then how will i get in the form of
#help-10
kind hawk
factor out the $(x-3)^{3/2}$
warm shaleBOT
Denascite
kind hawk
and simplify a bit
orchid root
okay lemme try
orchid root
**Denascite**
with the power ?
kind hawk
not sure what you mean?
orchid root
umm how to uk factor this step
kind hawk
what do you have so far
orchid root
this last step only
kind hawk
you need to integrate that
using $\int x^n dx = \frac{x^{n+1}}{n+1}$
what do you get?
warm shaleBOT
Denascite
slender kindle
why cant i see the other help channels?
kind hawk
why cant i see the other help channels?
seems like the bot is slow today
slender kindle
i see, alright
kind hawk
we have $(x-3)^{5/2} = (x-3)\cdot(x-3)^{3/2}$
warm shaleBOT
Denascite
kind hawk
yes
orchid root
whats the next step then
kind hawk
well I'm waiting for you to factor the (x-3)^3/2 out of the expression
orchid root
but i am not able to think of a way to do it 😐
kind hawk
we have $\frac{2}{5}(x-3)(x-3)^{3/2} + \frac{10}{3} (x-3)^{3/2}$
warm shaleBOT
Denascite
halcyon grotto
obtuse pebbleBOT
halcyon grotto
how do i calculate c and d?
i have the results, just interested in how to obtain them
obtuse pebbleBOT
@halcyon grotto Has your question been resolved?
obtuse pebbleBOT
@halcyon grotto Has your question been resolved?
obtuse pebbleBOT
@halcyon grotto Has your question been resolved?
obtuse pebbleBOT
@halcyon grotto Has your question been resolved?
timid silo
e
tardy epoch
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
queen wraith
obtuse pebbleBOT
queen wraith
I think the first step is to covert both to logarithmic form?
main cedar
yes, apply log to both sides (if that's what you mean)
main cedar
you're trying to solve $7(2.7)^x=59(1.5)^x$
warm shaleBOT
lirmirit
queen wraith
i thought since the bases are not the same, that you cant do anything
main cedar
we can still isolate the x though
queen wraith
$7/59(2.7)^x=1.5^x$
warm shaleBOT
Egg
queen wraith
could i just subtract the 2.7 from 1.5 and then divide it from both sides?
main cedar
apply log to both sides, then use the log rules to isolate x
main cedar
does this look familiar to you: log(ab)=log(a)+log(b)
queen wraith
yea but the bases need to be the same
main cedar
that's the base of the exponent
queen wraith
which is also the base of the log
main cedar
we can do:
$$(1.1)^x=(5.2)^x$$
$$\log(1.1^x)=\log(5.2^x)$$
$$x\log(1.1)=x\log(5.2)$$
warm shaleBOT
lirmirit
main cedar
the base of the exponent does not have to be the same as the base of the log
queen wraith
i didnt know that
cosmic falcon
The geometric mean of two numbers is 3.2, one number is increased by 8% the other is decreased by 12%. Calculate the new geometric mean to 2dp.
obtuse pebbleBOT
The geometric mean of two numbers is 3.2, one number is increased by 8% the othe...
cosmic falcon
im really stuck please could someone help
versed cave
What have you tried?
cosmic falcon
ive dont the root of a*b=3.2
but thats where i got stuck
i know u need to work backwards somehow
versed cave
What does "increased by 8%" mean in calculations?
cosmic falcon
*1.08
cosmic falcon
*0.88
versed cave
Yes
cosmic falcon
but then what
warm shaleBOT
Nonna
versed cave
That's our starting geometric mean
cosmic falcon
yeah
versed cave
Do you prefer if we use other names for the variables or are a and b fine?
cosmic falcon
a and b are fine
versed cave
Ok
let's make a increase and b decrease
as you said, a increased by 8% is just a * 1.08
and b decreased by 12 % is b * 0.88
let's use those to find our geometric mean
$\sqrt{a \cdot 1.08 \cdot b \cdot 0.88}$
warm shaleBOT
Nonna
warm shaleBOT
Nonna
versed cave
i just changed the order
cosmic falcon
ohhhhh so can i just shoe ab as 3.2
versed cave
Yes
versed cave
$\sqrt{ab} \cdot \sqrt{0.9504}$
warm shaleBOT
Nonna
versed cave
$3.2 \cdot \sqrt{0.9504}$
warm shaleBOT
Nonna
versed cave
it's not a very nice number, it's about 3.12
versed cave
cosmic falcon
ive got an early entry gcse statistics exam on tuesday
and its one of the things i didnt understand
cheers nonna
versed cave
Good luck, I hope it goes well ^^
cosmic falcon
.close
obtuse pebbleBOT
Available help channel!
