try to solve
x+y=-650
y+20=2x
#help-0
harsh pumice
x=y/2+10?
harsh pumice
that's the system of equations they gave you
oh
alpine sable
Please Help Me
lone heartBOT
Please Help Me
alpine sable
We are supposed to prove the thesis based on the hypothesis
Hypothesis is in the left and thesis is in the right
<@&286206848099549185>
whole wadi
Determine the range and domain of values for the function $$f\left(x\right)=3\tan \left(\frac{x}{2}\right)$$
ocean sealBOT
Theophania
whole wadi
$$D=\left{x\in \mathbb{R}::x\ne 90+n\cdot 180\right}$$
$$V=\left{y\in \mathbb{R}::-\infty \le y\le \infty \right}$$
ocean sealBOT
Theophania
silver marsh
You already have a channel open
torn turret
Can someone help me with this equation? how does (h1+h2)rho2g = h2rho1g get to this answer h1/h2 = (rho1 /rho2 ) -1 ? It`s a simple equation i struggle with in fluid mechanics
polar mist
$$
(h_1+h_2) \rho_2 = h_2 \rho_1 \newline
\Rightarrow \frac{h_1+h_2}{h_2} = \frac{\rho_1}{\rho_2} \newline
\Rightarrow \frac{h_1}{h_2}+1 = \frac{\rho_1}{\rho_2} \newline
\Rightarrow \frac{h_1}{h_2} = \frac{\rho_1}{\rho_2}-1
$$
ocean sealBOT
Gumiibear
whole wadi
Determine the range and domain of values for the function $$f\left(x\right)=3\tan \left(\frac{x}{2}\right)$$
whole wadi
is this correct?
$$D=\left{x\in :\mathbb{R}:::x\ne :180+n\cdot :360\right}$$
$$V=\left{y\in :\mathbb{R}::-\infty :\le :y\le :\infty :\right}$$
ocean sealBOT
Theophania
whole wadi
,w range of 3tan(x/2)
ocean sealBOT
vale wigeon
are you not allowed to write $V = \bR$?
ocean sealBOT
Ann
vale wigeon
your notation is TECHNICALLY correct but way redundant
whole wadi
oh, i don't know tbh
vale wigeon
if you're working in degrees, yes
surreal badger
help in solving this
lone heartBOT
help in solving this
lone heartBOT
@surreal badger Has your question been resolved?
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surreal badger
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surreal badger
help in solving this
anyone?
alpine sable
which part?
surreal badger
which part?
ii) and iii)
im stuck cause they are saying to find using ratios
and there isnt any ratio to use
alpine sable
this is what it means when it says ratios
surreal badger
this is what it means when it says ratios
isnt it this?
alpine sable
yes, for those angles only
alpine sable
a ratio is just one number divided by the other. that's it
so the length of one side divided by the length of the other side is a ratio
surreal badger
oh mb i was just finding a ratio angle
lmao
so i got the answers
can u check?
alpine sable
sure
surreal badger
workings?
alpine sable
so PN is separated by QM. we first solve for the line between point P and the line that intersects it, QM
the length of that segment is defined by x, so $sin(50) = \frac{x}{50}$, thus $x = 50 sin(50)$
ocean sealBOT
tinge
surreal badger
i took tan 50
alpine sable
but PQ is the hypotenuse
for you to access the length of hypotenuse, you need cos or sin
if we remember what x is, we can say that $sin(30) = \frac{x}{MP}$, so $MP = \frac{50\sin{50}}{sin(30)}$, finally $MP = 100 \sin(50)$ because $\sin(30) = \frac{1}{2}$
ocean sealBOT
tinge
surreal badger
for you to access the length of hypotenuse, you need cos or sin
no MP is the opposite side to MQP angle
so tan 50 = MP/50M
isnt it right?
wait im confused
how is PQ hypotenuse/?
