E.g., let the opposite side be of length 1 and the adjacent side be of length 2
#help-17
cursive fern
Sqrt 5
twin meteorBOT
cursive fern
And what would be arctan1/2
twin meteorBOT
river minnow
Yeah finding its closed form would be challenging
pliant eagle
vocal sleetBOT
pliant eagle
Hi, I have no idea how to do these types of problems. Could someone help me with #1 and I'll try the others on my own?
rose heart
HEY I WAS TYPING HERE
pliant eagle
HEY I WAS TYPING HERE
sigh have some respect for others please
paper depot
HEY I WAS TYPING HERE
ok and? just go to a different channel.
rose heart
just rude
outer warren
if you need help, stop arguing and move on
pliant eagle
Anyways here's my questions
karmic mica
not enough info
pliant eagle
If anyone can help I'd be grateful
karmic mica
how u supposed to get f(x)
pliant eagle
pliant eagle
not enough info
There is enough
karmic mica
when the only thing u know is f'(c)
pliant eagle
I think
paper depot
i mean yeah it is not uniquely detrmined
paper depot
but like ig you're supposed to look at the limit itself and how it's written
pliant eagle
They wouldn't just give you an impossible problem
pliant eagle
but like ig you're supposed to look at the limit itself and how it's written
Yeah exactly
pliant eagle
Yeah that was wrong
paper depot
not wrong. pointless.
paper depot
like you're supposed to know $f'(c) = \lim_{\Delta x \to 0} \frac{f(c+\Delta x) - f(c)}{\Delta x}$
twin meteorBOT
Ann
paper depot
and match that to the fraction in the limit
paper depot
6 - 4(1+Δx) is supposed to be f(c+Δx)
pliant eagle
Are we given enough info?
You mean c?
Nvm f(x) is not 2
@paper depot I'm unsure, sorry
Maybe we can try the second one?
It looks easier
C = -3
Ohhhh!
And y = x^3
Ok but #1 is still confusing me
outer warren
focus on the component in ()
compare $(1 + \Delta x)$ to $(c + \Delta x)$ \
similar to how you would've compared $(-3 + \Delta x)$ to $(c + \Delta x)$
twin meteorBOT
ℝαμΩℕωⅤ
outer warren
...
pliant eagle
Ok I'm sorry
outer warren
not listening to what i'm saying
pliant eagle
I'm trying my best
pliant eagle
not listening to what i'm saying
I was
I was trying to simplify it to see how to compare it
😭
Ok can u explain it?
outer warren
don't simplify / manipulate the expression given
pliant eagle
Ok
pliant eagle
Mhm
outer warren
compare $(1 + \Delta x)$ to $(c + \Delta x)$
twin meteorBOT
ℝαμΩℕωⅤ
outer warren
c = ?
pliant eagle
1
outer warren
yes
outer warren
$\lim_{x\to0} \frac{\overbrace{[6-4\red{(1+\Delta x)}]}^{f\red{(c+\Delta x)}} - \overbrace{2}^{f(c)}}{\Delta x}$
twin meteorBOT
ℝαμΩℕωⅤ
outer warren
$f\red{(1+\Delta x)} = 6-4\red{(1+\Delta x)} \
f(x) = ?$
twin meteorBOT
ℝαμΩℕωⅤ
twin meteorBOT
Gravitational Joey
pliant eagle
This time there's no addition
If I simplify it with conjugated I get
$\frac{49}{7\sqrt{x} + 21}$
@outer warren
twin meteorBOT
Gravitational Joey
outer warren
what's with the conjugation
you're not required to do that here
in the questions you're essentially being asked to compare what you have to certain limit definitions
$f'(c) = \lim_{x\to c} \frac{f(x)-f(c)}{x-c}$
twin meteorBOT
ℝαμΩℕωⅤ
pliant eagle
**Gravitational Joey**
Would this be f(x)
pliant eagle
$f'(c) = \lim_{x\to c} \frac{f(x)-f(c)}{x-c}$
I know I was just confused
I thought it was f(x + h)
Not just f(x)
So I didn't know how to compare hem
Then
Them
pliant eagle
yes, f(x) = 7sqrt(x)
Ohh ok
pliant eagle
<https://tutorial.math.lamar.edu/Classes/CalcI/DefnOfDerivative.aspx>
I'll read this
pliant eagle
yes, f(x) = 7sqrt(x)
So if f(c) = -21
outer warren
no
outer warren
f(c) is the amount being subtracted which is just 21
the value of c can also be idenified directly from the denominator
you could get it from solving f(x) = 7sqrt(x) = 21
but that's just more work
pliant eagle
you could get it from solving f(x) = 7sqrt(x) = 21
but that's just more work
That's what I did
outer warren
yes
high seal
.close
vocal sleetBOT
Available help channel!
errant granite
I need some explaination on what restricted values are.
vocal sleetBOT
I need some explaination on what restricted values are.
onyx totem
,rccw
twin meteorBOT
errant granite
Any idea?
warped relic
I need some explaination on what restricted values are.
restricted values are just values which will make your result undefined
1/0 is undefined. so the value which will result in the denominator of a fraction being 0 will be a restricted valoe
warped relic
in this case, -4 and 2 and restricted values of x since inputting those will make the denominator 0
errant granite
Ohhhhh
I see
Tysm
For the lcd
Do i have to multiply each sides?
