If both are < 0 then fraction as a whole is > 0
#help-13
wraith daggerBOT
Pluton
viscid jungle
Got it.
Thank you.
@shut reef@trim sentinel
Well, I'm closing the channel now.
bye
.close
dark olive
cedar kilnBOT
dark olive
I am not sure how to do this question
high coyote
Every second the position changes -3i+2j "times"
So you sum -3i+2j to the vector position
every very second
dark olive
If I use suvat, S=?, v=(-3i+2j) a = 0 and t =2 . S = vt- 1/2 * at^2. S = (-3i +2j)* 2 + 0
which is wrong
dark olive
Every second the position changes -3i+2j "times"
what makes you say that?
if the velocity of a particle is constant. then the rate of change of the particle is 0
high coyote
"A particle P is moving with constant velocity of (-3i+2j) m/s"
No, actually the particle is moving, so the rare of change of position is the velocity
Nonzero velocity = movement
What is 0 is the acceleration, the rate of change of the velocity (not the position)
dark olive
so when the velocity is constant, the rate of change is the velocity so a =v in this case?
high coyote
No a=0
velocity=rate of change of position m/s
acceleration = rate of changes of velocity (m/s)/s = m/s²
constant velocity = zero acceleration = movement but velocity does not change (a car moving always 100 km/h)
position changes with constant velocity every hour position changes 100 km
tribal token
didnt understand last step (a-a) to -ds
cedar kilnBOT
didnt understand last step (a-a) to -ds
tribal token
I need to find what is the sum of a^2 - a^2 +a^2... (second line)
velvet mortar
(a1-a2) gives -d
Same with (a3-a4)
Now you can take common and factor out -d from all the (a-a)
tribal token
then shouldnt it be d^2 * 100?
velvet mortar
That leaves all the (a+a)
velvet mortar
then shouldnt it be d^2 * 100?
How?
tribal token
ok i got confused
tribal token
in highschool we didnt have to think just do
velvet mortar
Which is -d S
tribal token
got it thank you
cedar kilnBOT
@tribal token Has your question been resolved?
dense panther
cedar kilnBOT
dense panther
How can i figure out if the lines lj and np are parallel?
hollow root
see if the JIM angle is the same as PNM
trim sentinel
Those 2 sides are parallel if those 2 triangles are similar
dense panther
Ok
And this too
On b it says calculate an approximate value of 0,1cm of the length Ec
I found out using pitagors theory that ec is 29,1 cm but dk whqt to do now
cedar kilnBOT
@dense panther Has your question been resolved?
cedar kilnBOT
@dense panther Has your question been resolved?
zinc saffron
the diagonal of a cube is $\sqrt{3} \cdot a$ where a is the side so 15cm so that gives 25.9 @dense panther i think thats it
wraith daggerBOT
brunood
cedar kilnBOT
@dense panther Has your question been resolved?
grand pine
Given vectors $\vec{a}=(2;4;3)$ and $\vec{b}=(-4;3;0)$, and also $\vec{x}$, $\vec{y}$ are vectors so:
\begin{itemize}
\item $\vec{x} + \vec{y}=\vec{a}$
\item $\vec{x}$ is parallel to $\vec{b}$
\item $\vec{x}$ is perpendicular to $\vec{y}$
\end{itemize}
a) Find $\vec{x} - \vec{y}$\
b) Find the volume of the parallelepiped generated by the vectors $\vec{x} - \vec{y}$, $\vec{a}$ and $\vec{v}=(0;-1;-1)$
wraith daggerBOT
Cesar___
grand pine
if someone could guide me on this one, can't even solve a)
tried on a semi-algebraic way but it gives weird fractions and the perpendicular property is not complied
$\vec{x}=(-4k;3k;0)$\
$\vec{y}=(f;g;3)$\\
$f-4k=2$\
$g+3k=4$\
$-4kf+g3k=0$\
wraith daggerBOT
Cesar___
grand pine
this is what I had so far but I'm not sure if I did something wrong
cedar kilnBOT
@grand pine Has your question been resolved?
cedar kilnBOT
@grand pine Has your question been resolved?
eternal cloud
The three points (0, 2), (p, 4) and (q, 5) lie on a straight line. Show that this means that q = 1, 5p.
eternal cloud
How do i start solving that?
west dome
Did you type this question correctly
halcyon swan
Did you type this question correctly
Yep, same doubt, questions sounds absurd
south dawn
The three points (0, 2), (p, 4) and (q, 5) lie on a straight line. Show that th...
