Answer:
exterior of an angle should add up to 180 with the other angle. so the angle next to the exterior angle should add up to 180. the exterior angle should be the one outside or facing the or opening up to the outside.
Step-by-step explanation:
Answer:
(0,5)
Step-by-step explanation:
when x=0። y=5
i guess
Answer:
See explanation.
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
Functions
- Exponential Property [Rewrite]:

- Exponential Property [Root Rewrite]:
![\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csqrt%5Bn%5D%7Bx%7D%20%3D%20x%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D)
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]: ![\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bcf%28x%29%5D%20%3D%20c%20%5Ccdot%20f%27%28x%29)
Derivative Property [Addition/Subtraction]: ![\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28x%29%20%2B%20g%28x%29%5D%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28x%29%5D%20%2B%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bg%28x%29%5D)
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:
We are given the following and are trying to find the second derivative at <em>x</em> = 2:


We can differentiate the 1st derivative to obtain the 2nd derivative. Let's start by rewriting the 1st derivative:

When we differentiate this, we must follow the Chain Rule: ![\displaystyle \frac{d^2y}{dx^2} = \frac{d}{dx} \Big[ 6(x^2 + 3y^2)^\big{\frac{1}{2}} \Big] \cdot \frac{d}{dx} \Big[ (x^2 + 3y^2) \Big]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%5E2y%7D%7Bdx%5E2%7D%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5CBig%5B%206%28x%5E2%20%2B%203y%5E2%29%5E%5Cbig%7B%5Cfrac%7B1%7D%7B2%7D%7D%20%5CBig%5D%20%5Ccdot%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5CBig%5B%20%28x%5E2%20%2B%203y%5E2%29%20%5CBig%5D)
Use the Basic Power Rule:

We know that y' is the notation for the 1st derivative. Substitute in the 1st derivative equation:
![\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 6y(6\sqrt{x^2 + 3y^2}) \big]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%5E2y%7D%7Bdx%5E2%7D%20%3D%203%28x%5E2%20%2B%203y%5E2%29%5E%5Cbig%7B%5Cfrac%7B-1%7D%7B2%7D%7D%20%5Cbig%5B%202x%20%2B%206y%286%5Csqrt%7Bx%5E2%20%2B%203y%5E2%7D%29%20%5Cbig%5D)
Simplifying it, we have:
![\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 36y\sqrt{x^2 + 3y^2} \big]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%5E2y%7D%7Bdx%5E2%7D%20%3D%203%28x%5E2%20%2B%203y%5E2%29%5E%5Cbig%7B%5Cfrac%7B-1%7D%7B2%7D%7D%20%5Cbig%5B%202x%20%2B%2036y%5Csqrt%7Bx%5E2%20%2B%203y%5E2%7D%20%5Cbig%5D)
We can rewrite the 2nd derivative using exponential rules:
![\displaystyle \frac{d^2y}{dx^2} = \frac{3\big[ 2x + 36y\sqrt{x^2 + 3y^2} \big]}{\sqrt{x^2 + 3y^2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%5E2y%7D%7Bdx%5E2%7D%20%3D%20%5Cfrac%7B3%5Cbig%5B%202x%20%2B%2036y%5Csqrt%7Bx%5E2%20%2B%203y%5E2%7D%20%5Cbig%5D%7D%7B%5Csqrt%7Bx%5E2%20%2B%203y%5E2%7D%7D)
To evaluate the 2nd derivative at <em>x</em> = 2, simply substitute in <em>x</em> = 2 and the value f(2) = 2 into it:
![\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = \frac{3\big[ 2(2) + 36(2)\sqrt{2^2 + 3(2)^2} \big]}{\sqrt{2^2 + 3(2)^2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%5E2y%7D%7Bdx%5E2%7D%20%5Cbigg%7C%20%5Climits_%7Bx%20%3D%202%7D%20%3D%20%5Cfrac%7B3%5Cbig%5B%202%282%29%20%2B%2036%282%29%5Csqrt%7B2%5E2%20%2B%203%282%29%5E2%7D%20%5Cbig%5D%7D%7B%5Csqrt%7B2%5E2%20%2B%203%282%29%5E2%7D%7D)
When we evaluate this using order of operations, we should obtain our answer:

Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
The answer is 3/9 or 1/3 chance of selecting a pair of white socks
Answer:
X=-3, Y=1
Step-by-step explanation:
Y=4x+13
Y=6x+19
4x+13=6x+19
-2x=6
X=-3
Y=1