2b - 15 > 21
add 15 to both sides:
2b-15+15 > 21 + 15
2b > 36
Divide both sides by 2 :
2b/2 > 36/2
2b = 36
b = 36 / 2
b > 18
hope this helps!
Answer:
Percentage of absentees on Tuesday = 16%
Step-by-step explanation:
Sum of all central angles representing days = 360°
Central angle of the sector representing Tuesday = 57.6°
Therefore, percentage absentees on Tuesday
= ![\frac{\text{Measure of central angle for Tuesday}}{\text{Sum of all central angles}}\times 100](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BMeasure%20of%20central%20angle%20for%20Tuesday%7D%7D%7B%5Ctext%7BSum%20of%20all%20central%20angles%7D%7D%5Ctimes%20100)
= ![\frac{57.6}{360}\times 100](https://tex.z-dn.net/?f=%5Cfrac%7B57.6%7D%7B360%7D%5Ctimes%20100)
= 16%
Percentage of absentees on Tuesday = 16%
Answer:
![\displaystyle \int {\frac{1}{1+(2x)^2}} \, dx = \frac{artan(2x)}{2} + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%7B%5Cfrac%7B1%7D%7B1%2B%282x%29%5E2%7D%7D%20%5C%2C%20dx%20%3D%20%5Cfrac%7Bartan%282x%29%7D%7B2%7D%20%2B%20C)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
<u>Calculus</u>
Derivatives
Derivative Notation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Antiderivatives - Integrals
Indefinite Integrals
U-Substitution
Integration Property [Multiplied Constant]: ![\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%7Bcf%28x%29%7D%20%5C%2C%20dx%20%3D%20c%20%5Cint%20%7Bf%28x%29%7D%20%5C%2C%20dx)
Arctrig Integration [arctangent]: ![\displaystyle \int {\frac{1}{a^2 + u^2}} \, du = \frac{1}{a}arctan(\frac{u}{a}) + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%7B%5Cfrac%7B1%7D%7Ba%5E2%20%2B%20u%5E2%7D%7D%20%5C%2C%20du%20%3D%20%5Cfrac%7B1%7D%7Ba%7Darctan%28%5Cfrac%7Bu%7D%7Ba%7D%29%20%2B%20C)
Step-by-step explanation:
<u>Step 1: Define</u>
![\displaystyle \int {\frac{1}{1+(2x)^2}} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%7B%5Cfrac%7B1%7D%7B1%2B%282x%29%5E2%7D%7D%20%5C%2C%20dx)
<u>Step 2: Integrate Pt. 1</u>
- [Integral] Rewrite:
![\displaystyle \int {\frac{1}{1^2+(2x)^2}} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%7B%5Cfrac%7B1%7D%7B1%5E2%2B%282x%29%5E2%7D%7D%20%5C%2C%20dx)
<u>Step 3: Identify Variables</u>
<em>Identify variables for u-substitution of arctrig.</em>
- Set <em>u</em>:
![\displaystyle u = 2x](https://tex.z-dn.net/?f=%5Cdisplaystyle%20u%20%3D%202x)
- Differentiate [Basic Power Rule]:
![\displaystyle \frac{du}{dx} = 1 \cdot 2x^{1 - 1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdu%7D%7Bdx%7D%20%3D%201%20%5Ccdot%202x%5E%7B1%20-%201%7D)
- [Derivative] Simplify:
![\displaystyle \frac{du}{dx} = 2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdu%7D%7Bdx%7D%20%3D%202)
- [Derivative] Rewrite:
![\displaystyle du = 2dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20du%20%3D%202dx)
- Set <em>a</em>:
![\displaystyle a = 1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20a%20%3D%201)
<u>Step 4: Integrate Pt. 2</u>
- [Integral] Rewrite [Integration Property - Multiplied Constant]:
![\displaystyle \frac{1}{2}\int {\frac{2}{1^2+(2x)^2}} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B2%7D%5Cint%20%7B%5Cfrac%7B2%7D%7B1%5E2%2B%282x%29%5E2%7D%7D%20%5C%2C%20dx)
- [Integral] U-Substitution:
![\displaystyle \frac{1}{2}\int {\frac{du}{a +u^2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B2%7D%5Cint%20%7B%5Cfrac%7Bdu%7D%7Ba%20%2Bu%5E2%7D%7D)
- [Integral] Arctrig Integration [arctangent]:
![\displaystyle \frac{1}{2}[\frac{1}{a}arctan(\frac{u}{a})] + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B2%7D%5B%5Cfrac%7B1%7D%7Ba%7Darctan%28%5Cfrac%7Bu%7D%7Ba%7D%29%5D%20%2B%20C)
- [Integral] Back-Substitute:
![\displaystyle \frac{1}{2}[\frac{1}{1}arctan(\frac{2x}{1})] + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B2%7D%5B%5Cfrac%7B1%7D%7B1%7Darctan%28%5Cfrac%7B2x%7D%7B1%7D%29%5D%20%2B%20C)
- [Integral] Divide:
![\displaystyle \frac{1}{2}[arctan(2x)] + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B2%7D%5Barctan%282x%29%5D%20%2B%20C)
- [Integral] Multiply:
![\displaystyle \frac{arctan(2x)}{2} + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Barctan%282x%29%7D%7B2%7D%20%2B%20C)
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integration of Arctrig
Book: College Calculus 10e
Answer:
the answer is B because there are 21 days in 3 weeks