Find m and b using y = mx +b
(0,2) ==> y=mx+b is 2 = m(0)+b so b = 2
once you found b, use m = (y2-y1)/(x2-x1) using tow points (p,4)(q,5) and write it in terms of p and q.
eternal cloud
No but it’s three points, and you have to like use mx + b in it to prove that q = 1.5p
south dawn
You will see that it wil be 3p=2q if you plug b and m into y = mx+b
dire geode
Find m and b using y = mx +b
(0,2) ==> y=mx+b is 2 = m(0)+b so b = 2
once you...
yea just do this
eternal cloud
Alr then I just divide it by 2 to get q right?
south dawn
Alr then I just divide it by 2 to get q right?
3p=2q yea, that is equivalent to 1.5.
Show that this means that q = 1, 5p.
You have three points (0, 2), (p, 4) and (q, 5) lie on a straight line y=mx + b. You have to show that this means that q = 1, 5p.
Use (0,2) to find b.
y=mx+b is 2 = m(0)+b so b = 2
Use (p, 4) or (q, 5) to find slope m in terms of p and q.
(0,2)(p,4)
(4-2)/p=2/p
Now use (q,5)
y=mx+b
5=(2/p)q+2
5=2q/p +2
3=2q/p ==>3p=2q
eternal cloud
Wow, thank you so much. That made it more clear.
south dawn
typo corrected-sorry
south dawn
Wow, thank you so much. That made it more clear.
np
You might want to double check my typo. I am getting confused with q and p. lol
eternal cloud
Haha nah nah, i get it. It’s all fine, thank yous 🙂
bronze fossil
cedar kilnBOT
bright river
Show work
bronze fossil
work?
bronze fossil
it means show what you've tried so far
#1 c2 = a2 + b2
a2 = c2 - b2
= 102 – 82
= 100 – 64
a2 = 36
find the area and perimeter. using the formula given
quaint ginkgo
You can use the Pythagoras theorem for question A
bronze fossil
yea
cedar kilnBOT
@bronze fossil Has your question been resolved?
spark igloo
$log_x4+log_2{(x^2-3)}=x$
cedar kilnBOT
$log_x4+log_2{(x^2-3)}=x$
wraith daggerBOT
GG・Goof
crimson sedge
$log_x4+log_2{(x^2-3)}=x$
solve for x?
spark igloo
solve for x?
Yes
crimson sedge
ok then
spark igloo
I tried substituting log_x 4 as 2/log_2 x
crimson sedge
lemme solve this first
spark igloo
Okie
crimson sedge
did u tried changing everything to log base 2?
cedar kilnBOT
@spark igloo Has your question been resolved?
spark igloo
<@&286206848099549185>
crimson sedge
indeed
I combined it in a single lograrithm
and exponentiated both side sides
with one log in the exponent
but never the less couldn't solve that equation either
lament kraken
let me try :)
@crimson sedge what I did was I did change of base as 4 for the first log, simplified multiplied bot hsides by log4 x and then solved like that
spark igloo
Hm
lament kraken
but never the less couldn't solve that equation either
lol I dont think you can do this without a calc
crimson sedge
lol I dont think you can do this without a calc
ya
using newtons method its solvable ig
lament kraken
oooo yea
crimson sedge
oooo yea
actually nvm i cant think of any way to do this
it has two solutions
i dont think newtons method can give both of them
but if this guy is grade 9-10 ig he will probably require trial and error to find one of the roots
lament kraken
lol true
spark igloo
<:catThink:526983414226747393> but if this guy is grade 9-10 ig he will probably...
im 12th passed :/
crimson sedge
im 12th passed :/
ok then i am using calc
spark igloo
hm okie
crimson sedge
do you want all solutions for x ?
spark igloo
only one will be helpful
lament kraken
oh.
crimson sedge
then its solvable
first
combine the logarithm
and exponentiate both sides
this will make the calculations simpler
spark igloo
ohh
spark igloo
but how can i combine all logs?
lament kraken
log rules
crimson sedge
but how can i combine all logs?
