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#help-26
topaz sinewBOT
topaz sinewBOT
Available help channel!
idle crypt
topaz sinewBOT
thorny flameBOT
Ousel
idle crypt
also TB = 0.707 TA
but for TB in terms of w doesnt =
thorny flameBOT
Ousel
idle crypt
<@&286206848099549185>
As far as I can tell im doing it correctly. Theres a figure (a) and its correct and im doing b the exact same.
just negative for both A values
topaz sinewBOT
@idle crypt Has your question been resolved?
dusky zephyr
Why is it just .336 not negative?
Where is the .336 from?
idle crypt
The last line
dusky zephyr
Nvm
idle crypt
Yeah, just didnt write the final step
I figured out why its not negative. Its T_B thats not making sense now.
dusky zephyr
What are we working out?
idle crypt
Top part is figure (a). Im working on (b)
Part D is find T_A shows w/.366 is correct
so TB which is = 0.707TA
means TB should = .707(w/.366)
@dusky zephyr
dusky zephyr
Here
I’m thinking
Why is T a =T b
If you look at d) it’s only in 60 degrees which is for A not B
idle crypt
Its not
TB = .707TA
$-0.5T_A + .707T_B = 0$
$T_B = \frac{-0.5T_A}{.707} = 0.707T_{A}$
thorny flameBOT
Ousel
idle crypt
$T_A = \frac{W}{-0.366}$
thorny flameBOT
Ousel
topaz sinewBOT
@idle crypt Has your question been resolved?
topaz sinewBOT
idle crypt
.reopen
topaz sinewBOT
✅
idle crypt
Ima try this again.
Thats figure (a). I got all those correct.
This is figure (b). Im stuck on part E.
Ive typed it in as 2.104w as well
loud oasis
60 degrees is the angle the cord A makes with the vertical, not the horizontal
idle crypt
not sure im understanding
its usually sin(60) = y cos(60) = x
unless youre saying it should be cos(240)? @loud oasis
loud oasis
that would be correct only if 60 was the angle that the vector makes with the horizontal direction
but in the original diagram 60 is the angle that cord A makes with the vertical direction
loud oasis
with some geometry
idle crypt
270-60?
idle crypt
So it is 30, was just trying to remember why lol
wait...
how did I get D right then since thats gonna change its equation?
cuz for part 2 is cos(60) which I then use in part 3 to get 4
loud oasis
because sin(30) = cos(60) and sin(60) = cos(30) so it came out to the same result
idle crypt
but I should be using cos(30) based on what you just said right?
loud oasis
yes. the mistake just happens to cancel itself out for the other part
idle crypt
I dont think im understanding so let me right out what it sounds like:
$F_y = -T_Asin(60)+T_B sin(45) = w$
$F_x = -T_Acos(30)+T_B cos(45) = 0$
loud oasis
you need to assign appropriate signs for that
loud oasis
also you should use 30 for both instances of A
idle crypt
so the T_A values should swap
loud oasis
basically, yes
idle crypt
For future reference, you work off the closest x-axis?
loud oasis
you have a choice here:
- work off nearest coordinate axis (x or y) but you have to swap whether you use cos or sin and assign appropriate signs
- work off nearest x-axis but you have to assign appropriate signs
- work off positive x-axis (counterclockwise) and the equations are always the same
so it's a tradeoff between how much you want your equations to be the same all the time vs. how much angle conversions you have to do
idle crypt
Im not understanding how this doesnt change the T_A value in terms of weight though.
because its gonna be:
$T_B = \frac{0.866 T_A}{0.707}$
thorny flameBOT
Ousel
loud oasis
applying the options in order, you would get
T_AX = -T_A sin(60) = -T_A cos(30) = T_A cos(210)
all of which are equivalent
near dirge
(please ignore my drawings)
It is given that AF and BE are heights
The area of the trapeze(ABCD) is 48
<BCD=30°
<ADC=45°
BC=8cm
I need to find the length of AB
And the area of ∆ABC
please correct me if my English is wrong
raven field
(please ignore my drawings)
It is given that AF and BE are heights
The area of ...
You know special right triangles ?
oh you did it
raven field
(please ignore my drawings)
It is given that AF and BE are heights
The area of ...
I think you should find EC too
near dirge
oh you did it
Ye it didn't help me much
near dirge
I think you should find EC too
I'll try
Oh yeah i already tried it
It's like 4.24......
raven field
Ye it didn't help me much
The area is given and AB=FE
A=h(b+B)/2=48
A=4(AB+DF+AB+EC)/2=48
raven field
Which is 4.24......
Nope
near dirge
Nvm
raven field
Recalculate sqrt(48)
near dirge
It's 6.9.....
raven field
I got 8x=80-√192
Lemme check it rq
near dirge
It's supposed to be 10 but idk how to get to that answer
I mean it could work without the -√192
Wait isn't the formula to calculate trapeze is something like
A=h+ab+fe/2 or something
Wait lemme check rq
raven field
Wait isn't the formula to calculate trapeze is something like
A=h+ab+fe/2 or som...
h(ab+fe/2)
near dirge
Just checked it
near dirge
h(ab+fe/2)
Ye
I'll try that
Still not 10
But almost
I wonder what were missing
Oh wait nvm
It's the whole dc not only fe
raven field
I got AB= 10-2sqrt(3)
near dirge
It's supposed to be perfectly 10 i think
Like there are answers
But it might be rounded up
raven field
I got AB= 10-2sqrt(3)
but rounding this would give ~7
next rain
Y is dat positive and dat negative
topaz sinewBOT
Y is dat positive and dat negative
raven field
topaz sinewBOT
topaz sinewBOT
Available help channel!