Multiply the lcd on each sides
Cuz im transforming it to a quadratic equation
vocal sleetBOT
@errant granite Has your question been resolved?
vocal sleetBOT
@errant granite Has your question been resolved?
vast shale
I messed up
vocal sleetBOT
I messed up
haughty narwhal
its Bx+c not B
you need a linear term in numerator if you have quadratic in denominator
distant umbra
vocal sleetBOT
distant umbra
Is this correct I'm finding behavior around vertical asymptote
My function is 1/x-3
split wind
twin meteorBOT
inland totem
HELP IS NEEDED
vocal sleetBOT
HELP IS NEEDED
inland totem
alright
so
what is the teraction of 12?
it's like the power sign but it is put at the top left
unlike the power sign
trail mesa
do you mean tetration?
trail mesa
what is the little number in the top left
trail mesa
trail mesa
?
inland totem
i'm currently doing my English homework
river minnow
Right, so it's gonna be $12^{12^{12^{12}}}$
twin meteorBOT
A Lonely Bean
river minnow
Does that answer your question?
inland totem
yes
i just wanted to know what it would look like if i wanted to multiply it by 2^12^12
no need to calculate the value, just keep the power sign up there
$2^{12^{12$
twin meteorBOT
Evan-H/ø/X
$2^{12^{12$
```Compilation error:```! Missing } inserted.
<inserted text>
}
l.57 $2^{12^{12$
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.```
twin meteorBOT
Evan-H/ø/X
vocal sleetBOT
@inland totem Has your question been resolved?
inland totem
No, nobody's been answering me
vocal sleetBOT
@inland totem Has your question been resolved?
idle temple
Should hopefully be an easier question:
Say that I roll a 6 sided dice, we know that I have 1/6 chance of rolling a six
Say I also roll an 10 sided dice every half second, meaning I have 1/10 chance of rolling a six, but it happens twice as often
How would I know which dice to expect to roll a 6 first?
vocal sleetBOT
Should hopefully be an easier question:
Say that I roll a 6 sided dice, we know ...
mild flower
think about rolling two d10s every second if that's simpler
idle temple
$1-(\frac{1}{10})^2$
twin meteorBOT
KirbysGames
idle temple
@mild flower would this be right then?
mild flower
99/100?
idle temple
wait not that can't be right
(I haven't taken an ounce of statistics 
)
$(1-(\frac{9}{10})^2)=19%$
mild flower
yeahh that looks much better!
vocal sleetBOT
twin meteorBOT
KirbysGames
vocal sleetBOT
Available help channel!
vestal vessel
hi
vestal vessel
is this the correct triangle?
soft walrus
soft walrus
not quite, do you know your properties of the transversal?
vocal sleetBOT
@vestal vessel Has your question been resolved?
vestal vessel
not quite, do you know your properties of the transversal?
No not on top of my head?
I think its 1
you know what just tell me if this is right
vocal sleetBOT
@vestal vessel Has your question been resolved?
vocal sleetBOT
@vestal vessel Has your question been resolved?
proper igloo
i just need help on setting up the integral
vocal sleetBOT
i just need help on setting up the integral
proper igloo
work is integral of force so am i just integrating the c/ (x^2 + y^2)^3/2
vocal sleetBOT
@proper igloo Has your question been resolved?
proper igloo
<@&286206848099549185>
vocal sleetBOT
@proper igloo Has your question been resolved?
craggy aurora
any idea how to solve this?
vocal sleetBOT
any idea how to solve this?
silk comet
integration by parts
silk comet
let u = (arcsin x)^2 and dv = dx
craggy aurora
is also doing the question
ah okay
how would you know when you have to use integration by parts?
silk comet
usually when nothing else works
craggy aurora
can you explain what dv = dx means
silk comet
look at the integration by parts formula
craggy aurora
okay 👍
twin meteorBOT
Tushar
half compass
vocal sleetBOT
fleet helm
I need help😭
Can anyone divide this
3x³+4x²+8 ÷ x+2
Long division
Division of polynomials is so hard for me😭
dark kiln
you can't get help in an occupied channel
fleet helm
Oh
dark kiln
scroll up, and look for available
fleet helm
Okay
dark kiln
How do u know if this is true
if a = bc + z, then a/2 = (b/2)c + z/2
what you're showing is just a specific case, with z = 0
and integers
vocal sleetBOT
@half compass Has your question been resolved?
fallen sandal
vocal sleetBOT
vocal sleetBOT
vocal sleetBOT
Available help channel!
