Answer: Angle A = 53.9 degrees
Step-by-step explanation: We have a right angled triangle with two sides clearly given and one angle to be calculated. If the angle to be calculated is angle A, then having angle A as our reference angle, line AC (10 units) is the adjacent, line CB is the opposite while line AB (17 units) is the hypotenuse. Having been given the adjacent and the hypotenuse, we can now use the trigonometric ratio as follows;
CosA = adjacent/hypotenuse 
CosA = 10/17
CosA = 0.5882
By use of the calculator or table of values,
A = 53.97
Approximately to the nearest tenth,
A = 53.9 degrees 
 
        
             
        
        
        
Answer:
Step-by-step explanation:
Answer:
(x-1)²+(y-3.5)² = 265/4
Step-by-step explanation:
first find the midpoint (center of the circle)
(9+-7)/2, (2+5)/2
(1, 3.5) = center
then distance formula to find diameter
√(9- -7)²+(2-5)²=√256+9 = √265 
The radius is half the diameter = (√265)/2
Formula for circle is (x-h)²+(y-k)²=r², where (h, k) is the center
Now you can plug everything in.
(x-1)²+(y-3.5)² = 265/4
 
        
             
        
        
        
The volume of the pyramid is 15 yd
        
             
        
        
        
Well, ....... X=57/2 or 28.5 but not are equivalent
        
             
        
        
        
Answer:

Step-by-step explanation:
Consider the revenue function given by  . We want to find the values of each of the variables such that the gradient( i.e the first partial derivatives of the function) is 0. Then, we have the following (the explicit calculations of both derivatives are omitted).
. We want to find the values of each of the variables such that the gradient( i.e the first partial derivatives of the function) is 0. Then, we have the following (the explicit calculations of both derivatives are omitted). 


From the first equation, we get,  .If we replace that in the second equation, we get
.If we replace that in the second equation, we get 

From where we get that  . If we replace that in the first equation, we get
. If we replace that in the first equation, we get 

So, the critical point is  . We must check that it is a maximum. To do so, we will use the Hessian criteria. To do so, we must calculate the second derivatives and the crossed derivatives  and check if the criteria is fulfilled in order for it to be a maximum. We get that
. We must check that it is a maximum. To do so, we will use the Hessian criteria. To do so, we must calculate the second derivatives and the crossed derivatives  and check if the criteria is fulfilled in order for it to be a maximum. We get that 


We have the following matrix,  
![\left[\begin{matrix} -10 & -2 \\ -2 & -16\end{matrix}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Bmatrix%7D%20-10%20%26%20-2%20%5C%5C%20-2%20%26%20-16%5Cend%7Bmatrix%7D%5Cright%5D) .
.
Recall that the Hessian criteria says that, for the point to be a maximum, the determinant of the whole matrix should be positive and the element of the matrix that is in the upper left corner should be negative. Note that the determinant of the matrix is  and that -10<0. Hence, the criteria is fulfilled and the critical point is a maximum
 and that -10<0. Hence, the criteria is fulfilled and the critical point is a maximum