Identity property of multiplication
Answer:0.2
Step-by-step explanation:
A=3
P(A)=P(3)
=0.2
Make two equations. Then solve. Let t and b represent the numbers of pages in the Tax Code and Bible, respectively.
t - b = 18,528 . . . . . tax code exceeds Bible by 18,528 pages
t + b = 21,472 . . . . .together, they total 21,472 pages
Add the two equations.
2t = 40,000
t = 20,000
The number of pages in the tax code is 20,000.
Goals per game. This is calculated per game so the rate will be number of goals divided by the games played hence “Goals Per Game”
Answer:
![\displaystyle y' = \frac{3cos(2x) -2(3x + 1)[sin(2x) + cos(2x)]}{e^{2x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B3cos%282x%29%20-2%283x%20%2B%201%29%5Bsin%282x%29%20%2B%20cos%282x%29%5D%7D%7Be%5E%7B2x%7D%7D)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Factoring
- Exponential Rule [Dividing]:

- Exponential Rule [Powering]:

<u>Calculus</u>
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
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)
Quotient Rule: ![\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5B%5Cfrac%7Bf%28x%29%7D%7Bg%28x%29%7D%20%5D%3D%5Cfrac%7Bg%28x%29f%27%28x%29-g%27%28x%29f%28x%29%7D%7Bg%5E2%28x%29%7D)
Trig Derivative: ![\displaystyle \frac{d}{dx}[cos(u)] = -u'sin(u)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bcos%28u%29%5D%20%3D%20-u%27sin%28u%29)
eˣ Derivative: ![\displaystyle \frac{d}{dx}[e^u] = u'e^u](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5Eu%5D%20%3D%20u%27e%5Eu)
Step-by-step explanation:
<u>Step 1: Define</u>

<u>Step 2: Differentiate</u>
- [Derivative] Quotient Rule:
![\displaystyle y' = \frac{\frac{d}{dx}[(3x + 1)cos(2x)]e^{2x} - \frac{d}{dx}[e^{2x}](3x + 1)cos(2x)}{(e^{2x})^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5Cfrac%7Bd%7D%7Bdx%7D%5B%283x%20%2B%201%29cos%282x%29%5De%5E%7B2x%7D%20-%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B2x%7D%5D%283x%20%2B%201%29cos%282x%29%7D%7B%28e%5E%7B2x%7D%29%5E2%7D)
- [Derivative] [Fraction - Numerator] eˣ derivative:
![\displaystyle y' = \frac{\frac{d}{dx}[(3x + 1)cos(2x)]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{(e^{2x})^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5Cfrac%7Bd%7D%7Bdx%7D%5B%283x%20%2B%201%29cos%282x%29%5De%5E%7B2x%7D%20-%202e%5E%7B2x%7D%283x%20%2B%201%29cos%282x%29%7D%7B%28e%5E%7B2x%7D%29%5E2%7D)
- [Derivative] [Fraction - Denominator] Exponential Rule - Powering:
![\displaystyle y' = \frac{\frac{d}{dx}[(3x + 1)cos(2x)]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{e^{4x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5Cfrac%7Bd%7D%7Bdx%7D%5B%283x%20%2B%201%29cos%282x%29%5De%5E%7B2x%7D%20-%202e%5E%7B2x%7D%283x%20%2B%201%29cos%282x%29%7D%7Be%5E%7B4x%7D%7D)
- [Derivative] [Fraction - Numerator] Product Rule:
![\displaystyle y' = \frac{[\frac{d}{dx}[3x + 1]cos(2x) + \frac{d}{dx}[cos(2x)](3x + 1)]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{e^{4x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5B%5Cfrac%7Bd%7D%7Bdx%7D%5B3x%20%2B%201%5Dcos%282x%29%20%2B%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bcos%282x%29%5D%283x%20%2B%201%29%5De%5E%7B2x%7D%20-%202e%5E%7B2x%7D%283x%20%2B%201%29cos%282x%29%7D%7Be%5E%7B4x%7D%7D)
- [Derivative] [Fraction - Numerator] [Brackets] Basic Power Rule:
]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{e^{4x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5B%281%20%5Ccdot%203x%5E%7B1%20-%201%7D%29cos%282x%29%20%2B%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bcos%282x%29%5D%283x%20%2B%201%29%5De%5E%7B2x%7D%20-%202e%5E%7B2x%7D%283x%20%2B%201%29cos%282x%29%7D%7Be%5E%7B4x%7D%7D)
- [Derivative] [Fraction - Numerator] [Brackets] (Parenthesis) Simplify:
]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{e^{4x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5B3cos%282x%29%20%2B%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bcos%282x%29%5D%283x%20%2B%201%29%5De%5E%7B2x%7D%20-%202e%5E%7B2x%7D%283x%20%2B%201%29cos%282x%29%7D%7Be%5E%7B4x%7D%7D)
- [Derivative] [Fraction - Numerator] [Brackets] Trig derivative:
![\displaystyle y' = \frac{[3cos(2x) -2sin(2x)(3x + 1)]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{e^{4x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5B3cos%282x%29%20-2sin%282x%29%283x%20%2B%201%29%5De%5E%7B2x%7D%20-%202e%5E%7B2x%7D%283x%20%2B%201%29cos%282x%29%7D%7Be%5E%7B4x%7D%7D)
- [Derivative] [Fraction - Numerator] Factor:
![\displaystyle y' = \frac{e^{2x}[(3cos(2x) -2sin(2x)(3x + 1)) - 2(3x + 1)cos(2x)]}{e^{4x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7Be%5E%7B2x%7D%5B%283cos%282x%29%20-2sin%282x%29%283x%20%2B%201%29%29%20-%202%283x%20%2B%201%29cos%282x%29%5D%7D%7Be%5E%7B4x%7D%7D)
- [Derivative] [Fraction] Simplify [Exponential Rule - Dividing]:

- [Derivative] [Fraction - Numerator] Factor:
![\displaystyle y' = \frac{3cos(2x) -2(3x + 1)[sin(2x) + cos(2x)]}{e^{2x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B3cos%282x%29%20-2%283x%20%2B%201%29%5Bsin%282x%29%20%2B%20cos%282x%29%5D%7D%7Be%5E%7B2x%7D%7D)
Topic: AP Calculus AB/BC
Unit: Derivatives
Book: College Calculus 10e