robust lintel
i misunderstood mb
#help-0
tranquil vortex
Can someone help me with this? I don't quite understand how to solve this
tranquil vortex
The only instructions given to me was
A. Identify the similar triangles. Observe correct correspondence. What similarity theorem justifies your answer.
B. Use the given information to find x and y. Show your solutions.
lone heartBOT
@tranquil vortex Has your question been resolved?
lone heartBOT
@tranquil vortex Has your question been resolved?
serene isle
so how do you find if a triangle is similar
coral prairie
lone heartBOT
hushed locust
that doesn't look like the correct formula for the area of a semicircle
coral prairie
that doesn't look like the correct formula for the area of a semicircle
ohh wait yea i messed up that
if i fixed this do you think that would make the right answer?
hushed locust
i would have 2 variables here, 1 for the horizontal wall length and on for the vertical wall length, which is also the diameter of the semicircle
coral prairie
ohh bet ill give that a go
coral prairie
i would have 2 variables here, 1 for the horizontal wall length and on for the v...
would this make sense so far ?
hushed locust
remember that y is the diameter of the semicircle, so the radius is half of that
i would also keep your variables in terms of π rather than an approximation
also, the cost of the walls is based on the circumference of the semicircle
lone heartBOT
@coral prairie Has your question been resolved?
fresh hill
fresh hill
remember that y is the diameter of the semicircle, so the radius is half of that
Would this be it?
hushed locust
you can distribute the square in (y/2)^2 to simplify
also remember that the cost of the glass wall is based on the circumference of the semicircle, not the radius
fresh hill
you can distribute the square in (y/2)^2 to simplify
Ohh true
fresh hill
also remember that the cost of the glass wall is based on the circumference of t...
Wait does this mean diameter to find the area if we use y
Cause I say that 2r =y
Then just re-arranged r
hushed locust
the area is correct, but the cost is from the circumference
lone heartBOT
lone heartBOT
Available help channel!
fresh hill
So it models the cost
lone heartBOT
So it models the cost
hushed locust
you have the area correct, but the cost is based on the length of the walls, so you need to find the perimiter
hushed locust
you need to find the area to satisfy the constraint of being 30 sq m, but you need to minimize the cost associated with the perimeter
fresh hill
So how can I combine area and perimeter?
hushed locust
use area to solve for one variable in terms of the other, then use that in your cost calculation
you’ve been doing that mostly right
fresh hill
Like plugging the x I modeled In the area equation and plugging that into the cost fuction of perimeter?
hushed locust
yes
hushed locust
i think you may have to redo some of the algebra in solving for x though
coral prairie
i think you may have to redo some of the algebra in solving for x though
oh yea i see an error i did
slate solar
how did we end up a/2000?
lone heartBOT
how did we end up a/2000?
hushed locust
plugging in bounds we get $-\frac{a}{2000}-\left(-\frac{a}{1000}\right)$
ocean sealBOT
cloud
slate solar
ahhh
last ether
$-\frac{a}{2000} - \parens{-\frac{2a}{2000}}$
ocean sealBOT
Umbraleviathan
hard marten
if
hard marten
covering systems of equation if i were eliminating top to bottom, if one is positive and one negative do i substract or add
hushed locust
show the problem you're working on
hard marten
-3x -6y -3z -12
-6x +3y -3z -57
i already eliminated z
but i forgot if i add or subtract -6 and +3 cuz theyre different signs
if different sign do i add or subtract
if the same sign do i add or subtract
hushed locust
if you're trying to eliminate a variable, you want to subtract it from itself, so you'd want to do what it takes to have opposite signs in the same equation (subtract if same, add if opposite)
proud crown
What is the probability of three individuals randomly selecting the number 3 when the range from 0 to 9?
alpine sable
What is the probability of three individuals randomly selecting the number 3 whe...
like all three selecting 3?
proud crown
yes
some thought it is a binomial meaning P(k)=(5nCr3)*(1/10)^k*(9/10)^(5-k) P(k=3) what its is need it but does not make sense!
proud crown
like all three selecting 3?
thats what I tried
echo socket
Is it not just 1/10^3?
lone atlas
lone heartBOT
lone atlas
where did the 6hx come from
brazen sapphire
(x+h)^2 = x^2 + 2xh + h^2
and then you multiply every factor by 3 bc there's a 3(x+h)^2
lone atlas
(x+h)^2 = x^2 + 2xh + h^2
and then you multiply every factor by 3 bc there's a ...
oh i never knew that
thank you
.close
lone heartBOT
long axle
lone heartBOT
Available help channel!
cyan nexus
Implicit derivative problem
lone heartBOT
Implicit derivative problem
cyan nexus
long axle
What have u tried
long axle
Ok what did u get
cyan nexus
3y^2=9+4
long axle
Have u learned implicit differentiation before?
cyan nexus
no
long axle
Ok I can link u a good YouTube video, here: https://youtu.be/LGY-DjFsALc
cyan nexus
thank you stephen I'll watch it and try again
long axle
No problem
cyan nexus
.close
long axle
lone heartBOT
cyan nexus
lone heartBOT
Available help channel!
wintry robin
Why is this answer wrong?
