james ruse 2019 maths q

[yolo tengo]

hey how do i do this question? i looked at the solutions but i still don't understand it. would be great if i got some help

 

[cossine]

hey how do i do this question? i looked at the solutions but i still don't understand it. would be great if i got some help

So the first step would be figuring out what you don't understand regarding the solution.

Also you have not defined "a". What is "a"?

 

[yolo tengo]

So the first step would be figuring out what you don't understand regarding the solution.

Also you have not defined "a". What is "a"?

a is the area

 

[cossine]

a is the area

The question is quite confusing still.

r: smaller radius
a: full area (not halved)

a/2 = 1/2*r^2*pi/6

=> a = r^2*pi/6
=> sqrt(a) = r*sqrt(pi/6)

There seems to be a mistake in the question.

 

[yolo tengo]

The question is quite confusing still.

r: smaller radius
a: full area (not halved)

a/2 = 1/2*r^2*pi/6

=> a = r^2*pi/6
=> sqrt(a) = r*sqrt(pi/6)

There seems to be a mistake in the question.

ill post the solution, but the thing is i still didnt understand the question even after seeing the solution

 

[Lith_30]

I think a is meant to be the length of PQ (from the answers) if we take the area of the triangle PQT, we get , and since that is meant to be half of the area of the sector, we get the relation .

 

[cossine]

ill post the solution, but the thing is i still didnt understand the question even after seeing the solution

So you should first figure out what it is you don't understand. Is there particular line. Is there theorem that you have forgotten or not aware about. What about an axiom or definition.

 

[yolo tengo]

So you should first figure out what it is you don't understand. Is there particular line. Is there theorem that you have forgotten or not aware about. What about an axiom or definition.

firstly, idk why they are dividing the area of a triangle with the area of a sector, it said to show that both of them are halved, so i’m assuming they are meant to be equal in area size?

 

[cossine]

firstly, idk why they are dividing the area of a triangle with the area of a sector, it said to show that both of them are halved, so i’m assuming they are meant to be equal in area size?

So what you are describing is another way to approach the question.

The key idea is establish an relation between "a" and "r" which they just happened to be able to do by dividing area_triangle/area_sector.

To put it simply it is just one step of the calculation.