Answer:
a)South East due to wind turbulance.
Step-by-step explanation:
B)Point south west to go east
Answer:
![\displaystyle y' = -(2x - 5)(6x - 25)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20-%282x%20-%205%29%286x%20-%2025%29)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Distributive Property
<u>Algebra I</u>
- Terms/Coefficients
- Factoring
<u>Calculus</u>
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Product Rule]: ![\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bf%28x%29g%28x%29%5D%3Df%27%28x%29g%28x%29%20%2B%20g%27%28x%29f%28x%29)
Derivative Rule [Chain Rule]: ![\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%20%3Df%27%28g%28x%29%29%20%5Ccdot%20g%27%28x%29)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
y = (2x - 5)²(5 - x)
<u>Step 2: Differentiate</u>
- Derivative Rule [Product Rule]:
![\displaystyle y' = \frac{d}{dx}[(2x - 5)^2](5 - x) + (2x - 5)^2\frac{d}{dx}[(5 - x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B%282x%20-%205%29%5E2%5D%285%20-%20x%29%20%2B%20%282x%20-%205%29%5E2%5Cfrac%7Bd%7D%7Bdx%7D%5B%285%20-%20x%29%5D)
- Chain Rule [Basic Power Rule]:
![\displaystyle y' = [2(2x - 5)^{2 - 1} \cdot \frac{d}{dx}[2x]](5 - x) + (2x - 5)^2\frac{d}{dx}[(5 - x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5B2%282x%20-%205%29%5E%7B2%20-%201%7D%20%5Ccdot%20%5Cfrac%7Bd%7D%7Bdx%7D%5B2x%5D%5D%285%20-%20x%29%20%2B%20%282x%20-%205%29%5E2%5Cfrac%7Bd%7D%7Bdx%7D%5B%285%20-%20x%29%5D)
- Simplify:
![\displaystyle y' = [2(2x - 5) \cdot \frac{d}{dx}[2x]](5 - x) + (2x - 5)^2\frac{d}{dx}[(5 - x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5B2%282x%20-%205%29%20%5Ccdot%20%5Cfrac%7Bd%7D%7Bdx%7D%5B2x%5D%5D%285%20-%20x%29%20%2B%20%282x%20-%205%29%5E2%5Cfrac%7Bd%7D%7Bdx%7D%5B%285%20-%20x%29%5D)
- Basic Power Rule:
![\displaystyle y' = [2(2x - 5) \cdot 1 \cdot 2x^{1 - 1}](5 - x) + (2x - 5)^2(1 \cdot -x^{1 - 1})]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5B2%282x%20-%205%29%20%5Ccdot%201%20%5Ccdot%202x%5E%7B1%20-%201%7D%5D%285%20-%20x%29%20%2B%20%282x%20-%205%29%5E2%281%20%5Ccdot%20-x%5E%7B1%20-%201%7D%29%5D)
- Simplify:
![\displaystyle y' = [2(2x - 5) \cdot 2](5 - x) + (2x - 5)^2(-1)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5B2%282x%20-%205%29%20%5Ccdot%202%5D%285%20-%20x%29%20%2B%20%282x%20-%205%29%5E2%28-1%29)
- Multiply:
![\displaystyle y' = 4(2x - 5)(5 - x) - (2x - 5)^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%204%282x%20-%205%29%285%20-%20x%29%20-%20%282x%20-%205%29%5E2)
- Factor:
![\displaystyle y' = (2x - 5)[4(5 - x) - (2x - 5)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%282x%20-%205%29%5B4%285%20-%20x%29%20-%20%282x%20-%205%29%5D)
- [Distributive Property] Distribute 4:
![\displaystyle y' = (2x - 5)[20 - 4x - (2x - 5)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%282x%20-%205%29%5B20%20-%204x%20-%20%282x%20-%205%29%5D)
- [Distributive Property] Distribute negative:
![\displaystyle y' = (2x - 5)[20 - 4x - 2x + 5]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%282x%20-%205%29%5B20%20-%204x%20-%202x%20%2B%205%5D)
- [Subtraction] Combine like terms (x):
![\displaystyle y' = (2x - 5)[20 - 6x + 5]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%282x%20-%205%29%5B20%20-%206x%20%2B%205%5D)
- [Addition] Combine like terms:
![\displaystyle y' = (2x - 5)(25 - 6x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%282x%20-%205%29%2825%20-%206x%29)
- Factor:
![\displaystyle y' = -(2x - 5)(6x - 25)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20-%282x%20-%205%29%286x%20-%2025%29)
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
AC is correct but it could also be BE.
Answer:
Step-by-step explanation:
Answer:
if I am correct it would be 25 degrees. hope this helps!
Step-by-step explanation: