Answer:

General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Addition/Subtraction]:
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Integration
Integration Rule [Reverse Power Rule]: 
Integration Rule [Fundamental Theorem of Calculus 1]: 
Integration Property [Addition/Subtraction]: ![\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%7B%5Bf%28x%29%20%5Cpm%20g%28x%29%5D%7D%20%5C%2C%20dx%20%3D%20%5Cint%20%7Bf%28x%29%7D%20%5C%2C%20dx%20%5Cpm%20%5Cint%20%7Bg%28x%29%7D%20%5C%2C%20dx)
U-Substitution
Area of a Region Formula: ![\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%20%3D%20%5Cint%5Climits%5Eb_a%20%7B%5Bf%28x%29%20-%20g%28x%29%5D%7D%20%5C%2C%20dx)
Step-by-step explanation:
<u>Step 1: Define</u>

<u>Step 2: Identify</u>
<em>Graph the systems of equations - see attachment.</em>
Top Function: 
Bottom Function: 
Bounds of Integration: [-1.529, 1.718]
<u>Step 3: Integrate Pt. 1</u>
- Substitute in variables [Area of a Region Formula]:

- [Integral] Rewrite [Integration Property - Addition/Subtraction]:

- [Right Integral] Integration Rule [Reverse Power Rule]:

- Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:

<u>Step 4: Integrate Pt. 2</u>
<em>Identify variables for u-substitution.</em>
- Set <em>u</em>:

- [<em>u</em>] Basic Power Rule [Derivative Rule - Addition/Subtraction]:

- [Limits] Switch:

<u>Step 5: Integrate Pt. 3</u>
- [Integral] U-Substitution:

- [Integral] Integration Rule [Reverse Power Rule]:

- Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:

- Simplify:

Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Set the equations equal to each other since the x will be the same. Get like terms on the same side and solve.
2x-5=-2/3x+3
2x-5+5=-2/3x+3+5
2x=-2/3x+8
2x+2/3x=-2/3x+2/3x+8
2 2/3x=8
8/3x=8
(3/8)8/3x=8(3/8)
x=3
x=3
Answer: dot plot 1 is 6
dot plot 2 is 15
dot plot 3 is 13
dot plot 4 is i dont know
Step-by-step explanation:
Answer:
Step 1: Write down the decimal divided by 1, like this: decimal 1.
Step 2: Multiply both top and bottom by 10 for every number after the decimal point. ...
Step 3: Simplify (or reduce) the fraction.
Step-by-step explanation:
Answer:
77
Step-by-step explanation:
c + 103 = 180
180- 103 = 77
c and b = 77