manic atlas
So, in no. 4 question, I've tried to do it and got the answer ∞ but the real answer is π. Where does π might come from?
obtuse pebbleBOT
So, in no. 4 question, I've tried to do it and got the answer ∞ but the real ans...
@manic atlas Has your question been resolved?
manic atlas
<@&286206848099549185>
obtuse pebbleBOT
@manic atlas Has your question been resolved?
manic atlas
<@&286206848099549185>
obtuse pebbleBOT
@manic atlas Has your question been resolved?
haughty coyote
I'm afraid the actual answer is that this limit is 0
valid crown
I'm afraid the actual answer is that this limit is 0
that's not guaranteed
you could wind up numerator
2k!! = (2^2k)(2k!)
try to figure something for denominator
silver dew
Hello.
Ez Algebra Phy 2 problem
obtuse pebbleBOT
Hello.
Ez Algebra Phy 2 problem
silver dew
Using V=IR and P=IV to to get P=V^2/R & P=I^2*R I'm getting two different answers.
Both of which are the inverse of eachother.
Which leads me to believe I made an algebraic mistake somewhere but I cannot find where.
jaunty frost
I need help
jaunty frost
are you a helper?
silver dew
are you a helper?
No im tryna get help. Read #❓how-to-get-help
obtuse pebbleBOT
@silver dew Has your question been resolved?
obtuse pebbleBOT
@silver dew Has your question been resolved?
tropic oak
how do i work this out
obtuse pebbleBOT
how do i work this out
cedar lichen
What have you tried?
tropic oak
so the function of f is equal to 3
but idk how to solve it cause of the vertex
im assuming its not related to it bc of how its not specified
tropic oak
k
tropic oak
x=0
cedar lichen
That's one
tropic oak
i dont understand
cedar lichen
We have f(g(x)) = 3
tropic oak
mhm
cedar lichen
We let g(x) = t for simplicity
tropic oak
mhm
tropic oak
right
tropic oak
ohh k
tropic oak
-1 and 4
tropic oak
1 n 2
tropic oak
-1 4 1 2?
cedar lichen
Yep
timid silo
obtuse pebbleBOT
scarlet locust
plug in the points as x and y
ex. for (0,0) you get
0 = log_b(0 + c)
or log_b(c) = 0
now can you find what c is?
scarlet locust
oh c is one
yes
now do the same for (3/2, 1/2)
but you already know c = 1
so 1/2 = log_b(3/2+1)
obtuse pebbleBOT
@timid silo Has your question been resolved?
small bloom
hi! sorry this is just a quick theory question- why is the horizontal stretch represented by 1/b and not just b?
obtuse pebbleBOT
hi! sorry this is just a quick theory question- why is the horizontal stretch re...
small bloom
I've used this rule so I know it works but idk why
and my teacher just kind of told us to use 1/b but I don't understand the logic of it
cedar lichen
Stretch vertically or horizontally?
cedar lichen
Consider f(x)
Let's assume that this function has a value k at a, aka, f(a) = k
Now consider f(x/b), b > 1
What value of x gives us k?
small bloom
If x and a were different values? And if k were the +k at the end of the formula?
cedar lichen
Wdym?
Let's try something concrete
Let's say f(2) = 4
Now what value of x in f(x/b) gives us 4?
small bloom
1/2
Oh
wait sorry
I'm not sure how I could calculate that with only 4?
Without knowing what b is?
sorry what I was referring to earlier was the formula I learned in class lol
y=af[b(x-h)]+k
cedar lichen
Do you see that if x = 2b, then f(x/b) = f(2b/b) = f(2) = 4?
cedar lichen
And do you see that if b > 1, then 2b > 2?
small bloom
Yes
cedar lichen
So it seems as though f(x/b) moved the point f(2) further to the right, to f(2b), yes?
