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:
7 months
Step-by-step explanation:
He plans on depositing $200 every month into the savings account that already has $600 in it.
We can represent the amount of money he will have after a certain number of months (x) as:
A = 600 + 200x
He needs to save $2000. Therefore, to find the months he needs to save, we need to find x when A is $2000:
2000 = 600 + 200x
200x = 2000 - 600
200x = 1400
x = 1400/200 = 7 months
He needs to save for 7 months.
Answer:
(-4, 2) and (4, -5)
m = (-5 - 2)/(4 - (-4)) = -7/8
y = -7/8 * (x - (-4)) + 2
y = -7/8 * (x + 4) + 2
y = -7/8 * x - 3/2
Answer:
Nearest ten thousand: 250,000 Nearest hundred thousand: 200,000
Step-by-step explanation:
For the nearest ten thousand, look at that place which is the 4 then look at the number next to it. Its a 6. That 6 is closer to ten than it is to 0 so you round up to the next number which is 250,000. For the hundred thousand place do the same thing. Look at the number next to it which is 4 which is closer to 0 than 10 so you round down to 200,000.
Answer:
Step-by-step explanation:
1) The Fundamental Theorem of Calculus in its first part, shows us a reciprocal relationship between Derivatives and Integration
2) In this case, we'll need to find the derivative applying the chain rule. As it follows:
3) To test it, just integrate:
