or does it not exist?
#help-27
silent mesa
it doesnt exist because the line suddenly juts upward at that point
to have a derivative the line at that point must be continuous
silent mesa
yea those 3 points should have derivative of 0
wait
idk if 0 is continuous though
at x = 0
silent mesa
ok maybe it said 0 was included somewhere on problem
tender grail
well thank you anyway wanna help me with my last one or you done for today 😭
silent mesa
i can help its better than this chemistry homework
tender grail
ok thanks
The graph of h'(x), the derivative of h(x) is shown below.
I think instead of max it should be min
silent mesa
so the graph shown is h'(x)
tender grail
right
tender grail
yeah i think so
silent mesa
h(x) is increasing whenever the derivative function line is > 0
and its decreasing whenever the derivative line is < 0
tender grail
h(x) is increasing whenever the derivative function line is > 0
sorry for the big pause (-inf, 0)?
silent mesa
yea thats what i think it would be
tender grail
and its decreasing whenever the derivative line is < 0
and then (0, inf)?
I put it in but doesnt mark it right
might be missing something
silent mesa
yea
it is wrong
(-1,2) (2, inf) is probably correct for increasing
nothing special happens at 0
tender grail
i put that
silent mesa
idk
you could try removing the 2 there and see if that does anything
i think that is correct though
i meant the 2 that splits the interval (-1, inf) not the horizontal tangent one
silent mesa
maybe the quiz key thinks that it is still increasing when the derivative equals 0
silent mesa
idk i forgot it have a chem test too
winter patrol
Derive
$$300(5)^{3x-1}$$
devout snowBOT
Derive
$$300(5)^{3x-1}$$
woven radishBOT
Kai Funaba
winter patrol
I got
$$ 900(ln 5) (5)^{3x-1} $$
woven radishBOT
Kai Funaba
winter patrol
However, Wolfram says this
I know how they got it but can I not do +1?
And just keep the original exponent?
hybrid snow
However, Wolfram says this
They're the same
winter patrol
Explains...
hybrid snow
What it's doing is rewriting 300 * 5^(3x-1) as 60 * 5^(3x)
winter patrol
Ye ik that part
I thought it was a rule or sth 🫠
Scared me for a while there
No such thing right?
hybrid snow
Wdym a rule
winter topaz
I’m not too sure where to approach from here
devout snowBOT
I’m not too sure where to approach from here
winter topaz
i do not understand how the angle comes into play
hybrid snow
$v \cdot w = |v| |w| \cos(\theta)$
woven radishBOT
Umbraleviathan
winter topaz
I’m not too sure where to approach from here
from there we get v dot w = -21, but how do we find magnitude 2v - 3w
woven radishBOT
Umbraleviathan
winter topaz
ah-
hybrid snow
So your 4(v • v) - 6(v • w) + 9(w • w) can be found
winter topaz
i get 268
4 * 49 - 6 * 42 + 9 * 36
is that just it…?
but how do we implement the angle into it
devout snowBOT
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winter topaz
<@&286206848099549185>
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fresh skiff
A delivery company has 15 trucks in their area. There are 5 new trucks and each of them has 5% that they wont work normally. There are 10 old ones and each of them has 10% that they wont work normally. A customer needs 14 trucks tomorrow for delivery.
Question:
How many percent that they will have enough trucks for the customer?
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A delivery company has 15 trucks in their area. There are 5 new trucks and each ...
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fresh skiff
<@&286206848099549185> can you help pls
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fair pond
If you wanna integrate this, would change in x be better or y
devout snowBOT
If you wanna integrate this, would change in x be better or y
wheat pebble
@fair pond what
that looks like a difference of 2 functions both of which seem to be y=±√x variants
what's the point of your question exactly?
fair pond
Oh yh mb
So those are two functions
And the q is calculating area between the two
And I could calculate it with respect to x or y
Let’s say I have bounds available for both
Would one be more complicated than the other?
Cause our prof wants us to decipher integration is better with respect to x or y using a graph
@wheat pebble
wheat pebble
<@336439942794444800>
i mean idk how your prof wants you to measure the hardness
but
if you flip x and y
calculating x^2 integral would be easier than integral of √x
but it's pretty simple in both cases
devout snowBOT
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restive river
Guys
I forgot how to show the solution of finding square roots
Like ik the exact stuff
lyric hornet
wdym by "finding sqaure roots"?
lyric hornet
$\sqrt{81}=9$ is sufficient
woven radishBOT
MrFancy
restive river
Huh
lyric hornet
well you could approximate it, or just try to find a number that upon squaring gives 81 using brute force
worthy smelt
prime factorisation, that works too
restive river
well you could approximate it, or just try to find a number that upon squaring g...
