#help-10
eager latch
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obtuse pebbleBOT
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naive onyx
Can someone check if my process is correct?
obtuse pebbleBOT
Can someone check if my process is correct?
tardy epoch
yes
vestal thorn
notation is wonky admittedly
naive onyx
what about the notation is wonky?
tardy epoch
this is missing limit expression
naive onyx
ah
vestal thorn
and usually you don't notate inf/4, you would just say lim f => inf
coarse ibex
this is missing limit expression
It is and isn't, the /xs don't disappear before the limit is taken
naive onyx
It is and isn't, the `/x`s don't disappear before the limit is taken
im dont understand what you mean by the /xs
coarse ibex
Expressions like 4/x become 0 once the limit is taken, so like lim_(x to inf) 4/x = 0. But I suppose it is valid to just say things like lim_(x to inf) 4- 4/x = lim 4
So scratch what I said
naive onyx
oh that, would it be better if i put 0 for those?
coarse ibex
Don't need to, matter of taste
dawn vale
is the area of the whole triangle?
obtuse pebbleBOT
is the area of the whole triangle?
dawn vale
<@&286206848099549185>
tardy epoch
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tidal cloud
repost since the channel closed when i tried to delete/rewrite problem statement
obtuse pebbleBOT
repost since the channel closed when i tried to delete/rewrite problem statement
@tidal cloud Has your question been resolved?
tidal cloud
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keen garnet
<@&286206848099549185>
try in #advanced-analysis
tardy epoch
definitely not the first one
rigid axle
obtuse pebbleBOT
rigid axle
Question 5
proper kelp
When does a quadratic have no real roots
rigid axle
Oh Yh thanks
proper kelp
b) is simply solving that inequality from a)
signal plover
Im learning tanjent, but i dont know how to do this. (I have to find "a")
signal plover
i tried 45 tan(48) = 49.98 which was wrong
nocturne minnow
i tried 45 tan(48) = 49.98 which was wrong
Do you know the ratio for tangent?
signal plover
ratio?
nocturne minnow
Like SOH CAH TOA
signal plover
oooh
nocturne minnow
The ratio for tangent
signal plover
i think
signal plover
?
nocturne minnow
And what's the ratio for tangent?
signal plover
o and a?
nocturne minnow
,tex .sohcahtoa
warm shaleBOT
dldh06
nocturne minnow
Those
signal plover
yea, i've seen them abonch but i think i know them
nocturne minnow
Where tan(theta) = opp/adj
nocturne minnow
Where tan(theta) = opp/adj
Can you fill in this equation with that info?
signal plover
yes (or i believe so)
nocturne minnow
So what would the equation be?
nocturne minnow
if it was a/o or o/a
Hence SOH CAH TOA, tan = o/a
signal plover
yes
nocturne minnow
Can you plug those values into that equation?
nocturne minnow
No
signal plover
..
nocturne minnow
**dldh06**
The equation here
Tan(theta) = opp/adj
Don't move numbers around yet
Just plug the values of theta and opp into that equation
That's all I'm asking
signal plover
so tan(48) = 45/a?
signal plover
so tan(48) 45 = 49.98. so i would guess tan(48) 45/49.98?
nocturne minnow
so tan(48) 45 = 49.98. so i would guess tan(48) 45/49.98?
No
a is in the denominator
signal plover
hmm
so tan(48) 49.98/45?
would that be right?
that would get me 1.23 which would be too low compared to the other things
slim cove
so tan(48) 49.98/45?
where are you getting the 49.98 from btw?
signal plover
i did 45 tan(48) and i gave me 49.98
slim cove
don't plug anything into the calculator yet
slim cove
so tan(48) = 45/a?
can you manipulate this to solve for a?
what can you do to get a by itself on one side?
signal plover
tan(48) 45/48?
slim cove
no, let's do a simpler example
signal plover
ok
signal plover
12 = 2/a?
slim cove
how did you get that?
signal plover
guessing
slim cove
okay, so what we have to do is apply the same operation to both sides of the equation
so we start with the equation 2 = 12/a
first, what could we do to both sides of the equation in order to get rid of the fraction?
slim cove
this doesn't have to do with tan right now
let's just focus on the simple equation 2 = 12/a
and then we'll see how to apply the same technique to the equation involving tangent
slim cove
let's just focus on the simple equation 2 = 12/a
so the first thing we could do to get rid of the fraction is to multiply both sides of the equation by a
so we'll get 2 * a = 12/a * a
Does that make sense?
signal plover
i think
slim cove
okay and then what is 12/a * a equal to?
signal plover
2?
slim cove
why 2?
signal plover
cause 2 * a = 12/a * a
slim cove
so 12/a * a is equal to 2 * a, not 2
but let's just think about (12/a) * a
you're dividing by something and then multiplying by the same thing right?
signal plover
so 12/a * a is equal to 2 * a, not 2
so just a squared
slim cove
No
We're dividing by a and then multiplying by a
What do you get if you divide by something and then multiply by the same number?
signal plover
We're dividing by a and then multiplying by a
12/2a = 6?
slim cove
Not quite
signal plover
What do you get if you divide by something and then multiply by the same number?
the same number you had at the beginning?
slim cove
So the point here is that division and multiplication are opposite operations
slim cove
the same number you had at the beginning?
