im definitely lost
#help-36
vapid kernel
I got b=2
-a + a + 4b = 8 - a
4b = 8 - a
a = 8 - 4b
(8 - 4b) + 4 - b - 2 = 8(8 - 4b) + 16 + 2b - 2
-8 + 5b = 64 - 32b + 14
37b = 78
b = 2
Im not sure what Im doing wrong
iron cove
I did get a=8-4b
final saddleBOT
@vapid kernel Has your question been resolved?
vivid walrus
Are you saying that because you used chatgpt to solve their question? cuz it seems you did
chatgpt is dumb in math
stuck tide
Are you saying that because you used chatgpt to solve their question? cuz it see...
No I didn't
I said it might be wrong because I used the remainder with different degreed polynomials
vivid walrus
ahh ok
final saddleBOT
final saddleBOT
Available help channel!
lusty vapor
Prove that the series x^n / n from n=1 to infinity converges, but not uniformly
ocean lintel
on what interval ?
lusty vapor
on what interval ?
Sorry, on (-1,1)
ocean lintel
!status
final saddleBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
Im not sure how to prove that it is convergent in the first place, weierstrass test will not work ... Am not allowed to use natural log either
i saw this online
ocean lintel
do you have any theory on power series ?
stuck tide
Prove that the series x^n / n from n=1 to infinity converges, but not uniformly
$\lim_{n\to\infty} |\frac{x^{n + 1}}{n + 1} \frac{n}{x^n}|$
$\lim_{n\to\infty} |\frac{xn}{n + 1}|$
$\lim_{n\to\infty} |\frac{xn + x - x}{n + 1}|$
$\lim_{n\to\infty} |x - \frac{x}{n + 1}|$
$|x| \in (0, 1)$
Therefore the series converge when $x \in (-1, 1)$
This is the Ratio Test
soft zealotBOT
Oğuzhan
lusty vapor
do you have any theory on power series ?
We just learned weierstrass test and root test to see if series is convergent ,
We did not really do ratio test either
lusty vapor
i saw this online
Based on this, what if Mn = x^n. Then f_n(x) = x^n / n is less than x^n right? why is this wrong way
ocean lintel
it isn't. It's just the comparison test
for convergence
for uniform convergence ofc you can't just fix x like that
stuck tide
The ratio test states that
Let $L = \lim_{n\to\infty} |\frac{a_{n + 1}}{a_n}|$
If $L \in [0, 1)$ then the series converge
If $L = 1$ it's inconclusive, so we can't be sure with this method
If $L > 1$ the series diverges
soft zealotBOT
Oğuzhan
empty spoke
lusty vapor
hat the
lusty vapor
**Oğuzhan**
This makes sense but we are only allowed to use things we have proved in class on our proofs
I think i see why it converges anyway ... But why it is not uniformly convergent I need to work out
ocean lintel
it goes to infinity at 1 so it makes sense that it wouldn't converge uniformly
lusty vapor
x is on open interval (-1,1) though
stuck tide
I think i see why it converges anyway ... But why it is not uniformly convergent...
Because if the next term is smaller than the last term near to infinity, it's getting close to 0
lusty vapor
if s_n(x) is the partial sums
for uniform convergence, if we are given eps>0 then $|f(x)-s_n(x)| < eps$ when $n>=some k$ for all of $\forall x$
so i need to prove that |f(x)-s_n(x)| >= epsilon
stuck tide
so i need to prove that |f(x)-s_n(x)| >= epsilon
You can put dollar signs around math expressions
ocean lintel
not needed here, it's not like the math is hard to read
stuck tide
Just a suggestion
soft zealotBOT
Purdue Pete
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
final saddleBOT
@lusty vapor Has your question been resolved?
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@lusty vapor Has your question been resolved?
