o
#help-0
tulip oasis
ionic jewel
either way its still the same problem on how ot solve
I dont know how to solve by hand
I guess you could do it somewhat quickly via guess and check using a calculator? but that seems unpleasant and unneccessary
tulip oasis
I hope they dont put this one on the exam
Its really the only one idk in the exam review
ionic jewel
oh wait
you have a calculator?
do you know how to find roots using it?
is it one of those kind?
ionic jewel
okay well this problem can be solved if you can use the calculator to find roots
this problem is equivalent to solving $x^3+3x-1 = 0$ which is easy on a calculator that can find roots
ocean sealBOT
lone heartBOT
@tulip oasis Has your question been resolved?
wraith marlin
how do I solve this
lone heartBOT
how do I solve this
lone heartBOT
@wraith marlin Has your question been resolved?
wraith marlin
.close
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
Hello, how is this not 468.
lone heartBOT
Hello, how is this not 468.
alpine sable
what am i doing wrong in the chinese remainder theorem
it is apparently supposed to be 588
<@&286206848099549185>
found an error but the inverse of 16 mod 27 is 22 not 24 but that makes my answer 198 at the end so theer is still smth im doing wrong
please
<@&286206848099549185>
but you combine the mods at the end for the final x
keen pasture
<@&286206848099549185>
If I may suggest another method: Let y = 16 + 22z. What is y mod 27 then?
lone heartBOT
@alpine sable Has your question been resolved?
winged summit
Stuck on 16f, ive acknowledged theres 14 people that play basketball and ghat theres a sample space of 13
winged summit
What i dont understand is what happens to the 6 girls that play bbal
Think ive got it brain went dead
.close
quasi marlin
How do I approach this? (This is right after the section for amgm, so something to do with that)
lone heartBOT
How do I approach this? (This is right after the section for amgm, so something ...
@quasi marlin Has your question been resolved?
lone heartBOT
@quasi marlin Has your question been resolved?
sick halo
Need help with where did the 0.95 came from
lone heartBOT
Need help with where did the 0.95 came from
@sick halo Has your question been resolved?
barren portal
lone heartBOT
barren portal
Is it easy to tell Table 3.1 is isomorphic to 3.3, if so can you help me?
barren portal
I tried a lot i could map b to x
I think it making sense now
a cannot be replaced with x
zealous lichen
both relabelling (y,z)->(a,c) and (y,z)->(c,a) work
barren portal
do you mean (y,z) as y*z?
zealous lichen
no
zealous lichen
both relabelling (y,z)->(a,c) and (y,z)->(c,a) work
I mean you can either map y to a and z to c
or map y to c and z to a
both give you an isomorhpism
barren portal
.Thanks
lone heartBOT
Available help channel!
verbal creek
Have tried to work it out, however I believe I may be getting this question wrong as the X is meant to be answered in fraction form so I have tried to write X as 1/3
vale otter
pls type te question
verbal creek
ok
vale otter
my eyes are dead
coral flower
Have tried to work it out, however I believe I may be getting this question wron...
seems correct
X should be 3 , did u try it?
actually no
coral flower
take - sign out , because the answer should be X(a + Yb + Zc)
u have X(-a + 3b +c)
X should be -3
verbal creek
That is still wrong apparently, I think it wants X to be in fraction form as seen in the previous examples
coral flower
That is still wrong apparently, I think it wants X to be in fraction form as see...
did u try Z = 1 or -1? cuz its -1
sleek swallow
how do i solve this
lone heartBOT
how do i solve this
coral flower
use cos law first angle and sin law for the rest 2
sleek swallow
use cos law first angle and sin law for the rest 2
where or how do i start
coral flower
or u can use cos law for first angle , sin law for 2nd angle and 3rd angle = 180 -1st angle - 2nd angle for the 3rd
coral flower
where or how do i start
do u know cos law?
pallid scarab
where or how do i start
a^2 = ...
coral flower
thats the start of cos law
vale otter
.open
sleek swallow
do u know cos law?
c^2 = a^2 + b^2 -2ab something
pallid scarab
!occupied
lone heartBOT
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).
coral flower
c^2 = a^2 + b^2 -2ab something
something = cos gamma
sleek swallow
something = cos gamma
where is gamma
coral flower
if u have all values given , why use the cos law ??
u use laws and formulas to find a unknown value , if all are given wheres the fun
coral flower
by cos law?