Yes!
So (12/a) * a = 12
So just to summarize, we started with
2 = 12/a
and then we wanted to get rid of the fraction, so we multiplied both sides by a to get
2 * a = (12/a) * a
and then we simplified down the right-hand side to get
2a = 12
Does that make sense?
slim cove
Yes it is, it's important to understand this stuff before we move on to more complicated stuff
So once we have 2a = 12, what can we do to both sides of the equation to get a by itself?
signal plover
times it
slim cove
Multiply both sides of the equation by what?
signal plover
itself?
slim cove
So you want to multiply 2a by 2a and 12 by 12?
signal plover
yeaaas.... (am i in the wrong direction)
slim cove
Yeah, that won't simplify things, only make them more complicated
Think about it this way: we have 2a on the left, and we want to undo the multiplication by 2 in order to get a by itself
What operation can we use to undo the multiplication by 2?
signal plover
btw i got the question right.
i did
tan(48) = 1.11
and then 45/1.11 = 40.54 which was correct
signal plover
Yeah, that won't simplify things, only make them more complicated
so we divide
slim cove
btw i got the question right.
i did
tan(48) = 1.11
and then 45/1.11 = 40.54 w...
Awesome!
slim cove
so we divide
Yeah, so we divide both sides of the equation by 2 to get
2a/2 = 12/2
or
a = 6.
The reason I brought up this example is that the example with the tangent works exactly the same way
We start with tan(48°) = 45 / a
And then we want to solve for a, so we multiply both sides by a to clear the fraction
tan(48°) a = 45
And then we divide by tan(48°) to get a by itself
a = 45 / tan(48°)
= 40.54 like you said
signal plover
And then we divide by tan(48°) to get a by itself
a = 45 / tan(48°)
but when i put 45/tan(48) it gives me 40.51 and not 40.54
slim cove
but when i put 45/tan(48) it gives me 40.51 and not 40.54
45/tan(48°) rounds to 40.52, which is correct. The reason you got 40.54 originally is probably because of the fact that you rounded tan(48°) to 1.11 but it's really 1.11061... etc
45/tan(48°) is the exact length of a
cloud dragon
i dont know how to go about this wouldnt everything in parenthesis end up being 0
obtuse pebbleBOT
i dont know how to go about this wouldnt everything in parenthesis end up being ...
fierce lagoon
obtuse pebbleBOT
@cloud dragon Has your question been resolved?
bright vessel
why is the answer not 1?
obtuse pebbleBOT
why is the answer not 1?
tardy epoch
why is the answer not 1?
Does it give you the answer
obtuse pebbleBOT
@bright vessel Has your question been resolved?
low matrix
because it's not 1
obtuse pebbleBOT
@bright vessel Has your question been resolved?
bright vessel
because it's not 1
Then how do you solve it
low matrix
do you know how to find limits on a graph
tardy epoch
But I selected 1
Do you mean 1 the choice or 1 the answer
bright vessel
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prime cove
A cube-shaped water tank having 4 ft side lengths is being filled with water. The bottom is solid metal but the sides of the tank are thin glass which can only withstand a maximum force of 200 lb. How high (in ft) can the water reach before the sides shatter?
(Assume a density of water 𝜌 = 62.4 lb/ft3.
Round your answer to two decimal places.)
obtuse pebbleBOT
A cube-shaped water tank having 4 ft side lengths is being filled with water. Th...
prime cove
Im not sure how to do this
urban patrol
density = mass/volume
bright vessel
Find the volume of the cube shaped water tank
obtuse pebbleBOT
@prime cove Has your question been resolved?
prime cove
No
violet pasture
please help me write the equation in blue
obtuse pebbleBOT
please help me write the equation in blue
timid silo
you can use the equation in red to reconstruct the one in blue
violet pasture
i tried but i’m confused on the shrinking part
because when i shrink it i don’t know how it gets halfway between two coordinates
prime cove
Find the volume of the cube shaped water tank
Thanks genius
obtuse pebbleBOT
@violet pasture Has your question been resolved?
solid copper
i am confused on number 2. i do not understand how to solve with the axis’s being labeled velocity and time.
obtuse pebbleBOT
i am confused on number 2. i do not understand how to solve with the axis’s bein...
cloud belfry
i am confused on number 2. i do not understand how to solve with the axis’s bein...
velocity at t=2
2.smthg correct?
well to be more precise
start with calulating slope
dv/dt= 20/5
solid copper
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pure jungle
determine if the following lines are skew:
L1: x = 1 + t, y = 1 + 6t, z = 2t
L2: x = 1 + 2t, y = 5 + 15t, z = -2 + 6t
If yes, find the distance between them
obtuse pebbleBOT
determine if the following lines are skew:
L1: x = 1 + t, y = 1 + 6t, z = 2t
L2...
pure jungle
i know these lines are skew but how do i find the distance between them
obtuse pebbleBOT
@pure jungle Has your question been resolved?
pale scaffold
obtuse pebbleBOT
pale scaffold
wants me to simplify it
tardy epoch
,tex .exp rules
warm shaleBOT
riemann
pale scaffold
ok
so it will be 5th root of (x^3) multiplied by x^2 and multiplied by square root of (1/x^2)
royal basin
you don't actually need to involve roots here...
it is better to keep the exponents as exponents
royal basin
well... yes, you apply literally the first rule in that table.
pale scaffold
so ive got x^12/5
i did x^(6/10) + (20/10) + (- 5/10)
oh wait i did it wrong
x^(21/10)
royal basin
x^(6/10 + 20/10 - 5/10)
royal basin
i mean imo x^(21/10) is fine to leave as-is
but if you have some explicit instruction to use roots like that then sure
pale scaffold
yeah but the instructions said to not have fractional exponents
alr thank you!
