just for context, i was talking about the lim x-> 0 cosx/x
#help-0
thick grail
sharp thorn
just for context, i was talking about the lim x-> 0 cosx/x
oh okay
heady void
oh ok
glass crest
wait what should i do after this 🥲
sharp thorn
$\lim_{x \to 0} \frac{\cancel{x}(1-\frac{tan x}{x})}{\cancel{x}(\frac{\sin x}{x} -1)}$
ocean sealBOT
bettim
sharp thorn
$\lim_{x \to 0} \frac{(1-\frac{tan x}{x})}{(\frac{\sin x}{x} -1)}$
ocean sealBOT
bettim
sharp thorn
after this i cant figure out anything so just use l'opitals rule
quasi vector
LMFAO
sharp thorn
lol
wintry zephyr
lone heartBOT
alpine sable
The question is saying there are 13 points on a plane and there exists only 5 particular points among them are colinear rest are not[unless of course those 3 points chosen is a subset of those 5 points]
So how many lines can be drawn on the plane
alpine sable
Can anyone explain what this question is asking
as a diagram something like this
wintry zephyr
as a diagram something like this
i see
and
is this question asking how many possible lines can be drawn, something to do with combinations or permutations? and if the line over the colinear points counts as one or multiple lines connected togather?
i know that for every 2 dots
1 line can be drawn
alpine sable
is this question asking how many possible lines can be drawn, something to do wi...
yes it does
it's a question of PnC
wintry zephyr
yes it does
the second part of this question
alpine sable
not sure with the notation
It's basically Permuation and Combination in short
wintry zephyr
line over the colinear points counts as one or multiple lines connected togather?
alpine sable
hmm, yes the line over the colinear points also counts as one
wintry zephyr
alright, lemme try to get something out of this
so talking about total amount of lines that can be on here
for 5 colinear dots, there are 4 lines
and for 8 remaining dots
there will be 7 lines
but the thing is
alpine sable
for 5 colinear dots, there are 4 lines
there is only 1 line for the 5 colinear ones though
wintry zephyr
there is only 1 line for the 5 colinear ones though
ohh sheet
forgot
the thing is that
wintry zephyr
yea
wintry zephyr
yea they arent
wintry zephyr
if i only look at the 8 dots
i am not able to see it yet
so i am trying to sort of trying to intuitively get it first
but no i cant see it yet
alpine sable
I think u should draw it probably
wintry zephyr
youre right
if i treat the 5 co linear lines as NOT co linear and treat them like all the other ones
i can connect any 1 point with any 12 of the remaining points to form a line
Lucid, is this assumption correct?
so i can connect P1 with 12, P2 with 12, P3 with 12, and so on
ill be able to connect 13 points with 12 possible dots, if i erase away the lines i draw in eachtime for each new dot i will be connecting with other dots
so 13^12
@alpine sable are these assumptions correct? so i can tweak and build upon these
ohh shit
ur offline
sorry for ping
lone heartBOT
@wintry zephyr Has your question been resolved?
alpine sable
<@456226577798135808> are these assumptions correct? so i can tweak and build up...
Ya but u made a mistake while implementing the fundamental principal of counting it's (13*12) /2 not 13^(12)
do you know nCr?
which basically tells the number of subsets of k elements from a set of n elements
not saying u can't solve it otherwise[if you know the number of diagonals of a polygon of n sides is n(n-3) /2 then also u can solve it or even just by the addition and multiplication principle but those are not the most straight forward apporaches]
lone heartBOT
@wintry zephyr Has your question been resolved?
wintry zephyr
Ya but u made a mistake while implementing the fundamental principal of counting...
why is it being divided by 2?
wintry zephyr
do you know nCr?
yes i know combinations, but i am not sure about how to implement it just yet
i went out to do something
now back to this
lone heartBOT
@wintry zephyr Has your question been resolved?
alpine sable
why is it being divided by 2?
i will recommend u not to take that approach[its because of repition the line from point of a to b is same as that of b to a] if you know nCr anyway then u are just choosing two points of 8 points dont you know thats C(8,2)=8!/(6!*2!)
odd hound
Is my calculation wrong or?
0.2 x 25 = 5
0.4 x 50 = 20
1 x 26 = 26
5+20+26 = 51
real parrot
Mb
odd hound
its alr
toxic umbra
Hi ! where i can fine Algabra rules
lone heartBOT
@odd hound Has your question been resolved?
odd hound
Hi ! where i can fine Algabra rules
???
toxic umbra
algebra rules and formulas?
odd hound
Is my calculation wrong or?