This is true for every point, not just 2 (though negative points go to the left)
Thus, f(x/b) causes the function to spread out horizontally, aka, to stretch
small bloom
Okay I kind of get it? But wouldn't the function have done that anyway? By multiplying it by b/b isn't that just one? and the reciprocal of one is still one
cedar lichen
Can you elaborate?
small bloom
I don't understand how b affects the function in this example? isn't it essentially multiplying x by one?
I just don't get how multiplying x by b/b is what causes it to stretch
cedar lichen
We aren't multiplying x by b/b
We're dividing x by b
We're turning f(x) into f(x/b)
For example, let b = 2
And let's say f(2) = 4
In f(x/2), we need x = 4 in order to output 4
The point (2, 4) got shifted to (4, 4)
peak hamlet
obtuse pebbleBOT
peak hamlet
How do I solve this question?
cedar lichen
What have you tried?
peak hamlet
I don’t even know where to start
cedar lichen
Do you know the equations for projectile motion?
peak hamlet
No
cedar lichen
It'd be really easy to use them, but I don't know if you're supposed to
Looking at it, I don't think it's possible without it
The relevant equation is $y = \frac{1}{2}at^2 + v_0 t + y_0$, where $a$ is the acceleration due to gravity, $v_0$ is the initial velocity of the ball, and $y_0$ is the initial height above ground
warm shaleBOT
Gamer Dio
peak hamlet
Ok I see
I think I’m gonna ask my teacher about this one, I doubt she would have asked me to use this equation before telling me about it before, thanks for the help though
.close
wanton dagger
obtuse pebbleBOT
timid silo
I just need to know if b) and c) are answerable, like I hope I'm not missing something crucial in my understanding of relations 
or if my professor just forgot to define T
cedar lichen
I just need to know if b) and c) are answerable, like I hope I'm not missing som...
This channels taken
cedar lichen
What have you tried?
wanton dagger
For this question,
cedar lichen
where should I post it
timid silo
so u have
$Simplify : \frac{1-tan^2(A/2)}{1+tan^2(A/2)}$
warm shaleBOT
sqrt(-1) is approx -30
timid silo
is that all?
wanton dagger
Where does it say in the question A = 2?
I had t=tan(A/2) so I found A
cedar lichen
How would you find A from that?
wanton dagger
Well A would be double the value since it’s divided by 2
cedar lichen
Says who?
timid silo
u have a arctan first
cedar lichen
A could be anything
there are infinite solutions for A
cedar lichen
Well, looks like you already got it. (1 - t²)/(1 + t²)
Don't see any further simplification
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
hi there
timid silo
for this question^
I don't understand the shaded area formula
how come they minus the equation twice?
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
How to solve the b₀, b₁, b₂, b₃, b₄ in multivariate regression? What is the formula? I've been on the google search bar for hours and it only shows resources for multivariate statistics on 2 predictor variables (I have 4 predictor variables.)
I already calculated X₁², X₂², X₃², X₄², X₁y, X₂y, X₃y, X₄y, X₁X₂, X₁X₃, X₁X₄, X₂X₃, X₂X₄, X₃X₄ and calculated regression sums.
obtuse pebbleBOT
How to solve the b₀, b₁, b₂, b₃, b₄ in multivariate regression? What is the form...
harsh dirge
steady lodge
by basic trigo , we know AC = 8/root 3
steady lodge
f
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
@timid silo Has your question been resolved?
prisma zodiac
The question is basically, what number is double in the dataset of six numbers
using this box plot
I know the largest and smallest numbers are 0 and 6
and that Q1 and Q3 are 1 and 4
So the numbers look like 01 a b 4 6
Now, the median is 3 so a+b=6
But the mean of the entire dataset should also be thee, that would imply that a+b=7
Leaving no solutions...
obtuse pebbleBOT
prisma zodiac
obtuse pebbleBOT
Available help channel!
silk moth
Does anyone know of any functions that map the left values to the right values like shown below? Cheers!