coral flower
18^2 = 34^2 + 20^2 - 2ab cos (gamma)
lime sigil
how do i solve this
find one angle using cosine rule. then use sin rule to find another. then the other you get from 180 - the other angles
dawn zephyr
there's a way of doing it without using law of sines and cosines if you don't know those
lime sigil
there's a way of doing it without using law of sines and cosines if you don't kn...
how
sleek swallow
18^2 = 34^2 + 20^2 - 2ab cos (gamma)
how do i get gamma
dawn zephyr
how
triange area using semi perimeter
set that equal to 1/2ab sinX
repeat 3 times
a very lengthy process yea
lime sigil
yea hella long bro
dawn zephyr
might be viable for people who don't know/like trig
rugged pebble
lone heartBOT
rugged pebble
Help with V
zealous lichen
the cartesian product AXB={(a,b)|a in A and b in B}
rugged pebble
ik
@zealous lichen
but
its like 30 tuples for each one
the teacher said just think about common
sleek furnace
Look at which one is in which, substract and count :)
lone heartBOT
@rugged pebble Has your question been resolved?
rugged pebble
Look at which one is in which, substract and count :)
there are 30 for each
60 in total
no way thats possible
even my teacher said dont do that
zealous lichen
If |A|=a and |B|=b then |AXB|=ab
lone heartBOT
@rugged pebble Has your question been resolved?
restive chasm
restive chasm
coral flower
i think its 25 news paper
300 students x 5 news papers = 1500 news papers
1500 / 60 = 25 news papers
sleek furnace
i think its 25 news paper
You’re no supposed to answer but to ask why they’re stuck 💀
coral flower
ik , but i cant explain this to them , its not like algebra or calculus
restive chasm
300 students x 5 news papers = 1500 news papers
1500 / 60 = 25 news papers
Got it. Tnx.
Your answer is correct.
.close
lone heartBOT
lone heartBOT
Available help channel!
lime sigil
whats up lads?
lone heartBOT
whats up lads?
lime sigil
can anyone help me rearrange the cosine rule to find a angle?
barren portal
post the question
lone heartBOT
@lime sigil Has your question been resolved?
alpine sable
lone heartBOT
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
1
alpine sable
```
What step are you on?
1. I don't know where to begin
2. I have begun but got...
1
!1
/commands
formal nebula
alpine sable
!occupied
lone heartBOT
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).
alpine sable
ocean sealBOT
QuasiStar 超新星
alpine sable
uhh what
ocean sealBOT
QuasiStar 超新星
alpine sable
no clue
i do not understand
do u know the answers
tell
please
im late
my quizs will be locked soon
❤️
nah
dw
can u explain it perhaps a lil?
ocean sealBOT
QuasiStar 超新星
alpine sable
**QuasiStar 超新星**
hmm
formula?
i've got like 5-4 more questions im confused about
ocean sealBOT
QuasiStar 超新星
alpine sable
so it's the third one?
right?
$\left(x^{\frac{1}{3}}\right)^{2}=\left(\sqrt[3]{x}\right)^{2}$
ocean sealBOT
Left2dye
lone heartBOT
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
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
alpine sable
!what hte hel
jagged cobalt
theres no command to summon helpers
jagged cobalt
**Left2dye**
just apply this
alpine sable
sure thats correct
YESSSSS
YESSSSSSSSSSSS
only 4 more to go
what do i do here
i am quite late so i don't have access to the lessons anymore
jagged cobalt
if you mean 125 * 2/3 then yes
brisk wharf
?
jagged cobalt
are you multiplying them
brisk wharf
Am I supposed to?
ocean sealBOT
AℤØ
jagged cobalt
$(\sqrt[3]{125})^2$
ocean sealBOT
AℤØ
alpine sable
oh
brisk wharf
25x5?
alpine sable
5
brisk wharf
5
alpine sable
5 2/3
brisk wharf
how did you get that
Nvm that
brisk wharf
whats the cube root of 125
So it’s 5 yeah
jagged cobalt
you have $(\sqrt[3]{125})^2$ and youve told me that $\sqrt[3]{125}=5$ so what do you have
ocean sealBOT
AℤØ
brisk wharf
3/5
jagged cobalt
no
alpine sable
5 3
jagged cobalt
no
jagged cobalt
you shouldnt be having fractions anywhere
alpine sable
you shouldnt be having fractions anywhere
exponet 3?
