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 equation of the straight line in Slope- intercept form
y = 3 x - 11
Step-by-step explanation:
<u><em>Explanation:-</em></u>
Given points are (2,-5) and (8, 13)
The Slope of the line

Equation of the line having slope 'm' and given point

(x₁ , y₁) = ( 2, -5 )

y + 5 = 3x - 6
The equation of the straight line in slope intercept form
y = m x + c
y = 3 x - 6-5
y = 3 x - 11
<u><em>Final answer:</em></u>-
The equation of the straight line in Slope- intercept form
y = 3 x - 11
Answer:
Hey there!
a)
10x-1=4x+2
6x-1=2
6x=3
x=1/2 cm.
10x-1=4 cm.
So the width of the rectangle is 10/4, or 2.5 cm.
b)
l=3w
2l+2w=24
2(3w)+2w=24
6w+2w=24
8w=24
w=3
l=9
The are is 27 units squared.
Let me know if this helps :)
Answer:
9 1/3 cm³
Step-by-step explanation:
First multiply two numbers.
2x2=4
Then multiply the product by the third number.
4x7/3
4 x 7
1 x 3
= 28/3 or 9 1/3
--
hope it helps
The answer is X is equal to 1.4