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obtuse pebbleBOT
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nimble gulch
obtuse pebbleBOT
nimble gulch
i did this
:
and stopped becauae it looks not good
but I know i need to use lhopitals rule because this chapter in book is about it
royal basin
may i suggest first stripping away some of the complexity?
consider $f(x) = \frac{\ln(\cosh(\sqrt{x}))}{x}$ first, and find $\lim_{x \to 0^+} f(x)$
warm shaleBOT
Ann
royal basin
and then introduce all of your constants...
hazy sun
Before the tanh step, notice that cosh(0)=1, and sinh x/x goes to 1 when x goes to 0
obtuse pebbleBOT
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ancient tangle
I need help
ancient tangle
no ones answering in the other channel
polar fossil
more channels aren't really going to help you
obtuse pebbleBOT
@ancient tangle Has your question been resolved?
ancient tangle
yes
ancient tangle
more channels aren't really going to help you
no need to be mean ?
tender stratus
I don't see how thats mean in any way, and that statement was true. You could ping @ helpers instead if you haven't got some help after 15 minutes
pinging is better way to get visibility than opening another channel
timid silo
yeah you'd waited for all of 3 minutes before opening a new channel
oh actually 2. 7:42 and 7:44
obtuse pebbleBOT
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heavy cloak
hi i need helpp
obtuse pebbleBOT
hi i need helpp
heavy cloak
obtuse pebbleBOT
@heavy cloak Has your question been resolved?
spark stump
is someone able to vc with me to assist me with a livesolve
obtuse pebbleBOT
is someone able to vc with me to assist me with a livesolve
obtuse pebbleBOT
@spark stump Has your question been resolved?
spark stump
<@&286206848099549185>
obtuse pebbleBOT
@spark stump Has your question been resolved?
warm canopy
Just post a question and people will help, people don't wanna download a pdf
atomic compass
is theta be used instead of alpha
obtuse pebbleBOT
is theta be used instead of alpha
ruby path
Context?
alpine raven
is theta be used instead of alpha
its just a matter of notation
you can use what you want
atomic compass
ok
royal shard
both are variables
you can name your variables whatever you want, just be clear with it
there are however conventions
in school we usually used alpha for angles
in university we used phi more often
theta and phi are usually used in spherical coordinates and are not the same angle there
with more context we can give more info
fluid snow
both are variables
you can name your variables whatever you want, just be clear ...
I feel like in Germany, we use alpha more often than theta in high school
It seems like in the US, theta is used more often than alpha
That is not the case at all here
royal shard
yes in highschool (gymnasium) we never really used theta
we only used alpha beta gamma in math
in physics we sometimes did use phi though
phi also just sounds nicer
also theta looks kinda weird
obtuse pebbleBOT
@atomic compass Has your question been resolved?
fluid snow
yes in highschool (gymnasium) we never really used theta
we only used alpha beta...
Ah, you are German too. Yeah, we never really use theta either in Gymnasium
orchid vector
how would I do this? A fair die is thrown 5 times, find the probability that the product of the 5 scores are even?
obtuse pebbleBOT
how would I do this? A fair die is thrown 5 times, find the probability that the...
@orchid vector Has your question been resolved?
lone echo
start by simplifying the problem. What's the probability of ONE single die rolling an even score?
orchid vector
1/2
lone echo
okay. You rolled the first dice. It rolled even.
After this having happened, what's the chance of a second die rolling even?
orchid vector
1/2
lone echo
So what's the chance of both happening simultaneously?
orchid vector
1/4?
lone echo
i dont like that question mark. It implies you're not sure
orchid vector
so do you basically do that but with odd and you take complement?
orchid vector
i dont like that question mark. It implies you're not sure
basically im pretty sure its 1/4 unless i missed something
lone echo
you know tree diagrams, right?
orchid vector
yeah
lone echo
draw these two steps on a tree diagram and answer me again
orchid vector
1/4
lone echo
now add the next branches (that you care about on the problem) to the tree
lone echo
the next three rolls. You're rolling it 5 times total
orchid vector
yeah ok i get it
you do that with odd
and take compleemmt
and you get 31.32
31/32
which is the answer
makes sense
ok thankns
lone echo
that's a mistake
31/32 is not the chance of getting 5 times an odd score
31/32 is the chance of getting at least one odd score
orchid vector
yeah
lone echo
because 1/32 is the chance of getting every single time an even
orchid vector
but couldnt you just do it with evens then?
since probability of odd is same as probability of even
each round
each roll*
so as long as you get at least 1 even roll
lone echo
that's correct. But getting every time odd is not the same as at least once odd
lone echo
31/32 would be the chance of getting either of the possibilities:
one odd, or two odds, or three odds, or four odds, or five odds
the probability of exactly 0 times odd (all are even) would be 1/32.
