3rd questtion

[bold knot]

It's from JEE practice?

[vale heath]

Yep

Our sir

Sended that

For mains exam not adv

@bold knot

[bold knot]

Oh yeah for mains!

Which class are you in rn?

[dreamy elbow]

Ok so we have a triangle formed from the lines, and you first wanna get vertices of it.

[vale heath]

12th

[vale heath]

K

[dreamy elbow]

You do that by calculating the intersections

[vale heath]

K

[bold knot]

OK

[dreamy elbow]

Yes can u do that?

[vale heath]

.

@dreamy elbow

After that

@dreamy elbow

[south raptor]

black book?

ig yea

[bold knot]

is answer (0,pi)

[vale heath]

Yep

[vale heath]

I don't have that one but maths sir send us to do that

[dreamy elbow]

My badd

[vale heath]

I listend about it

[dreamy elbow]

Yeah i assume this is correct ima trust u

[vale heath]

How

Kek

[dreamy elbow]

So now you wanna determine which side of the lines

[vale heath]

?

[dreamy elbow]

Which side of the lines is “inside” the triangle

[vale heath]

0 lines

They gaved 3 lines

All are interacting each other

[south raptor]

brilliant ques in that book tbh...

[dreamy elbow]

How do i explain this

[bold knot]

1. Find the vertices of the triangle ( intersection )
2. Set inequalities for a point inside the triangle:
   Consider first, second and third eqn as L1, L2, and L3 respectively.

Okay?

[vale heath]

I am getting stuck in inequalities

[dreamy elbow]

Yeah

[dreamy elbow]

I meant setting inequalities lol

[dreamy elbow]

what ru struggling with?

[vale heath]

Like if it lies inside it is greater than

[dreamy elbow]

Yeah exactly

[vale heath]

If it is touching it is equal

If it is out side less than

How can I write that expression

[bold knot]

Let me explain. See the line: let's say the x-2y+2 = 0, it divides the plane into points where x-2y+2 > 0 ( side 1 ) and x-2y+2 < 0 ( side 2 ).
To be inside the triangle, a point must be on the correct side of each line.... and the correct side depends on which side of the line the triangle is on.

[dreamy elbow]

Yeap

[vale heath]

The extra point is a,sina

In given questions

[bold knot]

For the line: x-2y+2 = 0, we can test a point known to be inside the triangle to determine the direction:
- Example: Take the intersection of the other two lines as a test point.
- Substitute that point inro x - 2y + 2; if it's positive, then " inside ", means x-2y+2 > = 0.

Similarly, for the other lines, substituting a point inside the triangle tells you wheter the inequality is <= 0 or >= 0

So, the choice of ≥ 0 or ≤ 0 is just to make sure the point is on the side of the line where the triangle actually lies.

[dreamy elbow]

You should have this

[vale heath]

K

[bold knot]

Now, let P(a,sina) lie inside the triangle, then it must satisfy all there inequalities corresponding to the triangle sides.

[vale heath]

K

[bold knot]

L1​: x−2y+2 ≥ 0 ⟹ a−2sina+2 ≥ 0 ⟹ 2sina ≤ a + 2

[vale heath]

Hey angles can be negative

[bold knot]

L2​: x+y ≤ 0 ⟹ a+sina ≤ 0

[vale heath]

Like a can be negative

Type

[bold knot]

L3​: x−y−π ≤ 0 ⟹ a−sina−π ≤ 0 ⟹ sina ≥ a−π

[vale heath]

K

Gotcha

[bold knot]

Yes, ‘a’ can be slightly negative, because the inequalities allow it.

[vale heath]

@dreamy elbow I understand

[vale heath]

K

Next step

[dreamy elbow]

Nice

[vale heath]

After finding inequality

[dreamy elbow]

You got the requirements

And then you have the answer

Sorta

[dreamy elbow]

Did u yet?

[vale heath]

Yeo

Ni

No

[bold knot]

sina ∈ [−1,1], so approximate constraints:

1. 2sina ≤ a+2 ⟹ 2(−1) ≤ a+2 ⟹ −2≤a+2⟹a≥−4 (always true for real a > 0 )
2. a + sin a < = 0 ==> a≤−sina≤1
3. sina≥a−π⟹ 1≥a−π⟹ a≤π+1

[dreamy elbow]

Bruh

[bold knot]

The tightest restriction:
a∈(0,π) for the point to be inside

[dreamy elbow]

Hey let him do it

[vale heath]

I always try to remember que type

[dreamy elbow]

You’re not supposed to just send them answers

[vale heath]

I don't get idea by my self

[bold knot]

Oh okay!

[dreamy elbow]

Alr hold oan

[bold knot]

Then?

I tried my best to think like a JEE student, now I'm in my 2nd year in Bachelors!

@dreamy elbow Did you attempt JEE?

[vale heath]

My phy is so bad

I can do chem and math

Maximum

[bold knot]

Even my physics too. I got -1 in Physics mains exams, and -2 in chemistry mains, Math was 100/100 both the times 😂

[vale heath]

Lol

[bold knot]

as per NTA key, I calculated my marks

[vale heath]

Adv

[dreamy elbow]

Nah

Not a chance

[bold knot]

after writing second shift I qualified to Advanced

once again, math was full, in both papers, but phy chem very very less

[vale heath]

I can easily get 40 to 60 marks in chem weekly exam

Math 60-70

Phy 5-10

Out of 100

[bold knot]

Quite similar in phy

[dreamy elbow]

Solve em

[bold knot]

I literally solved everything and gave him the soln

[vale heath]

It would be cheating

Cause I already seen the soln of pvssp_gg

K I stucked

I can't match the last 2 eqn

[dreamy elbow]

Uh

Wit

Wait

[vale heath]

Like I am getting

[dreamy elbow]

Did you get this somewhere

[vale heath]

Nope

[vale heath]

I tried

Nopre

@dreamy elbow

[vale heath]

I didn't got that

[bold knot]

bro, let's try this, search for MATH GPT in google, it'll generate videos also

[vale heath]

Thank you for giving me this tool

Can u give me some math boost up tips

And what should I do in exam first

[bold knot]

Be careful with the domain of the functions

[dreamy elbow]

Sorry im back

I did find a way tho

[vale heath]

What

[vale heath]

Not only chapter but full math sub tips

[vale heath]

?

[dreamy elbow]

Little vague

Uhm

[vale heath]

By differentiation u got max value right?

What about min

@dreamy elbow

[dreamy elbow]

Because g(a) goes up

So yk that its <0

[vale heath]

I understand

[dreamy elbow]

congrats

[vale heath]

Thanks

[twin flame]

you're welcome

[twin flame]

so the answer is (0, pi) option C

right?

I wonder if there's a way to solve algebraically

[vale heath]

What

[twin flame]

is my answer correct?

[vale heath]

Yep

[twin flame]

nice