9514 1404 393
Answer:
Step-by-step explanation:
The answer statement tells you the transformation is a rotation. The original is in the 2nd quadrant, and the image is in the 1st quadrant, representing a clockwise rotation. AB points east, while A'B' points south, a rotation of 90° (clockwise). Each image point is the same distance from the origin as its preimage point. The origin is the center of rotation.
__
∆ABC is transformed by a <u> clockwise </u> rotation <u> 90 </u> degrees with a center at the <u> origin </u>.
Answer:
<u>x = 1.07</u>
Step-by-step explanation:
13 ( 6x - 9) = -33
78x - 117 = -33 ( opening brackets and multiplying )
78x = 84 ( - 117 taken to the other side makes it positive)
x = 84 / 78
x = <u>1.07</u>
Answer:
The mode is the least used of the measures of central tendency
Step-by-step explanation:
Answer: A
Step-by-step explanation:
#
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