shadow spindle
Need to prove the Infimum is of this set is -2
vocal sleetBOT
Need to prove the Infimum is of this set is -2
shadow spindle
I already showed that -2 is a lower bound as it follows: (Consider n is even)
3 > 1/n
2 + 1 > 1/n
2 + (-1)^n > 1/n
2 > 1/n - (-1)^n
-2 < (-1)^n - 1/n
been stuck on how to prove that -2 is the Infimum of this set
ancient knoll
you’re pretty much there, a proof by contradiction would work
vocal sleetBOT
@shadow spindle Has your question been resolved?
shadow spindle
you’re pretty much there, a proof by contradiction would work
how would that be?
shadow spindle
∃δ>0; ∀y∈Set; y ≥ -2 + δ
shadow spindle
suppose the infimum is some number greater than -2…
Oh
shadow spindle
and go from there
Not quite sure if this works: (Define the set as C)
Suppose by contradiction that ∃δ>0; ∀y∈C; y ≥ -2 + δ
Then
(-1)^n - 1/n ≥ -2 + δ
(-1)^n - 1/n + 2 ≥ δ
Take n = 1, so:
-1 -1 + 2 ≥ δ
0 ≥ δ
Which is a contradiction because we supposed δ>0
ancient knoll
that will do
shadow spindle
thaaanks
vocal sleetBOT
@shadow spindle Has your question been resolved?
verbal birch
I need help on whether the limit exists or not.
vocal sleetBOT
I need help on whether the limit exists or not.
brittle wasp
well, at x=3, the function is -12
but you're right that the limit exists
and the limit is 12 because the limit doesn't care about the value at the point.
verbal birch
and the limit is 12 because the limit doesn't care about the value at the point.
Wait so for a limit, it doesn’t matter if the point is included or not as long as it’s being approached from both sides?
vocal sleetBOT
vocal sleetBOT
Available help channel!
wise sable
vocal sleetBOT
wise sable
can anyone help with this
I was thinking it would be
a) yes
b) yes
c) no
d) yes
e) yes
also can a graph be homeomorphic to a surface?
vocal sleetBOT
@wise sable Has your question been resolved?
vocal sleetBOT
@wise sable Has your question been resolved?
vocal sleetBOT
@wise sable Has your question been resolved?
vocal sleetBOT
@wise sable Has your question been resolved?
vocal sleetBOT
@wise sable Has your question been resolved?
snow moth
vocal sleetBOT
snow moth
what am i doing wrong here?
trying to solve for the system of linear equations at the top
im pretty sure im not supposed to end up at 56/10x = 428/10
<@&286206848099549185> could anyone help me?
flat whale
im pretty sure im not supposed to end up at 56/10x = 428/10
Did you check your answer
flat whale
the x is supposed to be 7
What about y and z
Plug the solution into every step and see which one is wrong first
snow moth
What about y and z
y is 9 and z is 5
wouldnt is be wildly off base if x is wrong in the first place anyways?
flat whale
Plug the solution into every step and see which one is wrong first
Did you do this
snow moth
ohh
from the website?
it uses a different method of solution from elimination so
its not rlly the same
flat whale
...
The solution can be obtained in multiple ways
The way you get the solution doesn't change the solution
snow moth
yah but i cant plug my steps into theirs to see what went wrong
snow moth
i see
flat whale
And see where your equation is false
snow moth
13x - 10y = 1
29x - 18y = 41
these are correct
y = 13/10x - 1/10
this is right
29x - 18(13/10x - 1/10) = 41
correct
29x - 234/10x - 18/10 = 41
but this is wrong
but why is it wrong?
oh
,- is supposed to be +
thank u for ur time that fixed it
.close
tired jewel
Suppose f is continous function on [10, infinity) and that f(x) >=1 for all x>=10 what can u say about the integrals?
vocal sleetBOT
Suppose f is continous function on [10, infinity) and that f(x) >=1 for all x>=1...
tired jewel
i think this is a direct comparison type of problem where if the integral of f(x) converges integral of g(x) will converge too or diverge and diverge
I believe that 0< Integral A< Integral B
I believe both of these integrals diverge if you consider f(x) a constant greater than 1 but my homework is telling me im wrong
do these actually converge? or maybe is there not enough info?
regal bane
Yes both integrals can diverge. Like you said, f(x) = 1 and both are divergent
A is less than B
tired jewel
so here are the answer options i originaly putt both are divergent and i got it wrong so im wondering if its something else
regal bane
Well, both could also converge.
For a choice of f(x) that shrinks fast enough
The only thing I think we can say for certain, is that there's no f(x) that will cause A to diverge and B to converge
tired jewel
thank you so much that helps me!
regal bane
OH f(x) ≥ 1
tired jewel
haha i put in that they could be either convergent or divergent and it said that that was right
regal bane
Well wait, that doesn't matter. f(x) is in the denominator
Okay cool lol. Weird how little we can say about these integrals. What a strange question
tired jewel
yeah the questions on this assignment were super theoritcal and not striaght forward at all thanks so much
.close
quaint lynx
How do I figure out (G o F)? i'm having trouble multiplying x-3/2 into 2x + 3, do I just multiply all of it by 2??
i.e.
