1 answer:
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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.
Answer:
a). The mean = 1000
The variance = 999,000
The standard deviation = 999.4999
b). 1000 times , loss
Step-by-step explanation:
The mean of geometric distribution is given as ,
And the variance is given by,
Given :
= 0.001
The formulae of mean and variance are :
a). Mean =
=
= 1000
Variance =
=
= 999,000
The standard deviation is determined by the root of the variance.
= = 999.4999
b). We expect to have play lottery 1000 times to win, because the mean in part (a) is 1000.
When we win the profit is 500 - 1 = 499
When we lose, the profit is -1
Expected value of the mean μ is the summation of a product of each of the possibility x with the probability P(x).
= $ 0.50
Since the answer is negative, we are expected to make a loss.