from inside the sqrt
like turn it into 4^2?
That u have already but u can’t take out cause u have a subtraction
Si u need to make x^2 = 16u^2
To take common factor the 16
How do u achieve this?
u need to know the solution to this right?
yeah
He knows the solution, doesnt know the steps 
ohhh wait i understand
thats good
i think i confused myself when i re-wrote it like this
yea probably
thank you so much :D
u dont rly need to make it complicated
glad to help
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how do i do this question? is it a quadratic formula one?
no its not a quadratic formula one, its not asking you to factorize
what do you think
have you taken calculus
no
yes
ok so stationary points are closely related to the derivative, theyre either the points that make your derivative function equal to zero or is undefined
Ok
start by taking the derivative and check for the points that make the function equal to zero or is undefined
i got the derivative but how do i check for the points that make it undefined or zero?
im sure you've taken how to get the domain of a function right?
check if the function is undefined at any points in its domain
if the domain is R then there are no points satisfying the undefined condition
just by looking at it, the domain is gonna be just R because its a normal quadratic function
if you wanna check if the function is equal to zero, just set it to zero and factorize
np
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Soh cah toa
Degrees or radians?
degrees
can you teach me the steps to solve question a
please
stuck on this for 30 minutes
the teacher gave the answer already which is 19.4 but im trying to know how to find it out
You know one side, you want to know the other
Compared to the angle you know
What's the side you know?
It's not adjacent to the angle
Adjacent = touches the angle
It's opposite
As it doesn't touch the angle
What's the side you want to know?
H is always opposite the right angle triangle
O is always opposite the angel
A is the 3rd one
soh
SOH
Write down the formula
Not ×
sin(31) = 10/a
Opposite/hypothenuse
That's why soh is in this order
Now you can find a
so is it sin (31) divided by 10??
No
im actually so confused this method worked for other questions but not this one
wdym
swap it
wdym by that
talk a bit more simple please, my brain is a bit foggy today
oh yeah
how do i do that with my equation though
since its only sin 31 and 10
what do i swap
.
Sure
wdym
oh yeah mb
my calculator was on rad
instead of deg
where does the 1 come from btw?
when we swapped
And then this
so basically a/10 and =1/sin31
is the same right
@obsidian oracle
okay i got it
thank you
very much
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I think RHS is incorrect
why do you think so
because if i put the formula a+b whole square on lhs,it’s in +
that's correct
now you need to express that in a formula
sin^2^2 + cos^2^2 +2sin2cos2
and what does this equal to
consider (sin^2(theta)+cos^2(theta))^2
yes
where am i supposed to bring - from
what does this equal to
1
exactly
add that chunk to both sides, of course
and now expand the brackets
nop u cant do that
im left with 1+2sin2cos2
sin⁴(theta) + cos⁴(theta) = 1 - 2 sin²(theta)cos²(theta)
sin⁴(theta) + cos⁴(theta) + 2 sin²(theta)cos²(theta) = 1
nooooo
you can solidly do that
my teacher said no
then they're wrong, really
what is the left-hand side equal to?
sin 4 +cos 4
you have to converge to my way to do it your way
im not used to it
sin⁴(theta) + cos⁴(theta) + 2 sin²(theta)cos²(theta) = (sin²(theta))² + (cos²(theta))² + 2 sin²(theta)cos²(theta)
can you rewrite it for me...?
when you do mine correctly, you'll see how you actually are used to all of them
(sin2+cos2)^2
and its numerical value is?
1
equal to 1 on right-hand side, right
can u tell me how to get the - sign pls😭😭
no….
you do this:
sin⁴(theta) + cos⁴(theta) = sin⁴(theta) + cos⁴(theta) - 2 sin²(theta)cos²(theta) + 2 sin²(theta)cos²(theta)
I made it work out ☠️
the solution is perfectly acceptable
ok what after
group sin⁴(theta), cos⁴(theta) and 2 sin²(theta)cos²(theta) together to get 1 as calculated here
we end up with 1 - 2 sin²(theta)cos²(theta)
huhhh….