0.2 x 25 = 5
0.4 x 50 = 20
1 x 26 = 26
5+20+26 = 51
<@&286206848099549185>
exotic belfry
why 1x26?
odd hound
.close
wicked hornet
.ask
junior warren
lone heartBOT
junior warren
how would i do parts b and c
lone heartBOT
@junior warren Has your question been resolved?
lone heartBOT
@junior warren Has your question been resolved?
lone heartBOT
@junior warren Has your question been resolved?
junior warren
.close
dim matrix
Is my differentiation wrong?
lone heartBOT
Is my differentiation wrong?
dim matrix
mortal trellis
,w diff (x-1)e^x +2
high rapids
Seems right
ocean sealBOT
mortal trellis
what
since when doesn't WA know diff anymore
but well anyway
use WA to check your work
ocean sealBOT
dim matrix
thanks @high rapids @mortal trellis
for some reason I was facing some problem to close the bracket.
mortal trellis
well you are using math input
which doesnt help
use the other input and just type
minor stump
lone heartBOT
minor stump
dont know how to do it
lone heartBOT
@minor stump Has your question been resolved?
potent garnet
lone heartBOT
potent garnet
!status
lone heartBOT
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
2
lone heartBOT
@potent garnet Has your question been resolved?
alpine sable
lone heartBOT
elder fog
x is your adjacent
elder fog
no
the unlabeled side is opposite
x is adjacent
cause its one of the
sides that make up the angle
and then 24 is your hyp
alpine sable
So is 24 the hyp
alpine sable
can you tell me it the calculator way
alpine sable
Alr
elder fog
what math are you in btw
cause itll help you in the future if you have the unit circle memorized
alpine sable
Sophomore math
alpine sable
But how do i identify whats the adjacent and whats the opposite
bc i always thought the opposite was opposite from the hypotenuse
elder fog
bc i always thought the opposite was opposite from the hypotenuse
noooooo
opposite is opposite from the angle
the way the angle is pointing
the angle is made up of two lines right
those two lines or sides
one is adjacent
the other is hyp
alpine sable
what angle
elder fog
the angle youre given
elder fog
i dont think this one is trig
alpine sable
It is
slate monolith
It is
slate monolith
That’s still trig
slate monolith
I guess
slate monolith
Do you know your 306090 triangle rizz
alpine sable
Do you know your 306090 triangle rizz
Ye
lone heartBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
ember citrus
Also how is this question not c
tangent is opposite over adjacent, so the tangent of a would be a/b, not b/a
alpine sable
but would b be the opposite
elder fog
well in answer C its angle A
ember citrus
it says tangent of A, so you have to look at it from the point of view of angle A
elder fog
the opposite of uppercase a is lowercase a
its usually like that but you cant rely on that when you like
actually have values ☠️
alpine sable
so what would be a triangle where the opposite is the opposite from the hyptorenuse
ember citrus
the hypotenuse is never the opposite
alpine sable
No im saying
What would a triangle look like when the opposite is b
From the triangle abovd
elder fog
the hypotenuse is never the opposite
well i mean 90deg
elder fog
What would a triangle look like when the opposite is b
angle B
ember citrus
What would a triangle look like when the opposite is b
if you ask for something with angle B, then side b is the opposite
elder fog
the opposite is whichever the angle does not touch and is facing toward
ember citrus
literally just draw an arrow from where the angle is and straight
to the side opposite from it
like i did
and thats the opposite
alpine sable
Tan q
ember citrus
the opposite for angle R and the opposiet for angle Q are different
junior warren
not entirely sure how to go about doing b here?
lone heartBOT
not entirely sure how to go about doing b here?
junior warren
i know i have the formula
that the error |R_n|=|S-S_n|<b_n+1
but im not sure how to apply that exactly
actually, since it has to be less than bn+1, would i just find the kth partial sum that makes the bn+1 value equal to that decimal?
but then again not sure how i could go about doing that
merry depot
you've got it backwards
|S - Sn| < b_(n+1)
so if you find the first k so that b_(k+1) < L
then |S - Sk| < L
merry depot
you have the formula written there for each a_n
junior warren
right
merry depot
calculate some of them until a_n < 10^-7
junior warren
hmm ok
is there any way to guarentee i land on the value besides plugging in random values?
merry depot
depends on the formula. Make an educated guess first.
junior warren
i tried throwing in 3 but im still only 4 decimals in
i guess since its decr ill throw in some bigger #s
junior warren
calculate some of them until a_n < 10^-7
actually wouldnt i be finding when b_n is < ?
merry depot
well... you need .0000001 = 1/10^7
7! ~ 5000
(1/2)^5 = 1/32
So that term is ~ 1/160000
That's where I'd start
junior warren
oh
thats a cool way to do it
let me try that
is there any reason you went with those values
merry depot
It's the last term given in the example. Just wanted to see what it was, roughly.
junior warren
should the (1/2) be ^7 then
merry depot
oh yeah. my bad
junior warren
i can atleast narrow it down to an odd number so that id have a positive value?
still struggling to find the value though lol
i had friends throw it into matlab and etc but i wanted to try doing it by hand
formal ginkgo
Hi
formal ginkgo
How can I calculate the sum of
1+5¹+5²+5³+...+5^n
prime badge
if it was 10 not 5
so calculate 1111111111
we could subtract 1 from 1000000000 to get 999999999 and divide by 9
i bet that works in base 5 too
lone heartBOT
@formal ginkgo Has your question been resolved?
lone heartBOT
@formal ginkgo Has your question been resolved?
ivory mica
I ned help
lone heartBOT
I ned help
ivory mica
1.Jose is p centimeters tall. Ben’s height is thrice Jose’s height. Express Ben’s
height algebraically.
2. Write an algebraic equation for the cost of 15 liters of gasoline, if x pesos per
liter is ₱810.00.
3. Noel is y years old now. Write the algebraic equation for Noel’s age if his age
10 years from now is 35.
4. Ten years ago, Art was four times as old as Ken. Write the algebraic equation
showing Art’s age.
5. If twice a number is increased by 15, the result is 45. Write the algebraic
equation of the given statement.
raven haven
did you do any work at all
ivory mica
Asian math is impossible
Broo they teach the wrong lesson for this problem
So 1. Is P3?
- Is 2+15=45?
vague coral
So 1. Is P3?
3p
ivory mica
Ohh oky ty
vague coral
i mean p3 is sort of fine? p*3 but
nobody writes "p3"
woven hornetBOT
Did you know Beemo supports Slash Commands? They are the new, recommended way to discover and run commands! Type / to see them all.
ivory mica
Is number 2. 15•X=8100.00
vague coral
15x = 810
ivory mica
Is num 3. 35y or 10y or am i wrong
Is num 4. 10y??
<@&286206848099549185>
<@&286206848099549185>
alpine sable
👋
ivory mica
Bro is my answer right?
ivory mica
Is num 3. 35y or 10y or am i wrong
.
ivory mica
Is my number 4 right,correct?
alpine sable
the idea is that you understand not just get givin the answer
35y and 10y both implying your multiplying 35 or 10 by y
Which represents years
Your looking for y (his age)
ivory mica
What word in the sentence of number 3 means addition?(Our teacher didnt show all the translate of + - x and divide
*translation
Is it from now?
alpine sable
.close
lone heartBOT
ivory mica
.reopen
lone heartBOT
✅
ivory mica
@alpine sable yo from is a switch word?
alpine sable
?
lone heartBOT
ivory mica
.reopen
lone heartBOT
✅
ivory mica
A B
- a number b subtracted from 12 a. 6y
- six times the number y b. 2x2
- the sum of five and thrice a number z c. 5 + 3z
- twelve divided by n d. 6x - 5
- one less than the product of 4 and y e. 9k
- a number z increased by ten f. z + 10
- twice the square of a number x g. 3 (4r)
- thrice the product of 4 and r h. 4y - 1
- nine times a number k i. 12 - b
- six times a number x minus five j. 12 ÷ n
My teacher ask to solve this with solution how can i solve it?
<@&286206848099549185>
I know the answers but my problem is how can i make a solution
wary stream
What do you mean make a solution?
ivory mica
My teacher said to make a solution
Like number 1. Is 12-b how do i make a solution? My teacher said to do it backwards like 12-b=b-12?
ivory mica
Sorry for wasting ur tine
*time
I sended the wrong question
Be right back
It said to write a
It said to write a v so is num 1. Y
Just need a help because im unsure
<@&286206848099549185>
ivory mica
a number less than a quotient of seventy-five and fifteen
I kinda need help with this
m-(75+15)?
Is my expression right?
*correct
<@&286206848099549185>
wary stream
You don't need to ping helpers repeatedly like that
You pinged 3 times in 20 minutes
lone heartBOT
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.
wary stream
Is my expression right?