We can deduce r=1 and it's a cilinder to 0 to 2pi. Then the expression is just replace in z, x by rcos(∅)
minor needle
What's the answer? 3pi?
and show your work if possible, how did you determine bounds
wintry robin
yes 3pi
minor needle
I've got
$$\int\limits^{\frac{\pi}{2}}{-\frac{\pi}{2}} \int\limits^{2\cos \theta}{0} (2r \cos \theta+1)r \dd{r} \dd{\theta}$$
wintry robin
and show your work if possible, how did you determine bounds
r = 1 by passing 2x to the left and seieing it's (x-1)^2 + y^2 = 1
delta 0 to 2pi because its a cilinder
equation just replaced x by rcos(delta)
ocean sealBOT
Modus
minor needle
r = 1 by passing 2x to the left and seieing it's (x-1)^2 + y^2 = 1
r would be 1 if the circle had a center at origin
but it hasn't
minor needle
no no, that's not how polar coords work
if you can't simply determine r or theta you can use equations given
x = rcos(theta)
y = rsin(theta)
substitute into equation of the circle:
(rcos(theta) - 1)^2 + (rsin(theta))^2 <= 1
from here (after dividing both sides by r) we'll get r <= 2cos(theta)
and r >= 0 is obvious
wintry robin
i thought r was just the radius of the circle?
minor needle
r in polar coords tells you how far the point is from the origin, if circle is centered in the origin then radius is constant and equal to the radius of the circle
but here it varies
wintry robin
Thank you a lot that actually helps a lot
although im trying to visualize it in geogebra
oh yeah it makes sense
minor needle
in order to understand it better
wintry robin
since it is on the x side only, angle goes from -pi/2 to pi/2
minor needle
look at this
wintry robin
i can understand now, it makes so much sense ahah
but that integral is so big to solve
minor needle
but that integral is so big to solve
not really
wintry robin
i was using photomath to do it, he complicated it a lot
minor needle
iterated integrals don't seem to be hard
wintry robin
maybe there's an easier way
wintry robin
iterated integrals don't seem to be hard
what do you mean
minor needle
$$\int\limits^{\frac{\pi}{2}}{-\frac{\pi}{2}} \int\limits^{2\cos \theta}{0} (2r \cos \theta+1)r \dd{r} \dd{\theta}=$$
$$=\int\limits^{\frac{\pi}{2}}{-\frac{\pi}{2}}\Bigg(\int\limits^{2\cos \theta}{0} 2r^2 \cos \theta + r \dd{r} \Bigg) \dd{\theta}$$
wintry robin
do you write all that by hand??
ocean sealBOT
Modus
minor needle
the inner integral is easy (you can split the sum into two integrals and treat cos(theta) as constant because it doesn't depend on r)
minor needle
it becomes
$$\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \frac{16}{3}\cos^{4}\theta + 2\cos^{2} \theta \dd{\theta}$$
ocean sealBOT
Modus
wintry robin
yeah, that gets kinda hard
minor needle
cos^2 is pretty simple, for cos^4 u can use reduction formula if you know
wintry robin
i don't
i don't think they're asking such complicated integrals in my exam anyways
we already were evaluated for that
wintry robin
that's a long one haha
wintry robin
yeah they're evaluating double integrals, triple integrals, and line integrals
you think they're much harder than doubles or?
minor needle
everything depends on an example (function to integrate)
"triple" doesn't necessarily mean it's hard
wintry robin
I mean, in an exam context
minor needle
I don't know your teachers haha, but I don't see any sense of giving complicated integrals for questions like that, it's about setting an integral rather than calculating it most of a time
wintry robin
thanks a lot tho
i had a flawed understanding of those polar coordinates
going to make it much simpler from now on
you're the boss
minor needle
np, good luck
upbeat plinth
Hi. state the domain of the given expression and then express this expression in a simpler form
alpine sable
which fraction?
upbeat plinth
which fraction?
I don't know what you mean, I do not speak english very well, its to separate examples
signal trellis
I don't know what you mean, I do not speak english very well, its to separate ex...