tribal birch
A tower 40m tall, has an elevation of 45 degrees from a point B on the ground, and 53 degrees from a point C on the ground. If a point A lies on the base of the tower 40m tall, then what is the distance between point B and C on the ground if angleBAC =90 (given sin37 =-0,644 3/4). Im stuck dont know how to start
topaz sinewBOT
A tower 40m tall, has an elevation of 45 degrees from a point B on the ground, a...
tribal birch
help what does angle of elevation mean
ive been trying to draw a triangle but it just doesnt make sense
sinful pumice
found this on google
tribal birch
if point A is in the base of the tower then its just a straight line no?
sinful pumice
explain more
tribal birch
in the second statement it says a point A lies on the base of the tower. and since points B and C are both on the ground then its should be a line
sinful pumice
yes there are lines AB and AC
tribal birch
shouldnt it be line ABC
tribal birch
in the second statement it says a point A lies on the base of the tower. and sin...
with this in mind, it should be impossible for angle BAC to be 90deg
tribal birch
explain pls
sinful pumice
the problem only says that all three points are on the ground
it doesn't say that they are all in a row
so you have to think of this in a third dimension
tribal birch
oh so there is a right triangle that lies flat on the ground
sinful pumice
yes
topaz sinewBOT
topaz sinewBOT
Available help channel!
indigo estuary
Are a and b right?
topaz sinewBOT
Are a and b right?
indigo estuary
,rccw
thorny flameBOT
topaz sinewBOT
@indigo estuary Has your question been resolved?
raven field
Are a and b right?
Wasn’t it 2πr/T
feral wyvern
topaz sinewBOT
feral wyvern
Could someone please help me with question 8? I keep getting 8.06 boxes but the answer says 13.9 boxes
broken niche
Show your work for how you got 8.06
feral wyvern
Yep, I used the distance formula and got (-1-6)^2 + (8-4) ^2
Does that look correct? (Before simplifying)
broken niche
You should have (8-(-4))^2. Do you see why?
broken niche
Wouldn’t that make it (8+4) ^2
Yes
broken niche
Because two negatives make a positive?
That isnt why we use that instead but it is why you get (8+4)^2
The formula is sqrt( (x1-x2)^2 + (y1-y2)^2 )
In this case we have y1 = 8 and y2 = -4, so by directly plugging that in you get 8-(-4)
feral wyvern
Got it, I’ll go recalculate it real quick and see if what I get is correct
Ahh got it
Rest of calculations matched answer, thanks for the help!
unreal quest
Got here a li'l late but one thing I think might help
unreal quest
Though you can use the formula directly, in case you ever forget it
See that the line is the hypothenuse of a triangle
So you could just calculate it by using pythagoras
You'd get the same result(that's actually where the formula comes from)
charred dome
can someone show me how to approach these problems and if possible a step by step way to try solve it
topaz sinewBOT
can someone show me how to approach these problems and if possible a step by ste...
@charred dome Has your question been resolved?
topaz sinewBOT
@charred dome Has your question been resolved?
hardy dust
if mew is a coeficiant then would it need to be either larger or smaller? i got the anwer choice down to these 2 and i think B might be correct not sure
topaz sinewBOT
if mew is a coeficiant then would it need to be either larger or smaller? i got ...
hardy dust
.close
placid turtle
How to do this
topaz sinewBOT
How to do this
acoustic tide
How to do this
i just did that so i might be able to give me a sec
placid turtle
Oh
acoustic tide
yea idk
restive inlet
try factorising the numerator and denominator
topaz sinewBOT
topaz sinewBOT
Available help channel!
mortal shadow
what does a* mean?
topaz sinewBOT
what does a* mean?
smoky sparrow
what does a* mean?
that's our new z-value we want to test for
we now have a standard normal distribution N(0, 1) with z
$a^* = \frac{a - \mu}{\sigma}$
thorny flameBOT
south's secret twin brother
smoky sparrow
yes
topaz sinewBOT
topaz sinewBOT
Available help channel!
lusty cedar
topaz sinewBOT
smoky sparrow
try to factor instead of dividing
so 10 sin(t) cos(t) - 9 tan(t) = 0 gives 10 sin(t) cos^2(t) - 9 sin(t) = 0
yeah so sin(t) (10 cos^2 (t) - 9) = 0
you forgot to solve sin(t) = 0
autumn plaza
topaz sinewBOT
autumn plaza
i got for one of the somutoons
x = 5pi/4
i dont get how theyre getting x = 2pi/3 and 4pi/3
nvm.
.close
mortal shadow
what does | mean
topaz sinewBOT
what does | mean
ionic oar
conditional probability
the occurrence of A on the condition that B has occurred
generally speaking it's written the other way round
thorny flameBOT
neon
mortal shadow
oh okay thank you
if A has to happen if B happens would P(A|B) = 1?
or would it just still be the same as it would be originally
ionic oar
if A has to happen if B happens would P(A|B) = 1?
yes because then A n B = B
topaz sinewBOT
topaz sinewBOT
Available help channel!
neon iron
topaz sinewBOT
neon iron
iron blaze
log_a ( b) = ln(b)/ln(a)
neon iron
(log_x 5) (log_5 x) = log_7 x
(log_x 5) = In(5)/In(x)
neon iron
(log_x 5) (log_5 x) = log_7 x
(log_x 5) = In(5)/In(x)
(log_5 x) = In(x)/In(5)
(log_x 5)*(log_5)
25x?
