Answer:
30%
i guess
Step-by-step explanation:
Answer:
The answer is the option C
The right answer is Nine.
Answer:
![\displaystyle A = 300](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%20%3D%20300)
General Formulas and Concepts:
<u>Calculus</u>
Integrals
- Definite Integrals
- Area under the curve
- Integration Constant C
Integration Rule [Reverse Power Rule]:
Integration Rule [Fundamental Theorem of Calculus 1]:
Integration Property [Multiplied Constant]:
Integration Property [Addition/Subtraction]:
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>
<em>Identify</em>
f(x) = 6x + 19
Interval [12, 15]
<u>Step 2: Find Area</u>
- Substitute in variables [Area of a Region Formula]:
![\displaystyle A = \int\limits^{15}_{12} {(6x + 19)} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%20%3D%20%5Cint%5Climits%5E%7B15%7D_%7B12%7D%20%7B%286x%20%2B%2019%29%7D%20%5C%2C%20dx)
- [Integral] Rewrite [Integration Property - Addition/Subtraction]:
![\displaystyle A = \int\limits^{15}_{12} {6x} \, dx + \int\limits^{15}_{12} {19} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%20%3D%20%5Cint%5Climits%5E%7B15%7D_%7B12%7D%20%7B6x%7D%20%5C%2C%20dx%20%2B%20%5Cint%5Climits%5E%7B15%7D_%7B12%7D%20%7B19%7D%20%5C%2C%20dx)
- [Integrals] Rewrite [Integration Property - Multiplied Constant]:
![\displaystyle A = 6\int\limits^{15}_{12} {x} \, dx + 19\int\limits^{15}_{12} {} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%20%3D%206%5Cint%5Climits%5E%7B15%7D_%7B12%7D%20%7Bx%7D%20%5C%2C%20dx%20%2B%2019%5Cint%5Climits%5E%7B15%7D_%7B12%7D%20%7B%7D%20%5C%2C%20dx)
- [Integrals] Integrate [Integration Rule - Reverse Power Rule]:
![\displaystyle A = 6(\frac{x^2}{2}) \bigg| \limits^{15}_{12} + 19(x) \bigg| \limits^{15}_{12}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%20%3D%206%28%5Cfrac%7Bx%5E2%7D%7B2%7D%29%20%5Cbigg%7C%20%5Climits%5E%7B15%7D_%7B12%7D%20%2B%2019%28x%29%20%5Cbigg%7C%20%5Climits%5E%7B15%7D_%7B12%7D)
- Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:
![\displaystyle A = 6(\frac{81}{2}) + 19(3)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%20%3D%206%28%5Cfrac%7B81%7D%7B2%7D%29%20%2B%2019%283%29)
- Simplify:
![\displaystyle A = 300](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%20%3D%20300)
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
1. 2 (x + 3) = x - 4
2x + 6 = x- 4
2x - x = -4 - 6
x = -4 + -6 = -10.
x = 10
2. 4 (5x - 2) = 2 (9x + 3)
20x - 8 = 18x + 3
20x - 18x = 3 + 8
2x = 11
x = 11/2 = 5.5
x = 11/2 or 5.5
These are the Answers.
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