To find the domain of each, look at what makes the denominator (bottom of each fraction) equal to 0. For the first one, x-7 is on the bottom, so x can't equal 7, otherwise you would get division by 0.
To simplify them, you would factor the top and bottom and look for things that are the same, so they can be cancelled
lone heartBOT
@upbeat plinth Has your question been resolved?
surreal oracle
lone heartBOT
surreal oracle
the white background is the answer
i got the same answer apart from i got 1 - e sinx rather than 1+ e sinx in the denominator
they've subtituted y and x after rearranging
but surely it would get me the same answer?
placid zinc
Yours doesn't satisfy the boundary condition, at least that much is true
surreal oracle
what does that mean
placid zinc
Your solution needs to pass through (x,y) = (0, 1/2)
placid zinc
Yes, that's the confusing bit.
surreal oracle
$ln|(0.5)-1| -ln|0.5| = sin(0) +k$
ocean sealBOT
yomiko
placid zinc
Reading and thinking on why your solution fails the boundary condition, despite you seemingly subbing it in correctly
What was done to get up to ln|y - 1| - ln|y| = sin(x) + k?
No need to share the work, like what method was used?
surreal oracle
i did 1/y(y-1) and did partial fraction
placid zinc
Oh wait it's seperable, duh
surreal oracle
i did 1/y(y-1) and did partial fraction
on the right had side 1/secx turns into cosx which integrates into sinx
placid zinc
So the line:
ln|(y - 1)/y| = sin(x)
Obeys the boundary condition, but the line after:
(y - 1)/y = e^(sin(x))
Fails it. I think this is about how the absolute value function just disappears when taking the exponential of both sides, which is commonly done in DE despite being technically incorrect
To be completely safe, don't evaluate the constant until after the absolute value is gone
tiny mango
how do i solve a question lets say sin(130) by finding its exact value
tiny mango
and showing how i got its exact value
tiny mango
so sin(130 / 2pi)?
wintry robin
might be bs sorry
placid zinc
Some angles are called "special angles" and their sin/cos has an exact value.
130 isn't one of them, so an exact value can't really happen here
tiny mango
so the answer would be none?
how would i prove that, would i just plug it in a calculator and since it continues and doesn’t end, it’s not an exact value?
placid zinc
Not too sure what your teacher wants, specifically
tiny mango
just says find the exact values of the given angles, find the exact value and show how you know
placid zinc
Note sin(60) = √2 / 2, which is an exact value, but will also continue without end on your calculator
Probably a typo. 135 is a special angle, and they probably meant to go for that
hot bluff
you can still find an exact answer if you convert degrees -> radians wouldnt 130 degrees be 130pi/90? or 13pi/9
but hes right the resulting ratio of sin will not be exact
tiny mango
not sure, i was given 4 questions i think and each one i just plugged into calc, wasnt sure what to do
i use degree so idk about radian
each value i got from plugging it in was a decimal number that kept continuing
let me find an example question
placid zinc
Revisit the lesson, it sounds like you're struggling with it
hot bluff
13pi/18**
hot bluff
lol he is right, it was 135
those are special angles
by knowing the unit circle/triangle you can find these
tiny mango
by knowing the unit circle/triangle you can find these
what do uou mean by this
hot bluff
these are the unit triangles
so the basics of it are that cos x is our x on the graph of the unit circle
sin x is the y
(cos x, sin x) are the coordinates of the unit circle
135 degrees = 45 * 3 = pi/4 * 3 = 3pi/4
tiny mango
what if a question doesnt have one of these special triangles
hot bluff
look at that link
that's the hard part of trig, is that you really really really need to know that unit circle
if you can remember special angles and their coordinates on the unit circle. thats 80% of all the trig you'll ever need
hot bluff
those unit triangles are specifically for isosceles and 30-60-90 triangles.
those are less important and kind of tangential to the unit circle
this helps me remember the first quadrant of coordinate values, which you can then derive all other quadrants from
tiny mango
so mainly just know this circle? its so strange to me
hot bluff
two things that helped me out a ton was the hand trick and the magic trig hexagon
tiny mango
it was a quiz we just did, i feel like my teacher wouldve shown us this wheel
i think im forgetting something
hot bluff
https://www.mathsisfun.com/algebra/trig-magic-hexagon.html this is for identities, while the hand trick is for the unit circle
austere compass
Why is this
$$
d(A,B) := \inf{d(x,y) \ | \ x \in A, y \in B} = 0
$$
true for sets
$$
A := {\mathbb{N}} \text{ and } B := \left{n+ \frac{1}{n} \ | \ n \in \mathbb{N}_{\geq 2} \right}?
$$
ocean sealBOT
Levens
austere compass
Oh and we're in the metric space (X,d)
And A and B are subsets of X
cause i get how the distance would be zero like visually but i dont know how to write it down on paper
So... what do you guys think?
