Answer and Step-by-step explanation:
To find the unit rate, divide the 4 cups of water and the
cups sugar by 4 to get a unite rate for 1 cut of water.
<u>4 divided by 4 equals 1.</u>
<u />
<u />
<u> divided by 4 equals </u>
<u>.</u>
<u />
<u>Now, we multiply </u>
<u> by 6.</u>
<u></u>
<u> is how many cups of sugar that needs to be measured for 6 cups of water.</u>
<u><em>#teamtrees #PAW (Plant And Water)</em></u>
Answer:

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
<u>Calculus</u>
Derivatives
Derivative Notation
Derivative Rule [Quotient Rule]: ![\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5B%5Cfrac%7Bf%28x%29%7D%7Bg%28x%29%7D%20%5D%3D%5Cfrac%7Bg%28x%29f%27%28x%29-g%27%28x%29f%28x%29%7D%7Bg%5E2%28x%29%7D)
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)
MacLaurin/Taylor Polynomials
- Approximating Transcendental and Elementary functions
- MacLaurin Polynomial:

- Taylor Polynomial:

Step-by-step explanation:
*Note: I will not be showing the work for derivatives as it is relatively straightforward. If you request for me to show that portion, please leave a comment so I can add it. I will also not show work for elementary calculations.
<u />
<u>Step 1: Define</u>
<em>Identify</em>
f(x) = ln(1 - x)
Center: x = 0
<em>n</em> = 3
<u>Step 2: Differentiate</u>
- [Function] 1st Derivative:

- [Function] 2nd Derivative:

- [Function] 3rd Derivative:

<u>Step 3: Evaluate Functions</u>
- Substitute in center <em>x</em> [Function]:

- Simplify:

- Substitute in center <em>x</em> [1st Derivative]:

- Simplify:

- Substitute in center <em>x</em> [2nd Derivative]:

- Simplify:

- Substitute in center <em>x</em> [3rd Derivative]:

- Simplify:

<u>Step 4: Write Taylor Polynomial</u>
- Substitute in derivative function values [MacLaurin Polynomial]:

- Simplify:

Topic: AP Calculus BC (Calculus I/II)
Unit: Taylor Polynomials and Approximations
Book: College Calculus 10e
Answer:
2 inches
Step-by-step explanation:
The scale means 1 inches on map equal 125 feet in real life
<em>We know in real life Jon lives 250 ft away from Max. 250 is twice of 125, hence in map</em>, it should be 1*2=2 inches.
On the map, it is 2 inches from Jon's home to Max's home.