convert the log base x term to log base 2 using change of basis formula
wraith daggerBOT
lim x -> 0 sin(x) / x = π/180
wraith daggerBOT
lim x -> 0 sin(x) / x = π/180
spark igloo
hmm .... yea
wraith daggerBOT
lim x -> 0 sin(x) / x = π/180
wraith daggerBOT
GG・Goof
wraith daggerBOT
lim x -> 0 sin(x) / x = π/180
crimson sedge
after which use the formula $\frac{1}{\log_a{b}}=\log_b{a}$
wraith daggerBOT
lim x -> 0 sin(x) / x = π/180
spark igloo
hm
spark igloo
**lim x -> 0 sin(x) / x = π/180**
but there is no rule in my book by which you can product logs like this
crimson sedge
but there is no rule in my book by which you can product logs like this
wha
$clog(a)=log(a^c)$
wraith daggerBOT
lim x -> 0 sin(x) / x = π/180
crimson sedge
this is a log rule
lament kraken
c can be anything
crimson sedge
i dont think thats mandatory
crimson sedge
c can be anything
complex as well btw?
crimson sedge
i thing im a bit confused
about which step
spark igloo
hm now clear yea
spark igloo
**lim x -> 0 sin(x) / x = π/180**
why you put * sign in between?
crimson sedge
aight so now use the formula $\log{a}+\log{b}=\log{ab}$
wraith daggerBOT
lim x -> 0 sin(x) / x = π/180
crimson sedge
hm now clear yea
for multplication?
i changed divison to multplication
by the denominators reciprocal
spark igloo
hmm
crimson sedge
interesting
true
wraith daggerBOT
lim x -> 0 sin(x) / x = π/180
spark igloo
$\log_2{4^{log_x{2}}}*(x^2-3)}=x$
wraith daggerBOT
GG・Goof
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
spark igloo
this is what i get now?
spark igloo
ok so...
crimson sedge
it will be better to use trial and error rather than newtons method actually
spark igloo
${4^{log_x{2}}}*(x^2-3)}=2^x$
wraith daggerBOT
GG・Goof
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
spark igloo
hm
spark igloo
**GG・Goof**
Compile Error! Click the <:errors:504266556054962196> reaction for m...
2 satisfy this eqn
crimson sedge
but cant we do it witout hit and try?
in my knowledge there isnt
but sure u can use numerical methods
like newtons method
which i said earlier
wraith daggerBOT
spark igloo
:/
spark igloo
,w log_x4+log_2{(x^2-3)}=x
wraith daggerBOT
spark igloo
hm 2 was correct
crimson sedge
yup
lament kraken
no worries :)
spark igloo
.close
severe sentinel
cedar kilnBOT
severe sentinel
so for this it wants me to find coterminal angles
all i want to know is if one has to be positive and one has to be negative
or if you can just add 360 and subtract it and if it happens to come out negative negative it will still work
tropic oxide
you are asked to find all angles coterminal to this, or just any two?
severe sentinel
it just says 2
severe sentinel
ok......so.....like alright i did not correctly read the directions the first time and it answers my own question for me i am really sorry for wasting your time .......
thats what it said but i jsut missed it
crimson sedge
Its ok 👌
severe sentinel
.close
static void
If i take the nullspace of a vector 3x1 matlab returns two vectors. How?
static void
I know these two vectors are orthogonal to the original vector but how?
What is solved?
south juniper
@static void You can think of the first vector as the normal of some plane. The other two vectors will be linearly independent vectors in the plane
south juniper
say the vector is (1,2,3) = v
For the null space, you need to find all X s.t vX = 0, where X=(x1,x2,x3) or X = (x,y,z), whichever you find more better
You get the equation x1 + 2x2 + 3x3 = 0
Or x + 2y + 3z = 0(the equation of the plane)
We set y=s, z=t, s,z can be any real numbers. We get x = -2s -3t.
That means all the vectors X = (x,y,z) will be of the form (-2s -3t, s, t)
Now you can rewrite $\begin{bmatrix} -2s - 3t \ s \ t \end{bmatrix} as $\begin{bmatrix} -2s -3t \ 1s + 0t \ 0s + 1t \ \end{bmatrix}. $\\$ This way you have $\begin{bmatrix} -2s \ 1s \ 0s \end{bmatrix} + \begin{bmatrix} -3t \ 0t \ 1t \end{bmatrix}$.
wraith daggerBOT
Sup?
