Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
<u>Algebra I</u>
- Terms/Coefficients
- Expanding
- Functions
- Function Notation
- Graphing
- Exponential Rule [Root Rewrite]:
<u>Calculus</u>
Integrals
- Definite Integrals
- Area under the curve
Integration Rule [Reverse Power Rule]:
Integration Rule [Fundamental Theorem of Calculus 1]:
Integration Property [Multiplied Constant]:
Integration Property [Addition/Subtraction]:
Shell Method:
- [Shell Method] <em>x</em> is the radius
- [Shell Method] 2πx is the circumference
- [Shell Method] 2πxf(x) is the surface area
- [Shell Method] 2πxf(x)dx is the volume
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
Graph of region
y = x²
x = 2
y = 4
Axis of Revolution: y = -1
<u>Step 2: Sort</u>
<em>We are revolving around a horizontal line.</em>
- [Function] Rewrite in terms of <em>y</em>: x = √y
- [Graph] Identify bounds of integration: [0, 4]
<u>Step 3: Find Volume Pt. 1</u>
- [Shell Method] Find distance of radius <em>x</em>:
- [Shell Method] Find circumference variable f(x) [Area]:
- [Shell Method] Substitute in variables:
- [Integral] Rewrite integrand [Exponential Rule - Root Rewrite]:
- [Integral] Expand integrand:
- [Integral] Integrate [Integration Rule - Reverse Power Rule]:
- Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:
- Multiply:
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Applications of Integration
Book: College Calculus 10e
3p + 2s + b...when p = 39.99 and s = 17.89 and b = 49
3(39.99) + 2(17.89) + 49 = 204.75 <==
If Mrs. Sapanaro paid 245 dollars for her and a group of six people (what makes seven people overall), then she paid 245 / 7 dollars per person:
245 / 7 = 35
Answer: Mrs. Sapanaro paid 35 dollars per person.