iron blaze
neon iron
(log_x 5) (log_5 x) = log_7 x
(log_x 5) x (log_5 x) = In(5)/In(x) x In(x)/In(5) = 1
neon iron
(log_x 5) (log_5 x) = log_7 x
(log_x 5) x (log_5 x) = In(5)/In(x) x In(x)/In(5) = 1
1 = log_7 x
log_7 - x = 0
verbal crater
log_a(b) = 1/log_b(a)
so you got the left side is 1
then the problem is just log_7(x) = 1
hopefully you know how to solve this
neon iron
No I don't
twin pendant
What don't you understand?
verbal crater
then do you know the definition of a logarithm?
neon iron
then do you know the definition of a logarithm?
no..
neon iron
I don't get it
twin pendant
Which part
neon iron
Everything
neon iron
Yes
twin pendant
And these are the rules. You can prove it urself or search it
neon iron
So were doing change of base rule
twin pendant
Yes
neon iron
(log_x 5) (log_5 x) = log_7 x
okay so what do I do?
twin pendant
Do this or
twin pendant
This are some of the rules rule log_x(5) can be changed to 1/ log_5(x)
Use the final rule
neon iron
(log_x 5) (log_5 x) = log_7 x
(log_x 5) x (log_5 x) = In(5)/In(x) x In(x)/In(5) = 1
1 = log_7 x
log_7 x = 1/ log_x 5 (5 =/ 1)
neon iron
Idk how..
twin pendant
And these are the rules. You can prove it urself or search it
Log of the same number as base
Since log_b(a) is b^c = a if b and a is the same number
Then c must be 1
neon iron
Something like log 7 = 1?
twin pendant
Log_a(a) = 1 cuz a^1 = a
neon iron
log_7 (7) = 1
twin pendant
Yes
neon iron
So..Is that the answer
twin pendant
X=7
neon iron
how?-
pearl fog
$$\log_{7}(x)=1$$
$$7^{\log_{7}(x)}=7^1$$
$$x=7^1=7$$
thorny flameBOT
Skill_Issue
neon iron
(log_x 5) (log_5 x) = log_7 x
(log_x 5) x (log_5 x) = In(5)/In(x) x In(x)/In(5) = 1
1 = log_7 x
7^log_7 x = 7^1
x = 7^1
x = 7
twin pendant
And these are the rules. You can prove it urself or search it
Use the power rule
neon iron
which one?
neon iron
(log_x 5) (log_5 x) = log_7 x
(log_x 5) x (log_5 x) = In(5)/In(x) x In(x)/In(5...
Can I do ths one?
twin pendant
log_2(4) is log_2(2^2)
neon iron
(log_2 4) (log_25 5) = x
(log_2 (2^2)) (log_5^5 5) = x?
twin pendant
Yes and use this
neon iron
(log_2 4) (log_25 5) = x
(log_2 (2^2)) (log_25 (5)) = x
oops
(log_2 4) (log_25 5) = x
(log_2 (2^2)) (log_25 (5)) = x
(log_2
UGHHH
WAIT
(log_2 4) (log_25 5) = x
(log_2 (2^2)) (log_25 (5)) = x
(log_2 (2^2)) = 25 log_25 (5))
(log_2 (2^2)) = 1/25 log_25 (5))
...?
twin pendant
25 is 5^2
neon iron
(log_2 4) (log_25 5) = x
(log_2 (2^2)) (log_5^5 (5)) = x
(log_2 (2^2)) = 25 log_5^5 (5))
(log_2 (2^2)) = 1/5^5 log_5^5 (5))
???
neon iron
(log_2 4) (log_25 5) = x
(log_2 (2^2)) (log_5^2 (5)) = x
(log_2 (2^2)) = 5^2 log_5^2 (5))
(log_2 (2^2)) = 1/5^2log_5^2 (5))
now what
twin pendant
Yes and use this
Omly the exponent comes out
neon iron
(log_2 4) (log_25 5) = x
(log_2 (2^2)) (log_5^2 (5)) = x
(log_2 (2)) = 2 log_2 (5))
(log_2 (2)) = 1/2 log_2 (5))
night imp
(log_2 4) (log_25 5) = x
(log_2 (2^2)) (log_5^2 (5)) = x
(log_2 (2)) = 2 log_2 (...
So
log_5^2(5) = 1/2 × log_5(5)```(log_2 4) (log_25 5) = x
(log_2 (2^2)) (log_5^2 (5)) = x
(log_2 (2)) = 2 log_2 (5)) = x
log_5^2(5) = 1/2 × log_5(5) = x
night imp
Where did your x go?
neon iron
. . .
twin pendant
It's like this
neon iron
It's like this
I don't get it
night imp
(log_2 4) (log_25 5) = x
(log_2 (2^2)) (log_5^2 (5)) = x
(log_2 (2)) = 2 log_2 (...
log_2(2^2) = 2log_2(2)
You have done it multiple times as far as I can remember
neon iron
Idk-
night imp
(log_2(2^2)) (log_5^2(5)) = x
2log_2(2)× 1/2(log_5(5)) = x```Can you move forward now?
neon iron
(log_2 4) (log_25 5) = x
(log_2(2^2)) (log_5^2(5)) = x
2log_2(2)× 1/2(log_5(5)) = x
2 × 1/2(log_5(5)) = x
night imp
Yes after that go ahead
neon iron
...
twin pendant
What's log_5(5)
neon iron
1-
neon iron
Okie
(log_2 4) (log_25 5) = x
(log_2(2^2)) (log_5^2(5)) = x
2log_2(2)× 1/2(log_5(5)) = x
2 × 1/2 = x
1 = x?
neon iron
(log_2 4) (log_25 5) = x
(log_2(2^2)) (log_5^2(5)) = x
2log_2(2)× 1/2(log_5(5)) = x
2 × 1/2 = x
1 = x?
pearl fog
combine and get rid of logs
neon iron
log(2x - 8) - log (x + 5) = log(2x)
log(2x - 8) - log (x + 5) - log(2x) = 0?
log(2x - 8) - log (x + 5) = log(2x)
log(2x - 8) - log (x + 5) - log(2x) = 0
(2x - 8) - (x + 5) - 2x = 0?
night imp
log(2x - 8) - log (x + 5) = log(2x)
log(2x - 8) - log (x + 5) - log(2x) = 0?
