Answer:

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>
<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)
Step-by-step explanation:
<u>Step 1: Define</u>

<u>Step 2: Differentiate</u>
- [Derivative] Product Rule:
 + (-8s - 9)\frac{d}{ds}[(-4s + 2)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20h%27%28s%29%20%3D%20%5Cfrac%7Bd%7D%7Bds%7D%5B%28-8s%20-%209%29%5D%28-4s%20%2B%202%29%20%2B%20%28-8s%20-%209%29%5Cfrac%7Bd%7D%7Bds%7D%5B%28-4s%20%2B%202%29%5D)
- [Derivative] Basic Power Rule:

- [Derivative] Simplify:

- [Derivative] Distribute [Distributive Property]:

- [Derivative] Combine like terms:

Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
Answer:
60m^2
Step-by-step explanation:
Ok so if you subtract the 18 by 12 then divide by two you get the missing lengths of each of te triangles. If you then use the area of a trapezoid formula (think about it like pulling one triangle off one side and putting it next to the other to make a rectangle) you just do L x W and get 60.
Answer:
41.29 cm²
Step-by-step explanation:
From the question,
Area of the shaded portion = Area of the circle - area of the square.
A' = πr²-L²...… Equation 1
Where A' = Area of the shade portion, r = radius of the circle, L = length of the square, π = pie
Given: r = 4 cm, L = 3 cm
Constant: π = 22/7.
Substitute these values into equation 1
A' = [(22/7)×4²]-3²
A' = 50.29-9
A' = 41.29 cm²
Hence the area of the shaded portion is 41.29 cm²
Answer: the rate of the passenger train is 100 mph.
Step-by-step explanation:
Let x represent the rate of the passenger train.
The rate of the freight train was 10 miles per hour slower than the rate of the passenger train. It means that the rate of the freight train is (x - 10) mph
The passenger train traveled 100 miles. It means that the time it took travel 100 miles is
100/x
In the same amount of time, it took a freight train to travel 90 miles. It means that the time it took travel 90 miles is
90/(x - 10)
Since the time is the same, then
100/x = 90/(x - 10)
Cross multiplying, it becomes
100(x - 10) = 90x
100x - 1000 = 90x
100x - 90x = 1000
10x = 1000
x = 100 mph
Answers are in the picture.