so many ppl, i dont even know who asked that lol
#help-33
thorny jungle
spark canopy
yeah i got it correct, thanks for the help!
marsh citrusBOT
@spark canopy Has your question been resolved?
opaque wolf
.close
placid gate
5-14x=4(3-7x)+7
marsh citrusBOT
5-14x=4(3-7x)+7
opaque wolf
So we gotta get x to one side
thorny jungle
expand right hand side..
placid gate
how
thorny jungle
what do u get
placid gate
so 4x3 and 4x7x
thorny jungle
7x, not 7
placid gate
okay
elfin berryBOT
Kurama
thorny jungle
what do u get,,
thorny jungle
how did u get that?
thorny jungle
5-14x=12-28x+7
ok, how about moving everything to the right hand side
placid gate
what
placid gate
OK
still temple
Then you can figure out the constant terms
thorny jungle
^your goal is to isolate for x. So write it out like x = something...
thorny jungle
do you see how -14x and 14x cancels to 0?
thorny jungle
ok...
on a number line
if you move 14 steps forwad
and 14 steps backwards
you didnt move
right
assuming you started at 0
thorny jungle
i cant tell if u are being sarcastic lol
placid gate
im not
i actually find that helpful thanks
im learning math in another language so it quite hard for me to understand what the teacher is talking abt
thorny jungle
okok,, anyways, you see the left hand side would just be 5, right?
placid gate
yes
thorny jungle
so you have 5=12-28x+7+14x
now, if you subtract 5 from both sides
you have 5-5=12-28x+7+14x-5
agree?
then the 5's cancel out
so you have 0=12-28x+7+14x-5
right?
placid gate
OH SO THE LEFT HAND SIDE IS TO DISTRIBUTE?
thorny jungle
are you convinced?
placid gate
okay
thorny jungle
again, think about that analogy
placid gate
where'd the - come from
placid gate
again, think about that analogy
YEAH LIKE WHAT WE DID WTH 14
thorny jungle
yeah.
placid gate
where'd the - come from
?
thorny jungle
-?
thorny jungle
we want to move everything to the right hand side of the equal sign
placid gate
does this method work on none distributive equations??
placid gate
to get 0 = 12 - 28x + 7 + 14x - 5
alr alr
thorny jungle
does this method work on none distributive equations??
what is none distributive equations?
placid gate
nvm lets continue
placid gate
to get 0 = 12 - 28x + 7 + 14x - 5
what now
thorny jungle
we did the exact same thing with the 14x
thorny jungle
so we do it again with the 5
thorny jungle
think of the terms with "x" and the terms without "x" as two types of objects
placid gate
okay
thorny jungle
and the rule is that different objects cannot be added, subtracted, multiplied, or divided
placid gate
yes im aware
placid gate
add 28x and 14x
placid gate
okay
placid gate
subtract
placid gate
-14
placid gate
i forgot abt the - sos
thorny jungle
0 = 12 - 28x + 7 + 14x - 5
placid gate
ill rewrite?
thorny jungle
0 = 12+7-5-14x
placid gate
ok
thorny jungle
ignore the -14x
placid gate
yes
thorny jungle
0 = 12+7-5 -14x
placid gate
wait
thorny jungle
what terms are you working with
placid gate
the ones without the x
thorny jungle
and they are?
placid gate
so 0=14-14x
placid gate
and they are?
12+7-5
thorny jungle
right
now, you are so close
you need to somehow isolate for x
can you see a way to do that?
thorny jungle
put what to the other side?
I agree with your idea
but you just need to be more specific
placid gate
14x=14 ?
placid gate
okay
thorny jungle
now. how do you isolate for x?
placid gate
how
thorny jungle
you have x multiplied by 14 on left hand side of the equality, right?
but you just want x to be alone, like x = something
so how do you get x to be alone?
thorny jungle
whats the opposite of multiplication
thorny jungle
do you see, on left hand side, its $14 \times x$?
elfin berryBOT
Kurama
thorny jungle
why 2>
placid gate
idk i saw my teacher do it
placid gate
oh yeah
thorny jungle
so i agree you have to divide by something to get the x by itself
placid gate
ok
thorny jungle
what is that something
placid gate
14?
placid gate
14/x ?
placid gate
okay
thorny jungle
what do u have
thorny jungle
so whats the answer
placid gate
oh
thorny jungle
it has to be 14
placid gate
okay !!!
placid gate
thank you sm !! i hope i'll remember all of this later on !!
granite crystal
@placid gate if you’re done with the page, please close it
granite crystal
.close
thorny jungle
It was closed
placid gate
ok
granite crystal
ye,
thorny jungle
Close it again…
marsh citrusBOT
Available help channel!
ebon karma
Excuse me ,may I know what is the ans of these two ?thanks
marsh citrusBOT
Excuse me ,may I know what is the ans of these two ?thanks
@ebon karma Has your question been resolved?
marsh citrusBOT
@ebon karma Has your question been resolved?
sleek crater
elfin berryBOT
geoxcaliber
sleek crater
Apart from it being a quadratic equation
If you were solving for x
I don't see why you wouldn't do just 12 = x
Another question:
elfin berryBOT
geoxcaliber
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
sleek crater
Why does $$\frac{\sqrt{5}}{\sqrt{m^2}}$$
elfin berryBOT
geoxcaliber
elfin berryBOT
geoxcaliber
sleek crater
with the m^2 remaining inside the radical
but the x^2 in question 17 go out of the radical?
bright jay
Stop opening multiple channels @sleek crater
sleek crater
I thought it would be easier to separate my questions
theres plenty available anyway
bright jay
theres plenty available anyway
Still, even if you have multiple questions, you don't open multiple channels
sleek crater
Ok
bright jay
So go ahead and close one of the channels
sleek crater
Can you confirm my question in the other channel
grim bluff
12=x^2-x, than x=12 isn't the answer
marsh citrusBOT
@sleek crater Has your question been resolved?
sleek crater
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
copper granite
How do I figure out the volume of a cone?
marsh citrusBOT
How do I figure out the volume of a cone?
novel fjord
do you know the formula
marsh citrusBOT
novel fjord
if you don't want help don't ask for it lmao
copper granite
I just don’t want help from you
novel fjord
i literally just said you should review basic algebraic notation 
marsh citrusBOT
Available help channel!
warm bone
Two bags have 4 white and 5 black balls. At random we take 2 balls from 1st bag to the second one.
What is the probability that we'll take 1 ball from the 2nd bag and it will be white?
Let's say we have pulled a white ball. What are the probability that in the second bag we put 1 white and 1 back ball?
so for the first question I got 120/1331
and for the second I got 5/18
are they correct?
marsh citrusBOT
Two bags have 4 white and 5 black balls. At random we take 2 balls from 1st bag ...
@warm bone Has your question been resolved?
warm bone
<@&286206848099549185>
vital fog
Two bags have 4 white and 5 black balls. At random we take 2 balls from 1st bag ...
could you show your method behind those two values?
vital fog
okay let's work on that first
warm bone
and these numbers is what I got when looking for a probability of each instance after the 2 balls were moved from 1st bag to the 2nd. So 2w - 6/11 2b - 4/11 1w1b - 5/11
ok
vital fog
and these numbers is what I got when looking for a probability of each instance ...
right that's a good direction, but there are two things missing: one is why you multiplied them together, and the second is that you didn't consider the probabilities of drawing two balls (2w, 2b, 1w1b, 1b1w) from the first bag
warm bone
I don't think it matters in which order you draw the 1:1 balls,
why would it, it's the same result and same probability
and for multiplying part, I am not sure, I think I saw somewhere that you do it like that when you want to find the chance of every possibility, without having all the concrete details. So... since with the pulling of 2 random balls, we only know exact number of total balls in the bag, but not how their variation changed after the instance. Like we know there are 11 now, but we don't know how many black or white exactly
vital fog
okay well first let's consider a simpler case
warm bone
ok
vital fog
let's work out the probability of picking up a white ball from the second bag AFTER randomly picking and moving two black balls from the first bag
warm bone
ok
vital fog
breaking it down, I'm asking for the prob of picking two black balls from bag1 AND picking a white ball from bag 2
does that make sense?
vital fog
perfect
and when we combine these two, we multiply them
that's because of the AND I wrote earlier, since they must happen together for our desire outcome to happen
that gives 10/99, I believe, which is the probability of picking up a white ball from bag 2 after randomly picking and moving two black balls from the first bag
vital fog
exactly, except you have to be careful
there's actually three more options
if you work out the probabilities for 1b1w, it's different to 1w1b
that's because there are an uneven number of white and black balls in the bag (4 vs 5)
warm bone
i'm pretty sure they're the same, but I'll run it
vital fog
sure
warm bone
there might be uneven number, but both instances take 1 of each
vital fog
you know what, I apologise, you're right
vital fog
let's see?
