so you ge how much finally ?
#help-49
honest kelp
it lok sin yoru result
65536
but you found for this:
$\sum_{n=1}^{\infty }\frac{n^{2}t^{n}}{65536^{n}}$
grand pondBOT
Joanna Angel
honest kelp
so what now you need to do ?
leaden matrix
I still haven't found the limit, do I need to use lhopitals?
honest kelp
🙂
no
normally you calcualte
take n^2 out of denomiantor
adn you reduce it with nominator
$\lim_{n \to \infty } \frac{n^{2}}{\left( n+1 \right)^{2}}=\lim_{n \to \infty } \frac{1}{\left( 1+\frac{1}{n} \right)^{2}}=1$
leaden matrix
im getting 65536 / 2n +1
so the limit tends to infinity?
grand pondBOT
Joanna Angel
honest kelp
that means R = 65536 , but again i remidn that it is radius for:
$\sum_{n=1}^{\infty }\frac{n^{2}t^{n}}{65536^{n}}$
grand pondBOT
Joanna Angel
grand pondBOT
Joanna Angel
honest kelp
you made wrong you cant reduce it this way
leaden matrix
Why not?
honest kelp
you have to take n^2
out of parnthesis
becaue there is addiotn
and yo need multipliction
leaden matrix
Oh wait im braindead
honest kelp
i can feel 🙂
leaden matrix
so the answer is 4?
leaden matrix
.close
unique lake
If Un and Sn respectively state the n number and the sum of n first sequence of an arithmetic sequence, and U2 - U4 + U6 - U8 + U10 - U12 + U14 - U16 + U18 = 20. Then S19 = ...
midnight plankBOT
If Un and Sn respectively state the n number and the sum of n first sequence of ...
unique lake
i'm stuck there
i did some calculations by substituting U10 to the equation then i found that d = 0, but i'm not sure whether the S19 equals 380 or not
midnight plankBOT
@unique lake Has your question been resolved?
unique lake
<@&286206848099549185> pls ;-;
timber summit
Balls
unique lake
.close
raw fjord
yo
raw fjord
ok so
suppose f(x)=p(q(x)) where p and q are differentiable. and suppose we have the following data
p(3)=5 p'(3)=3 p(4)=3 p'(4)=2 q(3)=4 q'(3)=7 q(4)=3 q'(4)=0
what is f'(3)?
I got f'(3) = 14
can anyone help confirm that?
rugged pumice
chain rule
f'(x) = p'(q(x))q'(x)
= p'(4)(7)
= 14
raw fjord
thank you ❤️
midnight plankBOT
@raw fjord Has your question been resolved?
midnight plankBOT
midnight plankBOT
Available help channel!
dusky island
4a) can someone start my off please?
midnight plankBOT
4a) can someone start my off please?
olive matrix
remainder theorem
elfin flax
23
elfin flax
@elfin flax
olive matrix
How would i start with this?
writing down the remainder theorem is a good idea
and noting that "has something as a factor" is equivalent to "has a remainder of 0 when divided by that thing"
dusky island
I know this yes but I’m not sure what to do next
round palm
I know this yes but I’m not sure what to do next
well did you use the remainder theorem as mentioned?
use remainder theorem on the first line (the polynomial.... has x+2 as a factor)
so basically p(-2) = 0
similarly for the second line, "when the polynomial.... the remainder is -36" basically tells you that p(1) = 36
now you have 2 equations to solve under 2 unknowns so you can uniquely determine the values of p and q
midnight plankBOT
midnight plankBOT
Available help channel!
stable halo
midnight plankBOT
stable halo
CAN someone please explain why when evaluated between the limits of a/2 and -a/2
$\frac{(\pi^2-6)a^3}{24\pi^2}$
grand pondBOT
Mortta
stable halo
why is it that
and not positive 6
you plug in a/2 or -a/2 sin is 0
HOW IS IT NEGATVIE 6 im lost
midnight plankBOT
@stable halo Has your question been resolved?
flat spire
Why does the domain of an (indefinite integral) integrand matter before integrating it?
midnight plankBOT
Why does the domain of an (indefinite integral) integrand matter before integrat...
surreal moon
!original
midnight plankBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
@flat spire Has your question been resolved?
flat spire
!original
It was just a problem from my book and the explanation said that notice the domain bla bla bla we can use bla bla bla
flat spire
I don’t quite understand what’s going on here? What absolute value are they talking about?
midnight plankBOT
I don’t quite understand what’s going on here? What absolute value are they talk...
fallow scarab
I don’t quite understand what’s going on here? What absolute value are they talk...
$\int \frac{dx}{x} = \log|x| + C$
grand pondBOT
riemann
flat spire
Ohhhh yeah
Right
Okay for the second part of the explanation
They made that sub because they wanted to get it into arctan form?
flat spire
$\int \frac{dx}{x} = \log|x| + C$
Also if I say left the answer with the absolute value signs even tho it’s not needed would it be considered incorrect or?
fallow scarab
Only your graders know that
flat spire
I would think it was like a general mathematics thing everyone agreed upon lol
halcyon trellis
Best to ask your graders 
but I’d imagine they wouldn’t deduct marks for that.
midnight plankBOT
@flat spire Has your question been resolved?
bleak tangle
midnight plankBOT
bleak tangle
Idk what I got wrong
midnight plankBOT
@bleak tangle Has your question been resolved?
bleak tangle
<@&286206848099549185>
midnight plankBOT
@bleak tangle Has your question been resolved?
midnight plankBOT
@bleak tangle Has your question been resolved?