1 - 1
0.75 - 0.25
0.5 - 0.075
0.25 - 0.025
0 - 0
obtuse pebbleBOT
Does anyone know of any functions that map the left values to the right values l...
kind hawk
,w interpolate (0,0), (0.25, 0.025), (0.5, 0.075), (0.75, 0.25), (1,1)
warm shaleBOT
kind hawk
but there are infinitely many functions that do this
leaden ibex
for more information, you can also read: https://en.wikipedia.org/wiki/Interpolation
silk moth
but there are infinitely many functions that do this
Yes, I understand, I was wondering if anyone knew off the top of their head any functions that can relatively speaking turn a linear line into a more "exponential-esque" line like so:
kind hawk
well you can define some piecewise function which is linear at one part and exponential at the other
otherwise you will have to define more clearly what you want with "linear" and "exponential". e.g exp(x) still looks kinda linear near 0
leaden ibex
Indeed no one would stop you from just defining a discrete function.
with exactly the mapping you want
silk moth
ok, sorry for not being clear enough. What I'm looking for is a function that takes an input value "n" and creates a line at varying levels of curvature depending on the value of n. The line will always go through 0, 0 and 1, 1 no matter what n is.
warm shaleBOT
silk moth
sorry, I forgot to also specify that it must be diagonally symmetrically if you get what I mean?
kind hawk
hmm
silk moth
like this
leaden ibex
like this
gotta say, this is one random line
we neither know the slope nor y-intercept
silk moth
gotta say, this is one random line
lol, sorry. from, 0, 1 to 1, 0
kind hawk
I think if you move the point at the bottom right of the first pic I think you could get what you want
silk moth
I think if you move the point at the bottom right of the first pic I think you c...
cheers! I'll take a look into it
kind hawk
move C to (1,1) and then move B on the diagonal you drew in red
no clue whether those give a nice explicit function tho
probably just a parametric curve
silk moth
hmm, but see after a certain point, the line goes outside of the (0, 0) (1, 1) "box". Sorry I should have also specified this haha, it needs to stay inside.
again, sorry if I'm explaining this in a weird way, I'm not a maths person.
leaden ibex
this feels like a moving goalposts situation
silk moth
haha, apologies
silk moth
yes, exactly!
silk moth
Thank you! I'll look into that.
kind hawk
,w plot 1-sqrt(1-x^2), 1-cbrt(1-x^3), 1-(1-x^10)^(1/10), x=0 to 1, y=0 to 1
warm shaleBOT
silk moth
sweet! That's perfect! Thanks so much Denascite!
kind hawk
wolframalpha doesn't like giving both axis the same scale apparently
silk moth
@kind hawk thank you so much! This is the exact answer I was looking for!
kind hawk
.close
silk moth
.close
lethal pier
obtuse pebbleBOT
lethal pier
topic Number and Algebra
royal basin
have you made any progress so far?
lethal pier
not rlly
royal basin
okay
lethal pier
Just the inner bit =18 and outer bit = 13
royal basin
would you like a hint or would you rather be taken through the whole thing step by step?
...what
lethal pier
hint please
royal basin
okay, here is my hint:
find the length and width of the outer rectangle in terms of x. then find its area, also in terms of x.
royal basin
...okay
look at the diagram
you see how it is composed of an inner rectangle surrounded by a path of length x all around, yes?
lethal pier
yes
lethal pier
6
lethal pier
6
royal basin
but yes, the width of the inner rectangle is 6.
now what is the width of the outer rectangle?
spiral pebble
6+2x
royal basin
this time your answer will have the letter x in it.
yes, correct.
similarly, can you now tell me the height of the outer rectangle?
lethal pier
3+2x
lethal pier
yh..
royal basin
@spiral pebble that question was not addressed to you and you should not have replied to it
lethal pier
but i understand it
spiral pebble
ok
lethal pier
3+2x*6+2x
lethal pier
3+2x*6+2x-18
royal basin
no,
you have not fixed the issue with your expression, and now you have subtracted 18 from it for no good reason.
lethal pier
9*4x
royal basin
even worse now.
parentheses. you were missing parentheses in your first attempt.
it's (3+2x)(6+2x).
lethal pier
oh shit yh
royal basin
now, we know from the problem statement that the area of the pool with the path, i.e. the entire outer rectangle, is a certain value. what is that value?
lethal pier
18+18x+4x^2
royal basin
no, that's not what i asked you for.
i asked you to read the problem statement and tell me how many square meters the area of the whole thing was said to be.