warm bone
for 2 whites - 1/6 ; 6/11 ; 1/11
1 white 1 black - 5/18 ; 5/11 ; 25/198
that's all for now
vital fog
looks good, but we do still have to consider the fact that we can pick either 1 white then 1 black or 1 black then 1 white
although the probability is the same, there are two permutations in that case
so the chances of picking 1 white and 1 black (regardless of order) from the first bag should be 5/18 * 2 = 5/9
warm bone
that got me stumped tbh, I wasn't sure if it was needed because it doesn't specify that white has to be the first ball
vital fog
yeah it's confusing when we have to consider different arrangements within a case
but a good sanity check for this is to consider the different cases when drawing from the first bag (BB: 5/18, WW: 1/6, WB 5/18, BW: 5/18) and seeing that they sum to 1, which makes sense as those four make up all the possible actions you can take
warm bone
oh yeah
vital fog
so now do you know what we can do with all these probabilties?
warm bone
so, now we have 'What is the probability that we'll take 1 ball from the 2nd bag and it will be white?' cleared yes?
What about the 'Let's say we have pulled a white ball. What are the probability that in the second bag we put 1 white and 1 back ball?'
vital fog
just to check, what's your final answer for the first part?
dry trail
If we consider that the 2 balls are taken one at the time, the event "the two balls pulled are white and black" is the union of events "the first ball pulled is white and the second is black" and "the first ball pulled is black and the second is white", and you are then applying the formula for the probability of union of events
Just as an additional note, if it can be helpful to you
warm bone
25/99?
vital fog
25/99?
not quite, that's the probability of moving 1 white and 1 black, then picking 1 white from the second bag
warm bone
If we consider that the 2 balls are taken one at the time, the event "the two ba...
not in this case no, there are such problems where it specifies "one after another" in this one it just says "take 2 balls", but I'll keep it in mind for those later on
do we multiply 1/11 5/11 and 6/11?
vital fog
not in this case no, there are such problems where it specifies "one after anoth...
Mat is correct here, he specifies that in the case of "take 2 balls", it's simply the combination (union) of the two cases where we pick "one after another"
warm bone
then I did not understood what he was trying to say, sorry, language barrier
dry trail
But nevermind, if what I said only confuses you leave it aside
Go on with the exercise
vital fog
do we multiply 1/11 5/11 and 6/11?
remember earlier how I said that we multiply when we need the events to happen together for our desired outcome? ie. AND
in this case we sum the probabilities, since each event individually lead to the desired outcome of picking one white ball out of bag 2
ie. OR
warm bone
wait now I got it. it's because you can pull 1w1b or 1b1w and even though they are statistically the same, they're technically different, that's why we multiply the answer of one by 2
(it's for what mat was saying) ^^
vital fog
actually I didn't notice, where did those three numbers come from
warm bone
nvrm, I looked at the wrong page
warm bone
sooo, 4/9?
warm bone
wait... how can it be 4/9 if there are 11 balls in the 2nd bag?
4/9 is the answer to the 1st one right?
dry trail
I get 4/9 as well
vital fog
wait... how can it be 4/9 if there are 11 balls in the 2nd bag?
the probability of drawing a white ball doesn't solely depend on the second bag, it doesn't have to be a fraction with 11 in the denominator (if that's what you're looking for)
I'm not very sure how to explain this
warm bone
well... if it doesn't have to be, then I guess it's fine
I understand that it doesn't have to be, but it just doesn't bode well, maybe in decimals it feels better
vital fog
think of it as a 44.4...% chance you'll get a white ball after this juggling act
on to part 2?
warm bone
yes
vital fog
are you familiar with conditional probability
warm bone
no
vital fog
this'll be a toughie, let me sketch something that might help then
warm bone
but wait, didn't we already found the probability of us putting 1 white and 1 black ball into the 2nd bag? wasn't it 5/9?
vital fog
that's right
but there's additional information: the fact that we pulled a white ball from bag 2 afterwards
warm bone
oh yeah, it didn't mention returning it
warm bone
but then why does it change the probability? actually, I'll wait for you to finish sketching it up
vital fog
I'll try to give you a textbook example of conditional probability to get you thinking: say I either walk or take the bus to school. On a clear day, the probability of me walking is 80%. On a rainy day, the probability of me walking is 10%. And let's say that the probability of any day raining is 20%
let's say I told you I took the bus today, and asked you for the probability of it having rained this morning, you'd say that the probability must be higher than 20% right?