2(x-3/2) + 3
2x-6/4 + 3
vocal sleetBOT
How do I figure out (G o F)? i'm having trouble multiplying x-3/2 into 2x + 3, d...
river kettle
Put 2x + 3 wherever you see an x in f(x)
spice anvil
How do I figure out (G o F)? i'm having trouble multiplying x-3/2 into 2x + 3, d...
not quite everything
spice anvil
you'd need to distribute the 2 to the terms of the numerator, leaving the denominator alone
river kettle
put f(x) wherever you see an x in g(x)*
spice anvil
$2(\frac{x-3}{2}) \implies \frac{2(x-3)}{2}$
twin meteorBOT
a disappointing son
quaint lynx
OOOoohhh
spice anvil
though in this specific example you don't need to expand, note what you can do with the two in both the numerator and denominator
quaint lynx
simplify?
spice anvil
you can, how so?
quaint lynx
i'd cancel the 2 from both sides so it'd end up as x-3?
quaint lynx
so the answer would be just x?
spice anvil
👍
vast shale
What is 2x x tanx
vocal sleetBOT
What is 2x x tanx
vast shale
Simple question just forgot
twin meteorBOT
!Yajat!
vast shale
**!Yajat!**
Yeah
tidal umbra
can you post the original question, this is already in the simplified form
tidal umbra
So your original question was to find the derivative of $x^2\tan{x}$?
twin meteorBOT
!Yajat!
tidal umbra
i barely have any knowledge about calculus, but do you know the product rule?
vocal sleetBOT
@vast shale Has your question been resolved?
vast shale
i barely have any knowledge about calculus, but do you know the product rule?
Someone told me its 2xtanx
tender leaf
i barely have any knowledge about calculus, but do you know the product rule?
$\frac{d}{dx}[f(x)g(x)]=f’(x)g(x)+g’(x)f(x)$
twin meteorBOT
% Openglobe %
tidal umbra
$\frac{d}{dx}[f(x)g(x)]=f’(x)g(x)+g’(x)f(x)$
yea ik, i just have not studied calculus yet, i only some of it through physics
tender leaf
Someone told me its 2xtanx
That’s part of the answer, but not the full answer
vocal sleetBOT
@vast shale Has your question been resolved?
pine lodge
how would i solve for x: x^(2)+x+y=y^(2)
vocal sleetBOT
how would i solve for x: x^(2)+x+y=y^(2)
kind light
does it want to find x in tdrms of y?
kind light
idk sorry
pine lodge
ur name
kind light
but like using logic there is a possible answer of x=-y, but im pretty sure there are 2 possible answers
pine lodge
u in 8th too
/
kind light
wait i got it
you could bring all of the equations to the left side and get x²-y²+x+y=0
and you can factor it
kind light
do you know how to factor x²-y²?
pine lodge
$\sqrt(x-y$
kind light
what
twin meteorBOT
Xanimates
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
pine lodge
that
kind light
$\sqrt{x-y}$
twin meteorBOT
Skill_Issue
pine lodge
but that square x and y (was to lazy) then square the other side?
somber path
ok i got it
kind light
that is x^2+y^2 btw if you accidentally skimmed the ^2
somber path
do you know how to factor x²-y²?
its this
kind light
brb
kind light
but that square x and y (was to lazy) then square the other side?
what
pine lodge
$\sqrt{x^2-y^2+x+y}=\pm\sqrt{0}=0$
twin meteorBOT
Xanimates
somber path
$x^{2}-y^{2}=-x-y$
twin meteorBOT
Danny
somber path
heres your hint
somber path
no. factor out the left side
pine lodge
i thought i did
or is factoring the one wher u have to us ethe parenthesis like like grandmas with their strawberry candy
kind light
ye
pine lodge
(x+y)(x-y)?
kind light
$x^{2}-y^{2}=-x-y$
whats your way of doing it? i caught all the terms in the left side and completely factored it
kind light
(x+y)(x-y)?
yes
pine lodge
ig i was thinking simplify
somber path
now factor out the right side
pine lodge
y*y
somber path
no. factor out a -1
pine lodge
or is it just y^2
pine lodge
no. factor out a -1
a-1?
somber path
should be -1 (x + y)
pine lodge
that would be -x-y
somber path
yup.
somber path
oh shoot 😅
kind light
OHH WAIT THIS I THOUGHT U WHERE TALKING ABT THE WHOLE PROBLEM
i mean danny said to factor out the right side
pine lodge
so $(x+y)(x-y)=-1(x+y)$
twin meteorBOT
Xanimates
kind light
yep
somber path
yes
kind light
do you see the way to continue?
pine lodge
no
somber path
one of your expression is going to cancel out
pine lodge
so x-y=-1
pine lodge
y=x+1
somber path
yup
kind light
i mean
pine lodge
would 2x+y=0 then too?
kind light
$(x-y)(x+y)=-1(x+y)
x-y=-1$ would be technichally correct but it would remove the other factor
twin meteorBOT
Skill_Issue
pine lodge
then y=-x right
kind light
yes
pine lodge
how can both be true
somber path
remember the original equation had a y squared.