The probablity of exactly 5 times odd (all are add) are also 1/32
orchid vector
wouldnt that just be the same for when you replace what you just said with evens?
yeah ok
so just then take complement
or just do it with evens
lone echo
yes. Your mistake is not computing the number.
Your mistake is making the assumption that the complement (31/32) means 5 times odds
the compliment means not 5 times even
which is valid for 0 even, 1 even, 2 even, 3 even, or 4 even
orchid vector
but 0 even is impossible?
lone echo
no
orchid vector
wdym
lone echo
you can roll all the times an odd number
orchid vector
oh i thought you meant on 1 roll nvm
lone echo
no, i mean on all 5 rolls
orchid vector
ok
lone echo
If we go by number of evens / number of odds, in 5 rolls, you can get:
0/5
1/4
2/3
3/2
4/1
5/0
orchid vector
ok so you just take each case and add them up
lone echo
the first and the last have the same probability. 1/32. All of them are even, or all of them are odd
on your tree, they would be the absolute top leaf, and the absolute bottom leaf
orchid vector
yes. Your mistake is not computing the number.
Your mistake is making the assump...
doesnt that just mean the same?
lone echo
if you do the full tree with all 32 leafs, you'd see that 1/4 and 4/1 have 5 valid leaves, so each have 5/32 probability
and both 2/3 and 3/2 would have 10 valid leaves each, so each would have 10/32 probability
orchid vector
you either roll a total of 5 odds or you dont roll a total of 5 odds which implies that you do roll some number of even
lone echo
you either roll a total of 5 odds or you dont roll a total of 5 odds which impli...
precisely. But some number of even is not the same as every roll being even
one single word changes completely which probability you're calculating
orchid vector
is there a way to do it with perms and combs?
lone echo
and depending on the specific problem, one single letter will change the probability you're calculating
orchid vector
precisely. But ***some*** number of even is not the same as ***every*** roll bei...
but i didnt assume that?
lone echo
you wrote that
orchid vector
i just assmed all cases where you dont roll all 5 odds
lone echo
you might have written something different than what you were thinking, but what you wrote is that the complement of 5 evens were 5 odds
orchid vector
ah ok i think u misinterpreted what i wrote then
lone echo
As per how to calculate it. It's a binomial distribution. You'd be looking at number of "successes" (in this case, times you got even), in a number of "tries" (number of rolls), with a fixed probability of "succeeding" (in this case, 1/2 as you stated at the start) in "independant" tries (each try doesnt care about the others, the probability keeps constant)
orchid vector
ok
lone echo
if you were to NOT have independant tries (for example, extracting cards from a deck WITHOUT replacing them after extracting) you'd be looking at an hypergeometric distribution
they work similarly, but the branches on the tree got changing probability since you're removing one item each extraction
in the die, it would be like rolling a different die without the number that you already rolled, and one less face
orchid vector
cos this was a sub question with other sub questions that required perms and combs when finding probabilities, is there a way to do it like of the numbers you roll you pick 1 as even and there are 3 cases for that and then pick the rest and the denomiator becomes 6^5? but i guess that becomes what you do with the fraction stuff with the tree diagram
ok
lone echo
not exactly.
The 6^5 would be the different possible rolls that you could get, assuming you do care about the order of the rolls
for example, 1,1,1,1,5 would be a different roll than 5,1,1,1,1
lone echo
that's why probability and combinatorics require EXTREMELY careful reading of the question
usually perms and combs are used to get the number of possibilities that are a "success", or the number of total possibilities.
Obviously the probability is the quotient of those
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lone dome
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crude coral
!status
obtuse pebbleBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
I don't know where to begin
crude coral
have u ever solved a simultaneous equation?
lone dome
Nope, not yet
crude coral
ok so basically u use 1 equation to find the value of x and y and use it in the other equation
there are more ways to solve it tho
crude coral
Nope, not yet
first take lcm of the first equation
lone dome
the lcm of 2 and 3?
crude coral
lcm are of denominators
crude coral
no
the lcm would be xy
i just like to simplify the equations in these type of equations
crude coral
then we find the values of either x or y from the 2nd equation
and then use it in the first one
lone dome
Okay how do we find the values of x and y?
crude coral
2x+3y=2
2x = 2-3y
x=(2-3y)/2
thats how we find value of x , and use it in the first equation
lone dome
So for that solution I can use the same for finding y?
crude coral
2x+3y=2
2x = 2-3y
x=(2-3y)/2
and then using this "equation of x" , add value of y and find x
rich plume
You can also get a bit fancy and multiply both the equations to get a hidden quadratic and then solve for x and y
lone dome
2x+3y=2
2x = 2-3y
x=(2-3y)/2
Wait, where does 2 come from?
crude coral
its in the question
lone dome
I got -1/2
crude coral
Use it in the x equation for y
lone dome
So y=(3-2x)/2?
