The first Ferris wheel took 9 minutes to make a complete revolution. How fast was the wheel moving?

Find the derivative of <img src="https://tex.z-dn.net/?f=%20y%20%3D%20%5Csqrt%5B3%5D%7Bx%7D%20" id="TexFormula1" title=" y =

MAXImum [283]

Answer:

$\displaystyle y'(27) = \frac{1}{27}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

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

Calculus

Derivatives

Derivative Notation

Basic Power Rule

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

y = ∛x

x = 27

Step 2: Differentiate

[Function] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y = x^{\frac{1}{3}}$
Basic Power Rule: $\displaystyle y' = \frac{1}{3}x^{\frac{1}{3} - 1}$
Simplify: $\displaystyle y' = \frac{1}{3}x^{-\frac{2}{3}}$
Rewrite [Exponential Rule - Rewrite]: $\displaystyle y' = \frac{1}{3x^{\frac{2}{3}}}$

Step 3: Solve

Substitute in x [Derivative]: $\displaystyle y'(27) = \frac{1}{3(27)^{\frac{2}{3}}}$
Evaluate exponents: $\displaystyle y'(27) = \frac{1}{3(9)}$
Multiply: $\displaystyle y'(27) = \frac{1}{27}$

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

Unit: Derivatives

Book: College Calculus 10e

8 0

3 years ago

Find the value of x 2-x7=25

o-na [289]

Answer: 3.285714286

Step-by-step explanation: subtract 2 from both sides then divide by 7

4 0

3 years ago

How many extraneous solutions does the equation below have?

Anna11 [10]

the answer is zero exstranues solutions

6 0

3 years ago

Read 2 more answers

How does an increase in thermal energy affect molecules?

zheka24 [161]

Answer:

The molecules become more active and it expands.

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Could someone help me with this?

umka2103 [35]

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Find area of one triangle
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Area of triangle = 1/2 x base x height
Area of triangle = 1/2 x 9 x 11.75
Area of triangle = 52.875 ft²

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Find area of two triangles
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Area of 2 triangles = 52.875 x 2
Area of 2 triangles = 105.75 ft²

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Find the cost of the flower beds
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1 ft² = $4.25
105.75 ft² = 105.75 x 4.25
105.75 ft² = $449.44 (nearest hundredth)

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Answer: $449.44
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8 0

3 years ago