pine lodge
4=3+1 is true but 4=-3 is not
kind light
$(x-y)(x+y)=-1(x+y)$
$(x-y)(x+y)+1(x+y)=$
$(x-y+1)(x+y)=0$
twin meteorBOT
Skill_Issue
kind light
do you get it now?
vast shale
do you get it now?
yo can i ask a quantitative reasoning question here?
vocal sleetBOT
yo can i ask a quantitative reasoning question here?
kind light
sure?
vast shale
i have to find the 5 number summary for a data set and i got 10, 10, 11, 12, 14
tender leaf
Find what
vast shale
the whole data set is 10, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 13, 13, 14
vast shale
Find what
i need to find outliers but are numbers allowed to repeat in the 5 number summary?
kind light
i have no idea what 5 number summary is sry, openglobe probably does
tender leaf
i need to find outliers but are numbers allowed to repeat in the 5 number summar...
Outlier>1.5(IQR)+Q1
Outlier<Q3-1.5(IQR)
vast shale
for the 5 number summary is it fine if numbers repeat?
tender leaf
Then the min isn’t an outlier
vast shale
but it is repeated
tender leaf
Still not an outlier because 10 is Q1
vast shale
so it's fine that both values are 10?
tender leaf
Absolutely
vast shale
i still dont really understand how to find the outlier
vast shale
are the outliers 8.5 and 13.5 then
vast shale
iqr is 2
vast shale
is it 10-1.5 (2)
tender leaf
That works
vast shale
i got 7
tender leaf
And any number less than the calculated value is an outlier
tender leaf
i got 7
If no numbers are below 7, there are no outliers on this end
Now we have to perform the other string
tender leaf
Potential outlier<7
vast shale
for the other one i got 15
tender leaf
Outlier>15
vast shale
it also asks me to draw a box plot, do i need to plot the outliers too?
tender leaf
There are no outliers
vast shale
do i still need to plot the potential outliers?
tender leaf
All are between 7 and 15 inclusive
tender leaf
do i still need to plot the potential outliers?
No
vast shale
does the box go from 10-12 and the whisker to 14?
vast shale
i drew this but i didnt know how to draw the whisker for 10
vast shale
ok can i also get help with a stocks question?
lost briar
6 numeros de 48 con mayor probabilidad de ser elegidos?
turbid charm
vocal sleetBOT
flat whale
<@&286206848099549185>
!15m
vocal sleetBOT
<@&286206848099549185>
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.
turbid charm
sorry
vocal sleetBOT
@turbid charm Has your question been resolved?
vocal sleetBOT
@turbid charm Has your question been resolved?
quartz helm
How do I answer this? I've tried rationalizing the top, but I'm not sure what I can do from that.
vocal sleetBOT
How do I answer this? I've tried rationalizing the top, but I'm not sure what I ...
obsidian stream
I doubt you will need to rationalize anything if you follow the hint instead.
quartz helm
I doubt you will need to rationalize anything if you follow the hint instead.
I'm not too sure on how to use the hint though
obsidian stream
Rewrite it as t^6 = x
quartz helm
I'm getting t^3 - 1 / t^2 - 1
I'm going to try expanding them
Thanks I got it 
.close
unreal nest
how would i solve linear transformations like this
vocal sleetBOT
how would i solve linear transformations like this
unreal nest
and also these questions
vocal sleetBOT
@unreal nest Has your question been resolved?
vocal sleetBOT
@unreal nest Has your question been resolved?
vocal sleetBOT
@unreal nest Has your question been resolved?
vocal sleetBOT
@unreal nest Has your question been resolved?
kind light
the distance between town A and town B is 36km, Alan left town A for town B and at the same time Betty left from town B for town A, after they met, Alan took 2h 30m to get to town B while Betty took another 1h 36m to reach town A, find Betty's speed
vocal sleetBOT
the distance between town A and town B is 36km, Alan left town A for town B and ...
kind light
choices are A.6 B.7 C.8 D.9 E.10
using dmthe distance formula i get
D=S×T
36=A(alans speed)×(W1+5/2) (W1 is the time for alan and betty to meet)
36=B×(W1+16/10) but idk how to continue after that
heres like a diagram for it
36-AX=A×5/2
AX=B×16/10
36=5A/2+16B/10
360=25A+16B
vocal sleetBOT
@kind light Has your question been resolved?
kind light
<@&286206848099549185>
vocal sleetBOT
@kind light Has your question been resolved?
vocal sleetBOT
@kind light Has your question been resolved?
vocal sleetBOT
@kind light Has your question been resolved?
kind light
no
kind light
It says “after they met”
they are at a constant speed and meet as in them being at the same place in the road
lament sandal
Ok so if at constant speed then they meet in middle
lament sandal
Oh so they meet at a different place
kind light
yea
lament sandal
But we don’t know what speed they were travelling before they met, nor do we know the speed before they met, nor the time too
lament sandal
Are you sure that’s the question?
kind light
yeah
lament sandal
Send the picture
kind light
i dont have the exact papers on me, so its abit blurry (this was for a diffrent thing) but here
kind light
i dont have the exact papers on me, so its abit blurry (this was for a diffrent ...