lethal pier
31m^2
lethal pier
(3+2x)(6+2x)=31
spiral pebble
Hi anyone can help me with my question no one is replying
proven zephyr
Hi anyone can help me with my question no one is replying
no
it's unsolvable
i think it's unsolvable*
spiral pebble
oh
lethal pier
i dont think thats right
spiral pebble
nono it is correct
lethal pier
ok yes
spiral pebble
have you learned the quadric formula
spiral pebble
umm
how about you think of it this way
the total area is 18+4x^2+2times3x+2times6x
lethal pier
yes
lethal pier
yh
spiral pebble
4x^2+18x-15=0
lethal pier
4x^2+18x=13
spiral pebble
You can directly calculate the x with the quadratic formula with that equation
4x^2+18x-15=0
But sadly you haven't learnt it
lethal pier
i dont think ill need that for the exam its not in the exam
spiral pebble
um
lethal pier
the teachers alwsays put questions exactly like these in tests
but weve never learmt the quadratic formula
spiral pebble
then you are not suppose to calculate the formula
ok Let me calculate first
72cm?
Not sure
Might have calculation errors
lethal pier
the text book said 63 or 63 but its defo wrong
limber vapor
Hello, how do i do question number 11-14?
obtuse pebbleBOT
Hello, how do i do question number 11-14?
high lily
-7 = -49
bad
limber vapor
what is bad
limber vapor
my bad
high lily
you should've written
-7x = -49
keen wadi
obtuse pebbleBOT
lusty cedar
why do you want it to be rechecked?
summer spire
first q is good
lusty cedar
first q is good
i feel both are the same and boring
keen wadi
why do you want it to be rechecked?
I haven’t been checked
lusty cedar
but i tried solving them independently anyways
keen wadi
I am just not good at mechanics and have test coming up
summer spire
final vertical velocity should not be = 0
keen wadi
I am just not good at mechanics and have test coming up
So need to iron out flaws
summer spire
second q
keen wadi
Why not?
summer spire
your soccer ball is accelerating
meaning therse an increase in velocity
since acceleration is the rate of change of velocity
lusty cedar
in both cases initial velocity is horizontal and vertical is zero
summer spire
it means velocity should be increasing or decreasing
lusty cedar
wait
keen wadi
Oh…
lusty cedar
i think one person at a time
summer spire
in both cases initial velocity is horizontal and vertical is zero
what question?
keen wadi
does it make sense conceptually
The acceleration part does
lusty cedar
what question?
both
summer spire
word of advice: always try and visualise what youre saying
summer spire
both
nah not q2, q2 must have an initial horizontal velocity
otherwise it wouldnt go away from the initial horizontal position
same with q1
lusty cedar
i said both have only horizontal
summer spire
it states that thers a horizontal velocity?
summer spire
in both cases initial velocity is horizontal and vertical is zero
vertical
you did say vertical
keen wadi
See I didn’t want to assume no vertical
summer spire
when something is shot off the horizontal
you assume theres no vertical initial velocity
keen wadi
I thought of golf and how it goes up
summer spire
thats when its not to the horizontal
keen wadi
But I understand why there would be no vertical now
keen wadi
So for both Q1 and Q2 vertical velocity would be 0
summer spire
So for both Q1 and Q2 vertical velocity would be 0
yes
keen wadi
But I can still get time from s = 1/2at^2 using the vertical height
summer spire
right because theres no initial vertical velocity
lusty cedar
But I can still get time from s = 1/2at^2 using the vertical height
that's the only place i believe you can get time from
keen wadi
So then I would just need to times horizontal velocity by the time and that would give the answer for Q1
summer spire
u could also use s = (u+v)t/2
keen wadi
But then in Q2 I would divide 35 by the time to get the horizontal speed?
lusty cedar
exactly
keen wadi
Ok so the cos stuff wasn’t needed
lusty cedar
idts
keen wadi
?
