Pablo : 3(2x) = 6x
Sofia : 2x
Mia : x
Assuming x = 10
Mia : x = 10
Sofia : 2x = 2(10) = 20
Pablo : 3(2x) = 3(20) = 60
10 + 20 + 60 = 90
90/3 = 30 candy eggs per person
Pablo: 60 x 1/2 = 30
Sophia: 30-20 = 10 : 10
Mia : 30 - 10 = 20 : 20
Ratio of eggs given to sophia from pablo's set = 10/60 = 1/6
Ratio of eggs given to mia from pablo's set = 20/60 = 2/6 = 1/3
A) [-7,-4] U [4,7]; B) [-4,-1]; C) [1,4]
Simplify the first numerator first
-2(x+1)
-2x-2
Then you can set up an equation using cross multiplication
5(-2x-2)= 3x
Simplify and solve
-10x-10=3x
-10=13x
-10/13=x
Final answer: x=-10/13
P(rolling a 4)=1/6
Explanation:
The probability of rolling a 4 or higher on a 6-sided number cube is 1/6
Answer: 1/6
Answer:
Point N(4, 1)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality<u>
</u>
<u>Algebra I</u>
- Coordinates (x, y)
- Functions
- Function Notation
- Terms/Coefficients
- Anything to the 0th power is 1
- Exponential Rule [Rewrite]:
- Exponential Rule [Root Rewrite]:
<u>Calculus</u>
Derivatives
Derivative Notation
Derivative of a constant is 0
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>
<u />
<u />
<u />
<u />
<u />
<u>Step 2: Differentiate</u>
- [Function] Rewrite [Exponential Rule - Root Rewrite]:

- Chain Rule:
![\displaystyle y' = \frac{d}{dx}[(x - 3)^{\frac{1}{2}}] \cdot \frac{d}{dx}[x - 3]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B%28x%20-%203%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5D%20%5Ccdot%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bx%20-%203%5D)
- Basic Power Rule:

- Simplify:

- Multiply:

- [Derivative] Rewrite [Exponential Rule - Rewrite]:

- [Derivative] Rewrite [Exponential Rule - Root Rewrite]:

<u>Step 3: Solve</u>
<em>Find coordinates</em>
<em />
<em>x-coordinate</em>
- Substitute in <em>y'</em> [Derivative]:

- [Multiplication Property of Equality] Multiply 2 on both sides:

- [Multiplication Property of Equality] Multiply √(x - 3) on both sides:

- [Equality Property] Square both sides:

- [Addition Property of Equality] Add 3 on both sides:

<em>y-coordinate</em>
- Substitute in <em>x</em> [Function]:

- [√Radical] Subtract:

- [√Radical] Evaluate:

∴ Coordinates of Point N is (4, 1).
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e