,rccw
twin meteorBOT
lament sandal
Maybe it’s trial and error?
kind light
how would you trial and error that
lament sandal
Betty
Time = 1h36m
Let Speed = 6
Distance = 1h36*6= 1.6 * 6 = 9.6km
Betty
Time = 1h36m
Let Speed = 7
Distance = 1.6 * 7 = 11.2km
Time = 1h36m
Let Speed = 8
Distance = 1.6 * 8 = 12.8km
Time = 1h36m
Let Speed = 9
Distance = 1.6 * 9 = 14.4km
Time = 1h36m
Let Speed = 10
Distance = 1.6 * 10 = 16km
Idk I’m lost too now
kind light
oh wait
you could check alan's speed for each betty speed and find if the time for alan from point x to town b matches the question
lament sandal
But how
kind light
wait
lament sandal
We only know Alan’s time and distance for each of the choices
So what will we do with the speed
kind light
Betty
Time = 1h36m
Let Speed = 7
Distance = 1.6 * 7 = 11.2km from a (24.8km from b)
Time = 1h36m
Let Speed = 8
Distance = 1.6 * 8 = 12.8km from a (23.2km from b)
Time = 1h36m
Let Speed = 9
Distance = 1.6 * 9 = 14.4km from a (21.6km from b)
Time = 1h36m
Let Speed = 10
Distance = 1.6 * 10 = 16km from a (16km from b)
wait
Betty
Time = 1h36m
Let Speed = 6
Distance = 1h366= 1.6 6 = 9.6km from a (26.4km from b)
lament sandal
36-16=20km
20km/2.5h=8kmph
36-14.4=21.6km
21.6/2.5h=8.64 kmph
kind light
if we use speed=6 we can get that the distance Alan traveled 26.4km took 5/2h
yeah basically trial and error
tysm!
lament sandal
I’m making a Python code for it lol
kind light
ok ima just let this open cause i wanna see
lament sandal
‘ ‘ ‘
import math
BettyDistance=[]
for speed in range(6,11):
BettyDistance.append(speed*16/10)
print (BettyDistance)
AlanDistance=[]
for x in range(len(BettyDistance)):
AlanDistance.append((BettyDistance[x] - 36)*-1)
print(AlanDistance)
AlanSpeed = list(Distance/0.25 for Distance in AlanDistance)
for speed in AlanSpeed:
speed = speed/10
print (f"When Alan's speed is {speed}, Betty's speed is {(36-speed*2.5)/1.6}")
‘ ‘ ‘
import math
BettyDistance=[]
for speed in range(6,11):
BettyDistance.append(speed*16/10)
print (BettyDistance)
AlanDistance=[]
for x in range(len(BettyDistance)):
AlanDistance.append((BettyDistance[x] - 36)*-1)
print(AlanDistance)
AlanSpeed = list(Distance/0.25 for Distance in AlanDistance)
for speed in AlanSpeed:
speed = speed/10
print (f"When Alan's speed is {speed}, Betty's speed is {(36-speed*2.5)/1.6}")
[9.6, 11.2, 12.8, 14.4, 16.0]
[26.4, 24.8, 23.2, 21.6, 20.0]
When Alan's speed is 10.56, Betty's speed is 6
When Alan's speed is 9.92, Betty's speed is 7
When Alan's speed is 9.28, Betty's speed is 8
When Alan's speed is 8.64, Betty's speed is 9
When Alan's speed is 8.0, Betty's speed is 10
Thanks this was a good project! @kind light
Ping me if you need
Going now bye
vocal sleetBOT
@kind light Has your question been resolved?
lament sandal
Still?
vocal sleetBOT
vocal sleetBOT
Available help channel!
vague vessel
vocal sleetBOT
vague vessel
? How’s this wrong
thin vale
? How’s this wrong
!show
vocal sleetBOT
? How’s this wrong
Show your work, and if possible, explain where you are stuck.
wide fiber
vague vessel
Bruh doesn’t work
On top it says enter all answers using the appropriate multiplicities
Idk what that means
fleet blade
pls help me
Jasim has seven cards numbered 2 to 8
2345678
Jasim takes at random three of these cards.
He works out the sum of the numbers on the three cards and records the result.
