N + (n+1) + (n+2) = -369
3n + 3 = -369
3n = -366
n = -122
so the three consecutive integers are : -124 ; -123 ; -122
        
             
        
        
        
Given that the sides of the acute triangle are as follows:
21 cm
x cm
2x cm
Stated that 21 cm is one of the shorter sides of the triangle2x is greater than x, so it follows that 2x MUST be the longest side
For acute triangles, the longest side must be less than the sum of the 2 shorter sides
Therefore, 2x < x + 21cm
2x – x < 21cm
x < 21cm
If x < 21cm, then 2x < 42cm
Therefore, the longest possible length for the longest side is 42cm
        
                    
             
        
        
        
Answer:
The equation that represents the motion of the string is given by:
 .....[1] where t represents the time in second.
     .....[1] where t represents the time in second.
Given that: A = 0.6 cm (distance above its resting position) , k = 1.8(damping constant) and frequency(f) = 105 cycles per second.
Substitute the given values in [1] we get;
 
  
or
 
  
(a)
The trigonometric function that models the motion of the string is given by:
 
(b)
Determine the amount of time t that it takes the string to be damped so that 
Using graphing calculator for the equation 
  
 
let x = t (time in sec)  
Graph as shown below in the attachment: 
we get:
the amount of time t that it takes the string to be damped so that  is, 0.5 sec
 is, 0.5 sec
 
        
             
        
        
        
Answer:
They are complementary angles.
Step-by-step explanation:
The sum of their measurements equals 90 degrees.