#help-10
obtuse pebbleBOT
royal basin
replace S with W for your purposes
@hasty perch
looking at the truth table though it appears this huge thing is equivalent to q&r&w
hasty perch
oh wow thank you
what did you set it to?
I use that tool but it never returns the CNF form
This is for another formulal
royal basin
are you unhappy with it giving you FALSUM?
hasty perch
i want the cnf form tho
obtuse pebbleBOT
@hasty perch Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
white basin
Hi there, I do not understand how to solve the following problem.
Problem: What are the coordinates of the point P relative to the coordinate system (Q, (u, v))
obtuse pebbleBOT
Hi there, I do not understand how to solve the following problem.
Problem: What...
white basin
Ping me if you can help me pls.
white basin
So its the exact same thing as the other problem?
warped flume
its a bit different
white basin
so -v -u = QP
warped flume
cause u have to show it relative to Q
so u have to minus the coordinate of Q from the position vector
white basin
Not following
warped flume
Hi there, I do not understand how to solve the following problem.
Problem: What...
are (u,v) coordinates of Q or just the vectors
white basin
are the cordonnants the same thing as components?
warped flume
in this case no
white basin
are (u,v) coordinates of Q or just the vectors
technically they are just vectors
warped flume
o
white basin
warped flume
then its just -u-v
warped flume
well ur gonna learn vectors in respect to the origin later
so
unless the question specifies it, we just treat them as vectors
white basin
unless the question specifies it, we just treat them as vectors
wait what exactly would it say?
warped flume
sth like the coordinates of P with respect to the origin is ->U - -> v
white basin
oh ok ok
white basin
sth like the coordinates of P with respect to the origin is ->U - -> v
So for the problem I currently have, they say i have to add Q, u, v.
Would this be appropriate:
QP = - u - v
warped flume
yep
warped flume
PQ is u+v
white basin
Yes
it says P relative to ....
Why did you decide to do QP and not PQ.
wait its the same thing
white basin
True.
warped flume
Sth u will learn later in the course
cosmic badge
Could someone help with question 7 , I'm kinda lost on what to do
obtuse pebbleBOT
Could someone help with question 7 , I'm kinda lost on what to do
keen crane
Could someone help with question 7 , I'm kinda lost on what to do
Since we know the total (60, which you calculated and I am assuming is correct), we can simply find x from $5+x+2x+1=60$. With $x$ we can find the amount of yellow flowers and then the probability is simply $\frac{2x+1}{60}$.
warm shaleBOT
CoreByte
cosmic badge
Since we know the total (60, which you calculated and I am assuming is correct),...
So is 2x + 1 / 60 the final answer?
keen crane
that's the probability that the flower is yellow, yes.
keen crane
you need x to find the amount of yellow flowers still
cosmic badge
you need x to find the amount of yellow flowers still
But the question Doesn't ask to so I don't have to right?
keen crane
you need the amount of yellow flowers to find the probability that the flower is yellow
cosmic badge
you need the amount of yellow flowers to find the probability that the flower is...
I don't know how to do that part
keen crane
5+x+2x+1=60 -> solve for x, yellow flowers = 2x+1
probability is yellow flowers divided by total flowers
cosmic badge
5+x+2x+1=60 -> solve for x, yellow flowers = 2x+1
Ohh , but that's already in the question
So all i just had to do was find the total and divide it by the equation given for yellow flowers?
keen crane
yes
cosmic badge
So that was all
keen crane
yes
lament atlas
obtuse pebbleBOT
lament atlas
This is the equation that gives the area of a body
This is the body
So for what value of x is the area maximum
I found the first derviate and made it equal to 0
frosty river
$S'(x)=2x-\frac{12000}{x^2}=\frac{2x^3-12000}{x^2}=0\$
$2x^3=12000\$
$x^3 = 6000\$
$x =\sqrt[3]{6000}$
frosty river
Yes, that is right.
lament atlas
I made that equal to 0
frosty river
Yes.
lament atlas
Which leads to 0=2x^3 -12000
pine sail
Which leads to 0=2x^3 -12000
Yep.
lament atlas
Yeah that s what i did
pine sail
1200 again.
warm shaleBOT
Categorist
lament atlas
Which is 8.8 right?
pine sail
NO
lament atlas
My book says 18.2
pine sail
Its 18.2
frosty river
18.1712059283...
lament atlas
What
pine sail
Well that.
fierce lagoon
Bro what how did you get 8.8
lament atlas
My calculator must be broken then
frosty river
Rise 6000 to 1/3
lament atlas
Either i am crzy or my calculator is not working
pine sail
I just told you the error.
lament atlas
If i take twice the sqrt of 6000
fierce lagoon
No
lament atlas
Is it the same as cubic root
fierce lagoon
That's not how it works
frosty river
$6000^{\frac{1}{3}}=18.1712059283...$
fierce lagoon
That's 4th root
warm shaleBOT
Categorist
fierce lagoon
,calc cube root of 6000
warm shaleBOT
The following error occured while calculating:
Error: Undefined symbol root
fierce lagoon
Burn
pine sail
Fr.
fierce lagoon
,calc 6000^(1/3)
warm shaleBOT
Result:
18.171205928321
So i can t take 2 times the sqrt
fierce lagoon
See
fierce lagoon
So i can t take 2 times the sqrt
No
That would be taking the quartic root
Not the cube root
pine sail
So i can t take 2 times the sqrt
There's no sqrt.
fierce lagoon
If you take the square root of the square root that's the quartic root
pine sail
Yeah.
fierce lagoon
But if i am at a test is there a way i can find it?
Raise it to the 1/3 power
lament atlas
Oh
pine sail
Yeah.
frosty river
Yes, many times
frosty river
You're welcome
lament atlas
.close
rain coral
obtuse pebbleBOT
timid silo
why isn’t this 4a+b?
how did you get this?
timid silo
if we appeal to the diagram for intuition, the vector b goes from top right to bottom left. So -b goes from bottom left to top right (the red arrow). So if we do the sum you gave, we will end up with the green arrow which isn't BM
rain coral
ohhhh
timid silo
So yes, the working in red in your original picture is the correct way to do it.
rain coral
I never knew vectors work like this
timid silo
I think you were thinking of them like lengths
rain coral
yea
timid silo
but vectors have both a length and a direction
timid silo
as an aside, if we were only looking at magnitude, we also cannot just subtract by b, because the length AD and BC might not be the same (although the diagram makes it look that way)
timid silo
they are definitely not parallel in the 'not to scale' image lol
obtuse pebbleBOT
devout solar
so what answer did you get
obtuse pebbleBOT
Available help channel!
silent drum
obtuse pebbleBOT
frosty river
I understand all the words but the funny fact is that for me → is the definition of soundness and ← is the definition of completeness if I'm not misunderstanding something so if someone can help...
devout solar
afaik that arrow means if and only if
obtuse pebbleBOT
@silent drum Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
twilit forge
hi
brave bramble
Literally subbing in f and integrating over 0 to 2
Looks like it's piecewise, so two integrals will be needed
Exact same process as part 1, really
pseudo swift
@twilit forge
obtuse pebbleBOT
@twilit forge Has your question been resolved?
meager fiber
obtuse pebbleBOT
patent silo
meager fiber
excuse me, this channel is being occupied by me
meager fiber
So where I can get help lol
please read the rules of the server. and.
meager fiber
<@898817909449707560> <#903430334681608232> ｜an-elite 💀
can you delete your message pls
@patent silo please delete your messages here to make this channel easier to read for my doubt
narrow wyvern
can you delete your message pls
i just helped someone dude 💀
meager fiber
as it is currently being used by me
meager fiber
i just helped someone dude 💀
my bad
but i assume they had already moved on from this channel :0
sorry tho
meager fiber
my solving process:
let slopes be m1 and m2
m1 = 3 m2 (according to question)
using the relations-
m1+m2 = -2h/b ----- (1)
and
m1 * m2 = a/b --------(2)
solving (1)
3 m2 + m2 = -2h/b = -4/lamda
=> 4 m2 = -4/lamda
=> m2 = -1/lamda
similarily solving (2)
m1 * m2 = a/b = 3/4
3m2 * m2 = 3/4
3 m2^2 = 3/4
m2 = 1/2
i equated it with lambda, i get lamda = -2
the answer given in the textbook is lamda = 1
where am i going wrong
storm rose
I really need some help here, i have spent 4 hours in trying to figure this out and I cant. How can I solve this?
obtuse pebbleBOT
I really need some help here, i have spent 4 hours in trying to figure this out ...
storm rose
Can it be explained so a dummie can understand it?
timid silo
hi it's me again lol. So from your working before, we have that $\frac{x-2}{\sqrt{x+1}}=2$ if $x=,0,8$; and it's not defined for $x<-1$. We now consider the sign of $\frac{x-2}{\sqrt{x+1}}-2$ on the three intervals $(-1,0),(0,8),(8,\infty)$
the easiest way is to choose random numbers in each of these intervals, and plugging it in (since we know that the function is continuous on each of these intervals). Eg, plugging in -.5
storm rose
the thing is, i really dont understand what you are saying. Cant it be solved it the normal way?
timid silo
what's the normal way for you?
storm rose
1s
knotty crow
I really need some help here, i have spent 4 hours in trying to figure this out ...
$$\frac{x-2}{\sqrt{x+1}}<2$$
Domain:
$$x+1>0 \iff x>-1$$
Solution:
$$\frac{x-2}{\sqrt{x+1}}-2<0$$
$$\frac{x-2}{\sqrt{x+1}}-\frac{2\sqrt{x+1}}{\sqrt{x+1}}<0$$
$$\frac{x-2-2\sqrt{x+1}}{\sqrt{x+1}}<0$$
Denominator is always positive, hence it's enough to solve:
$$x-2-2\sqrt{x+1}<0$$
$$(x+1)-2\sqrt{x+1}<3$$
Now u can sub $u=\sqrt{x+1}$ and solve quadratic inequality.
eh
warm shaleBOT
Modus
storm rose
Like this
knotty crow
u can multiply by sqrt(x+1) both sides and without reversing sign of the inequality since sqrt(x+1) > 0
storm rose
I see, but why does the in the last ecuation, where does the X + 1 and the 3 come from?
knotty crow
isn't x - 2 equal to x + 1 - 3?
storm rose
dont worry
so lets say im in the last ecuation
I still need the zero points, i dont see how to find them
knotty crow
$$u^{2}-2u<3$$
$$u^{2}-2u-3<0$$
$$u^{2}-2u+1-4<0$$
$$(u-1)^{2}-2^{2}<0$$
$$(u-1-2)(u-1+2)<0$$
$$(u-3)(u+1)<0$$
Therefore $u \in (-1,3)$.
From here it's enough to do:
$$-1<\sqrt{x+1}<3 \iff \sqrt{x+1}<3 \iff x+1<9 \iff x<8$$
Assuming domain was $x>-1$ final solution is:
$$x \in (-1,8)$$
warm shaleBOT
Modus
obtuse pebbleBOT
tardy epoch
what are you calculating?
and what have you tried
$\log_{|x-y|}((x + y - 1)/2) = 2$
warm shaleBOT
riemann
tardy epoch
$|x-y|^2 = (x+y-1) / 2$
warm shaleBOT
riemann
tardy epoch
yea that's not helpful
feral island
What will the answer will this be? I just wanna double check my answer before handing it in
obtuse pebbleBOT
What will the answer will this be? I just wanna double check my answer before ha...
feral island
I got y= 5/2 + -1
frosty river
That is a number
x lacks
You did not well even with the x
Look at the parentheses
$y=\frac{5}{2}(x-4)-3$
warm shaleBOT
Categorist
frosty river
How is 5/2 distributed over them?
obtuse pebbleBOT
@feral island Has your question been resolved?
fresh flax
obtuse pebbleBOT
obtuse pebbleBOT
@fresh flax Has your question been resolved?
keen wadi
Try using differentiation from first principles
keen wadi
Try using differentiation from first principles
Actually nvm this
keen wadi
Those fractions aren’t equal
(1 / 14 + h) - 1/ 14 = (14- 14 - h) / 14(h + 14)
I can go and write this out better on a piece of paper to make it clearer
Do you sorta see?
keen wadi
Yeah
keen wadi
I am also assuming that this is the correct answer you are trying to get to based on your working out?
fresh flax
I am also assuming that this is the correct answer you are trying to get to base...
Thank you so much for explaining it to me
I got the answer correct
keen wadi
No problem 👍
fresh flax
.close
supple epoch
Let D ⊆ R and let f : D → R. Show that f is continuous if and only if the two functions f+ : D → R and f− : D → R are continuous, where
f+(x) := max(f, 0)
f−(x) := min(f, 0)
obtuse pebbleBOT
Let D ⊆ R and let f : D → R. Show that f is continuous if and only if the two fu...
haughty coyote
A sum of continuous functions is continuous
Try to express f as a combination of f+ and f-
The other direction of the proof is quite easy as well
supple epoch
Yeah I'm new to continuous functions
haughty coyote
What theory do you know about continuity?
haughty coyote
Absolutely nothing but the definition ? Nothing like "the sum of 2 continuous functions is continuous" ?
supple epoch
i think we've covered some of it, but as i said, im really behind😅
haughty coyote
The first thing to do is do get your head around the things you saw in class. Then when you have them in mind, you can move on to exercises to ingrain them and learn to use them
A subtle part of this is that every property for which you can say "according to the lesson" is one fewer thing that needs to be proven
supple epoch
which theories would be used for that question? cause the topic does overlap with other ones
haughty coyote
Theory of continuity. Here mainly the fact that continuity is preserved through summation. And potentially the fact that some usual functions are continuous, though that's not necessary.
This exercise is so elementary it wouldn't take much to do it from scratch, but as I've said, anything that's in the lesson doesn't need to be proven again
haughty coyote
which theories would be used for that question? cause the topic does overlap wit...
Also you should know all the other things already anyways because they're previous topics
obtuse pebbleBOT
@supple epoch Has your question been resolved?
timid silo
In ABC the segment CN is bisector of ACB, CNB = 70 ° and AN = CN. The measure of ABC is?
obtuse pebbleBOT
timid silo
(referring to 14.)
timid silo
If i had more figuring and less pain inside then maybe I'd already solved it
I don't understand
No matter what logic i try to apply to it
I don't see how i can get anything other than 70
devout solar
whats 180-70?