lusty cedar
no need of that stuff
summer spire
ngl im too lazy to calculate it myself so can ou send your work
lusty cedar
16.517896630349431113039021572692 is the answer i think
keen wadi
keen wadi
16.517896630349431113039021572692 is the answer i think
Yeah I got that as well
Well thanks 🙏 It seems I still need to revise projectiles 
.close
timid silo
given $f: B \to C,\ g: A \to B$ are total functions, prove/disprove the following
if $f$ is invertible then $f \circ g$ is invertible
$f$ being invertible means for every $b \in B$ there exists a single $a \in A$ such that $(b,a) \in B \times A$
for $f \circ g$ to be invertible, for every $(a,c) \in f \circ g$ there has to exist a single $(c,a) \in f^{-1} \circ g^{-1}$ but we cant know if $g$ is invertible for sure so this statement is false
obtuse pebbleBOT
given $f: B \to C,\ g: A \to B$ are total functions, prove/disprove the followin...
warm shaleBOT
mahmooz
timid silo
im not sure of this
pseudo swift
if g isn't injective, we're gonna have a problem indeed
timid silo
hmmmm but is it correct to write $f^{-1} \circ g^{-1}$
warm shaleBOT
mahmooz
timid silo
i just made that up because i thought to invert a value we un-apply the functions in order
like we unapply g^-1 then f^-1
because before we applied f and then g
summer spire
oml its mooseguy
timid silo
im not sure what you guys mean
pseudo swift
nah sorry I was talking to JC at the same time
timid silo
oh ok lol
pseudo swift
yeah we don't know whether g is invertible, so assuming an inverse is problematic
we can think the other way though, ie trying to disprove the thing
timid silo
ofc
timid silo
passing x_1 and x_2 to g could give us the same y which is then passed to f and f outputs the same value for both of x's because it was passed the same value for both of them so f(g) isnt injective which means its not invertible
pseudo swift
yeah perfect
timid silo
imma rewrite that properly tho lol
pseudo swift
well we found ourselves a pretty huge counterexample lol
timid silo
gotta provide a counter example too
pseudo swift
yeah you can give a specific example if you want
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
boreal zenith
i don't know how to solve this can someone solve it to me please?
obtuse pebbleBOT
i don't know how to solve this can someone solve it to me please?
tranquil arch
use double angle formula
tranquil arch
yes, what's cos(pi/4)?
boreal zenith
1 over root 2
tranquil arch
yes, so you get the answer
tranquil arch
$$\frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}$$
warm shaleBOT
秋水
boreal zenith
how the root of two became in the numerator?
tranquil arch
$$\frac{1}{\sqrt{2}} =\frac{1 \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}} = \frac{\sqrt{2}}{2}$$
warm shaleBOT
秋水
obtuse pebbleBOT
Available help channel!
compact pagoda
obtuse pebbleBOT
compact pagoda
Unsure about how to solve
grizzled shore
What does a double root mean
timid silo
like one root is double another?
compact pagoda
out of the 3 roots 2 are the same
compact pagoda
c?
grizzled shore
Typo sry
compact pagoda
So if you were you factor P(x) what should it look like
Isnt that my first line of working or have I messed it up
I wasnt sure if you had to include the p
scarlet locust
if you factor it, it should look like a(x-b)(x-c)^2 =
grizzled shore
What where is the +p
compact pagoda
ohh ok i see
scarlet locust
where a, b, c are some constants
compact pagoda
What where is the +p
the remainder at the end
compact pagoda
ok
grizzled shore
the remainder at the end
No but your first line doesn’t have it
compact pagoda
Yeah I just realised I forgot to ad it
scarlet locust
differentiating wont help, that only gives you the extremas
compact pagoda
ok
scarlet locust
expand this a(x-b)(x-c)^2
grizzled shore
differentiating wont help, that only gives you the extremas
Differentiating is helpful
compact pagoda
expand this a(x-b)(x-c)^2
ax^3-2ax^2c+axc^2-ax^2b+2abcx-abc^2
grizzled shore
It shows you where you can have a double root
scarlet locust
ax^3-2ax^2c+axc^2-ax^2b+2abcx-abc^2
now equate coefficients with P(x)
scarlet locust
It shows you where you can have a double root
ah yes I see
compact pagoda
now equate coefficients with P(x)
since a = 1 can i rule those out?
