ratio exam question

hi , there are so many different type of ratio questions that come up that I don't know which method to use
there are between 25 and 35 students in a class
ratio of boys to girls is 4:7
how many students are in the class?

the only step I know is you add 4 and 7 =11

Good start. The total number of people must be a multiple of this number (11 in this case). Do you understand what to do now?

thank you and no i dont know

If the total number of people must be a multiple of 11, and you have a range, you should be able to narrow down which number(s) it can be. In this case, you will be left with only one choice, which is the answer. So yes, it is to do with multiples of 11.

thank you so much i understand now

No problem.

do you mind helping me with this question
do you first find out the area of the whole triangle using the cosine rule?
thats all i know

Yes, then you can take away the area of the sector.

You know the angle and the radius which is enough info to work out the area of the sector.

do you mind helping me with this question
do you first find out the area of the whole triangle using the cosine rule?
thats all i know

thanks so the sector area is
60/360 multiplied by 3²

The triangle is equilateral, so all angles are going to be 60 degrees.
AQ and PQ are both going to be 3cm, as P and Q are midpoints.
The white area is going to be a sector of a circle - it will be a sixth of a circle.

-First you want to find the area of the whole triangle using the SINE rule. This is
Area = 0.5*a*b*sin(C), where a and b are sides, and C is the angle between them.
-Next you want to work out the area of the white/non-shaded area. To do this, work out what the area of a whole circle with radius 3cm would be, and use that to work out what the area of this sector is going to be, using the information I gave above.


Hope this helps

EDIT: Beaten to it by God-on-Earth himself.

and the sector area is 1.5 pie, but why do you divide by 6 and not any other number

There are 360 in a circle. You find the area of the whole circle radius 3 to be $9\pi$

There are only 60 degrees of the full circle that we want here. So we need to find what fraction of 360 degrees 60 degrees is, we do 360/60=6

So the area of our 60 degree sector is a 6th of the full circle.