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
south juniper
And then you have $s \begin{bmatrix} -2 \ 1 \ 0 \end{bmatrix} + t \begin{bmatrix} -3 \ 0 \ 1 \end{bmatrix}$
wraith daggerBOT
Sup?
south juniper
And so the nullspace of (1,2,3) is span{(-2,1,0), (-3,01)} and the basis of the nullspace is {(-2,1,0), (-3,0,1)}
The nullspace will be the plane x + 2y + 3z = 0 which has the normal (1,2,3).
static void
And so the nullspace of (1,2,3) is span{(-2,1,0), (-3,01)} and the basis of the ...
Thanks for the explanation. Can this be done by gram schmidt process too?
Also you wrote you need to find all X s.t vX = 0 is it not v'X?
south juniper
Yes, actually we need $\vec{v} \cdot \vec{X} = \vec{0} \iff \vec{v^{T}} \vec{X} = \vec{0}$
wraith daggerBOT
Sup?
static void
Yes, actually we need $\vec{v} \cdot \vec{X} = \vec{0} \iff \vec{v^{T}} \vec{X} ...
Can you explain if this can be done by gram schmidt?
Or you dont know?
This is my last question
static void
I think it can be
I think am gonna drop that idea.
south juniper
It depends on what n is tho
static void
It depends on what n is tho
My vector is 3x1 (a vector in r3)
south juniper
basically you use the standard basis of R^3
and drop one of the vectors in that basis and add your vector
and then apply gram-schmidt on those vectors(remember that after dropping one of the vectors in the standard basis and adding your vector should still give a LI set which spans R^3)
static void
and then apply gram-schmidt on those vectors(remember that after dropping one of...
tried it think i did it incorrectly. I think I am just gonna use the first one.
But thanks for the time and help
.close
charred sand
how do i do this?
cedar kilnBOT
how do i do this?
obsidian coral
how do i do this?
Apply the concept of the discriminant
charred sand
yep i did that
obsidian coral
Then post your work if you made an attempt
charred sand
a^2-24a
obsidian coral
Book answer or teacher answer?
obsidian coral
Then I suggest you should ask your teacher
obsidian coral
yea i did that to get a=0 or a=24
This is correct
violet cobalt
investigate uniform convergence of
[ I(\alpha) = \int_1^\infty \frac{\ln^\alpha(x)}{x} \sin{x} \dd{x} ]
on:
\begin{enumerate}
\item $\alpha \in [0, 1]$
\item $\alpha \in [1, \infty)$
\end{enumerate}
wraith daggerBOT
rept1d
cedar kilnBOT
@violet cobalt Has your question been resolved?
cedar kilnBOT
@violet cobalt Has your question been resolved?
quiet coyote
cedar kilnBOT
quiet coyote
someone tell me what went wrong plz
high coyote
You cannot simply take the exponents that way.
You should solve $$2^{x+1}-2^{2x}=1$$ taking $t=2^x$ so we have
wraith daggerBOT
jnkena
high coyote
$$2t-t^2=1$$
wraith daggerBOT
jnkena
livid hound
$\log(a\pm b) \neq \log(a) \pm \log(b)$
wraith daggerBOT
ℝamonov
high coyote
Solve $-t^2+2t-1=0$ and then you have $t_0=2^x$ and $t_1=2^x$ so you can get $x_1$ and $x_2$, but be careful because positive exponential functions can't be negative.
wraith daggerBOT
jnkena
cedar kilnBOT
@quiet coyote Has your question been resolved?
velvet mortar
sasuke uchiha doing math? have you given up shinobi?
austere plume
Can someone explain this to me please. Idk why but it just so confusing to me
amber pier
what have you tried?
austere plume
Yes but I got it wrong
I understand proportions
But this I just don’t
I looked at how people answered it and I just get more confused
cedar kilnBOT
@austere plume Has your question been resolved?
mossy cargo
@austere plume what's the answer
wraith daggerBOT
logicallll
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
cedar kilnBOT
@crimson sedge Has your question been resolved?
tawny warren
Do u have the answer?