lone dome
so y=(3-2*-0.5)/2
crude coral
I got -1/2
I'm solving this rn
lone dome
Alright
crude coral
U should get 2 answer for y
And secondly ur answer is wrong
If possible, can you show your working so i can see the mistake
lone dome
U should get 2 answer for y
Okay, so then the value of x would be 2 and the solution is 2x+3y=2?
crude coral
no
crude coral
Okay, so then the value of x would be 2 and the solution is 2x+3y=2?
by that i meant there are 2 answers for y
not 1
cuz its a quadratic equation
lone dome
ohh okay
crude coral
step 1 is that u need to find value of x in terms of y
crude coral
2x+3y=2
2x = 2-3y
x=(2-3y)/2
which i showed u , here
Step 2 is that now u need to do is use this value of x in the OTHER equation to find values of y
lone dome
I'm not sure how to put this on my calculator
crude coral
no
u cant do this using a calculator
this is physical work , do it on a paper or something
lone dome
alright
crude coral
I'm not sure how to put this on my calculator
also how was that the first thought that came to ur mind was that u are going to use calculator to find x and y ? thats pretty much impossile
obtuse pebbleBOT
crude coral
bro ill just continue this tomorrow, its getting late
its a simple question
u could do it in like 5 mins
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drifting merlin
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drifting merlin
Hi this is the Gauss-Jordan elimination to get inverse
I'm not sure how they got those zeros after the uppermost matrix
Somehow two zeroes appeared in place of 1 and -2
Can someone explain to me what they did exactly?
somber kite
can someone help me with my math
pearl bison
I'm not sure how they got those zeros after the uppermost matrix
They used the third row
Row 2 = Row 2 + 2*Row 3
Row 1 = Row 1 - Row 3
obtuse pebbleBOT
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spring python
how do you differentiate √6*x?
obtuse pebbleBOT
how do you differentiate √6*x?
royal basin
sqrt(6x) = sqrt(6) * sqrt(x), and sqrt(x) is x^(1/2)
i recommend NOT using the product rule here, actually.
spring python
why not?
royal basin
it's painful and gives you like 5 times more mistake opportunities than necessary.
harsh remnant
Have you heard of chain rule?
spring python
yeah
royal basin
Have you heard of chain rule?
also unnnecessaary here.
harsh remnant
Why?
royal basin
OP's function is $\sqrt{6} \cdot x^{3/2}$ and needs nothing more than the power rule to differentiate.
warm shaleBOT
Ann
harsh remnant
how do you differentiate √6*x?
Oh I thought this was the original question
high lily
chain rule not needed for that either
somber kite
question
harsh remnant
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obtuse pebbleBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
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obtuse pebbleBOT
Show your work, and if possible, explain where you are stuck.
harsh remnant
^
somber kite
i don’t understand the question
pls
what does it means
<@&286206848099549185>
CAN SOEMONE HELP ME
LIKE
harsh remnant
!15m
obtuse pebbleBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
harsh remnant
I don't understand the handwriting
somber kite
If one angle of a right angled triangle is of 30 degrees the hypotenuse is twice as long as the side opposite to the angle..prove it
fluid snow
If one angle of a right angled triangle is of 30 degrees the hypotenuse is twice...
Do you know of anything, like a formula, identity, ... that connects the hypotenuse with the opposite side of an angle?
fluid snow
not at all
Do you know trigonometry?
somber kite
no
somber kite
we did it by this method and it’s confusing
fluid snow
no
Oh, I would've done it by trigonometry. sin(30°) = 1/2 and we have that sin(30°) = o/h, thus, 1/2 = o/h and so 2o = h.
obtuse pebbleBOT
@somber kite Has your question been resolved?
fluid snow
we haven’t been taught that
Then we can do it like they did it. Drop a line from B to AC, calling the intersection point D, in a way so that it forms a 30° angle at DBC. The angle BDC will be 120°, thus, the angle ADB will be 60°. Because the angle DBC is 30°, the angle ABD will be 60° and so ABD will be an equilateral triangle. BDC is an isosceles triangle (since the angles DBC and DCB are equal).
Let the lengths of the equilateral triangle ABD be denoted by a. One of the sides of ABD is also a leg of our isosceles triangle BDC, so DC will also be of length a.
Thus, the length of the hypotenuse is 2a and a is the length of the side opposite to 30°.
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
gusty scaffold
I already have the antiderivative which is x^3/3-x^2/2+8x now I need to evaluate it and simplify it I already added the numbers of the integral 1 and 0 to the antiderivative which is (1)^3/3-(1)^2/2+8(1) - (0)^3/3-(0)^2/2+8(0) but I can't get the define integral
obtuse pebbleBOT
I already have the antiderivative which is x^3/3-x^2/2+8x now I need to evaluate...
sage geode
Are you sure that the antiderivative of 2x is x^2/2 ?
gusty scaffold
.close
wooden edge
For parts b and c, I'm a little confused by the questions..
obtuse pebbleBOT
For parts b and c, I'm a little confused by the questions..
wooden edge
Don't nth roots of complex number have n roots? Which one am I supposed to choose?
