Take the derivative of x^2 to get 2x.
Take the derivative of -2xy to get -2y +-2x
![\frac{dy}{dx}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%20)
(Everytime you take the derivative of y, you write
![\frac{dy}{dx}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%20)
.
Take the derivative of -3y^2 to get -6y
![\frac{dy}{dx}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%20)
.
Get the terms with
![\frac{dy}{dx}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%20)
on one side to get:
-2x
![\frac{dy}{dx}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%20)
- 6y
![\frac{dy}{dx}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%20)
= 2x - 2y
Take out the common factor of
![\frac{dy}{dx}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%20)
to get:
![\frac{dy}{dx}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%20)
[-2x - 6y] = 2x - 2y
Divide by -2x - 6y to get:
![\frac{dy}{dx}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%20)
=
Answer:
0.6341 = 63.41% probability that his commute today took more than 35 minutes
Step-by-step explanation:
Randomly distributed = Uniform distribution.
A distribution is called uniform if each outcome has the same probability of happening.
The uniform distributon has two bounds, a and b, and the probability of finding a value higher than x is given by:
![P(X > x) = \frac{b - x}{b - a}](https://tex.z-dn.net/?f=P%28X%20%3E%20x%29%20%3D%20%5Cfrac%7Bb%20-%20x%7D%7Bb%20-%20a%7D)
Randomly distributed with a minimum of 20 minutes, a maximum of 61 minutes.
This means that
.
What is the probability that his commute today took more than 35 minutes?
![P(X > 35) = \frac{61 - 35}{61 - 20} = 0.6341](https://tex.z-dn.net/?f=P%28X%20%3E%2035%29%20%3D%20%5Cfrac%7B61%20-%2035%7D%7B61%20-%2020%7D%20%3D%200.6341)
0.6341 = 63.41% probability that his commute today took more than 35 minutes
Answer:
the y<5+5=10
Step-by-step explanation: