compared to x being bigger than 0
#help-36
terse dagger
i think so
warm summit
🗿 it worked ty
terse dagger
i think you accidentally got the right answer without knowing what a piecewise function means 😄
jovial ermine
HI I had to find the taylor series for sin(x) and sin (x^3) at a=0. For sin (x^3) would all the terms of the polynomial just be 0?
final saddleBOT
HI I had to find the taylor series for sin(x) and sin (x^3) at a=0. For sin (x^3...
desert mantle
no
jovial ermine
i was thinking that because if I get the 4 derivatives then all the terms would have an x in them
so if i sub x=0 then all the terms become 0?
desert mantle
not all of them
jovial ermine
im unsure which terms don't become 0?
distant hawk
HI I had to find the taylor series for sin(x) and sin (x^3) at a=0. For sin (x^3...
If you have series for sin(x), you actually don’t have to recompute for sin(x^3). Just put x^3 in place of x in the series for sin x
distant hawk
Well you may still want to show steps even if intuitively using previous result make sense. But at least this can serve as a hint on what you should expect during these derivative calculations in sin x^3 🙂
desert mantle
but well the next one would be x^9, so finding that by hand would take a while
jovial ermine
ill just think about this some more and get back to this
so i think the reason im confused is because even if i substitute x^3 into the first taylor series, the corresponding derivatives (which i calculated a couple on the bottom) would have an x in every term. So when i sub in x=0 into the above series all numerators of all the factorials would be 0?
jovial ermine
the first term that doesn't vanish is x^3
and i thought that the first term would be 0 because teh second derivative was 3x^2 cosx -> since theres an x then the term would be 0?
desert mantle
let me reword: the first coefficient that doesn't vanish is the coefficient of x^3 in the taylor series
the coefficients before that are 0, yes
jovial ermine
let me reword: the first coefficient that doesn't vanish is the coefficient of x...
oh thats the 3rd derivative which i didnt calculate yet?
desert mantle
yes
intuitively, eventually when you differentiate polynomials enough, you get a constant which is nonzero
jovial ermine
oh lol i stopped right before that term because i assumed they will all have an x term in them
desert mantle
when you then differentiate again the constant vanishes so you have to start "over". but eventually you will get a constant somewhere again
jovial ermine
intuitively, eventually when you differentiate polynomials enough, you get a con...
im not sure why this happens?
desert mantle
well what happens when you differentiate x^3 a couple of times?
jovial ermine
ahh the x term is eventually gone
desert mantle
yes
that will happen for every polynomial eventually. and here you kind of have to wait until the stars "align" and the constant is not multiplied by sin(x^3) and so on. but when that happens, you get something nonzero
in this case every 6 terms
final saddleBOT
desert mantle
If you have series for sin(x), you actually don’t have to recompute for sin(x^3)...
but easier is this
jovial ermine
okie
final saddleBOT
Available help channel!
quick phoenix
How can I calculate arctan(3/2) without calculator?
final saddleBOT
How can I calculate arctan(3/2) without calculator?
tired walrus
you can't
quick phoenix
Use Taylor series expansion
The real question calculate arg(z) if z = 2 + 3i?
And I came with arctan(3/2). Is there any other way to solve arg(z)?
distant hawk
The real question calculate arg(z) if z = 2 + 3i?
I don’t see what is stopping you from using series, or else you may just use calculator for this.
There are no closed form solution to arctan in general so…
final saddleBOT
@quick phoenix Has your question been resolved?
brittle ember
anyone can explain to me why by comparing those 2, we get the equation
soft zealotBOT
jimmy1234
distant hawk
LHS and RHS are expressions in different variables. The only way to equate them is to impose LHS = 0 = RHS.
Hence “by comparing the two” we get what h(x) is.
brittle ember
then how about the $xln sin(t)$?
soft zealotBOT
phngs
soft zealotBOT
phngs
distant hawk
then how about the $xln sin(t)$?
By row 1 I mean $\frac{\partial h}{\partial x}$, row 2 I mean $\frac{\partial h}{\partial t}$, if you substract one from another, the term $x\ln \sin t$ will vanish 🙂
soft zealotBOT
jimmy1234
brittle ember
yes but i wanna know how to find h(x,t)
the answer $h(t,x)$ is $xln sin(t)-x^3 +2t^2$, but u said it vanished
soft zealotBOT
phngs
distant hawk
I mean when you subtract the two partials, the term will vanish.
And the reason why i do the subtraction is because I want to show you why “comparing the two” can give you the full form of $h$.
soft zealotBOT
jimmy1234
brittle ember
what is the full form of $h$?
soft zealotBOT
grim nebula
but the left doesnt depend on t and the right doesnt depend on x
well
not equal
but
theyre both constant
soft zealotBOT
phngs
brittle ember
this equation here
grim nebula
wait i totally messed it up
brittle ember
hmm?
soft zealotBOT
grim nebula
because they cant depend on x and t at the same time
soft zealotBOT
brittle ember
ok i get what ur saying now
soft zealotBOT
grim nebula
very good
final saddleBOT
@brittle ember Has your question been resolved?
tranquil pine
Due to insecurities i must know if this is mathematically correct or accurate.
tranquil pine
void crest
sees right
tranquil pine
AC = AD
AB = CD
angle CAD = 20
I have to find angle ABD
final saddleBOT
AC = AD
AB = CD
angle CAD = 20
I have to find angle ABD
tranquil pine
I tried using isosceles triangle and I managed to find angle ACD and angle ADC but I don't know what do to now
<@&286206848099549185>
grim nebula
!15m
final saddleBOT
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.
grim nebula
jk
grim nebula
can i 🤔
tranquil pine
sry i havent learnt sin yet
grim nebula
dont doxx yourself
tranquil pine
I was told I should use properties of triangles
brittle ember
I was told I should use properties of triangles
what is this for?
i guess is the isosceles part only
tranquil pine
I learnt similar congruent and equilateral triangles as well
brittle ember
u got learn area of triangle?
tranquil pine
half base * height
brittle ember
$(1/2) absin(c)$
soft zealotBOT
phngs
tranquil pine
I have never seen that
brittle ember
what grade are u in?
primary 5?
like 11 y/old?
alright
then u shouldn't be learning that sin in ur syllabus
grim nebula
absin
soft zealotBOT
grim nebula
like 11 y/old?
11 year olds arent allowed on discord
tranquil pine
yea im 13
grim nebula
its against the ts n cs
tranquil pine
im old for my grade yes
brittle ember
11 year olds arent allowed on discord
ping moderator here AHAHA
btw
did the person tell u what property u shud use?
like which property of triangle
cuz there are many
wet moon
I think I’ve seen a similar problem before… I think for many of these problems just construct an equilateral triangle and the problem is magically solved
tranquil pine
How do I do that?
wet moon
Idk, still trying
wet moon
??
brittle ember
AHAHAHA
tranquil pine
yea cool name lol
tranquil pine
How
wet moon
||Construct E such that ADE is equilateral as shown. Then AD = AE so after angle chasing one can find angle ADE = 70
But notice that triangles BAD and DCE are congruent. So angle ABD = angle CDE = 150. ||
Goofy problem
brittle ember
tranquil pine
Is there a way to do it without adding a triangle?
wet moon
Is there a way to do it without adding a triangle?
Not without ugly trig stuff I believe
brittle ember
Not without ugly trig stuff I believe
sin rule?
tranquil pine
aw so maybe ill learn it in awhile
grim nebula
somehow the diagram is horribly out of scale
final saddleBOT
@tranquil pine Has your question been resolved?
tropic sentinel
final saddleBOT
tropic sentinel
Whats a good strategy for graphing this
peak oyster
You can really grpah this function by visualising it, at least it is the only way i know how. Since sin(x) only alternates, and y=x is a linear line, you should expect the graph to have a decreasing amplitudeas you approach infinity.
tropic sentinel
Can you show me how you would?
So should I just know what the graph of sinx/x looks like then move it up to y=1 and so on
peak oyster
tropic sentinel
Ok that makes sense
peak oyster
Sorry i made a mistake. Should be as x approached infinity, f(x) becomes smaller
Graph is ok though i think
jade lantern
doesnt't 1-2(x+1) lead to 1-2x-2 ?
final saddleBOT
doesnt't 1-2(x+1) lead to 1-2x-2 ?
jade lantern
near spoke
doesnt't 1-2(x+1) lead to 1-2x-2 ?
it does
jade lantern
how come they have -2x-1 then?
near spoke
what's 1-2
tranquil pine
how do i solve this
final saddleBOT
how do i solve this
chrome cove
To do that you have to make sure that what's on the other side of the __x² term is positive, and just then you can take the square root, remember that you can only square root positive numbers in the real numbers
Also, doing that doesn't really help
You need to have x² on one side
With what you said, we get
-2x² + 122 = 24
-2x² - 24 = -112
grizzled tusk
Easier:
add 2x² and substract 24
chrome cove
Try moving stuff around and doing other operations until you get x² = ....
tranquil pine
chrome cove
same thing
tranquil pine
i get x^2=-36
what to do right here
nvm
on this i did
-b+- square root of b^2 -4ac over 2a
and i get
-8+- square root of 52 over 2
idk what to do now
tranquil pine
it says wrong
grizzled tusk
so in the end, the answers can be written as -4-sqrt(13) and -4+sqrt(13)
your answers are right too, tho, so maybe it's expecting decimal form
the answers are right, it's a matter of how the site expects you to write them unfortunately
tranquil pine
grizzled tusk
that's equal to your answers, the site was just expecting you write them in this form
tranquil pine
how do i get to that answer
grizzled tusk
by completely simplifying
final saddleBOT
@tranquil pine Has your question been resolved?
tranquil pine
hello
i get
6+- square root of 136 over 2
if i do 4 times 34
and get 2 square root 34
do i have to do now 4 times 8
and 2 square root 8
then 4 times 2
2 square root 2
.close
tranquil pine
$\int W(x) dx = \int f^{-1}(x) dx$
final saddleBOT
$\int W(x) dx = \int f^{-1}(x) dx$
soft zealotBOT
Alham
tranquil pine
Not sure where to go from here
btw, just for reference
$f(a) = ae^a = W(f(a)) = a$
??
frigid sierra
soft zealotBOT
Alham
tranquil pine
Oh lol
tranquil pine
https://en.wikipedia.org/wiki/Lambert_W_function#Integral
Do they show integral here? I was readingg a bit of it earlier
wise lantern
final saddleBOT
wise lantern
i have no idea what i'm doing with either #5 or #6 here
i don't even understand what the questions are asking me
the meme where what the teacher teaches and how difficult the test is in comparison is very true here
because this was on just the previous page:
wise lantern
to anyone who sees this channel:
the message i replied to has the questions
#5: The f be the function given by 9 + 2xe ^ -(x-4) / cos( x / 2 )
The Intermediate Value Theorem applied on *f* on the closed interval [24, 28] guarantees a solution in (24, 48) to which of the following equations?
a) f(x) = 0
b) f(x) = 9.090
c) f(x) = 12.235
d) f(x) = 76.999
here's number 5 in a written out format ^
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final saddleBOT
final saddleBOT
Available help channel!
oak arrow
Is the answer 60? I did (4x6)+2(6x3)
final saddleBOT
Is the answer 60? I did (4x6)+2(6x3)
trail mango
I got something else but I might be wrong
distant hawk
A more clever way is to realize that, you have 9 steps to be made, 6 right-move and 3 up-move. You just have to mess with generating different patterns of RRRRRRUUU.
trail mango
yea that's what I was thinking lol
distant hawk
Think about how n-choose-r can help you solve the problem 🙂
oak arrow
A more clever way is to realize that, you have 9 steps to be made, 6 right-move ...