sacred gate
@bleak tangle still need help?
bleak tangle
yeah
tiny drum
well first, your answer isn't correct for t=0
midnight plankBOT
@bleak tangle Has your question been resolved?
tiny steeple
doing binomial theorem, where do i go from here
midnight plankBOT
doing binomial theorem, where do i go from here
tiny steeple
isnt there some easier way to do all the multiplication
hearty rune
there is yes
$\frac{14!}{3!\cdot 11!}=\frac{14\cdot 13\cdot 12}{3!}$
grand pondBOT
AℤØ
hearty rune
doing binomial theorem, where do i go from here
you can see from your long fraction that most of them cancel
tiny steeple
**AℤØ**
ty
i have another question once i do this next part
term is 364c^3 y^11
so what am i putting in
hearty rune
364
tiny steeple
.close
queen thistle
midnight plankBOT
queen thistle
Not sure what exactly is happening here
From what I remember about mean value theorem is that I should get the f'(c) and set it equal to f(b)-f(a)/b-a?
or something like that?
or better put I know that somewhere between (0,1) and (6,4) f'(c) or f(c) = 0?
I went back in my mean value theorem section of the book and the lectures but nothing has really applied to this enough to where I can get it
olive matrix
the MVT just says that this equation has a solution
the equation will be easier to solve than it might look
just put in the definition of f(x)
queen thistle
Definition?
fallow scarab
Definition?
midnight plankBOT
@queen thistle Has your question been resolved?
midnight plankBOT
@queen thistle Has your question been resolved?
kindred swift
the integration of a function f from a to b is equal to F(b) - F(a). Then, you just calculate c by an equation.
queen thistle
Gotcha so F(b)-F(a) = 3
kindred swift
idk how to calculate the primitive of this function
queen thistle
The primitive?
kindred swift
Have you heard about that ?
queen thistle
Depends on what it means
kindred swift
the derivative of the primitive of a function is the function
queen thistle
but what's the primitive of a function
if the primitive is defined by the derivate of the primitive of a function
kindred swift
idk i havnt studied it yet
queen thistle
oh
okay well that word shouldn'
shouldnt really apply here
unless its a synonym for something else
but I have F(b) - F(a) now
So how do I calculate c here
1/2c+1 = 3?
kindred swift
Actually, c = 3
midnight plankBOT
@queen thistle Has your question been resolved?
obsidian glen
if i have two matrices A and B $(3 \times 3)$ Which commute each other and also satisfy: $A^2 = B^4$\
It is also given $A \neq B^2$\
then can i say $A + B^2$ is singular
midnight plankBOT
if i have two matrices A and B $(3 \times 3)$ Which commute each other and also ...
grand pondBOT
ginny
obsidian glen
i want to say yes but like I have this:\
$(A-B^2)(A+B^2) = 0$
grand pondBOT
ginny
obsidian glen
i know the first matrix isn't a null matrix, but can I really say it's not singular?
if it is singular, then the latter doesn't have to be singular, does it?
wide olive
if i have two matrices A and B $(3 \times 3)$ Which commute each other and also ...
Im not an expert, buut doesn't A need to be (nx3) in order for matrix multiplication to be even defined?
obsidian glen
both A and B are 3×3
wide olive
Oh nvm
obsidian glen
no worries
atomic jolt
i want to say yes but like I have this:\\
$(A-B^2)(A+B^2) = 0$
If what you've written there is a zero matrix then in particular you know that it's determinant is zero
obsidian glen
yes
atomic jolt
then you might be able to use properties of determinants to conclude something about the determinant of A+B^2
obsidian glen
how would I do that?
i know the determinant of either A-B^2 or A+B^2 is zero
but i can't really say which one it is
<@&286206848099549185>
atomic jolt
I thought about it for a while. Is there reason to suspect that the claim is actually true in the first place?
obsidian glen
yes, i am given the answer
atomic jolt
I think that's where we all got stuck
obsidian glen
yes
atomic jolt
det(A)^2 = det(B)^4
but that doesn't feel helpful because det(A-B^2) is difficult to work with
I suppose somehow
det(AB - BA) = 0
has to save the day
but idk feels kinda hopeless to me
finite field
so we need to know if |A-B^2| could be 0
If A and B^2 differ by something else then a factor of -1 then if the statement is true it must be zero because you can take out a factor of -1 from A I think
wide olive
If A and B^2 differ by something else then a factor of -1 then if the statement ...
you mean whenever B^2 = -A ??
we would need 2A = 0
atomic jolt
I don't understand the reasoning for why A is a zero matrix
finite field
no the determinant you said could be zero must be zero I said
atomic jolt
must be zero given that the original statement holds or must be zero due to non-circular reasoning?
also which determinant exactly
finite field
must be zero given that the original statement holds or must be zero due to non-...
If the statement holds than both determinants of the factors must be zero by symmetry once you factor -1 out
finite field
Ok Just a moment I write it
lunar ocean
i'm fairly sure that if the product of two nonzero matrices is zero then they're both singular
finite field
lunar ocean
suppose CD = 0 and C is invertible, then D = C^-1*C*D = C^-1*0 = 0
finite field
Problem solved than
midnight plankBOT
@obsidian glen Has your question been resolved?
obsidian glen
let me read it all
atomic jolt
How do you know that -A is not equal to B^2 ?
idk I don't really understand what's going on there
obsidian glen
suppose CD = 0 and C is invertible, then D = C^-1\*C\*D = C^-1*0 = 0
no, but what if C is NOT invertible?
lunar ocean
then it's singular
obsidian glen
yes and?
atomic jolt
suppose CD = 0 and C is invertible, then D = C^-1\*C\*D = C^-1*0 = 0
I agree but how does this help with the problem?
obsidian glen
I don't see it either
atomic jolt
i'm fairly sure that if the product of two nonzero matrices is zero then they're...
or rather I agree with this
lunar ocean
so we're looking at (A-B^2)(A+B^2) = 0, where A-B^2 is not zero
obsidian glen
but it might still be singular
finite field
How do you know that -A is not equal to B^2 ?
