Answer:

General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
<u>Calculus</u>
Implicit Differentiation
The derivative of a constant is equal to 0
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Product Rule: ![\frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bf%28x%29g%28x%29%5D%3Df%27%28x%29g%28x%29%20%2B%20g%27%28x%29f%28x%29)
Chain Rule: ![\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%20%3Df%27%28g%28x%29%29%20%5Ccdot%20g%27%28x%29)
Quotient Rule: ![\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=%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)
Step-by-step explanation:
<u>Step 1: Define</u>
-y - 2x³ = y²
Rate of change of tangent line at point (-1, -2)
<u>Step 2: Differentiate Pt. 1</u>
<em>Find 1st Derivative</em>
- Implicit Differentiation [Basic Power Rule]:

- [Algebra] Isolate <em>y'</em> terms:

- [Algebra] Factor <em>y'</em>:

- [Algebra] Isolate <em>y'</em>:

- [Algebra] Rewrite:

<u>Step 3: Differentiate Pt. 2</u>
<em>Find 2nd Derivative</em>
- Differentiate [Quotient Rule/Basic Power Rule]:

- [Derivative] Simplify:

- [Derivative] Back-Substitute <em>y'</em>:

- [Derivative] Simplify:

<u>Step 4: Find Slope at Given Point</u>
- [Algebra] Substitute in <em>x</em> and <em>y</em>:

- [Pre-Algebra] Exponents:

- [Pre-Algebra] Multiply:

- [Pre-Algebra] Add:

- [Pre-Algebra] Exponents:

- [Pre-Algebra] Divide:

- [Pre-Algebra] Add:

- [Pre-Algebra] Simplify:

5/12 equals to 20/48.
48÷12=4
5×4=20
Answer:
coordinates of H = (1, 0)
Coordinates of G = ( - 3.6, -2) or (5.6, -2)
Step-by-step explanation:
E(5,3) and F (2,-1) are two vertices of a square EFGH and H is in the x-axis.
Let the coordinates of H is (x, 0) and G is (a, b).
The length of side EF is

So,

And

Now

Solving (1) and (2)
b = - 2 ,
The solution is x=5/4.
We use the properties of logs to rewrite the equation:
![\log[(\frac{x}{2})(\frac{20}{x^2})]=\log8 \\ \\\log(\frac{20x}{2x^2})=\log8 \\ \\\log(\frac{10}{x})=\log8](https://tex.z-dn.net/?f=%5Clog%5B%28%5Cfrac%7Bx%7D%7B2%7D%29%28%5Cfrac%7B20%7D%7Bx%5E2%7D%29%5D%3D%5Clog8%0A%5C%5C%0A%5C%5C%5Clog%28%5Cfrac%7B20x%7D%7B2x%5E2%7D%29%3D%5Clog8%0A%5C%5C%0A%5C%5C%5Clog%28%5Cfrac%7B10%7D%7Bx%7D%29%3D%5Clog8)
Get all of the logs on the same side of the equation y subtracting log 8:

Use the properties of logs to rewrite:

Exponentiate:

Multiply both sides by 8x:
1*8x = (10/8x)*8x
8x=10
Divide both sides by 8:
8x/8 = 10/8
x = 10/8 = 5/4
Answer:
6.00
Step-by-step explanation:
Use Pythagorean theorem:
c² = a² + b²
9.22² = a² + 7²
85.0 = a² + 49
a² = 36.0
a = 6.00