brisk wharf
So just 5????
jagged cobalt
$\sqrt[3]{125}=5$ then $(\sqrt[3]{125})^2=5^2$
ocean sealBOT
AℤØ
jagged cobalt
because the cube root of 125 is 5
so the cube root of 125 squared is 5 squared
brisk wharf
OH-
brisk wharf
I thought we were supposed to find the cube root but also add 3 n 2 somewhere
But now I understand
Thanks
alpine sable
isn't it the 2nd one
jagged cobalt
seems fine to me
jagged cobalt
seems fabulous to me
alpine sable
bhahaa
icy brook
its correct
brisk wharf
Why thank you
brisk wharf
seems fabulous to me
That’s more like it thanks
jagged cobalt
i wouldnt really use the absolute value signs
jagged cobalt
this is fine to me
brisk wharf
Okay
jagged cobalt
the square root function returns positive values by default
even though the negative ones are valid
brisk wharf
Okay
alpine sable
okay
alpine sable
very bad quality
brisk wharf
Shsuh
Could u explain ?
Do u know left2dye
I think mine is right but I need double check
brisk wharf
That’s exactly what I wrote u peace of ####
alpine sable
That’s exactly what I wrote u peace of ####
woah woah calm down
jagged cobalt
id accept that
alpine sable
id accept that
alr
brisk wharf
Thanks
jagged cobalt
uh huh
jagged cobalt
i didnt say that🤦♂️
brisk wharf
Yeah u did
alpine sable
Yeah u did
no
jagged cobalt
because the cube root of 125 is 5
so the cube root of 125 squared is 5 squared
i said this, not that it was the final answer
jagged cobalt
thats fine for a simplification, though the brackets are unnecessary
brisk wharf
Then tell us that
jagged cobalt
brisk wharf
<:sully:651816820122189834>
Sorry but😭😭😭
jagged cobalt
i did say not to use the ||
brisk wharf
I ddint
alpine sable
i did say not to use the ||
Yeah true but i checked with mathway it said that
so i thought it was fine
jagged cobalt
bruh
brisk wharf
Yeah appreciate it
jagged cobalt
your answers are numerically correct, just not presented properly
brisk wharf
Ohh
lone heartBOT
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
alpine sable
!close
alpine sable
Would this be how I found the slope intercept form of x-4y=12?
clear zealot
Hi, I have a question about math statements
fallen sierra
x-4y=12 -- Subtract x
-4y=12-x -- Divide by -4
(12-x)/-4
close?
alpine sable
one sec
alpine sable
equate to y
so to convert to slope intercept form, just solve for y
to clarify right?
fallen sierra
yep
y = slope * x + y coordinate of the y intercept
like y=3x+4
slope = 3
y intercept is (0,4)
lone heartBOT
cobalt summit
Is this t or f?
lone heartBOT
Available help channel!
topaz cove
isn't every prime number form of 6k+1 or 6k-1?
lone heartBOT
isn't every prime number form of 6k+1 or 6k-1?
violet urchin
isn't every prime number form of 6k+1 or 6k-1?
What about 2
violet urchin
but 91 is not
91 is not prime (7*13)
violet urchin
https://www.quora.com/Is-every-prime-number-other-than-2-and-3-of-the-form-6k%C2...
Oh
Other than 2 and 3
topaz cove
91 is not prime (7*13)
but as the 6k+-1
91 = 6*15+1
can we really check every prime with this?
violet urchin
can we really check every prime with this?
I mean
It seems like it but that’s pretty inefficient
We have better ways to do that I believe
violet urchin
There’s a starting resource
Prime generation is useful in a couple applied fields so we’ve gotten kinda good at it
maiden swift
lone heartBOT
bronze wing
This goes back to volume, which can show capacity.
V = Length x Width x Height
You know that the W = H -3 and that the tank has a square base. Think about what you know about squares and how that shows how the width and length are related.
bronze wing
There's going to be solving involved, they want the dimensions in integers.
lone heartBOT
@maiden swift Has your question been resolved?
maiden swift
Alr
rough axle
hello
echo socket
!status
lone heartBOT
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
1
echo socket
Have you considered the hint given?
