Irrational numbers can not be precisely represented in decimal form because they are non-terminating, non-repeating decimals. Also they cannot be written as a fraction as well.
This is the concept of algebra, to solve the expression we proceed as follows;
cos 2x-cosx=0
cos 2x=cosx
but:
cos 2x+1=2(cos^2x)
thereore;
from:
cos 2x=cos x
adding 1 on both sides we get:
cos 2x+1=cos x+1
2(cos^2x)=cosx+1
suppose;
cos x=a
thus;
2a^2=a+1
a^2-1/2a-1/2=0
solving the above quadratic we get:
a=-0.5 and a=1
when a=-0.5
cosx=-0.5
x=120=2/3π
when x=1
cos x=1
x=0
the answer is:
x=0 or x=2/3π
For (x, f(x)) = (5, -4), you want to find (x, -1/4·f(x)). That will be
... (5, -1/4·(-4)) = (5, 1)
To give every angle a label:
First angle = 2x
Second angle = x
Third angle = x + 68
So, because the sum of the interior angles of the triangle is 180°, we can say that: 2x + x + (x + 68) = 180
2x + x + x = 4x
4x + 68 = 180
Isolating for x we get: x = (180-68)/4 x = 28
Because the first angle is twice as large and the third angle is greater than the second angle, the measure of the smallest angle is 28°.