<@&286206848099549185>
lone heartBOT
@austere compass Has your question been resolved?
coral prairie
lone heartBOT
@coral prairie Has your question been resolved?
sand pendant
lone heartBOT
sand pendant
...
lone heartBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
sand pendant
...
<@&286206848099549185>
<@&286206848099549185>
...................................
<@&286206848099549185>
hardy tangle
State your reasoning so far
sand pendant
well i know the basics of the topics like the formulas
but like for this question i dont even know what the load is
hardy tangle
So do you know which quantity remains equivalent in a parallel circuit
sand pendant
voltage
hardy tangle
voltage
Good
Now you need to use that
What part exactly
Wait
This requires understanding of parallel cell circuit
Do you know that
sand pendant
no
sand pendant
what is the formula for parallel cell circuit
hardy tangle
$\epsilon = r_{eq}(\frac{\epsilon_1}{r_1}+\frac{\epsilon_2}{r_2})$
hardy tangle
Resistance
hardy tangle
Yes internal Resistance
E stands for emf of the cell
That formula is only specific to that condition
ocean sealBOT
[ɸ]=1.618033988749....
lone heartBOT
@sand pendant Has your question been resolved?
lone heartBOT
@sand pendant Has your question been resolved?
peak juniper
im confused
solemn juniper
About?
peak juniper
when tgere asking for no rolling 3 on a six sided dye
wouldnt it be 4/6
5/6
i meant
solemn juniper
5/6 yes
peak juniper
not an option thho
placid venture
Hi! I'm very rusty to math. can anyone help me with the procedure to solve this?
I am studying for a test next month
placid zinc
Make sure you know how to factor a perfect square trinomial
Breaks this question wide open
subtle birch
Hi! I'm very rusty to math. can anyone help me with the procedure to solve this?...
Both the terms under square root are perfect squares
Try to factor them
lone heartBOT
@placid venture Has your question been resolved?
placid venture
Both the terms under square root are perfect squares
thanks
honest sage
lone heartBOT
Available help channel!
wanton pebble
amber plover
how do i tell which quadrants these are in?
lone heartBOT
how do i tell which quadrants these are in?
amber plover
is sin in quadrant 4 since it's domain is in the positive side but it's negative
rich quiver
how do i tell which quadrants these are in?
which quadrant lies in [π,3π/2]?
amber plover
quad 1 and 4 right?
amber plover
which quadrant lies in [π,3π/2]?
that's the positive side isnt it
amber plover
oh is it the angle
rich quiver
Yes
rich quiver
What is the question?
amber plover
ok and i'm guessing the other one is in quadrant 2
amber plover
What is the question?
find tan a + b
rich quiver
ok and i'm guessing the other one is in quadrant 2
Yes
amber plover
alright thanks i thought for a sec that meant was meant to be x values for some reason
lone heartBOT
Available help channel!
vale ginkgo
Hey can someone please help me on this question? What do I do first?
There are 12 chickens and dogs. If there are 40 legs altogether, how many dogs are there?
A. 4
B. 5
C .6
D. 8
subtle birch
Hey can someone please help me on this question? What do I do first?
There are ...
Let number of chickens to be x and number of dogs to be y
form two equations
vale ginkgo
2x + 4y = 40?
placid zinc
That's a good one! The other one is just how many animals there are
subtle birch
no
silent vault
Bro! Help me 😭
subtle birch
12 chickens and some dogs
subtle birch
Bro! Help me 😭
subtle birch
I can't get help, I have to solve a function exercise
Open a new channel
This is occupied
subtle birch
Hey can someone please help me on this question? What do I do first?
There are ...
wait, you dont even need variables
vale ginkgo
how so?
subtle birch
There are 12 chickens
vale ginkgo
no
vale ginkgo
12 chickens AND dogs
subtle birch
?
subtle birch
12 chickens AND dogs
Okay
vale ginkgo
not only chickens
subtle birch
so x+y=12 and 2x+4y=40
vale ginkgo
yes
subtle birch
Use substitution
vale ginkgo
explain further?
subtle birch
x+y=12
find y from here in terms of x
Put this value of y into next equation which is 2x+4y=40
vale ginkgo
you mean solve for y?
vale ginkgo
yep
subtle birch
so put this value of y into next equation
vale ginkgo
ok
subtle birch
2x+4(12-x)=40
subtle birch
noo
vale ginkgo
sorry x
subtle birch
we got y=12-x
subtle birch
yeah okay
subtle birch
no
subtle birch
Won't the equation be 4x + 2y = 40
=> 2x + y = 20?
we can do it but not necessary
also it is 2x+4y=40
vale ginkgo
exactly
stone gulch
Dogs have 4 legs, isn't it?