MQ is the hypotenuse?
right
cause MPQ = 90 AND NMP = 90
alpine sable
ohhhh I see what you did, yeah you're definitely right
it's hard without a diagram, my fault
surreal badger
it's hard without a diagram, my fault
help to find that angle?
forgot the pen marks
alpine sable
help in solving this
you have the necessary angles here
surreal badger
you have the necessary angles here
i dont need to use any ratio to find it?
alpine sable
you might, but you can also use quadrilateral rules
triangle has 180 degrees, quadrilateral has 360 degrees
lone heartBOT
@surreal badger Has your question been resolved?
gloomy forge
lone heartBOT
gloomy forge
would i sub into y=ax^2+bx+c?
wary stream
would i sub into y=ax^2+bx+c?
Yes
wary stream
You need to create all 3 equations first
You have 3 points, use that to create 3 equations
wary stream
Also, even if you have multiple questions, just stick to one channel. One, it allows more people to ask questions and two, you don't have to go back and forth
wary stream
these are what i got now
You created 3 equations, do you know how to solve a system of equations?
lone heartBOT
@gloomy forge Has your question been resolved?
rugged lynx
lone heartBOT
inner mauve
You can just sub in x-1 for y in the first equation and use that to solve for x
lone heartBOT
@rugged lynx Has your question been resolved?
smoky cloud
can anyone help me with this
lone heartBOT
can anyone help me with this
smoky cloud
open a separate channel
covert zinc
ok
smoky cloud
so that ppl can access u easily
covert zinc
ok
lone island
Have you tried integration by parts?
smoky cloud
not working
wary stream
Post your attempt
smoky cloud
Post your attempt
what attempt ?
wary stream
What did you try? Do you have work on what you tried to do?
smoky cloud
What did you try? Do you have work on what you tried to do?
I found out that sqrt part can't be integrated
if it was a square I could have done something but cube gives no idea
smoky cloud
u mean apply parts ?
wary stream
It's been a while since I did calculus but I mean something like make u = 1 + x - x^3 so then du = 1 - 2x^2. But now looking at that, I don't think it really helps
toxic cove
if you put it into wolfram alpha you get something truly horrific
lone heartBOT
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lone heartBOT
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strong iris
Can someone explain this more to me please?
lone heartBOT
Can someone explain this more to me please?
echo socket
Which is step is the one confusing you?
strong iris
Which is step is the one confusing you?
How did we get 2yz in line 2?
echo socket
We wrote $8$ as $4\cdot{2}$, then $y^9$ as $y^8y$
ocean sealBOT
Touch Our Beans
strong iris
Okay, i get it the second part. How did we end up with 2xyto 4 on the left sife
side**
lone heartBOT
@strong iris Has your question been resolved?
void verge
Okay, i get it the second part. How did we end up with 2xyto 4 on the left sife
they took the square root of the terms and it simplifed to that
strong iris
I don't follow
void verge
whats the sqrt(4)...
strong iris
2
dense gust
Okay, i get it the second part. How did we end up with 2xyto 4 on the left sife
They've taken the square root of 4, x^2 and y^8
void verge
^^^
dense gust
Which is 2 * x * y^4
void verge
y^4 but yea
dense gust
o
strong iris
Sorry guys I get lost within chatting. Can you demonstrate that on a paper or something, help your brother, brothers.
void verge
$\sqrt{4x^2y^8}$
ocean sealBOT
SavageShrikar
ocean sealBOT
SavageShrikar
strong iris
thank you josh, and guys y'all real MVPS
dense gust
np lol, real MVPs will be people who will solve the previous question-integral
it did quite brain dmg to me
dense gust
no problemo
lone heartBOT
@strong iris Has your question been resolved?
runic obsidian
multiplied the top polynomials together
lone heartBOT
multiplied the top polynomials together
runic obsidian
but none of the answers are of those values, so im not sure if im doing something wrong here
ohh wait nvm i think i got it now
.close
lone heartBOT
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strong iris
Is my simplifying correct?
lone heartBOT
Is my simplifying correct?
strong iris
strong iris
is this correct?
buoyant kayak
where did z come from
strong iris
sorry it is in the original operation but i forgot to writi it
what did i do wrong?