warm bone
isn't it 2%?
vital fog
don't do any calculations just yet, just think about it intuitively
if I took the bus, you might assume that it rained since it's so unlikely for me to take the bus otherwise (100%-80%=20%)
but why would you assume that it rained? especially since the probability for rain is so low? it's because you have extra information: the fact that I took the bus
so that effectively 'updates' the probability of it having rained that specific day (in this case raising it to about 47%)
warm bone
well yeah, because it's not guaranteed that you took the bus BECAUSE it rained, there's still 20% chance that you'll take the bus any other day
vital fog
but that's relatively unlikely, so mentally you'd go to the more likely option of me taking the bus because it was raining
warm bone
ok, yes, as if it rained, taking bus would be 90% right?
vital fog
conditional probability considers these types of problems, as if explaining why the numerically less likely option of it raining (20%) is actually the 'intuitively more likely option'
I'm not quite sure why I'm attempting to teach this topic, it's very broad and you might be better off looking for other resources
let me know if you just want me to give you a step by step to part 2 of your problem and you can take a look after learning a bit more about the topic
warm bone
let's get back to the problem, seeing numbers interact with one another will make it easier to understand
elfin berryBOT
dino
vital fog
the left side can be read as "the probability of A given B"
eg. the probability of it raining given I took the bus, or the probability of moving 1W1B given I drew a white from bag 2 after
warm bone
ok
vital fog
are you familiar with the symbols on the right side?
warm bone
well P stands for probability but, not sure about the arc, is it A to B?
vital fog
it translates to A intersect B, effectively the probability of A happening AND B happening
warm bone
alright, got it
vital fog
so let's apply this to our case
$P(\text{moved 1 white and 1 black}|\text{drew a white})\=\frac{P(\text{moved 1 white and 1 black AND drew a white})}{P(\text{drew a white})}$
hmm..
elfin berryBOT
dino
vital fog
not quite sure what was wrong but I'll just keep it on two lines
could you find the respective probabilities for our fraction?
warm bone
let me think
vital fog
take your time
warm bone
wait, the A|B part I don't need to find do I?
vital fog
the P(A|B) part is the answer we're looking for
the right side is how we'll get that answer
warm bone
ok, that's what I thought, but picture confused me
vital fog
my bad my bad, texit doesn't like long equations
vital fog
it was more correct before the edit, remember that AND is multiply
vital fog
but you can think about the numerator more simply, the probability of moving 1 white ball + 1 black ball to bag 2, and then drawing a white ball from that bag
which would be 2 * 5/18 * 5/11, as we worked out earlier right? When we were doing cases
warm bone
oohhh ok, yes
vital fog
so what would the fraction be?
warm bone
it's the pulling of 1w1b and then probability to pull a white from a 2nd bag with +2 balls
vital fog
which would be 2 * 5/18 * 5/11, as we worked out earlier right? When we were doi...
yup, that's this right
vital fog
**dino**
but I meant what would our P(A|B) be now that we have the individual probabilities
warm bone
wait, no, maybe I still don't get it after all.
vital fog
it's the pulling of 1w1b and then probability to pull a white from a 2nd bag wit...
here you're describing the probability in the numerator
the P(moved 1 white and 1 black AND drew a white)
warm bone
well yeah, I get that, but having the P(drew a white) denominator, makes it a 5/9 no?
ok wait, step by step
P(moved 1 white and 1 black AND drew a white) is 5/9 * 5/11?
then P(Drew a white) is 5/11
vital fog
ah I see the confusion, the drew a white in the numerator is not quite the same as the drew a white in the denominator - I should've specified when I wrote the equation
the one at the top is specifically considering the case where we move 1w1b then draw a white, the one on the bottom is simply "the chance of drawing a white ball from bag 2, without any knowledge of how we moved balls from bag 1"
warm bone
yes
vital fog
notice how the numerator is a sub-case of the denominator? that's kind of how you can intuitively make sense of the P(A|B) formula I gave you. It as if after receiving the additional information, our space of all possible events was shrunken to only the ones were we draw a white ball at the end - that becomes our denominator
and our numerator is the specific case that we're looking for, within that new shrunken possibility space
if that doesn't make sense no worries, you'll certainly have a chance to cover conditional probability more formally than within a discord channel
very very important concept in applicational statistics
warm bone
don't know what that means but it sounds threatening
ok, so the part two answer is 25/44 right?