So 4x
subtle birch
Dogs have 4 legs, isn't it?
So 4x
we assumed number of dogs to be y
vale ginkgo
I substituted the thing from earlier
stone gulch
Ok
vale ginkgo
to 2x + 4(12 - x)
subtle birch
2x + 4(12 - x) = 40
just solve this
vale ginkgo
ohh I found my mistake
stone gulch
Where did the x+y = 12 come from?
vale ginkgo
take a look at the question
vale ginkgo
Hey can someone please help me on this question? What do I do first?
There are ...
here
subtle birch
Where did the x+y = 12 come from?
please read the question and do not interfere unnecessarily. This may confuse the OP
vale ginkgo
please read the question and do not interfere unnecessarily. This may confuse th...
op?
subtle birch
original poster
stone gulch
You
vale ginkgo
its okay
stone gulch
What if the 12 total wasn't there?
vale ginkgo
wdym
subtle birch
What if the 12 total wasn't there?
It would become a diophantine
stone gulch
Total legs are 40
Find possible composition of dogs and chickens
subtle birch
@vale ginkgo Continue with your work
vale ginkgo
I am
subtle birch
Total legs are 40
Find possible composition of dogs and chickens
Why even you are going out of question?
stone gulch
I thought he's done with the answer
vale ginkgo
<@788348632599363626> Continue with your work
x = 4?
subtle birch
Yes
vale ginkgo
ok but one question
subtle birch
Now you can find y as well
subtle birch
okay
vale ginkgo
then I took away 4x from 2x
becomes -2x + 48 = 40
then I half it
-x + 24 = 20
-x = 24 - 20
-x = 4
but its negative x?
does that make any difference?
subtle birch
your process is wrong
vale ginkgo
-x = 20 - 24?
subtle birch
Yes
vale ginkgo
but there cannot be -4 chickens?
subtle birch
so -x = -4?
yes
vale ginkgo
You make it +x
oh okay
subtle birch
-x=-4
-x+4=0
4=x
stone gulch
Thank him more
I just confused you for no reason🤦♂️
vale ginkgo
no its alright
you also tried helping as well
Here's another one I need help with
Tom is 3 times younger than his father. The difference between their ages is 32. How old is Tom?
A. 16
B. 18
C. 32
D. 48
stone gulch
Let both their age be some different variables, your choice
subtle birch
I'll leave it to TesmiT
stone gulch
Let's say the father's age be 'f'
Tom's age be 't'
stone gulch
Will wait, no problem
When I first read the problem, I look for relations and numbers
What I noticed here are:
"Tom is 3 times younger than his father"
And
"Difference between their ages is 32"
So I got 2 info (times, difference), for 2 people (tom, father)
Hence, 2 equations & 2 variables is what I would aim to make
vale ginkgo
I'm back
here's what I did
Let T be tom and Father be F
so I did T = F divided by 3
and T - F = 32
wait so
I think I got it
do we just substitute?
stone gulch
I think father will be older so F-T
stone gulch
You can substitute now
vale ginkgo
with the first equation?
stone gulch
Yes
vale ginkgo
T = 3 ÷ (32 + t)
stone gulch
Where did the small t come from?
vale ginkgo
how so?
stone gulch
Sorry
stone gulch
😂 you know, i used to get father being younger than son when i used to solve these questions
vale ginkgo
Lol
vale ginkgo
3T - T = 32?
stone gulch
Yes
stone gulch
Yep
vale ginkgo
52
stone gulch
Yes
stone gulch
Haha, calculation error
vale ginkgo
lol
I wouldn't dare to do that on my upcoming selective test
Man
its like a month away
some small things its just
stone gulch
You'll be up and running at not time.
Just remember to be calm while calculating
stone gulch
some small things its just
Yes
It happens with me too.
I do silly mistakes like you too, at my age
stone gulch
Wow
vale ginkgo
this question is in the quantitative ones
stone gulch
How many total questions?
vale ginkgo
60 in 30 min
vale ginkgo
well
those questions are probably hard
like take a long time
these questions can be solve faster then those
stone gulch
I don't remember tbh 🤔
But you're on the right path for solving them
Do you have any other questions?
vale ginkgo
its a long one but
Kimberly walked at an average speed of 3.9km/h, while her sister walked at an average speed of 55m/min. If they walked from each other opposite directions from the same starting point, how long would it take for them to be 360m apart?
