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Marianna [84]
3 years ago
10

A recycling plant process an average of 1/3 ton of glass each minute. At approximately what rate does the recycling plant proces

s glass,in tons per day? (1 day = 24hrs)
Mathematics
2 answers:
guapka [62]3 years ago
5 0
1/3 * 60 minutes * 24 hours = 480 tons/day
Katyanochek1 [597]3 years ago
5 0
480 tons per day
multiply one-third by 60 and by 24
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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

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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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