"Start by writing the equation in the form y = (x - p)(x - q)(x - r)"
rough axle
idk what to do
echo socket
Are you familiar with root-factor theorem?
rough axle
no
echo socket
It says that a polynomial p(x) is divisible by (x - a) if and only if a is a root of the polynomial, i.e., p(x) = 0
E.g., if we are given that 5 is a root of some polynomial f(x), then f(x) = (x - 5) * [some other polynomial]
echo socket
Given the graph of x^3 + bx^2 + cx + d here, can you find its roots?
rough axle
is it
echo socket
It could be helpful to look at the x-coordinates of the intersections with the x-axis
rough axle
-3 -2 and 1
rough axle
yeah
echo socket
It follows that x^3 + bx^2 + cx + d is (x + 3)(x + 2)(x - 1)
Note: We don't have any other linear terms in the product as the polynomial is cubic, meaning it cannot have more than 3 roots; Also, we would normally have some constant getting multiplied by (x + 3)(x + 2)(x - 1) here, but we can say that a = 1 since the coefficient of x^3 in x^3 + bx^2 + cx + d is 1
Can you expand (x + 3)(x + 2)(x - 1)?
echo socket
Right, so x^3 + bx^2 + cx + d = x^3 + 4x^2 + x - 6 and therefore b = 4, c = 1 and d = -6 as two polynomials are equal if and only if the corresponding coefficients are equal
For part b, simply let x = 0 in y = x^3 + 4x^2 + x - 6
rough axle
thank you !!!!
alpine sable
Hello, I need to solve perimeter of triangle DEF
lone heartBOT
Hello, I need to solve perimeter of triangle DEF
lone heartBOT
@alpine sable Has your question been resolved?
scarlet anvil
Hi, I need help with this part
lone heartBOT
Hi, I need help with this part
steady mantle
tan(alpha) != tan(theta)
deep grotto
lone heartBOT
deep grotto
can i show this in a more easier way?
i was thinking if i can calculate the angle through vectors or something
but i thought this was the most practical way
serene isle
"using pythagoras' theorem" implies you just need to show that a^2 + b^2 = c^2
nothing else
deep grotto
so i couldn't have done it any other way
serene isle
if lines meet at a right angle they are perpendicular and so their gradients multiply to give -1
then as long as the third line meets the other two lines
its a right angled triangle
deep grotto
aha
so for this problem it would be very complicated due to having to construct the lines first
getting slope from Cartesian coordinates and then isolating b to find y intercept for all of them
serene isle
you would have to find the gradients of the three lines, show that two of them multiplied to give -1 and the third one wasnt parallel to either of the other two
y intercept wouldnt be necessary to find in this case
serene isle
simply the gradient
deep grotto
makes sense
serene isle
if you were asked to find the point where the right angle is then you would need to find b
brisk wharf
lone heartBOT
brisk wharf
all i have is 3 3/8 -4/9
am i supoosed to find comman denominator?
or just minus it??
<@&286206848099549185>
brisk wharf
minus
pastel jolt
yes
then when u do the minus of a fraction do they need to be on the same base ?
lets say
1/3 - 1/4
brisk wharf
we find comman denominater
pastel jolt
yes
then after finding that one
lets say you have
a^b
then
(a^b)^c
what is the rule for that
pastel jolt
lemme look
brisk wharf
what is the rule for that
i donr knwo
pastel jolt
yeah i suppose
brisk wharf
i dont understand
brisk wharf
so i find comman denomnater of 3/8 - 4/9?
brisk wharf
yeah but lets say we solved that part right
okay
pastel jolt
so then what you would be left with is
(a^b)^c
tahts the second part of the problem
brisk wharf
wait
pastel jolt
its 3 to the something that you can figure out (because you know how) to the something else out of the brackets
you have (3^(3/4 -3/8))^(4/9)
can u solve the interior
ocean sealBOT
Left2dye
alpine sable
i had the same problem
pastel jolt
yeah so that part
then they are like this
what happened was
lets say you have
x^8
its (x^4)^2
think about
brisk wharf
uh
brisk wharf
so is it 3 12/81?
alpine sable
so is it 3 12/81?
