Answer:
Maximum rate of change at the point (-1,2) = √17
Direction is the direction of the gradient
Step-by-step explanation:
The gradient of a function (scalar or vectorial ) is a vector in the direction of maximum rate of change then
f( x,y ) = x*2y + 2y
grad = δ/δx i + δ/δy j + δ/δz k
grad f(x,y) = [ δ/δx i , δ/δy] = [ 2y , x+2 ]
at the point ( -1 , 2 )
grad f(x,y) = [4 , 1]
| grad f(x,y) | = √ (4)² + (1)² = √17
Answer:
a) 
b) 
And replacing we got:
![P(X \geq 3) = 1- [0.2+0.3+0.1]= 0.4](https://tex.z-dn.net/?f=%20P%28X%20%5Cgeq%203%29%20%3D%201-%20%5B0.2%2B0.3%2B0.1%5D%3D%200.4)
c) 
d) 
e) 
f) 
And replacing we got:

And the variance would be:
![Var(X0 =E(X^2)- [E(X)]^2 = 6.4 -(2^2)= 2.4](https://tex.z-dn.net/?f=%20Var%28X0%20%3DE%28X%5E2%29-%20%5BE%28X%29%5D%5E2%20%3D%206.4%20-%282%5E2%29%3D%202.4)
And the deviation:

Step-by-step explanation:
We have the following distribution
x 0 1 2 3 4
P(x) 0.2 0.3 0.1 0.1 0.3
Part a
For this case:

Part b
We want this probability:

And replacing we got:
![P(X \geq 3) = 1- [0.2+0.3+0.1]= 0.4](https://tex.z-dn.net/?f=%20P%28X%20%5Cgeq%203%29%20%3D%201-%20%5B0.2%2B0.3%2B0.1%5D%3D%200.4)
Part c
For this case we want this probability:

Part d

Part e
We can find the mean with this formula:

And replacing we got:

Part f
We can find the second moment with this formula

And replacing we got:

And the variance would be:
![Var(X0 =E(X^2)- [E(X)]^2 = 6.4 -(2^2)= 2.4](https://tex.z-dn.net/?f=%20Var%28X0%20%3DE%28X%5E2%29-%20%5BE%28X%29%5D%5E2%20%3D%206.4%20-%282%5E2%29%3D%202.4)
And the deviation:

Answer:
1. is no
Step-by-step explanation:
.
Ah yes, good ol’ Pythagorean’s theorem.
The hypotenuse is the opposite of the 90 degree angle, the longest side of the triangle.
The legs are opposite of the acute angles
Formula: a^2 + b^2 = c^2
2:
Let’s plug in some values
(6)^2 + (3)^2 = c^2
C = 6.7
The side will be 6.7 units
3)
Let’s plug in some values
(13.3)^2 = (9.7)^2 + (b)^2
(13.3)^2 - (9.7)^2 = b^2
176.89 - 94.09 = b^2
b = 9.1
The side will be 9.1 units