Answer:
a.  
b. 
c. 


  
Step-by-step explanation:
a) The marginal cost function is given by the derivative of the total cost function, in this way the marginal cost function for this company is:

b) The income function is given by the relation  .
.
The marginal revenue function for the company is given by the derivative of the revenue function, in this way the marginal revenue function is:

  
(c) The profit function of the company is given by the relation  , and the marginal utility function is given by the derivative of the utility function, in this way , the marginal utility function is:
, and the marginal utility function is given by the derivative of the utility function, in this way , the marginal utility function is:

When q = 2000, the marginal utility is:

When q = 7000, the marginal utility is:

 
        
             
        
        
        
The value of tangent theta is equal to the negative 1.  At this value the value of secant theta is  .
.
<h3>What is tangent theta?</h3>
The tangent theta in a triangle is the ratio of sine theta and cos theta. It can be written as,

Given information-
The value of tangent theta is equal to the negative 1. 

The tangent theta in a triangle is the ratio of sine theta and cos theta. It can be written as,

The value of tangent theta is equal to the negative 1. Thus put the value in above expression as,

Simplify it further as,

When the value of cosine and sine theta is equal, then the angle exist in 4th quadrant with the value of  . Which extent to the
. Which extent to the  for the cosine function.
 for the cosine function.
In the trigonometry cosine theta is the reciprocal of the secant theta. Thus,

Thus the value of secant theta is 
Learn more about the tangent theta here;
brainly.com/question/29190
 
        
                    
             
        
        
        
Answer:
given:
height[h]=8mm
radius [r]=5mm
Now,
Volume of cone=1/3 πr²h=⅓×3.14×5²×8=209mm³
<u>C) 209 </u><u>mm³</u><u> </u><u>is</u><u> </u><u>a</u><u> </u><u>required</u><u> </u><u>answer</u><u>.</u>
 
        
                    
             
        
        
        
Answer:  
The area of the parallelogram is:_______________________________________________________ in² = 1174 ⅛  in² = 1174.125 in²
  in² = 1174 ⅛  in² = 1174.125 in² .
_______________________________________________________Explanation:_______________________________________________________Area of a parallelogram: 
_______________________________________________________ A = base * height = b * h ;
From the figure (from the actual "question"):
_______________________________________         b = 50.5 in.
         h = 23.25 in.
____________________________________________________________Method 1)  A = b * h =                  
                     =  (50.5 in) * (23.25 in) = 1174.125 in² ; or, write as:  1174 <span>⅛ .
</span>
____________________________________________________________Method 2)  A = b * h =             
                      =  (50 ½ in) * (23 <span>¼ in) =    
                      =    (</span>

 in) * (

<span> in) ;
</span>
___________________________________________________________Note:  "50 ½ " = [(50*2) + 1 ] / 2  = 

 ;
Note:  "23 ¼ " = [(23*4) + 1 ] / 4  = 

 ;
____________________________________________________________
→  A =  (

 in) * (

 in) ; 
→  A = 

  in² = 

  in² ;           
→  A = (9393/8) in² =           
→  
A  =  in² = 1174 ⅛  in² = 1174.125 in²
  in² = 1174 ⅛  in² = 1174.125 in² .
________________________________________________________