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dedylja [7]
2 years ago
6

Four runners start at the same point; Lin, Elena, Diego, Andre. For each runner write a multiplication equation that describes t

heir journey.
Lin runs for 25 seconds at 8.2 meters per second. What is her finish point?
Elena runs for 28 seconds and finishes at 250 meters. What is her velocity?
Diego runs for 32 seconds at -8.1 meters per second. What is his finish point?
Andre runs for 35 seconds and finishes at -285 meters. What is his velocity?
Mathematics
1 answer:
Burka [1]2 years ago
7 0

<u>Answer:</u>

Lin: 25 × 8,2 =<em> 205 meters</em>

Elena: 250 ÷ 28 = <em>8,9 meters per second</em>

Diego: 32 × (-8,1) = <em>-250,2 meters</em>

Andre: -258 ÷ 25 = <em>-10,32 meters per second </em>

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Urgent. Please show all work
myrzilka [38]

Answer:

\displaystyle f'(x) = \frac{4}{x^2}

General Formulas and Concepts:

<u>Calculus</u>

Limits

  • Limit Rule [Variable Direct Substitution]:                                                    \displaystyle \lim_{x \to c} x = c

Differentiation

  • Derivatives
  • Derivative Notation

The definition of a derivative is the slope of the tangent line:                             \displaystyle f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify.</em>

<em />\displaystyle f(x) = -\frac{4}{x}

<u>Step 2: Differentiate</u>

  1. [Function] Substitute in <em>x</em>:                                                                            \displaystyle f(x + h) = -\frac{4}{x + h}
  2. Substitute in functions [Definition of a Derivative]:                                   \displaystyle f'(x) = \lim_{h \to 0} \frac{-\frac{4}{x + h} - \big( -\frac{4}{x} \big)}{h}
  3. Simplify:                                                                                                        \displaystyle f'(x) = \lim_{h \to 0} \frac{4}{x(x+ h)}
  4. Evaluate limit [Limit Rule - Variable Direct Substitution]:                          \displaystyle f'(x) = \frac{4}{x(x+ 0)}
  5. Simplify:                                                                                                        \displaystyle f'(x) = \frac{4}{x^2}

∴ the derivative of the given function will be equal to 4 divided by x².

---

Learn more about derivatives: brainly.com/question/25804880

Learn more about calculus: brainly.com/question/23558817

---

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

Unit: Differentiation

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