2. 8x -28 = -140
8x -28 + 28 = -140 + 28
8x = -112
8x/8 = -112/8
x = -14
3. -9 + x/3 = -23
-9 + 9 + x/3 = -23 + 9
x/3 = -14
x/3/3 = -14/3
x = -14/3
4. x/-1.5 - 3.5 = -13.5
x/-1.5 - 3.5 + 3.5 = -13.5 + 3.5
x/1.5 = -10
x/-1.5/-1.5= -10/-1.5
x = 20/3
5.-6(x + 3) = -36
-6x - 18 = -36
-6x - 18 + 18 = -36 + 18
-6x = -18
-6x/-6 = -18/-6
x = 3
6. k + 3.7/9.8 = -0.22
k + 3.7/9.8/9.8 = -0.22/9.8
k + 3.7 = -2.156
k + 3.7 - 3.7 = -2.156 - 3.7
k = -5.856
7. 12(x - 6) = -108
12x - 72 = -108
12x - 72 + 72 = -108 + 72
12x = -36
12x/12 = -36/12
x = -3
8. -21.83x - -19.9 = -23.83
-21.83x + 19.9 = -23.83
-21.83x + 19.9 - 19.9 = -23.83 - 19.9
-21.83x = -43.73
-21.83x/-21.83 = -43.73/-21.83
x = 2
9. -10x - 68 + x = 40
-9x - 68 = 40
-9x -68 + 68 = 40 + 68
-9x = 108
-9x/-9 = 108/-9
x = -12
10. -34 - 3x - 2x = 71
-34 - 5x = 71
-34 + 34 - 5x = 71 + 34
-5x = 105
-5x/-5 = 105/-5
x = -21
11. 3x - 77 - 8x = 23
-5x - 77 = 23
-5x - 77 + 77 = 23 + 77
-5x = 100
-5x/-5 = 100/-5
x = -20
12. 3x - 5(2x - 12) = 123
3x - 10x + 60 = 123
-7x + 60 = 123
-7x + 60 - 60 = 123 - 60
-7x = 63
-7x/-7 = 63/-7
x = -9
13. -3x + 6(x + 6) = 15
-3x + 6x + 36 = 15
3x + 36 = 15
3x + 36 - 36 = 15 - 36
3x = -21
3x /3 = -21/3
x = -7
14. 5x + 2(4x - 9) = -174
5x + 8x - 18 = -174
13x - 18 = -174
13x - 18 + 18 = -174 + 18
13x = -156
13x/13 = -156/13
x = -12
15. -3x + 6(5x + 3) = -171
-3x + 30x + 18 = -171
27x + 18 = -171
27x + 18 - 18 = -171 - 18
27x = -189
27x/27 = -189/27
x = -7
Answer: 2 197/1000
Explanation:
(1 3/10)^3
= (13/10)^3
= 13^3/10^3
= 2197/1000
= 2 197/1000
Answer:Graphs of inverse functions have a domain and range just like any other graph of a function. The domain of an inverse function is the range of the original, and the range of an inverse function is the domain of an original.
Step-by-step explanation:
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