They could be if B^2=-A originally
atomic jolt
i'm fairly sure that if the product of two nonzero matrices is zero then they're...
how do we know that they're BOTH nonzero?
finite field
By assumption I think
atomic jolt
so we're looking at (A-B^2)(A+B^2) = 0, where A-B^2 is not zero
these ones
lunar ocean
well... is 0 singular?
lunar ocean
yes i mean the zero matrix
obsidian glen
then it is singular
finite field
Bee Thankyou for showing me that my linear algebra is lacking
lunar ocean
alright so if A+B^2 is zero then we're just done, because then it's obviously singular
obsidian glen
how exactly is A+B^2 zero?
atomic jolt
^
obsidian glen
if the product of two matrices is 0, they both can be non zero
just one of them has to be singular
lunar ocean
both of them have to be singular
lunar ocean
ok do you have an example of a singular matrix multiplied by a nonsingular matrix to get 0?
obsidian glen
that's just one example, there's more
atomic jolt
proof by "well can you come up with a counterexample then"
lunar ocean
ok so what's an example where neither of them are zero
lunar ocean
proof by "well can you come up with a counterexample then"
i already proved it earlier
obsidian glen
there's plenty, i can easily work that up
but given it holds when one of them is infact null matrix, shouldn't that be plenty?
singular * non singular being zero
lunar ocean
ok well i didn't claim that a singular matrix multiplied by a nonsingular matrix can't be zero, i claimed that a nonzero singular matrix multiplied by a nonzero matrix can't be zero
which is a claim you've given no counterexamples to at all
lunar ocean
i already proved it earlier
suppose CD = 0 and C is invertible, multiply both sides by C^-1 on the left, D = 0
so if D isn't zero, C must be singular
and by the same argument the other way around, if C isn't zero, D must be singular
obsidian glen
ok well i didn't claim that a singular matrix multiplied by a nonsingular matrix...
you didn't mention the non zero part initially
finite field
The only case that remains is if B^2= -A originally because one factor becomes zero and it’s exactly the one you want so no problem.
lunar ocean
to clarify: are we still trying to solve the original problem or are you two just trying to annoy me now
lunar ocean
alright here's the solution then
we've deduced that (A-B^2)(A+B^2) = 0
we are given that A-B^2 is not zero
it follows that A+B^2 is singular
done
finite field
i'm fairly sure that if the product of two nonzero matrices is zero then they're...
He did say nonzero
obsidian glen
take an identity matrix, multiply it by any matrix with the entries in a particular row to be zero, rest all non zero entries (it's not a null matrix)
lunar ocean
the result of that is also not a zero matrix
obsidian glen
ah shit
you're right
it's the same matrix again
I'm starting to think you're right, but do we know for sure that (non zero) singular* non singular can never be null matrix?
lunar ocean
yes
suppose CD = 0 and D is invertible
multiply on the right by D^-1
we get C = 0 and this is a contradiction
therefore D cannot be invertible
atomic jolt
Okay I get it now.
Assume A+B^2 is invertible. Then A-B^2 = 0. But this is a contradiction. Thus A+B^2 is not invertible. Thus its determinant is zero.
@obsidian glen
Thanks @lunar ocean
wait
lunar ocean
Thus A-B^2 is not invertible. Thus its determinant is nonzero.
uh... no
atomic jolt
yeah no that doesn't work my bad XD
obsidian glen
you wrote it incorrectly lol
you misplaces A-B^2 and A+B^2
but your work is somewhere along bee's work
i think i get it now
atomic jolt
I did actually, I used to hear that a lot back when I was chronically online as a kid
atomic jolt
sorry for being so useless but it was a good problem lol
midnight plankBOT
sorry for being so useless but it was a good problem lol
atomic jolt
.close
sinful olive
hey was wondering if anyone could help me with this
midnight plankBOT
hey was wondering if anyone could help me with this
elder zephyr
which question
sinful olive
3(a)(i)
wary epoch
Wait, I'm working on another person getting stuck with the same problem. Exactly the same. ||#help-7｜zen1thxyz||
elder zephyr
the standard basis is (0,1) and (1,0)
write f(0,1) and f(1,0) as a linear combination of both vectors
@sinful olive you still there ?
vital yarrow
(assuming sampling with replacement), my book says that, picking 5 numbers from 1 to 100 forms a Binomial(5,0.21) distribution (with the Bernoulli trial being that the number is at least 80), but I'm wondering why 0.21 and not 0.20?
midnight plankBOT
(assuming sampling with replacement), my book says that, picking 5 numbers from ...
vital yarrow
Isn't the probability for success in the individual trial 20/100?
midnight plankBOT
@vital yarrow Has your question been resolved?
midnight plankBOT
Available help channel!
kind sundial
in a right triangle the sides are 9 12 and hypotnus is 15 i need to find the distance between bisectures center to center of median
midnight plankBOT
in a right triangle the sides are 9 12 and hypotnus is 15 i need to find the d...
kind sundial
<@&286206848099549185>
fresh sparrow
in a right triangle the sides are 9 12 and hypotnus is 15 i need to find the d...
might help drawing the picture first
kind sundial
wait
Need to find the distance between thoea dots
one of thoes dots is bisectors go thro it
wich is r
r eaquels 3
from the formula
but idk about the median
the second dot
@fresh sparrow
fresh sparrow
try using sine rule or cosine rule to find the angles
kind sundial
sin rule?
