Green's theorem says the circulation of  along the rectangle's border
 along the rectangle's border  is equal to the integral of the curl of
 is equal to the integral of the curl of  over the rectangle's interior
 over the rectangle's interior  .
.
Given  , its curl is the determinant
, its curl is the determinant

So we have

 
        
             
        
        
        
Answer:
-  ∠R = 56° 
-  ∠Q = 90°
-  ∠S = 34°
Step-by-step explanation:
The given triangle is a right angled triangle. 
So, the angles in the triangle are : 
- 90° 
- (2x + 38)° 
- (5x - 11)°
Solving according to <u>angle sum property</u>, 
Sum of all angles in a triangle is 180° 
 90° + (2x + 38)° + (5x - 11)° = 180°
 90° + (2x + 38)° + (5x - 11)° = 180°
 117° + 7x = 180°
 117° + 7x = 180°
 7x = 180° - 117°
 7x = 180° - 117° 
 7x = 63°
 7x = 63°
 x = 9
 x = 9 
Angles = 
 2(9) + 38
 2(9) + 38
 56°
 56° 
 5(9) - 11
 5(9) - 11
 34°
 34° 
-  ∠R = 56°
-  ∠Q = 90°
-  ∠S = 34°
The angles are 56°, 90° and 34°.
 
        
             
        
        
        
Answer:
6 packs
Step-by-step explanation:
you add $4.00 and $2.50 together, and get 6.50 and then divide 39 bye $6.50
 
        
             
        
        
        
System of Linear Equations entered :
 [1] 5x - 6y = 7
 [2] 6x - 7y = 8
Graphic Representation of the Equations :
 -6y + 5x = 7 -7y + 6x = 8 
 Solve equation [2] for the variable x 
 [2] 6x = 7y + 8
 [2] x = 7y/6 + 4/3
// Plug this in for variable x in equation [1]
 [1] 5•(7y/6+4/3) - 6y = 7
 [1] - y/6 = 1/3
 [1] - y = 2
// Solve equation [1] for the variable y 
 [1] y = - 2 
// By now we know this much :
 x = 7y/6+4/3
 y = -2
// Use the y value to solve for x 
 x = (7/6)(-2)+4/3 = -1 
        
             
        
        
        
Answer:
x² + y² = 85
Step-by-step explanation:
Using the expansion
(x - y)² = x² + y² - 2xy , then
x² + y² - 2xy = (x - y)² ( add 2xy to both sides )
x² + y² = (x - y)² + 2xy ← substitute given values
           = 9² + 2(2)
           = 81 + 4
           = 85