Not all of them have the same real parts too
thin star
did you do a yet?
wooden edge
I did
thin star
what did you get?
wooden edge
8e^i(3pi/4)
tardy epoch
,w 8e^(i(3pi/4))
warm shaleBOT
tardy epoch
,w -4sqrt(2) * (1-i)
warm shaleBOT
tardy epoch
yes
tardy epoch
wolfram alpha is a popular online calculator yes
tardy epoch
8e^i(3pi/4)
you use this. find the 6th root of this
wooden edge
There are 6 different roots, aren't there?
tardy epoch
probably the principal branch
wooden edge
i can generalise it: sqrt(2)cis[((3+8k)pi)/24]
tardy epoch
i can generalise it: sqrt(2)cis[((3+8k)pi)/24]
k=0
wooden edge
I didn't know there's such thing as complex principle root
you know, i asked my teacher this, after seeing some questions asking roots of expressions, not in the context of equations
he told me to write down all of the roots possible
wooden edge
If you mean 8e^i(3pi/4), it isn't 6th rooted yet
thin star
ill write back if this works or not
It does, I just did it
massaging the equation to get the one the problem wants is a bit tedious, but that formula you gave is all you need
wooden edge
pi/8 is a cheeky angle..
thin star
yeah
wooden edge
I can edit both sides though, i guess..
it says 'show,' so it isn't really like a "RIGOROUSLY PROVE THIS!" type of question right?
thin star
uh, what?
wooden edge
hahahhh
sorry for that
I meant to say this
the question just tells me to show, so it doesn't have to be as formal as a normal proof question, right?
meaning I can apply operations on both sides, rather than directly proving by changing one side
So this would be a valid answer, i think:
sqrt(2)cos(pi/8) = sqrt(2sqrt2 + 4)/4
squaring both sides
2cos^2(pi/8) = [2sqrt(2)+4]/4
2cos^2(pi/8) = sqrt(2)/2 + 1
2cos^2(pi/8) - 1 = sqrt(2)/2
Using the double angle identity, the left hand side is equivalent to cos(pi/4)
which is equal to sqrt(2)/2
anyways... thanks
.close
fallow tusk
obtuse pebbleBOT
fallow tusk
well for the first set, 8 is the x value, 4 is the y, 7 is the z yes?
wooden edge
at t=0
fallow tusk
ok
wooden edge
He means find the time such that the z component is equal to 0, as that will be when the meteor hits the surface
you can form a parametric equation if it helps
wooden edge
z = 7 -2t
fallow tusk
arent we setting that to 0?
wooden edge
sure, do it
wooden edge
that's how I understood it
cerulean ridge
Option A: You pay 5000; with probability 0.2 you will get 10000 and with probability 0.8 you will get 0
Option B: You pay 1000; with probability 0.3 you will get 2000, with probability 0.4 you will get 1500 and with probability 0.3 you will get 0
Option C: You pay 500; with probability 0.4 you will get 1000, with probability 0.3 you will get 500, with probability 0.2 you will get 200 and with probability 0.1 you will get 0
Option D: You pay 100; with probability 0.6 you will get 200 and with probability 0.4 you will get 100
Use the octave code that gives expected utility for the various options (util_demo.m). Modify the code for the above four options, and use exponential utility function with R values given in the table below. Fill up the blanks in the table to 2 decimal places (marked as P,Q,R,S)
Fill up the blank P in the table to 2 decimal places
0.5 points
Fill up the blank Q in the table to 2 decimal places
0.5 points
Fill up the blank R in the table to 2 decimal places
0.5 points
Fill up the blank S in the table to 2 decimal places
obtuse pebbleBOT
Option A: You pay 5000; with probability 0.2 you will get 10000 and with probabi...
@cerulean ridge Has your question been resolved?
tardy epoch
but the due time was over
do .close if you're done
cerulean ridge
.close
lethal marsh
Hi! Can someone help me at number 2?
obtuse pebbleBOT
Hi! Can someone help me at number 2?
lethal marsh
Express decimal to fraction
The 0.2315
That I needed it to be turned into a fraction
warm canopy
You have the answer beside it no?
lethal marsh
You have the answer beside it no?
I have it right like 2315/10000
I need to put it on
warm canopy
Oh, then try finding common factors of 2315 and 10000
warm canopy
Something that divides both of them
E.g. 3/6 -> 1/2, since 3 and 6 are both divisible by 2
lethal marsh
What if, I could divide it on both of it but everytime I did it theres like a decimal
Like 30.9
Not perfectly whole number
warm canopy
Divide them by things that don't give you a decimal
lethal marsh
OkAy.. so I have to go.. like.. starting to 1to what.. till I got it to something that wouldn't give me any decimal? Is that correct?
If that's correct then that will be all
warm canopy
I'm not sure what you just said
warm canopy
You need to find numbers that divide them and give whole numbers yes
lethal marsh
Okay! I got it now I gotta use the calculator over and over again
Thank you!!
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
mystic osprey
i've been stuck on this question and have absolutely no clue what to do, can someone help?
obtuse pebbleBOT
i've been stuck on this question and have absolutely no clue what to do, can som...
@mystic osprey Has your question been resolved?
mystic osprey
<@&286206848099549185>
coarse hound
i've been stuck on this question and have absolutely no clue what to do, can som...
,rotate
warm shaleBOT
solemn swallow
I think it could help if you trace the triangles A-C1-M (where M is the midpoint) and B-C2-M
undone sluice
You already know the radius of C1 and C2.