Let the right hand side remain where it is
Work on left hand side first
Log(a) - log(b)
Do you know the formula?
neon iron
this one?
night imp
No there is no base here
pearl fog
neon iron
Do you reverse?-
pearl fog
yes
neon iron
log(2x - 8) - log (x + 5) = log(2x)
log (2x-8)/(x+5) = log(2x)?
pearl fog
mhm
neon iron
.
neon iron
1
neon iron
I am a man of my word
It's 1 min
neon iron
also... isn't it not allowed to give out the answers without teaching someone?-
grand ether
also... isn't it not allowed to give out the answers without teaching someone?...
I it's a step by step
The properties of logarithms
log(x/y) = log(x)-log(y)
thats all you need to know
grand ether
I showed you a step by step if you have question if you have any other question feel free to ask
neon iron
I... don't think
Wait can I confirm the moderators first?
Sorry I don't wanna get in trouble
grand ether
Sorry I don't wanna get in trouble
for what ??
neon iron
I remember your just suppose to guide the helpees step by step
grand ether
I did that but with writing
neon iron
not yeah you showed it as in having them figure it out?
topaz sinewBOT
I it's a step by step
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
night imp
log(2x - 8) - log (x + 5) = log(2x)
log (2x-8)/(x+5) = log(2x)?
If log(a) = log(b)
You can write a = b
topaz sinewBOT
@neon iron Has your question been resolved?
lethal stag
topaz sinewBOT
lethal stag
I tried using natural logarithm in both questions, but I cannot solve them.
topaz sinewBOT
@lethal stag Has your question been resolved?
lethal stag
<@&286206848099549185>
chilly walrus
what is f(x)?
lethal stag
f(x) was not given.
topaz sinewBOT
@lethal stag Has your question been resolved?
cedar solar
I'm pretty sure the answer to the first one is one. because the base of the first expression approaches 1. I'm not sure. but I think that's it.
Or actually maybe at zero. Because it becomes zero to the power of Infinity.
lethal stag
I'm pretty sure the answer to the first one is one. because the base of the firs...
Actually the answer is 1/e
near coral
Number of terms after expanding this (combine all similiar terms)
near coral
Please its urgent
keen plinth
binomial theorem can help you
near coral
binomial theorem can help you
can you tell how
keen plinth
keen plinth
yes, apparently the largest coefficient of x would be?
keen plinth
no
near coral
yeah
keen plinth
the what is the greatest power of x in the whole expansion
keen plinth
yes 4
keen plinth
exactly
near coral
so then how will it help in finding number of terms?
keen plinth
would there exist x^299?
keen plinth
yes nop
near coral
x^296 will exist
keen plinth
then you just need to find how many different positive power of x exists, and also negtive power of x exists, then adding them up
smoky sparrow
Number of terms after expanding this (combine all similiar terms)
so ((1 + x^4) + (1/x))^75 has terms being constant * (x^4m)^k * (1/x)^(75 - k)
so the exponents will always be in the form 4mk + (-1)(75 - k)
near coral
then you just need to find how many different positive power of x exists, and al...
so is it 75 + 75 + 1
151 terms?
@keen plinth man its a bit urgent pls help
near coral
how do i know which numbers are getting added in between except the multiples of 4
like x^3, x^7
keen plinth
I added another further example
if you can find the pattern, you should be able to solve this
keen plinth
emm, think about this
notice how there is no term for x
keen plinth
I added another further example
and no term for x^5
keen plinth
no i cant tell you, you need to figure it out by urself
near coral
no i cant tell you, you need to figure it out by urself
bro its just some numbers like how can i find the pattern randomly
keen plinth
then i recommend you to learn binomial theorem, it is a very helpful tool in this situation
near coral
then i recommend you to learn binomial theorem, it is a very helpful tool in thi...
but the hw is logic!
keen plinth
binomial theorem is based on logic, so if you understand it, you can explain by logic and finish the hw
near coral
ok then atleast can you help find number of terms in (x+x^3 + x^5)^17
near coral
binomial theorem is based on logic, so if you understand it, you can explain by ...
i have to explain how i got the answer 💀
keen plinth
!nosols
topaz sinewBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
keen plinth
i have to explain how i got the answer 💀
so you should understand the logic behind instead of applying it directly
you can memorise 5!=120, but if you don't know 5!=5x4x3x2x1 then it is meaningless
keen plinth
I added another further example
16-12=4, 11-8=3, 6-4=2, and afterwards...
grand ether
.Close
keen plinth
.close
grand ether
how do i close this channel or smth?
use binomial theorem
keen plinth
if you only want to find the answer, you can go to google to search for it, but if you want to understand the mechanism or logic behind it, you should think more actively
grand ether
I don't think he wants
keen plinth
yeh
grand ether
As a helper, please do not give out answers that could be copied as a homework s...
.
@near coral ^
topaz sinewBOT
@near coral Has your question been resolved?
livid quail
topaz sinewBOT
livid quail
How to solve for t
topaz sinewBOT
@livid quail Has your question been resolved?
topaz sinewBOT
@livid quail Has your question been resolved?
pseudo pond
My answer should be 57/2 however I fail to see my mistake, can someone point me out where I went wrong? Problem 29
topaz sinewBOT
My answer should be 57/2 however I fail to see my mistake, can someone point me ...
pseudo pond
what integral did you get?