And no
ivory mica
Oh okay srry
ivory mica
M-(75 divide15)
Division
m-75 divided by 15
Where do i put the grouping symbol
(m-75) divide 15?
wary stream
What do you mean by "grouping symbol"?
ivory mica
Gemdas
wary stream
ivory mica
no 💀
wary stream
PEMDAS is order of operations
ivory mica
Grouping
Exponent
Multiply
Division
Subtraction
wary stream
No one calls it grouping
wary stream
It's definitely not referred to as GEMDAS
ivory mica
M-(75 divide15)
So this is wrong??
wary stream
You wouldn't need parentheses due to order of operations
sage gull
It works either way but yeah they aren’t necessary there.
ivory mica
Oh okay
- Joseph bakes same number of cupcakes each day. He used 2 cups of flour
in each cupcake. Write the algebraic expression to represent the number of
cups of flour Joseph uses each day in baking cupcakes.
Is the answer 2d?
wary stream
Looks fine
wary stream
Also, your naming of variables, for word problems, is definitely not how most people would do it
wary stream
- Joseph bakes same number of cupcakes each day. He used 2 cups of flour
in each cupcake. Write the algebraic expression to represent the number of
cups of flour Joseph uses each day in baking cupcakes.
That describes cups, so the more appropriate variable is c, and I'm 90% sure the key uses c
ivory mica
How do i solve it?
It said to make a solution for 2c
wary stream
What exactly do you mean solve?
There's nothing to solve
It's literally making an equation from words
ivory mica
So u cant make a solution for 2c maybe its because Its not an equation like 12+n=13-12=1
Ah so maybe it only works for unkown numbers like variables
Example
12+n=20
Solution
ivory mica
12+n=20-12=8 so n8
wary stream
It equals something
ivory mica
Okay finally understanded it
wary stream
1. Joseph bakes same number of cupcakes each day. He used 2 cups of flour
in ea...
Notice how this says algebraic expression
wary stream
You're not providing context
Teacher said to do it with solution
How do i solve it?
You're saying this. This is my response
What exactly do you mean solve?
There's nothing to solve
It's literally making an equation from words
ivory mica
No,he litterally said to answer it with sollution
wary stream
You realize a solution means an answer to the problem
ivory mica
Ik but on the other one says answer only
wary stream
You created an algebraic expression, which is a valid answer to that problem
ivory mica
Okay
wary stream
You are so focused on the words of your teacher saying "answer it with solution", where you keep assuming you need to solve the equation. A solution to a problem doesn't mean you have to solve for a variable
lone heartBOT
@ivory mica Has your question been resolved?
empty forge
Hey guys, I need help with this PDE
lone heartBOT
Hey guys, I need help with this PDE
empty forge
I was able to separate the variables and integrate to find a set of solutions:
I am having troubles with the boundaries
The examples I found online have boundaries of x = 0, u = 0, x = L, u = 0 but its a little different here. Its messing me up. I could use some help.
This is what I got for the first boundary:
When trying to compute the secondary boundary, its gets ugly fast.
lone heartBOT
@empty forge Has your question been resolved?
empty forge
<@&286206848099549185>
molten lotus
lone heartBOT
molten lotus
For this question am I suppose to find out what a is?!
reef iris
Oops
molten lotus
@reef iris can you delete this?
wary stream
For this question am I suppose to find out what a is?!
What's the full q?
It looks cut off
wary stream
Then no, you're not solving for a
It's in terms of a still
Meaning a will still exist
molten lotus
Ohh okay wait let me show you my work
wary stream
Basically the question wants you to take the derivative then plug in 3 for x, and simplify
wary stream
,rotate
ocean sealBOT
lunar lintel
lone heartBOT
digital prawn
if u tried dividing by highest power, the numerator k^8/k^9 is not 1
it will be 1/k
how did your k^8 go to a k^9?
were u trying to use the limit comparison test with 1/k?