strong iris
i seperated 45 = 40. 5 so i can be able to sqaure 40 into 2
so i put 5 on the other side
buoyant kayak
what
strong iris
here
buoyant kayak
yeah it ain't right
strong iris
look into the second attachment they did the same
but i don't know where 9 came from
buoyant kayak
they did not do the same
strong iris
explain it to me brother
buoyant kayak
$\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}$
ocean sealBOT
a disappointing son
buoyant kayak
you split it into $\sqrt{40x^2y^8}\cdot\sqrt{5yz}$ which is equivalent to $\sqrt{40x^2y^8\cdot 5yz}$
ocean sealBOT
a disappointing son
buoyant kayak
which is not $\sqrt{45x^2y^9z}$
ocean sealBOT
a disappointing son
strong iris
ok then?
buoyant kayak
this already showed you the steps
i told you what you did wrong
what are you confused on
strong iris
I am a slow learner. I need to see the work on paper.
can you walk me through it plz
buoyant kayak
sorry it is in the original operation but i forgot to writi it
this is the work
lone heartBOT
@strong iris Has your question been resolved?
strange rampart
lone heartBOT
strange rampart
How would you go about this? (I have an answer, but I'm not sure if it's an efficient method)
The 4th
Oh
Yeah
I tried to reverse engineer the limit to find what f(x) was
as well as the interval being considered
No imaginary numbers are involved lol
But I can see how it looks that way
peep the sigma
lol
How would you have solved it?
glass lichen
$\Delta x=\frac{(\pi / 4)}{n}\implies b-a=\frac{\pi}{4}$
ocean sealBOT
Mosh
glass lichen
Just extract the information for the definite integral.
bleak ridge
Del tuh
strange rampart
I tried to reverse engineer the limit to find what f(x) was
So this is the way to go?
glass lichen
yeah, just write it as the definite integral.
worthy verge
lone heartBOT
lone heartBOT
@worthy verge Has your question been resolved?
worthy verge
Need help for 3 only now
ancient saddle
Need help for 3 only now
Hello, what have you tried?
worthy verge
I have tried subbing in z like it said
Diff both sides i get d2y/dx2 = 2zdx
Im just completely lose
lost
ancient saddle
mmm I think you should diff both sides in z = 9x + 4y +1 with respect to x
then you can find a relation between z' and y'
ancient saddle
ok, isolate the arctan, then take tan on both sides so the arctan is cancelled
worthy verge
ah so
2z/3 =tan(6x-c)
then move 3 over and put z back
i got the ans
ty so much
is it the same with arcsin and arccos?
worthy verge
ok, isolate the arctan, then take tan on both sides so the arctan is cancelled
for thsi step
ancient saddle
yes it's the same
lone heartBOT
worthy verge
tyso much
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Available help channel!
stoic mantle
any hints on how to get started with this differential equation problem? I attempted plugging in y into the given dy/dx equation and also tried taking the derivative of y, which one should I do? or neither?
raven rover
any hints on how to get started with this differential equation problem? I attem...
I think your approach is good
You can find y and dy/dx in terms of m, b, and r
You can plug those expressions into the differential equation and equate coefficients
Equate coefficients
Set the coefficients of the exponentials (e^(rx))to be the same.
Set the coefficients of the linear terms (x) to be the same.
Set the coefficients of the constants to be the same.
@stoic mantle
stoic mantle
by the first part do you mean taking the derivative of the y equation and setting it equal to the 3x+2y+1?
@raven rover
raven rover
You can find y and dy/dx in terms of m, b, and r
Yeah, you can find dy/dx by taking the derivative of y with respect to x
In other words:
dy/dx = d/dx (y) = d/dx (mx + b + e^(rx))
stoic mantle
yea so I got m + re^rx
raven rover
Now you can plug this expression in for dy/dx on the LHS
stoic mantle
LHS?
raven rover
Left hand side - sorry about that
stoic mantle
oh nah you’re good
raven rover
$\text{LHS} = \text{RHS}$
$\vspace{10pt}$
$\frac{dy}{dx} = 3x + 2y + 1$
ocean sealBOT
Shen
stoic mantle
so from here i’m not sure how to deal with the fact I have 4 variables
raven rover
What do you have so far?
stoic mantle
m + re^rx = 3x + 2y + 1
raven rover
$m + re^{rx} = 3x + 2mx + 2b + 2e^{rx} + 1$
ocean sealBOT
Shen
raven rover
Yeah - you have y in terms of m, b, and r: so you can plug that into the RHS
You can then equate coefficients
$(r)e^{rx} + (m) = (2)e^{rx} + (3 + 2m)x + (2b + 1)$
ocean sealBOT
Shen
raven rover
> Equate coefficients
Set the coefficients of the exponentials (**e^(rx)**)to b...