Can you handle with simple Variables to make it easier
substitute sin²(theta) as a and cos²(theta) as b ;)
that’s so complicated
(X + Y)² = x² + 2xy + y² ( adding -2xy both sides)
(X+Y)² -2xy = x² + y²
It's the same technique
your way of making both sides equal is even more complicated
doesnt the -2cos2sin2 cancel with +2cos2sin2
that's exactly why you do this
it's to satisfy your request here
Deal with that like a formula
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I think I miss out something here with this one.
Of course, I am not going to find the cube of a 3x3 matrix. At least, I assume that, since a matrix with elements a,b,c,d,e,f,g,h and j would be a cumbersome task when cubing.
But I don't know where to begin with this problem.
For nxn matrices you have det(AB) = det(A)det(B) and det(kA) = k^n det(A)
Hm, in that case, I have two questions
- What is the "B" matrix here?
- What is the "n" in k^n?
The part "For nxn matrices" should answer both questions
Ohhhh so det(AxAxA) + i^3 det(A)
Yeah
Yeah, didn't fully realise the nxn connection to what you said
Makes a ton of sense! Thanks!
Have a good day.
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I don't understand with the statement in the yellow line
Can someone explain to me
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Can someone tell me how they got e^2 ?
so since the lim as x -> 0 can approach 0 from either the positive or the negative side you have to consider those scenarios
in those scenarios you will see something interesting happen to ln(1+x) and x
just plugging in 0 for x wont always work especially in cases where a numberr is being divided by x
e^(2/x)ln(1+x) = e^(ln(1+x))^2/x = (1+x)^2/x = ((1+x)^1/x)^2 = e^2
ln(1+x) when x=>0 its equivalent to just x and so ln(1+x)=>x and you get e^2
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Two fair dice are thrown simultaneously. The random variable D is the difference
between the smaller and the larger score, or zero if they are the same. Tabulate the
probability distribution of D! can someone help me explain this probability and distribution?
you can start by counting the total number of possible cases
First, difference can actually be expressed as sum if you change the faces of the second dice: x - y = x + (7 - y) - 7 = x + y' - 7
Then https://mathinsight.org/image/two_dice_distribution has this nice chart, and you just subtract 7 from the sum
A bar chart illustrating the probability distribution for a random variable $X$ that is given by the sum of the result of rolling two six-sided dice.
Second (minuand) dice: 1 -> 6, 2 -> 5, …, 6 -> 1
For example,
Dice [4] - Dice [5] = Diff [-1]
Dice [4] + Dice' [2] - 7 = -1
So you can just subtract 7 from the X axis of the chart and get your answer
i fopund it
@cerulean sluice Has your question been resolved?
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intergrate this using by parts?
use the ILATE rule
ILATE = Inverse Logarithmic Algebraic Trigonometric Exponential. Whatever function is later in this sequence, is the one that is set as dv
so, here we have an algebraic function and an exponential one
so $\dd{v} = e^{\frac{x}{2}}$
maxim
and $u = (2x - x^2)$
maxim
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How is set difference generally defined for countable inifinite sets? For example, can I consider that the difference of two inifinite sets might give a finite set? For example, the difference of the set of all natural numbers with the set of natural numbers greater than 10. Can I consider the result to be a finite set (numbers 0 to 10), or is it simply undefined?
@autumn fjord Has your question been resolved?
@autumn fjord Has your question been resolved?
You are right
There is no problem for infinit sets
$$ A \setminus B = { x \in A \mid x \notin B } $$
A shot
@autumn fjord
Thanks @past pelican
You get it or you have other quetions?