72 you multipied 8 and 9 wrong
brisk wharf
oh
brisk wharf
is it the same thing
the way u formated it i dont understdn
pastel jolt
wdym
brisk wharf
3 12/72 so now i simplify ?
brisk wharf
😭
brisk wharf
yeah but its annoying
pastel jolt
i know, lol
brisk wharf
DAMN
pastel jolt
im jsut sayign it wont get easier if u just try to get the answers
but it will if u understand what the exponents mean
brisk wharf
yeah
pastel jolt
they have a reasoning behind them compared to arts or whatever
if u understand the logic its 100000x easier
no one can argue with you if u get it right
pastel jolt
np
alpine sable
yes
pastel jolt
yes
and the reason why (2^x)^y is 2^xy
is because
lets say (2^4)^2
its
(2^4)*(2^4)
which is
2^(4+4)
makes sens ?
spare kayak
2-1
spare kayak
2-1
sly mantle
dark spade
Does anyone have any resources for understanding how to read recursion formulas and what they mean? Ex:
dark spade
I can get to this point but I completely forgot what that represents as I did calc 2 years ago
harsh swallow
can you explain a bit what you mean?
lone heartBOT
@dark spade Has your question been resolved?
dark spade
@harsh swallow im just trying to solve diff eqs using power series
I get to this point but completely forgot how to read these recursion formulas and turn them into solutions
harsh swallow
The recursion formulae give you the coefficients of the power series that solve the differential equation
You have the power series $\sum_{k = 0}^{\infty} a_k x^k$
ocean sealBOT
Katharine
harsh swallow
you claim it solves the differential equation
and you go about finding the $a_k$ that show that it does
ocean sealBOT
Katharine
harsh swallow
the recursion formulae are a way to find all of the $a_k$ by knowing some small finite group of them and their relation with the rest
ocean sealBOT
Katharine
harsh swallow
for example you know $a_2 = 0$
ocean sealBOT
Katharine
lost dirge
lone heartBOT
lost dirge
Can someone please help with question 11
exotic canopy
Can someone please help with question 11
note that $(X \triangle Y) \cup (Y \triangle Z) = X \triangle Y \triangle Z = (X \triangle Z) \triangle Y$
ocean sealBOT
artemetra
lone heartBOT
@lost dirge Has your question been resolved?
crimson cliff
lone heartBOT
crimson cliff
idek how to approach this to be honest
i was thinking squeeze theorem but i also dont think thats right since it doesnt really work
alpine sable
i was thinking squeeze theorem but i also dont think thats right since it doesnt...
l'hopitals?
ik if that works might be worth a try
idk
tacit arch
multiply top and bottom by 2 sin^10 (3x)?
tacit arch
(ab)^10 = ?
uncut junco
lone heartBOT
uncut junco
Hi I need help with 8
There is a hole at x=3 but idk how to write the limit statement for that
Pls help
Should I write that it doesn't exist
misty blade
Well if I'm not mistaken you could write $\lim_{x\to 3} f(x) = \lim_{x\to 3}\frac{x+3}{x}$ and evaluate the left-hand and right-hand limits using the reduced form
ocean sealBOT
MKing
hot bluff
it's a removable limit, in other words, you can manipulate the equation to fill in the discontinuity and evaluate the limit from there.
misty blade
Sorry there was a lot of errors
misty blade
it's a removable limit, in other words, you can manipulate the equation to fill ...
Yeah
solid fog
full canopy
Loga(b) = ln(b)/ln(a)
Write all of the terms in this way and basically all of them cancel out
lone heartBOT
@solid fog Has your question been resolved?
late palm
lone heartBOT
ocean sealBOT
rustic coral
I'm going to assume your logic for doing the arithmetic is correct
frank gull
Given ω>0, and the graph of function f(x)=sin〖(ωx-π/4)〗 between (π/2,π) has and only has one line of symmetry, determine the domain of ω.
frank gull
Given ω>0, and the graph of function f(x)=sin〖(ω(x-π/4))〗 between (π/2,π) has and only has one line of symmetry, determine the domain of ω.
I assumed this one line of symmetry was only a vertical one
and found that there is such symmetry when f(x) has a crest or trough at pi/2
in which case ω can be any odd integer
is that right?
are there any more values for ω? Is it fair to assume the line of symmetry can only be vertical?
near apex
It's a sinusoidal curve so it is indeed fair to assume that line of symmetry is vertical.
Other than that, show your working.
frank gull
Since the line of symmetry is vertical, it makes sense that the only values for which the function would be symmetrical in that interval is when f(x) has a peak at 3pi/4 (halfway between the given interval). So We need f(x) = sin (ω(pi/2)) to have a peak. This is true when w=1,3,5,7,... So the domain of w is the positive odd integers.
