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Pepsi [2]
3 years ago
10

Mike took a taxi from his home to the airport. The taxi driver charged an initial fee of $6 plus $3 per mile. The total fare was

$24, not including the tip. How many miles did Mike travel by taxi on his ride? (Please show work)
Mathematics
2 answers:
snow_tiger [21]3 years ago
8 0

Answer:

x=6

Step-by-step explanation:

Put the problem into y=mx+b format we knoe the inital value b is 6 now m is 3 and y the overall price is 24. Use the distributive property.

24=6+3x y=6+3x y=24

-6  -6

<u>18</u>=<u>3x</u>

3    3

6=x

x=6

lyudmila [28]3 years ago
6 0

Answer:

6 miles

Step-by-step explanation:

let m equal miles

3m + 6 = 24

       -6      -6

3m = 18

18 / 3 = 6

6 miles

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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>

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

Basic Power Rule:

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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>

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<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

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