I always use second
lyric hornet
$18=23^2$, $9=3^2$, $28=2^27$, and $156=2^2313$ etc
restive river
Idk mannnee
woven radishBOT
MrFancy
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glass valve
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glass valve
Why does (k+1)!(2+k)(k+1)! go to (k+1)!*(2+k)
if thats to hard to read how do i go from the 3rd line to the 4th
abstract escarp
glass valve
just confused on the factorials
silver fjord
Why does (k+1)!*(2+k)*(k+1)! go to (k+1)!*(2+k)
that is not (2+k)
Those are two terms and (k+1)! is the common factor
wooden wraith
someone else already claimed this channel #❓how-to-get-help
glass valve
Those are two terms and (k+1)! is the common factor
does that mean that line 4 is just the terms factored?
normal tree
im lost on how to figure this out
devout snowBOT
im lost on how to figure this out
trail eagle
Try plugging into the formulas you're given with the unknown parameters for simple value (say x = 0, x = 1). This should help you in some ways : you'll be able to single out the exponential one and figure out the values of c and k,
normal tree
okay so just any random numbers will work?
trail eagle
Well say you plug in t = 0. Then both monomials are 0 and the exponential is equal to a, so the only way one of them is not 0 at t = 0 is if it is the exponential right?
Since a*b^0 = a
Now for the monomial ones, you can just try to assign say ct^2 to the first function and see if the values work out
bleak breach
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winged wyvern
hi guys, if the question wants me to make something the subject of an equation, should i leave the other part factorised or expand it? z = (x-1)^2, or z= x^2+1-2x
devout snowBOT
hi guys, if the question wants me to make something the subject of an equation, ...
willow helm
If it doesn't state otherwise, I'd always simplify in these equations
thick inlet
hi
thick inlet
does anyone in here know chem?
pseudo basin
you are better off just asking your question.
people will redirect you if necessary.
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upbeat cairn
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turbid raptor
u can prove that AM/OM=7/4
raven mason
Write formulas of these graphs
devout snowBOT
Write formulas of these graphs
brittle burrow
I think the question is expecting that you'd recognise the general shape of these graphs and the formulas attached to them.
the top right, for example, would be y=|x-a|+b
brittle burrow
how much do you know about these graphs, first off
brittle burrow
well you're in luck because that's all that's needed
brittle burrow
fr
brittle burrow
hm
well we'll leave the bottom left til last
what about absolute value
y=|x-1| for example
raven mason
?
brittle burrow
i see, i'll be careful
raven mason
I'm not from Eng speaking country
raven mason
y=|x-1| for example
First time seeing this tbf
brittle burrow
then how did you work with absolute value before?
brittle burrow
so did you do stuff like |-3|=3?
raven mason
Yea
brittle burrow
uh huh
well we can use it in functions to cover everything, like you see in the top right
we can start with a simple example like y=|x-1|
it's just y=x-1, but when it goes below 0, you flip it above 0
like this
brittle burrow
you're ahead of me!
you add another absolute value
to flip it again
| |x-3| -1 |
raven mason
Ooh
brittle burrow
we good?
raven mason
Isn't h = x
brittle burrow
i saw the edit afterwards, yeah
raven mason
I'll need to write that down
Ok so I understood the top right one, it was pretty easy but
What about the rest
They seem hard
brittle burrow
do you want to do the bottom right first?
raven mason
It doesn't really matter
random summit
We write it separately
no it's okay to write it this way
brittle burrow
ok
brittle burrow
so when i show you this
so you add conditions like this
do you know how the black circle and white circle work?
raven mason
No
brittle burrow
so the black circle means you include the point, which is written as x<=0
white circle means you don't include it --> x>0
brittle burrow
yeah
hold on, that's the wrong way
it's x^2 for negative values and 0
so x<=0
brittle burrow
so the black circle means you include the point, which is written as x<=0
i might've confused you, i was talking about the image i sent here
for the actual question, it's different
you have x^2 for negative numbers and 0 because of the black circle, so it's x<=0
and then for 4-x^2, the white circle means you don't count it, so x>0
raven mason
Negative numbers as in negative x-es?
