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sveticcg [70]
3 years ago
8

Make a table of values fo each equation y=3/8x-5

Mathematics
1 answer:
Harlamova29_29 [7]3 years ago
3 0
You can type that equation into a grphing calculator and get the table for from there or you can use desmos graphing calculator site and type in your equation to the column then hit the little settings icon and choose convert to table !!! 
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5^12

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5 to the 12th power because 4x3 =12

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What is the derivative of 1/square root 4x.
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Answer:

\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4x^\bigg{\frac{3}{2}}}

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

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  2. Parenthesis
  3. Exponents
  4. Multiplication
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  • Left to Right

<u>Algebra I</u>

Exponential Properties

  • Exponential Property [Rewrite]:                                                                   \displaystyle b^{-m} = \frac{1}{b^m}
  • Exponential Property [Root Rewrite]:                                                           \displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}

<u>Calculus</u>

Differentiation

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

Derivative Rule [Basic Power Rule]:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify.</em>

\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg]

<u>Step 2: Differentiate</u>

  1. Simplify:                                                                                                         \displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \bigg( \frac{1}{2\sqrt{x}} \bigg)'
  2. Rewrite [Derivative Property - Multiplied Constant]:                                   \displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{1}{\sqrt{x}} \bigg)'
  3. Rewrite [Exponential Rule - Root Rewrite]:                                                 \displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{1}{x^\Big{\frac{1}{2}}} \bigg)'
  4. Rewrite [Exponential Rule - Rewrite]:                                                           \displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( x^\bigg{\frac{-1}{2}} \bigg)'
  5. Derivative Rule [Basic Power Rule]:                                                             \displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{-1}{2} x^\bigg{\frac{-3}{2}} \bigg)
  6. Simplify:                                                                                                         \displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4} x^\bigg{\frac{-3}{2}}
  7. Rewrite [Exponential Rule - Rewrite]:                                                           \displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4x^\bigg{\frac{3}{2}}}

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

Unit: Differentiation

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