2R eaquels a/sinA?
<@&286206848099549185>
<@&286206848099549185>
.close
rough siren
.close
midnight plankBOT
rough siren
.close
midnight plankBOT
Available help channel!
mellow plover
hi
mellow plover
So I have a problem that I'm extremly stuck with
here it is:
On a street with 50 houses, three students with paper routes deliver 28 Toronto Stars, 24 Globe and Mails, and 20 Toronto Suns. A house may receive no papers, one paper, or two papers. (No houses receive all three.) No house, of course, receives more than one copy of the same newspaper. What is the least number houses that could have two papers delivered? What is the greatest number of houses that could have two papers delivered?
now all I know is the total which is 72.
I did 72-50 and got 22
Now I'm not sure where to go now
<@&286206848099549185>
fair sleet
I would first look at the probability for each paper it's
28/50 for toronto stars
24/50 for Globe and Mails
20/50 for Toronto Suns
Beyond that i'm not 100% sure but you could multiply for each possibility of two
T'stars × GS
T'Stars × T'Suns
GS × T'Suns
Then add them all up
fair sleet
For each probability you want to do available possibilities over total possibilities if that makes sense
mellow plover
Oh
fair sleet
There are only 28 papers for T'Stars with a total of 50 houses it could go to
So that is a 28 in 50 chance 1 house will get it
Now when it comes to two possibilites that kind of rely on eachother you multiply them together
mellow plover
And how is that supposed to get me to the least and greatest number?
fair sleet
That's the part I am unsure
mellow plover
hmm
So I did what you said, and got to 428/625 as a fraction 0.6848 as a decimal
Well it doesn't seem like it does anything, or leads me anywhere, but thank you very much for your time.
.close
tardy scroll
I just need help with the general sequence of 2,14,122,1094... with the next value, if possible for the n term
midnight plankBOT
I just need help with the general sequence of 2,14,122,1094... with the next val...
fallow scarab
Did you check if it's a geometric series
tardy scroll
it doesn't seem to be
grand pondBOT
Result:
108
strange meadow
,Calc 1094-122
grand pondBOT
Result:
972
,Calc 972- 108
grand pondBOT
Result:
864
I tried with cubics, at least in my case I didn't find any relation :/
tardy scroll
this problem is supposed to be done pre calculus
tardy scroll
I'm not sure though, this sequence comes from the original problem that is a trigonometric one, which tbh is just a summatory
tardy scroll
122/14 is decimal
so the original problem is arctan(1/2)+arctan(3/14)+arctan(9/122)+arctan(27/1094) in an infinite sequence, but I just need the sequence from below so I can get a grasp on the summatory
strange meadow
That is very unclear
tardy scroll
they are asking to reduce that to a value for the N terms that it has (for 2 terms it would be arctan(1/2)+arctan(3/14)
I got (pi/4)-arctan(1/3^n) which validates with the n terms, but that was by testing for 1 and 2 values with the options, which is not the formal way to solve it
midnight plankBOT
@tardy scroll Has your question been resolved?
midnight plankBOT
@tardy scroll Has your question been resolved?
midnight plankBOT
@tardy scroll Has your question been resolved?
midnight plankBOT
@tardy scroll Has your question been resolved?
tardy scroll
Um, could anyone help? <@&286206848099549185>
gloomy sandal
whats the question
tardy scroll
I just need help with the general sequence of 2,14,122,1094... with the next val...
this one
gloomy sandal
ok, so the sequence is from multiplying the previous term by an increasing consecutive integer especially the second term (14) is the result of multiplying the first term (2) by 7, the third term (122) is derived from multiplying the second term (14) by 8, and the fourth term (1094) is by multiplying the third term (122) by 9. this pattern is from "a_n = a_{n-1} × (n + 6)," where "a_n" represents the "n"-th term and "a_{n-1}" denotes the previous term, applying this relation to find the next term ("a_5"), we calculate "1094 × (5 + 6)," then a value of 12034 so the next term in the sequence is 12034
i assume
tardy scroll
that's why I asked here, I couldn't find any other way to get around that sequence
tbh I think that there might be an easier way to get to the next term, but I just can't seem to find it
empty meteor
I just need help with the general sequence of 2,14,122,1094... with the next val...
I found a similar pattern at quora but the sequence is longer being 2, 5, 14, 41, and 122
The pattern was
2 * 3 - 1 or 2 + 3¹ = 5
5 * 3 - 1 or 5 + 3² = 14
And so on
If we skip some of the patterns then we can get
(2 * 3 - 1)*3 - 1 = 2nd term
Or
2 + 3¹ + 3² = 2nd term
If we take the second formula then try to get the 3th term (122) then it would be
2 + 3¹ + 3² + 3³ + 3⁴
Turning it into a formula for the n term would be
Shout out to the quora post
https://www.quora.com/Which-number-comes-next-in-this-series-2-5-14-41-122/answer/Priyanshu-Kumar-496?ch=15&oid=368289262&share=ca004bd4&srid=ve24H&target_type=answer
tardy scroll
you know, that is quite helpful
that answers the question why in my answers of the original question of the book it said 3^n+1
I'll figure the rest out, thanks for the link to the post
.close
vocal shale
midnight plankBOT
midnight plankBOT
midnight plankBOT
Available help channel!
terse wedge
for a vector to be orthogonal it's dot product has to be zero right?
midnight plankBOT
for a vector to be orthogonal it's dot product has to be zero right?
