Internal angle of regular hexagon = angle P = 120 degrees
So QOP and PQO are 30 degrees each (because there are 180 degrees in a triangle)
OL bisects angle NOP so LOP = 60
Now subtract angle QOP (found earlier to be 30)
60 - 30 = 30 = LOQ
You have it correct in your musings......this is the IMAGE produced by the FIRST (concave) mirror......this IMAGE is then used as a VIRTUAL OBJECT (as it is not a REAL object) for the SECOND (convex) mirror calculations.....
If you had an ACTUAL object of the same size and orientation placed at the first image location, it would produce the same results in the calculations for the second mirror.....but you are using the IMAGE as an object instead...a VIRTUAL OBJECT.
OK?
Draw a line straight across from point B...then you have a right triangle with legs 5 and 3
the hypotenuse is BA sqrt (3^2 + 5^2) = ~5.8 units
A rhombus has 4 equal sides..... 148/4 = 37 side length
The diaonals of a rhombus bisect each other (at right angles)....we can find the 1/2 length of the other diagonal
since 1/2 of the diagonal given and the other 1/2 form a right triangle with one side of the rhombus (37) as a hypotenuse
24/2 = 12 12^2 + x^2 = 37^2 x = 35 so the other diagonal is 2*35= 70
Area Rhombus = diagonal1 x diagonal2 / 2 = 24 x 70/2 = 840 sq units
So ...in interval notation
(6,7)
What about the negative options? Oh yah.... y>0 Haha
Never mind......
see below
You're welcome, of course !
Line c slope = -8 parallel slope of new line = -8 also
y= -8x + b Must include point -1,-2 sub this in to the equation to find 'b'
-2 =-8(-1) + b
-10 = b
y = -8x - 10 === line d
Thanx for pointing that out !
BUT ACTUALLY, we need interval notation with a disjunction....
it should look like this:
(-inf, -11) U (3.5, +inf)
Sorry for the confusion !
I think when you multiply by 6/6 in your solution, you should wind up with
30x + 30 in the numerator.