scarlet locust
yes
compact pagoda
i think i may have messed the squaring
scarlet locust
$$(x-b)(x-c)^2 \newline
= (x-b)(x^2 + c^2 - 2cx) \newline
= x^3 + c^2x - 2cx^2 - bx^2 + bc^2 - 2cbx \newline
= x^3 + x^2(-2c- b) + x(c^2-2cb) + bc^2 \newline
$$
scarlet locust
compact pagoda
whoops
scarlet locust
$$(x-b)(x-c)^2 \newline$$
$$= (x-b)(x^2 + c^2 - 2cx) \newline$$
$$= x^3 + c^2x - 2cx^2 - bx^2 + bc^2 - 2cbx \newline$$
$$= x^3 + x^2(-2c- b) + x(c^2-2cb) + bc^2 \newline$$
scarlet locust
so 6 = -2c-b
9 = c^2 - 2cb
p = bc^2
compact pagoda
ok
scarlet locust
by comparing coefficients with p(x)
compact pagoda
ok i can see now
scarlet locust
now you have 2 equations in 2 variables
6 = -2c-b
9 = c^2 - 2cb
solve for b, c
,w 6 = -2c-b and
9 = c^2 - 2cb
warm shaleBOT
timid silo
was this needed tho?
we can also use vietes
formula
b+2a=-6
ab+ba+a^2=9
if a and b are ur roots
hope I didn't mess the formulas
and multply all the roots
to get q
,w b+2a=-6,ab+ba+a^2=9
warm shaleBOT
compact pagoda
alr i see i see
compact pagoda
is it two possible solutions?
timid silo
ye
compact pagoda
ok
timid silo
@scarlet locust s method is somehow ignoring the 4 solution ig
compact pagoda
wait so which one is correct
timid silo
wait so which one is correct
between Swas and me?
compact pagoda
yeah
timid silo
mine looks better ig
compact pagoda
ok
timid silo
compact pagoda
yeah its prtty close
noble kindle
obtuse pebbleBOT
noble kindle
So $\psi \in Aut(\mathbb(Z_n))$. So psi is just some isomorphism from Zn to Zn.
warm shaleBOT
Kurama
noble kindle
oh yeah
noble kindle
thats just a capital letter of phi
tardy epoch
**Kurama**
It's just another potential candidate for an automorphism. The sentence is stating it's equal to $\psi$.
warm shaleBOT
riemann
spark flume
hi
obtuse pebbleBOT
@noble kindle Has your question been resolved?
noble kindle
.close
crystal stream
Hi there. Can someone help me understand what does it mean : "Clearly, as F vanishes on the x axis we should obtain F'_x(x,0) = F''_x(x,0) for every x in R" ?
obtuse pebbleBOT
Hi there. Can someone help me understand what does it mean : "Clearly, as F vani...
crystal stream
That is the question + (a)
warm canopy
your function is zero everywhere on the x axis, $F^{'}_x(x,0)$ is asking what the rate of change of your function is along the x axis
warm shaleBOT
ΣAC
obtuse pebbleBOT
@crystal stream Has your question been resolved?
crystal stream
do you see why that would mean its equal to zero?
I don’t think I get it
What you’re saying
Sorry for my late response I am away from my PC now
Anyways, I don’t understand why is it 0?
I calculated the derivative, and then I should plug zero?
You plug zero for the y
And then you get that the whole term is zero and you don’t have anything to derive?
obtuse pebbleBOT
@crystal stream Has your question been resolved?
warm canopy
your function is zero everywhere on the x axis, $F^{'}_x(x,0)$ is asking what th...
think about this, the function is always zero on the x axis, so if you're asking for the rate of change along the x axis, there is no change, because its constant on the x axis
@crystal stream
obtuse pebbleBOT
@crystal stream Has your question been resolved?
crystal stream
think about this, the function is always zero on the x axis, so if you're asking...
Yeah but is that because it is in the point (0,0)?
limber quartz
can you multiply either equation by a number that makes every term the same?