Sorry what do you mean? I just evaluated the problem 29 as I stated and used Rimann sum to evaluate
fair thorn
why would you use riemann su- oh
well...
riemann sums are at the least tedious to work with
so we don't usually use riemann sums when evaluating integrals
pseudo pond
I attached a image idk if it was clear
fair thorn
lemme see
golden blade
when you factor 5 it's 2/5 not 2
raven field
when you factor 5 it's 2/5 not 2
They did not factor
fair thorn
okay i looked over it
oh bacc already mentioned that fantastic
that's your issue, yeah
bacc add \lim_{n\to\infty}
thorny flameBOT
bacc (unhelpful)
golden blade
bad habits of Light
pseudo pond
when you factor 5 it's 2/5 not 2
Wait I’m little confused cause I’m a dumb Asian person or whatever but where did the 2/5 come from
thorny flameBOT
bacc (unhelpful)
golden blade
and when you factor 5 it's 2/5
pseudo pond
Oh right yeah I see now
raven field
I thought they didn’t factor damn
topaz sinewBOT
golden blade
Thank you <@587715738484211754>
Thank you too
topaz sinewBOT
Available help channel!
final roost
Hi, can someone help me explain how to solve this problem? Given a set M= {1, 2, 3, ..., 99, 100}. How many placements without repetitions exist of the elements of the set M of four elements each that contain: a) number 47, b) simultaneous 17 and 47
topaz sinewBOT
Hi, can someone help me explain how to solve this problem? Given a set M= {1, 2,...
@final roost Has your question been resolved?
final roost
Hi, can someone help me explain how to solve this problem? Given a set M= {1, 2,...
I tried to solve this problem, but i don't know is my solution correct. Solutions 4 options for the number 47 and placement from 99 to 3. 4*A(97, 3)
topaz sinewBOT
@final roost Has your question been resolved?
runic urchin
How do i leave this
obsidian vigil
Am i missing something here?
obsidian vigil
is it just p=3q for a?
burnt badger
No a linear combination is a sum of vectors with "different scalar weights"
For example
Given any vectors from the same space, u and v
A linear combination of those vectors would include all of these:
u + v
2u + 10v
0u + 0v
-11u - 13v
I would assume that elsewhere in this assignment vectors P and Q must have been defined
Your goal is to show the
i + 3j = <1, 3> can be expressed as a "combination" of P and Q
obsidian vigil
I would assume that elsewhere in this assignment vectors P and Q must have been ...
no, its just that
that's why im confused
burnt badger
Do you have some other definition for p or q ?
Like maybe your course named certain vectors like that
If not, I'd say this question is missing information
obsidian vigil
Do you have some other definition for p or q ?
no, this is the only slide
burnt badger
I mean if you read the question the grammar is already suspect xD
"If express the following"
obsidian vigil
yeah, but wanted to confirm, hence my question if i was missing something
worn willow
Can I have it pointed out what happened each line
topaz sinewBOT
Can I have it pointed out what happened each line
worn willow
u(x) = sqrt(x)
But then why does -aps disappear in (w-aps) and how does (ps+RH) turn into (RH-psr)
I think it may be intuition
(value minus price)
but I'd just like to see if it was done algaebraically otherwise
And then also what the foc was wrt
I can't put my finger on it
1/2(sqrtx) is obvious
So the whole expression drops to the denom
Was it chain rule? That RL+psr remains on top
topaz sinewBOT
@worn willow Has your question been resolved?
topaz sinewBOT
@worn willow Has your question been resolved?
topaz sinewBOT
@worn willow Has your question been resolved?
worn willow
where does the 2 come from
topaz sinewBOT
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visual flame
I’ll teach 10individuals to earn $30k more within 72 hours but you will pay me 10% of your profit when you receive it. Note only interested people should apply, drop a message let's get started by asking (HOW)
topaz sinewBOT
I’ll teach 10individuals to earn $30k more within 72 hours but you will pay me 1...
hollow drum
<@&268886789983436800>
woeful drift
topaz sinewBOT
@visual flame Has your question been resolved?
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tropic osprey
is the premise here that a definite integral by definition is equal to the upper minus the lower limit
topaz sinewBOT
is the premise here that a definite integral by definition is equal to the upper...
tropic osprey
im not sure what else it would mean by combining ftc and integrals by parts
raven sparrow
Yes, the idea is that if $\int f(x) g'(x) dx = f(x)g(x) - \int g(x) f'(x) dx$, then turning this into a definite integral yields $$\int_a^b f(x) g'(x) dx = \left[ f(x)g(x) - \int g(x) f'(x) dx\right]_a^b = \left[f(x)g(x) \right]_a^b - \int_a^b g(x) f'(x) dx$$
thorny flameBOT
Azyrashacorki
topaz sinewBOT
@tropic osprey Has your question been resolved?
viral thicket
who can explain the idea here
topaz sinewBOT
@viral thicket Has your question been resolved?
sweet shard
!1c
topaz sinewBOT
Please stick to your channel.
grim prairie
topaz sinewBOT
grim prairie
<@&286206848099549185> how should i solve the first question?
sonic escarp
fitst question means goal to goal?
grim prairie
so we ignore the imag axis?
burnt badger
I would approach this question in a pre calc way
Just treat it like an ellipse centered at origin
With foci at +/-20 left and right
sonic escarp
just look at the sketch and move X to one goal, you will see everything you need.
grim prairie
(left goal) - F1 = 140 - 2*40 = 60?
sonic escarp
left goal to F1 + left goal to F2 = 140, right?
sonic escarp
you dont even need to know the single parts. you know left goal to F1 = right goal to F2 therefore goal to goal is always k.
topaz sinewBOT
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daring sundial
topaz sinewBOT
daring sundial
where did the -1/1-p go from the end of the second line?
also i dont see lhopitals rule being used, am i missing something?
loud oasis
it's a constant so they take it out of the limit
you can see that it shows up in the final answer when p > 1 (because then it's being added to 0)
still robin
topaz sinewBOT
still robin
What can I do to isolate dy/dx onto one side.
thick lily
looks like you have a mistake on the right side with (x^2-y^2) derivative
thick lily
you have a mistake
still robin
keen plinth
anyways, do factorization
thick lily
the (x^2-y^2) term shouldn't be multiplying (2x-2y y')
keen plinth
and also expansion in this case
thick lily
there's no chain rule there
still robin
So mistake is after my equal sign?
thick lily
thick lily
yeah
still robin
And to isolate?