@near apex good?
near apex
How did you figure that 3Pi/4 would be the peak?
frank gull
because the middle of the interval pi/2 and pi is 3pi/4
and the peak would have to be in the middle if its symmetric
frank gull
Since the line of symmetry is vertical, it makes sense that the only values for ...
if it was elsewhere, it would be asymmetric
frank gull
How did you figure that 3Pi/4 would be the peak?
is that good?
frank gull
So the domain is the odd numbers then?
near apex
Yes.
frank gull
is there any way to ensure that the line of symmetry could not be some random diagonal one?
for example, why can we assume that there is not a line of symmetry that makes an angle like 47.68 degree with the positive x-axis that works
.close
ebon gyro
i need help evaluating this limit
lone heartBOT
i need help evaluating this limit
hoary hearth
<@&286206848099549185>
lone heartBOT
<@&286206848099549185>
lone heartBOT
<@&286206848099549185>
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.
hoary hearth
Please only use the <@&286206848099549185> ping **once** if your question has no...
Sure
Can someone help me with my question
Bruh
Let me take screenshots
Sorry if links are not allowed
sour dove
Sorry if links are not allowed
no problem, was just about to tell you but it looks like you got it 🙂
links aren't not allowed but most likely nobody would be willing to open them since discord doesn't check for file vailidity
winged lava
links aren't not allowed but most likely nobody would be willing to open them si...
its a .pdf file so its likely safe
hoary hearth
links aren't not allowed but most likely nobody would be willing to open them si...
Got u
I got hacked on discord once so no prob
But ye these
lone heartBOT
@hoary hearth Has your question been resolved?
hoary hearth
Is anyone going to help
lone heartBOT
@hoary hearth Has your question been resolved?
latent elm
can someone help
lone heartBOT
can someone help
latent elm
i need to find x and y
balmy grail
i need to find x and y
What have you done so far?
latent elm
nothing much i only know volume is 1/3 x base area x height
balmy grail
So what does that give you?
latent elm
volume which is 0.392
balmy grail
Is equal to
latent elm
volume
balmy grail
nothing much i only know volume is 1/3 x base area x height
Can you write this as an equation?
latent elm
how?
lone heartBOT
@latent elm Has your question been resolved?
balmy grail
How about can you find x given both sides are x?
lone heartBOT
@latent elm Has your question been resolved?
latent elm
How about can you find x given both sides are x?
yea i think si
so
square root 0.49 i think
lone heartBOT
@latent elm Has your question been resolved?
zealous juniper
can anyone explain how did they get the ln of c pls ? :
lone heartBOT
can anyone explain how did they get the ln of c pls ? :
glacial patrol
Integrating constant, they just call it ln|c| for convenience later on. It works since ln|c| can be any real number
zealous juniper
Integrating constant, they just call it ln|c| for convenience later on. It works...
ohh ic, that'd be totally wrong without the absolute value i guess
glacial patrol
they don't even need the absolute value for ln(c) to represent any real number, but they do need it along with the properties of the logarithms to combine the terms the way they did in the 2nd to last expression
Cus |a|/|b| = |a/b|
But not |a|/b
zealous juniper
got it, ty!
glacial patrol
np
zealous juniper
.close
wicked forge
how do you solve 2cos^2 x + sinx = 1 for 0<=x<=360
lone heartBOT
how do you solve 2cos^2 x + sinx = 1 for 0<=x<=360
wicked forge
i think im overthinking it i tried using t formula etc to solve but didnt work
split mantle
Convert cos^2 x to sin.
wicked forge
ok im indeed overthinking
thx got it now
i just moved 1 over to rhs and sinx to lhs
.close
lone heartBOT
wicked forge
.reopen
lone heartBOT
✅
wicked forge
wait hold up
i only got 1 answer
is that right or wrong
got x = 30 degrees
cuz it has the 0<=x<=360
coral flower
u should get 2 solutions
changing cos^2 into sin gives u a quadratic
which gives u 2 solutions
2 more solution cuz sin is positive in 2 quadrants
wicked forge
i moved it and got 2cos^2 x - 1 = sinx
coral flower
split mantle
Think of Pythagoras theorem.