vital fog
correct
warm bone
ok, just wanted to make sure, it was over.
vital fog
^^
warm bone
well I have another problem, but it is different from the previous, though still in the realm of statistics
if you're able, I'd like some help with it too, but I understand if you're tired
vital fog
it'd be best if you start another channel in case I can't help - it'll be easier for other helpers to find
warm bone
ok, well, still, much appreciate the help, thank you for your time and have a beautiful day.
vital fog
not saying I'll leave without taking a look at least~ I'll help if I can
warm bone
oh, well, should I post it here then and then delete if you can't help?
vital fog
no no, just post it in a new channel so the bot'll pin it
rigid canyon
if you have an exponential equation that looks like this $f(x)^{g(x)}=f(x)^{h(x)}$, one of the things you need to do to solve it is to make the $f(x)=-1$ where both exponents have to be either even or odd numbers. What if one of the numbers is 0 and the other even? Is it valid?
marsh citrusBOT
if you have an exponential equation that looks like this $f(x)^{g(x)}=f(x)^{h(x)...
elfin berryBOT
hyperlix26
proven timber
0 is even, so both exponents are even in that case
dense crater
marsh citrusBOT
dense crater
Given that a,b,c are positives
So I proved that the inequality is equivalent to $a^2+b^2+c^2>bc+ca+ab$
elfin berryBOT
Trenton
dense crater
What can I do next?
In order to conclude the inequality is valid for positive numbers a,b,c
odd ingot
odd ingot
wouldn't have thought of it if I didn't know it was an absolute inequality from the start
dense crater
marsh citrusBOT
dense crater
I tried my best to factorise the term
But I still cant draw a proper conclusion
Can anyone help me
coral hazel
I assume your numbers need to be positive
Given this, have you heard of the AM-GM inequality?
If you haven't we'll need to do this a different way
marsh citrusBOT
@dense crater Has your question been resolved?
dense crater
I assume your numbers need to be positive
Yes sorry I forget to mention
coral hazel
Start from $a^2b + a^2c + b^2a + b^2c + c^2a + c^2b$
What happens when you apply AM-GM directly?
elfin berryBOT
Camilleone
coral hazel
Sorry i typoed
dense crater
What happens when you apply AM-GM directly?
Ok
dense crater
That is enough hints
Thx a lot
I will try
Nice I proved it successfully
Tysm guys!!!
.close
prisma owl
Claim
low star
It looks like the domain is x => 5
vestal bison
marsh citrusBOT
buoyant stone
ok
what is the the value of y at the x intercept
what is the value of x at the y intercept
vestal bison
(5,-3) ?
vestal bison
.close
marsh citrusBOT
buoyant stone
shortest help session ever lmao
buoyant stone
no wait for it it'll go away
it doesn't say reopened again so no problems on your end
rigid canyon
do i need to do .close again or something
no
marsh citrusBOT
Available help channel!
still temple
So i have two questions
marsh citrusBOT
So i have two questions
still temple
In geometry
First one is
how many degrees is an equal angle if the sum of its two adjacent angles is 320 °
And second one is
the difference of the angles alpha = 80 ° and beta = 32 ° 50'20" is:
Idk how to solve eithrr
Either
weak hatch
Can you post an image to the full question? There seems to be information missing.
still temple
Which one
Also im afraid I can't due to the fact, the question is in Bulgarian since that's my home language
@weak hatch
Which one is missing
weak hatch
Can you post it anyway? If there are diagrams it would be more clear.
weak hatch
For the second one, you probably want to convert beta from dms to a decimal degree, then subtract, and then convert back to dms. I dont understand what the first is asking
,rotate
elfin berryBOT
still temple
the difference alpha-beta of the angles alpha = 80 ° and beta = 32 ° 50'20" is:
This is the second one
,rotate
elfin berryBOT
weak hatch
Can you translate #2, since the translation you gave above doesnt seem to make sense.
still temple
Can you translate #2, since the translation you gave above doesnt seem to make s...
how many degrees is an equal angle if the sum of its two adjacent angles is 320°
weak hatch
Ive never heard of an equal angle before.
still temple
Hmm...
Perhaps im using the wrong term
Due to the fact im translating it literally
I think it means
Straight angle
Im not completely sure though
Since there is no graph
weak hatch
straight angle usually refers to an 180 degree angle, so I dont think thats it
still temple
Oh no nvm it means
Right angle
I believe
Those are the two possible ones
I can think of
weak hatch
Still, a right angle is always 90 degrees. Neither of them would be 20 degrees
still temple
Yeah it means
Straight
I just figured it out
Idk
<@&286206848099549185>
I figured out how to solve
The second one
marsh citrusBOT
@still temple Has your question been resolved?
still temple
ok good, how did you figure it out?
320 degree one
I still dont understand the first one
weak hatch
Do you know how to convert an angle from degree minute second to a decimal value?
weak hatch
Basically, you want to take the degree part, add the minute part divided by 60, and then add the second part divided by 3600
still temple
Basically, you want to take the degree part, add the minute part divided by 60, ...
So how do i do this
With my problem
?
And if so will it solve it
weak hatch
$d^om's'' = d+\frac{m}{60}+\frac{s}{3600}$
elfin berryBOT
opfromthestart
still temple
Actually
I think this problem
Will be easier for u
Since its graphed
"if AD || CE and CD || BE, then the size of >BAD is:"
Wtf
It deleted the stuff
weak hatch
use \ before the |
still temple
"if AD || CE and CD || BE, then the size of >BAD is:"
weak hatch
So since CD and BE are parallel, you can say that DCE=BEC.
weak hatch
And basically you can make a triangle out of the three angles on the outside, and solve it from there
still temple
Can u show me?
weak hatch
So, since CD is parallel to BE, the two angles formed by them being intersected with EC are the same, so BEC is 40 degrees
And since AD is parallel to CE, you can kinda make up a triangle where the angles are 40, x+20, 2x, and since it is a triangle the angles must add to 180, and then you solve it from there
weak hatch
That basically was the rundown, im just not sure on how to actually do some of the steps
weak hatch
Ill try
still temple
After making the triangle
weak hatch
Because of the parallel parts, you can say that certain angles are the same. I created a point f that completes a triangle, and you can use parallel lines to say that that angle is equal to 40 degrees, and then use traingle equation
weak hatch
you solve 40+x+20+2x=180
weak hatch
Yes
nocturne flicker
hello
nocturne flicker
this is my question, and info:
im sruck on the red ones
for b), 0 to the infinity i put 0 to correct that
and but im not sure for f)
since symbolab also says its 1
these are the answers to choose also
.close
tiny elk
I'm trying to find DEF's area
marsh citrusBOT
I'm trying to find DEF's area
graceful gust
ohh i think that would be easy
Angle FCE=120 degrees
apply cosine law ro triangle FCE
find side EF
and hence find the area
tiny elk
it should be doable without it.
graceful gust
maybe lemme think
maybe someone else would be there who could do it
well it turns out we can do it without cosine law but we would have to do some constructions and what i would be doing is basically proving cosine law and using it
and it would basically look like i didn't use cosine law👀
sorry maybe someone else can do without that
tiny elk
doesn't but thanks
echo moat
Im sorry i could do that with the (1/2)ab sin A to find the area but ig you havent done that too right?
tiny elk
yes
echo moat
Oh ok
tiny elk
no sine and cosine
untold herald
Yes
tiny elk
perfect
tiny elk
bruh
tiny elk
constructed an equilateral triangle with side length 4
still temple
my bad
tiny elk
well, I get the same result I would be getting if I used cosine law
still temple
well, I get the same result I would be getting if I used cosine law
i think u need to do the demonstration of the cosine law
still temple
u did it?
tiny elk
by constructing an equilateral triangle here
using pythagorean theorem to get the hypothenuse and just find the area and perimeter
so thanks for the help
.close
marsh citrusBOT
tiny elk
ty ahahah
marsh citrusBOT
Available help channel!
light swift
would the answer to A also be the mean for B?
marsh citrusBOT
would the answer to A also be the mean for B?
light swift
dont question my answers
my brain died
the black pen is the correction i got
nvm in got it
.close
marsh citrusBOT
marsh citrusBOT
@onyx sorrel Has your question been resolved?
quaint arrow
Can someone please help me with this problem? I got the answer by using my calculator but I am supposed to know how to solve this problem without the use of a calculator
marsh citrusBOT
Can someone please help me with this problem? I got the answer by using my calcu...
quaint arrow
if you can ping me if you can help me that would be great
plush elk
The derivative of ( integral of f(t) , t from g(x) to h(x) ) in terms of x =f(h(x))h’(x)-f(g(x))g’(x)
quaint arrow
The derivative of ( integral of f(t) , t from g(x) to h(x) ) in terms of x =f(h(...
where did you get g(x) from?
is g(x) just sin squared x?
plush elk
It could be constant function
quaint arrow
and is h(x) just -pi/4?
quaint arrow
oh I see. But does it really matter which function we assign g/h to?
plush elk
No but at least I should give a correct formula
quaint arrow
The derivative of ( integral of f(t) , t from g(x) to h(x) ) in terms of x =f(h(...
oh wait, i think i understand this, hang on
So would that look like this?
plush elk
It is easy to prove but I don’t think it’s that obvious…
quaint arrow
sorry its sideways
quaint arrow
that's what I got initially. But my friend (who's the valedictorian in my school) got something else
also I plugged the question into my calculator and its telling me d is the right answer
cloud bramble
It's not b, since you also have to multiply by the derivative of sin^2(x)
quaint arrow
wait so how should i go about solving this problem
plush elk
Oh yes d
quaint arrow
i have no idea how to do it, i just used my calculator, but its suggested that i dont use my calculator on this question
is what I did in the pic correct so far?
plush elk
I gave you the general form already
quaint arrow
yeah so is what I did in the 2nd pic i sent correct so far?
plush elk
The derivative of ( integral of f(t) , t from g(x) to h(x) ) in terms of x =f(h(...
Here
quaint arrow
why do you multiply by h'(x)
oh wait a sec
wait so first of technically just finding the antiderivative of csc(t^4+1), right?
quaint arrow
The derivative of ( integral of f(t) , t from g(x) to h(x) ) in terms of x =f(h(...
Is there a video on khan academy or some other site that you would recommend to learn more about this?
quaint arrow
Can someone please help me with this problem? I got the answer by using my calcu...
<@&286206848099549185> is there a video online that you would recommend me watching to learn more about this material? Preferably something on khan academy
still temple
,rotate
elfin berryBOT
elfin berryBOT
earnest monolith
<@&286206848099549185> is there a video online that you would recommend me watch...
Here ya go: https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-4/v/fundamental-theorem-of-calculus
marsh citrusBOT
@quaint arrow Has your question been resolved?
river yew
Could I get help on this question? I'm having difficulty finding the area of the triangle because I can't really visualise the vectors
marsh citrusBOT
Could I get help on this question? I'm having difficulty finding the area of the...
river yew
I've tried the magnitude and using A=1/2bh but it's not correct
static quarry
Your drawing looks wrong. Isn't L the line connecting P and Q? In which case OQ as drawn is not perpendicular to L.
river yew
It probably is wrong, I wasn't really sure how to draw it out
static quarry
What did you get for b and h? And how do you know your answer is wrong?
river yew
For the points I found how would I use them?
I have the solution in a booklet
I got 1/2xsqrt300 in my attemp at finding it
solution is sqrt 66 u^2
static quarry
What is u
river yew
units
river yew
for b i got 6 and 50 for h
static quarry
which line segment are you using for the base?
static quarry
Yeah this is your problem, the right angle is not where you have shown it
river yew
Ohh
static quarry
then the base is PQ and the height is OQ
river yew
I'll try again with that
static quarry
(or vice versa, doesn't really matter)
river yew
If you dont mind me asking how would you draw line L, or the triangle for the question
I get how to calculate the answer but I don't really understand whats going on with the points
static quarry
I would draw similar to what you have, except I would draw OQ vertically instead of at a slant like you have it
Then it is perpendicular to L as required
river yew
Ohhh
river yew
I was not too sure on the perpendicular part
static quarry
O is not on L
static quarry
"The point Q lies on L such that OQ is perpendicular to L"
It's a bit hard to visualize until you experiment with drawing it
and then modify the drawing until it satisfies the requirements 😆
river yew
Yeah, I also don't know why i didn't put PQ on line L
Ah I see I see, I'll try more anytime I have another question
.close
amber rapids
marsh citrusBOT
amber rapids
where does the (0,-4) come from?
main idol
plug in $x=0$ to $y$
elfin berryBOT
riemann
amber rapids
but why do we do that
ah makes sense we can pick any point on y = -x-4 and it mst always be at a distance of \sqrt{128} to y = -x+c
amber rapids
why do we ignore c = 20?
tulip idol
why do we ignore c = 20?
,w plot y = x^2 and x + y = -20
elfin berryBOT
tulip idol
do you think they ever intersect?
marsh citrusBOT
marsh citrusBOT
Available help channel!
gusty surge
gusty surge
noble nebula
Is this an exam/quiz?
gusty surge
past exam so there’s answer provided
but i still don’t know how to solve it
can someone remind me how to solve (b)’s P(X<2)
or how to get the value of it
marsh citrusBOT
@gusty surge Has your question been resolved?
marsh citrusBOT
@gusty surge Has your question been resolved?
main idol
or how to get the value of it
Plug in the definition of the binomial distribution
marsh citrusBOT
@gusty surge Has your question been resolved?
merry ivy
Im stuck on part a. I used geometric formula.
marsh citrusBOT
Im stuck on part a. I used geometric formula.
noble nebula
you need a recursive formula
So the expression for $C_n$ should include $C_{n-1}$ somehow
elfin berryBOT
Remavas
marsh citrusBOT
@merry ivy Has your question been resolved?
merry ivy
so n-1 is not an exponent
glacial hedge
It asks for a recursive formula. That's most likely linked to the fact it gave a syntax error
merry ivy
9(n-1) 1.1
glacial hedge
I would recommend reading the entirety of the question again
noble nebula
Ok, let's say we have concentration $C_{n-1}$. According to the task, what is its concentration going to be the next day? (for any $n>1$)
elfin berryBOT
Remavas
noble nebula
just 1.1?
glacial hedge
You know what a recursive formula is right ?
noble nebula
$C_n = f(C_{n-1})$, where f is some function you have to find
elfin berryBOT
Remavas
noble nebula
That is what a recursive formula is
noble nebula
$C_n$ is the concentration after $n$ days
elfin berryBOT
Remavas
noble nebula
Says so in the task
merry ivy
im still having syntax errors. I followed the directions
noble nebula
well what did you type in
elfin berryBOT
riemann
still temple
$9_{n-1}$ is not valid, sub number (like on the bottom) are only valid on variables (letters)
elfin berryBOT
aspwil
still temple
@merry ivy assuimg you had not figgured that out yet
still temple
is it this?
yes you need this, but the vairable is "C" instead of "a"
merry ivy
Like this? still wrong
still temple
no, thats wrong
like i jsut said you need C instead of A in this equation
and this is exponentail; increse not liner so you answer will be in the form
$x_n = a * x_{n-1}$
elfin berryBOT
aspwil
merry ivy
so my a = 9
xn = 1.1
still temple
no
9 is the starting value its not listed in this equaiton
"A" is the persentage its going up by
still temple
yes, were multipliing though, so its 1.1
cause the consentation is increseing by 10% each day so we end up with 110% of the previous consentation
elfin berryBOT
aspwil
merry ivy
how we find c7?
still temple
the same rule $C_7 = 1.1 * C_6$
merry ivy
do we go down until c1?
elfin berryBOT
aspwil
still temple
we go down unitll the starting day
merry ivy
which is 9
still temple
yes $C_0 = 9$
elfin berryBOT
aspwil
still temple
so just use that rule to find C_8
merry ivy
u add 1.1 everytime?
still temple
you times by 1.1
merry ivy
or would it be 1.2
elfin berryBOT
aspwil
still temple
every time you increase n by 1 we times by 1.1
merry ivy
i used desmos
c2 = 1.1 (9.9) = 10.89 is the same as 1.1(1.1)(9)
merry ivy
^
still temple
yes
$C_2 = 1.1 * 1.1 * 9 = 1.1^2 * 9$
elfin berryBOT
aspwil
still temple
so $C_2 = 1.1^2 * 9$
elfin berryBOT
aspwil
still temple
and if we times by 1.1 to get c_3 then we just add 1 to the power
merry ivy
what dp should i round to?
still temple
$C_3 = 1.1^3 * 9$
elfin berryBOT
aspwil
still temple
etc
merry ivy
ok.
still temple
im not sure does it say a decimal point to round to?
still temple
dont round then i guess?
merry ivy
alright to 2 or 4 dp?
still temple
just use 2 i guess