Answer:
-20
Step-by-step explanation:
x/5=3-7
x/5=-4
x=-4×5
x=-20
Answer:
I only did this for the points.
Step-by-step explanation:
I am buff boi
Answer:
132
Step-by-step explanation:
Divide it into 2 shapes : a triangle and a rectangle.
The triangle's base length is 20-(8+6) = 6
The height is 10-6 = 4
The triangle's area = 6*4/2 = 12
The rectangle's area is 6 * 20 = 120
Add the two together, and you get 12+120 = 132
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]:
![\displaystyle y = (x - 3)^{\frac{1}{2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%3D%20%28x%20-%203%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D)
- 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:
![\displaystyle y' = \frac{1}{2}(x - 3)^{\frac{1}{2} - 1} \cdot (1 \cdot x^{1 - 1} - 0)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28x%20-%203%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%20-%201%7D%20%5Ccdot%20%281%20%5Ccdot%20x%5E%7B1%20-%201%7D%20-%200%29)
- Simplify:
![\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}} \cdot 1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28x%20-%203%29%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%20%5Ccdot%201)
- Multiply:
![\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28x%20-%203%29%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D)
- [Derivative] Rewrite [Exponential Rule - Rewrite]:
![\displaystyle y' = \frac{1}{2(x - 3)^{\frac{1}{2}}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B1%7D%7B2%28x%20-%203%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D)
- [Derivative] Rewrite [Exponential Rule - Root Rewrite]:
![\displaystyle y' = \frac{1}{2\sqrt{x - 3}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B1%7D%7B2%5Csqrt%7Bx%20-%203%7D%7D)
<u>Step 3: Solve</u>
<em>Find coordinates</em>
<em />
<em>x-coordinate</em>
- Substitute in <em>y'</em> [Derivative]:
![\displaystyle \frac{1}{2} = \frac{1}{2\sqrt{x - 3}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B2%7D%20%3D%20%5Cfrac%7B1%7D%7B2%5Csqrt%7Bx%20-%203%7D%7D)
- [Multiplication Property of Equality] Multiply 2 on both sides:
![\displaystyle 1 = \frac{1}{\sqrt{x - 3}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%201%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7Bx%20-%203%7D%7D)
- [Multiplication Property of Equality] Multiply √(x - 3) on both sides:
![\displaystyle \sqrt{x - 3} = 1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csqrt%7Bx%20-%203%7D%20%3D%201)
- [Equality Property] Square both sides:
![\displaystyle x - 3 = 1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%20-%203%20%3D%201)
- [Addition Property of Equality] Add 3 on both sides:
![\displaystyle x = 4](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%20%3D%204)
<em>y-coordinate</em>
- Substitute in <em>x</em> [Function]:
![\displaystyle y = \sqrt{4 - 3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%3D%20%5Csqrt%7B4%20-%203%7D)
- [√Radical] Subtract:
![\displaystyle y = \sqrt{1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%3D%20%5Csqrt%7B1%7D)
- [√Radical] Evaluate:
![\displaystyle y = 1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%3D%201)
∴ Coordinates of Point N is (4, 1).
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
Answer:
a) 0.17 is greater than 0.13
b) 5.2 and 5.20 are the same thing so they are equal.
c) 0.5 is greater than 0.07