coral flower
cos^2x =
1 - sin^2 x
split mantle
cos^2x =
1 - sin^2 x
1 - sin^2 x
coral flower
my bad
wicked forge
sinx = sin(90-2x) (just fliped rhs and lhs)
x = 90-2x
x=30
wait lemme try ur method
coral flower
that is the only method i think
coral flower
$$cos^{2}x=1-sin^{2}x$$
ocean sealBOT
JustToPro
coral flower
$$2cos^{2}x=2(1-sin^{2}x)$$
wicked forge
oh ye right
ocean sealBOT
JustToPro
wicked forge
and then sin x = -1/2 or 1
could there be 4 answers if u use the general solutions formula thing
coral flower
yea
lime light
a little help please, a is said to be zero in the answers, but that wouldnt make sense, as R^2 -> R^1 implies only one dimension should be yielded in the final answer. If a is zero, then it still has x, y; thus still two dimensional?
alpine sable
[
\env{bmatrix}{
x \
y} = \env{bmatrix}{
x&y }
]
ocean sealBOT
vale wigeon
a little help please, a is said to be zero in the answers, but that wouldnt make...
you're confusing dimension of domain and dimension of range...
lime light
oh i see, because '+ a' does not follow through with properties of linear transformations? T(u+v) = T(u) + T(v), T(au) = aT(u), T(0) = 0?
so what does R^2 -> R^1 mean
stark crater
so what does R^2 -> R^1 mean
Input is a vector of dimension 2, output is a scalar
lime light
so by that logic 'a' must be of some value that turns the output matrix into a 1x1 matrix, or scalar
so why are the answers saying a=0 then
stark crater
so by that logic 'a' must be of some value that turns the output matrix into a 1...
Why do you think the output is a matrix
lime light
a little help please, a is said to be zero in the answers, but that wouldnt make...
when this implies
stark crater
Hmm I do not think so
lime light
what would be your take on it
stark crater
The function is taking inputs x and y, and mapping to to x+y+a
stark crater
when this implies
How did you get this
lime light
i just rearranged it into parametric form and grouped it together
thinking it might have significance
stark crater
oh i see, because '+ a' does not follow through with properties of linear transf...
I do not see the point of doing that. The way I would go about doing this is using the properties you have here.
But replace T with x+y+a
Since they are equivalent
vapid shuttle
first step is deleting your message from my channel
lone heartBOT
serene hedge
OK
sharp thorn
vapid shuttle
from my channel
not this channel
this one was fine
@serene hedge
I meant what you put in #help-19
serene hedge
ok i know
vapid shuttle
since the original message got deleted
serene hedge
.close
lone heartBOT
Available help channel!
frozen jacinth
Find number of straight line passing through (2, 4) and forming a triangle of 16 sq. cm with the
coordinate axis.
frozen jacinth
I have tried this question, the correct answer is 3 and mine is 2
This is my working
paper quartz
frozen jacinth
???
Wut
<@&286206848099549185> pls help
<@&286206848099549185> ...
Is the server dead
Nvm
!close
.close
crimson cliff
lone heartBOT
crimson cliff
i want to prove that the limit doesn’t exist using the negated definition
i think i’m on the right track, i just don’t understand how the condition of |x/|x| - L| >= 1/2 can always be satisfied since were considering any real number L
lone heartBOT
@crimson cliff Has your question been resolved?
serene hedge
Why the tanx turned into x?
lone heartBOT
Why the tanx turned into x?
solemn juniper
Looks like a taylor series
spare moss
I need help with my homework im absent today so i didn't know what's k or m only in venn diagram or k and c only or k or c but not m exactly 1 of the 3 atleast 1 of the 3 etc
lone heartBOT
Please show the original problem, exactly as it was stated to you. A picture or screenshot is best.
If the original problem is not in English, then post it anyway! The additional context might still help helpers help you. Do your best to translate.
vale wigeon
...
vale wigeon
ok then let me double check that this is correct
does your first picture say 87 people liked K and C?
spare moss
What is confusing to me is k or m only, k or c but not m, k and c only, m and c but not k, and more in the lower
spare moss
yes
vale wigeon
so definitely eighty seven...
how can the number of kalamari juice likers be 66, which is less than that?
spare moss
Is that k or m only? Question
vale wigeon
no i am looking at the problem data
spare moss
how can the number of kalamari juice likers be 66, which is less than that?
Idk my I've just copied it from my classmate
It's a three set venn diagram