As I'm not 100% sure if my answer is correct
Ok I'll tell u what I did anyway
ok so first if $c^{2022}+c^{1010}+a$ is a multiple of b, then can u show that $(b-c)^{2022}+(b-c)^{1010}+a$ is also a multiple of b?
wraith daggerBOT
newbienoob
tawny warren
@crimson sedge
yes
ok expand it binomially
b-c^2022
yes
done?
hmm ok so that would mean that for any a, if c satisfies the condition then b-c also does
agreed?
and also b-c is in the same range as c?
so for any a u have at least 2 values satisfying ur conditions?
unless c=b-c
yes c and b-c
they can be called c1 and c2
which satisfy ur condition
but what we want is only 1 value should exist
as per question
so only possibility is c=b-c?
since if they weren't equal we would have at least 2 values
so 2c=b
and that means b should be even
and b is prime
now makes sense?
and c can only be 1 in that case
and u can proceed from here i suppose
crimson sedge
yeah i have a problem and i need some time to explain it can you help me?
oh sry its occupied nvm
i thought you were a teacher sry my bad
good luck!
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@craggy pond Has your question been resolved?
north plover
hey, how can i solve this? I don't know where to even start
cedar kilnBOT
hey, how can i solve this? I don't know where to even start
north plover
crimson sedge
we need to find angle MNK?
crimson sedge
How would you approach this problem?
if we look at triangle MLK we can see it's a right angled triangle and we know two of it's sides, so we can calculate LM from pythagoras theorem
Additionally, hint: use similar triangles
cedar kilnBOT
Available help channel!
vapid narwhal
I have 2 questions from my worksheet/hw I didnt really understand. Can someone check my work?
vapid narwhal
cedar kilnBOT
@vapid narwhal Has your question been resolved?
vapid narwhal
<@&286206848099549185>
half zealot
in the second questuon, you're proving ABC ~= DEF right?
cedar kilnBOT
@vapid narwhal Has your question been resolved?
neat mortar
neat mortar
<@&286206848099549185>
bitter reef
assuming 0 is sea level, he starts at -82 feet depth right? descending 19 feet you have -82 - 19
crimson sedge
but it says his depth is 82 feet
positive
so depth is a positive direction i guess
in this context
bitter reef
depth could also mean take this as negative, since this seems like some practice question for negatives and positives..?
bitter reef
I'd say, since write depth as integer is in bold, we take it as negative
otherwise they wouldn't put so much focus on the integer part
trim sentinel
I dont think so
trim sentinel
^
crimson sedge
so positive depth
trim sentinel
Its all about what you are viewing
crimson sedge
is negative height
and since he's diving
he's at a negative height
and a positive depths
neat mortar
assuming 0 is sea level, he starts at -82 feet depth right? descending 19 feet y...
This was correct
glossy citrus
cedar kilnBOT
glossy citrus
It looks like this is referencing some sort of variation on the limit definition
But I'm not exactly sure what it is asking here
stone tide
But I'm not exactly sure what it is asking here
Just take f(a), f(a+2), etc “literally” according to the graph
One side of the inequality is negative and one side is positive
snow leaf
Guys
snow leaf
2+2=fish
crimson sedge
amazing
glass panther
🫥
crimson sedge
absolutely briliant
frank tangle
cedar kilnBOT
@snow leaf Has your question been resolved?
snow leaf
Yes
cedar kilnBOT
cedar kilnBOT
Available help channel!
true vortex
f(5) = 2(5) + 8 = 18 si
cedar kilnBOT
f(5) = 2(5) + 8 = 18 si
gaunt hamlet
That's f(g(5))
true vortex
yes
gaunt hamlet
The question is asking for g(f(5))
true vortex
but the way they taught it works the same
gaunt hamlet
Not in this case
quartz frost
18 is correct
crimson sedge
g will always return it to 5
gaunt hamlet
18 is correct
It is not
quartz frost
same haha
true vortex
o
crimson sedge
but g is always 5
true vortex
bruh i am blind
crimson sedge
so no mater what
crimson sedge
maybe take a break
true vortex
ye ive been going for 3 hours
crimson sedge
you've been at it for the past 4 hours
true vortex
true
crimson sedge
eat something
true vortex
i
ok yea
ill go make a sandwhich
ill be back later
but before I go
answer would be
g(f(2(3)+8))=..
wait
yea still where do i put the 14 in
sus
crimson sedge
into g
true vortex
ok brb
crimson sedge
so
true vortex
wait
true vortex
bu its a 5
crimson sedge
yeee
plush shore
Am I doing this right? I know how to continue the exercise but I feel I've made a mistake when taking the derivate of sen²(5x)
plush shore
hold on
I must be wrong because when you plug the result in, it should be 25/3
Just in case, sen(x) actually means sin(x), the thing is that in spanish we write it like that
sage forge
Where do you get the 1250 from?In your numerator it should be 50. Therefore, 50/6 = 25/3
plush shore
bc I did 10 times 5 times 25
sage forge
I think the issue is that Lim x goes to 0 of cos 5x is 1 not 5
plush shore
Now I redid it, but still, I get 250/6
plush shore
I think the issue is that Lim x goes to 0 of cos 5x is 1 not 5
You are right................
