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Alex
4 years ago
5

Numbers fall into several broad categories: natural numbers, integers, rational numbers, irrational numbers, and even complex nu

mbers. How many of these categories are you familiar with? Why is it important to have categories of numbers and to know which categories you are dealing with in a given expression? One category that is important to understand is rational numbers. A rational number is a number that can be expressed as an integer divided by another integer. In this unit you will encounter rational expressions, which are a form of polynomial. Knowing what the definition of rational numbers is, what form do you expect rational expressions to take?
Mathematics
1 answer:
PilotLPTM [1.2K]4 years ago
4 0
Multiply by the reciprocal by 3 and divide the common denominator by 14
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Which of the following functions is represented by the statement, “A number is ten less than four times another number”? f ( x )
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f ( x ) = 4 x − 10

Step-by-step explanation:

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Help please <br> Find the circumference of the object.
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18.84

Step-by-step explanation:

We have to use the circumference formula: pi x r x 2. The diameter is 6, so the radius is 3. 3.14 is pi in this scenario. 3.14 x 3 x 2 = 18.84

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The volume of a sphere is decreasing at a constant rate of 116 cubic centimeters per second. At the instant when the volume of t
nirvana33 [79]

Answer:

\frac{dr}{dt}  = -1.325 \ cm/s

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

<u>Calculus</u>

Derivatives

Basic Power Rule:

  • f(x) = cxⁿ
  • f’(x) = c·nxⁿ⁻¹

Taking Derivatives with respect to time

Step-by-step explanation:

<u>Step 1: Define</u>

Given:

<u />V = \frac{4}{3} \pi r^3<u />

<u />\frac{dV}{dt} = -116 \ cm^3/s<u />

<u />V = 77 \ cm^3<u />

<u />

<u>Step 2: Solve for </u><em><u>r</u></em>

  1. Substitute:                    77 = \frac{4}{3} \pi r^3
  2. Isolate <em>r</em> term:               \frac{77}{\frac{4}{3} \pi} = r^3
  3. Isolate <em>r</em>:                        \sqrt[3]{\frac{77}{\frac{4}{3} \pi}}  = r
  4. Evaluate:                       2.63917  = r
  5. Rewrite:                         r = 2.63917 \ cm

<u>Step 3: Differentiate</u>

<em>Differentiate the Volume Formula with respect to time t.</em>

  1. Define:                                                                                                            V = \frac{4}{3} \pi r^3
  2. Differentiate [Basic Power Rule]:                                                                   \frac{dV}{dt}  = \frac{4}{3} \pi \cdot 3 \cdot r^{3-1} \cdot \frac{dr}{dt}
  3. Simplify:                                                                                                           \frac{dV}{dt}  = 4 \pi r^2 \cdot \frac{dr}{dt}

<u>Step 4: Find radius rate</u>

  1. Substitute in variables:                    -116 \ cm^3/sec  = 4 \pi (2.63917 \ cm)^2 \cdot \frac{dr}{dt}
  2. Isolate dr/dt rate:                             \frac{-116 \ cm^3/s}{4 \pi (2.63917 \ cm)^2} = \frac{dr}{dt}
  3. Evaluate:                                          -1.3253 \ cm/s = \frac{dr}{dt}
  4. Rewrite:                                           \frac{dr}{dt}  = -1.3253 \ cm/s
  5. Round:                                             \frac{dr}{dt}  = -1.325 \ cm/s

Our radius is decreasing at a rate of -1.325 cm per second.

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3 years ago
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Answer:

g(x)=(x+1)^2-2

Step-by-step explanation:

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3 0
4 years ago
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Round 8.36 to the nearest one decimal place
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8.4 because 6 would round up to 10 and 10+30 =40 for 8.40 or just 8.4
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