Answer:
Step-by-step explanation:
1, Find (g-f)(x)
we know (g-f)(x) = g(x) - f(x) = ( 5x -2) -( 2x^2 +3x +6)
= 5x -2 - 2x^2 - 3x - 6
= -2x^2 + 2x -8
So the function (g-f)(x) = - 2x^2 + 2x - 8
2, Find (fg)(x)
we know that (fg)(x) = f(x) * g(x)
= (2x^2 +3x +6 ) *( 5x -2)
= 5x* (2x^2 +3x +6 ) - 2*(2x^2 +3x +6 )
= 10x^3 + 15x^2 +30x -4x^2 -6x - 12
= 10x^3 + 11x^2 + 24x - 12
The answer is (fg)(x)= = 10x^3 + 11x^2 + 24x - 12
Answer:
Step-by-step explanation:
Let y = sin(x+y)
Differentiating with respect to x on both sides.
![\frac{dy}{dx} = \frac{d}{dx} \sin(x + y) \\ \\ \frac{dy}{dx} = \cos(x + y)\frac{d}{dx} (x + y) \\ \\ \frac{dy}{dx} = \cos(x + y)(1 + \frac{dy}{dx}) \\ \\ \frac{dy}{dx} = \cos(x + y) +\cos(x + y) \frac{dy}{dx} \\ \\ \frac{dy}{dx} - \cos(x + y) \frac{dy}{dx} = \cos(x + y) \\ \\ \frac{dy}{dx} [1 - \cos(x + y)] = \cos(x + y) \\ \\ \purple {\bold {\frac{dy}{dx} = \frac{ \cos(x + y)}{[1 - \cos(x + y)] }}}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20%20%5Cfrac%7Bd%7D%7Bdx%7D%20%20%5Csin%28x%20%2B%20y%29%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20%20%5Ccos%28x%20%2B%20y%29%5Cfrac%7Bd%7D%7Bdx%7D%20%20%28x%20%2B%20y%29%20%5C%5C%20%20%5C%5C%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20%20%5Ccos%28x%20%2B%20y%29%281%20%2B%20%5Cfrac%7Bdy%7D%7Bdx%7D%29%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20%20%5Ccos%28x%20%2B%20y%29%20%2B%5Ccos%28x%20%2B%20y%29%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%20-%20%5Ccos%28x%20%2B%20y%29%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%20%5Ccos%28x%20%2B%20y%29%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%5B1%20-%20%5Ccos%28x%20%2B%20y%29%5D%20%3D%20%20%5Ccos%28x%20%2B%20y%29%20%5C%5C%20%20%5C%5C%20%5Cpurple%20%7B%5Cbold%20%7B%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20%20%5Cfrac%7B%20%5Ccos%28x%20%2B%20y%29%7D%7B%5B1%20-%20%5Ccos%28x%20%2B%20y%29%5D%20%7D%7D%7D%20)
1 foot is shorter that 20 centimeters
Answer:
0.6
Step-by-step explanation:
2×3x+4+4=12
6X+8=12
6x=12-8
6x=4
Divide by 6
X=0.6
Answer:
2*2 = 4
4^4 = 16
16 > x + 4
Step-by-step explanation:
X is any real number less than 12