@terse wedge Has your question been resolved?
terse wedge
ni
proud owl
pop quiz, how many vectors do you need for the dot product?
grave flicker
How to derive this?
midnight plankBOT
How to derive this?
frosty veldt
integration by parts
midnight plankBOT
Available help channel!
finite cloud
midnight plankBOT
finite cloud
ive got a few questions about this.
one how do you get a(t). is it integral of v(t) or derivative?
and i think its either b or c but im unsure if you need to take the abs value?
fallow scarab
Acceleration is the derivative of velocity
finite cloud
to get position you need to take integral of velocity and then plug in number?
midnight plankBOT
@finite cloud Has your question been resolved?
last slate
Guys i suck at integrating
midnight plankBOT
Guys i suck at integrating
keen crest
where is the question
last slate
$$\frac{1}{2} \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} (\frac{1}{\cos(\theta)} - 2 \cos(\theta))^2 d \theta$$
grand pondBOT
we
grand pondBOT
we
worn sequoia
when you multiply out the square what do you get
last slate
$$\frac{1}{2} \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{1}{\cos^2(\theta)} -4 + 4cos^2(\theta) d \theta$$
$$\frac{1}{2} \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{1}{\cos^2(\theta)} -4 +2 +2 cos(2\theta) d \theta$$
$$\frac{1}{2} \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{1}{\cos^2(\theta)} -2 +2cos(2\theta) d \theta$$
keen crest
thats
last slate
sec doesn't exist
keen crest
thats the same thing
last slate
Nope
last slate
$$\frac{1}{2} \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{1}{\cos^2(\theta)} -2 +2 cos(2\theta) d \theta$$
$$=$$
$$\frac{1}{2} ( \tan(x) - 2\theta + sin(2\theta)) + C$$
worn sequoia
and the bounds?
grand pondBOT
we
worn sequoia
big
grand pondBOT
we
last slate
uuh
the bounds?
-pi/4 to pi/4 ?
an uuh
this becomes
$$\frac{1}{2}( -1 +\frac{\pi}{2} - \frac{\sqrt{2}}{2}) - \frac{1}{2}(1 - \frac{\pi}{2} + \frac{\sqrt{2}}{2})$$
grand pondBOT
we
grand pondBOT
we
last slate
which is negative
negative area
Okay
i just spent like 5 seconds solving three other problems
now this is my last one, i think this will take me longer than 5 seconds!
<@&286206848099549185> WHY DO I HAVE A NEGATIVE AREA?!?!
keen crest
i think your math is wrong
(-2(pi/4) + sin(2(pi/4)) + tan(pi/4)) - (-2(-pi/4) + sin(2(-pi/4)) + tan (-pi/4))
this is a positive number
-2x + sin(2x) + tan(x) + C is the answer of your integral
the answer evaluated at the bounds is 4-pi
last slate
oh
yep
I evaluated it wrong
I still have no fucking idea what I'm doing
Just wrote down the answer for this question on my note sheet
hopefully it shows up on my test
TY
.close
last slate
DUDE
grand pondBOT
we
last slate
I used best friend
so
I got
$4 \frac{1}{1 - (\frac{-3}{2}x)}$ which becomes $\sum (-1)^n (\frac{3}{2}x)^n$
right?
grand pondBOT
we
lilac sage
oh oops i put the - on mine by default
$\sum_{n=0}^{\infty} \left(-\frac{3x}{2}\right)^n$
grand pondBOT
last slate
bprp takes the minus out so i did it as well
last slate
$\abs{\frac{3}{2}x} < 1$ so uuuuh $ \abs{x} < \frac{2}{3}$ ?
grand pondBOT
we
last slate
blackpen red pen
lilac sage
$\frac{2}{2+3x} = \sum_{n=0}^{\infty} \left(-\frac{3x}{2}\right)^n$ for $|x| < \frac23$
grand pondBOT
last slate
True!
if i wanted to check the endpoint at uuuh
-2/3
wold i do
$\sum_{n=0}^{\infty} (-1)^n$ because 3/2 * 2/3 = 1
grand pondBOT
we
lilac sage
well if you wanted to check -2/3 then the negatives cancel out so its just $\sum_n n$
grand pondBOT
lilac sage
so true
lilac sage
ya neither side works
midnight plankBOT
midnight plankBOT
Available help channel!
arctic cipher
could i get a hint on how to do this?
midnight plankBOT
could i get a hint on how to do this?
twilit rampart
try to find a pattern
how many digits in 2^1? in 2^2? in 2^k?
and prove that pattern
arctic cipher
and prove that pattern
lets say i find a pattern, how would i prove it
twilit rampart
try to find a pattern first
you cant prove something if you dont know what you are trying to prove
next rover
i don't see the trick if there is one
arctic cipher
i dont see a pattern
wait i do
for powers of 2
every 3 the number of digits increases by 1
twilit rampart
yessir
arctic cipher
but this is an exception
next rover
no okay yeah log(2) + log(5) would become log(10)
twilit rampart
yes
arctic cipher
the only one?
twilit rampart
no
arctic cipher
no okay yeah log(2) + log(5) would become log(10)
i should take log?