I think my algebra is rust. Im having such a hard time deciding what to do
thick lily
now I'd distribute the whole 4(x^2+y^2) to each term 2x and 2yy'
basically you don't want to break that apart if you can help it, but you want to try to get y' term free if that makes sense
still robin
Same with 25?
thick lily
yup perfect
still robin
No not 25
thick lily
yeah you want to distribute it to those two terms
that way the term with y' in it is free from the other 2x term there
still robin
Is the 2y(dy/dx) a term?
thick lily
once it's just terms added together, you can move them around to one side with addition or subtraction
thick lily
Is the 2y(dy/dx) a term?
yeah, I guess so, I'm kind of using the word "term" vaguely here. But basically they're the stuff that's all multiplied together like a monomial
thick lily
,rotate
thorny flameBOT
thick lily
that will make it tough to isolate dy/dx here's what I meant:
now you can add or subtract to move the the terms with dy/dx to the same side and the terms without to the other side, that make sense?
still robin
Lemme mess with it
ty kind sir
Is there any tips for the algebra part? I often get stuck there not knowing how to isolate dy/dx
sweet shard
do a lot of problems
still robin
.close
burnt swift
topaz sinewBOT
burnt swift
Find a function ( f : \mathbb{R} \to (0, +\infty) ) such that ( \f'(x) = f(x) , x e^{x - 7} ) and ( f(7) = 1 ).
thorny flameBOT
938c2cc0dcc05f2b68c4287040cfcf71
burnt swift
,, \frac{dy}{dx} = yxe^{x-7} \ \frac{1}{y} dy = xe^{x-7} dx \ \int \frac{1}{y} dy = \int xe^{x-7} dx \ \int y^{-1} dy = \int xe^{x-7} dx \ \ln(y) + C = \int xe^{x-7} dx
thorny flameBOT
938c2cc0dcc05f2b68c4287040cfcf71
burnt swift
,, \int xe^{x-7} dx
thorny flameBOT
938c2cc0dcc05f2b68c4287040cfcf71
thorny flameBOT
938c2cc0dcc05f2b68c4287040cfcf71
burnt swift
,, \int xe^{x-7} = xe^{x-7} - \int e^{x-7} dx \ \int xe^{x-7} = xe^{x-7} - e^{x-7} + C \ \int xe^{x-7} dx = e^{x-7} \left(x - 1\right) + C
thorny flameBOT
938c2cc0dcc05f2b68c4287040cfcf71
thorny flameBOT
938c2cc0dcc05f2b68c4287040cfcf71
burnt swift
,, \ln(y) + C = (x-1)e^{x-7} \ \ln(y) = (x-1)e^{x-7} + 6 \ y = e^{(x-1)e^{ x-7}+ 6}
thorny flameBOT
938c2cc0dcc05f2b68c4287040cfcf71
burnt swift
.solved
topaz sinewBOT
topaz sinewBOT
Available help channel!
ivory sorrel
topaz sinewBOT
ivory sorrel
So My idea is to use induction here
topaz sinewBOT
@ivory sorrel Has your question been resolved?
ivory sorrel
We can trivially see that $dim(V_1) \leq dim(V_1)$
\
We now assume that $dim(V_1+V_2 + \dots + V_m) \leq dim(V_1)+ dim(V_2)+ \dots dim(V_m)$
\
We now attempt to prove. that from this it follows that $dim(V_1+V_2+ \dots V_{m+1} \leq dim(V_1)+ dim(V_2)+ \dots + dim(V_m)$
\
It's trivially true that $dim(V_1+V_2+ \dots + V_n+ V_{m+1}) \geq dim(V_1+V_2+ \dots + V_m)$
Hmm, this approach doesn't seem to help too much
thorny flameBOT
A dense set
ivory sorrel
We however, know that $dim((V_1+V_2+ \dots +V_m)+V_{m+1})= dim(V_1+V_2+ \dots + V_m) + dim(V_{n+1}- dim[(V_1+V_2+ \dots + V_n) \cap V_{m+1}$.
\
We also know that $dim(V_1+V_2+\dots + V_m) \leq dim(V_1)+ dim(V_2)+ \dots dim(V_m)$.
This gives us that $dim(V_1+V_2+\dots V_{m+1}) \leq dim(V_1)+ dim(V_2)+ \dots dim(V_m)+ dim(V_{m+1}) -dim[(V_1+V_2+ \dots + V_n) \cap V_{m+1}$.
