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
A. T= d/r
A good way to remember this is by making a pyramid with 3 parts and putting distance at the top and rate and time in the other two parts. This way you can visibly see the equation and use it if you need to find one for rate.
B. It's reasonable to write distance as a positive number because distance is always positive. You are not able to have a negative distance. Imagine someone standing on a side walk. Even if they are not moving, their distance is 0 which is positive. If they move backwards or forwards, their distance is still positive because it is more than that 0 and they are gaining something.
C. Just plug in the numbers into the formula.
T= d/r
T= 32.12 m /<span>8.8 m/min
T= 3.65 min
</span>
Answer:
x = -9°
m∠A = 37°
Step-by-step explanation:
(8-5x) + (10-3x) = 90
8-5x + 10-3x = 90
18-8x = 90
-8x = 72
x = -9°
m∠A = 10- (-9*3) =
10-(-27) = 37°
If my answer is incorrect, pls correct me!
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-Chetan K