I since there are 9 moves to be made in total, i did 9!/((3!)(6!)), is that right?
i got 84
distant hawk
I since there are 9 moves to be made in total, i did 9!/((3!)(6!)), is that righ...
Correct.
oak arrow
Correct.
hot damn, that is such a methodical way of doing the problem. Thank you so much!
i never woulda thought to do that lol
oak arrow
so i feel like the answer is just 3! but that seems way too simple i feel like im missing something:
final saddleBOT
so i feel like the answer is just 3! but that seems way too simple i feel like i...
oak arrow
please @ me if anyone knows
trail mango
yea it does seem that simple to me lol
final saddleBOT
@oak arrow Has your question been resolved?
oak arrow
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ember storm
sqrt
ember storm
sqrt(t)/t^2
I am trying to use my exponent laws but I've hit a road block
sqrt(t)=t^1/2
(t^1/2)/t^2
.skip
LOL
.close
silver cloud
Yo tbh I would like some help w my algebra 1 class I can’t fail yk
final saddleBOT
Yo tbh I would like some help w my algebra 1 class I can’t fail yk
silver cloud
Tbh I’m stuck at these types of questions
cold gorge
Expand
silver cloud
?
cold gorge
Expand 4(-9w-4)
cold gorge
Write the entire thing.
silver cloud
O
silver cloud
9w-36w-16>w+1+7
green verge
Combine like terms.
junior patrol
Can someone teach me what is 3 and 4 above 6 divided by 2 and 6 above 8
silver cloud
34/6 divided by 6/8?
green verge
I believe you have an algebra error.
weary lake
9w-36w-16>w+1+7
Do the simplification step by step here
silver cloud
I believe you have an algebra error.
?
green verge
Essentially in problems like this, you move all of the w's on one side, and all of the whole numbers on the other side.
junior patrol
3- 4/6 ÷ 2 6/8
green verge
Trying to combine like terms and isolate the variable.
silver cloud
9w-36w-16>w+1+7
-26w>8
weary lake
3- 4/6 ÷ 2 6/8
Make 3 into an improper fraction where it is divided by 6, 2 into one divided by 8, so that you can combine numbers
junior patrol
Make 3 into an improper fraction where it is divided by 6, 2 into one divided by...
Thx cos I kinda forgot
green verge
3/1
weary lake
Thx cos I kinda forgot
Yw just combine using LCM
green verge
-27w - 16 > w +8
weary lake
Then subtract w from both sides
green verge
is what you should have from that then
Move the whole number on the left to the right, and the w on the right to the left.
green verge
What about the 16.
silver cloud
?
green verge
When you distributed this 4(9w-4)
weary lake
-27w - 16 > w +8
Add all of the w terms to the right side
silver cloud
I don’t got paper on me n it’s p/o me
weary lake
Ok say we are at -27w-16>w+8
silver cloud
Yeah
green verge
Do you see where the 16 came from?
weary lake
How do you remove the -27w from the left side?
silver cloud
Subtract -27 and add it to the other side
silver cloud
Do you see where the 16 came from?
Ye
weary lake
Yea
rigid iris
Dont mind me lurking
silver cloud
Add -27w to 1w
weary lake
Well what I meant was
rigid iris
Is the answer in fraction?
green verge
Well, you are trying to remove 27 from the side, so you wouldn't add the negative, you would add the whole number, just like you would subtract to remove a positive number.
silver cloud
Is the answer in fraction?
weary lake
So technically you are subtracting -27w from both sides
But since there are two negatives from that, you end up adding 27w to both sides
silver cloud
Well, you are trying to remove 27 from the side, so you wouldn't add the negativ...
OH
silver cloud
But since there are two negatives from that, you end up adding 27w to both sides
OH
Gotcha
weary lake
So after doing that
silver cloud
So then
weary lake
What is your equation
silver cloud
Ok say we are at -27w-16>w+8
E
green verge
If you are trying to do this in your head, it would be significantly easier if you could write it down.
green verge
Always remember, when you do something on one side, it must happen to the other.
weary lake
You have to perform the same operation to both sides
green verge
If you subtract the 8 from one side, it must be subtracted from the other.
