Answer:
david biked 6 miles every hour!
Step-by-step explanation:
Distribute the four which makes it A+4B-24
Answer:
85°
Step-by-step explanation:
m∠4 measures 85 degrees.
m∠4 and m∠5 are alternate interior angles.
The alternate interior angles theorem states that <u>all pairs of alternate interior angles are congruen</u>t, or equal.
m∠4 ≅ m∠5
So, m∠5 should also be 85° as well as m∠4.
Answer:
See explanation.
General Formulas and Concepts:
<u>Algebra I</u>
- Terms/Coefficients
- Factoring
<u>Algebra II</u>
<u>Pre-Calculus</u>
<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 [Quotient Rule]: ![\displaystyle \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=%5Cdisplaystyle%20%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)
Parametric Differentiation: ![\displaystyle \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B%5Cfrac%7Bdy%7D%7Bdt%7D%7D%7B%5Cfrac%7Bdx%7D%7Bdt%7D%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
![\displaystyle x = 2t - \frac{1}{t}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%20%3D%202t%20-%20%5Cfrac%7B1%7D%7Bt%7D)
![\displaystyle y = t + \frac{4}{t}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%3D%20t%20%2B%20%5Cfrac%7B4%7D%7Bt%7D)
<u>Step 2: Find Derivative</u>
- [<em>x</em>] Differentiate [Basic Power Rule and Quotient Rule]:
![\displaystyle \frac{dx}{dt} = 2 + \frac{1}{t^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdx%7D%7Bdt%7D%20%3D%202%20%2B%20%5Cfrac%7B1%7D%7Bt%5E2%7D)
- [<em>y</em>] Differentiate [Basic Power Rule and Quotient Rule]:
![\displaystyle \frac{dy}{dt} = 1 - \frac{4}{t^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%201%20-%20%5Cfrac%7B4%7D%7Bt%5E2%7D)
- Substitute in variables [Parametric Derivative]:
![\displaystyle \frac{dy}{dx} = \frac{1 - \frac{4}{t^2}}{2 + \frac{1}{t^2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B1%20-%20%5Cfrac%7B4%7D%7Bt%5E2%7D%7D%7B2%20%2B%20%5Cfrac%7B1%7D%7Bt%5E2%7D%7D)
- [Parametric Derivative] Simplify:
![\displaystyle \frac{dy}{dx} = \frac{t^2 - 4}{2t^2 + 1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7Bt%5E2%20-%204%7D%7B2t%5E2%20%2B%201%7D)
- [Parametric Derivative] Polynomial Long Division:
![\displaystyle \frac{dy}{dx} = \frac{1}{2} - \frac{7}{2(2t^2 - 1)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20-%20%5Cfrac%7B7%7D%7B2%282t%5E2%20-%201%29%7D)
- [Parametric Derivative] Factor:
![\displaystyle \frac{dy}{dx} = \frac{1}{2} \bigg( 1 - \frac{9}{2t^2 + 1} \bigg)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cbigg%28%201%20-%20%5Cfrac%7B9%7D%7B2t%5E2%20%2B%201%7D%20%5Cbigg%29)
Here we see that if we increase our values for <em>t</em>, our derivative would get closer and closer to 0.5 but never actually reaching it. Another way to approach it is to take the limit of the derivative as t approaches to infinity. Hence
.
Topic: AP Calculus BC (Calculus I + II)
Unit: Parametrics
Book: College Calculus 10e
Simplify the equation to find X:
7/8 (-32 - 48x) +36 = 2/3( - 33x - 18) - 10x
Distribute the terms in parentheses:
-28 - 42x + 36 = -22x - 12 - 10x
Collect like terms
-42x + 8 = -32x - 12
Add 32x to both sides, and subtract 8 from both sides:
-10x = - 20
Divide both sides by -10
x = 2