Now what
thorny flameBOT
A dense set
ivory sorrel
We can trivially see that $dim(V_1) \leq dim(V_1)$
\
We now assume that $dim(V_1+V_2 + \dots + V_m) \leq dim(V_1)+ dim(V_2)+ \dots dim(V_m)$
\
We now attempt to prove. that from this it follows that $dim(V_1+V_2+ \dots V_{m+1} \leq dim(V_1)+ dim(V_2)+ \dots + dim(V_m)$
\
It's trivially true that $dim(V_1+V_2+ \dots + V_n+ V_{m+1}) \geq dim(V_1+V_2+ \dots + V_m)$
\
We however, know that $dim((V_1+V_2+ \dots +V_m)+V_{m+1})= dim(V_1+V_2+ \dots + V_m) + dim(V_{n+1}- dim[(V_1+V_2+ \dots + V_n) \cap V_{m+1}$.
\
We also know that $dim(V_1+V_2+\dots + V_m) \leq dim(V_1)+ dim(V_2)+ \dots dim(V_m)$.
This gives us that $dim(V_1+V_2+\dots V_{m+1}) \leq dim(V_1)+ dim(V_2)+ \dots dim(V_m)+ dim(V_{m+1}) -dim[(V_1+V_2+ \dots + V_n) \cap V)]_{m+1}$.
\
From this the desired result is evident
thorny flameBOT
A dense set
topaz sinewBOT
@ivory sorrel Has your question been resolved?
topaz sinewBOT
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topaz sinewBOT
autumn plaza
part A
brisk estuary
I don't know how to solve this question using the inscribed angle theorem into this question: **Find m<2 given the measure of arc AC(70 degrees); AC & BD are equal. **
pearl fog
I don't know how to solve this question using the inscribed angle theorem into t...
!occupied
topaz sinewBOT
I don't know how to solve this question using the inscribed angle theorem into t...
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
@autumn plaza Has your question been resolved?
hoary burrow
Use formula for kinetic energy
The distance of the hammer above the nail doesn't matter here since it's travelling at constant velocity
Unless I'm majorly tweaking
@autumn plaza
autumn plaza
Use formula for kinetic energy
they did kinetic energy
and gravitational potential energy
hoary burrow
The answer sheet?
hoary burrow
@autumn plaza
hoary burrow
Feels off
Maybe I'm tweaking
I mean like if it's constant speed then even if I start moving the hammer down from 100m up the work done wont change right
hoary burrow
<@&286206848099549185>
heady mulch
g
heady mulch
Find a vector perpendicular to the plane passing through P(1,4,6), Q(-2,5,-1) and R(1, -1, 1).
need help for this
idk how to find the perpendicular vector
smoky sparrow
Find a vector perpendicular to the plane passing through P(1,4,6), Q(-2,5,-1) an...
find vectors PQ and PR first
then cross PQ and PR to find the normal vector to the plane
heady mulch
then cross PQ and PR to find the normal vector to the plane
why we need to cross PQ and PR to find the normal vector to the plane
glass maple
why we need to cross PQ and PR to find the normal vector to the plane
a plane is spanned by 2 linearly independent vectors
smoky sparrow
why we need to cross PQ and PR to find the normal vector to the plane
the normal vector is perpendicular to any vector on the plane, by definition
so if u, v are on the plane, the normal vector is perpendicular to u and also perpendicular to v
but because there are only three dimensions, the vector that is perpendicular to u and to v must not lie on the plane
if that makes sense
so in 3D since there are only 3 linearly independent basis vectors
if a, b are perpendicular and a, c are also perpendicular
and b and c are not scalar multiples of each other
then the perpendicular vector to both b and c must be a
we've taken up 2 of the perpendicular dimensions, leaving the 3rd one which is the last one
heady mulch
ok tyt
topaz sinewBOT
@heady mulch Has your question been resolved?
smoky sparrow
.close
topaz sinewBOT
topaz sinewBOT
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neon iron
a
pearl fog
whar 😭
fading owl
??
river marsh
neon iron
P1/T1 = P2/T2
3000mL/20 C = P2/50 C
0.3 L/293K = P2/323K
0.3L (323K)/293K P2
0.247193877?
Gay-Lussac's Law
fading owl
gay law fr
neon iron
P1/T1 = P2/T2
3000mL/20 C = P2/50 C
0.3 L/293K = P2/323K
0.3L (323K)/293K P2
0....
Is ths correct?
fading owl
sorry my physics sucks 😭 i cant help
river marsh
i dont even know what these letters mean lol
golden blade
P1/T1 = P2/T2
3000mL/20 C = P2/50 C
0.3 L/293K = P2/323K
0.3L (323K)/293K P2
0....
Can you post the original?
river marsh
i think its off
neon iron
wdym?
oh..
A 3000 mL sample of nitrogen inside a metal combines at 20 C is placed inside an oven whose temperature is 50 C. The pressure inside the containers at 20 C was 3.0 atm. What is the pressure of the nitrogen after its temperature is increased?
river marsh
i think this was a simple rearranging error
neon iron
ye..
river marsh
neon iron
Ohhhh
earnest apex
A 3000 mL sample of nitrogen inside a metal combines at 20 C is placed inside an...
PV/T = constant
you can use that
empty nova
neon iron
No like uhhh it's at another question
A sample gas at 3.00 x 10^3 mmHG inside a steal tank is cooled from 500 C to 0 C. What is the final pressure (in atm) of the gas in the steel tank?
Answer:
3.00 x 10^3 mmHg/500 C = P2/0 C
3.00 x 10^3 mmHg/773 K = P2/273 K
3.00 x 10^3 mmHg (273 K)/773 K = P2
1,059 mmHg = P2
correct?
wary tulip
"what we lookin for"
neon iron
The final pressure
neon iron
Answer:
3.00 x 10^3 mmHg/500 C = P2/0 C
3.00 x 10^3 mmHg/773 K = P2/273 K
3.00...
<@&286206848099549185>
flint stump
Is ths correct?
Why is your pressure in mL? mL is for volume. You need to use the pressure (3atm) here.
neon iron
How to convert mm Hg to atm?