brittle burrow
yes
raven mason
brittle burrow
yeah, so do you understand how that works now?
raven mason
Maybe but I don't recall reacher explaining it
woven radishBOT
chlamydia
raven mason
nah
brittle burrow
so hyperbolas are special because they're split apart
this is because you put x on the bottom of the fraction
if you have x=1 for y=1/(x-1), you get y=1/0 right?
brittle burrow
good?
raven mason
The formula is y= 1/(x-h) + k?
brittle burrow
the problem here is that we can't have 1/0 on the graph, so that turns into a split (called an asymptote):
yes
do you know already?
brittle burrow
cool
raven mason
So the answer is y=1/(x-3) + 2
brittle burrow
yeah
brittle burrow
good job man
brittle burrow
fast learner
untold vector
How can I solve this, upon putting x = 0 and x = 1 I'm getting -10 and -5 respectively, and here one root needs to be positive and another one needs to be negative.
devout snowBOT
How can I solve this, upon putting x = 0 and x = 1 I'm getting -10 and -5 respec...
near trout
you don't want to actually use 0 and 1
you want to do like
something below 0, and then something above 0
and do that a bit
and then separately do something below 1 and something above 1
and do that a bit
or something like that
untold vector
f(2) = 14
I'm getting a positive value at x=2
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rugged jewel
Write in cartesian form a+bj with w, L, R, C element of ℝ
devout snowBOT
Write in cartesian form a+bj with w, L, R, C element of ℝ
pseudo basin
!status
devout snowBOT
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
do you know in general how to divide complex numbers
near trout
ooh fancy command
rugged jewel
do you know in general how to divide complex numbers
Uh, you mean with multiplying with the complex conjugate and stuff?
pseudo basin
yes
you may notice here that the two denominators are already complex conjugates of one another
so you can just add the fractions as normal
near trout
it's been a thing for like half a year now
i haven't been here in like a year so that checks out
near trout
you should still have some j's on top from somewhere
pseudo basin
no, i did not mean just adding their numerators and denominators together!
that's not how you add fractions!
do you know how to add fractions?
rugged jewel
Yes
Its been 6m since ive done any math
Forgive me
Like that
Now multiply w complex conj
Correct me if im wrong
Okay I got it.
Thxx
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long elbow
im confused if resulting downward acceleration is 0 or 4.9
devout snowBOT
im confused if resulting downward acceleration is 0 or 4.9
long elbow
i think this website takes 9.8
dry oxide
yes, you have to take 9.8 if not stated
dry oxide
there is no gravity factor in the upper block, its only acting on the lower block which causes it to move downwards
long elbow
so if there is friction nothing moves?
long elbow
the top cube against the floor
dry oxide
if the friction opposing the top cube is 10 N or more then this system would be at equilibrium
because the upper block is having a tension towards right equal to 10N
so you have to apply this much amount of force on the opposite side so that it doesnt move
long elbow
i see
dry oxide
but therrs no friction here
so it will just fall downward
just think it practically, and it all would be resolved
devout snowBOT
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hard valve
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cinder mesa
,rotate
woven radishBOT
pseudo basin
When I have x^2+x+1 shouldn’t the numerator he bx+cx+d
bx + cx + d is (b+c)x + d
what point is there to having two separate linear terms
hard valve
Sorry I didn't understand can you repeat please
hard valve
bx + cx + d is (b+c)x + d
oh so it has to look like (b+c)x + d
here it can't be factored so I keep it as it is
what
pseudo basin
you only need one linear term not two
devout snowBOT
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winter patrol
Complete the square
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restive river
Q. Find the coefficient of $x^4$ when $(x + 4)(x-3)^6$ is expanded
woven radishBOT
hodor776
restive river
My working:
By intuition, one observes that x^4 occurs when
- the "x" from (x + 4) is multiplied with kx^3 from the expansion of (x-3)^6 {k being the coefficient of x^3}
- x^4 from the expansion of (x - 3)^6
if we find the coefficient and add em' up, we should be able to get the value of x^4's coefficient
I did that:
$$^6C_2 (x^4)(-3)^2 = 135x^4$$
and
$$^6C_3 (x^3)(-3)^3 = -540x^3$$
when this $x^3$ is multiplied with the x from (x + 4), it becomes $-540x^4$\par
adding these two coefficients gives us: -405
woven radishBOT
hodor776
woven radishBOT
restive river
there is no x^4 term here!
