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:
4:1 or 4/1
Step-by-step explanation:
Original surface area: Each side is 1 * 1 = 1 and there are 6 sides, so 1 * 6 = 6.
New surface area: Each side is 2*2 = 4, and there are 6 sides, so 4 * 6 = 24
The ratio would be 24:6, or 4:1. As a fraction, this would be 4/1
Answer:
The number is -1/2.
Step-by-step explanation:
I am assuming they are fractions. So we have the equation:
5/2 x + 2/3 = -7/12
We multiply through by 12 to eliminate the fractions:
5/2 * 12 x + 2/3 * 12 = -7/12 * 12
30x + 8 = -7
30x = -15
x = -15/30
x = -1/2.
Answer:
A: Neither is a better deal, they cost the same person cubic foot
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B: The large truck's volume is 2.3 times greater than the small truck's
C: At least: three vans, or two small trucks, or one large truck
Step-by-step explanation:
V=Lhw R=$/ft³
Vv=10.5(6)(6)
Vv=378 ft³
Rv=94.5/378
Rv= 25¢ per ft³
Vs=12(8)6.75
Vs=648 ft³
Rs=162/648
Rs=25¢ per ft³
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Vl=20(8.75)8.5
Vl=1487.5 ft³
1487.5=648n
2.295=n
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D is correct. U is incenter of the triangle.