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:
t>28
Step-by-step explanation:
work is shown and pictured
Step-by-step explanation:
- To find the E(X) expected value, you come up with the different probabilities for each outcome
- your set of outcomes after 3 tosses would be = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} where H is heads and T is tails
- Each element has a probability of 1/8 so let x represent number of tails
- The E(x)=Summation (x times P(x))
- Now which probability is 1.5 tails? None, so it is either 2 tails or 1 tails
- So you can expect to lose money in 1 game
- But as you play more games the probability of getting 3 tails becomes more and more likely, so you can expect to win in a 100 games
Answer:
the 0,2 does beautiful as it comes