timid silo
70
devout solar
whats 70/2
timid silo
35
devout solar
whats 180-(35*2+35)
timid silo
180-70+35, 110+35= 145
devout solar
try again
timid silo
But how do i figure that out? You never gave me an explanation you just made me look dumb
💀
timid silo
why tf do you have ABVG as choises btw
Idk
Think about it from the standpoint from a primate such as myself
You just gave me a what.. 60 second quizlet until i got the answer without giving me any actual explanation besides showing me I don't know basic math
devout solar
ight so
the angle between 2 straight lines is 360
but we can use 180
we knew one angle so 180-70=110
and the 2 sides next to that angle were the same length so both of the base angles are the same
so 180-110=70
70/2=35
because CN bisects the angle we know that it's the angle next to CN times 2
so we have 2 of the 3 angles, 35 and 70
so 180-35-70=75
timid silo
Oh, makes sense could you help me on another few since i have an exam in a few hours
And im obviously not ready for it 💀
Im kind of picking this shit up as we speak since i haven't studied all year
Specifically haven't done geometry at all
devout solar
imma sleep
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
stray summit
Ijustmadethisupitis is a deadly disease which kills everyone it infects within one year and affects one in million people on average. The CDC has just announced they have developed a test for Ijustmadethisupitis that is known to be 99.9% accurate. If someone just tested positive for Ijustmadethisupitis what is the probability they actually have the disease?
obtuse pebbleBOT
Ijustmadethisupitis is a deadly disease which kills everyone it infects within o...
stray summit
Is it a 99.9% chance?
gilded needle
probably need to make precise what is meant by "known to be 99.9% accurate" - does this represent P(test says you have it | you have it) + P(test says you don't have it | you don't have it), or just P(test says you have it | you have it)
or perhaps P(you have it | test says you have it)
stray summit
probably need to make precise what is meant by "known to be 99.9% accurate" - do...
Not sure this is all the information that my teacher provided
I assume it would mean p(test says you have it)
gilded needle
that wouldn't make sense, the test is 99.9% likely to say you have it, whether or not you do?
my best guess is that it means P(you have it | test says you have it) = 99.9%, but I could be wrong
obtuse pebbleBOT
@stray summit Has your question been resolved?
stray summit
that wouldn't make sense, the test is 99.9% likely to say you have it, whether o...
Yeah that's what I thought it would be asw
Kind of a stupid question tbh
But thx
obtuse pebbleBOT
@timid moss Has your question been resolved?
obtuse pebbleBOT
@timid moss Has your question been resolved?
alpine karma
Can i help?
cursive jolt
Is the "standard matrix" the matrix in the canonical basis ?
Like in the basis $(1,0,0,0), (0,1,0,0), \dots$
warm shaleBOT
Twenty
cursive jolt
Or are you asked to give the matrix in the basis $\alpha_i$ ? 🤔
warm shaleBOT
Twenty
cursive jolt
Don't give the answer straight away, but rather explain it to him 👀
cursive jolt
Or you can just explain the answer you gave I guess
jaunty lotus
Is the standard matrix just the matrix that corresponds to the transformation?
cursive jolt
Actually it's okay you can show the answer and explain at the same time
Sorry didn't meant to mess with your response @alpine karma I'll let you explain, I'm leaving 😅
alpine karma
Is the standard matrix just the matrix that corresponds to the transformation?
Standard matrix is the matrix in which it's columns are the images of the basis vectors. @jaunty lotus
jaunty lotus
ah
alpine karma
Lemme know if this is correct or not 😅
alpine karma
Actually it's okay you can show the answer and explain at the same time
Sorry di...
Ooh it's fine :)))
Aaah
Lol only last column is correct
I have method but idk how they got this answer
Standard matrix(let A) = [ T(alpha1) T(alpha2) T(alpha3) T(alpha4) ]
Now we have to just put given values and values
alpine karma
Lemme know if this is correct or not 😅
Is my 1st 2 lines matches? T(alpha 1 )?
Elementary matrices, u mean- e1 = ( 1 0 0 0) ?
e2 = (0 1 0 0 ) ?
Similarly in e3 & e4... We will have one at 3rd and 4th place of a column
It will
obtuse pebbleBOT
@timid moss Has your question been resolved?
obtuse pebbleBOT
@timid moss Has your question been resolved?
cursive jolt
@timid moss are you still on it ?
timid silo
obtuse pebbleBOT
timid silo
I don’t even know how to approach this problem
nocturne sun
intersecting x axis means p(-4) = 0 and p(-2) = 0, intersecting y axis means p(0) = -24
timid silo
ah I see
nocturne sun
I think you'll mostly go off of the x intersections
timid silo
by find p(x) does it mean do something like p(x)=x^3 plus x^2 plus x plus 1?
like find the equation that'd make it intercept at all these points?
timid silo
I don't know how to do that?
is it just guess and check?
or is there a more elegant way of finding it
timid silo
eh its fine
I would take a lot longer than 10 minutes and I'm grateful that you've taken time out of your day to help a stranger
nocturne sun
I keep making a mistake somewhere
nocturne sun
but the general route should be:
- A cubic factors as (x + k)(ax^2 + bx + c)
- Because of 1) we can say that p(x) = (x + 4)(ax^2 + bx + c) where ax^2 + bx + c = 0 should have one solution (x = -2)
- Use p(0) = 24 to find whatever is remaining and expand p(x)
timid silo
um
high lily
consider factor theorem
timid silo
I just got to the functions unit of my algebra 2 textbook
I mean I'm halfway through it
I don't remember this showing up
should I know this by now?
high lily
factor theorem?
timid silo
what is that
nocturne sun
when you're solving some polynomial e.g.
x^2 - 5x + 6 = 0
what do you do? (no quadratic formula)
timid silo
just factor
high lily
if you've been given a question, usually you would've been taught the necessary skills
nocturne sun
just factor
exactly
timid silo
(x-2)(x-3)
nocturne sun
we have two solutions to p(x) = 0, they are x = -4 and x = -2, we can factor either (x + 2) or (x + 4) and the remaining part will be a quadratic
high lily
you're given all 3 zeroes
high lily
it's is however important to introduce a scaling factor/coefficient so that the curve passes through the given y-intercept
timid silo
how so?
