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Gennadij [26K]
3 years ago
5

a coin must have diameter of 27.13 millimeters.To the nearest hundredth, what is the circumference of this coin millimeters

Mathematics
1 answer:
Bas_tet [7]3 years ago
4 0
To find the circumference, you will use the formula for finding circumference of a circle.

I used the true value of pi for the calculations.

C = pi x d
pi x 27.13
C = 85.77mm

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Answer:

See Explanation.

General Formulas and Concepts:

<u>Pre-Algebra</u>

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  • Reciprocals

<u>Algebra II</u>

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<u>Calculus</u>

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Basic Power Rule:

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Chain Rule: \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)

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Step-by-step explanation:

<u>Step 1: Define</u>

ln(\frac{2x-1}{x-1} )=t

<u>Step 2: Differentiate</u>

  1. Rewrite:                                                                                                         t = ln(\frac{2x-1}{x-1})
  2. Rewrite [Ln Properties]:                                                                                 t = ln(2x-1) - ln(x - 1)
  3. Differentiate [Ln/Chain Rule/Basic Power Rule]:                                         \frac{dt}{dx} = \frac{1}{2x-1} \cdot 2 - \frac{1}{x-1} \cdot 1
  4. Simplify:                                                                                                          \frac{dt}{dx} = \frac{2}{2x-1} - \frac{1}{x-1}
  5. Rewrite:                                                                                                          \frac{dt}{dx} = \frac{2(x-1)}{(2x-1)(x-1)} - \frac{2x-1}{(2x-1)(x-1)}
  6. Combine:                                                                                                       \frac{dt}{dx} = \frac{-1}{(2x-1)(x-1)}
  7. Reciprocate:                                                                                                  \frac{dx}{dt} = -(2x-1)(x-1)
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