If this equation is true (or in other words, the LHS is equal to the RHS), then the following must be true ^^
raven rover
You're right in thinking it isn't necessary
It's just for clarity: we will end up equating coefficients soon
Are you familiar with equating coefficients?
I briefly explained it
stoic mantle
isn’t it where you for example set r=2 and m= 3+2m?
raven rover
If this equation is true (or in other words, the LHS is equal to the RHS), then the following must be true:
The coefficients of the exponentials (e^(rx)) must be the same.
The coefficients of the linear terms (x) must be the same.
The coefficients of the constants must be the same.
raven rover
isn’t it where you for example set r=2 and m= 3+2m?
You have the right idea, but the second equation you proposed is slightly incorrect
raven rover
If this equation is true (or in other words, the LHS is equal to the RHS), then ...
If we follow this, then we can see the following:
For the e^(rx) terms, we have: r = 2 (This is where you were right 🙂)
For the x terms, we have: 0 = 3 + 2m (The LHS here is 0 because there is no x term on the LHS. You can think of the LHS as having a 0x.)
For the constant terms, we have m = 2b + 1.
stoic mantle
ah i forgot m was a constant
raven rover
The equations obtained from the above analysis/reasoning will allow you to solve for m, b, and r:
- r = 2 (We already know r!)
- 0 = 3 + 2m (This is an easy equation to solve for m.)
- m = 2b + 1 (After solving Equation 2 for m, we can then solve for b
raven rover
The equations obtained from the above analysis/reasoning will allow you to solve...
I've bolded the variables we are solving for here because it might be easier to see that way
raven rover
Np - take care
stoic mantle
.close
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kindred glacier
lone heartBOT
kindred glacier
Help please
severe sluice
$y=mc \Rightarrow m=\frac{\Delta y}{\Delta x}$
ocean sealBOT
bob (bean toucher)
frigid hatch
that
raw shard
$m = \frac{\Delta y}{\Delta x}$
ocean sealBOT
quantum
placid zinc
raven shale
lone heartBOT
raven shale
Is this right?
placid zinc
Yes
placid zinc
Plot a number?
raven shale
But idk if I should put in 0.006 on a table of values
bleak ridge
raven shale
placid zinc
Sounds like ohms should go on the x-axis, current should go on the y-axis
Plot your points see a curve
raven shale
So the number that I should write is 0.006? Smth like that?
Should I not multiply it to 1000 to get a whole number?
placid zinc
Nuu
bleak ridge
Is that for an actual quarter test
raven shale
Yes
alpine sable
ok
lone heartBOT
Available help channel!
leaden isle
So I have been trying to solve this equation for t but somehow I end up with one side below and one above zero, but I can't find out where I went wrong
leaden isle
swift shore
What are those lines | on the side
wild pendant
no offence, but light blue on white, bruh
lethal tendon
check your expansion on the third line (with the +c on the right)
there seems to be a stray negative sign
lone heartBOT
@leaden isle Has your question been resolved?
leaden isle
check your expansion on the third line (with the +c on the right)
But what specifically is the problem with it?
Like what did I do wrong
lethal tendon
you multiplied the -c into the parentheses right?
leaden isle
What are those lines | on the side
no just c
lethal tendon
well then you have to keep the parentheses
leaden isle
OUUUU
ocean sealBOT
dino dik
lethal tendon
happy to help
lone heartBOT
@leaden isle Has your question been resolved?
frail rivet
guys why are the eigenvectors switched when calculating a homogeneous system of DE when it has complex eigenvalues?
frail rivet
and also the - to + sign on sin(2t)
misty bobcat
$R = \varnothing$ is this relation reflexive, symmetric and transitive ?
