Answer:
Step-by-step explanation:
2π/3 radians is equivalent to
2π 180°
-------- * ---------- = 120°
3 π rad
This angle (120°) is 30° past 90°. The 'opposite side' of the triangle formed by this ray of length 1 is √3 and the 'adjacent side' is 1.
adj side -1
cos 120° is in Quadrant II. cos 120° = --------------- = ---------
hyp 2
√3
and sin 120° = --------
2
Answer:
- f(x) = x^3
- g(x) = (2x+4)^2
Step-by-step explanation:
There are many ways to decompose h(x) into f(x) and g(x). The main purpose of the exercise seems to be to get you to think about the operations that are performed on x, then divide that list of operations into two parts.
In the function ...
h(x) = (2x +4)^6
the variable x is ...
- multiplied by 2
- 4 is added to the sum
- the sum is raised to the 6th power
Of course, the 6th power can be considered as the cube of a square or the square of a cube, if you like.
In the decomposition shown in the answer above, we have chosen to put most of this list in g(x), including the square of the sum. Then we have made f(x) be the cube of that square.
h(x) = f(g(x)) = (2x+4)^6
When f(x) = x^3, this is ...
h(x) = f(g(x)) = g(x)^3 = ((2x+4)^2)^3
so ...
g(x) = (2x+4)^2 . . . and . . . f(x) = x^3
_____
Other possible decompositions are ...
or
- g(x) = (x+2)
- f(x) = (2x)^6
or
or ... (many others)
iedikdtep-by-step explanation:
Answer:
-15/16 or -0.9375
Step-by-step explanation:
3/5x=6 +7x
3x=30+35x
3x-35x=30
-32x=30
x= -15/16
