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NARA [144]
3 years ago
13

Write the explicit formula for the geometric sequence. Then find the fifth term in the sequence.

Mathematics
2 answers:
Korvikt [17]3 years ago
7 0

Answer:

B. an = -4 *(-2)^n-1;-64

mr_godi [17]3 years ago
6 0
The sequence:  a 1 = - 4,  a 2 = 8,  a 3 = -16,...
a 2 = a 1 * r
8 = - 4 * r
r = 8 : ( - 4 ) 
r = - 2
a n = a 1 * r^(n-1)
a 5 = - 4 * ( - 2 ) ^4 = - 4 * 16 = - 64
Answer:
The fifth term in the sequence is - 64. 
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masya89 [10]
L.S.A.=1/2pl where p represents the perimeter of the base and l the slant height.
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#12 with explanation please
4vir4ik [10]

Answer:

  • 30.01 units

Step-by-step explanation:

<u>Given vertices WXYZ:</u>

  • W(-4,5), X(2,4), Y(3, -4), Z(-1, -6)

Perimeter is the sum of the side length.

<u>Use distance formula to find each side:</u>

  • WX = \sqrt{(2+4)^2+(4-5)^2} =\sqrt{37} ≈ 6.08
  • XY = \sqrt{(3-2)^2+(-4-4)^2} =\sqrt{65} ≈ 8.06
  • YZ = \sqrt{(-1-3)^2+(-6+4)^2} =\sqrt{20} ≈ 4.47
  • WZ = \sqrt{(-1+4)^2+(-6-5)^2} =\sqrt{130}\sqrt{(-1+4)^2+(-6-5)^2}=\sqrt{130} ≈ 11.40

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3 years ago
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3 years ago
If f(x) = 9x10 tan−1x, find f '(x).
djverab [1.8K]

Answer:

\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + \frac{9x^{10}}{x^2 + 1}

General Formulas and Concepts:

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Derivative Property [Multiplied Constant]:                                                           \displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)  

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Derivative Rule [Product Rule]:                                                                             \displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle f(x) = 9x^{10} \tan^{-1}(x)

<u>Step 2: Differentiate</u>

  1. [Function] Derivative Rule [Product Rule]:                                                   \displaystyle f'(x) = \frac{d}{dx}[9x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]
  2. Rewrite [Derivative Property - Multiplied Constant]:                                  \displaystyle f'(x) = 9 \frac{d}{dx}[x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]
  3. Basic Power Rule:                                                                                         \displaystyle f'(x) = 90x^9 \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]
  4. Arctrig Derivative:                                                                                         \displaystyle f'(x) = 90x^9 \tan^{-1}(x) + \frac{9x^{10}}{x^2 + 1}

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

7 0
3 years ago
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