I suggest u try using the integral test
@lunar lintel
lunar lintel
were u trying to use the limit comparison test with 1/k?
yea
i did limit comparison
what
my solution also got 1
from this
<@&286206848099549185>
.clsoe
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nimble trail
How do you prove a range is a subset of N
lone heartBOT
How do you prove a range is a subset of N
@nimble trail Has your question been resolved?
buoyant depot
lone heartBOT
gusty gorge
do you know how to do integration by parts
buoyant depot
yes
am i just integrating x/e^px
i got
-x/pe^px for g(x)
which was correct
but my h(x) is wrong
nvm i got it
.close
ebon otter
$X_n ~ G(\alpha =n; \beta)$ \
$M_{X_n}(t)=E(e^{tX_n})=(1-\beta t)^{-\alpha}$ where $t<\frac1\beta$. \ \
Let $Y_n=\frac1{X_n}$, what will this thing bellow be \
$M(t;n)=M_{Y_n}(t)=E(e^{tY_n})=E(e^{t\frac1{X_n}})=$ (?)
ocean sealBOT
Welf
ebon otter
Statistic
lone heartBOT
Available help channel!
modern crescent
I am studying for my test on two units, and am completely lost on four homework questions where I have the answer from practiciing previously but cannot remember how to do them anymore.
Find all solutions to the equation in the interval [0, 2pi)
5. sin2x = 2 sin x (My teacher explained this one to me earlier this month, and showed me how it was 0, pi, but I cannot remember how she showed me)
9. sin 2x - tanx = 0 (even my old work makes no sense to me now)
Review Question on proofs
4. 2cot2x = cotx - tanx (I do not even now where to start, and there is no answer key for me to find some sort of guidance)
ocean sealBOT
Stephen
modern crescent
then i subtract the 2sinx
long axle
sure, then what do we have
modern crescent
an equation i can factor
long axle
whats the equation
strange meadow
**Stephen**
????
long axle
what
strange meadow
double angle for sin is not since
modern crescent
2sinx * cosx - 2sinx
strange meadow
Sin x
long axle
thats the problem, we're solving on 0,2pi
modern crescent
its solving
strange meadow
Sorry I’m stupid
modern crescent
all good im the one here day before my test struggling for hours on likely simple questions haha
modern crescent
2sinx * cosx - 2sinx
so this
modern crescent
can be turned to 2sinx(cosx - 1) = 0, buti dont really know how to put each individual one into a x = form
modern crescent
no sorry.. is it anything * 0 = 0 but that seems very unrelated
modern crescent
so essentially from this it would be
2 sin x = 0 and cosx = 0?
long axle
close
modern crescent
cos x -1?
long axle
yep
modern crescent
ohhh
thanks i got it then since its just sin x = 0 cps x = 1 and unit circle
sin gets me 0 and pi, and cos gets me 0
modern crescent
thank you
long axle
i can do the next one with you as well if you like
modern crescent
i would really appreciate it it helps
ocean sealBOT
Stephen
long axle
what are ur thoughts on this
modern crescent
uhh
i honestly have no clue where to start that gets me a good answer...
wait actually
i can substitiue the sin 2x for 2sinxcosx because of the identity
long axle
yep
long axle
no need to apologize
modern crescent
i can change the tan to sin/cos and then factor it
to sinx(2cosx - 1/cosx) = 0
and then use that fancy property from earlier to get sin x = 0, 2 cos x - 1/cosx = 0
and then get cosx = +- 1/root 2, root2/2, which gives me a bunch of numbers but I am quite confused from here
wait nevermind I get it
thanks for your time stephen, have a nice day.
long axle
you as well kamkam
modern crescent
I am quite new to this help system, and not sure if I am supposed to resend when I still need help for another question, so I apologize if this is wrong to whatever admin checks this.
Question I still need help:
4. 2cot2x = cotx - tanx (I do not even now where to start, and there is no answer key for me to find some sort of guidance)
pine helm
maybe turn everything in terms of tan
modern crescent
so like
2cosx/2sinx = cosx/sinx - sinx/cosx?
wait im stupid
2(1/tan2x) = 1/tanx - tanx
?
i shall just pray that there wont be any questions like this ty for help impractical
.close
frozen viper
Let f(x) = ax^2 + bx +c. where a is [1, +inf). Assume that x1 and x2 are the roots of f and x1 - x2 = 1. We know that the graph of f cuts OY at the point (0,a). Find the formula f in a factorised form
lone heartBOT
Let f(x) = ax^2 + bx +c. where a is [1, +inf). Assume that x1 and x2 are the roo...
