Answer:
- commutative
- not commutative
Step-by-step explanation:
1. The functions in a composition will be commutative if they are inverses of each other.
f(g(x)) = 1/4(4x-20) +5 = x -5 +5 = x
g(f(x)) = 4(1/4x +5) -20 = x +20 -20 = x
The functions f and g are inverses of each other and are commutative. Application of these functions in either order will give the same result--the original function's argument.
__
2. f(g(x)) = 2(x^2 -3) +4 = 2x^2 -2
g(f(x)) = (2x +4)^2 -3 = 4x^2 +16x +13
f(g(x)) gives a different result than g(f(x)), so the functions are not commutative.
4 sin(<em>x</em>) + 9 cos(<em>x</em>) = 0
4 sin(<em>x</em>) = -9 cos(<em>x</em>)
tan(<em>x</em>) = -9/4
<em>x</em> = arctan(-9/4) + <em>nπ</em> … … … (in radians)
or
<em>x</em> = arctan(-9/4) + 180<em>n</em> ° … … … (in degrees)
where <em>n</em> is any integer.
I'm guessing you're solving for <em>x</em> over some domain, probably 0° ≤ <em>x</em> < 360°. In that case, you would have two solutions for <em>n</em> = 1 and <em>n</em> = 2 of
<em>x</em> ≈ 113.96° and <em>x</em> ≈ 293.96°
Add up all the miles- 11.74+12.12+11.26 is 35.12. 34.12 minutes is the answer
6 i’m think i’m not a 100% sure tho
Hi!! What options are you given because I would say feet if you didn't have the option of yards or anything like that :)
