4.) Mindy works for an ice cream cart vendor. She receives $38 for taking the cart out for a
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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.
Hi there!
Let's solve this equation step by step!
First add 7 to both sides.
Next we need to take a look at the meaning of the stripes between our variable. Those stripes mean we are dealing with an absolute value function. The absolute value stripes make everything between the stripes positive; also when we plug in a number. In this particular question we can plug in both -13 and 13 at the position of n, because when -13 is made positive, it fulfils the equation.
Hence,
or 
~ Hope this helps you!
Let's solve this equation step by step!
First add 7 to both sides.
Next we need to take a look at the meaning of the stripes between our variable. Those stripes mean we are dealing with an absolute value function. The absolute value stripes make everything between the stripes positive; also when we plug in a number. In this particular question we can plug in both -13 and 13 at the position of n, because when -13 is made positive, it fulfils the equation.
Hence,
~ Hope this helps you!