A. 180 sec
B. 240 sec
C. 300 sec
D. 360 sec
stone gulch
When I first read the problem, I look for relations and numbers
What I noticed ...
Step 1 :
Step 2 : Take variables that will help you identify the people in the question easily (rather then using traditional X & Y)
stone gulch
Step 3 : Write down the given info with the variables you're using
Step 4: Make necessary changes (depending on question) on the equations
Step 5: Substitute and calculate
vale ginkgo
okay
stone gulch
There?
vale ginkgo
yes
vale ginkgo
Kimberly walked at an average speed of 3.9km/h, while her sister walked at an av...
I need help with this question but if you are free 2.5 hours later I'll ping you
I can't do it right now
but
stone gulch
Sure
stone gulch
You can dm me
storm sable
which test do i use for this question
lone heartBOT
which test do i use for this question
@storm sable Has your question been resolved?
lone heartBOT
@storm sable Has your question been resolved?
jagged swan
1, When is the DVD deal more advantageous than the clothes?
2, When is the kids’ and babies’ denim deal most cost effective?
3, Explain, based on cost effective buying, how you would spend your $40. Include the calculated savings and percentages off.
wheat isle
assignment 
jagged swan
assignment <:sotrue:826971355542192148>
Yeahh
ocean sealBOT
jagged swan
<@&286206848099549185> please someone
violet flare
yeah that's not a question
jagged swan
yeah that's not a question
What’s not a question?
upbeat hornet
Can you take a picture of the questions in Question 1
violet flare
read what you sent, and tell me what you're having a problem with
jagged swan
Can you take a picture of the questions in Question 1
Here
jagged swan
Do you understand the terms in the question?
I do not
upbeat hornet
Wait. I’m confused what you’re asking
What words do you not get?
jagged swan
Oh wait, my bad. I get all the words, just not what the questions are asking
upbeat hornet
When you put the words together, what do you not understand
jagged swan
When you put the words together, what do you not understand
Wdym?
Sorry 😭 I struggle understanding clear questions sometimes
upbeat hornet
Wdym?
Sorry 😭 I struggle understanding clear questions sometimes
If you understand the words by themselves, what do you not understand when you put them together?
jagged swan
If you understand the words by themselves, what do you not understand when you p...
Oh. Idk. I just don’t understand what the questions are trying to ask
upbeat hornet
Oh. Idk. I just don’t understand what the questions are trying to ask
Can you understand what they want you to do?
jagged swan
Can you understand what they want you to do?
I don’t understand that, no.
upbeat hornet
What are the prices of the clothes and dvds
lone heartBOT
@jagged swan Has your question been resolved?
jagged swan
<@&286206848099549185>
lone heartBOT
@jagged swan Has your question been resolved?
alpine sable
1, When is the DVD deal more advantageous than the clothes?
2, When is the kids...
what?
what does it mean by cost effective?
these questions seem really dumb
If cost effective means the most effective way to bring joy to your little brother
then how would anyone know that?
lone heartBOT
@jagged swan Has your question been resolved?
feral scroll
I just need help to get started
lone heartBOT
I just need help to get started
feral scroll
like some hint
stone gulch
like some hint
Embibe?
prime badge
yeah get wasted on gin & tonic
lone heartBOT
@feral scroll Has your question been resolved?
lone heartBOT
@feral scroll Has your question been resolved?
feral scroll
.close
sick gulch
Trying to find the generating function $A(x)$ of the sequence $a_n = P(n)$ (a polynomial in n) where $n\geq 0$, by multiplying both sides by $x^n$ and summing over $n \geq 0$
sick gulch
So I get $A(x)=\sum_{n\geq 0} a_n x^n = \sum_{n\geq 0} P(n)x^n$
ocean sealBOT
bostock
sick gulch
I let $P(n)=\sum_{k=0}^m p_k n^k$ as the polynomial P(n) is order m
sick gulch
After rearranging I get $A(x)=\sum_{k=0}^m p_k \sum_n n^k x^n$
ocean sealBOT
bostock
sick gulch
My question is: how do I get the generating function of the sum in n
My attempt: I tried doing the x d/dx operator method. I need to do it k times to get the geometric series expression so $\sum_n n^k x^n = D_x^k \frac 1 {1-x}$ where $D=x\dv{x}$
ocean sealBOT
bostock
sick gulch
Dunno how to get a kth term expression though as the expressions for k=1 and 2 and 3 don't give an obvious expression that I can prove by induction on
lone heartBOT
@sick gulch Has your question been resolved?