my baddd
sage forge
Well, it's already late. So things like that could happen 😂
plush shore
sage forge
Not sure if I read it correctly. But it should be (-10)*... and not 10-
plush shore
plush shore
Not sure if I read it correctly. But it should be (-10)*... and not 10-
I know, but since sin(x) (if X->0) approaches 0, I just ignored it
But thanks, could've been a really big oof if the cos was negative instead
plush shore
Not sure if I read it correctly. But it should be (-10)*... and not 10-
And what I tried to write was 10.(-sen(5x)), should've written the parenthesis
sage forge
Just an advice: You could have just taken out the ^2 in first place, which would have safed time
In an exam
plush shore
Yes! You are right, to be fair I tried it the other way because I was sceptical about whether my first derivative was right
Turns out it was, as you pointed out, but I was imagining that the cos(5x) was 5 instead of 1
sage forge
OK, good night
plush lagoon
How do I do 60% to a decimal and a fraction
cedar kilnBOT
How do I do 60% to a decimal and a fraction
agile cradle
$(x^2-17x+71)^(x^2+4)=1$
cedar kilnBOT
$(x^2-17x+71)^(x^2+4)=1$
wraith daggerBOT
jabba
round fossil
Try taking ln both sides
agile cradle
what does that mean
round fossil
It's logarithm to the base of (e)
agile cradle
x^2-17x+71(1) = x^2+4 ?
round fossil
Well it depends on what base you use for the logarithmic function and the property that you're using is log(x^y)=ylogx
So that's what I was trying to use to reach (x^2+4)×ln(x^2-17x+71)=0
Then solve for X either (x^2+4)=0 that will give X to be 2,-2
agile cradle
Then solve for X either (x^2+4)=0 that will give X to be 2,-2
imaginary numbers
agile cradle
kinda
would be very useful if u could solve it on paper and show me the steps
since i dont rlly understand traditional usage of logarithm yet
round fossil
Alright wait a second I'll see what I can do
agile cradle
appreciated
round fossil
Any time
agile cradle
.close
stoic basin
How are the derivatives of tan^-1x and tan^-1(2x) related?
cedar kilnBOT
How are the derivatives of tan^-1x and tan^-1(2x) related?
stoic basin
I see that the derivative of tan^-1x is 1/(1+x^2)
and that the derivative of tan^-1(2x) is 2/(1+4x^2)
but how does that come out?
Not necessarily by doing the entire equation again, but how intuitively would that work?
round fossil
I think it would be d/dx (tan^-1(f(X))) = f'(X)/(1+(f(X))^2)
That's it's generalization
You get it ?
little pebble
[I'm rather new at this, I hope to improve my skill overall for the record]
I was sent this question, I just help understanding it and how to solve it
little pebble
do you understand what the problem is asking?
[Thanks for responding]
Not quite as embarrassing at it is to admit
violet flume
nah its not embarrassing
a picture helps
lmc
have you seen a picture like this before?
little pebble
I have indeed
violet flume
the distribution is centered at some value
how quickly the numbers trail off as you move away from the center is determined by sigma
the problem is asking here for the blue area
so from 60.7 to 74.3
or, if we move 6.8 (you get this by 67.5-60.7) to the right from the center
and 6.8 to the left from the center
how much of the total distribution did we capture
make sense?
little pebble
Yes
violet flume
ah, okay
you should always try using the empirical rule first
can the distance youre moving away from the mean be expressed as an integer multiple of the standard deviation?
what is the distance? what is the standard deviation?