sand dove
Where did you take into account the 4 coefficient?
sand dove
(x***+4***)(x-3)⁶
So indeed, there are two ways to get x⁴
Either we get the coefficient in x³ for (x-3)⁶
sand dove
Or we get 4× the coefficient in x⁴ for (x-3)⁶
woven radishBOT
restive river
and since 4 * 135 is 540 anyways
540-540 = 0
which is the coefficient for x^4
that is why x^4 doesn't appear when I use wolfram to expand
this clears everything up!
tysm
have a great day
.close
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wise mauve
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wise mauve
I don’t think I’m correctly understanding
I put down my current thoughts but i have a feeling im just doing this very wrong
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wise mauve
<@&286206848099549185>
lusty drum
If you simplify f(x)=e*(2ln(x))
It will make it easier for you to do your exercise
Never leave x on top
Always use exp and ln to simplify
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halcyon raven
i dont understand how to do basic algebra problems, for instance 3(x−1)=2(x+3)
halcyon raven
what does the parenthesis mean?
how am i supposed to find x here?
4(x+3)=1 or this
how would i find X?
what do the parenthesis signify
willow helm
In this case multiplication: the fact that 3 is multiplying both x and -1 on the left and that 2 is multiplying both x and 3 on the right
Let's leave variables alone for a second and let's say you are presented with this problem: 4*(3-1)
How would you go about solving this?
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final ridge
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acoustic hornet
What is the probability of getting one six when rolling one-five dice
What is the probability of getting two sixes when rolling one-five dice
What is the propability of getting
One five or six when rolling one to five dice
What is the probability of getting two dice of fives and/or sixes when rolling five dice
devout snowBOT
What is the probability of getting one six when rolling one-five dice
What is t...
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woven radishBOT
jan Niku
Show that the infinite solutions $0<x_1<x_2<\dots$ to $x\sin x = 1$ are given by $$x_n = n\pi + (-1)^n z_n$$ where $z_n >0$.
timber pebble
could I ask for guidance on this guy? I'm not certain if this is a standard problem...I can say I don't think my notes from class shed any light
it seems reasonable
The problem also asserts what seems like correctly that $z_{n+1} < z_n$
woven radishBOT
jan Niku
The problem also asserts what seems like correctly that $z_{n+1} < z_n$
devout snowBOT
timber pebble
oh fuck off
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lofty elm
devout snowBOT
lofty elm
is this correct?
ot sure if i did this correct
does this show the span is apart of p?
how would we do this question
i understand to prove a basis it needs to be in the span and linearly independent but not sure what they are meaning by the equation and hyperplane part
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bleak fulcrum
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bleak fulcrum
i made a mistake in this question, but I do not see how
the first part of the statement is true for 3|5*3, 3|5 is false
am I misunderstanding the question?
devout snowBOT
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dawn herald
im not good at this
dont even know what this is hahahahah
didnt take math proof course
but i hope u get help soon
bleak fulcrum
thanks
bleak fulcrum
didnt take math proof course
same, first proof course of uni
dawn herald
oh wow ur in math major?
dawn herald
ah well that must be tough
bleak fulcrum
i just started so it's alright for now
dawn herald
ah ok. im more into the applied math like calculus
im going in engineering so I like calculus
its basically the furthest i go in math. maybe tensors and numerical methods if ur in soft eng
bleak fulcrum
i see
dawn herald
anyway lemme ping helpers again cuz we got off topic haha and post question again
<@&286206848099549185>
!status
use that to say whic step ur on
bleak fulcrum
bleak fulcrum
the first part of the statement is true for 3|5*3, 3|5 is false
I am unsure why this is true
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frail igloo
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lyric hornet
looks right :) then that DE, is just separable
frail igloo
i think i'm exhausted but i want to get just one more before bed. gah. it's not accepting this
im a little concerned about the LHS
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river gorge
frail igloo
aw thank you so much. i am exhausted atm but i will give it a look tomorrow.
long horizon
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hard valve
Question 19
devout snowBOT
Question 19
dull totem
Which one
hard valve
Question 19
I can get the values of D and C
But how do we I get the values of A,B
dull totem
,rotate
woven radishBOT
dull totem
Do u have to do it with partial fractions?