Work out the probability that the result is an odd number.
vague vessel
Webassign is literal L website I pay $40 for this
vocal sleetBOT
@vague vessel Has your question been resolved?
spiral inlet
On top it says enter all answers using the appropriate multiplicities
multiplicities
x^3(x^2-16)
notice that you have x=0 three times
webassign is probably looking for 0, 0, 0, -4, 4
static ore
vocal sleetBOT
static ore
Can I get some help
karmic crane
First of all they state that 0<a<1, so which of the three equations should you choose
vocal sleetBOT
@static ore Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
frosty robin
vocal sleetBOT
vocal sleetBOT
@frosty robin Has your question been resolved?
ebon rapids
Think the solution factored out the thing so that you wouldn’t have fractions in the square root
frosty robin
@ebon rapids how does that get factored
I see that they how they got rid of the fraction inside the square root
But where did the outside fraction come from
twin meteorBOT
CST (please ping when replying)
ebon rapids
Does this make sense?
frosty robin
@ebon rapids yes but why do we need that 1/(3y)^(1/3) outside the square root
ebon rapids
Again, the solution just doesn’t want fractions inside the square root
It’s a style choice more than anything
twin meteorBOT
CST (please ping when replying)
velvet cove
$\int d(x+2)$
vocal sleetBOT
$\int d(x+2)$
twin meteorBOT
Jash
velvet cove
ye
velvet cove
youre integrating 1 wrt (x+2)
so is it just x+2+C
pale perch
indeed
wooden stump
vocal sleetBOT
wooden stump
I went about the proper way to find the derivative and used quotient rule on both df/dx and dy/dx
but it resulted in (x^2+y^2)^2 in the denominator which is 0 when (x,y) = (0,0)
so i thought maybe the partial derivative doesn't exist
but the answer is literally just
i feel like you can't just use that right? something feels wrong, like how in considering if a limit exists, you have to think of infinite ways to approach the point, not just along the x and y axis
vocal sleetBOT
@wooden stump Has your question been resolved?
wooden stump
got it, using definition of partial derivative so $\frac{\partial f}{\partial x}|{(x,y) = (0,0)} = \lim{h \to 0} \frac{1}{h} f(h,0) - f(0,0)$
vocal sleetBOT
twin meteorBOT
omgatriple
vocal sleetBOT
Available help channel!
sullen dragon
i don't know how to keep doing this problem
vocal sleetBOT
i don't know how to keep doing this problem
vocal sleetBOT
@sullen dragon Has your question been resolved?
vocal sleetBOT
@sullen dragon Has your question been resolved?
thorny rapids
@viscid halo
viscid halo
@thorny rapids hey!
@thorny rapids just wondering if I can help with the final problem on this order of operations sheet
It's the bottom one I can't solve
viscid halo
<@511785932484116480>
And exponentiation is allowed on any of the numbers
fallow gorge
I am unsure what to do with this problem, it's a linear expression problem
fallow gorge
.close
pliant urchin
Hi
vocal sleetBOT
@pliant urchin Has your question been resolved?
timber marlin
I'm getting 625.1 years for c but the answer is 6251 years where am I losing a power
vocal sleetBOT
I'm getting 625.1 years for c but the answer is 6251 years where am I losing a p...
flat whale
Did you do a correctly
south ruin
I'm trying so solve for -k because it's the constant I need in order to find the rest of the problem, but I'm stuck on what to do after I get to the point where it's shown on my paper. I included the original problem in case I left out any information
vocal sleetBOT
I'm trying so solve for -k because it's the constant I need in order to find the...
mild flower
use the fact that after 10 minutes it's at 240F
south ruin
I tried that on my first attempt but it didn't work, I tried dividing 240 by 365 and using that as the constant but it said I was wrong
I'm pretty sure it wants me to simplify the original equation and then take the natural log but idk how to do that or steps after that
mild flower
but like set up your equation of cooling
like set up $T = T_s + (T_0 - T_s)e^{-kt}$ for the time from 0 to 10 minutes
twin meteorBOT
hayley
mild flower
and you'll get your answer for k
south ruin
Oh ok that makes a lot more sense than what I was doing
Oh yeah 0.0556 there it is, thank you so much!
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
elfin moon
vocal sleetBOT
elfin moon
Is this true?
peak axle
Looks good to me
I can't think of any column operations, I don't think they exist in a capacity in which they would be useful
pliant urchin
Prove
(1-cosx)/(1+tan^2x)^2 = 1/((1+cosx)(3+cot^2x+3tan^2x+tan^4x))
regal parrot
[ \frac{1-\cos x}{(1+\tan^2x)^2} = \frac{1}{((1+\cos x)(3+\cot^2x+3\tan^2x+\tan^4x))} ]
twin meteorBOT
daniGhost (ping reply in help)
regal parrot
This?
vocal sleetBOT
@pliant urchin Has your question been resolved?
graceful marlin
Hello what's the most significant term between these two?
in our module, it says that both of them are equally significant. but how come they are?
hard atlas
!original
vocal sleetBOT
Please show the original problem, exactly as it was stated to you. A picture or screenshot is best.
If the original problem is not in English, then post it anyway! The additional context might still help helpers help you. Do your best to translate.
