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Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
- Left to Right
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
<u>Algebra I</u>
- Functions
- Function Notation
- Coordinates (x, y)
<u>Calculus</u>
Derivatives
Derivative Notation
Antiderivatives - Integrals
Integration Constant C
Integration Rule [Reverse Power Rule]:
Integration Property [Multiplied Constant]:
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
Point (0, 18)
<u>Step 2: Find General Solution</u>
<em>Use integration</em>
- [Derivative] Rewrite:
- [Equality Property] Integrate both sides:
- [Left Integral] Integrate [Integration Rule - Reverse Power Rule]:
- [Right Integral] Rewrite [Integration Property - Multiplied Constant]:
- [Right Integral] Integrate [Integration Rule - Reverse Power Rule]:
- Multiply:
<u>Step 3: Find Particular Solution</u>
- Substitute in point [Function]:
- Simplify:
- Add:
- Rewrite:
- Substitute in <em>C</em> [Function]:
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integration
Book: College Calculus 10e
By definition of the binomial coefficient,
so we have
as required.