Not added.
silver cloud
-27w-16>w+8
+27. +27
-16>28w+8
-8 -8
——————-
-24>28W
weary lake
Yes
weary lake
Then you isolate w
That 28 has to move to the other side
So what operation do you do
silver cloud
28W<-24
silver cloud
So what operation do you do
?
green verge
You want to get w all by itself, because if you look at your answer, you are solving for the inequality of a number compared to w alone.
weary lake
I mean like do you divide, add, multiply, subtract
green verge
If we have -28w > 24, how do we get w by itself and get the 28 away.
silver cloud
Divide?
weary lake
What do you do to move the 28 in front of w to the other side
green verge
Yes.
weary lake
Yes
green verge
Once you devide the -28 from one side, it must occur on the otherside aswell.
silver cloud
28W<-24
——. ——
28. 28
W<-.8
weary lake
Your dividing on the right side
Because the 28 is technically multiplying by the w before you do this
weary lake
You want to isolate w
So yes, you divide by the same number for both
But it’s the number that is with w
So in this case you divide by 28
rigid iris
28W<-24
——. ——
28. 28
W<-.8
🧍
rigid iris
The last part howd u get w<8
rigid iris
You just turned it into a decimal.
Yes
green verge
Some teachers won't allow you to turn it into a decimal and want it as a fraction though.
So it is important to know how to do that as well.
green verge
If you wanted to turn -24/28 into a simple fraction, what would it be?
weary lake
It allows an exact answer
green verge
A demical is long and more like an estimate.
Since we don't write down the whole decimal that may be 100s of characters long.
silver cloud
So
green verge
To find a more simple fraction out of a bigger raction, you find the greatest common factor out of both numbers, and divide them both by that number.
silver cloud
-24/28 is -4/5?
silver cloud
O
weary lake
What can you multiply together to get 24?
green verge
You have to find the biggest number that can go into 24 and 28.
silver cloud
4
silver cloud
Wdym
green verge
Since 4 is the biggest number that goes into both -24 and 28.
You must simplify the numbers by dividing both of them by 4
weary lake
Yes
green verge
there you go.
the simplified version of -24/28
is
-6/7
that's the exact answer
silver cloud
Na I don’t need one🥳
But Fr thank you for the help
weary lake
If you multiply the same number on both the top and bottom, it equals the same thing
Ok
No
Np
final saddleBOT
grim badger
.
silver cloud
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✅
silver cloud
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grim badger
It takes a few minutes for it to actually close
final saddleBOT
Available help channel!
odd sigil
Hello, in Collatz conjecture how do you find lowest number in given iteration?
final saddleBOT
Hello, in Collatz conjecture how do you find lowest number in given iteration?
@odd sigil Has your question been resolved?
odd sigil
<@&286206848099549185>
final saddleBOT
@odd sigil Has your question been resolved?
final tangle
wdym by lowest number in given iteration
odd sigil
steps
final tangle
can you give an example of exactly what you mean
final saddleBOT
@odd sigil Has your question been resolved?
gaunt kernel
For what quadratic equations can you use this
final saddleBOT
For what quadratic equations can you use this
gaunt kernel
because I tried to use this for another equation that I used factorising for (Which I got the answer right for btw) and I got different answers
final tangle
For what quadratic equations can you use this
all of them
its called the quadratic formula for a reason
show work
final saddleBOT
@gaunt kernel Has your question been resolved?
