Question

© (e) 3sin’r-8sinx-3=0, 0sxs2 MHF 401 Page 3 3) 2. Sketch the function f(x) = 206.X + 3)(x-4) 3) 3. Given: f(x)= x + 2x -5 and g(x)=3r-1 determine (fog)(x): 3 5. The displacement of an object, in metres, is given by f(t)=573 -472 +1-3, where t is time in seconds. (a) Find the average rate of change of displacement with respect to time from t = ls to t = 4s. MIL o

solve for x for the first question , please show steps.
if others are done that would be greatly appreciated

Answer 1

(e) 3sin²x -8sinx -3 =0

or, 3sin²x -9sinx + sinx -3 = 0

or, 3sinx(sinx -3) + 1(sinx -3) =0

or, (sinx -3) (3sinx +1) = 0

or, sinx =3 or sinx = -⅓

But sinx ≠ 3

so sinx =-⅓

So x = -19.47°

Which is in fourth quadrant.

So x = 360° - 19.47°

x = 340.53 ° ≈ 341° = 341 π /180

3. f(x) = x² +2x -5

g(x) = 3x-1

(f • g)(x) = (3x -1)² +2(3x-1) -5

= 9x² - 6x +1 +6x -2 -5

= 9x² -6

2.

2. f(x) = 2x (x+ 372 (2-4) 0 -3 41-2 0 24 f(x)0 +24 -3

5 . f(t) = 5t³ -4t² +t -3

f(1) = 5 - 4 +1 -3

= -1

f(4) = 5(4)³ -4(4)² +4 -3

= 320 - 64 +1

= 257

Average rate of change

= {257 -(-1)} /(4-1)

=258/3

=86 m/s