twilit rampart
$2^k = 10^{\log(2)k}$
grand pondBOT
LF
arctic cipher
oh
twilit rampart
10^k has k+1 digits
twilit rampart
every 3 the number of digits increases by 1
its every three because log(2) = 0.3 roughly
next rover
(2^2023) has length of log_10(2^2023) + X and
(5^2023) has length of log_10(5^2023) + Y
we can easily add them, it's 2023(log 2) + 2023(log 5) + X + Y =
2023(log(2×5)) + X + Y
= 2023 + X +Y
X and Y are each between 0 and 1
so the answer is 2023, 2024 or 2025, and no way it's 2023
the question is how you decide between 2024 and 2025
oh but they aren't 1 either
it has to be 2024
i'm almost not confused 🤣
it's the other way around, X and Y are never 0, and they can be 1 but certainly not in this case
either way it means they add up to one
midnight plankBOT
@arctic cipher Has your question been resolved?
arctic cipher
(2^2023) has length of `log_10(2^2023) + X` and
(5^2023) has length of `log_10(5...
what do X and Y represent
next rover
it's literally unknown difference between the length and the logarithm
,calc log(66) / log(10)
grand pondBOT
Result:
1.8195439355419
,calc log(125) / log(10)
grand pondBOT
Result:
2.0969100130081
always more than 0, never more than 1
they add up to an integer, so we have sufficient information to say this integer is 1
it could be 2, if X=Y=1
but it's not the case, neither is 1
arctic cipher
i see
arctic cipher
it's the other way around, X and Y are never 0, and they can be 1 but certainly ...
why cant they be 1
next rover
so if we were given 3 numbers instead of 2, I wouldn't be able to decide what X+Y+Z is, could be 1 or 2
maybe it can be figured out too idk
,calc log(10000) / log(10)
grand pondBOT
Result:
4
yep
midnight plankBOT
midnight plankBOT
Available help channel!
unkempt rune
is there an easier way to compute this derivative ?
midnight plankBOT
is there an easier way to compute this derivative ?
unkempt rune
with u sub or something?
midnight plankBOT
@unkempt rune Has your question been resolved?
midnight plankBOT
midnight plankBOT
Available help channel!
tidal forge
need help
tidal forge
Not sure how to start at all.
midnight plankBOT
@tidal forge Has your question been resolved?
tidal forge
<@&286206848099549185>
frosty hound
the trapezoidal rule states the following. Now split the intervall into 4 smaller ones of equal length and plug the limits into the formula
tidal forge
the trapezoidal rule states the following. Now split the intervall into 4 smalle...
I have to use this formula 4 times correct? Than add it all up?
frosty hound
I have to use this formula 4 times correct? Than add it all up?
correct
floral plinth
Struggling with this.
So, just sticking with solving for x, we can multiply the first equation by d and the second equation by b.
Giving us:
abx + bdy = d
bcx + bdy = 2b
After subtracting, we get:
abx - bcx = d - 2b
Now is where I'm having an error in understanding.
I can't figure out how to separate the x without making it 2x.
For example, if I divide by ab - bc, I'm left with:
x + x = d - 2b / ab - bc
I'm sure that I'm just making a very silly arithmetic error and some grade school misunderstanding of division or something.
midnight plankBOT
Struggling with this.
So, just sticking with solving for x, we can multiply the...
floral plinth
I've been out of school for a very, very long time and going back to college next week, so wanted to revisit some stuff lol
Oh, wait, I just factor out the x.
x(ab - bc) = d - 2b
then divide both by ab - bc
I'm gonna get roasted in my calc course lmfao
kindred torrent
floral plinth
.close
grizzled blade
Test.
Ignore this.
midnight plankBOT
Test.
Ignore this.
grizzled blade
.close
midnight plankBOT
jagged saffron
was not ignored
midnight plankBOT
Available help channel!
midnight plankBOT
how does this work
midnight plankBOT
@craggy fjord Has your question been resolved?
rustic verge
midnight plankBOT
rustic verge
is showing that two sides of an equation are equal enough to prove the property?
or do i have to manipulate it somehow algebraically
rustic verge
for #25
midnight plankBOT
@rustic verge Has your question been resolved?
midnight plankBOT
@rustic verge Has your question been resolved?
midnight plankBOT
@rustic verge Has your question been resolved?
bronze nimbus
midnight plankBOT
bronze nimbus
i made both equal to another
then did cross multiplication
then i got b/a=a
which doesnt explain ab/a+b=x=y
idek where the x and y went
.close
slate talon
How do I solve this limit
midnight plankBOT
How do I solve this limit
sharp coral
if you plug in x = 3, what form does it look like?
slate talon
I will get /0 which is not possible
sharp coral
what about on top?
slate talon
you get 0/0
slate talon
oh okay i got it
its 3/8 right?
I took the conjugate
canceled out the x-3
and then just plugged in x=3
thanks for your help
.close
calm cliff
Can someone tell me how to determine if that is linear or nonlinear
wary thorn
Look up the definition in your textbook or notes
Of what makes a differential equation linear or nonlinear
calm cliff
ok
calm cliff
Look up the definition in your textbook or notes
In a differential equation, when the variables and their derivatives are only multiplied by constants, then the equation is linear. The variables and their derivatives must always appear as a simple first power. Here are some examples. Similar rules apply to multiple variable problems.
