Hi there!


We can calculate dy/dx using implicit differentiation:
xy + y² = 6 
Differentiate both sides. Remember to use the Product Rule for the "xy" term:
(1)y + x(dy/dx)  + 2y(dy/dx) = 0 
Move y to the opposite side:
x(dy/dx) + 2y(dy/dx) = -y 
Factor out dy/dx:
dy/dx(x + 2y) = -y
Divide both sides by x + 2y:
dy/dx = -y/x + 2y 
We need both x and y to find dy/dx, so plug in the given value of x into the original equation:
-1(y) + y² = 6 
-y + y² = 6 
y² - y - 6 = 0 
(y - 3)(y + 2) = 0
Thus, y = -2 and 3. 
We can calculate dy/dx at each point:
At y = -2: dy/dx = -(-2) / -1+ 2(-2) = -2/5. 
At y = 3: dy/dx = -(3) / -1 + 2(3) = -3/5.
 
        
             
        
        
        
Answer:
$ 9.5
Step-by-step explanation:
total money is $20
on lunch = 1/8 × 20 = 5/2 = $2.5
on movies = 2/5 × 20 = $8
total spent = 2.5+8 =$ 10.5
left money = 20-10.5 = $ 9.5
 
        
             
        
        
        
Answer:
x + (4/ x-2) + (2/ x-1)
Step-by-step explanation:
x + (6x/ x^2 + 2x - x -2)
x + (6x/ (x + 2) X (x - 1))
(6x/ (x + 2) X (x - 1))
(A/ x+2) + (B/ x-1)
(6x/ (x + 2) X (x - 1)) = (A/ x+2) + (B/ x-1)
6x = Ax + Bx - A + 2B
6x = (A+B)x + (-A+2b)
{0 = -A+2B
{6 = A+B
(A,B) = (4, 2)
(4/ x+2) + (2/ x-1)
 x + (4/ x-2) + (2/ x-1)
 
        
             
        
        
        
Answer:
14x +2
Step-by-step explanation:
(8x + 6x) +3 -5 = (14x) +3-5
14x (+ 3-5) = 14x (+ 2)