ocean sealBOT
Michal
misty bobcat
reflexive: $(\forall x)[x \in \varnothing \implies xRx]$
symmetric: $(\forall x,y \in \varnothing)[xRy \implies yRx]$
transitive: $(\forall x,y,z \in \varnothing)[xRy \wedge yRz \implies xRz]$
ocean sealBOT
Michal
misty bobcat
reflexive: $(\forall x)[x \in \varnothing \implies xRx]\$
symmetric: $(\forall x,y \in \varnothing)[xRy \implies yRx]\$
transitive: $(\forall x,y,z \in \varnothing)[xRy \wedge yRz \implies xRz]$
ocean sealBOT
Michal
misty bobcat
.close
boreal barn
Hey
I need help with sets
Bruh
Tommorow is my math exam
<@&286206848099549185>
Bro
They dead 💀
Hey
<@&286206848099549185>
<@&286206848099549185>
<@&286206848099549185>
Pls
Bruh
I have exam tommprow
placid zinc
Please see the rules on helper pings
lone heartBOT
@boreal barn Has your question been resolved?
raw shard
dude just pinged helpers 4 times and didn’t even send a question
lone heartBOT
@boreal barn Has your question been resolved?
stoic pendant
lone heartBOT
echo socket
Use the definition of tan in a right triangle
lone heartBOT
@stoic pendant Has your question been resolved?
elfin ermine
How do I prove that
$e = \cos(-i)+i\sin(-i)$
Without using euler
ocean sealBOT
Luca
glass lichen
exponential version of sine and cosine?
ruby summit
How do I prove that
$e = \cos(-i)+i\sin(-i)$
Without using euler
trigonometric functions with imaginary inputs? How would you solve that?
elfin ermine
I thought of using the taylor representation of sin and cos
ruby summit
Well to prove a number is e then you have to take the derivative
And if it is the same as the result
$e^x = (\cos(-i) + i\sin(-i))^x$
ocean sealBOT
Bman
ruby summit
Not sure how you are going to do that
It does appear to change if you would take a direvative
Unless the $\ln(\cos(-i) + i\sin(-i)) = 1$
ocean sealBOT
Bman
lone heartBOT
@elfin ermine Has your question been resolved?
alpine sable
Hello
alpine sable
Bro
bleak lintel
I need explanation
bleak lintel
Brooo my question. Is ez anyone can solve except mee
alpine sable
Like one of the available ones
Bro
Rupee momento
This some indian stuff right here
alpine sable
Brooo my question. Is ez anyone can solve except mee
Bro, none of the options are right
@bleak lintel Ur teacher messed this one up
It should have at least a nother variable
Should be something like
Rs x +(z-40)y
Where z is the distance travelled in kilometres
All of the multiple choice options that were given are wrong
.close
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alpine sable
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raw shard
it takes a few minutes
lone heartBOT
Available help channel!
bleak lintel
Hi
twilit plank
stop using 2 channels
bleak lintel
They ain’t answering in that one
twilit plank
then ping helpers after 15 mins as rules say, dont use other channels
raw shard
@bleak lintel you’re only allowed to have one channel open at a time
twilit plank
read #❓how-to-get-help
half epoch
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dreamy cedar
.close
lone heartBOT
bleak lintel
.close
twilit plank
9pm = 21:00
bleak lintel
Ye Ik
twilit plank
the number of hours in a day is 24
bleak lintel
Nah dude
twilit plank
so 24-21 = 3
bleak lintel
Thx tho
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Available help channel!
hollow zephyr
is there an app for pc where I can post a screenshot of equation and get result?
hollow zephyr
such as photomath for phones
lone heartBOT
@hollow zephyr Has your question been resolved?
pliant zephyr
is there an app for pc where I can post a screenshot of equation and get result?
symbolab
pliant zephyr
but u can't post screeshots there
lone heartBOT
pliant zephyr
u have to type
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orchid thorn
ask
orchid thorn
Can anyone help me with this problem
<@&286206848099549185>
hello <@&286206848099549185>
ancient saddle
Can anyone help me with this problem
Hello, for the function to be continuous, the limit at the discontinuity should be equal to the value of the function at that point
So the limit of f as (x,y) approaches (0,0) must be 0 if the function is continuous
Find the limit at (0,0) and you will know if it is continuous or not
urban pine
doesn't the limit need to agree from all directions as well?
orchid thorn
yes that's done
ancient saddle
Yes, I didn't mention a specific direction
orchid thorn
that is equals to one
ancient saddle
Wait, did you cancel the x^2?
orchid thorn
no
orchid thorn
that's my question
ancient saddle
The solution with y=mx is just wrong, they are cancelling the x^2
grizzled field
Happy New Years all: Got a probablility question I'm confused on...
