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.
N-8 or 8-n I would assume
Answer:
14201.63
Step-by-step explanation:
14187.63
+ 14.50
=14201.63
First we need to make both fractions equal to each other, and that means having to have the denominators the same.
What both 3 and 12 easily go into is 12.
So we need to make both fractions have a denominator of 12, so we multiply.
2/3 * 4/4 = 8 / 12
1/4 * 3/3 = 3 / 12
Now, we know that she has 8 / 12 pounds, and she uses 3 / 12 of it, so now we subtract to find how much she has left.
8 - 3 = 5
Out of the 12 pounds of roast beef, she now has 5 / 12 left.
The longer side is at first 7cm and the shorter is 2cm.
So since 7cm(the longer side)×5=35cm then the shorter side(2cm) multiplied by 5 should give you the right answer.
