The initial investment was 3.03 because this is the value that does not change and comes before the value with the exponent "2x" is mentioned.
<u>Given</u>:
The equation of the circle is 
We need to determine the center and radius of the circle.
<u>Center</u>:
The general form of the equation of the circle is 
where (h,k) is the center of the circle and r is the radius.
Let us compare the general form of the equation of the circle with the given equation
to determine the center.
The given equation can be written as,

Comparing the two equations, we get;
(h,k) = (0,-4)
Therefore, the center of the circle is (0,-4)
<u>Radius:</u>
Let us compare the general form of the equation of the circle with the given equation
to determine the radius.
Hence, the given equation can be written as,

Comparing the two equation, we get;


Thus, the radius of the circle is 8
Answer:
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Step-by-step explanation:
i nu speak that language
Answer:
General Formulas and Concepts:
<u>Pre-Calculus</u>
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Integration
- Integrals
- Definite/Indefinite Integrals
- Integration Constant C
Integration Rule [Reverse Power Rule]: 
Integration Rule [Fundamental Theorem of Calculus 1]: 
U-Substitution
- Trigonometric Substitution
Reduction Formula: 
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>

<u>Step 2: Integrate Pt. 1</u>
<em>Identify variables for u-substitution (trigonometric substitution).</em>
- Set <em>u</em>:

- [<em>u</em>] Differentiate [Trigonometric Differentiation]:

- Rewrite <em>u</em>:

<u>Step 3: Integrate Pt. 2</u>
- [Integral] Trigonometric Substitution:
![\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \int\limits^a_b {cos(u)[1 - sin^2(u)]^\Big{\frac{3}{2}} \, du](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5Ea_b%20%7B%281%20-%20x%5E2%29%5E%5CBig%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D%20%5C%2C%20dx%20%3D%20%5Cint%5Climits%5Ea_b%20%7Bcos%28u%29%5B1%20-%20sin%5E2%28u%29%5D%5E%5CBig%7B%5Cfrac%7B3%7D%7B2%7D%7D%20%5C%2C%20du)
- [Integrand] Rewrite:
![\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \int\limits^a_b {cos(u)[cos^2(u)]^\Big{\frac{3}{2}} \, du](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5Ea_b%20%7B%281%20-%20x%5E2%29%5E%5CBig%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D%20%5C%2C%20dx%20%3D%20%5Cint%5Climits%5Ea_b%20%7Bcos%28u%29%5Bcos%5E2%28u%29%5D%5E%5CBig%7B%5Cfrac%7B3%7D%7B2%7D%7D%20%5C%2C%20du)
- [Integrand] Simplify:

- [Integral] Reduction Formula:

- [Integral] Simplify:

- [Integral] Reduction Formula:
![\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg|\limits^a_b + \frac{3}{4} \bigg[ \frac{2 - 1}{2}\int\limits^a_b {cos^{2 - 2}(u)} \, du + \frac{cos^{2 - 1}(u)sin(u)}{2} \bigg| \limits^a_b \bigg]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5Ea_b%20%7B%281%20-%20x%5E2%29%5E%5CBig%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D%20%5C%2C%20dx%20%3D%20%5Cfrac%7Bcos%5E3%28u%29sin%28u%29%7D%7B4%7D%20%5Cbigg%7C%5Climits%5Ea_b%20%2B%20%5Cfrac%7B3%7D%7B4%7D%20%5Cbigg%5B%20%5Cfrac%7B2%20-%201%7D%7B2%7D%5Cint%5Climits%5Ea_b%20%7Bcos%5E%7B2%20-%202%7D%28u%29%7D%20%5C%2C%20du%20%2B%20%5Cfrac%7Bcos%5E%7B2%20-%201%7D%28u%29sin%28u%29%7D%7B2%7D%20%5Cbigg%7C%20%5Climits%5Ea_b%20%5Cbigg%5D)
- [Integral] Simplify:
![\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg| \limits^a_b + \frac{3}{4} \bigg[ \frac{1}{2}\int\limits^a_b {} \, du + \frac{cos(u)sin(u)}{2} \bigg| \limits^a_b \bigg]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5Ea_b%20%7B%281%20-%20x%5E2%29%5E%5CBig%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D%20%5C%2C%20dx%20%3D%20%5Cfrac%7Bcos%5E3%28u%29sin%28u%29%7D%7B4%7D%20%5Cbigg%7C%20%5Climits%5Ea_b%20%2B%20%5Cfrac%7B3%7D%7B4%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B2%7D%5Cint%5Climits%5Ea_b%20%7B%7D%20%5C%2C%20du%20%2B%20%5Cfrac%7Bcos%28u%29sin%28u%29%7D%7B2%7D%20%5Cbigg%7C%20%5Climits%5Ea_b%20%5Cbigg%5D)
- [Integral] Reverse Power Rule:
![\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg| \limits^a_b + \frac{3}{4} \bigg[ \frac{1}{2}(u) \bigg| \limits^a_b + \frac{cos(u)sin(u)}{2} \bigg| \limits^a_b \bigg]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5Ea_b%20%7B%281%20-%20x%5E2%29%5E%5CBig%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D%20%5C%2C%20dx%20%3D%20%5Cfrac%7Bcos%5E3%28u%29sin%28u%29%7D%7B4%7D%20%5Cbigg%7C%20%5Climits%5Ea_b%20%2B%20%5Cfrac%7B3%7D%7B4%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B2%7D%28u%29%20%5Cbigg%7C%20%5Climits%5Ea_b%20%2B%20%5Cfrac%7Bcos%28u%29sin%28u%29%7D%7B2%7D%20%5Cbigg%7C%20%5Climits%5Ea_b%20%5Cbigg%5D)
- Simplify:

- Back-Substitute:

- Simplify:

- Rewrite:

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

Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e