A bag contains lettered tiles. The Theoretical probability of choosing a vowel is 30%. The bag contains 63 consonants. How many tiles are in the bag.
I've done .30 x 63 = 18.9
18.9 + 63 = 81.9 to get 82.
Answer book says 90 Tiles. What am I doing wrong?
covert agate
let there be x tiles, consider the formula for probability
grizzled field
I'm more or less looking for a walk through tutorial on it because I've been struggling on this for half the morning
and math isn't my strongest subject as a teacher
misty roost
The issue is .3 * 63 would be if the bag contained 30% as many vowels as consonants, but the bag actually has 30% of it's total tiles as vowels
grizzled field
that means i have 30% chance of drawing a vowel out of a total tiles. 63 are consenants meaning i'm looking for the remaining of tiles that are vowels
misty roost
To put it another way, it contains 70% consonants
covert agate
that means i have 30% chance of drawing a vowel out of a total tiles. 63 are con...
nonono
in terms of quantity
of vowels/consonants
misty roost
So say x is the total number of tiles in the bag. Then you have 0.7x = 63 right?
And then you should be able to solve from there
grizzled field
so 0.7x = 63; 63 x 0.70 = 44.1
misty roost
No
You need to divide by 0.7
Just like if I had 2x=4 I wouldn't multiply both sides by 2, I'd divide both sides by 2
misty roost
,w 63/0.7
ocean sealBOT
grizzled field
thanks
wild tundra
grizzled field
.close
plush basalt
lone heartBOT
plush basalt
did you enter using correct format
You mean {-5},{6}
I tried but this system so strict
It just wants correct form
covert agate
try 5,6
plush basalt
I did
covert agate
5, 6
covert agate
can you report the system
plush basalt
No
covert agate
what website is this lol
covert agate
i think there’s a report bug button somewhere
covert agate
then space it i guess
plush basalt
How
covert agate
correct grammar requires spacing
plush basalt
Can u do this
covert agate
wdym
median dirge
What did you get?
plush basalt
I found -5 and 6
Look
plush basalt
What did you get?
.
plush basalt
I can say I am right but system does not accept
gray isle
-5 and 6 aren't points
plush basalt
Look at this
median dirge
,w graph (x^2+10x+25)/(x^2+x-30)
ocean sealBOT
median dirge
Well.
gray isle
you've just given a list of numbers
median dirge
What do you think now.?
plush basalt
Yeah true but question wants discontinutiy
covert agate
this is a technical issue more than math problem
plush basalt
Look
covert agate
your answers should be correct
plush basalt
this is a technical issue more than math problem
I totally agree
gray isle
how are you getting -5,6
median dirge
Thats what Im thinking.
gray isle
this is also a poorly phrased/worded question
median dirge
Well points of discontinuity obviously mean their x-coords
gray isle
not really no
median dirge
Yeah not in every case
gray isle
x coords aren't points
median dirge
Yeah
median dirge
Good job!
covert agate
systems are dumb sometimes
plush basalt
.close
plush basalt
lone heartBOT
median dirge
Oh hello again
plush basalt
Oh hello
gray isle
wheres c=x-4 coming from
echo socket
c can't be x - 4, it's supposed to be constant
gray isle
you're also making this way more complicated than needed
plush basalt
How can I finished
covert agate
the issue when substituting x = 4 is denominator = 4
gray isle
the question gives you a major hint
covert agate
so we ‘remove’ the (x - 4) by making the numerator factorise-able into (x - 4) and something else
this way (x - 4) cancels out
median dirge
this way (x - 4) cancels out
yeh
gray isle
no
plush basalt
What is your answer
gray isle
not 20
covert agate
how do you factorise x² + x + 20?
plush basalt
Does not exist
gray isle
applying factor theorem would be the simplest approach
gray isle
your mistake is I have nfi what you did
spark latch
“Demonstrate Rolle’s Theorem using f(x) = xsin(x) on the interval [0, pi].”
lone heartBOT
“Demonstrate Rolle’s Theorem using f(x) = xsin(x) on the interval [0, pi].”