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Available help channel!
tranquil pine
Can someone please tell me the formula for this?
final saddleBOT
Can someone please tell me the formula for this?
sick roost
you need to find the area of the triangles then the base
we know all the triangle are the same, and there are 5, so we only need to find the area of 1 triangle
then 5 times that area
then add the area of the pentagon
final saddleBOT
@tranquil pine Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
crisp fog
The question and what I have so far I am struggling
final saddleBOT
The question and what I have so far I am struggling
@crisp fog Has your question been resolved?
opaque totem
hwo do you do this question?
final saddleBOT
hwo do you do this question?
opaque totem
pls help
tired hull
alr i think i can do this one.
with this, we can apply pythag
where the line on P = 5
and we know A = 2, B = 3
meaning the small left over length in the B circle = 1
25 - 1 = 24 which is (black line)²
so we have the height of the trapezoid
The area of the trapezoid = (2+3)/2 * Root (24)
= 3 * root (24)
tired hull
oh wait im dumb i just spent so long trying to calculat the angle
hold on that makes no sense
what am i even doing
i cant think
doing math at 1 am
final saddleBOT
@opaque totem Has your question been resolved?
hexed oriole
final saddleBOT
hexed oriole
i need help doing b c and d
zinc geyser
ok for B take log on both sides
hexed oriole
like this?
log_5 3x and log_5 7x-2?
soft zealotBOT
bettim
hexed oriole
right
zinc geyser
$\log 5^{3x}=\log 5^{7x-2}$
soft zealotBOT
bettim
zinc geyser
yes
so it is
$3x \cancel{\log 5} = (7x-2) \cancel{\log 5}$
i cancelled log 5 on both sides okay?
hexed oriole
right
soft zealotBOT
bettim
soft zealotBOT
bettim
zinc geyser
you can solve further
hexed oriole
can it also be 7x-2=3x
zinc geyser
both mean the same
hexed oriole
7x=2?
hexed oriole
forgot about that side
zinc geyser
ye
hexed oriole
whats the ultímate goal? solve for x?
hexed oriole
can you also help with c or d?
zinc geyser
yes sure
why is you image 8 mb bro lo
ok for c
do the same thing
take log on both sides
what do you get?
hexed oriole
log7^x=log9
hexed oriole
being down the x?
zinc geyser
yes
hexed oriole
the 7 too?
zinc geyser
no
hexed oriole
so just 7x
zinc geyser
$x \log 7 = \log 9$
soft zealotBOT
bettim
zinc geyser
you should get the x out of log
hexed oriole
right
hexed oriole
x=log9/log7???
soft zealotBOT
bettim
soft zealotBOT
bettim
zinc geyser
so now what would x be?
hexed oriole
right
zinc geyser
the way you wrote in this
so now what would x be?
using the formula i just told you
hexed oriole
log9/log7=x9 x7?
hexed oriole
i dont get the formula
zinc geyser
$x=\frac{\log 9}{\log 7}$
soft zealotBOT
bettim
zinc geyser
i dont get the formula
so wait
hexed oriole
are we putting log back into x?
hexed oriole
i hope so yes
hexed oriole
log_b a
zinc geyser
yes
so
suppose you have log a/ log b
where a and b can be any variable or literals
we can write it as log a to the base b
zinc geyser
**bettim**
now you get this?
hexed oriole
log_7 9?
hexed oriole
so 7 9
zinc geyser
log_7 9
hexed oriole
is there more?
zinc geyser
add 3^y on both sides
hexed oriole
2^4y+1=3^y
hexed oriole
4y+1 log2= y log3?
hexed oriole
5y+1= log2 log3?
soft zealotBOT
bettim
zinc geyser
ok so what will you get if you divide both sides by y?
zinc geyser
$\frac{4y+1}{y} \log 2= \log 3$
soft zealotBOT
bettim
hexed oriole
oh
soft zealotBOT
bettim
zinc geyser
yes
hexed oriole
to get it on the right
zinc geyser
yes
hexed oriole
does the left side stay like that?
@zinc geyser sorry to ping but i gotta go soon
soft zealotBOT
bettim
soft zealotBOT
bettim
final saddleBOT
@hexed oriole Has your question been resolved?
hexed oriole
so that you would be
because you multiplied by y right
zinc geyser
yes
zinc geyser
**bettim**
this is the final yea
hexed oriole
tysm bro, i appreciate your patience
final saddleBOT
final saddleBOT
Available help channel!
solemn mason
hello 🙂
solemn mason
this is the problem i am on right now
and ik that the formula is V= pi r^2 h
but im a little confused on what its asking
robust mulch
You want just the pipe
So you have two cylinders, the pipe and the inside of the pipe
vapid urchin
hi, this's a calculus problem. is this a right triangle on graph? or is there two pieces (rectangle above the triangle)?
final saddleBOT
hi, this's a calculus problem. is this a right triangle on graph? or is there tw...
bleak granite
hi, this's a calculus problem. is this a right triangle on graph? or is there tw...
