Answer:
The angle it subtend on the retina is   
    
Explanation:
 From the question we are told that
      The length of the warbler is  
       The distance from the binoculars is    
         The magnification of the binoculars is  
Without the 8 X binoculars the  angle made with the angular size of the object  is mathematically represented as
           
         
            
Now magnification can be represented mathematically as 
          
Where  is the angle the image of the warbler subtend on your retina when the   binoculars i.e the  binoculars zoom.
 is the angle the image of the warbler subtend on your retina when the   binoculars i.e the  binoculars zoom.
 So 
       
 =>    
             
 Generally the conversion to degrees can be mathematically evaluated as 
              
                
   
 
        
             
        
        
        
The net force = sum of all forces acting on the body
If we take left side as -ve and right side as +ve,
then,
The net force here would be equal to,
10N + (- 3N)
= 7N.
Therefore, a net force of +7N ( + indicates it's moving towards right) is acting on the book of mass 2kg.
        
             
        
        
        
Answer:
The rate of change of the area when the bottom of the ladder (denoted by  ) is at 36 ft. from the wall is the following:
) is at 36 ft. from the wall is the following:

Explanation:
The Area of the triangle is given by  where
 where  (by using the Pythagoras' Theorem) and
 (by using the Pythagoras' Theorem) and  is the length of the base of the triangle or the distance between the bottom of the ladder and the wall.
 is the length of the base of the triangle or the distance between the bottom of the ladder and the wall.
The area is then

The rate of change of the area is given by its time derivative


 Product rule
 Product rule
 Chain rule
 Chain rule


In here we can identify  ,
,  and
 and  .
.
The result is then