sick gulch
Solved, there is no closed form solution so I got $A(x)=\sum_{k=0}^m p_k D^k \frac 1 {1-x}$
ocean sealBOT
bostock
sick gulch
$\sum_{k=0}^m p_k D^k = P(D)$ so $A(x)=P\left(x\dv{x}\right) \frac 1 {1-x}$
ocean sealBOT
bostock
sick gulch
.close
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
Are all subsets of X with disc metric open and closed?
lone heartBOT
Are all subsets of X with disc metric open and closed?
torn elk
yes
patent swallow
how can I find g'(0)
lone heartBOT
how can I find g'(0)
patent swallow
full frost
chain rule
patent swallow
yeah I'm stucked there
idk if I'm applying it correctly
I'll tell you what I've got
outer lark
Already clapped
cyan seal
Do you only have that? @patent swallow
patent swallow
nono I've more but I'm stuck in this part of the excercise
cyan seal
Can you send all of it?
patent swallow
for what its worth:
f(3) = 21
f'(3) = 5
thats what I got, I need to find the equation of the tangent of g in x = 0
so now I'm trying to find the derivative of g in 0 for the slope
I suck at derivation
cyan seal
When x = 0, g(0) = f(3) = 21
So g'(0) = f'(3)
I'm not sure if that's right, that's my try
still jungle
what is the biggest value of the function in this range?
lone heartBOT
what is the biggest value of the function in this range?
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
outer lark
how would you find a local maximum normally
still jungle
find the derivative then find the zero of the derivative and then put the x in the original function
outer lark
and what is stopping you from doing that here?
outer lark
find the derivative then find the zero of the derivative and then put the x in t...
checking the functions value at the endpoints is also a good idea. required.
still jungle
yeah this as well
outer lark
so what is f'(x)?
jaunty wasp
still jungle
for the maximum and minimum I get pi/12 + sqrt(3)/2 and 5pi/12 - sqrt(3)/2. But which one is minimum and which one is maximum?
outer lark
what do you think?
have you tried evaluating them to see which is greater if you're having a hard time by just looking at it?
still jungle
How would I do that?
outer lark
do you have a calculator???
still jungle
yeah
outer lark
plug them in a see which is greater
still jungle
ok I see but how do I determine it without a calc?
nvm I figured it out
ty @outer lark
lone heartBOT
@still jungle Has your question been resolved?
burnt wolf
Can someone explain this for me? I am confused
lone heartBOT
Can someone explain this for me? I am confused
burnt wolf
I know a pmf $p(x)$ satisfies $F(x)=\sum_{y=0} ^x p(y)$
ocean sealBOT
Douglas57721
burnt wolf
But here we could have something like $b=x=0.1$ and so $F(b)=1/2$, but I'm not really sure how that works with the summation
ocean sealBOT
Douglas57721
burnt wolf
And if it's supposed to be a density function, then you will have $F(x)=\int_0 ^x f(y) \dd{y}$, but if the integral between 0 and b is a half then its derivative is zero
ocean sealBOT
Douglas57721
lone heartBOT
@burnt wolf Has your question been resolved?
burnt wolf
Can someone explain this for me? I am confused
<@&286206848099549185> Please can I have some help with this?
lone heartBOT
@burnt wolf Has your question been resolved?
burnt wolf
@fierce herald I assume I'm doing something wrong and that's why I'm not getting answers. What am I doing wrong?
finite flax
@burnt wolf does the book have an answer to check against?
burnt wolf
No
finite flax
I guess I would have assumed that the piecewise-defined function is the probability mass function
alpine sable
Out of all people surveyed here what percentage were males that preferred skating.
alpine sable
Is this question marginal relative frequency, conditional relative frequency or joint relative frequency
<@&286206848099549185>
surreal meadow
i can answer your first question but not the second
lone heartBOT
lone heartBOT
Available help channel!
wild olive
can anyone explain how they went from the first step to the 2nd?
tacit arch
common denominator
raven rover
1 = x + 2 overbitself
steady basin
hi
lone heartBOT
@steady basin Has your question been resolved?
steady basin
.close
quartz panther
lone heartBOT
lone heartBOT
lament forge
.reopen
lone heartBOT
✅
tacit arch
,tex .exp rules
ocean sealBOT
riemann
quartz panther
yep ik those
tacit arch
turn f into just one single power of x
quartz panther
its likea wombo combo of those idk what to do
ik i have to get on single power but im unsure how
4x(x^-1/2)
?