There are two parts yes, but remember this is a decreasing linear function so there is a triangle above the rectangle
vapid urchin
well i tried finding both parts
of y values
but couldnt
can you please help me @bleak granite
bleak granite
Ok, so plug in both 0 and 5 into $f(x)=19-2x$, which value is lesser?
soft zealotBOT
XxMrFancyu2xX
vapid urchin
is it c?
bleak granite
?
vapid urchin
bleak granite
well this time you didn't so clearly your doing omething right
vapid urchin
btw
how did u know
there was rectangle
above a triangle
and not just
only a TRIANGLE
cause at first i thought it was just a triangle
bleak granite
well for 1. at some point you look at too many lines to really just yk know it straight away but 2. I just logiced it, if 5 is what the integral is going to then 19-2x on {0<=x<=5} doesn't cross 0 so there must be a rectangle
final saddleBOT
@vapid urchin Has your question been resolved?
tranquil pine
can someone help w this
final saddleBOT
can someone help w this
final saddleBOT
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.
lethal estuary
why quickly? is this for a test?
muted coral
can someone help w this
with which question
muted coral
you can see the axis of symm visually
muted coral
the parabola has vertical symmetry
tranquil pine
the axis no?
muted coral
it should be x = something
muted coral
no
muted coral
what’s the x coord of the middle of parabola A
muted coral
domain is always R for vertical parabola
tranquil pine
so
muted coral
range, you have to ask yourself what y values can be found on the curve
tranquil pine
so..
muted coral
and -2
tranquil pine
for graph a
muted coral
ye
tranquil pine
what about range
muted coral
can you find y = -10 on graph A
tranquil pine
ya
muted coral
where
muted coral
giving the answers isn’t the point here
muted coral
graph A points up
muted coral
so you know it’s x^2, not -x^2
tranquil pine
its b
muted coral
indeed
final saddleBOT
final saddleBOT
Available help channel!
sonic tapir
final saddleBOT
lethal estuary
,rccw
soft zealotBOT
sonic tapir
The Angeles are small ones .So tan or sin are linear apöroximations
With tan a =a and sin a = a
Need s or x
tranquil pine
Hey
tranquil pine
How to evaluate cos 4pi/11
final saddleBOT
@tranquil pine Has your question been resolved?
vital crag
How to evaluate cos 4pi/11
,calc cos(4pi/11)
soft zealotBOT
Result:
0.41541501300189
Does it want the exact value? @vital crag
vital crag
idk i can't read your teacher's mind
rustic birch
Unfortunately there is no way to evaluate cos(4pi/11) without a calculator because 11 is not a "friendly" fraction in this case
I mean there could be an identity you could use
tranquil pine
@rustic birch secant 2pi/3
What’s my first step?
It’s going to be in the first quadrant right
rustic birch
<@768298835306741781> secant 2pi/3
Secant = 1 / cosine so it is 1 / cos(2pi/3). Cos(pi/3) equals 1/2 so we next need to find the quadrant 2pi/3 is in which is 120 degrees which is the second quadrant. Cosine is negative in the second and third quadrants so the answer is 1 / (-1/2) = -2
tranquil pine
Secant = 1 / cosine so it is 1 / cos(2pi/3). Cos(pi/3) equals 1/2 so we next nee...
We only use radians, but it wouldn’t matter if I use degrees
@rustic birch I had an idea what if I drawed it out and showed it to you
rustic birch
We only use radians, but it wouldn’t matter if I use degrees
If you are using radians you don't need to use degrees I was just thinking of degrees because it was easier to visualize it
rustic birch
But pi/2 < 2pi/3 < pi so it is in between 90 and 180 degrees which is the second quadrant
rustic birch
<@768298835306741781> I had an idea what if I drawed it out and showed it to yo...