little pebble
Sorry give me a second 
violet flume
if it helps
ignore the heavier maths
the formula looks scary but you wont need it and he doesnt use it
little pebble
It's so simple yet it blows my mind 
violet flume
well where are you stuck
little pebble
Sorry everything sorta just clicked
little pebble
@violet flume Thank you so much, I'm really out of practice
violet flume
np
little pebble
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
ionic blade
cedar kilnBOT
ionic blade
i am stuck on this question
cosmic steppe
Expand $4^{4x+5}$
wraith daggerBOT
Umbraleviathan
ionic blade
i know them but am unsure of their application
cosmic steppe
Well let's break up the addition part:
$$4^{4x+5}$$
$$\= 4^{4x}4^{5}$$
$$\=(4^4)^x4^5$$
I lied hold on
wraith daggerBOT
Umbraleviathan
cosmic steppe
I will say that two of the functions are the same
cosmic steppe
i know them but am unsure of their application
So if you were to follow the steps and see where I land, you can see we can get an initial value and a ratio
twilit badge
g(x) seems to be equal to h(x) only
cosmic steppe
Mmhm
That requires, unless you have a calculator, the will to compute 4^4 and 4^5, or memorizing them
ionic blade
this is in prep for a test that does not allow calculators
twilit badge
another trick id say before expanding is always check their domains and range
since if they need to be same/identical their domains and range need to be same
ionic blade
i have been having trouble with domain and range so im not super sure if that is reliable for me
twilit badge
what trouble ?
ionic blade
because i dont know how to find them without a graphing calculator
twilit badge
oh my
ionic blade
?
twilit badge
can you see here x can take all values ?
ie from -inf to inf
so x's domain would be R
id say practice domains and range a bit that would help you
ionic blade
i do not know how to find them without looking at a graph
twilit badge
its quite easy once you learn how to find them without a graph
you wont have the time to graph it every time
torpid wave
how do i find the range of this 😭
cedar kilnBOT
how do i find the range of this 😭
obsidian coral
You can graph it
winged owl
you can try factoring the numerator and denominator and cancel them out
buoyant latch
i think it's everything?
as x tends to -infinity
x^3 will grow faster than x
wait it's divide
so negative really big divided by negative not so big
positive so there's a lower limit maybe
buoyant latch
you could try long division
winged owl
also if there is a common factor in the numerator and denominator from factoring then a hole is created at that x and y
oh wait actually i don't think there's a horizontal asymptote bc the degree on the numerator is greater than the degree on the denominator
so just find the hole and other from the hole it hsould be all real values
winged owl
u don't need to use long division
buoyant latch
the asymptote line is at
then solve the bottom equals zero, cancel out the 2x-5
then for me i would find the derivative of the long division'd equation to find the turning poitns
and then deduce there would be nothing in between as the form of that given equation is an oblique + vertical asymptote in kind of like an x shape
torpid wave
the asymptote line is at
thats for slant asymptote right
cause thats what i got for that part
buoyant latch
yes that's after long division
torpid wave
i just dont get how to write the range for it
like the (-infinity,??)U(??,infinity) stuff
buoyant latch
so find the derivative
sinful girder
cedar kilnBOT
obsidian coral
Did you try anything?
sinful girder
Brute forceing it
I did
the
Ok
So on the right
is 256 i think
Lemme re check
Yes
256
Then i square rooted it
And I got
16...
so diffrences between the 2 left ones is 16...
And now Im stuck...
obsidian coral
You're going about it the wrong way
obsidian coral
Recall exponent rules $(a^b)^c = a^{b \cdot c}$
wraith daggerBOT
dldh06
obsidian coral
Correct?
obsidian coral
So you have 2^8 meaning when you simplify the parentheses, you want (2^a)^b
So when you do a * b = 8
sinful girder
Ya
obsidian coral
So a can either be 2 or 4 and b has to be either 4 or 2, respectively
obsidian coral
Meaning if a = 2 then b = 4 or a = 4 then b = 2
obsidian coral
So let's say a = 2 and b = 4
sinful girder
ok
obsidian coral
You're not done yet
sinful girder
I know
obsidian coral
You know that some number minus another number equals 4
So you can try base 2 numbers, starting with 2^4
2^4 = 16
16 minus what equals 4?
obsidian coral
16 - 20 = 4?
buoyant latch
you're thinking about this in the wrong mindset
buoyant latch
this question is all about the 2's
sinful girder
12
buoyant latch
2's and their powers
sinful girder
mhm
obsidian coral
And can you get 12 with powers of two or 4?
buoyant latch
the first thing i realise is a^b - c^d has to be equal to some power of 2
sinful girder
And can you get 12 with powers of two or 4?
no...