gaunt kernel
alrighjt
alright*
ill shiow you
show*
3x^2 - 33x + 54 = 0
This I got the answers:
-2 - 9
Since if we divide the whole thing by 3
we get
x^2 - 33x + 54 = 0
I mean
x^2 - 11x + 18 = 0
and what numbers product together is 18
and sum is -11
ofc -2 and -9
and if we put these in a equation
x - 2 = 0
x = 2
x - 9 = 0
x = 9
now
If I do this
with this formula
A = 1
B = -11
C = 18
11 + Square root of -11^2 - (4.1.18)/2
11 + Square root of -121 - (72)/2
final tangle
missing a ton of ()
final tangle
then write it properly
gaunt kernel
11 + square root of 193/2
square root of 193 is 14 Approx
11 +- 14/2
11 + 14/2 = 12.5
final tangle
because your lack of parentheses are what's causing issues
final tangle
apart from clearly indicating the numerator of your fraction here
you also seemed to have ignored that its b^2 in the QF
and after substituting in the value of b=-11,
that's the value you should be squaring
i.e you should have had (-11)^2
(also you're missing the - case in the QF)
gaunt kernel
i.e you should have had (-11)^2
that is 121 tho
final tangle
yes it is
gaunt kernel
same as what I wrote
final tangle
and you shouldn't be rounding like that either
gaunt kernel
13.9?
final tangle
you shouldn't be rounding at all
gaunt kernel
alright
final tangle
and this is all assuming you're continuing on from your first mistake
final tangle
no
gaunt kernel
what do I do abt the i
final tangle
don't round at all
and this is all assuming you're continuing on from your first mistake
gaunt kernel
I didnt round
gaunt kernel
so I have to keep every single digit?
soft zealotBOT
final tangle
if valid work led you up to sqrt(193) you'd keep sqrt(193) exactly as it is unless told otherwise
but anyway as mentioned earlier,
you made mistakes that led to that, so that's not really relevant for this question
final tangle
you've yet to fix the mistakes i mentioned
gaunt kernel
yes I know
final tangle
specifically the issue with the (-11)^2
(unless you did that and didn't tell me)
gaunt kernel
oh
I am meant to work it out while you talk
alright
X = 11 +- (square root of (121 - (4x1x18))
X = 11 +- (square root of 121 - 72)
X = 11 +- (square root of 49)
X = (11 +-7)/2
right?
final tangle
missing ()
i must insist that you include those where appropriate
and no
b is -11,
-b is not that
gaunt kernel
huh
oh sorry its 11
11 + 7/2 = 9
11 - 7/2 = 2
oh woah
alright I see
(btw this is my first time doing quadratics)
Okay thanks for the help!
very informative and helpful
👍
.close
final saddleBOT
final saddleBOT
Available help channel!
sterile jay
final saddleBOT
grave oracle
is calculus allowed or how ??
final saddleBOT
@sterile jay Has your question been resolved?
sterile jay
is calculus allowed or how ??
No, this question is under the lesson Quadratic equations
grave oracle
ohkk
sterile jay
So, I don’t think calculus can be used
I tried factorising
But I’m not sure how to find Max and min values
grave oracle
ohkk
I've a method in hand
lemme solve first then
may I try to explain ??
sterile jay
Sure
sterile jay
Yea
grave oracle
put y=that equation
sterile jay
Ok
grave oracle
y(x^2+3x+4)=x^2-3x+4
then convert it into one equation with y in co-efficients
ig u'll end up with
(y-1)x^2+3(y+1)x+4(y-1)=0
understood so far ?
sterile jay
Yea
grave oracle
we know that x has real values right ?
sterile jay
Yea, so D is greater or equal to 0 ryt?
sterile jay
Ohhh I get it now
grave oracle
so u'll get max and min ryt ??
sterile jay
put y=that equation
I didn’t think of doing this
sterile jay
Thanks, one question, if we have other questions, can I post here, or should I approach other channels?
grave oracle
solve it and lemme know once u get
grave oracle
ya ya
sterile jay
Oh grt, thanks
grave oracle
my pleasure
sterile jay
I have other doubts, may I post here?
grave oracle
related to same topic ?
grave oracle
ok sure
sterile jay
Remainder theorem?
grave oracle
ya
sterile jay
Idk that
grave oracle
if f(x) is a function
f(a) is a remainder when the function is divided by x-a
use that
sterile jay
So r we supposed to substitute a, B in that function?