hard valve
Yes
dull totem
Well there are faster and clever way but ok
hard valve
I didn’t take the inverse of sec/tan
Well I did take arctaj
Arctan*
But this question asks about repeated linear factors
And to solve it using sum of partial fraction
dull totem
Ur sol?
hard valve
The books solution
dull totem
Let me try first
dull totem
But how do we I get the values of A,B
Can't u just put 1 for the value of B
hard valve
I did find B and D sorry
dull totem
Oh
hard valve
But A and C are no where to be found😂
dull totem
Try random numbers and make two equations then solve it
hard valve
But I don’t think calculators are allowed during my exam
And the roots of B and D are only 1 and -1
dull totem
Yeah 2 equations
hard valve
System of 2 equations?
dull totem
Yeah solve for the two variables
hard valve
Ok will try now
hard valve
Okay
dull totem
Try 0 and 3
dull totem
But like this is a hard problem if no calculator yea?
But it do them like this regularly
We are never allowed to use calculators
hard valve
I mean I will try plugging numbers and combining
But no calculator one mistake and it’s gone
dull totem
Yeah it all come down to ur calculation skills
If I can find any other way I will let u know
hard valve
The thing is this is the way the progessor want it
dull totem
But 1 and -1 are only the factors so i don't think there is any other way
hard valve
Yes exactly
dull totem
The thing is this is the way the progessor want it
Oo
If want to try other ways u can try dividing numerator and denominator with x² u will see some magic happens
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ember cargo
One leg of a right triangle is 6cm longer than the other leg. If the length of the hypotenus is sqrt(68), find the area and the perimeter of the triangle.
devout snowBOT
One leg of a right triangle is 6cm longer than the other leg. If the length of t...
ember cargo
so i got the values of the 2 sides
it’s 2 and 8
how do i find the area and perimeter
rugged sparrow
draw a diagram
ember cargo
rugged sparrow
well, are you sure?
Oh okay
that is correct
Now for the perimeter part, it is just the sum of three sides
you know the hypotenuse length (given)
ember cargo
how about the area?
rugged sparrow
area of a right triangle is given by (1/2)*base*height
ember cargo
oh is that it?
okay i got it then
thx
wait nvm
how do i find the height
im not normally this stupid 😭
<@&286206848099549185>
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rugged sparrow
how do i find the height
well you have already calculated that as 2
ember cargo
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restive river
What to do when there is a number before a root?
devout snowBOT
What to do when there is a number before a root?
smoky gyro
What do you mean?
queen estuary
@restive river
restive river
Just like square root
queen estuary
when there is a number before root like 2√3
winter patrol
a: \ $\sqrt[\text{here}]{k}$ \
or \
b: \ $(here)\sqrt{k}$
woven radishBOT
ℝam()n()v
smoky gyro
it means 2 is being multiplied to sqrt3
queen estuary
when there is a number before root like 2√3
it means that 2 multiplied by sqrt of 3
one more example is when
3√4
here we are multiplying 3 with root of 4 that is 2
so we get 3 times 2 that is 6
devout snowBOT
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dry atlas
hi , can anyone help me solve this problem? Given the circumscribed triangle ABC (I). (I) contact BC,CA,AB at D,E,F. Let K be symmetric I through EF, BI ∩ CA = P and CI ∩ AB = Q. Prove that DK ⊥ PQ
devout snowBOT
hi , can anyone help me solve this problem? Given the circumscribed triangle ABC...
devout snowBOT
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dry atlas
<@&286206848099549185>
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ivory bluff
hi , can anyone help me solve this problem? Given the circumscribed triangle ABC...
Can you send a picture you have drawn of this? Not sure what the question is stating at some points
dry atlas
Can you send a picture you have drawn of this? Not sure what the question is sta...
Of course
dry atlas
Can you send a picture you have drawn of this? Not sure what the question is sta...
My teacher gave an hint: Let J be the center of the circular field corresponding to angle A and O be the center of the circle circumscribing triangle ABC. Prove that OJ is perpendicular to PQ
ivory bluff
What is point K once again?
ivory bluff
As I understand K is a symmetric point to I, and the line of symmetry is PQ?
By circular field corresponding to angle A you mean the excenter?
