Answer:
The answer is B. 
Step-by-step explanation:
Because 
So the answer in this question is B.
 
        
             
        
        
        
Answer:
The positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12
Step-by-step explanation:
To determine the positive values of k that the function y = sin(kt) satisfy the differential equation y''+144y=0.
First, we will determine y''.
From y = sin(kt)
y' = 
y' = 
y' = kcos(kt)
Now for y''
y'' = 
y'' = 
y'' = 
Hence, the equation y'' + 144y = becomes
 +
 +  
 


∴ 
 ±
 ±
 ±
 ± 
∴  or
 or 
Hence, the positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12
 
        
             
        
        
        
3 6/25 would be your answer!!!