(spoiler: no)
so that means __ isn't the answer
review the conditions for the number of solutions to systems of linear equations
devout solar
you could also just make the second equation to be in the form y=ax+b
obtuse pebbleBOT
Available help channel!
queen wraith
obtuse pebbleBOT
acoustic pawn
sorry haha, this channel was unoccupied a sec ago
queen wraith
o sheet
acoustic pawn
Anyway i'll try helping you out. What have you tried out yet?
queen wraith
$1890(0.024^t)$
warm shaleBOT
Egg
queen wraith
but when i searched it on google i saw people putting a +1 in there
not sure why you would need the 1+
or if thats even correct
whats that
drowsy girder
That seems like increasement
Actually you can generalise it
If you let r be negative
Here you have decreasment so just plug -0.024 for r
drowsy girder
Yes
queen wraith
$1890(1-0.024)^t$
warm shaleBOT
Egg
queen wraith
or
drowsy girder
Seems right
queen wraith
$1890(-0.024)^t$
warm shaleBOT
Egg
warm shaleBOT
Egg
drowsy girder
Yes but thats not fun
warm shaleBOT
Egg
drowsy girder
Thats just confusing
queen wraith
ok thank you for your help tho
drowsy girder
increasing
Then 1 + 0.024
obtuse pebbleBOT
@queen wraith Has your question been resolved?
drowsy girder
how would i go about finding the h^-1 of it?
Take the log
queen wraith
$log_0.976(h/1890)=t$
warm shaleBOT
Egg
drowsy girder
Seems right
But couldve just used ln
$$t = \frac{ln(\frac{h}{1890})}{ln(1 - 0.024)}$$
warm shaleBOT
Pluton
queen wraith
thats the inverse??
drowsy girder
Mine
queen wraith
ur e genius
drowsy girder
Its same thing tho
obtuse pebbleBOT
@queen wraith Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
ancient heart
Does anyone know a website to learn the normal multiplication inside out for an example 2×3, 7×6, 8×6 etc?.
obtuse pebbleBOT
Does anyone know a website to learn the normal multiplication inside out for an ...
limber quartz
Does anyone know a website to learn the normal multiplication inside out for an ...
Not me
The best way to learn multiplication tables is with flashcards
And actually, you can find a phone app for that
ancient heart
Whats the app
limber quartz
Dunno
Don't remember
The free one, I guess, lol
When I was in school I just bought a stack of note cards, wrote on them, and practiced them a few several times a day for a week. That was it.
obtuse pebbleBOT
@ancient heart Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
gilded pasture
If x can complete a work in 8 hours and
y can do the same work in 24 hours. If
both are working together then the
task will be finished in how many hours
obtuse pebbleBOT
If x can complete a work in 8 hours and
y can do the same work in 24 hours. If
b...
gilded pasture
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
vagrant spruce
help
somber mural
you can see it is exponential
so in form a^x
y=ab^x
sub in y and x for both point
then sovle simultaneously
vagrant spruce
idk
keen jetty
what is b^0
1
Can I give my input on this?
Im not sure if its 100% right but crom my knowledge
somber mural
@vagrant spruce what is anything to the power of 0
vagrant spruce
1
somber mural
ok so what does that mean a is?
vagrant spruce
2?
vagrant spruce
1 = ab^6
vagrant spruce
what is it
vagrant spruce
oh yes 2
warm shaleBOT
IntelligentCake
somber mural
solve for b
somber mural
do you know how to use logarithms
torn wave
logarithms are not needed to solve for b
vagrant spruce
nope
keen jetty
By the way i was qondering this from the start but was the initial equation not wrong? Is it not just y=a^x + c
somber mural
y=ab^x + c
keen jetty
Based on the formula you gave is the answer you get not y=2*root6(1/2)^x
somber mural
but c is 0
keen jetty
C is not 0
somber mural
yes it is
keen jetty
somber mural
you will see you shift entire graph up by 1
yeah
exactly
the asymptote is not at y=1
keen jetty
torn wave
IntelligentCake is correct on this one. The horizontal asymptote of the exponential function determines its vertical shift
somber mural
Wait so coefficwient of a^x causes that?
coefficient of a^x tells you value at x = 0
vagrant spruce
so how do i find the equation
keen jetty
coefficient of a^x tells you value at x = 0
Ooh ok ty ^^
somber mural
how do you get b on its own
you have 1/2 = b^6
so how do you get rid of the power of 6
vagrant spruce
square root?
vagrant spruce
idk then i only know the square root way
torn wave
also I'm just gonna let you know @somber mural that you have the equation set up incorrectly
torn wave
Damon is correct on this one
keen jetty
Yeah i was wondering why the answer i got from it wasnt right xD
keen jetty
6 = 2 * b^1
somber mural
darn latex
keen jetty
XD
warm shaleBOT
IntelligentCake
somber mural
there we go
vagrant spruce
is the equation