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dry atlas
As I understand K is a symmetric point to I, and the line of symmetry is PQ?
The line of symmetry is EF
vast violet
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vast violet
hi i asked about this earlier but had to go afk
So i plotteed the points
I am not sure waht they want from me
main gull
It's asking you to graph the lines with the different slopes
You have multiple lines
When m = 0, plot that line
When m = 1/4, plot that line
Then m = -1/4
Etc
vast violet
So the ones i plotted is wrong?
vast violet
OH
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@vast violet Has your question been resolved?
scenic osprey
can someone help me with a please?
devout snowBOT
can someone help me with a please?
random temple
do you know triangle inequality
scenic osprey
ive heard about it
i was away when it was taught
i can do a algebraiclly but not geometrically
random temple
you could do some goofy stuff with loc to prove it but idk any simple ways to do it
scenic osprey
like i can see that OQ and OP together 'look' longer than QP
but how do i explain that
random temple
i can do a algebraiclly but not geometrically
do you have to do geometrically
because I think it's kinda tricky
scenic osprey
am i allowed to do it algebraiclly?
random temple
why wouldn't you be allowed
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kind sable
What does \ mean in B \ A?
devout snowBOT
What does \ mean in B \ A?
viscid phoenix
Are you referring to sets?
B\A means objects that belong to B but not belong to A.
kind sable
Yeah
@viscid phoenix
What about
This?
Is there like a list of these math symbols on the web
main gull
Subset
viscid phoenix
Here is a list of set symbols
kind sable
One thing I'm confused abt right now
Uhh
So I have to prove B \ A <=> A intersection B = o with a slash
I get now how B \ A becomes B intersection A^c = B
What do I do from here
kind sable
viscid phoenix
If B\A=B, then B intersects A^c=B, then B is a subset of A^c
If B is a subset of A^c, then B must not have any elements the same as A
You can draw a diagram to clarify that
For the other direction, if A and B does not have any same elements, then B\A=B
kind sable
You can draw a diagram to clarify that
Hmmmm......
wiay
wait
I'm imagining a situation like this
In this case how is B a subset of A^C?
viscid phoenix
If B intersects another set equals to B, then B is a subset of that set
(A intersects B=B --> B is a subset of A)
It's a formula
devout snowBOT
@kind sable Has your question been resolved?
kind sable
If B intersects another set equals to B, then B is a subset of that set
That makes sense thanks!!
But one more quesrtion
Suppose that f : [−3, ∞) → [−8, ∞)
Here what does the arrow mean?
Or the arrow here?
.close
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Available help channel!
orchid glade
looking at the inequality my mans pointing at
devout snowBOT
looking at the inequality my mans pointing at
orchid glade
i can see why both the LHS and RHS are greater than 1
why one is greater than the other
wooden wraith
it says they're equal, no?
orchid glade
nope; the e^((pi/e)-1) is greater than pi/e apparently
wooden wraith
oh my bad I thought you meant before the > sign
orchid glade
yes this
wooden wraith
well I suppose it comes down to showing e^(pi/e) > pi
which is equivalent to pi/e > ln(pi)
and x/e > ln(x) is true except for at a single point where there's a point of tangency
$\frac{x}{e} \geq \ln(x)$ is true with equivalency at $x=e$
woven radishBOT
tatpoj
vocal tartan
Can also look at the function ln(x)/x and see it has a maximum at x=e
orchid glade
well I suppose it comes down to showing e^(pi/e) > pi
well thats actually what im supposed to derive from here...
orchid glade
Can also look at the function ln(x)/x and see it has a maximum at x=e
ok so for that f(x) 1/e is the maximum? and..
vocal tartan
So 1/e > ln(pi)/pi
vocal tartan
=> pi/e > ln(pi)
=> e^(pi/e) > pi
placid rover
which is equivalent to pi/e > ln(pi)
this is taking ln of both sides (ln is strictly increasing)
show
x - 1 > ln x
and if u plot the 2 graphs, it should be clear this is the case
how u want to show it, depends on your class. calculus is one way
grim wraith
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grim wraith
could anyone tell me what i did wrong here?
smoky gyro
I'm integrating $\int_{0}^{2}\left|x^{2}-1\right|dx$ and wanted to know if what I had so far was correct
devout snowBOT
I'm integrating $\int_{0}^{2}\left|x^{2}-1\right|dx$ and wanted to know if what ...
woven radishBOT
water beam
smoky gyro
$\int_{0}^{2}\left|x^{2}-1\right|dx=\int_{1}^{2}\left(x^{2}-1\right)dx+\int_{0}^{1}\left(-x^{2}+1\right)dx$
woven radishBOT
water beam
polar fern
$\int_{0}^{2}\left|x^{2}-1\right|dx=\int_{1}^{2}\left(x^{2}-1\right)dx+\int_{0}^...