@frozen viper Has your question been resolved?
frozen viper
Yes
pine helm
ok so f(0) = a which means c = a so ax^2 + bx + a
a(x^2 + 1) + bx
1 = -sqrt(b^2 - 4a^2)/a (pretty easy to derive this one(hint : quadratic formula))
1 = (b^2 - 4a^2)/a^2
b^2 - 4a^2 = a^2
b^2 = 5a^2
b = sqrt(5)a
a(x^2+1) +sqrt(5) a x
btw is a supposed to be known
lone heartBOT
@frozen viper Has your question been resolved?
frozen viper
btw is a supposed to be known
Oh right I forgot. Yes it is
lone heartBOT
vale wigeon
log_64(x) = log_2(x)/log_2(64)
64 and 16 are both powers of two.
64 is a power of two (2^6) and 16 is also a power of two (2^4)
stuck void
lone heartBOT
balmy peak
<@&286206848099549185>
lone heartBOT
<@&286206848099549185>
ocean sealBOT
lone heartBOT
@balmy peak Has your question been resolved?
lone heartBOT
@balmy peak Has your question been resolved?
balmy peak
No
lone heartBOT
@balmy peak Has your question been resolved?
leaden estuary
reef moss
if tan+cot =5 then tan2+cot2=/
lone heartBOT
if tan+cot =5 then tan2+cot2=/
delicate jacinth
if tan+cot =5 then tan2+cot2=/
you have tan + cot
and you want information on tan^2+cot^2
how do you get from tan to tan squared?
gray isle
do you have a pic of the original question
reef moss
YES
gray isle
the notation is extra dodge
reef moss
NO
quasi vector
if $\tan(\theta) + \cot(\theta) = 5$, then find the value of $\tan^2(\theta) + \cot^2(\theta).$
is this the question?
reef moss
NO
ocean sealBOT
kheerii
reef moss
YES THIS IST THE QUESTION
quasi vector
notice $\tan(\theta) \cdot \cot(\theta) = 1$
ocean sealBOT
kheerii
gray isle
well we don't know what the actual question is supposed to be
until we know that, we can't really do much to help
quasi vector
well we don't know what the actual question is supposed to be
they said it's correct
what I wrote
gray isle
they said IST, not sure if that was supposed to be IS or isn't
them saying NO in caps also doesn't help
reef moss
it is guys
reef moss
@quasi vector was correct
quasi vector
**kheerii**
.
reef moss
yeah
quasi vector
so use that fact
reef moss
but ans is wrong
quasi vector
what did you get?
reef moss
25
quasi vector
how
reef moss
squaring both sides
quasi vector
so what did you get after doing that
reef moss
25
quasi vector
on the left side
quasi vector
no
reef moss
but solution says no
gray isle
$\fdream$
ocean sealBOT
ℝamonov
quasi vector
$(a+b)^2 \ne a^2 + b^2$
ocean sealBOT
kheerii
reef moss
so ans is 23 ?
quasi vector
yes
reef moss
ok thnx'
sharp thorn
$a^2 + b^2= (a+b)^2 - 2ab$
ocean sealBOT
bettim
lone heartBOT
@reef moss Has your question been resolved?
sturdy forum
What is the difference between log3 and log base of 3?
lone heartBOT
What is the difference between log3 and log base of 3?
sturdy forum
$log_3$
ocean sealBOT
stitch
sturdy forum
$log3$
ocean sealBOT
stitch
mortal trellis
well one is base 3 and the other has an unspecified base
depending on context maybe e or 2 or 10
wary stream
What is the difference between log3 and log base of 3?
Log3 assumes the base is 10
Because most of the time, when no base is defined, then it's automatically assumed as base 10
ocean sealBOT
stitch
median oar
Depends on the base
mortal trellis
if anything, log(1000)=3
sturdy forum
Can I know what it means if it does not have a base? but has a result provided?
sturdy forum
oh
ivory fern
What is the difference between log3 and log base of 3?
Also $\log 3$ is a number (which depends on the base you choose) and $\log_3$ is a function, so $\log_3 x$ will be a number when you substitute $x$ with some number
ocean sealBOT
d឵
sturdy forum
is it like log 10 to power multiplied by 2 and the value which is 2 times is also the base?
sturdy forum
is it like log 10 to power multiplied by 2 and the value which is 2 times is als...
am I wrong here?
mortal trellis
lg specifically is notation for log_10
mortal trellis
khan academy probably has stuff
sterile marlin
AC: y = -2x + 1 DB: y = 0.5x - 1.5 A(-2,5) B(5,1). how do I calculate coordinates of M?
lone heartBOT
AC: y = -2x + 1 DB: y = 0.5x - 1.5 A(-2,5) B(5,1). how do I calculate...