@graceful marlin Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
chrome peak
can anyone help me with this problem? I have no idea where to start, I already found the derivative in a previous part to be -y/x+y
vocal sleetBOT
can anyone help me with this problem? I have no idea where to start, I already f...
heavy yoke
you need the derivative inverse formula https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/03%3A_Derivatives/3.07%3A_Derivatives_of_Inverse_Functions
vocal sleetBOT
@chrome peak Has your question been resolved?
chrome peak
you need the derivative inverse formula https://math.libretexts.org/Bookshelves/...
okay so would I just find f prime of 2 because (2 , 1) would be the points on the inverse function?
heavy yoke
yes
chrome peak
.close
dull blade
How do I plot this in Excel?
vocal sleetBOT
How do I plot this in Excel?
dull blade
What I mean by that is
I have the data and I know my plot is supposed to look like that
Just dk how to get that plot
Here's the data
with a correspondence between flowrates of 1 - 10, 2 - 13, and 3 - 16
vocal sleetBOT
@dull blade Has your question been resolved?
dull blade
.close
pliant urchin
Prove
pliant urchin
[ \frac{1-\cos x}{(1+\tan^2x)^2} = \frac{1}{((1+\cos x)(3+\cot^2x+3\tan^2x+\tan^4x))} ]
twin meteorBOT
Radin
tidal umbra
!status
vocal sleetBOT
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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
@pliant urchin Has your question been resolved?
tidal umbra
!show
vocal sleetBOT
Show your work, and if possible, explain where you are stuck.
vocal sleetBOT
@pliant urchin Has your question been resolved?
placid osprey
[ \int_0^{\infty} \frac{2x - 4}{x^3 + 1} dx ]
I am attempting to demonstrate that this integral is convergent. I have been considering the comparison test for integrals, particularly comparing the given expression with (\frac{1}{x^2}) for (x \geq 1), as (x^3 + 1) grows faster than (x^2) as (x) approaches infinity.
For (x \geq 1), I've established the following:
[0 \leq \frac{2x - 4}{x^3 + 1} \leq \frac{2x}{x^3} = \frac{2}{x^2}]
Now, I am looking to integrate these expressions from 1 to infinity, and I am aware that the integral of (\frac{2}{x^2}) from 1 to infinity converges to 2.
However, I would appreciate any insights, suggestions, or alternative approaches that might help me solidify this conclusion and effectively demonstrate the convergence of the given integral.
twin meteorBOT
dgh
vocal sleetBOT
@placid osprey Has your question been resolved?
vocal sleetBOT
@placid osprey Has your question been resolved?
vocal sleetBOT
@placid osprey Has your question been resolved?
hushed flint
vocal sleetBOT
hushed flint
Anyone understand this? I'm confused as I thought R^2 would be like x, y but this question has x, y, z
sly sierra
T takes a vector in R^3 and maps it to a vector in R^2
that's what the notation T : R^3 --> R^2 means
(x y z) is the "input" vector from R^3
(x+y, y-z) is the "output" vector in R^2
hushed flint
T takes a vector in R^3 and maps it to a vector in R^2
that's what the notation ...
Ah thanks so would this look correct for first half of the proof?
I was thinking not since I have 3 values at the right side ?
cyan talon
you just need to take two vectors not 3 yeah
also you forgot to apply the transformatin
that's not T(x+y+z)
@hushed flint
hushed flint
also you forgot to apply the transformatin
the transformation?
do I need to multiply it by that other matrix or something?
cyan talon
wym mutiply
you still don't know the matrix of T
T(x, y, z) is (x+y, y-z), with (x, y, z) is one vector
hushed flint
oh..
cyan talon
also calling your 3d vectors x, y and z might be confusing
hushed flint
I thought T(x, y, z) was my T(x + y) and then the (x+y, y-z) was the T(x) + T(y)
In my textbook the only example similar is this, is this what I’m trying to do ?
hushed flint
So I’m a bit confused why mine is wrong haha
cyan talon
T(3d vector) is a 2d vector in your new question
cyan talon
that's not even the case in your working
you straight up just recopied x+y+z
it's like if I say f(x) = 2x+5, and I ask you what f(2) is and you tell me it's 2
hushed flint
How do u know what matrix to apply to the T(x y z) to turn it into x+y, y-z
cyan talon
ofc I know
you don't need to find the matrix to show it's a linear transformation tho
hushed flint
But how do I show it without multiplying by the matrix
cyan talon
you straight up have the defnition of what T(x, y, z) is
use it
if $a = \begin{bmatrix} a_1\a_2\a_3\end{bmatrix} $ and $b = \begin{bmatrix} b_1\b_2\b_3\end{bmatrix}$ then $$T(a+b) = T\left(\begin{bmatrix} a_1+b_1\a_2+b_2\a_3+b_3\end{bmatrix}\right) = \begin{bmatrix} (a_1+b_1) + (a_2+b_2)\(a_2+b_2)-(a_3+b_3)\end{bmatrix}$$
twin meteorBOT
aPlatypus
cyan talon
it's like you forgot the T was even there
T is a function taking 3d vectors and outputting 2d vectors
@hushed flint
hushed flint
**aPlatypus**
Ohh but then how does that prove that T(x, y) = T(x) + T(y)
@cyan talon
cyan talon
Ohh but then how does that prove that T(x, y) = T(x) + T(y)
T(x+y) = T(x)+T(y)
be mindful of your notation