I get that there might be a finite number of elements that are in A but not in B. Thus the difference of two infinite sets can be finite
At least I think that's what you're saying
Yeah
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Is Sx or ox the standard deviation?
dumb question but i cant seem to find the answer
they both are
Sx is the standard deviation of a sample
So is the standard deviation of the population
i meant to ox, the one bellow Sx
it's the other way around. Sx is of the sample, ox is the one from the pop
theyre different numbers so im kinda confused
oml im so sorry, typed it too fast
^corrected
so ox is the standard deviation of everything and Sx is the standard deviation of a specific group?
ox (it's actually a sigma, not an o) is the standard deviation, assuming that the data you're entered is the full population.
sx is the standard deviation of the sample, which assumes that the data you're entered is just a portion of the full pop
sx = sqrt(n/(n-1)) ox
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,, a = \f{\Delta v}{\Delta t}
also open a new help channel
this formula is akin to finding the slope for a v-t graph
the velocity from time 0-8 is obviously growing at a constant rate, so the acceleration is constant. So pick any two points on that range and find the slope and thats ur max acceleration
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do you know what a minute is
1 radian would be 60 mins
no
....no
o
1 degree is 60 mins
angular displacement is like, d(theta)/dt
convert rad to deg and deg to min
what
if its this
then it should be 5156.4 mins
thanks sorry that confused me
how much is that in degrees?
85.94 degrees
then you can just differentiate it
okay, were not talking about differntiation to find angular acc or smg, sorry
i just check rn
im not sure if the final answer would be 85.94 or 5156.4 mins
the second one
they said to convert to rad to degree to min
if we would be talking about acceleration, we'd use like 3rd eqn for vel and thn find an eqn and differentiate it
pun intended lol
i missed the pun
same here
the second one
anyway
oh......haha i dont get it
same what
thats not a pun if its onyl one thing that has two options
or it went over my head
5k-ish sounds aboht right
k
This would be angular velocity = angle turned/ time taken pi radians by five, so angular velocity would be 0.628 rad/s
Result:
0.628 rad / s
,calc 12 * 0.628
Result:
7.536
,calc 7.536 * 5
Result:
37.68
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What does this mean by simplify be removing factors of 1?.
lets say we had 4/6
a factor of 1 would be 2/2
by removing 2/2 you get 2/3
basically "simplify"
thats what they shouldve wrote
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when x = 0, y = 2 just plug that into your equation
I don't need to solve for y?
when you put x=0 and y=2 you get the value of C
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.if you wanted to solve for y though, you could notice that y/(y - 1) = 1 + 1/(y-1), but as before you may not have to!
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is this correct?
if someone could explain altitude it would help me a lot as well, thank you!
draw an imaginary line from a corner to the other side (perpendicularly)
since this is an equilateral triangle the imaginary line will split the side into two equal pieces
Like this
that imaginary line is our altitude
We have a 30-60-90 triangle
so the altitude will be equal to 5[root]3
equilateral triangle has the same altitude at any corners
okay thank you so much 🙂
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Hi, this is an example problem for finding the directional derivative of a point on a gradient given a direction. I dont understand how the last step multiplies out to the answer, where does 8 * 5 come from?
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<@&286206848099549185>
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I mean, how is u defined?
u is that second vector
its defined like that before?
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could someone help me understand why this isn't correct?
Show your work, and if possible, explain where you are stuck.
the gradient is not a sum of partial derivatives
its a vector of partial derivatives
i and j here are the unit vectors
cuz your function goes from R^2 to R
a derivative of this function must be 2 d also
here is the provided example from the book
I wonder if it wants me to put it in vector form though
I just have limited attempts...
yea I'd agree with the answer. But what are P and u for?
they're for later parts of the problem
this is just the first part, each are graded independently
ah 😐
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is D correct?
It's the only one that is a tangent line, so yes.
are you sure?
Yes.
ok it was right can you help with more?
Is this a test?
Ok, can you show your work?
its right
are you sure
should be
I put it in the equation of the tangent line
adn got y=3+4(x-1)
yeah thats right
That's correct.
@old sequoia #❓how-to-get-help
And please delete your comment.
One moment.
ok thanks
Looks good.
Looks good.
Sorry, working on dinner.
ok
Can you show your work or at least how you approached the problem?
ok
call
what
ok
That looks correct.
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is my teacher contradicting herself here?
she shows an area as negative whereas previously she does the absolute value of areas under the x-axis
yeah but why in the third screenshot the answer is -14
for that integral
so we can say the total area (-9) is a valid answer?
i would, but apparently your teacher is allergic to the idea of negative area
but that's not what the question asks
it asks what is the integral
and that is indeed -9
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anybody can do this without any theorem from some real analysis book ?
just pre-university level question
Isnt that like that famous JEE problem or idk
yup and i cant solve it
💀
Yeah apparantly its really hard
have you tried ?