@sterile marlin Has your question been resolved?
sterile marlin
<@&286206848099549185>
ionic umbra
AC: y = -2x + 1 DB: y = 0.5x - 1.5 A(-2,5) B(5,1). how do I calculate...
ur given y = -2x+1 for AC and DB to be y = 0.5x - 1.5, to calculate the coordinate for M, is to simply find where line AC and DB intersect
so u can take the 2 lines, and since each sides are both set =y, you can SET THE -2X+1 to be equaled to 0.5X - 1.5 and find the x value. and then use that x value in either AC or DB to find ur y value
(it should not matter which equation u plug this x in for)
(since u should get the same answer(
i hope that helps!
llmk if u need any clarification
lone heartBOT
lone heartBOT
Available help channel!
subtle delta
lone heartBOT
subtle delta
Why isnt this [5,6,7]
gray isle
the notation is whack
can you describe in words what you're trying to represent
subtle delta
its a book im studying in
its teaching about intersection of two intervals
they r trying to say
alpine sable
do you mean {5,6,7}?
gray isle
describe in your own words what you were trying to represent with
Why isnt this [5,6,7]
subtle delta
why isnt the intersection of the two sets 5 6 and 7
lNvm
Nvm
💀
,close
.close
gray isle
you'll you're forgetting all the non-integers
lone heartBOT
Available help channel!
violet surge
Hello, this isn't exactly homework but it's just that my brain really isn't working right now and I need some help with my average grading ratios haha
So basically I want to achieve higher than 65% average for my course - and I've recieved grades for 57.5% of my course already. These grades average out to 72.1%.
I have two modules left to do, and these both have two assignments. Each module counts for 9.625% of my overall grade.
I also have my dissertation to do, which counts for 23% of my entire grade.
Is it possible to calculate an average grade to achieve on each assignment to hit 65%?
violet surge
Wait maybe I'm being stupid here
is it impossible to calculate this since the grades are weighted?
.close
lunar lintel
lone heartBOT
lunar lintel
how do we solve this by AST
gusty gorge
write out a few terms
and see that they're alternating
and then apply the alternating series test?
gusty gorge
did I say "factor the cos out" or did I say "write out a few terms, see if they're alternating, and then apply the alternating series test"?
lunar lintel
did I say "factor the cos out" or did I say "write out a few terms, see if they'...
to do the AST
you factor out the alternating part
like (-1)^n
gusty gorge
no
lunar lintel
yes?
gusty gorge
no
lunar lintel
yes it is
small panther
Yes that's it
lunar lintel
Yes that's it
👍
gusty gorge
alternating series test is if it's alternating and |a_n| -> 0, then the sum converges
wtf are you on about
lunar lintel
If Sequence An is positive and decreasing and if Lim of An = 0
small panther
If An is like that then the sum of (-1)^n * An converge
lunar lintel
it converges
gusty gorge
If Sequence An is positive and decreasing and if Lim of An = 0
like what the fuck does this even mean
lunar lintel
like what the fuck does this even mean
To determine if converge??
lunar lintel
If An is like that then the sum of (-1)^n * An converge
yes
gusty gorge
that's not even a mathematical statement
lunar lintel
yes it is?
small panther
that's not even a mathematical statement
Your statement and his are the same
gusty gorge
Your statement and his are the same
no, his is a bunch of garbled nonsense
small panther
You are just taking the absolute value
gusty gorge
I'm aware that you can state it as if you have a positive, decreasing sequence and then alternate it
then it converges
small panther
That's what we are saying to you
fringe sleet
saccharine even if its not exactly a rigorous statement doesnt mean it doesnt cover the ballpart of what it is. i think its reasonably easy to see that they are on the right track there
gusty gorge
then what's the issue? if this person actually can state the definition of it
lunar lintel
my prof wrote it
gusty gorge
then why isn't it immediately straightforward
gusty gorge
my prof wrote it
does this match the words you wrote
lunar lintel
yes it does
gusty gorge
no it doesn't
lunar lintel
If Sequence An is positive and decreasing and if Lim of An = 0
💀
gusty gorge
do you want me to do a word-by-word comparison
small panther
do you want me to do a word-by-word comparison
You're playing on words here
gusty gorge
If Sequence An is positive and decreasing and if Lim of An = 0
compare to
If the sequence {a_n} is positive decreasing and lim n->infinity a_n = 0, then sum (-1)^n a_n converges
lunar lintel
🤣
small panther
Yes what he wrote was not really correct but you could see that he knew what he was talking about
lunar lintel
bro
gusty gorge
Yes what he wrote was not really correct but you could see that he knew what he ...
dude he doesn't
fringe sleet
i really dont think this is worth arguing about
gusty gorge
he writes the words but doesn't understand the meaning
lunar lintel
yes i do?
small panther
i really dont think this is worth arguing about
+1
gusty gorge
like I've seen this the last 4 times he's asked about the series stuff
lunar lintel
I understand the meaning
gusty gorge
then why isn't this immediately a consequence of the alternating series test?
lunar lintel
then why isn't this immediately a consequence of the alternating series test?
Because all the examples we did always revolved around something like this
gusty gorge
okay, so?
lunar lintel
Ok and you would not involve the (-1)^n+1 when taking the limit
fringe sleet
then why isn't this immediately a consequence of the alternating series test?
it may not be obvious to them that they can rewrite cos(nπ) into (-1)^n
gusty gorge
it may not be obvious to them that they can rewrite cos(nπ) into (-1)^n
that's why I said to write out a few terms of it
lunar lintel
to cos
small panther
Here you have to see what's cos(n*pi) @lunar lintel
gusty gorge
and then apply the alternating series test
it's not that deep
you don't even need to know what cos(n * pi) is generally
lunar lintel
Here you have to see what's cos(n*pi) <@1023853486783336499>
yes i see it is alternating now
fringe sleet
well you gotta know why you can "ignore" the cos, ignore is not really the word i would use but it is in general what you are supposed to be doing
lunar lintel
well you gotta know why you can "ignore" the cos, ignore is not really the word ...
whats the world called for it
because we dont involve it when we take the limit so i assumed we ignore
fringe sleet
get it on the form $(-1)^nb_n$ and take the limit of $b_n$ as $n\to\infty$
ocean sealBOT
Duh Hello
fringe sleet
ignore sort of implies that you arent working with an alternating series anymore
gusty gorge
why would you waste a ton of effort renaming the indices to get it to (-1)^n b_n
lunar lintel
meaning the Sum converges?
fringe sleet
why would you waste a ton of effort renaming the indices to get it to (-1)^n b_n
$a_n=(-1)^nb_n$ is the standard notation for AST
ocean sealBOT
Duh Hello
fringe sleet
i dont see the issue with it
gusty gorge
$a_n=(-1)^nb_n$ is the standard notation for AST
yeah I'm aware of the standard statement of it, but you have to re-number to get rid of all of the zeroes
fringe sleet
i feel like this cherry picking arguments you are starting are more of a time waster than using this notation
gusty gorge
to be fair, the question only asks for an answer C or D
fringe sleet
yeah I'm aware of the standard statement of it, but you have to re-number to get...
wait what zeroes?
gusty gorge
cos (pi n) hits zero on every odd n, does it not?
ocean sealBOT
Duh Hello
ocean sealBOT
fringe sleet
?
fringe sleet
sine would always be 0
gusty gorge
yeah I was thinking it looked like the increment was pi/2 and it was going to go 0, +1, 0, -1, 0, etc
fringe sleet
either way, @lunar lintel do you see why $\cos(n\pi)=(-1)^n$?
ocean sealBOT
Duh Hello
fringe sleet
ait, so yeah you probably got it from there then
fringe sleet
!show
lone heartBOT
Show your work, and if possible, explain where you are stuck.
gusty gorge
it's a sqrt n on top of an n
gusty gorge
not a sqrt n on top of a sqrt (n+5)
fringe sleet
uhh, no?
lunar lintel
what
gusty gorge
the inside of the square root
fringe sleet
not quite
im not even sure how you could have gotten to that
maybe im misunderstanding what you wrote
lunar lintel
ast is to check for convergence
wdym
fringe sleet
how would you write this $a_n$ in summation notation?
ocean sealBOT
Duh Hello
lunar lintel
Inf
Summation A_n
n = 1
fringe sleet
and what is A_n?
lunar lintel
the sequence
fringe sleet
which is
lunar lintel
An
fringe sleet
$A_n=?$
ocean sealBOT
Duh Hello
lunar lintel
10/10^n
fringe sleet
then how does it become negative on every other term?
fringe sleet
well you are getting close
fringe sleet
oh wait actually yeah you are right, you can simplify it tho
i was thinking wrong
you can rewrite $\f{10}{10^n}$ to $\f1{10^{n-1}}$
ocean sealBOT
Duh Hello
lunar lintel
$\f{(-1)^\f{n+1}*10}{10^n} $