
Regardless of the sign of 

, we have 

 (never negative). But multiplying by -1 makes it negative.
On the other hand,

which can never be negative for real 

.
 
        
             
        
        
        
Basically just do the problem backwards.
72÷9=8
72÷8=9
        
             
        
        
        
Answer:
0.128rad/sec
Step-by-step explanation:
Let x represent the between the man and the point on the path
 θ = the angle 
dx/dt = 4 ft/s
dθ/dt = rate is the searchlight rotating when the man is 15 ft from the point on the path closest to the searchlight 
tan θ = x/20 ft
Cross Multiply
20tan θ = x
dx/dt = 20sec² θ dθ/dt
dθ/dt = 1/20 × cos² θ dx/dt
dθ/dt= 1/20 × cos² θ × 4
dθ/dt = 1/5 × cos² θ 
Note : cos θ = 4/5
dθ/dt = 1/5 × (4/5)²
dθ/dt = 16/125
dθ/dt = 0.128rad/sec
 
        
             
        
        
        
Answer:
according to coordinates the answer to that question should be 4,-4