No im not from india its just this is the second time i see this today
many guys here were giving me some theorems from some maths books, which arent even taught to us for jee xd
fr ? who asked it first time tho ??
Apparantly there are videos on yt of solutions.
i dont want that
would be great if i can discuss it here with some person
Idk you can search the server for messages like JEE and see ig
kay
@lean otter found you!
look at the question i asked
probably this will be the procedure to solve, try to make it in summation format ( like using sigma and limit) then take 1/n as common that will be ur dt and by taking 1/n as common, u gonna make x/n that gonna treat as t , then integrate
integration limits would be according to options
may be this will be lengthy , but right now I only got this method on my mind
yup
yeah i will try this
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How to approach this?
Have you tried graphing it?
I have tried but I get confused why y is equal to two things
They are different lines
Let me attempt draw
Like one line is y = x and another line is y = 8x and a third line is y = 4
These three lines give a figure whose area we need to evaluate
Yes
Looks right to me
Write both functions in terms of x
Is it same limits
Yes
Wait actually we made a mistake in the last part
We shouldn't have used upper limit 4
We should have used upper limit = 4 * 8 = 32
For part a?
Why is it 4x8
Wait no lets redo part a from scratch aight
Yes
Yup
Do we need to re establish integrals
I think we can trivially remove the big one on the bottom by integrating x = y yea?
From 0 to 4
No the whole reasoning is flawed there tbh
I understand all of it except the upper bound of 1/2
well the line y = 8x and y = 4x intersect where
I added the rectangle from 0 to 1/2
And subtracted the lower area
To get the upper area
We now can subtract that area from our total
This question is much simpler in y btw
Yup put in the limits
I got 7
Me too
Now try with y
You can use 0 and 4 and the functions we wrote earlier (y/8 and y)
Just subtract
The other way around im afraid
Because the bigger area is represented by the area under y not y/8
Answer is back at 7
Thats good yea
👍 no worries
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nah
like why
@cinder pewter Has your question been resolved?
Do you know what a continuous function is?
I do but I can’t picture a graph for these definitions
There isn't a specific graph for these, no
It's more about intuitively understanding the definition of continuity
As an example, consider gas prices as a function of time.
Absolutely not continuous. Gas prices can change by an amount at any time, jumping around from any value to any other value
It could be 4.50 one moment, then instantly go to 4.70
It's not continuous because the price has a sudden jump
So, for the first one, can temperature instantaneously jump from one value to the next? Or does it move smoothly?
"continuous functions are functions which you can graph without lifting your pencil"
more or less, yea
I would say it’s continuous then
I would agree. Temperatures changes smoothly. It may rapidly change, say if you start a fire. But that change would not be instant
Okay, what about the second one?
The wording is throwing me off
Is it the temperature at a certain time but the distance is different each time?
Basically, it's temperature as a function of your location
I’d say discontinuous then because the temperature could jump based on the distance
I’ll try the last 3 and let u know cuz I get 3 attempts anyways, ty for the help
I can see how you might think that. Say if there's a hot cup of coffee in a cold room. You may even be right. But more realistically, I would call that a rapid change, but not a sudden jump.
That's hard to say precisely though.
On a large scale, I would argue the temp is continuous
@cinder pewter Has your question been resolved?
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@cunning cloak
i put down left and down which are correct
Oh this one
but i just dk what im doing wrong for the first fill in blank\
Could it possibly be right 8 units
So we know that the left 8 units is correct
indeed
Can u try swapping them out and identifying which part of yoru answer is wrong
What other options are there instead of reflect
Is there a “flip” option
most of the options are here
compress, stretch, shift, reflect
i think ive tried everyone
@lean otter Has your question been resolved?
