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
Answer: it is 49 or -49
Step-by-step explanation:
if you divide 49 by 7 it comes out to seven because 7 times 7 is 49.
Use trigonometry.
tan30° = perpendicular / base
Here for angle 30° , x is perpendicular while 10 is the base.
tan30° = 1/√3
1/√3 = x/10
x = 10/✓3
By rationalising
x = 10√3/3
Hope This Helps You!
Answer: C (0,0), (-4,0) and (0, -5)
Step-by-step explanation:
<span><span> p9/p3</span> </span>Final result :<span> p6
</span>Reformatting the input :
Changes made to your input should not affect the solution:
(1): "p3" was replaced by "p^3". 1 more similar replacement(s).
Step by step solution :<span>Step 1 :</span><span> p9
Simplify ——
p3
</span>Dividing exponential expressions :
<span> 1.1 </span> <span> p9</span> divided by <span>p3 = p(9 - 3) = p6</span>
Final result :<span> p<span>6</span></span>