@spark latch Has your question been resolved?
elder sedge
maybe start by looking at rolls theorem and seeing if it applies here
spark latch
I do believe it applies
glacial perch
“Demonstrate Rolle’s Theorem using f(x) = xsin(x) on the interval [0, pi].”
0sin(0)=pi.sin(pi)=0
sin is differnciable and continuous in [0,pi]
spark latch
but I am not sure what exactly the wuestjon is asking
spark latch
0sin(0)=pi.sin(pi)=0
sin is differnciable and continuous in [0,pi]
yeah this, I knew f(0) and f(pi) were equal and that its differentiable and continuous but thats all I really write?
glacial perch
i think thats all the conditions of rolles
glacial perch
which it will*
spark latch
Ight that was quite a bit more simple than I thought
elder sedge
i believe you simply formally state that the conditions apply followed by stating the existence of c in the interval st etc etc...
there is not much more to do
orchid pulsar
I did part a but im not sure how to do part b
lone heartBOT
Available help channel!
bronze glen
i need help with this
lone heartBOT
i need help with this
glacial perch
arithmetic sequence and series means same?
glacial perch
that is the definition
glacial perch
so, we can write the series as k^2 , k^2+k , k^2+2k , k^2+3k , k^2+4k
bronze glen
why?
glacial perch
k^2+4k is 41
glacial perch
that is the definition
..
glacial perch
read ques ig
bronze glen
k
glacial perch
u know what arithmetic sequence is??
bronze glen
yes
glacial perch
so, we can write the series as k^2 , k^2+k , k^2+2k , k^2+3k , k^2+4k
u get this step then?
bronze glen
yes now i do
molten zenith
Btw answer for 9 is 8 and 1/2
glacial perch
Btw answer for 9 is 8 and 1/2
i c
glacial perch
k^2+4k is 41
u get this step??
bronze glen
yes
glacial perch
Y/N
bronze glen
Y
glacial perch
nice
bronze glen
for 10
glacial perch
u know how to solve quadratic?
bronze glen
the last number in the sequence would be 41
glacial perch
5th term
glacial perch
nice
tight locust
@bronze glen nice hats
bronze glen
thx
tight locust
what samples
tight locust
add me
bronze glen
yh
lavish finch
So I have this:
lone heartBOT
So I have this:
lavish finch
$$d\vec{T} \cdot \vec{X} = - sin \theta d\theta$$
$$d\vec{B} \cdot \vec{X} = - sin \phi d\phi$$
ocean sealBOT
PyRet
lavish finch
T and B are vectors that vary, X is a constant vector
now I want to divide equation 1 by equation 2
how do I go about that
and again, since X is an arbitrary constant vector, I can't tell the angle between dT and X or dB and X
lone heartBOT
@lavish finch Has your question been resolved?
lavish finch
<@&286206848099549185>
lone heartBOT
@lavish finch Has your question been resolved?
alpine sable
Why do we integrate with respect to the opposite variable when rotating a curve around an axis?
alpine sable
Like for example if I rotate y = x^2 around the y axis
Oh wait I’m sorry I mean why do we rotate it around the same variable
I’ll try to draw what I mean
honest quail
You can do either way, depending on using shell or disc method
But at least with disc method, you imagine approximating your area with 2d discs that run parallel to your axis of rotation
So the ‘steps’ between the discs (your differential) should represent changes parallel to your axis
So if your axis is x=0 (the y axis) then your steps go in the y direction and your integration variable is y!
alpine sable
For y = x^2, wouldn’t we have disks with radius x
honest quail
Yep! And since our integration variable (from above discussion) should be y, we need to express that radius in terms of y instead
If y=x^2, what is the radius x in terms of y?
alpine sable
Sqrt(y)
honest quail
Boom!
alpine sable
But I know that from a video
Should I try another function
Ok thank you I think understand
honest quail
Sure! If y=1/(1+x) and our radius was again x, what would it be in terms of y?