grave oracle
ya
sterile jay
Should we equate the fn to 0?
grave oracle
ya
sterile jay
Ok lemme try
sterile jay
If equate this 2 fns, constant term 2c^3 will get cancelled ryt?
sterile jay
And find X?
grave oracle
no no
sterile jay
I’m confused
sterile jay
Ohh ok
grave oracle
got it ??
sterile jay
Yea
grave oracle
so did u get c ??
grave oracle
find f(a)
sterile jay
So should I substitute B in place of c in that fn?
sterile jay
I’m not sure how to proceed
sterile jay
I’m getting a^3+ 3b^2a+ 2b^3
= 0
Should I take a common or B common?
If I take B common of those 2 last terms
I’m still left with a B
grave oracle
wait wait
here is something u need to observe
but it is hard to get in 1 try but by practice u can
sterile jay
Ok
grave oracle
take (a-b) common
grave oracle
I’m getting a^3+ 3b^2a+ 2b^3
-3b^2a
sterile jay
Yea it’s - … typing mistake
sterile jay
Yes….
grave oracle
divide what u got by (a-b)
sterile jay
Ok, 1 min
grave oracle
just ping me once u get
sterile jay
Something like this ryt?
sterile jay
What if all the terms have no a anymore
The remainder will be not zero, but with B ryt?
grave oracle
Something like this ryt?
u can divide further my frnd
sterile jay
Can u show how to divide this, cos I’m not used to doing division with more than 1 variable
sterile jay
Ok
sterile jay
1 min, let me try to understand
grave oracle
sure sure tk ur time
grave oracle
my pleasure
sterile jay
Okkk
grave oracle
we know that
a(a+b)=2b^2
right ??
sterile jay
Yes
sterile jay
I did this…
grave oracle
ya ya
now we are equating that other part to 0
bcos optn c has one more part ryt ?
grave oracle
I have no idea how to do this….
.
sterile jay
Yess
grave oracle
so when a=b we get tht right ?
as well as a=(-2b) right ??
grave oracle
a(a+b)=2b^2
jus substitute and see
or just factorize
a^2+ab-2b^2=(a-b)(a+2b)
understood ??
sterile jay
1 min
grave oracle
kk
sterile jay
Ohh ok
sterile jay
I totally forgot abt that term a^2+ab-2b^2
grave oracle
ohkk lol
sterile jay
I was wondering where did u get that lol
grave oracle
lol kk
grave oracle
nice
my pleasure !!
sterile jay
Will u be online, got few more problems
grave oracle
sure
sterile jay
Ok 1 min
grave oracle
kk
sterile jay
The image is not uploading
grave oracle
size ??
sterile jay
2.13 mb
grave oracle
try again
sterile jay
K
If X is real, the fn (X-a)(X-B)/(X-cw will assume all real values , provided
Options:
A) a>B>c
B) a<B<c
C) a>c<B
D) a<c<B
sterile jay
If X is real, the fn (X-a)(X-B)/(X-cw will assume all real values , provided
This is the Question
Can u understand the text?
grave oracle
do that y =
discriminant
u'll get some y^2....... >=0
for it to be true the roots of y^2.... should be imaginary
so put d<=0
sterile jay
How can we be sure it will be imaginary? As a, B, c are variables
grave oracle
no no
the equation y^2.... is always greater than 0
so it can't be -ve
so it shud either have 1 root or imaginary
sterile jay
If y^2 is greater that 0 shouldn’t it be real or 1 root?
grave oracle
are you aware of graphs ?
grave oracle
so if the roots are imaginary
it won't touch or cut anywhere right ??
sterile jay
Yes
grave oracle
Know them, but not well enough to solve problems
just for visualization
grave oracle
just think of the graph of x^2+x+1
it doesn't tough x axis and is always up ie positive
sterile jay
But we have been thot, that if Discriminant is greater that or equal to 0, we will have real or equal, real roots
grave oracle
it doesn't tough x axis and is always up ie positive
grave oracle
But we have been thot, that if Discriminant is greater that or equal to 0, we wi...
ya ya u neednot use that here
I'm just telling u bcos u asked why imaginary means positive
grave oracle
and btw imaginary doesn't mean always positive
it depends on the sign of the x^2
sterile jay
According to graph
grave oracle
if it is positive it is positive or else negative
sterile jay
and btw imaginary doesn't mean always positive
it depends on the sign of the x^...