It passed y at -24 x at 3,-2,-4
I didnt know you could reverse engineer a polynomial from the roots even though common sense says so 🤦♂️
Thank you very much
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
lament atlas
Abcd has 12 angles( sorry for my bad translation i don t know the name of a figure with 12 angles in english) i need to fimd how many anglee does pbcm has
obtuse pebbleBOT
Abcd has 12 angles( sorry for my bad translation i don t know the name of a figu...
lament atlas
My answer is 15 but i m not sure
obtuse pebbleBOT
@lament atlas Has your question been resolved?
lament atlas
I guess so
exotic anvil
anyone that is good or decent with R that can help me
obtuse pebbleBOT
anyone that is good or decent with R that can help me
cursive jolt
anyone that is good or decent with R that can help me
wdym
Oh, R the language ? I thought R the set of real numbers lol
obtuse pebbleBOT
@exotic anvil Has your question been resolved?
wintry prism
I need to solve this i really want answers rn my deadline is like an hour from now
obtuse pebbleBOT
I need to solve this i really want answers rn my deadline is like an hour from n...
wintry prism
also this
obtuse pebbleBOT
@wintry prism Has your question been resolved?
obtuse pebbleBOT
@wintry prism Has your question been resolved?
obtuse pebbleBOT
@wintry prism Has your question been resolved?
autumn tinsel
if for every natural number n the sum of the first n members of an arithmetic sequence is equal to 5n ^ 2-4n, then the product of the first three members of that sequence is equal to
obtuse pebbleBOT
if for every natural number n the sum of the first n members of an arithmetic se...
pine sail
Find the nth term of the sequence.
autumn tinsel
how?
teal prawn
Sum of n terms - sum of (n - 1) terms
pine sail
Exactly cause that difference gives you the nth term.
Like sum of first five terms would be
Sum of first second third fourth and fifth.
While sum of first four would be sum of first second third and fourth term.
Sun of five - sum of four terms gives you the fifth term. Hence, sum of n terms - sum of (n-1) terms gives you the nth term.
autumn tinsel
sorry but how i can get 5n^2 - 4n with that?
sharp crow
sorry but how i can get 5n^2 - 4n with that?
to find the first term of the Arithmetic Progression put n = 1 in 5n^2 - 4n
cuz sum of 1 terms is the first term
then put n =2 to find sum of first 2 and then from substract the first term to get the second term
and then put n = 3 to find the sum of first three terms and then substract the sum of first two terms from it to find the third term
and then multiply the first, second and third term which we found and that is your answer
obtuse pebbleBOT
@autumn tinsel Has your question been resolved?
autumn tinsel
to find the first term of the Arithmetic Progression put n = 1 in 5n^2 - 4n
ok thank you
i will do that
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
severe wyvern
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
spark magnet
obtuse pebbleBOT
spark magnet
help me pls
timid silo
we want something of the form $\frac{A}{x}+\frac{B}{x^2+2}$. Try putting that on a common denominator then comparing coefficients with the question
warm shaleBOT
Toby
timid silo
if I were doing that, I would expand $A(x^2+2)+(Bx+c)(x)$ out, then equate the coef of $x^2$ with $0$, coef of $x$ with $1$ and constant with $-4$
warm shaleBOT
Toby
timid silo
But substituting zero in should also work: it will give you -4=2A
spark magnet
alright, mind if i ask where you get -4 from?
timid silo
it's the constant of the LHS=x-4
spark magnet
i was tryna follow along this method
oh mb i’m not talking abt this
timid silo
it's the coefficient of the linear term $1\cdot x$
warm shaleBOT
Toby
obtuse pebbleBOT
@spark magnet Has your question been resolved?
gilded olive
Hello, I am currently trying to prove a limit using the epsilon delta definition of a limit. Neither epsilon nor delta is given, I am trying to build intuition about algebraically finding delta in terms of epsilon
Let f(x) = 2x+1
limit of f(x) as x approaches 1
So far I have:
|(2x+1)-3| < epsilon
|2x-2| < epsilon
|x-1| < (epsilon)/2
delta = (epsilon)/2
I'm mostly confused about how 3rd and 4th lines, I dont understand where delta is coming from
obtuse pebbleBOT
Hello, I am currently trying to prove a limit using the epsilon delta definition...