So height is h, where h = C1 + C2 + ?. Find the ? using those triangles
mystic osprey
.close
timid silo
Verify if V = {(x, y) ∈ R²: 3x-2y=0} with the regular R² operations is a vector space.
(1) how do I show that V contains zero and
(2) what properties does the "with the regular R² operations" spare me of proving?
thanks
obtuse pebbleBOT
Verify if `V = {(x, y) ∈ R²: 3x-2y=0} with the regular R² operations` is a vecto...
@timid silo Has your question been resolved?
slow maple
For (2), this means that we can assume:
\begin{align*}
\overline{v} + \overline{w} &= (v_x, v_y) + (w_x, w_y) = (v_x + w_x, v_y + w_y) \
c \cdot \overline{v} &= (c \cdot v_x, c\cdot v_y)
\end{align*}
and any other elementary $\bR^2$ operations I may be forgetting.
warm shaleBOT
@slow maple
timid silo
For (2), this means that we can assume:
\begin{align*}
\overline{v} + \overlin...
thanks
slow maple
Are you still needing help with figuring out what properties that helps with/how to approach (1)?
timid silo
yes
slow maple
Alright; which of those would you like to start with?
timid silo
a sec, im searching my notes
obtuse pebbleBOT
timid silo
Ive seen places where it was simply written, eg for W = {(x, y, z): ax+by+cz=0} where a, b, c ∈ R are fixed, under the identity element of vector addition, simply that a0 + b0 + c0 = 0 ⇒ 0 ∈ W.
so all I have to do in my first example is write that 3*0 - 2*0 = 0 ⇒ 0 ∈ V?
@slow maple
.reopen
obtuse pebbleBOT
✅
slow maple
Ive seen places where it was simply written, eg for `W = {(x, y, z): ax+by+cz=0}...
Yep! That works to demonstrate that $\overline{0} \in V$
warm shaleBOT
@slow maple
full oar
could some help
obtuse pebbleBOT
could some help
full oar
I’m getting a little confused
so 16 / 1000 is 0.016 so that would be how many
wait that doesn’t make sense
cuz I would have to jut multiple by 1000 to get 16
so what do I do
native inlet
so the snail travels $16\frac{m}{h}$, right?
warm shaleBOT
MrFancy
obtuse pebbleBOT
@full oar Has your question been resolved?
dawn vale
i have this so far but not too sure what to do now
obtuse pebbleBOT
i have this so far but not too sure what to do now
dawn vale
could you shair your working out please so i can understand the steps
hexed flame
which part do you not get?
dawn vale
i just dont understand how you are getting from one thing to anouther
hexed flame
ah okay so do you get the first two equations?
dawn vale
not really
hexed flame
sarah thought that the price was 0.10 less than what it is so she thought the cost was (c-0.10)
and she was going to get n of these prizes
the total of getting n prizes for (c-0.10) adds up to 6
yes?
hexed flame
exactly
dawn vale
ah ok i was getting a bit confuesed with the decimal but now i realise that is the same
hexed flame
so does the working make sense now then?
dawn vale
i dont think one of your calculatons is right
hexed flame
yeah i just realised i deleted it
dawn vale
so then you rearange n(c-0.1)=6 into -6n(c-0.1)
obtuse pebbleBOT
@dawn vale Has your question been resolved?
dawn vale
<@&286206848099549185>
hexed flame
so then you rearange n(c-0.1)=6 into -6n(c-0.1)
sorry i don't really see how you got there?
if we're making n the subject we can divide both sides by c-0.1
so that n=6/(c-0.1)
then from the earlier equation: 6=c(n-5)
we can expand then sub n in
6=cn-5c
6=6c/(c-0.1)-5c
hexed flame
that was from earlier it was the second equation that we got from the question - that she still spends 6 but now she's paying the real price, c, and because it's more expensive she has to buy 5 less than initially, n i.e. (n-5)
hexed flame
6=6c/(c-0.1)-5c
times everything by (c-0.1)
6(c-0.1)=6c-5c(c-0.1)
6c-0.6=6c-5c^2+0.5c
5c^2-0.5c-0.6=0
which you can then factorise
okay i keep making a small mistake somewhere I can't really find it
the answer was 0.4 hopefully from there you can work backwards
dawn vale
i dont understand why we are timesing n-5 by c
hexed flame
that was from earlier it was the second equation that we got from the question -...
do you follow this explanation?
dawn vale
not really
hexed flame
okay do you remember how we got 6=(c-0.1)n?
dawn vale
yes
dawn vale
1 sec
hexed flame
ahh how would you do it?
timesing is saying that you a certain number of the same thing
so you're right, instead I could basically add up (c) n-5 times
but it's just easier to write it as c*(n-5) but that is the same as saying c+c+c+c+c+.... until we've added (n-5) Cs
sorry if I'm 'babying' the maths, I just want to ensure you fully get it and I don't really know your ability
hexed flame
because you have (n-5) lots of c
hexed flame
i would think it was 6/c=n-5
this is the same equation
dawn vale
is it?
hexed flame
multiply both sides by c!
hexed flame
okay let's use your one to then sub into the other equation
dawn vale
thank you
hexed flame
is it all good now then?
dawn vale
yea
hexed flame
😄
dawn vale
okay let's use your one to then sub into the other equation
how would we sub it in?