Sure!
tranquil pine
Then you will help me from there
rustic birch
Yes
rustic birch
Remember this:
- Sine is positive in first and second quadrants and negative in third and fourth quadrants (Positive up, negative down)
- Cosine is positive in first and fourth quadrants and negative in second and third quadrants (Positive right, negative left)
- Tangent is sine/cosine
- Secant is 1 / cosine (Reciprocal of cosine)
- Cosecant is 1 / sine (Reciprocal of sine)
- Cotangent is 1 / tangent or more easier, cosine / sine (Reciprocal of tangent)
rustic birch
Sin(pi/3) = Cos(pi/6) = sqrt(3)/2
Sin(pi/6) = Cos(pi/3) = 1/2
Sin(0) = sin(pi) = 0
Sin(pi/2) = 1
Sin(3pi/2) = -1
Cos(0) = 1
Cos(pi) = -1
Cos(pi/2) = cos(3pi/2) = 0
Think of it this way: Cosine is horizontal and sine is vertical
@tranquil pine What is the question?
final saddleBOT
@tranquil pine Has your question been resolved?
mint crown
final saddleBOT
mint crown
i have zero clue how to solve this
final saddleBOT
@mint crown Has your question been resolved?
mint crown
No
final saddleBOT
rain cloud
i have zero clue how to solve this
Start by multiplying everything inside the brackets with ³√(y²)
final saddleBOT
Available help channel!
radiant burrow
a toy rocket of mass 0.2kg is projected vertically upwards from rest by means of a force which decreases uniformly in 2 seconds from 2g to zero and thereafter ceases. Assume that g has a numerical value of 9.8 and that air resistence is negligible. Find the max speed
final saddleBOT
a toy rocket of mass 0.2kg is projected vertically upwards from rest by means of...
radiant burrow
For some reason I keep getting way off the solution not entirely sure why
I considered the Force applied to be represented by the equ 2g - gt
then the net force being
2g-gt-0.2g = 1.8g-gt
so then the acceleration is 9g-gt/5
which if you integrate and then sub in t = 1.8s * for time when acceleration stops being positive ) i get 155m/s
not sure what I did wrong here
paper zodiac
I considered the Force applied to be represented by the equ 2g - gt
You got ur net for wrong
paper zodiac
Isn't net force F1-F2
g is not force it's acceleration
it's acceleration due to gravity
and even if it is a force
Ur multiplying time and force
Cause net force is just F1-F2 = 0
So F1 = F2 must be equal
radiant burrow
i'm a bit lost now
paper zodiac
Ok so a net of something is just the total of something in an overall system
radiant burrow
yes
paper zodiac
Like if I buy something from you
You get the money I get the item
But the item and money is still in the system which is you and me
radiant burrow
ok
radiant burrow
no but thats only the case if the net force = 0
paper zodiac
u said that 2g - gt = 0
radiant burrow
like the net force does not equal to zero
paper zodiac
so 2g = gt and t would be 2 again
paper zodiac
no but thats only the case if the net force = 0
Yes and in this case our net force is zero
since no force was added in the system aside from the force from the start and gravity
Which is already being accounted on our problem
radiant burrow
ummmm
paper zodiac
This is physics right?
paper zodiac
Oh
radiant burrow
physics
paper zodiac
So we need a math answer?
radiant burrow
yes
but its just asking for max speed
so idk if thered be any difference between phy & math for this
question anuywasy
paper zodiac
In the problem, is the end of the question when the ball reach it's maximum height?
paper zodiac
Its easy
radiant burrow
lol
paper zodiac
😎
radiant burrow
i mean the question seems simple
but i keep getting the wrong answer
can i see your working then
radiant burrow
okay
paper zodiac
So actually note here
The weight isn't really needed for the equation here
Since we already have the final velocity, acceleration, and time
We can have the initial velocity here
paper zodiac
Max speed
paper zodiac
Since the initial velocity will be the max speed
Since when it reach the max height, it stops and would become 0g
Since our initial acceleration here is not g but 2g, the experiment might be done underground
radiant burrow
ohhhhhhhhh
radiant burrow
i'm just confused what these details have to do though
because object is being projected upwards
paper zodiac
Yeah, I just want u to visualize it so that u can probably understand the problem
But that's on me, that's how I do to get the problem, u can probably not think about it though
radiant burrow
wait but why would it be underground. Like why can't it just be upwards? Since object is projected upwards
okay but no wrories
keep going
paper zodiac
In the problem, is the end of the question when the ball reach it's maximum heig...
That's why earlier I know about this
paper zodiac
wait but why would it be underground. Like why can't it just be upwards? Since o...