WTF
smoky gyro
what
polar fern
Bro what are you calculating
polar fern
I wish the best of luck
restive river
**water beam**
yes this is correct
smoky gyro
I wish the best of luck
well thanks 😂
restive river
keep going
polar fern
i swear to god if this is the bs il be needing to know in high school am going to kill myself
smoky gyro
yes this is correct
ok coolio. Am I good to plug in F(2) - F(0) now?
stone stump
no. you have to solve each integral individually
restive river
yes just don't fuck up the algebra
smoky gyro
dry oxide
😭
smoky gyro
.close
zealous ether
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pine rock
do what
pseudo basin
without realizing it's a 30-60-90
you don't know that it is
x/sin(y) = 2x/sin(z) tho?
zealous ether
you don't know that it is
really? i thought u could infer from the side ratio
at least that's what someone told me
zealous ether
x/sin(y) = 2x/sin(z) tho?
yeah i did this
it didn't look nice to proceed though
z = arcsin(2sin(y))
pseudo basin
cos(y)<1
pseudo basin
y lies between 0 and 90°
zealous ether
y lies between 0 and 90°
right but i was told for this set of questions the picture doesn't have to be representative of the actual figure
pseudo basin
i mean y can't be obtuse can it?
ac you don't even need to know if it's obtuse or not
just that it isn't 0
-1<cos(y)<1 is still good enough
zealous ether
-1<cos(y)<1 is still good enough
right
zealous ether
-1<cos(y)<1 is still good enough
what follows? sin(z) > 2sin(y)cos(y)
zealous ether
sin(z)>sin(2y)
oh bruh
pseudo basin
now how do we know z is acute...
zealous ether
now how do we know z is acute...
because sin is increasing on on 0 to pi/2
okay makes sense, this makes alot of sense but honestly would've never though of multiplying by cos(y)
is there a more "dumb" way to solve it where u don't use much brain power and just brute force?
zealous ether
not that i know of
makes sense
okay so just tryna clarify my trig here
sin(z) > sin(2y)
when can you say z > 2y
i wouldn't mind a general answer ig
oh wait
u can apply increasing function on inequalities
and order is preserved?
pseudo basin
when 2y and z belong to [-pi/2,pi/2] i think.
devout snowBOT
zealous ether
.reopen
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✅
zealous ether
when 2y and z belong to [-pi/2,pi/2] i think.
i forgot something lol
what about if z was obtuse?
then inequality is reversed?
zealous ether
oh sorry i haven't mentioned how this question works:
A) quantity A is bigger
B) quantity b is bigger
C) both quantities are equal
D) can't be determined
the answer is B ig
@pseudo basin is the answer just D? is my answer key wrong again?
,w arcsin(2sin(y)) series expansion at x = 0
woven radishBOT
zealous ether
it looks correct 
but z being obtuse is bothering me
pseudo basin
bweh
zealous ether
bweh
i'm sorry if i'm missing something, but is the answer D?
and not as the markscheme suggest (B)?
pseudo basin
idk im a little busy rn
zealous ether
oh okay
devout snowBOT
@zealous ether Has your question been resolved?
devout snowBOT
@zealous ether Has your question been resolved?
devout snowBOT
@zealous ether Has your question been resolved?
devout snowBOT
@zealous ether Has your question been resolved?
thorny sinew
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steel halo
why, when completing the square, does it equate (y-1)^2 ? shouldn't it be (y+1)^2?
devout snowBOT
why, when completing the square, does it equate (y-1)^2 ? shouldn't it be (y+1)^...
pseudo basin
yeah they typoed
restive river
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wild yew
so this are vectors?
restive river
yeah
wild yew
so || is the magnitude
wild yew
the direction vector for BD
restive river
is?
placid coyote
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restive river
i dont understand this at all
devout snowBOT
i dont understand this at all
restive river
ancient ravine
,rotate
woven radishBOT
