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.
Let
x--------> the number of gray bricks
y--------> the number of red bricks
we know that
------> inequality 1
<em>-----> </em>inequality 2
therefore
<u>the answer is</u>
x > 0
0.45x+0.58y≤200
A) 19m because 3 times 6 is 18 then you add m, which would be 19m
Point-slope form of a line is
y=mx+b
where m is the slope and b is your y intercept
So, if the slope is 5, then that is your m value
y=5x+b
To find the value of b, that is just the value of where the line passes the y axis
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