<@&286206848099549185>
karmic mural
how would u tell if something is a hyperbolic paraboloid
cuz for other ones u can tell what it is
and imagine it in ur mind
but for hyperbolic paraboloid its hard to imagine
obtuse pebbleBOT
how would u tell if something is a hyperbolic paraboloid
cuz for other ones u ca...
karmic mural
u can do like cross sections and tell by the different planes right
but with a hyperbolic paraboloid i cant really
obtuse pebbleBOT
@karmic mural Has your question been resolved?
karmic mural
<@&286206848099549185>
Is it always just a=db^2-dc^2
abc are Some variable x y z
D is some constant
obtuse pebbleBOT
@karmic mural Has your question been resolved?
crisp shoal
Hey I have some issues with this integral
obtuse pebbleBOT
Hey I have some issues with this integral
crisp shoal
This is what I have done:
u= 1+2x^2, so x= √(u-1/2)
x^3= (√(u-1/2))^3
du = 4xdx, so du/4 = xdx
then, in theory it would look like this
issue, I don't know how to continue
obtuse pebbleBOT
@crisp shoal Has your question been resolved?
crisp shoal
<@&286206848099549185> , can someone help me?
civic zealot
where did you get your x from for your du substitution?
crisp shoal
isn't the derivate of 2x^2 -> 4x?
civic zealot
yes
civic zealot
sure, that can work
crisp shoal
I can cancel that, right?
so I can cancel the square root and the ^2
ok I think I have it
thank you so much!
.close
random notch
hii!! i just wanted to check if this is how you would graph the inequality & if it isnt if you could help me see how its done
obtuse pebbleBOT
hii!! i just wanted to check if this is how you would graph the inequality & if ...
barren wing
hii!! i just wanted to check if this is how you would graph the inequality & if ...
well -2 < y, not <= so I think you shouldn't fill in the bubble there
random notch
where should i put it then??
barren wing
sorry I meant like the filled in bubble
random notch
oh
barren wing
you probably want the hollow one since it's only 2 < y
random notch
ohhhhh
so the way i graphed it was fine just the little circles were wrong?
& why do the circles even matter??
barren wing
You want to make sure if the endpoints are included or not
pale scaffold
& why do the circles even matter??
the circles tell you whether it is a <= or <
random notch
if its a filled circle its equal to it then?
pale scaffold
the circles tell you whether it is a <= or <
A open circle tells you that it is < while a closed circle tells you it is <=
random notch
oh
pale scaffold
A open circle tells you that it is < while a closed circle tells you it is <=
oh wait its reversed
random notch
yeah i was confused 😭
barren wing
pale scaffold
nvm i was right before
pale scaffold
uh that number line is a bit wrong
pale scaffold
well it would be a open circle at -4 going to the left of the line
because < or > is a open circle
random notch
i did that
pale scaffold
oh ok, but your line is wrong, while you did get the open circleright
its supposed to be facing to the left
pale scaffold
yeah it wouldn't make sense if -4 is greater than positive numbers
random notch
i get it now!! w the circle, the fraction didnt matter then? i didnt have to graph it?
pale scaffold
wait what
random notch
the 8/3
pale scaffold
you have to graph the x > 8/3
pale scaffold
because it is also apart of your solution
or is a key word for that the space between -4 and 8/3 will not be filled
let me reword that
random notch
how would i graph the fraction then??
pale scaffold
You would be graphing 8/3 by having a open circle at 8/3 and it facing positive infinity
8/3 is around 2.5
well specifically 2.6 repeating
random notch
& it would be an open circle right
pale scaffold
yes it would be a open circle
pale scaffold
yes but 8/3 is around 2.5 not -1.5
pale scaffold
yeah but i would put it one tick mark to the right
pale scaffold
ok
pale scaffold
ok it looks good to me
pale scaffold
np
random notch
.close
timid silo
obtuse pebbleBOT
timid silo
need help with this, someone please help asap
well do you know how a piecewise function works
😔
not really
fervent tusk
look at the domains
timid silo
i did the one previous to this one
i just dont know how to do this one
so id like to see the answers to know how to do this stuff in the future
tbh i don't really see how youd do this one if you don't know how a piecewise function works
fervent tusk
i did the one previous to this one
if you did this question, I don't understand how you can't do 2
they work exactly the same
timid silo
i substitued the -5 for the x in the 2x then solved the equation but it said incorrect
idk what im doing wrong
fervent tusk
by 2x, do you mean the last equation
timid silo
yes
fervent tusk
okay is -5 > 3
timid silo
no
fervent tusk
so then why are you substituting it their
timid silo
i didnt know that i had to substitute the -5 for the other x too
timid silo
fervent tusk
ah
there is a comma
that separates those two
that other x is not part of the function
that other is basically the domain
timid silo
the right one or left?
fervent tusk
the x > 3
timid silo
yes
i substituted the -5 for both of these x's and got a very wrong answer
what did i do wrong
timid silo
-215
timid silo
whatd you get
fervent tusk
-340
timid silo
oh that was right