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iragen [17]
3 years ago
13

Find the diameter of the given radius: (i) Radius = 7 cm (ii) Radius = 12 cm​

Health
2 answers:
balu736 [363]3 years ago
6 0

Explanation:

diameter 2×radius

R=7

2×7=14

R=12

2×12=24

dimaraw [331]3 years ago
4 0

Answer:

<h3>1. 14cm</h3><h3>2. 24cm</h3>

Explanation:

diameter = 2× radius

thus,

R= 7 cm

diameter= 7×2= 14cm

R=12cm

diameter = 12×2 = 24cm

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Answer:

\displaystyle y' = (1 + x)^2(4x + 1)

General Formulas and Concepts:

<u>Algebra I</u>

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<u>Calculus</u>

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Derivative Notation

Derivative Property [Addition/Subtraction]:                                                                \displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(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)

Derivative Rule [Chain Rule]:                                                                                       \displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)

Explanation:

<u>Step 1: Define</u>

<em>Identify</em>

y = x(1 + x)³

<u>Step 2: Differentiate</u>

  1. Product Rule [Derivative Rule - Chain Rule]:                                                  \displaystyle y' = \frac{d}{dx}[x] \cdot (1 + x)^3 + x \cdot \frac{d}{dx}[(1 + x)^3] \cdot \frac{d}{dx}[1 + x]
  2. Derivative Property [Addition/Subtraction]:                                                    \displaystyle y' = \frac{d}{dx}[x] \cdot (1 + x)^3 + x \cdot \frac{d}{dx}[(1 + x)^3] \cdot (\frac{d}{dx}[1] + \frac{d}{dx}[x])
  3. Basic Power Rule:                                                                                             \displaystyle y' = x^{1 - 1} \cdot (1 + x)^3 + x \cdot 3(1 + x)^{3 - 1} \cdot (0 + x^{1 - 1})
  4. Simplify:                                                                                                             \displaystyle y' = (1 + x)^3 + 3x(1 + x)^2
  5. Factor:                                                                                                               \displaystyle y' = (1 + x)^2 \bigg[ (1 + x) + 3x \bigg]
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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

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