Answer:
b. 
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Functions
- Function Notation
- Exponential Rule [Rewrite]:
- Exponential Rule [Root Rewrite]:
<u>
</u>
<u>Calculus</u>
Derivatives
Derivative Notation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Chain Rule]: ![\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%20%3Df%27%28g%28x%29%29%20%5Ccdot%20g%27%28x%29)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
<em />
<em />
<em />
<u>Step 2: Differentiate</u>
- Rewrite function [Exponential Rule - Root Rewrite]:
![\displaystyle H(x) = [F(x)]^\bigg{\frac{1}{3}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20H%28x%29%20%3D%20%5BF%28x%29%5D%5E%5Cbigg%7B%5Cfrac%7B1%7D%7B3%7D%7D)
- Chain Rule:
![\displaystyle H'(x) = \frac{d}{dx} \bigg[ [F(x)]^\bigg{\frac{1}{3}} \bigg] \cdot \frac{d}{dx}[F(x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20H%27%28x%29%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5BF%28x%29%5D%5E%5Cbigg%7B%5Cfrac%7B1%7D%7B3%7D%7D%20%5Cbigg%5D%20%5Ccdot%20%5Cfrac%7Bd%7D%7Bdx%7D%5BF%28x%29%5D)
- Basic Power Rule:
![\displaystyle H'(x) = \frac{1}{3}[F(x)]^\bigg{\frac{1}{3} - 1} \cdot F'(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20H%27%28x%29%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5BF%28x%29%5D%5E%5Cbigg%7B%5Cfrac%7B1%7D%7B3%7D%20-%201%7D%20%5Ccdot%20F%27%28x%29)
- Simplify:
![\displaystyle H'(x) = \frac{F'(x)}{3}[F(x)]^\bigg{\frac{-2}{3}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20H%27%28x%29%20%3D%20%5Cfrac%7BF%27%28x%29%7D%7B3%7D%5BF%28x%29%5D%5E%5Cbigg%7B%5Cfrac%7B-2%7D%7B3%7D%7D)
- Rewrite [Exponential Rule - Rewrite]:
![\displaystyle H'(x) = \frac{F'(x)}{3[F(x)]^\bigg{\frac{2}{3}}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20H%27%28x%29%20%3D%20%5Cfrac%7BF%27%28x%29%7D%7B3%5BF%28x%29%5D%5E%5Cbigg%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D)
<u>Step 3: Evaluate</u>
- Substitute in <em>x</em> [Derivative]:
![\displaystyle H'(5) = \frac{F'(5)}{3[F(5)]^\bigg{\frac{2}{3}}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20H%27%285%29%20%3D%20%5Cfrac%7BF%27%285%29%7D%7B3%5BF%285%29%5D%5E%5Cbigg%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D)
- Substitute in function values:

- Exponents:

- Multiply:

- Simplify:

Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
She used 3/8 of the cheese. Since she used 1/2 <em>of</em> 3/4, you multiply 3/4 times 1/2. If you multiply straight across, the answer should be 3/8. If you need further explanation, just ask! Hope this helps! =D :D
<span>=<span><span><span><span><span>(3)</span><span>(x)</span></span>+<span><span>(3)</span><span>(4)</span></span></span>+<span><span>(2)</span><span>(<span>5x</span>)</span></span></span>+<span><span>(2)</span><span>(2)
</span></span></span></span><span>=<span><span><span><span>3x</span>+12</span>+<span>10x</span></span>+<span>4
</span></span></span><span>=<span><span><span><span>3x</span>+12</span>+<span>10x</span></span>+4
</span></span><span>=<span><span>(<span><span>3x</span>+<span>10x</span></span>)</span>+<span>(<span>12+4</span>)
</span></span></span><span>=<span><span>13x</span>+<span>16
Answer = </span></span></span><span>13x</span>+<span>16
(hope this helps)</span>
Answer:
It takes 4 minutes per block and she can walk 12.5 blocks in 45 minutes.
Step-by-step explanation:
20 / 5 = 4 minutes per block
20 + 20 + 5 = 45
5 + 5 + 2.5 = 12.5
Hope this helps, I did the test last year.
Answer:0.11111111111
Step-by-step explanation:0.1 with a repeating decimal over the 1 because when you multiply 1/3 by 1/3 thats what you get.