No one is answering the question
I had no choice but to answer as it is
flint stump
No one is answering the question
760mm Hg is one atm
but tbf, you can google that yourself as well, just so you know
earnest apex
How to convert mm Hg to atm?
760 mm Hg = 1 atm
earnest apex
"what we lookin for"
hi layla
wary tulip
hi
neon iron
Answer:
3.00 x 10^3 mmHg/500 C = P2/0 C
819,000 atm/772K = P2/273K
819,000 atm (273K)/772K = P2
289 atm = P2
<@&286206848099549185>
flint stump
no no no thats wrong conversion
neon iron
I don't get it
flint stump
why would you multiply 3000 mm Hg by 273?
flint stump
760 mm Hg = 1 atm
This is the conversion
dim ruin
760 mm Hg = 1 atm
since 760mmHg=1atm, then 1atm/760mmHg = 1. Then, since you can multiply by 1 without changing the value of something, you can multiply 1atm/760mmHg without problem. That, you multiply to 3x10^3mmHg
neon iron
Okauy
earnest apex
since 760mmHg=1atm, then 1atm/760mmHg = 1. Then, since you can multiply by 1 wit...
bro wrong ping?
dim ruin
bro wrong ping?
im sorry 😭
neon iron
3000 mm Hg * (1 atm / 760 mm Hg)
4 atm??
flint stump
approximately
neon iron
3.947368421 atm
flint stump
you need specific values in your calculations tho. So better use 3.947 atm
neon iron
okay
flint stump
3.947368421 atm
yea use this
neon iron
3.00 x 10^3 mmHg/500 C = P2/0 C
3.947368421 atm/772K = P2/273K
3.947368421 atm (273K)/772K = P2
1.394090012 atm = P2?
<@&286206848099549185>
The temperature of a sample of gas in a steel container at 30.0KPa is increased gtom -148 F to 1.0 x 10^3 C. What is the final pressure (in atm) inside the tank?
Answer:
P1/T1 = P2/T2
0.00986923 atm/-100K = P2/1273K
0.00986923 atm (1273K)/-100K = P2
-0.125635297 atm = P2
<@&286206848099549185>
keen plinth
PV=nRT(use SI unit)
keen plinth
ok, so why would there be -100K, K is not possible to be negative
keen plinth
Answer:
P1/T1 = P2/T2
0.00986923 atm/-100K = P2/1273K
0.00986923 atm (1273K)/-10...
only this Question right?
neon iron
ok, so why would there be -100K, K is not possible to be negative
I convert F to C and C to K temp.
keen plinth
-148F=-100 °C=173.15K
neon iron
huh?
keen plinth
Kelvin is a unit to measure temperature Above absolute zero temperature, so Kelvin is always positive
I believe your conversion has some issues
check it
neon iron
-148 F - 32/ 1.8
keen plinth
°C = (°F - 32) × 5/9
neon iron
oh
keen plinth
atm= 101.325 kPa.
keen plinth
don’t tell me u plug in to calculator wrongly
neon iron
THATS IT IM USING ALL WEBSITES UNTIL I CAN MAKE KELVIN POSITIVE
neon iron
atm= 101.325 kPa.
-148 F - 32 X 5/9
neon iron
I give up...
keen plinth
-148 F - 32 X 5/9
this is different
keen plinth
yes
-100 is correct
then -100+273.15=173.15 K
Kelvin is defined as 0 when celsius is -273.15, or K=C+273.15
so now you have T1
you need to calculate P1
neon iron
0.00986923 atm/173K = P2/1273K
0.072621559 atm = P2
neon iron
keen plinth
congrats
neon iron
0.29607698 (1,273) / 173 K
2.178647373 atm = p2??
neon iron
YES
topaz sinewBOT
@neon iron Has your question been resolved?
patent light
$\begin{pmatrix} k & 0 & k & k \ 0 & k & 2 & 2k \ 1 & k & k & k \end{pmatrix}$
thorny flameBOT
alee
patent light
To calculate the rank I considered
patent light
the first determinant is k³ - 3k²
the second // is -k³-k²
the third // is -2k³-4k²-2k
the fourth // is 2k³-2k²
setting them = 0 to check where the determinant was 0
I found that the determinant is 0 for:
(1) k = 0; k = 3
(2) k = -1; k = 0
(3) k = 0; k = 1
(4) k = 0: k = 1
so the rank of the 3x4 matrix is 3 except when k takes on these values?
opal vault
if you find AT LEAST one of those determinants being non zero
then you have a sub 3*3 matrix of rank 3
so your matrix is of rank 3
the only way the rank of original matrix is not 3
is if ALL the determinants you found are 0
patent light
if you find AT LEAST one of those determinants being non zero
I found that all determinants can be 0 if k takes the values I marked for each of them
opal vault
I found that all determinants can be 0 if k takes the values I marked for each o...
no, the first determinant is 0 if k=0 or k=3
the second is 0 when...
etc...
if you want rank < 3
you need ALL determinants = 0
if only one is non zero
then rank = 3
patent light
no, the first determinant is 0 if k=0 or k=3
Yes
opal vault
so which particular values of k are you going to consider?
patent light
k ≠ 0 and k ≠ 3
patent light
Ah maybe I understood
I noticed that k = 0 appears in all 4 determinants
So if k = 0 the rank Is not 3
patent light
Ok for all other values the rank is 3
patent light
so you need to check k = 0 separately
When k = 0 the rank Is 2
thorny flameBOT
alee
opal vault
When k = 0 the rank Is 2
yes
topaz sinewBOT
@patent light Has your question been resolved?
ruby magnet
i need help with b-d
topaz sinewBOT
i need help with b-d
