Answer:
B) 4√2
General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Parametric Differentiation
Integration
- Integrals
- Definite Integrals
- Integration Constant C
Arc Length Formula [Parametric]: ![\displaystyle AL = \int\limits^b_a {\sqrt{[x'(t)]^2 + [y(t)]^2}} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20AL%20%3D%20%5Cint%5Climits%5Eb_a%20%7B%5Csqrt%7B%5Bx%27%28t%29%5D%5E2%20%2B%20%5By%28t%29%5D%5E2%7D%7D%20%5C%2C%20dx)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>

Interval [0, π]
<u>Step 2: Find Arc Length</u>
- [Parametrics] Differentiate [Basic Power Rule, Trig Differentiation]:

- Substitute in variables [Arc Length Formula - Parametric]:
![\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{[1 + sin(t)]^2 + [-cos(t)]^2}} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20AL%20%3D%20%5Cint%5Climits%5E%7B%5Cpi%7D_0%20%7B%5Csqrt%7B%5B1%20%2B%20sin%28t%29%5D%5E2%20%2B%20%5B-cos%28t%29%5D%5E2%7D%7D%20%5C%2C%20dx)
- [Integrand] Simplify:
![\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20AL%20%3D%20%5Cint%5Climits%5E%7B%5Cpi%7D_0%20%7B%5Csqrt%7B2%5Bsin%28x%29%20%2B%201%5D%7D%20%5C%2C%20dx)
- [Integral] Evaluate:
![\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx = 4\sqrt{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20AL%20%3D%20%5Cint%5Climits%5E%7B%5Cpi%7D_0%20%7B%5Csqrt%7B2%5Bsin%28x%29%20%2B%201%5D%7D%20%5C%2C%20dx%20%3D%204%5Csqrt%7B2%7D)
Topic: AP Calculus BC (Calculus I + II)
Unit: Parametric Integration
Book: College Calculus 10e
Answer:
The area is 11317.51
Step-by-step explanation:
The sum of 2 sides must be less than the third side (largest side) for a triangle to be formed.
b+c<a
133+174 < 240
A triangle can be formed
To use Herons formula for the area
We find S = 1/2( a+b+c)
= 1/2(240+133+174)
= 1/2 (547)
= 273.5
Area = sqrt( S (S-a) (S-b)(S-c))
sqrt((273.5 ) (273.5 -240) (273.5-133) (273.5-174))
sqrt((273.5)(33.5) (140.5) (99.5))
sqrt(128085964.4)
11317.50699
The area is 11317.51
Answer:
x = -96
Step-by-step explanation:
Answer:
c = - 2, c = 7
Step-by-step explanation:
Given
c² - 14 = 5c ( subtract 5c from both sides )
c² - 5c - 14 = 0 ← in standard form
To factorise the quadratic
Consider the factors of the constant term (- 14) which sum to give the coefficient of the c- term (- 5)
The factors are - 7 and + 2, since
- 7 × 2 = - 14 and - 7 + 2 = - 5, hence
(c - 7)(c + 2) = 0
Equate each factor to zero and solve for c
c - 7 = 0 ⇒ c = 7
c + 2 = 0 ⇒ c = - 2