The constants of y is 2, therefore that is linear
nova yoke
where are you getting this from? what is the source of that quote
calm cliff
wary thorn
I said your textbook or notes
nova yoke
even a simple wikipedia check will give you a correct definition
(the one above is incorrect)
midnight plankBOT
@calm cliff Has your question been resolved?
warm island
midnight plankBOT
warm island
So because of how this sigma algebra is set up, if one set of A isn't countable then the compliment is right?
If I'm right with that, then does the last line mean that for the An0 that's uncountable, then the intersection of the compliments of A is a subset of the compliment of the uncountable set?
strong lava
They are indeed saying that
Basically because A n B subset A
nova yoke
bonus: you can show that this is the smallest sigma algebra that contains all the singletons of X
strong lava
That does make sense
warm island
bonus: you can show that this is the smallest sigma algebra that contains all th...
So it's like a diskrete metric
nova yoke
So it's like a diskrete metric
a bit analogous to that, yea
except the discrete metric is more akin to the power set
which is the largest sigma algebra that contains all the singletons
every set is open in the discrete metric
ebon belfry
im workin on exploring y=ax+b and theres a problem with a graph and a<-1 and i dotn even know what im suposed to do
midnight plankBOT
im workin on exploring y=ax+b and theres a problem with a graph and a<-1 and i d...
fallow scarab
negative rise = down
gray pumice
a<-1 means the graph of the function is slanted downwards more than 45°
alternatively, it means tht for each increase of x by one, y decreases by more than 1
etc. There's alot of equivalent interpretations here
void obsidian
YESSSSS
ebon belfry
whats the question trhat im suposed to awnser
fallow scarab
whats the question trhat im suposed to awnser
???
ebon belfry
idk man
fallow scarab
we're not your teacher
ebon belfry
ight
lyric charm
whats the question trhat im suposed to awnser
if you don't know, then neither do we.
how are we meant to know what you've been assigned?
midnight plankBOT
@ebon belfry Has your question been resolved?
midnight plankBOT
midnight plankBOT
Available help channel!
zenith garden
zenith garden
does this seem like enough info?
midnight plankBOT
@zenith garden Has your question been resolved?
zenith garden
<@&286206848099549185>
dawn goblet
this is correct
zenith garden
nice thanks
theres also this
im p sure im correct
but i wont get the grade back for a while so
dawn goblet
so for this one
you can plug in each possible choice and see if it's correct
for example
on the left of the equal sign, it's 2(x+3) whihc means you do distributive
2 times x
and then add that to 2 times 3
small yoke
Or you just solve the equation
zenith garden
yeah thats what i did
small yoke
Which can be faster than actually trying each one
zenith garden
does my answer look ok?
small yoke
Ye
last slate
A man lifted a 281.5 kg load off the ground using his teeth. Suppose he holds just three times that mass on a 30-degree slope using the same force. What is the coefficient of static friction between the load and the slope? (You have to draw a free-body diagram.)
midnight plankBOT
A man lifted a 281.5 kg load off the ground using his teeth. Suppose he holds ju...
last slate
hai I asked this question yesterday but i was afk and got my help channel closed. Either way I have the answer but it doesn't make sense
(3sin(30) - 1) / (3cos30)
Ok I get 3sin30 over 3cos30, but why do you subtract one
midnight plankBOT
@last slate Has your question been resolved?
midnight plankBOT
@last slate Has your question been resolved?
last slate
NO bro my question is not resolved
midnight plankBOT
@last slate Has your question been resolved?
last slate
NO
last slate
<@&286206848099549185> maybe
last slate
hai
storm siren
Let u be the coefficient of static friction
Force applied F = mg
Static Friction Force = u3mgcos (theta)
The gravitational Force = 3mgsin (theta)
So the force equation = 3mgsin (theta) - (u3mgcos (theta) + mg) = 0
So 3mgsin (theta) = (u3mgcos (theta) + mg) => 3sin (theta) = (u3cos (theta) + 1)
=> u = (3sin (30) - 1) / 3cos (30) => u = (3(1/2) - 1) / (3 x 0.866)
=> u = (1.5 - 1) / 2.59 = 0.5 / 2.59 = 0.5 / 2.598
Coefficient of Static Friction u = 0.19.
storm siren
we subtract 1 from 3sin(30) because we are accounting for the force of gravity. The force equation is set equal to 0, so we need to subtract the force of gravity from the force applied in order to find the coefficient of static friction.
last slate
sorry im having a little trouble understanding
yes the force equation is set equal to 0, and yes subtract fg from fa to find us but how do you get 1 from that?
dense latch
Still on the problem?
midnight plankBOT
@last slate Has your question been resolved?
last slate
Still on the problem?
yep sorry I had pe
dense latch
So you understanded untill here?
...So 3mgsin (theta) = (u3mgcos (theta) + mg)
last slate
So you understanded untill here?