gilded olive
i didnt finish my bad
i have a specific question
coming up
oops
ok ill take a look at this soon my phone is bout to die
thanks
obtuse pebbleBOT
@gilded olive Has your question been resolved?
winter sparrow
Jacob and Joe play a game in which they take turns tossing a fair coin. The winner of a game is the first person to obtain a head. Jacob and Joe play this game several times with the stipulation that the loser of a game goes first in the next game. Suppose that Joe goes first in the first game. Find the probability that he wins the sixth game.
obtuse pebbleBOT
Jacob and Joe play a game in which they take turns tossing a fair coin. The winn...
timid silo
@devout solar you help them smh
devout solar
<@852256521986768957> you help them smh
Imma say that Jacob wins
obtuse pebbleBOT
@winter sparrow Has your question been resolved?
obtuse pebbleBOT
@winter sparrow Has your question been resolved?
fresh bramble
@winter sparrow
i mean i found this lolhttps://artofproblemsolving.com/wiki/index.php/1993_AIME_Problems/Problem_11
it actually makes sense
whoever goes first has a 2/3 chance of winning the game, and the 2nd player has 1/3 chance
which u can calculate using the sum of a geometric series
devout solar
so Jacob wins
fresh bramble
once you have that, getting the 6th game is easy
if first game probability is 2/3 for joe and 1/3 for jacob,
then probability for joe for second game would be (probability he wins first game )*1/3 + (probability he loses second game)*2/3
which is 4/9
and keep going from there
indigo bronze
@rich plover this optimization problem is killing me
obtuse pebbleBOT
<@403257113360728064> this optimization problem is killing me
rich plover
sry i cant help with that
indigo bronze
@silver ore you think you can help me with this problem
indigo bronze
sry i cant help with that
thx anyways
timid silo
aw this is so pretty
indigo bronze
fresh bramble
<@403257113360728064> this optimization problem is killing me
hey
i can help
what do u have so far
fresh bramble
lmaoo sorry im bored
indigo bronze
first time I seen people figthing to tutor cal
I don't know how to even get the equation to optimize
I am so lose in this optimization problem
timid silo
form a right angle triangle first
timid silo
fuck if i know this is hard
timid silo
obtuse pebbleBOT
hoary coral
do you know where (c, d) is on a sin function graph
obtuse pebbleBOT
@timid silo Has your question been resolved?
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@timid silo Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
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normal steeple
obtuse pebbleBOT
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@normal steeple Has your question been resolved?
tardy epoch
Need to find range of function
Multiply by the conjugate
normal steeple
And?
obtuse pebbleBOT
@normal steeple Has your question been resolved?
obtuse pebbleBOT
@normal steeple Has your question been resolved?
tranquil arch
$$\begin{aligned}
h(x) &= \sqrt{x^2+x+1}-\sqrt{x^2-x+1}\
& = \sqrt{(x+\frac{1}{2})^2+(0-\frac{\sqrt{3}}{2})^2}-\sqrt{(x-\frac{1}{2})^2+(0-\frac{\sqrt{3}}{2})^2}
\end{aligned}$$
warm shaleBOT
秋水
tranquil arch
set $P(x,0)$, $A(-\frac{1}{2},\frac{\sqrt{3}}{2})$, $B(\frac{1}{2},\frac{\sqrt{3}}{2})$, then
$$h(x) = |PA|-|PB|$$
warm shaleBOT
秋水
tranquil arch
$|AB|=1$ and $P$ cannot be on the line $AB$, so
$$| |PA|-|PB||<1$$
the range of $h(x)$ is $(-1,1)$
warm shaleBOT
秋水
hidden bronze
obtuse pebbleBOT
hidden bronze
i think im fkn stupid
how do i find the mode
oh
wait
its a straight fkn line
domain is 4
lol
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fading pollen
obtuse pebbleBOT
https://cdn.discordapp.com/attachments/978956143114211328/987321751291695104/99E...
fading pollen
how would you find the sum of a series without the n ?
warm canopy
Then they want the infinite sum
obtuse pebbleBOT
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red snow
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nocturne sun
I think it's a quadratic
so in the form ax^2 + bx + c
but I'm just going off of how the graph "looks"
maybe you have to go off of just the graph rather than make an equation?
red snow
sry what do u mean by that 😭
nocturne sun
I've never seen this type of problem tbh
nocturne sun
do u think i can just use a y=mx+c
that's the equation for a line
we don't have a straight line
red snow
ik but what else can i do 😭
timid silo
Hold up... Am I crazy or, can this be solved through literally the most basic Math ever?
Let me make a diagram of what I see
red snow
whaa
red snow
48
nocturne sun
yeah
timid silo
Literally just 6*9-3*2
48
...
Folks, sometimes in Math, all you need is a little creativity, not calculus
nocturne sun
I think it's a quadratic
I wonder if my guess was correct though
even by pure chance
red snow
can't believe it
timid silo
Hold up, I'm starting to doubt my own ability to do Math...