Ye!😄
alpine sable
Oh so perform backwards operations on y?
alpine sable
Ok I’m gonna practice that thank you. I always just need to know what I need to practice. Thank you
.close
alpine sable
can someone please tell me how i go through 7b
learnt it a few months ago and forgot to know how to solve this question
alpine sable
noble sinew
After doing (a) you notice b is a telescoping series
alpine sable
what is a telescoping series
noble sinew
,w telescoping series
ocean sealBOT
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
@alpine sable Has your question been resolved?
runic obsidian
lone heartBOT
runic obsidian
From December to May that's 5 months
isnt that what you plug in for t?
runic obsidian
ah gotcha
thorny patio
therefore t = 5/12
runic obsidian
therefore t = 5/12
so what would i plug in for n?
thorny patio
Well it's the pe^rt formula
For continuous interest
There is no n here
Just rate and time
thorny patio
The n for number of compounding periods is just for compound interest
Although technically continuous interest is actually compound interest with infinitely many compounding periods.....
But thats another topic altogether probably
runic obsidian
Although technically continuous interest is actually compound interest with infi...
so the equation would be A=1050e^(.15)*(5/12)?
thorny patio
Yes that should be it
@runic obsidian
Iffff they want you to use the pe^rt continuous interest formula
Which it doesn't actually say in the question
runic obsidian
oof
thorny patio
It's not simple interest maybe?
pure trellis
Hello
rose sable
Hi
lone heartBOT
lone heartBOT
Available help channel!
chrome plank
find the length of the sides of a parallelepiped, knowing that they are in geometric progression, that their sum is 21 and that the volume of the parallelepiped is 216 cm^3
chrome plank
At the end I found 5 solutions of r, how do I choose which one is the correct one?
I found 1, 1/2, 2, (-18 ± 2 sqrt(65) )/ 8
<@&286206848099549185>
chrome plank
find the length of the sides of a parallelepiped, knowing that they are in geome...
It comes down to a geometric progression and the answer should be r = 2
But how do I choose it over the other solutions?
lone heartBOT
@chrome plank Has your question been resolved?
celest zinc
I think r should be 6, not 2
If {a, b, c} are in geometric progression
{a, b, c} = {1, r, r²}
so
216 = abc = 1·r·r² = r³
i.e.
∛216 = r
which is 6
oh
sorry, that's so wrong
I didn't take the other equation into account
chrome plank
My textbook gives the following answers: a1 = 3, a2 = 6, a3= 12
So I just assumed r = 2
chrome plank
So do I just have to check for every solution I found?
celest zinc
My textbook gives the following answers: a1 = 3, a2 = 6, a3= 12
which are clearly these
because {a,b,c}={C,Cr,Cr²} so abc is C³r³=(Cr)³
so Cr is 6 (no r=6, my mistake)
then use the other equation and it's done.
chrome plank
The problem is that I've found a lot of solutions for r
celest zinc
how?
chrome plank
I set up a system of equations
chrome plank
I found 1, 1/2, 2, (-18 ± 2 sqrt(65) )/ 8
.
chrome plank
I ended up with
36r^6 - 441r^4 + 810r^3 - 441r^2 + 36
celest zinc
:1
chrome plank
Uhm
celest zinc
look
I don't know how you got there
but the simplest way is just replace {a,b,c} with {C,Cr,Cr²} and you get a quadratic with solutions 2, 1/2
\begin{align*}
a+b+c &= 21
\
abc &= 216
\end{align*}
ocean sealBOT
Fede Bosio
celest zinc
so in no particular order
\begin{align*}
C+Cr+Cr^2 &= 21
\
C^3 r^3 &= 216
\end{align*}
ocean sealBOT
Fede Bosio
celest zinc
\begin{align*}
C \left( 1 + r + r^2 \right) &= 21
\
{\left( Cr \right)}^3 &= 6^3
\end{align*}
ocean sealBOT
Fede Bosio
