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:
(x, y) = (77/240, -3/10)
Step-by-step explanation:
It is convenient to write the equations in standard form.
Multiplying the first equation by 21 gives ...
21y = 24x -14
Multiplying the second equation by 8 gives ...
24x +9y = 5
Then the system of equations in standard form is ...
Subtracting the first from the second, we get ...
(24x +9y) -(24x -21y) = (5) -(14)
30y = -9
y = -9/30 = -3/10
Substituting this into the second equation, we have ...
24x +9(-3/10) = 5
24x = 7.7 . . . . . . . add 27/10
x = 7.7/24 = 77/240
The solution is (x, y) = (77/240, -3/10).
Answer:
4
Step-by-step explanation:
36 = 9*h
9*h = 36
h = 36/9
h = 4
Answer:
- p=0.7103 (4-game series)
- p=0.6480 (2-game series)
Step-by-step explanation:
Let X be the random variable equal the the first 4 straight wins. An overall win for the stronger team implies a negative binomial function with the parameters n=4, p=0.6:
#We find probabilities for the different values of i:
Hence, probability of the stronger team winning overall is:
#Define Y as the random variable for winning 2/3 games.:
Hence, probability of the stronger team winning in 2 out 3 game series is 0.6480
The stronger team has a higher chance of winning in a 4-game series(0.7103>0.6480)
