The answer is B becasue if you have 20 less 5 its going to be 15
Answer:
in triangle BCD
relationship between base and hypotenuse is given by cos angle
cos 71=b/h
cos71=BD/BC
cos71=67/x
x=67/cos71=205.8ft.
the length of BC to the nearest tenth of a foot is 206ft.
Step-by-step explanation:
I hope you are 100% clear.
Answer:
n = 0
Step-by-step explanation:
Multiply parenthesis by 3 and get:
1.) 18 + 9n = 5n + 18 + 3n
Then cancel the equal terms:
9n = 5n + 3n
Collect like terms:
9n = 8n
Move variable to the left:
9n - 8n = 0
n + 0
Plugin the value of 0 into x:
3 (6 + 3 x 0) = 18
5 x 0 + 3 x 0 + 18 = 18
*If the plugged in value have the same result than the answer is correct because 18 + 18.
Answer:
![\displaystyle A = \frac{1}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
- Left to Right
<u>Algebra I</u>
- Terms/Coefficients
- Functions
- Function Notation
- Graphing
<u>Calculus</u>
Area - Integrals
Integration Rule [Reverse Power Rule]: ![\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%7Bx%5En%7D%20%5C%2C%20dx%20%3D%20%5Cfrac%7Bx%5E%7Bn%20%2B%201%7D%7D%7Bn%20%2B%201%7D%20%2B%20C)
Integration Rule [Fundamental Theorem of Calculus 1]: ![\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5Eb_a%20%7Bf%28x%29%7D%20%5C%2C%20dx%20%3D%20F%28b%29%20-%20F%28a%29)
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:
*Note:
<em>Remember that for the Area of a Region, it is top function minus bottom function.</em>
<em>Also remember that finding area and evaluating are two different things.</em>
<u>Step 1: Define</u>
f(x) = x
g(x) = x³
Bounded (Partitioned) by x-axis
<u>Step 2: Identify Bounds of Integration</u>
<em>Find where the functions intersect (x-values) to determine the bounds of integration.</em>
Simply graph the functions to see where the functions intersect (See Graph Attachment).
Interval: [-1, 1]
1st Integral: [-1, 0]
2nd Integral: [0, 1]
<u>Step 3: Find Area of Region</u>
<em>Integration.</em>
- Substitute in variables [Area of a Region Formula]:
![\displaystyle A = \int\limits^0_{-1} {[x^3 - x]} \, dx + \int\limits^1_0 {[x - x^3]} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%20%3D%20%5Cint%5Climits%5E0_%7B-1%7D%20%7B%5Bx%5E3%20-%20x%5D%7D%20%5C%2C%20dx%20%2B%20%5Cint%5Climits%5E1_0%20%7B%5Bx%20-%20x%5E3%5D%7D%20%5C%2C%20dx)
- [Area] Rewrite Integrals [Integration Property - Subtraction]:
![\displaystyle A = (\int\limits^0_{-1} {x^3} \, dx - \int\limits^0_{-1} {x} \, dx) + (\int\limits^1_0 {x} \, dx - \int\limits^1_0 {x^3} \, dx)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%20%3D%20%28%5Cint%5Climits%5E0_%7B-1%7D%20%7Bx%5E3%7D%20%5C%2C%20dx%20-%20%5Cint%5Climits%5E0_%7B-1%7D%20%7Bx%7D%20%5C%2C%20dx%29%20%2B%20%28%5Cint%5Climits%5E1_0%20%7Bx%7D%20%5C%2C%20dx%20-%20%5Cint%5Climits%5E1_0%20%7Bx%5E3%7D%20%5C%2C%20dx%29)
- [Area] [Integrals] Integrate [Integration Rule - Reverse Power Rule]:
![\displaystyle A = [\frac{x^4}{4} \bigg|\limits^0_{-1} - (\frac{x^2}{2}) \bigg|\limits^0_{-1}]+ [\frac{x^2}{2} \bigg|\limits^1_0 - (\frac{x^4}{4}) \bigg|\limits^1_0]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%20%3D%20%5B%5Cfrac%7Bx%5E4%7D%7B4%7D%20%5Cbigg%7C%5Climits%5E0_%7B-1%7D%20-%20%28%5Cfrac%7Bx%5E2%7D%7B2%7D%29%20%5Cbigg%7C%5Climits%5E0_%7B-1%7D%5D%2B%20%5B%5Cfrac%7Bx%5E2%7D%7B2%7D%20%5Cbigg%7C%5Climits%5E1_0%20-%20%28%5Cfrac%7Bx%5E4%7D%7B4%7D%29%20%5Cbigg%7C%5Climits%5E1_0%5D)
- [Area] Evaluate [Integration Rule - FTC 1]:
![\displaystyle A = [\frac{-1}{4} - (\frac{-1}{2})] + [\frac{1}{2} - \frac{1}{4}]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%20%3D%20%5B%5Cfrac%7B-1%7D%7B4%7D%20-%20%28%5Cfrac%7B-1%7D%7B2%7D%29%5D%20%2B%20%5B%5Cfrac%7B1%7D%7B2%7D%20-%20%5Cfrac%7B1%7D%7B4%7D%5D)
- [Area] [Brackets] Add/Subtract:
![\displaystyle A = \frac{1}{4} + \frac{1}{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%20%3D%20%5Cfrac%7B1%7D%7B4%7D%20%2B%20%5Cfrac%7B1%7D%7B4%7D)
- [Area] Add:
![\displaystyle A = \frac{1}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Area Under the Curve - Area of a Region (Integration)
Book: College Calculus 10e