Okkk that’s what I meant
grave oracle
yess
so first put y=
then make and equation
then d>=0
then for that equation again make d<=0
sterile jay
It’s difficult to understand in typing, if u don’t mind can u send a pic
sterile jay
Ok
sterile jay
so first put y=
then make and equation
then d>=0
then for that equation again ...
So we r assuming and doing for both D >= or <=
sterile jay
Mm
grave oracle
first when we equate y=---
and we get a quadratic in x
for that discriminant will be greater than or equal to 0
sterile jay
Mm
sterile jay
I’m sorry I’m not able to make my mind understand
It’s pretty late here and I’m sleepy
grave oracle
kk lol
sterile jay
So ig we can wrap it up …. I’m sorry
grave oracle
I sent u frnd req
sterile jay
It’s just tomo is Monday and school, so don’t wanna sleep in class
sterile jay
I sent u frnd req
Ohh ok….
grave oracle
bcos idk if this channel will be there
sterile jay
Is it night where u live too?
sterile jay
Same then
grave oracle
kk lol
sterile jay
I sent u frnd req
Oh ok….
grave oracle
accepted ??
sterile jay
U r really good in math, I suck at math…. R u a teacher or something? Or Mayb a topper?
sterile jay
accepted ??
1 min
grave oracle
U r really good in math, I suck at math…. R u a teacher or something? Or Mayb a ...
no no lol I'm just a 12th pass out student
final saddleBOT
@sterile jay Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
spring violet
I'm having trouble setting up this problem integral
final saddleBOT
I'm having trouble setting up this problem integral
spring violet
this is the original problem... where am I messing up?
nvm I think i got it - wrong bounds and forgot fraction on integral
.close
final saddleBOT
final saddleBOT
Available help channel!
oak kraken
final saddleBOT
oak kraken
Just to verify am I missing any here?
I came up with 5 possibilities for how to write the same exponent. Are there more ways to write this?
And is “exponent” the correct word here or depends? One is written as a radical exponent and one as an exponent radical
- rational exponent 2. radical 3. exponent 4, rational exponent 5. exponent?
grim badger
They're all still exponents
oak kraken
oh..
We don’t classify them with sub classes for how they are written differently?
Only two include an actual radical symbol. Even if it was just plain “sqrt(9)” we would still call this an exponent?
soft zealotBOT
dldh06
grim badger
Let me clarify, it's based on what you see
It's mainly called radical exponent and not the other way
oak kraken
Oh
- rational exponent 2. radical exponent 3. radical exponent 4, rational exponent 5. rational exponent?
This is a better way to word them?
(2 radical exponents and 3 rational exponents)
grim badger
That's fine, I guess
white rock
final saddleBOT
white rock
can i get a explanation of this please
uneven linden
Let's start with (i)
Imagine we drew a horizontal line across the top, connecting S and T but perpendicular to both of those north lines
Lemme open paint
white rock
ok
uneven linden
uneven linden
Any quadrilateral has total angle 360
from that you should be able to get angle PQT
uneven linden
Yeah
uneven linden
Give me just a moment
white rock
alr
uneven linden
Should be able to find angle QPR, since you now have all 3 sides
We've got another quadrilateral here, with the extra lines I've drawn
going like SPR and an unlabeled point
angle SPR is just SPQ + QPR
we want that angle at R, and we can again use the sum of the angles in a quadrilateral being 360
Then bearing will just be 360 - that since it's measured clockwise
white rock
is that left side a quadrilateral?
uneven linden
white rock
ye that