Ah no, it's being thrown upwards since it goes from 2g - 0g
But from where it was thrown here from earth, they be doing it under the ground or on a hyperbolic time chamber from dragon ball z
Sry gotta search if I have the right reference
radiant burrow
lmfao
paper zodiac
I actually have the final answer since earlier but the problem is that it's a math question
If it's a physics one, I can probably get away from leaving the mass of toy car
Since u don't need it anymore
It's already been accounted for when it says about the time and initial velocity
paper zodiac
I reference it from a question on the internet
It's not that the time is 2 seconds
I thought that from the initial height to the final height, it took 2 seconds
So since gravity is going upwards g is negative
Since normally gravity goes down so opposite of it is upwards
F= -g(t-2)
Then sub 9.8 there
F = -9.8(t-2)
radiant burrow
is this net force?
paper zodiac
Nah Net force is diffferent
paper zodiac
That is for the initial force
radiant burrow
wait i think i might have found my error
it may be because i let gravity be positive
when its supposed to be negative
paper zodiac
Nah even if u make it positive it still works
Since negative and positive only accounts for the direction of the object
Not the actual speed itself
Since u know there's actually no negative speed
paper zodiac
It would be going back in time
radiant burrow
so what'd do wrong?
paper zodiac
Maybe ur formula used?
I dunno
So let's get back
So the Force used during those 2 seconds = -g(t-2) - mg
radiant burrow
yes
paper zodiac
We only need to find for a so we can do F=ma
radiant burrow
yup
paper zodiac
a =f/m
radiant burrow
yup
paper zodiac
Then integrate the a with respect to t
since the derivative of velocity is acceleration
By definition of acceleration
Since acceleration is just the change in speed
And ur good to go, sub t with 2 and final answer
jovial crane
This isn't necessarily homework or a problem, it's actually a research paper I'm doing for English. Does anyone know what a T value is or how I could explain it in simpler words? I've tried looking it up and my brain explodes
final saddleBOT
This isn't necessarily homework or a problem, it's actually a research paper I'm...
rich mason
This isn't necessarily homework or a problem, it's actually a research paper I'm...
for statistics? T value is related to Z values. the Z value is the number of standard deviations above or below the mean
t measures distance from hypothesized value i think
jovial crane
Yeah its a T value from a study
rich mason
limited knowledge but hopefully that helps a little bit
jovial crane
So statistics likely
rich mason
definitely yeah
jovial crane
Okay so a T value of 62.52
rich mason
can you share the context
jovial crane
Yes
rich mason
what is it being used for
jovial crane
A research paper on social media's impact on children/adolescents
rich mason
i mean, specifically in the study what are they using the T-value to do?
rich mason
ok so the Z value there is indicative of how far above/below the mean amount of social impact excessive use of social media causes
so, lots of social media usage causes above mean social isolation for instance
indicated by the positive Z value .54
whereas the inverse is true with cyberbullying
indicated by the negative value
rich mason
T does almost exactly what Z does, but it is resistant to abnormality
jovial crane
but doesn't effect education much?
rich mason
yeah excessive social media usage indicates an increase in social media addiction (duh tbh) and what would appear to be a benefit to education
of course, according to the study
what they define as the mean value for these rather broad topics matters a lot
jovial crane
I see
rich mason
i would not trust this study entirely because there seems to be lots of confounding variables
then again i havent read into it
jovial crane
Okay I got what you mean
That helps out a lot I was kinda like uhhh what the heck is a T value and a Z score
rich mason
no worries hope i helped
final saddleBOT
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Available help channel!
tranquil pine
final saddleBOT
tranquil pine
for this, i thought u=3x would be good but its wrong
neat sable
for this, i thought u=3x would be good but its wrong
try u = -x^2
tranquil pine
so lower bound is -1 and upper is -9?
neat sable
so lower bound is -1 and upper is -9?
no bc we have to switch it around
bc higher number has to be upper
tranquil pine
so you cant have the upper bound be lower than the lower bound?
im just wondering because i have seen integrals where the top number is lower than the bottom number
neat sable
so you cant have the upper bound be lower than the lower bound?
well u can have that but then the integral jus works out to be a negative number
neat sable
yep
tranquil pine
for this i got C=9 which is correct
and y=-2cos(x^1/2)+9
when i plug it in, 9.32 is incorrect and idk if i did something wrong
neat sable
im not entirely sure for part b
but like do they want u to sub x = 3 into our y" equation?