<@&286206848099549185>
What's your question
im just curious as how the fill in the blank is incorrect
left and down are right
but reflect isnt
even if i put shift its incorrect
is there a translate
ask your query
im just curious what im doing wrong
it goes left 8 units and down 4 units which is correct
so 2/3 is correct
but reflect is wrong
i need help
ok
so it shifts left?
yes
it is kinda reflecting about the x axis and also shifting towards left
hm
i understand what youre saying
just confused on what to put to fill in the blank
try writing both reflects and shifts
still marked as incorrect
could it be one of these perhaps
think its just gonna be one word
like compress or something
ohh
yea no ones been able to tell me what it is
cant you just consult your teacher?
are you in university?
and what country are you from?
@lean otter Has your question been resolved?
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W = kx * x
k is the spring constant which I thought was found by doing 5/(0.11)^2
but apparently I'm supposed to use some other calculation using the natural length of 32 instead?
@nocturne hinge Has your question been resolved?
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do i pick numbers to plug in based on the limit?
No. 2^- means that x < 2 which means you need to use the first case.
You evaluate the limit as x->2^- for f(x). f(x) is determined by if x <=2 or x >2.
For this problem, yes, you can just use x=2.
Closed by @half berry
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Can anyone help me how to prove this?
I’m stuck for the (1/m + 1/M)^2
Like I don’t see how it changed to that
Is it I let (mM)^2 then only I can get the term I want?
if you were more specific on a "letting of a (mM)^2" then itd be correct
what you do is rewrite mM to be inside the square root
(mM) = square root of (mM)^2
this gets moved in to be that (mM)^2 youd need to finish the simplification
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Got ssstuck
@naive pendant Has your question been resolved?
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A floor plan has a 40: 1 scale. In the drawing, one of the rooms measures 38 inches by 1 1 inches. I need to show my answers to the nearest hundredth, even if it means I need to type zeros. I need to answer the actual dimensions would be # feet by # feet.
The area of the room would be # ft². How should I start to solve this problem?
How should I start to solve this problem? This is a Proportion assignment.
<@&286206848099549185>
hey, help me out plz
How should I start to solve that problem?
Is the room actually 38inches by 11 inches or did you mess up the formatting
yeah sorry. That's it.
Or are those the dimensions of the drawing
There is no drawing. That's a word problem.
I need to solve # which are blanks
#, means number
Hello?
<@&286206848099549185>
Youre question says there is a drawing: In the drawing, one of the rooms measures 38 inches by 1 1 inches.
no, there is no drawing.
It's telling you there's a drawing
An abstract one
it's a word problem.
Draw it yourself
Yes word problems make you use your imagination
Like word problems with apples and oranges don't actually give you apples or oranges
oh ok give me a minute.
Ok, I drew a pic. Now what?
can I send a pick? do I send a pick?
<@&286206848099549185>
Convert the dimensions to feet then multiply it by the scale to get the room dimensions
1 inch = ? feet
1 feet in the map/plan/drawing is 40 feet in reality.
and do not ping every 5-10 minutes.
oh sorry...
I told you
Here
hm...
Do you know this or not?
no, sorry, can you explain?
,w feet in 1 inch
do I convert 40in to feet?
as well as 38, and 11?
sorry, I still don't get what I am suppose to do? This is a Proportion problem.
Yes
38 in is 31.6666667 ft, 11in is 0.91666667, and 40 in is 3.33333. Now what?
No
First one is incorrect
38 inches is not 31.67 feet
Use this
You know the drawing in feet. Then convert that to real dimensions by using the scale
how do I do that?
No
40:1 does not mean 40 inches to 1 feet
40:1 means this
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not sure what to do :D.
ah
you multiplied up and down by x
oopsie
yes
yes
multiply 4 both sides
so /4 disappears
cancel out with 4
and the right side is multiplied by 4 also
3(1+x) = 4x-4
3+3x = 4x-4
ohhh ok
subtract 3x from both sides
.close
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Yes
on which one?
Btw I figured it out
The first one first please
for all of these, what you want to do is convert the given information into tangible equations you can work with
before we do anything else, it helps to know that the number XY where X and Y are digits can be written as 10X + Y
1 + C = 10
does this make sense?
Wait so I’m gonna give all the letters a number except for A?