You need to find your own help channel
nocturne sun
you can google but it's basically completing the square
timid silo
red snow
ok thanks so much y'all 🙏🙏
timid silo
Next time try to visualize the problem first before doing it
nocturne sun
Folks, sometimes in Math, all you need is a little creativity, not calculus
the next step is proof by intimidation to make your visual & creative proof rigorous
timid silo
Uhm... This is not what these channels are for, but I recommend the Texas Instrument
obtuse pebbleBOT
kind cobalt
Too many channels sorry i Got confused
timid silo
Happens
kind cobalt
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Available help channel!
hollow epoch
Q9and Q10
somber mural
what have you tried?
hollow epoch
the equations for the graphs in q9 is
5sin(theta-0.64 rads)
root(13)sin(theta-0.98 rads)
idk what to plot on the x axis for the first equation for example, ik its translated to right by 0.64 rads and amp is 5 how do i go from there
hollow epoch
yes
somber mural
ok look at the values it intersects x axis
then shift them by 0.64 rads as you said
then draw the graph with a larger amplitude
hollow epoch
normal sine graph one period is 2pi right
somber mural
yes
somber mural
wdym?
somber mural
just draw it starting at 0.64 rads
rather than 0
everything is shifted right
the period hasn't changed
hollow epoch
could u draw it for me lol
somber mural
nope
hollow epoch
what do i write 0.64 rads on the x axis and start it there?
somber mural
yes
might be helpful to plot all major points first
then draw
so plot coordinates that it crosses x axis
maxima
minima
then draw
hollow epoch
so major points aka (pi/2, 5) as max, (3pi/2, 5) as min, and then pi as middle of period and 2pi as period
somber mural
everything is shifted by 0.62 rads
the entire graph
not just where it crosses x axis
so max is no longer at pi/2
somber mural
estimates?
hollow epoch
i plot for example pi/4,pi/2,3pi/4,pi etc. and just put the 0.64 translation roughly within that scaling
i dont put 0.64 rads on x axis for scaling
somber mural
ok
hollow epoch
is that what u would do
im just confused on how to plot 0.64 rads wioth everything its very specific
somber mural
use a scale
just like how you would plot a normal sine graph
but shifted
if you can't maybe use desmos to help
hollow epoch
never used desmos before
how do u get the scaling with normal graph so pi and 2pi on x axis
somber mural
in desmos?
hollow epoch
yes
hollow epoch
ok thats fine
hm idk i guess ill skip for now i drew it but looking ood
odd
.close
obtuse pebbleBOT
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sage furnace
Formulate the appropriate null and alternative
hypotheses for each research problem. Determine the type of
alternative hypothesis formulated and the classification of a
statistical test of the hypothesis.
- A survey claims that the proportion of people who regard global
warming as a serious problem is 60%.
obtuse pebbleBOT
Formulate the appropriate null and alternative
hypotheses for each research prob...
@sage furnace Has your question been resolved?
worldly lark
um Hello
its a question on logarithm and I have no idea how to even start solving this
obtuse pebbleBOT
um Hello
its a question on logarithm and I have no idea how to even start solvin...
summer spire
looks interesting will give it a try
slim lake
um Hello
its a question on logarithm and I have no idea how to even start solvin...
Maybe use the fact $e^{log(x)}=x$
warm shaleBOT
Max..
night fox
um Hello
its a question on logarithm and I have no idea how to even start solvin...
Ooh, lemme gib a try.
night fox
um Hello
its a question on logarithm and I have no idea how to even start solvin...
Take all ratio equal to some constant, k.
slim lake
think it is 1
summer spire
you dont need to make it a constant
worldly lark
think it is 1
yes
night fox
Providing hint is obviously better than giving a solution.
worldly lark
Take all ratio equal to some constant, k.
I tried that
but what after that
hmm
let me try again
night fox
Using base as 10 instead of e doesn't make any changes right?
summer spire
yeah shouldnt, as long as its a change of base rule
night fox
Mhm alr
slim lake
Trust me you don't need to do any of this complicated stuff
use a basic fact as I said above, this allows you to include log a,log b ext. which is part of the useful information they expect us to use. Then it's all about manipulating and simplifying
and you'll realise something quite nice
summer spire
Trust me you don't need to do any of this complicated stuff
thats also a nice appraoch :)
obtuse pebbleBOT
@worldly lark Has your question been resolved?
worldly lark
Solved it!
using the constants method
worldly lark
use a basic fact as I said above, this allows you to include log a,log b ext. wh...
I tried this
but couldn't solve it
Anyways, thanks a lot!
obtuse pebbleBOT
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glacial gale
is there a way to find the value of theta if u know already its cos?
obtuse pebbleBOT
is there a way to find the value of theta if u know already its cos?
fresh bramble
yes
but there are infinite answers
because cos(x) is perioidic every 2 pi
you have to use cos^-1(x) on ur calculator, which will spit out an answer between 0 and pi
and then if you have more context and know which quadrant the angle is in, you may need to do a slight transformation
rough stratus
is there a way to find the value of theta if u know already its cos?