obsidian coral
the first thing i realise is a^b - c^d has to be equal to some power of 2
Hence I said, (2^2)^4 = 2^8
buoyant latch
well it doesn't have to be 4
buoyant latch
it could be 2 as well since 8 is divisible by 2 as well as 4
obsidian coral
So try 2^3
sinful girder
8
buoyant latch
if u want to make a power of 2 minusing things
sinful girder
=8
obsidian coral
Meaning if a = 2 then b = 4 or a = 4 then b = 2
Hence
sinful girder
it = 8
buoyant latch
you want to do 2^x - 2^(x-1) = 2^(x-1)
sinful girder
ok im confused
buoyant latch
that's a power of 2 right there
sinful girder
who am i to listen
obsidian coral
Stop, I'm helping, I figured it out already
buoyant latch
aight ok
obsidian coral
There are multiple ways to solve it
sinful girder
12
obsidian coral
8 - 12?
sinful girder
im getting confused with how you say it dudeee
Ok sorry
I aint used to 8 minus
8-4=4
4
obsidian coral
8 minus what means 8 - x = 4
sinful girder
ya that sbetter thank you
obsidian coral
Saying what minus 8 would be x - 8
sinful girder
2^2
obsidian coral
So then 2^3 - 2^2 = 4, correct?
sinful girder
..
obsidian coral
And we wanted (4)^4
obsidian coral
So then you know that (2^2)^4 = 2^8
From this statement
sinful girder
but that is 256 already..
obsidian coral
I'm saying (2^2)^4 is what the left side should look like
sinful girder
Oh you like expanding them
obsidian coral
So $(a^b - a^c)^4 = 2^8$
wraith daggerBOT
dldh06
obsidian coral
And $a^b - a^c = 2^2$
wraith daggerBOT
dldh06
obsidian coral
So if a^b = 2^3 then that means a^c = 4
obsidian coral
Yes
obsidian coral
I gave you all the parts, you just need to combine them
obsidian coral
Now, starting from the beginning, recall that I said to apply exponent rules
Specifically this $(a^b)^c = a^{b \cdot c}$
wraith daggerBOT
dldh06
obsidian coral
And that's getting applied to the left hand side
sinful girder
yes
obsidian coral
Then recall that I stated, because the right side is 2^8 then b * c = 8
sinful girder
a c = 2 b = 3
obsidian coral
**dldh06**
The b and c from here
sinful girder
(2^3)^2= 2^(2*3)?
obsidian coral
So then that meant b = 2 and c = 4 or b = 4 and c = 2
sinful girder
first one...
obsidian coral
(2^3)^2= 2^(2*3)?
Applying exponent rules does 2 * 3 = 8?
sinful girder
nope
wraith daggerBOT
dldh06
sinful girder
and that is 256
wraith daggerBOT
dldh06
obsidian coral
Because the right side was 2^8 that means the base is 2, so then the left side, the base should be 2
Meaning a = 2
sinful girder
ok now i understand
obsidian coral
So we now have (2^2)^4
I simplified 2^2 to be 4, just because it's easier to work with than 2^2
So the original problem had (w^x - y^z). Because we know that (w^x - y^z) = 2^2, then that means w and y should be the same base
obsidian coral
I used w, x, y, and z, to prevent confusion from the a, b, c
obsidian coral
2
Yes
So now we know (2^x - 2^z) = 4
So it's better to start with the largest number first, because of subtraction
sinful girder
4
sinful girder
mhm
obsidian coral
And then I asked 16 - x = 4
obsidian coral
But 12 is not possible to make using 2, 3, or 4
obsidian coral
So 2^3 = ?
obsidian coral
So 8 - x = 4
sinful girder
x=4\
obsidian coral
And can you make 4 using 2, 3, or 4?
obsidian coral
So then that means z = 2
sinful girder
YAAA
obsidian coral
So now, can you properly write out the final answer?
sinful girder
😐
nope man sorry its to late for me
i cant think
i followed right up to the end
when you said
obsidian coral
So now we know (2^x - 2^z) = 4
Here's the form
sinful girder
So now, can you properly write out the final answer?
this
then i stpumped
becuase am tired
how do i connect them?
sinful girder
2
obsidian coral
I then said let's go with the case b = 2 and c = 4
.
obsidian coral
Now what does x equal?
obsidian coral
And z?
obsidian coral
So then that means z = 2
.
obsidian coral
So with all those pieces, can you write out the final answer?
obsidian coral
You know that (2^x - 2^z)^c = 2^8
By plugging in the values here
obsidian coral
Yes
sinful girder
🟡
obsidian coral
Now you just need write that on your paper