> ...So 3mgsin (theta) = (u3mgcos (theta) + mg...
yep precisely
dense latch
and you are confused how it gets to
3sin (theta) = (u3cos (theta) + 1)
?
mint pulsar
hai
mint pulsar
e im have a math assignment to rush idk why im here 😄
last slate
gl
last slate
he divided
3mgsin (theta) = (u3mgcos (theta) + mg)
here both sides by mg?
oh okay i see.
but
I'm confused, why is the one there
is it aresult of divding both sides of mg? or is it a result of something else?
dense latch
he divded mg by mg, so became 1
last slate
omg
im so stupid
thank you so much. One last question, I get it becoming 1 but why does it turn negative
dense latch
idk you will still reading this, but he add -1 on both sides
then divided with 3cos(theta)
last slate
idk you will still reading this, but he add -1 on both sides
dw i'm still reading this
yes he adds -1 on both sides but why -1?
mg/mg = 1 , but is there a reason to why you subtract 1 instead of adding 1 ?
because yes it becomes 3sin (theta) = (u3cos (theta) + 1) but then it becomes (3sin (30) - 1) / 3cos (30) and that +1 turns into a -1...
sorry if i'm missing something
midnight plankBOT
@last slate Has your question been resolved?
last slate
NO!!!!!!!
last slate
yeah I'm stupid
it just clicked
@storm siren @dense latch Thank you both
❤️
.close
gritty hatch
I have to graph the function f(x) = -(x-4)(x-1)^2(x-5). I know its zeros are +4, +5, and it touches +1 but to prove it mathematically I am having trouble knowing what (x-1)^2 does to the equation, I was attempting to find the complete function instead of its factors by multiplying the factors but I got tripped up on what to do with the exponent... Am I meant to distrubute it and go from there??
midnight plankBOT
midnight plankBOT
Available help channel!
round mural
midnight plankBOT
round mural
what did they do with the 1/2 to factor the square??
round mural
try expanding it back out
I see
so on a different problem, how would you determin fit its a perfeact square tirnomial
restive igloo
can any1 help with all 3 pls
midnight plankBOT
can any1 help with all 3 pls
restive igloo
<@&286206848099549185> ?
modest crystal
Can I get an answer checked really quick
midnight plankBOT
Can I get an answer checked really quick
modest crystal
Here's the question and the answer up to c
midnight plankBOT
@modest crystal Has your question been resolved?
modest crystal
<@&286206848099549185>
dont necessarilly need a final answer, just wanna know if i have the right idea
wicked ledge
how did it become 20pi?
modest crystal
I think thats where i messed up
i multiplied each term by 4 to get rid of the fractions
so 5(x-pi/4) became 20(4x-pi)
Wait
i see the mistake there
apart from my terrible job at manipulating the final equation does the rest seem like the correct method of doing this?
wicked ledge
yeah everything looks correct
grand pondBOT
woods
blissful pier
IBP
rose trout
Or u sub :p
blissful pier
Or u sub :p
wait yeah that'd probably be easier haha 
rose trout
You can do. Here it looks fine because the derivative of what's inside ln is roughly what is outside (x).
blissful pier
https://tenor.com/view/forest-gump-wave-hi-hello-howdy-gif-22164679
woah it's been a minute haha
rose trout
So many llamas
blissful pier
So many llamas
not enough* 
rose trout
Never
And then you'll end up integrating ln(u), which you can use the hint for 😲
I think you're missing the 1/2 in the first line.
From the u-sub
But otherwise it should be right
midnight plankBOT
midnight plankBOT
Available help channel!
tender sphinx
Here is this proof that I am stuck on.
Let a be a nonzero real number.
• Prove 1/a does not equal 0.
midnight plankBOT
Here is this proof that I am stuck on.
Let a be a nonzero real number.
• Prove ...
tender sphinx
I know that any number that is divided by a nonzero number cannot be 0 unless its infinity.
but im not really sure how to go about writing that
fallen galleon
proof by contradiction?
tender sphinx
so I should try to equate a to any integer as an example to show that it cant equal 0?
fallen galleon
no?
it wants you to prove that 1/a is not 0 for a nonzero real number
now we just assume that 1/a is 0
if 1/a is 0
then you should see that its false
tender sphinx
false because there is no integer that would solve 1/a=0 correct?
tender sphinx
sick thx for the help
fallen galleon
false because there is no integer that would solve 1/a=0 correct?
also its not an integer
since your question told you its a real number
tender sphinx
integer isnt a real num?
fallen galleon
it can be any number, doesnt have to be integers only
tender sphinx
Having trouble with this proof:
Let a be a nonzero real number. Prove 1/(1/a) = a
Am I able to just break down the equation and use the reciporacal to turn 1/(1/a) into 1 * a/1 to prove it? Is there any properties that are involved with this process?
midnight plankBOT
Having trouble with this proof:
Let a be a nonzero real number. Prove 1/(1/a) = ...
candid rampart
I gather that you have to use the very fundamental properties?
tender sphinx
yes
candid rampart
What have you tried so far?
You can also share a screenshot of the properties you are supposed to follow
tender sphinx
just turning 1/(1/a) into 1 * a/1 but I dont think there are any properties that are involved with this
ill get a ss
these would be the only ones that would apply im pretty sure
last slate
You slayed @tender sphinx you slayed fr
candid rampart
alr so what do you think should be done first
So you first know that a is different from zero so from P5 you know that the inverse exists and so a(1/a) = 1
tender sphinx
yeah, so would I multiply the other side by 1/a?
candid rampart
Do you first agree that 1/a is a real number too?
tender sphinx
ye
candid rampart
Okay, so here is the outline of the proof. We want to prove that 1/a is not zero so that we can find its inverse and so when we multiply a(1/a) = 1 times the inverse of 1/a we will get to our desired result
So, let us first prove that 1/a is not zero. I know it is intuitive, but if you are doing things from fundamentals you should prove that
Let us prove that 1/a is not zero. By contradiction suppose that 1/a = 0. The only way in which this could be zero would be if the numerator were zero but 1 is not 0 so 1/a is not zero
tender sphinx
ive proved that 1/a isnt 0 in a previous problem where we did it by contradiction
candid rampart
Okay perfect
Then by P5 you know that the inverse of 1/a exists and is a real number too
tender sphinx
yeah