Something called inverse functions may help you.
glacial gale
because cos(x) is perioidic every 2 pi
I dont get why its periodic every 2pi
the function is f(x)=cos x
rough stratus
I dont get why its periodic every 2pi
It is like a wave pattern
Go to a graphing website and graph cos x
It will look like a wave
fresh bramble
I dont get why its periodic every 2pi
how come you don't get it?
tbh, that's kind of just a definition
rough stratus
Try explaining in degrees.
fresh bramble
true
rough stratus
Instead of radians.
fresh bramble
I dont get why its periodic every 2pi
cos(x) is defined as the x value on a unit circle as you move around from 0 degrees all the way back to 360 degrees
do you understand now , why it is periodic over 2 pi (360 degrees)
fresh bramble
yes exactly
2 pi=360 degrees
1 pi = 180
3 pi is the same as 1 pi
just like 540 degrees is the same as 180 degrees
glacial gale
ok I understand
glacial gale
the function is f(x)=cos x
so this function works like this
from a value of an angle
u get a cos for that angle
but how did people find the x value?
i.e the cos
?
like u have an angle
72⁰
and u don't know the adjacent
how do u find the cos?
obtuse pebbleBOT
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eternal bloom
yes, but -15 = 32 mod 47
summer stone
.close
fresh sequoia
1
obtuse pebbleBOT
@fresh sequoia Has your question been resolved?
balmy tapir
Hi.
balmy tapir
I have to find x from this:
gritty island
do trig
arctic tartan
yes
balmy tapir
then?
gritty island
12cos(60)=x
arctic tartan
polar kettle
you actually dont need that 30 degrees just do cosinus
arctic tartan
he probably dont know trigo
balmy tapir
i know trigo
but we just learn simple things
about trigo
which means im very simpleknowledge on trigo
gritty island
yh use the adjacent and hypotenuse
arctic tartan
use that
balmy tapir
cos = hypotenuse / x which means cos = 12/x => cos(60) = 12/x = > cos(60)/12 = x
right?
polar kettle
cos (60) * 12 because its cos 60 = x /12
polar kettle
6sqrt(3) is the bottom one
you need
x which is 6
cos 60 = 0.5 and 0.5 / 12 is 6
balmy tapir
may u just tell me why we using 60 degrees when we are finding the bottom side?
shouldnt it be 90?
polar kettle
we are? i mean the x is defined for the left side
balmy tapir
Yea, but when we did the calculation, we actually find the bottom side(adjacent)
then the left side
polar kettle
no we dont we find x because cosinus is adjacent side over the longest side and sinus is opposite side over the longest side
adjacent side for cos 60 degrees is x
obtuse pebbleBOT
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rain coral
obtuse pebbleBOT
rain coral
I don’t rly get how I can find the domain and range
so do I find the range of the normal function
and find range of inverse?
so domain would be anything but 3 and range would be >-1
actually I know now
.close
obtuse pebbleBOT
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rocky cosmos
The number x is somewhere between the numbers 17 and 23 x is p% greater than 17 and p% less than 23. Determine x
obtuse pebbleBOT
The number x is somewhere between the numbers 17 and 23 x is p% greater than 17 ...
willow ravine
Write out what you just said:
Here is part of it: x = 17 + (17*p)
x = 23 - ...
Then set those two equations equal to each other and solve for p.
rocky cosmos
@willow ravine
$\begin{gathered}17+\frac{p}{100} \times 17=23-\frac{p}{100} \times 23\ \underbrace{17}{-17} +\frac{p}{100} \times 17=\underbrace{23}{-17} -\frac{p}{100} \times 23\ \frac{17p}{100} =6-\frac{23p}{100} \ \underbrace{\frac{17p}{100} +\frac{23p}{100} }_{\frac{17p}{100} +\frac{23p}{100} =\frac{43p}{100} } =6\ \frac{43p}{100} \times 100=6\times 100\rightarrow 43p=600\rightarrow \frac{43p}{43} =\frac{600}{43} \rightarrow p=\frac{600}{43} =13,953\end{gathered}$
warm shaleBOT
AuHasard
willow ravine
So, P = 13.953 % now use your two equations of what x equaled and plug in p.
rocky cosmos
?
$x=17+\frac{p}{100} \times 17\rightarrow x=17+\frac{13.953}{100} \times 17\rightarrow x=19,37201$
warm shaleBOT
AuHasard
willow ravine
Actually, I see the mistake.
P is already the percent value so there is no need for you to divide by 100.
So try this:
17 + 17P = 23 - 23P
Solve for P and then plug P back into for x and this should give you the correct answer.
obtuse pebbleBOT
@rocky cosmos Has your question been resolved?
obtuse pebbleBOT
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timid silo
can someone confirm me if this is correct please?
obtuse pebbleBOT
can someone confirm me if this is correct please?
timid silo
the exercise is as follows:
consider the four points A, B, C, D in space (the coordinates are in the image). determine the point P on the line CD for which the sum PA^2+PB^2 is minimal
HAELP
lethal sand
yes it is correct
obtuse pebbleBOT
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proud coral
Hello !!
visual onyx
just ask
proud coral
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