y'*
oh wait no i dont think
neat sable
when i plug it in, 9.32 is incorrect and idk if i did something wrong
how do you know 9.32 is incorrect
neat sable
nice ha
tranquil pine
i did 9.32, 9.31, 9.33 and none of them works
tranquil pine
im trying right now
neat sable
grand sorry wasnt sure if u saw my message
tranquil pine
nah nah you good
wait i got a question
sorry
in this case, would e^3x be consider a constant?
tranquil pine
and that's through the chain rule right?
neat sable
so was my answer correct lol?
neat sable
so its not when x=3 in y' or y
when you put in x=3 y'= 0.57
thats how i got 0.57 for that
tranquil pine
im asking my teacher right now, i think there's a mitake or something but im pretty sure 9.32 is the correct answerr
but thank you very much for your help today mah friend
tranquil pine
you are very blessed
neat sable
you too
tranquil pine
how did it go from the big expression to the smaller expression with e
soft zealotBOT
Toby
tranquil pine
usually its that limit
idk
check your notes/book
i dont think it has it
which one here looks the most familiar? https://en.wikipedia.org/wiki/Exponential_function#Formal_definition
oh this one kind of models the situation
indeed
that's why I'm asking you how you are defining the exponential
tranquil pine
oh this one kind of models the situation
so I can point you to the proof of equivalence to this form
it makes sense, thanks
.close
carmine plaza
i got 15 questions to do heres my first
final saddleBOT
i got 15 questions to do heres my first
carmine plaza
i dont entirely recall the formula but i remember it was somethg like
dot product a*b over the magnitude of b^2
then distribute that into component form of v
i think thats right?\
final saddleBOT
@carmine plaza Has your question been resolved?
final saddleBOT
@carmine plaza Has your question been resolved?
wooden dust
hi
final saddleBOT
@carmine plaza Has your question been resolved?
carmine plaza
hi
final saddleBOT
@carmine plaza Has your question been resolved?
amber holly
dot product a*b over the magnitude of b^2
(u*v/|u|^2) * u
Wait the other way it is
(u*v/|v|^2) * v
Their dot product is forty and the magnitude of v squared is 85
So you just have to multiply the vector v by 8/17
carmine plaza
v is <-10,5> right
amber holly
Yes
carmine plaza
,w ((-10*-7)+(-6*-5))/125
soft zealotBOT
amber holly
Btw where’s 125 coming from
carmine plaza
its the magnitude of v right
carmine plaza
,w (-10*-7) + (-6*-5))/125
soft zealotBOT
amber holly
,w (-10 * (-7) + 6 * (-5))/125
soft zealotBOT
carmine plaza
,w 40/125
soft zealotBOT
soft zealotBOT
carmine plaza
,w -80/25
soft zealotBOT
carmine plaza
<-16/5 , 8/5> ?
amber holly
Yes
final saddleBOT
@carmine plaza Has your question been resolved?
wanton tangle
pls help me
amber holly
Post your question in an available help channel
wanton tangle
which one is availiable
amber holly
Scroll up the list and you will see a group of channels named ‘MATH HELP (AVAILABLE)’
Pick one from there
final saddleBOT
final saddleBOT
Available help channel!
buoyant perch
How can i form that
final saddleBOT
How can i form that
final saddleBOT
@buoyant perch Has your question been resolved?
final saddleBOT
@buoyant perch Has your question been resolved?
final saddleBOT
final saddleBOT
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viral geode
why is he x by 4?
final saddleBOT
why is he x by 4?
viral geode
<@&286206848099549185>
brisk tendon
why is he x by 4?
what is your question?
viral geode
why is he timzing by 4
you replied to my question
its 9:16 why did he x by 4 to go to 36:64
?????
brisk tendon
any number will work
viral geode
like how would i answer the question
brisk tendon
ah but how would u solve this
you have two of the points
(9, 16) and (36,64)
you can plot those points on a graph and then draw a line connecting them.
viral geode
thats the answer?
brisk tendon
yes
final saddleBOT
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safe dew
safe dew
/close
rich tide
final saddleBOT
safe dew
.close
final saddleBOT
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winter kernel
Hey, I believe my teacher made a mistake in this question, can anyone validate or tell me how she got the answer if it isn't wrong?
final saddleBOT
Hey, I believe my teacher made a mistake in this question, can anyone validate o...
hearty zephyr
what do you think it should be?