tacit arch
but they have differetn co-efficients?
so?
tacit arch
the right is a single power
x and y are different here
tacit arch
4x(x^-1/2)
or do you mean the 4
that's being multiplied so you factor it out
4 * a * b = 4 * (a * b)
simplify the parentheses
quartz panther
or do you mean the 4
i mean the 4
tacit arch
the power isn't on the 4 anyway
quartz panther
the co-efficient is 4 no>?
quartz panther
the power isn't on the 4 anyway
ok
tacit arch
the 4 is completely irrelevant
quartz panther
okie
tacit arch
exponent rules is on the base x
lone heartBOT
lone heartBOT
Available help channel!
vital wyvern
The ratio of the number of erasers to the number sharpeners in a box was 1:2. When 9 more erasers were added to the box, the ratio became 5:4. How many erasers and sharpeners were there in the box at first?
vital wyvern
What I tried to do was
I made eraser as x, sharpeners 2x. So then when 9 more erasers were added, I knew we had to do eraser as x + 9, when the ratio became 5:4, it should be (x + 9) : 2x, but when I was told it should be (x + 9) / 2x = 5:4. I'm a bit confused and believe I might have mixed up my calculations
rustic coral
I made eraser as x, sharpeners 2x. So then when 9 more erasers were added, I kne...
that seems correct to me so far
lone heartBOT
@vital wyvern Has your question been resolved?
vital wyvern
that seems correct to me so far
oh lets continue then
so both should be equal correct?
vital wyvern
<@&286206848099549185>
lone heartBOT
@vital wyvern Has your question been resolved?
cinder sundial
lone heartBOT
surreal meadow
Why the area is (sqrt3)/4 * 1^2
what do you think the area should be?
ocean sealBOT
XxMrFancyu2xX
proven leaf
carmine reef
The *1^2 doesn't change anything
1^2 is 1
multiplying by 1 doesn't change a number
Its probably there because (s²√3)/4 is a formula for area of an equilateral triangle and thats what they used
cinder sundial
The *1^2 doesn't change anything
I know but why we get the square of 1
proven leaf
you shouldn't
A=1/2bh
b=1
h=sqrt(3)/2
A=1 x sqrt(3)/2 x 1/2
idk where you got your 1 squared from man 😂
carmine reef
Its probably there because (s²√3)/4 is a formula for area of an equilateral tria...
^
proven leaf
$A=\frac{s^2\sqrt{3}}{4}$
carmine reef
Or you can just find an altitude again
ocean sealBOT
XxMrFancyu2xX
proven leaf
this can be derived from finding the altitude and using the A=bh/2 formula
cinder sundial
What’s the s in that formula
proven leaf
side length
cinder sundial
side length
why there’s a square in it
proven leaf
Area of an Equilateral Triangle with respect to its Side Length—creative ik 
there are probably a billion derivations on the internet
if you so wish to delve into that
flat vale
what does invariant mean
lone heartBOT
what does invariant mean
vapid shuttle
"In mathematics, an invariant is a property of a mathematical object (or a class of mathematical objects) which remains unchanged after operations or transformations of a certain type are applied to the objects.[1][2] The particular class of objects and type of transformations are usually indicated by the context in which the term is used. For example, the area of a triangle is an invariant with respect to isometries of the Euclidean plane. The phrases "invariant under" and "invariant to" a transformation are both used. More generally, an invariant with respect to an equivalence relation is a property that is constant on each equivalence class.[3]"
For your example there, if you take a line and transform it by either I or -I
you get the same line
so the transformation would be invariant
here's a decent visual with some notes I put in desmos aswell
That matrix btw is just a type of rotation matrix, it will rotate your input vector by an angle of theta
so it makes sense that when theta is an integer multiple of pi, it rotates your input vector by an angle of 180 degrees
which explains why it is invariant under those conditions
rotating a line 180 degrees gives you the same line
rotating a line 180*k degrees gives you the same line (for k an integer)
@flat vale
lone heartBOT
@flat vale Has your question been resolved?
dawn flax
hola , me podrian ayudar con este problema? el ejercicio dice en el punto (0,2) pero en verdad es en el punto (2,0)
remote heron
sorry i dont know spanish 
seems like a typo though
lone heartBOT
@dawn flax Has your question been resolved?
shadow oxide
I am unable to eliminate the constant a&b and for a Partial differential equations of the following equation.
$$ax^2 + by^2 + z^2 = 1$$
ocean sealBOT
d-kanti
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
crisp cargo
can you provide more information please