winter kernel
I got 6/x * e^(ln(x^6))
soft zealotBOT
Zybikron
oak kraken
final saddleBOT
oak kraken
for part a
oops
should be -1
OK i get it now
b) looks alright?
i think i answered it myself
.close
lapis cypress
final saddleBOT
lapis cypress
what i'm struggling to understand is how the definition of a basis leads to the set in the highlighted line to be linearly dependent
definition of basis is above the proposition
hearty zephyr
a basis has the maximum number of vectors that can be linearly independent.
final saddleBOT
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tranquil pine
log_7 (x^2 + 3x + 9) = 2
final saddleBOT
log_7 (x^2 + 3x + 9) = 2
muted coral
log_7 (x^2 + 3x + 9) = 2
rewrite as exponential
muted coral
true
tranquil pine
49 = (x^2 + 3x + 9)
40 = (x^2 + 3x)
0 = (x^2 + 3x - 40)
then i am just confused
but i do believe you must factorize -40
muted coral
you can factor that yes
or you can use the quadratic formula
or complete square for extra fun
tranquil pine
i’d prefer understanding how to find it this way first
i know the answer
but i want to understand the steps
muted coral
you need to find 2 numbers that have a product of ac and a sum of b
so, a product of -40 and a sum of 3
muted coral
yep
then split the middle term:
x^2 + 8x -5x - 40
then factor each
x(x + 8) - 5(x + 8)
undistribute
tranquil pine
from what i understand you must turn it to (x + 8)(x - 5)
muted coral
yes
tranquil pine
okay
muted coral
and then that equals 0
tranquil pine
so
tranquil pine
then factor each
x(x + 8) - 5(x + 8)
does this get you to (x+8)(x-5)
muted coral
ye
if you were to distribute you would get x(x + 8) -5(x+8)
so you go in reverse
pull an (x + 8) out of every factor
tranquil pine
so
tranquil pine
pull an (x + 8) out of every factor
but i do not quite understand why you are taking (x+8)
muted coral
ac + bc = (a+b)c
that turns it into multiplication instead of addition which allows us to use zero product property
that's kind of a justification for why this is the goal
tranquil pine
so what is a, b and c?
muted coral
a is x
c is x + 8
b is -5
tranquil pine
ohhh
tranquil pine
ac + bc = (a+b)c
so you use this
muted coral
from what i understand you must turn it to (x + 8)(x - 5)
to get this
muted coral
ye
tranquil pine
i see
muted coral
not really a formula just distributive property
muted coral
nah
tranquil pine
one more question if you dont mind
muted coral
sure
tranquil pine
why is x = -8, x = 5
muted coral
(x + 8)(x - 5) = 0
because remember you set the other side = 0
zero product property says at least one of the things being multiplied, must be 0
tranquil pine
they are saying that x = -8, x = 5
the answer says
tranquil pine
so, a product of -40 and a sum of 3
actually, sorry for asking another question but why 3
okay
muted coral
actually, sorry for asking another question but why 3
the middle term (b) has a coefficient of 3
muted coral
0 = (x^2 + 3x - 40)
from this
tranquil pine
understood everything up till (x-5)(x+8)
muted coral
they are saying that x = -8, x = 5
because (x - 5)(x + 8) = 0,
x - 5 = 0
or
x + 8 = 0
because xy = 0 means that x = 0, y = 0, or both
tranquil pine
okay
muted coral
because (x - 5)(x + 8) = 0,
x - 5 = 0
or
x + 8 = 0
and you solve those 2 eqs to get x = 5, x = -8
tranquil pine
but why is x -8 instead of 8
hold on
ohhhhhh
ohhhhhhhhhhhh
x -5 = 0
x - 5 + 5 = 0 + 5
ohhhh ok
muted coral
exactly
tranquil pine
i understand
muted coral
yay
tranquil pine
a is x
c is x + 8
b is -5
but why is c x+8
sorry
i just want to underatand one more thing
muted coral
then split the middle term:
x^2 + 8x -5x - 40
from this
tranquil pine
would c always be like this
muted coral
would c always be like this
well no it wouldn't always be x + 8
but if the quadratic is factorable
then you would get something like x - r
or x + r
(if it's not factorable, you can use quadratic formula)
tranquil pine
then factor each
x(x + 8) - 5(x + 8)
but why is -5 multiplied to x+8
muted coral
well in some sense yes